- Email: [email protected]
Application of an improved MCKDA for fault detection of wind turbine gear based on encoder signal
Journal Pre-proof Application of an improved MCKDA for fault detection of wind turbine gear based on encoder signal
Yonghao Miao, Ming Zhao, Kaixuan Liang, Jing Lin PII:
S0960-1481(19)31687-8
DOI:
https://doi.org/10.1016/j.renene.2019.11.012
Reference:
RENE 12559
To appear in:
Renewable Energy
Received Date:
10 July 2019
Accepted Date:
03 November 2019
Please cite this article as: Yonghao Miao, Ming Zhao, Kaixuan Liang, Jing Lin, Application of an improved MCKDA for fault detection of wind turbine gear based on encoder signal, Renewable Energy (2019), https://doi.org/10.1016/j.renene.2019.11.012
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
Journal Pre-proof
Application of an improved MCKDA for fault detection of wind turbine gear based on encoder signal
Yonghao Miao, PhD School of Reliability and Systems Engineering, Beihang University, Xueyuan Road No. 37, Haidian District, Beijing 100083, China Email: [email protected]
Ming Zhao, PhD, Associate Professor 1. School of Mechanical Engineering, Xi’an Jiaotong University, Xi'an 710049, China 2. School of Reliability and Systems Engineering, Beihang University, Xueyuan Road No. 37, Haidian District, Beijing 100083, China Email: [email protected]
Kaixuan Liang, PhD candidate School of Mechanical Engineering, Xi’an Jiaotong University, Xi'an 710049, China Email: [email protected]
Jing Lin*, PhD, Professor School of Reliability and Systems Engineering, Beihang University, Xueyuan Road No. 37, Haidian District, Beijing 100083, China Email: [email protected]
*
Corresponding author 1
Journal Pre-proof
Abstract
Due to severe working condition, unexpected failures in wind turbine gearbox become rather frequent and may lead to long downtime or even catastrophic casualties. However, traditional diagnosis techniques based on vibration, acoustic emission etc. still face some problems when they are used for failure identification of wind turbine gearbox. Encoder signal carries rich diagnostic information which may be considered as an alternative tool for the wind turbine condition monitoring. Motivated by this, the encoder signal is initially introduced for the fault diagnosis of wind turbine gear in this paper. A novel adaptive filtering method, improved maximum correlated kurtosis deconvolution adjusted (IMCKDA), is proposed to eliminate the diverse noises in encoder signal. Additionally, to overcome the limitation from the sensibility of discontinuity point and filtered signal in traditional deconvolution methods (DMs), convolution adjustment definition is introduced. And correlated Gini index (CG) is originally designed to guide the selection of filter length. Finally, the encoder signal is verified to be an alternative tool for the fault diagnosis of wind turbine gear by real experimental cases. And without any prior knowledge and the least input parameters, IMCKDA is more suitable for processing encoder signal than existing state-of-the-art DMs.
Keywords: Wind turbines, Rotary encoder, Adaptive filtering, Gearbox fault diagnosis, Deconvolution
2
Journal Pre-proof Nomenclature Abbreviation IMCKDA
improved maximum correlated kurtosis deconvolution adjusted
DM
deconvolution method
CG
correlated Gini
CNC
computer numerical control
IAS
instantaneous angular speed
IAA
instantaneous angular acceleration
MED
minimum entropy deconvolution
MCKD CK
maximum correlated kurtosis deconvolution
correlated kurtosis
MOMED
multipoint optimal minimum entropy deconvolution
IMCKD
improved maximum correlated kurtosis deconvolution
2D
2-dimensional
SNR
signal to noise ratio
Mathematical notations t
time or time shift
x(t)
measured signal
g(t)
fault component
n(t)
noise component
y(t)
filtered signal
f N
FIR filter length of signal 3
Journal Pre-proof M
order of shift
T
period
Ts
sampling number
fs
sampling frequency
t
constant vector
L
filter length
X
shift matrix of signal x
f
matrix of FIR filter coefficient
y
vector of filtered signal y
x
analytic signal of x
j
symbol of imaginary number
x
vector of signal x in ascent order
x
vector of root of signal x and its shift signal
K
number of periods being averaged in time synchronous averaging
s
IAA signal
s e(t) A
IAA signal after time synchronous averaging simulated de-trend encoder signal amplitude
Zp gear tooth number Greek symbols
matrix of signal y and y2 or y2 and y autocorrelation matrix of signal y shift of signal x 4
Journal Pre-proof width of g(t) Superscripts T
transposition operation
5
Journal Pre-proof 1. Introduction Due to the low cost and high flexibility, wind energy has gained increasing attractiveness [1]. The past decades have witnessed a rapid advancement of wind power generation. It is reported that the cumulative installed capacity of wind power had over 148 GW in Europe and just in China the number had exceeded 125 GW in 2015 [2]. However, because of severe condition, the unexpected failures in the drivetrain of wind turbines, such as the gearbox system, become rather frequent and they may lead to long downtime or even catastrophic casualties. Therefore, the condition monitoring and in-time maintenance of wind turbine gearbox are of great significance [3, 4]. According to statistics[5, 6], to ensure the safety operation, the maintenance costs account for about 25%-30% of the overall energy generation cost. Recently, numerous signal processing techniques based on the vibration information [6-11], the acoustic emission [12, 13], temperature information [14] etc. are successively proposed for the fault identification of wind turbines. These works did make important contributions for the maintenance of wind turbines. Yet, traditional maintenance techniques, especially the most-used vibration-based methods, are confronting more and more challenges. The difficulties from both the signal measurement and analysis, such as the varying speed and low speed conditions, have been summarized in Ref. [3, 4, 15]. Recently, it has been reported that the built-in information, such as rotary encoder signal, carries rich diagnostic information and has been considered as an alternative tool to address the bottle neck issue of gearbox fault diagnosis [16, 17]. Actually, rotary encoders have been widely equipped in wind turbines for motion and speed control [18]. Benefiting from the close connection to the critical components, the signal from the rotary encoders carries rich condition information about the equipment being monitored, which also showcases the potential of encoder information in the condition monitoring of wind turbine gearbox. The prospect development of encoder signal in the application of wind turbine fault diagnosis has gained positive 6
Journal Pre-proof outlook in the latest review research [19]. Compared with the traditional monitoring approaches, such as vibration, acoustic emission and temperature information etc., the encoder information enjoys the following advantages which make the failure identification of the gearbox easy to realize: (1)High fault-sensibility. The idea behind using encoder signal as a fault detection tool is that the fault in the machinery equipment, for example the gear fault, has a direct expression of torsional vibration. Therefore, encoder signal which mainly reflects the torsional behavior is more susceptible to weak faults than vibration and acoustic emission signals [16]. (2) Short transfer path. The vibration or acoustic emission sensors are typically mounted on the gearbox casing in wind turbines. Therefore, the measured signal is obtained after a long and complex transfer path, which seriously attenuates the useful feature. As an important built-in sensor, encoder has been installed in the system and its signal would be less affected by the transfer path [20]. (3) Low speed robustness. Since low-frequency response of accelerometers is not satisfactory，low speed is still one of the main challenges for the fault diagnosis of wind turbine gearbox by the vibration analysis [4]. In contrast, the encoder signal has been verified to be as an alternative or a complementary tool for its better performance in low speed machine monitoring [21]. (4) Low cost. The main cost of the maintenance of wind turbines is from the measurement. Unlike the vibration measurement, liquids analysis and other monitoring patterns, the encoder signal-based analysis is easily accessible and has a lower cost without any measurement sensors [22]. Actually, the signal directly recorded by rotary encoder is the position series. By the differential operation, the position series could be converted into more meaningful kinetic variables, such as instantaneous angular speed (IAS) series [23], instantaneous angular acceleration (IAA) series [16] and jerk [24]. In virtue of these merits, the research of fault diagnosis based on encoder signal has attracted considerable attention in recent years. 7
Journal Pre-proof Lin et al. [25] found that IAS is less affected by the background noise, and they proposed IAS spectrum for the fault diagnosis of diesel engines. Moustafa et al. [21] thought vibration and acoustic emission analysis have a bad visual inspection ability for the detection of low speed bearings fault, and introduced IAS-based method to compensate for the shortcoming. Roy et al. [26] achieved much in terms of gearbox diagnosis by applying time synchronous averaging to eliminate the interference from load variation in IAS signal. Similarly, to separate the fault information from other interferences, empirical mode decomposition [17, 27], ensemble empirical mode decomposition [28] and other advanced processing methods in the vibration analysis are introduced for denoising of encoder signal. Recently, Zhao et al. [16] established a health assessment of machinery fault diagnosis by IAA signal and proposed a lowpass filter to enhance the fault component. In practice, the load variation, the rotation and motion of other components and data acquisition all inevitably generate noise which highly complicates the encoder signals, containing IAS, IAA and jerk. The fault feature is easily buried by these interferences and noise. Therefore, some of these existing methods which just provided the simple and coarse denoising scheme hardly attain the expected goal. Addressing the key issue from the root is to design an adaptive filter motivated by the particular feature of the fault in the encoder signal. Deconvolution methods which could adaptively design an FIR filter by iteratively choose the filter coefficients to maximize the prespecified objective [29] provide an alternative to solve the problem. Actually, DMs have been extensively studied and successfully employed in vibration analysis for machinery fault diagnosis. In 2006, minimum entropy deconvolution (MED) which used kurtosis value of the signal as the objective is firstly introduced to enhance the fault feature of the vibration signal [30]. Since then, improvements and applications of MED have attracted considerable attention. McDonald et al. [31] found the preference of the MED algorithm is to deconvolve the independent impulse, then proposed a new method named the maximum correlated kurtosis deconvolution (MCKD) which can overcome the 8
Journal Pre-proof shortcoming of MED by introducing correlated kurtosis (CK) as the new objective. Yet, the efficiency of MCKD exceedingly relies on the prior period [32]. In view of this, multipoint optimal minimum entropy deconvolution (MOMED) [33] and improved maximum correlated kurtosis deconvolution (IMCKD) [34] are proposed successively. These works make a great contribution for the theory expansion of DMs. However, some drawbacks still limit the performance of DMs. On the one hand, MED, MCKD and its variants are susceptible to the effect of filtered signal and the discontinuity point. It is easy to make these methods lose efficacy [33]. On the other hand, the filter length as the most critical parameter affects the effectiveness of DM. Till now, the selection of the filter length just relies on the experience [34]. In this paper, IMCKDA is proposed to overcome these disadvantages of the traditional DMs and used for fault detection of wind turbine gear based on the encoder signal. Firstly, using the convolution adjustment, the proposed method can be free from the interference of the discontinuity point and the effect of the filtered signal. Then a new index, CG, is structured and combined with a specific selection strategy, to adaptively select the appropriate filter length. Finally, the proposed IMCKDA is verified to be more suitable for processing of the encoder signal than the existing state-of-the-art DMs and an alternative tool for the fault diagnosis of wind turbine gear by the real experimental cases. The main contributions of this paper are summarized as follows: (1) The analysis based on built-in encoder signal is firstly used for gearbox fault detection in wind turbines. It provides a new alternative tool for addressing the bottle neck issue of wind turbine gear fault diagnosis. (2) The adaptive filtering method is initially applied for denoising of encoder signal in this paper. Benefiting from the superiority of proposed method, a better result with high SNR can be obtained which will make the diagnosis decision easy to give. (3) Compared with the traditional DMs, the proposed IMCKDA has more merits: ① It can be applied 9
Journal Pre-proof without any prior knowledge and the least input parameters; ② The proposed method is free from the interference of the discontinuity point and the effect of filtered signal; ③ It can adaptively choose the filter length. The rest of this article is organized as follows. Section 2 makes a brief review of the deconvolution theory. In Section 3, the proposed method is introduced in detail from 3 subsections. Section 4 displays the application framework of the proposed method for the fault diagnosis of wind turbine gearbox. Section 5 further validates the robustness of the proposed method by three real datasets from the gearbox, containing root crack, corrosion fault and two worn teeth fault of the planet gear. Finally, the conclusion is drawn in Section 6.
2. Deconvolution theory Analogous to vibration signal, encoder signal could be viewed as a mixed signal. After transmission path effect, encoder signal is compounded by the components caused by the fault and other noise. It can be defined: x(t ) g (t ) n(t ) * h(t )
(1)
where x(t), g(t) and n(t) are the measured signal, fault component and noise, respectively. h(t) is the response of the transmission path effect. * denotes the convolution operation. The idea of DMs is to design an FIR filter to make the filtered signal restore the fault component by maximizing the objective function. The process can be represented as shown in Fig. 1:
y (t ) x(t ) * f (l ) g (t )
(2)
10
Journal Pre-proof n (t )
hn
g (t )
hg
x(t )
f (l )
y (t ) g (t )
FIR filter
Fig. 1. The process of the deconvolution. In the field of machinery fault diagnosis, different filter methods, including wavelet transform [35], the intelligent filter method [36], decomposition methods [37] and the filter methods based on 1/3-binary tree filter bank, such as kurtogram [38] and its variants [39-41] have been successfully applied. However, different from the filter methods based on the fixed filter bank, DMs can adaptively design the shape and the position of the filter by iteratively updating the filter coefficients. Therefore, the filtered results of DMs are more accurate and informative when the selection of the objective function and the filter parameters is appropriate. To process the fault signal under different scenarios, numerous of indexes, such as kurtosis, CK etc., are used as the objective function in the traditional DMs. The description about the traditional DMs can be referred in Appendix A. As one of the most widely used adaptive filtering methods, DMs had achieved much in terms of machine diagnosis with the vibration signal, especially in the denoising of the complex signal. However, the selection of filter length, the susceptibility to discontinuity point and the effect from filtered signal still seriously undermine the usefulness of the existing DMs. Furthermore, in the analysis of encoder signal, the adaptive filtering methods are still the unexplored territory. Therefore, to overcome these drawbacks, IMCKDA is proposed in this paper.
3. Proposed method 11
Journal Pre-proof To clearly describe the proposed method, three subsections are organized as follows. Firstly, the derivation process of IMCKDA using the convolution adjustment definition is elaborated in Section 3.1. Secondly, through algorithm introduction and performance analysis, Sections 3.2 and 3.3 respectively illustrate the solution for the selection of prior period and filter length in the proposed method. 3.1. Convolution Adjustment Definition for the Derivation The ultimate goal of DMs is to find the optimal filter coefficients. With the objective function method, the expression of the filter can be deduced. Similarly, IMCKDA chooses CK as the objective function. Since the performance of the proposed method does not rely on the order of shift, M =1 is fixed in the objective function, that is N
max CK1 (Ts ) max f
f
(y y n 1
n
n T s
N 2 yn n 1
)2 (3)
2
where f [ f1 , f 2 ,..., f L ]T is an FIR filter with the length L. By the derivation of (4), the expression of the filter can be deduced.
d CK1 (Ts ) 0, k 1, 2,..., L df k
(4)
Generally, the convolution definition of the filter process is given: L
yn ∑ fl xn l 1 , n 1, 2,..., N
(5)
l 1
Then, by taking the derivatives of the optimization function (4) and taking the inverse filtering expression (5) into consideration, the final iterative expression of optimal filter can be obtained. Yet, numerous examples have verified DMs are sensitive to discontinuity point and the filtered signal by the derivation above [31, 33]. To overcome the weakness, a new convolution adjustment definition as shown in (6) is introduced to 12
Journal Pre-proof replace of the traditional one in this paper. Through making a delay in the input signal, the preference to deconvolve the spurious impulse can be avoided. L
yn ∑ fl xn L l , n 1, 2,..., N L 1
(6)
l 1
Firstly, by taking the derivatives of the numerator portions, the expression can be presented: d d CK1 (Ts ) Numerator df k df k
N
n 1
yn yn Ts
2
N
N
n 1
n 1
2 xn L l yn yn2Ts 2 xn Ts L l yn Ts yn2
(7)
Similarly, the derivative of denominator can be presented: 2
d d N 2 N 2 N CK1 (Ts ) Denominator y 4 n yn yn xn L l df k df k n 1 n 1 n 1
(8)
Then, the expression (4) can be deduced: 2
N N N 2 N 2 2 y 2 x y y 2 x y y 4 yn yn Ts n n L l n n T n T L l n T n s s s n 1 n 1 n 1 n 1
2
N 2 yn n 1
3 N
y x n 1
n n L l
0
(9)
For the sake of conciseness, the expression (9) is denoted: 2
2
2 β 2 X0 y y 2 ( X0α 0 XTs α1 ) xL t 0 where Xt 0 ... 0
(10)
xL 1t
xL 2 t
...
xL t 0 ... 0
xL 1t xL t ... 0
... ... ... ...
xN t xN 1t xN 2 t ; ... xN L t 1 LbyN L 1
α 0 [ y1 y12Ts , y2 y22Ts ,..., yN yN2 Ts ]T ; α1 [ y1Ts y12 , y2Ts y22 ,..., yN Ts yN2 ]T ; β [ y1 y1Ts , y2 y2Ts ,..., yN yN Ts ]T . And the symbol T denotes the transposition operation,
.2
is defined as
the Euclidian norm. The expression for inverse filtering (6) can be simplified: y XT0 f
(11)
Finally, the expression of IMCKDA filter is given: 13
Journal Pre-proof f
y 2β
2 2 2
X X 0
T 1 0
( X0α 0 XTs α1 )
(12)
2
3.2. Update of Iterative Period As mentioned above, the key of the methods based on CK lies in the accurate period provided. However, the fault period is very difficult to be accurately estimated in real world applications. Due to random slip of rollers, the bearing fault impulses are generated with not exactly equal intervals even under the stationary scenario [34]. Different from the bearing fault, the impulses caused by gear fault are exactly period without the effect from the random slip. Even so, it is hard to ensure the performance of DMs based on CK, since the speed and operation variation will bring the fluctuation of the period. With the advantage of the iteration algorithm, Miao et al. [34] proposed an estimation method of iteration period according to the filtered signal. Without any prior knowledge, the proposed method could update the iterative period to ensure the updated period converge to the fault period. The procedure can be described as follows:
x%(n) x(n) j Hilbert x(n)
(13)
N Ts arg max x (t )x (t )dt , min( ) , N t 1 N r ( ) x (t )x (t )dt 0
(14) (15)
t 1
Firstly, the analytic signal of the input signal or the filtered signal is obtained by Hilbert transform by (13). Secondly, through calculating the autocorrelation of the analytic signal according to (14), the maximum of the autocorrelation is chosen as the candidate of the period for the iteration. It worth mentioning here the range of the candidate does not contain the part of 0 to the first point which makes the autocorrelation equal to 0, just shown in (15). Based on the description above, the algorithm of IMCKDA is illustrated in Table І.
14
Journal Pre-proof TABLE I IMCKDA ALGORITHM Input:
x- the raw signal or the iterated signal; L-the filter length; n-the number of iterations;
Output:
y-the filtered signal.
Initialization: f = [0 1 0 0 …]T
x Ts according to (13)-(15);
Start:
x, Ts X0 , X0 XT0 , XTs ; 1
y xf ;
Loop:
Update y Ts according to (13)-(15); Update x, Ts X0 , X0 X0T , XTs ; 1
y , Ts β, α 0 , α1 ; y , β, X0 XT0 , X0 , α 0 , XTs , α1 f according to (12); 1
End Loop Obtain filtered signal y. End Compared with IMCKD proposed in [34], the proposed IMCKDA has two merits. Firstly, IMCKDA is free from the interference of the discontinuity point and the filter operation by the convolution adjustment. Secondly, it can adaptively select the appropriate filter length under different scenarios. 3.3. Selection of Filter Length In this section, a selection strategy of filter length is introduced. Firstly, a new index, CG, is structured based the definition of Gini index. Actually, Gini index was originally introduced in economics and used 15
Journal Pre-proof to measure the wealth inequality or sparsity [42]. Benefiting from its remarkable performance in the evaluation of the sparsity, Gini index has been widely applied in field of signal process [43-45]. The definition of Gini index is given as follows: N
Gini index 1 2 n 1
1 xn N n 2 x1 N
(16)
where x=[x1 , x2 ,..., xN ] and its elements are sorted in ascent order, that is x1 x2 ... xN . . and . 1 are the absolute value and L1 norm, respectively. Fig. 2 shows the 2-dimensional (2D) distribution of kurtosis and Gini index. Note that Gini index is only applied to the distribution with the positive. Therefore, the 2D distribution is constructed by symmetry operation from the part of (0,1] with x1 = 0 and x2 = 0 as the symmetry axis. It can be seen that both of kurtosis and Gini index are scale invariant, but they have the different gradients according to the change of color. Through the analysis of the curve lines, Gini index has a better consistency with the change of amplitude than kurtosis. Making full use of the advantage, CG is originally structured as shown in (17) to guide the selection of filter length. N
CG ( x) 1 2 n 1
1 xn N n 2 x1 N
(17)
where x =[ x1 x1Ts , x2 x2Ts ,..., xN xN Ts ] .
16
Journal Pre-proof
Fig. 2. Distribution of kurtosis (a) and Gini index (b) in the 2D coordinate. Just like CK in (A.2), the period is inset into the definition of Gini index to generate CG. To verify the feasibility of the new index and compare their performance, a simulated de-trended encoder signal with gear fault as shown in (18), is used in the numerical test. e(t ) g (t iT )
(18)
i
where g (t ) A exp(t 2 / 2 2 ) , T is the period of transient impulses caused by gear fault, A and are the amplitude and width of g(t), respectively. They can be used to control the landscape of the transient impulse. In the simulated mode, suppose a localized defect occurs on the planet gear of 20 teeth. The other parameters of simulated encoder signal are listed in Table II. TABLE II PARAMETERS OF THE SIMULATED DE-TRENDED ENCODER SIGNAL A(degree)
(s)
T(s)
0.05
0.001
0.1
By increasing the SNR of the tested signal from -15 to 25 dB, the results are investigated as shown in Fig. 3. First and most importantly, they have a rising tendency with the increase of SNR. In other words, both could measure the fault information quantificationally. Yet, the difference is that CG has a better consistency with the change of SNR than CK. It is significantly important for accurately evaluating the 17
Journal Pre-proof efficiency of the filtering operation. 10-4 0.8
3
0.6
2
1
-15
Correlated Gini index
Correlated Kurtosis
CK CG
0.4
-10
-5
0
5
10
15
20
25
SNR [dB]
Fig. 3. The trend of CG and CK with the change of SNR. It has been reported that a priori estimation of the optimal FIR filter length is not possible [46]. However, the dominant effect of the filter length for the efficiency of the IMCKDA could be attenuated. Since the proposed method has a synthetically consideration for the fault feature, both the impulsiveness and periodicity, the appropriate filter length which makes the proposed method obtain a satisfactory result is easy to be screened from a definite range. The selection strategy of filter length can be concluded in Table III.
18
Journal Pre-proof TABLE III SELECTION STRATEGY OF FILTER LENGTH Initialization: The range of filter length L [20, 300] Start: Loop:
i=1; n=1; Run IMCKDA from L = 20; cg(i) = CG(y); i+1; if i>=10; cgm(n)=mean(cg); n+1; i=1; if cgm(n+1)<= cgm(n); break;
End Loop L arg max[CG(IMCKDA(y , L))], L [20,10* n] L
End The selection strategy introduced above provided an alternative scheme for the denoising of encoder signal using IMCKDA and its strong practicability will be validated by the real experimental cases.
4. Application framework It has been mentioned that the signal directly recorded by rotary encoder is the position series. As shown in Fig. 7, intuitively, it is a gradient straight line. It is impossible to detect any fault information from the raw encoder signal. Therefore, this section introduces the application framework of the proposed method for the fault diagnosis of wind turbine gearbox. To excavate the rich fault information from the encoder signal, it is necessary to transfer the raw position series into more meaningful kinetic variables. IAA is believed to directly reflect the torsional vibration introduced by faults and it can be obtained easily by the second-order difference of the position series. Therefore, IAA is considered to be the suitable variables for the fault diagnosis [16]. In addition, noise inevitably exists in the measured signals because of the interference and computational error, which often hinders the feature extraction from the different signal styles [47-49]. 19
Journal Pre-proof Comb filtering, also known as time synchronous averaging, is the effective tool for the enhancement of synchronous components and the elimination of asynchronous components by taking the ensemble average of the segments with the specified period. Especially for the gear fault, the fault period is fixed when the rotating speed is constant. This process can be denoted as follows [50]: s ( n)
1 K
K 1
s(n kT ) k 0
(19)
s
where s(n) is the IAA signal. K denotes the number of periods being averaged. Generally, in the diagnosis of gearbox fault, K≥ 3 is chosen for the measurement of periodicity. In this paper, K = 5 is applied in all simulation and experiments. Due to the period fluctuation caused by the speed and operation variation, the comb filtering just provides a coarse filter operation. Therefore, a more reliable filter should be designed for the extraction of fault feature. To meet the requirements driven by the advancement of industrial engineering, large-scale and high-complex modern equipment, such as wind turbine, is being widely used. Numerous synchronous and asynchronous interference highly complicate the signal even with comb filtering. It has been mentioned that the existing DMs did not gain any benefit from the filtered signal. In view of this, IMCKDA is proposed to overcome the disadvantage by using convolution adjustment definition. Therefore, the fault feature can be further enhanced for the diagnosis. To verify the effectiveness of the proposed method, the real experiment of the gear fault is carried out in the following subsections. To further highlight the superiority of IMCKDA in process of IAA after comb filtering, other three existing state-of-the-art DMs, i.e., MED [30], MEDA [33] and MOMEDA [33], are used in the comparative study. Without loss of generality, all methods use the same number of iterations n=30 and the same selection strategy of filter length in Table III. In addition, the fault period is provided in MOMEDA.
20
Journal Pre-proof 5. Case study 5.1. Experimental setup In this subsection, three experimental cases are employed to further compare with the proposed IMCKDA and the traditional DMs. Fig. 4(a) illustrates the experimental bench which reflects the operation condition of the real wind turbine gearbox and Fig. 4(b) elaborates the schematic diagram of the experimental bench. The planetary gearbox is driven by an AC motor. By controlling the motor, different conditions with different speeds can be simulated. The magnetic break is used to model the wind loading for the fun. Two rotary encoders (Heidenhain ERN100) are mounted on the input and output shaft of the planetary gearbox, respectively. The resolution is 5000 pulses/ revolution. As shown in Fig. 5, the encoder signal is measured by an IK220 counter card with 5000 Hz sampling rate. The data acquisition system is integrated into the PC. Through data transformation and pretreatment, the measured signal can be analyzed using the proposed method in this paper. Additionally, the configuration with detailed parameters of the planetary gearbox is shown in Fig. 4(c). One can see that the motion of the planet gear is most complicated, since it couples the autorotation and revolution around the sun gear. The interference from the complex motion could undermine the fault feature. Furthermore, several main fault styles of the wind turbine gearbox, including root crack, corrosion fault and two worn teeth fault of the planet gear as shown in Fig. 6, are considered. Root crack and corrosion fault belong to the weak and early fault. Therefore, the fault feature is rather weak and easily buried by noise. The signal with two worn teeth fault contains more fault information and the distribution discipline of the impulses is more complex. It will make the methods based on periodicity puzzled easily. To highlight the superiority of IMCKDA, these challenging experimental cases are tested in this paper.
21
Journal Pre-proof (a)
(b)
Magnetic Break
Motor
Output Planetary Input Encoder Gearbox Encoder
Input encoder
Driving Motor
Output encoder Break
Planetary gearbox Wind fan
(c) Planet gear Zp = 31 Np = 3
Sun gear Zs = 20 Ring gear Zr = 82
Fig. 4. (a) Experimental bench, (b) its schematic diagram and (c) schematic view of the planetary gearbox.
22
Journal Pre-proof Encoder Heidenhain ERN100
Planetary gearbox
Heidenhain IK220
200 100
Data acquisition system
0 -100
0
20
40
60
80
position [tooth]
Signal Analysis
Fig. 5. The process of the data acquisition and analysis.
Fig. 6. Physical maps of different planetary gear faults. 5.2. Case 1: Root Crack The experimental case with root crack is firstly carried out. Raw encoder signal from the output encoder is presented in Fig. 7. By the operations of converting and comb filtering, the IAA signal is depicted in Fig. 8. Although the synchronous components are enhanced by comb filtering, the obvious periodic impulses are difficult to be detected. Compared with the simulation model, the signal from the industrial field is more complicated. Contrasting the results of MED and MEDA, it can be inferred that the two sharp peaks with red dotted line in Fig. 9(a) caused by the effect of the sensibility of MED for the filtered signal. Obviously, the fatal drawback makes MED completely lose the inspection ability for the 23
Journal Pre-proof fault. Overcoming the weakness of MED, the periodic impulses are highlighted in the filtered signal in Fig. 9(b). A fixed interval with 31 teeth indicates the fault of the planetary gear. Yet, the impulses with1
Amplitude [deg]
tooth fixed interval enhanced by MOMEDA in Fig. 9(c) which means MOMEDA fails to detect the fault.
4000 2000 0
0.5
1
1.5
2
2.5
3
Time [s]
104
2
Amplitude [rev/s ]
Fig. 7. Measured encoder signal with root crack fault.
1 0 -1 0
50
100
150
position [tooth]
2
Amplitude [rev/s ]
Fig. 8. IAA after comb filtering in the experiment case 1.
(a)
(b)
MED
5000 0
2
Amplitude [rev/s ]
-5000 0
50
100
150
position [tooth]
(c)
2000 0 -2000 -4000
MEDA
31 teeth 0
50
(d)
MOMEDA
0.02 0.01 0 -0.01 50
100
150
150
IMCKDA
31 teeth
4000 2000 0 -2000 0
100
position [tooth]
0
50
position [tooth]
100
150
position [tooth]
Fig. 9. Results of MED (a), MEDA(b), MOMEDA(c) and IMCKDA(d) in the experiment case 1.
24
0.32 0.31 0.3 0.29 0.28 20
CG Maximum point Mean value
30
Sample Number
Correlated Gini index
Journal Pre-proof 1000
2*Ts Ts
800 600 400 200 5
40
10
15
20
25
30
Iteration
Filter Length
(a)
(b)
Fig. 10. IMCKDA: (a) Selection of the filter length and (b) the change of iterative period in the experiment case 1. The filtered signal of IMCKDA is presented in Fig. 9(d). Similarly, the periodic impulses indicate the fault of the planetary gear. However, it obviously has a higher SNR compared with the filtered signal of MEDA. Fig. 10 displays the selection of the filter length and the change of iterated period in the filtering of IMCKDA. Using the selection strategy, L = 49 is chosen as the filter length as shown in Fig. 10(a). From Fig. 10(b), one can see the true fault period is identified from the 5th iteration, which verifies the advantage that IMCKDA can automatically adjust iterative period to close the true period. 5.3. Case 2: Corrosion Fault In this subsection, a corrosion fault is artificially rooted on the planetary gear by wire-electrode cutting. After converting and comb filtering, IAA signal is generated as displayed in Fig. 11. Obviously, the serried impulses with single tooth interval highlight the effect from the gear meshing. Due to the sensibility of MED for the filtered signal, the landscape of the filtered signals is dominated by two sharp peaks in Fig. 12(a). Even without the abnormal peaks, the impulses are barely visible from the filtered signals of MEDA and MOMEDA from Fig. 12(b) and (c). This may be attributed to the fact that the weak change caused by the corrosion fault in the IAA is difficult to be detected. By contrast, without any prior knowledge, IMCKDA can enhance the weak fault information from the 25
Journal Pre-proof result in Fig. 12(d). With the selected filter length L = 34, the true fault period is locked from the 4th iteration from Fig. 13. The clear impulses with 31 teeth interval manifest the feasibility and effectiveness of the proposed method in denoising of encoder signal. 2
Amplitude [rev/s ]
104 1 0 -1 -2
0
50
100
150
position [tooth] Fig. 11. IAA after comb filtering in the experiment case 2.
2
Amplitude [rev/s ]
2
Amplitude [rev/s ]
(a)
(b)
MED
5000
0
0
-2000
-5000 0
50
100
150
position [tooth]
(c) 0.06 0.04 0.02 0 -0.02 -0.04
MEDA
2000
0
100
IMCKDA
1000 0 -1000 -2000 -3000 0
50
100
150
position [tooth]
(d)
MOMEDA
50
150
31 teeth 0
position [tooth]
50
100
150
position [tooth]
0.24 0.22 CG Maximum point Mean value
0.2 0.18 20
40
Sample Number
Correlated Gini index
Fig. 12. Results of MED (a), MEDA(b), MOMEDA(c) and IMCKDA(d) in the experiment case 2.
60
600 400
2*Ts Ts
200 5
Filter Length
10
15
20
Iteration
(a)
(b) 26
25
30
Journal Pre-proof Fig. 13. IMCKDA: (a) Selection of the filter length and (b) the change of iterative period in the experiment case 2. 5.4. Case 3: Two Worn Teeth Fault It has been mentioned that two worn teeth fault on the planetary gear is rather challenging. Firstly, the distribution discipline of the impulses caused by fault is more intricate than the single fault. Secondly, the determination of the relative positions of two worn teeth fault is necessary for the diagnosis of gear fault. Despite this fact, this task which needs to accurately restore all fault impulses without any deviation is a
104
2
Amplitude [rev/s ]
challenge for all filtered methods.
2 0 -2 0
50
100
150
position [tooth]
(a)
0
50
100
position [tooth]
2
MOMEDA
0.02 0 -0.02
0
MEDA
5000 0 -5000 -10000
5000 0 -5000 -10000 -15000
(c) Amplitude [rev/s ]
(b)
MED
2
Amplitude [rev/s ]
Fig. 14. IAA after comb filtering in the experiment case 3.
50
100
150
0
(d) 3000 2000 1000 0 -1000 150 0
position [tooth]
50
1
100
150
teeth position [tooth] 13 31 teeth IMCKDA 31 teeth 1
2
2
50
3
3
4
100
4
5
5
150
position [tooth]
Fig. 15. Results of MED (a), MEDA(b), MOMEDA(c) and IMCKDA(d) in the experiment case 3. 27
0.3 0.25 CG Maximum point Mean value
0.2 0.15 20
40
60
Sample Number
Correlated Gini index
Journal Pre-proof
80
800
2*Ts Ts
600 400 200 5
10
15
20
25
30
Iteration (b)
Filter Length (a)
Fig. 16. IMCKDA: (a) Selection of the filter length and (b) the change of iterative period in the experiment case 3. Fig. 14 shows the IAA signal after comb filtering. The distinct impulses depict the dominant function of the gear meshing in the encoder signal. Without the sharp peak in the filtered signal of MED from Fig. 15(a), it can be explained that the impulse components bury the effect from sensibility of MED for the filtered signal. Intuitively, MEDA and MOMEDA just further enhance the impulses caused by the gear meshing, from which one cannot find any fault information from Fig. 15(b) and (c). The result of IMCKDA is displayed in Fig. 15(d). The impulses are clearly extracted. To present a better visual display, different marks are added on the figure of the filtered signal. It can be observed that the interval of the impulses with same color and adjacent numbers is 31 teeth which indicates two faults on the planetary gear. The interval of the impulses with same number and different colors is 13 teeth which indicates the relative position of the two faults. From Fig. 16(a), it is clear that L = 50 should be chosen as the filter length. From the change of iterative period in Fig. 16(b), IMCKDA also locks a specified sampling number which is exactly the number of sampling points during the planetary gear period Ts. With the same iterated period, the impulses caused by different faults are enhanced simultaneously. This can be explained by the envelope spectrum analysis in Fig. 17. Note that the characteristic frequency of planetary gear fault and its harmonics are the main components. Essentially, 28
Journal Pre-proof the different planetary gear faults have the same fault period which meets the requirements of IMCKDA
2
Amplitude [rev/s ]
to deconvolute the impulses with same feature.
2fs/Ts
300
fs/Ts 3fs/Ts
200 100 0
0
50
100
150
200
Frequency [Hz] Fig. 17. The envelope spectrum of the filtered signal of IMCKDA in the experiment case 3.
6. Conclusion Due to the harsh operation environment, gearboxes as the key part of the wind turbine are prone to damage. However, the difficulty from both the measurement and analysis is undermining the superiorities and usefulness of these existing methods based on the vibration and acoustic emission. In contrast, encoder signal carries rich diagnostic information which may be considered as an alternative tool for the wind turbine condition monitoring. To the denoising of encoder signal for the wind turbine gear fault diagnosis, a novel adaptive filtering method, IMCKDA, is initially introduced in this paper. By the convolution adjustment definition, the drawbacks of the sensibility to the filtered signal and the discontinuity point, are overcome. Moreover, CG is originally proposed to guide the selection of the filter length. Combined with the selection strategy, the appropriate candidate is easy to be screened from a definite range which makes the proposed method converge to a satisfactory result. Benefiting from these superiorities, IMCKDA becomes the alternative tool for denoising of encoder signal. The feasibility and effectiveness of IMCKDA are verified by the experimental cases with the existing state-of-the-art DMs, containing MED, MEDA and MOMEDA used in the comparative study. In addition, this study can be considered as the first investigative step since it concerns a single 29
Journal Pre-proof application of the method to specific type of gear failure modes and to unique specimen and therefore its effectiveness has to be proved with further investigations.
Acknowledgment This work is supported by the National Natural Science Foundation of China (No. 51421004, 91860205 and 51905017) and the Defense Industrial Technology Development Program (Grant No. JCKY2018601C013), which are highly appreciated by the authors.
Appendix A. Brief review of Deconvolution methods By using kurtosis in (A.1) as the objective function, MED [30] can enhance the impulse components caused by fault. Kurtosis is verified to be a measured index for the impulsiveness of the signal. As a result, MED is considerably susceptible to the random impulse noise. The reason for the result may attribute to that kurtosis just highlights the impulsiveness of the signal, but ignores the periodicity. Motivated by this, McDonald et al. [31] incorporated the period into the definition of kurtosis and proposed CK as shown in (A.2). By maximizing CK of filtered signal, MCKD is generated. To resolve the problem of MCKD which depends on the prior period, multipoint kurtosis in (A.4) is proposed by adding a constant vector t to the definition of kurtosis. And then, MOMED is proposed [33].
Kurtosis
1 N 1 N
N
y
4
y
n 1 N
y y
n 1
2
(A.1)
2
where y and N are the mean and length of signal y, respectively.
CK M (Ts )
N
M
n 1
m0 N
( ynmTs )2
(A.2)
( y ) n 1
2 M 1 n
30
Journal Pre-proof where M is the order of shift. Ts is the sampling number that can be denoted:
Ts f s T
(A.3)
where fs is the sampling frequency and T is the period.
Multiponit kurosis t
1 N 1 N
N
y n 1 N
y n 1
4
y
2
y
(A.4)
2
where t is a constant vector, which is used to define the locations and weightings of the goal impulses to be deconvolved.
References
[1] Z. Li, Y. Jiang, Q. Guo, C. Hu, Z. Peng, Multi-dimensional variational mode decomposition for bearing-crack detection in wind turbines with large driving-speed variations, Renewable Energy, 116 (2018) 55-73. [2] T.E.W.E.A. (EWEA), https://windeurope.org/, 2015. [3] Y. Feng, Y. Qiu, C.J. Crabtree, H. Long, P.J. Tavner, Monitoring wind turbine gearboxes, Wind Energy, 16 (2013) 728-740. [4] S.T. Kandukuri, A. Klausen, H.R. Karimi, K.G. Robbersmyr, A review of diagnostics and prognostics of low-speed machinery towards wind turbine farm-level health management, Renewable and Sustainable Energy Reviews, 53 (2016) 697-708. [5] F.P. García Márquez, A.M. Tobias, J.M. Pinar Pérez, M. Papaelias, Condition monitoring of wind turbines: Techniques and methods, Renewable Energy, 46 (2012) 169-178. [6] G. He, K. Ding, W. Li, X. Jiao, A novel order tracking method for wind turbine planetary gearbox vibration analysis based on discrete spectrum correction technique, Renewable Energy, 87 (2016) 364-375. [7] J. Chen, J. Pan, Z. Li, Y. Zi, X. Chen, Generator bearing fault diagnosis for wind turbine via empirical wavelet transform using measured vibration signals, Renewable Energy, 89 (2016) 80-92. [8] J. Chen, J. Pan, C. Zhang, X. Luo, Z. Zhou, B. Wang, Specialization improved nonlocal means to detect periodic impulse feature for generator bearing fault identification, Renewable Energy, 103 (2017) 448-467. [9] Y. Kong, T. Wang, F. Chu, Meshing frequency modulation assisted empirical wavelet transform for fault diagnosis of wind turbine planetary ring gear, Renewable Energy, 132 (2019) 1373-1388. [10] W. Teng, X. Ding, H. Cheng, C. Han, Y. Liu, H. Mu, Compound faults diagnosis and analysis for a wind turbine gearbox via a novel vibration model and empirical wavelet transform, Renewable Energy, 136 (2019) 393-402. [11] S. Shanbr, F. Elasha, M. Elforjani, J. Teixeira, Detection of natural crack in wind turbine gearbox, Renewable Energy, 118 (2018) 172-179. [12] J. Tang, S. Soua, C. Mares, T.-H. Gan, An experimental study of acoustic emission methodology for in service condition monitoring of wind turbine blades, Renewable Energy, 99 (2016) 170-179. 31
Journal Pre-proof [13] Y. Zhang, W. Lu, F. Chu, Planet gear fault localization for wind turbine gearbox using acoustic emission signals, Renewable Energy, 109 (2017) 449-460. [14] P. Guo, D. Infield, X. Yang, Wind Turbine Generator Condition-Monitoring Using Temperature Trend Analysis, IEEE Transactions on Sustainable Energy, 3 (2012) 124-133. [15] M. Elforjani, E. Bechhoefer, Analysis of extremely modulated faulty wind turbine data using spectral kurtosis and signal intensity estimator, Renewable Energy, 127 (2018) 258-268. [16] M. Zhao, J. Lin, Health Assessment of Rotating Machinery Using a Rotary Encoder, IEEE Transactions on Industrial Electronics, 65 (2018) 2548-2556. [17] B. Li, X. Zhang, J. Wu, New procedure for gear fault detection and diagnosis using instantaneous angular speed, Mechanical Systems and Signal Processing, 85 (2017) 415-428. [18] W. Qiao, D. Lu, A Survey on Wind Turbine Condition Monitoring and Fault Diagnosis—Part I: Components and Subsystems, IEEE Transactions on Industrial Electronics, 62 (2015) 6536-6545. [19] Z. Liu, L. Zhang, A review of failure modes, condition monitoring and fault diagnosis methods for large-scale wind turbine bearings, Measurement, (2019) 107002. [20] J. Jiao, M. Zhao, J. Lin, J. Zhao, A multivariate encoder information based convolutional neural network for intelligent fault diagnosis of planetary gearboxes, Knowledge-Based Systems, 160 (2018) 237-250. [21] W. Moustafa, O. Cousinard, F. Bolaers, K. Sghir, J. Dron, Low speed bearings fault detection and size estimation using instantaneous angular speed, Journal of Vibration and Control, 22 (2016) 3413-3425. [22] F. Gu, I. Yesilyurt, Y. Li, G. Harris, A. Ball, An investigation of the effects of measurement noise in the use of instantaneous angular speed for machine diagnosis, Mechanical Systems and Signal Processing, 20 (2006) 1444-1460. [23] L. Renaudin, F. Bonnardot, O. Musy, J.B. Doray, D. Rémond, Natural roller bearing fault detection by angular measurement of true instantaneous angular speed, Mechanical Systems and Signal Processing, 24 (2010) 1998-2011. [24] M. Zhao, J. Jiao, J. Lin, A Data-Driven Monitoring Scheme for Rotating Machinery Via Self-Comparison Approach, IEEE Transactions on Industrial Informatics, 15 (2019) 2435-2445. [25] T.R. Lin, A.C. Tan, L. Ma, J. Mathew, Condition monitoring and fault diagnosis of diesel engines using instantaneous angular speed analysis, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229 (2015) 304-315. [26] S.K. Roy, A.R. Mohanty, C.S. Kumar, Fault detection in a multistage gearbox by time synchronous averaging of the instantaneous angular speed, Journal of Vibration and Control, 22 (2016) 468-480. [27] B. Li, X. Zhang, A new strategy of instantaneous angular speed extraction and its application to multistage gearbox fault diagnosis, Journal of Sound and Vibration, 396 (2017) 340-355. [28] Y. Zhou, T. Tao, X. Mei, G. Jiang, N. Sun, Feed-axis gearbox condition monitoring using built-in position sensors and EEMD method, Robotics and Computer-Integrated Manufacturing, 27 (2011) 785-793. [29] R.B. Randall, J. Antoni, Rolling element bearing diagnostics—A tutorial, Mechanical Systems and Signal Processing, 25 (2011) 485-520. [30] H. Endo, R.B. Randall, Enhancement of autoregressive model based gear tooth fault detection technique by the use of minimum entropy deconvolution filter, Mechanical Systems and Signal Processing, 21 (2007) 906-919. [31] G.L. McDonald, Q. Zhao, M.J. Zuo, Maximum correlated Kurtosis deconvolution and application on gear tooth chip fault detection, Mechanical Systems and Signal Processing, 33 (2012) 237-255. [32] Y. Miao, M. Zhao, J. Lin, X. Xu, Sparse maximum harmonics-to-noise-ratio deconvolution for weak fault signature detection in bearings, Measurement Science and Technology, 27 (2016) 105004. [33] G.L. McDonald, Q. Zhao, Multipoint Optimal Minimum Entropy Deconvolution and Convolution Fix: Application to vibration fault detection, Mechanical Systems and Signal Processing, 82 (2017) 461-477. [34] Y. Miao, M. Zhao, J. Lin, Y. Lei, Application of an improved maximum correlated kurtosis deconvolution method for fault diagnosis of rolling element bearings, Mechanical Systems and Signal Processing, 92 (2017) 173-195. [35] J. Chen, Z. Li, J. Pan, G. Chen, Y. Zi, J. Yuan, B. Chen, Z. He, Wavelet transform based on inner product in fault 32
Journal Pre-proof diagnosis of rotating machinery: A review, Mechanical Systems and Signal Processing, 70-71 (2016) 1-35. [36] J. Zarei, M.A. Tajeddini, H.R. Karimi, Vibration analysis for bearing fault detection and classification using an intelligent filter, Mechatronics, 24 (2014) 151-157. [37] Y. Miao, M. Zhao, J. Lin, Identification of mechanical compound-fault based on the improved parameter-adaptive variational mode decomposition, ISA Transactions, 84 (2019) 82-95. [38] J. Antoni, Fast computation of the kurtogram for the detection of transient faults, Mechanical Systems and Signal Processing, 21 (2007) 108-124. [39] Y. Lei, J. Lin, Z. He, Y. Zi, Application of an improved kurtogram method for fault diagnosis of rolling element bearings, Mechanical Systems and Signal Processing, 25 (2011) 1738-1749. [40] J. Antoni, The infogram: Entropic evidence of the signature of repetitive transients, Mechanical Systems and Signal Processing, 74 (2016) 73-94. [41] A. Moshrefzadeh, A. Fasana, The Autogram: An effective approach for selecting the optimal demodulation band in rolling element bearings diagnosis, Mechanical Systems and Signal Processing, 105 (2018) 294-318. [42] C. Gini, Measurement of inequality of incomes, The Economic Journal, 31 (1921) 124-126. [43] D. Zonoobi, A.A. Kassim, Y.V. Venkatesh, Gini Index as Sparsity Measure for Signal Reconstruction from Compressive Samples, IEEE Journal of Selected Topics in Signal Processing, 5 (2011) 927-932. [44] Y. Miao, M. Zhao, J. Lin, Improvement of kurtosis-guided-grams via Gini index for bearing fault feature identification, Measurement Science and Technology, 28 (2017) 125001. [45] C.A. Loza, J.C. Principe, Transient model of EEG using Gini Index-based matching pursuit,
2016 IEEE International
Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016, pp. 724-728. [46] M. Buzzoni, J. Antoni, G. D'Elia, Blind deconvolution based on cyclostationarity maximization and its application to fault identification, Journal of Sound and Vibration, 432 (2018) 569-601. [47] S.T. Kandukuri, J.S.L. Senanayaka, V.K. Huynh, H.R. Karimi, K.G. Robbersmyr, Current signature based fault diagnosis of field-oriented and direct torque–controlled induction motor drives, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 231 (2017) 849-866. [48] Y. Wang, Z. He, Y. Zi, Enhancement of signal denoising and multiple fault signatures detecting in rotating machinery using dual-tree complex wavelet transform, Mechanical Systems and Signal Processing, 24 (2010) 119-137. [49] M. Zhao, X. Jia, J. Lin, Y. Lei, J. Lee, Instantaneous speed jitter detection via encoder signal and its application for the diagnosis of planetary gearbox, Mechanical Systems and Signal Processing, 98 (2018) 16-31. [50] S. Braun, The synchronous (time domain) average revisited, Mechanical Systems and Signal Processing, 25 (2011) 1087-1102.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Journal Pre-proof
Highlights 1. The built-in encoder signal as a new alternative tool is firstly used for gearbox fault detection in wind turbines. 2. An improved MCKDA is proposed to denoise the encoder signal without any prior knowledge and the least input parameters. 3. Compared with the traditional DMs, the proposed IMCKDA is more suitable for fault diagnosis based on the encoder signal. 4. The proposed method can expand the application to the vibration, sound and current etc. other data styles.
1
Yonghao Miao, Ming Zhao, Kaixuan Liang, Jing Lin PII:
S0960-1481(19)31687-8
DOI:
https://doi.org/10.1016/j.renene.2019.11.012
Reference:
RENE 12559
To appear in:
Renewable Energy
Received Date:
10 July 2019
Accepted Date:
03 November 2019
Please cite this article as: Yonghao Miao, Ming Zhao, Kaixuan Liang, Jing Lin, Application of an improved MCKDA for fault detection of wind turbine gear based on encoder signal, Renewable Energy (2019), https://doi.org/10.1016/j.renene.2019.11.012
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
Journal Pre-proof
Application of an improved MCKDA for fault detection of wind turbine gear based on encoder signal
Yonghao Miao, PhD School of Reliability and Systems Engineering, Beihang University, Xueyuan Road No. 37, Haidian District, Beijing 100083, China Email: [email protected]
Ming Zhao, PhD, Associate Professor 1. School of Mechanical Engineering, Xi’an Jiaotong University, Xi'an 710049, China 2. School of Reliability and Systems Engineering, Beihang University, Xueyuan Road No. 37, Haidian District, Beijing 100083, China Email: [email protected]
Kaixuan Liang, PhD candidate School of Mechanical Engineering, Xi’an Jiaotong University, Xi'an 710049, China Email: [email protected]
Jing Lin*, PhD, Professor School of Reliability and Systems Engineering, Beihang University, Xueyuan Road No. 37, Haidian District, Beijing 100083, China Email: [email protected]
*
Corresponding author 1
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Abstract
Due to severe working condition, unexpected failures in wind turbine gearbox become rather frequent and may lead to long downtime or even catastrophic casualties. However, traditional diagnosis techniques based on vibration, acoustic emission etc. still face some problems when they are used for failure identification of wind turbine gearbox. Encoder signal carries rich diagnostic information which may be considered as an alternative tool for the wind turbine condition monitoring. Motivated by this, the encoder signal is initially introduced for the fault diagnosis of wind turbine gear in this paper. A novel adaptive filtering method, improved maximum correlated kurtosis deconvolution adjusted (IMCKDA), is proposed to eliminate the diverse noises in encoder signal. Additionally, to overcome the limitation from the sensibility of discontinuity point and filtered signal in traditional deconvolution methods (DMs), convolution adjustment definition is introduced. And correlated Gini index (CG) is originally designed to guide the selection of filter length. Finally, the encoder signal is verified to be an alternative tool for the fault diagnosis of wind turbine gear by real experimental cases. And without any prior knowledge and the least input parameters, IMCKDA is more suitable for processing encoder signal than existing state-of-the-art DMs.
Keywords: Wind turbines, Rotary encoder, Adaptive filtering, Gearbox fault diagnosis, Deconvolution
2
Journal Pre-proof Nomenclature Abbreviation IMCKDA
improved maximum correlated kurtosis deconvolution adjusted
DM
deconvolution method
CG
correlated Gini
CNC
computer numerical control
IAS
instantaneous angular speed
IAA
instantaneous angular acceleration
MED
minimum entropy deconvolution
MCKD CK
maximum correlated kurtosis deconvolution
correlated kurtosis
MOMED
multipoint optimal minimum entropy deconvolution
IMCKD
improved maximum correlated kurtosis deconvolution
2D
2-dimensional
SNR
signal to noise ratio
Mathematical notations t
time or time shift
x(t)
measured signal
g(t)
fault component
n(t)
noise component
y(t)
filtered signal
f N
FIR filter length of signal 3
Journal Pre-proof M
order of shift
T
period
Ts
sampling number
fs
sampling frequency
t
constant vector
L
filter length
X
shift matrix of signal x
f
matrix of FIR filter coefficient
y
vector of filtered signal y
x
analytic signal of x
j
symbol of imaginary number
x
vector of signal x in ascent order
x
vector of root of signal x and its shift signal
K
number of periods being averaged in time synchronous averaging
s
IAA signal
s e(t) A
IAA signal after time synchronous averaging simulated de-trend encoder signal amplitude
Zp gear tooth number Greek symbols
matrix of signal y and y2 or y2 and y autocorrelation matrix of signal y shift of signal x 4
Journal Pre-proof width of g(t) Superscripts T
transposition operation
5
Journal Pre-proof 1. Introduction Due to the low cost and high flexibility, wind energy has gained increasing attractiveness [1]. The past decades have witnessed a rapid advancement of wind power generation. It is reported that the cumulative installed capacity of wind power had over 148 GW in Europe and just in China the number had exceeded 125 GW in 2015 [2]. However, because of severe condition, the unexpected failures in the drivetrain of wind turbines, such as the gearbox system, become rather frequent and they may lead to long downtime or even catastrophic casualties. Therefore, the condition monitoring and in-time maintenance of wind turbine gearbox are of great significance [3, 4]. According to statistics[5, 6], to ensure the safety operation, the maintenance costs account for about 25%-30% of the overall energy generation cost. Recently, numerous signal processing techniques based on the vibration information [6-11], the acoustic emission [12, 13], temperature information [14] etc. are successively proposed for the fault identification of wind turbines. These works did make important contributions for the maintenance of wind turbines. Yet, traditional maintenance techniques, especially the most-used vibration-based methods, are confronting more and more challenges. The difficulties from both the signal measurement and analysis, such as the varying speed and low speed conditions, have been summarized in Ref. [3, 4, 15]. Recently, it has been reported that the built-in information, such as rotary encoder signal, carries rich diagnostic information and has been considered as an alternative tool to address the bottle neck issue of gearbox fault diagnosis [16, 17]. Actually, rotary encoders have been widely equipped in wind turbines for motion and speed control [18]. Benefiting from the close connection to the critical components, the signal from the rotary encoders carries rich condition information about the equipment being monitored, which also showcases the potential of encoder information in the condition monitoring of wind turbine gearbox. The prospect development of encoder signal in the application of wind turbine fault diagnosis has gained positive 6
Journal Pre-proof outlook in the latest review research [19]. Compared with the traditional monitoring approaches, such as vibration, acoustic emission and temperature information etc., the encoder information enjoys the following advantages which make the failure identification of the gearbox easy to realize: (1)High fault-sensibility. The idea behind using encoder signal as a fault detection tool is that the fault in the machinery equipment, for example the gear fault, has a direct expression of torsional vibration. Therefore, encoder signal which mainly reflects the torsional behavior is more susceptible to weak faults than vibration and acoustic emission signals [16]. (2) Short transfer path. The vibration or acoustic emission sensors are typically mounted on the gearbox casing in wind turbines. Therefore, the measured signal is obtained after a long and complex transfer path, which seriously attenuates the useful feature. As an important built-in sensor, encoder has been installed in the system and its signal would be less affected by the transfer path [20]. (3) Low speed robustness. Since low-frequency response of accelerometers is not satisfactory，low speed is still one of the main challenges for the fault diagnosis of wind turbine gearbox by the vibration analysis [4]. In contrast, the encoder signal has been verified to be as an alternative or a complementary tool for its better performance in low speed machine monitoring [21]. (4) Low cost. The main cost of the maintenance of wind turbines is from the measurement. Unlike the vibration measurement, liquids analysis and other monitoring patterns, the encoder signal-based analysis is easily accessible and has a lower cost without any measurement sensors [22]. Actually, the signal directly recorded by rotary encoder is the position series. By the differential operation, the position series could be converted into more meaningful kinetic variables, such as instantaneous angular speed (IAS) series [23], instantaneous angular acceleration (IAA) series [16] and jerk [24]. In virtue of these merits, the research of fault diagnosis based on encoder signal has attracted considerable attention in recent years. 7
Journal Pre-proof Lin et al. [25] found that IAS is less affected by the background noise, and they proposed IAS spectrum for the fault diagnosis of diesel engines. Moustafa et al. [21] thought vibration and acoustic emission analysis have a bad visual inspection ability for the detection of low speed bearings fault, and introduced IAS-based method to compensate for the shortcoming. Roy et al. [26] achieved much in terms of gearbox diagnosis by applying time synchronous averaging to eliminate the interference from load variation in IAS signal. Similarly, to separate the fault information from other interferences, empirical mode decomposition [17, 27], ensemble empirical mode decomposition [28] and other advanced processing methods in the vibration analysis are introduced for denoising of encoder signal. Recently, Zhao et al. [16] established a health assessment of machinery fault diagnosis by IAA signal and proposed a lowpass filter to enhance the fault component. In practice, the load variation, the rotation and motion of other components and data acquisition all inevitably generate noise which highly complicates the encoder signals, containing IAS, IAA and jerk. The fault feature is easily buried by these interferences and noise. Therefore, some of these existing methods which just provided the simple and coarse denoising scheme hardly attain the expected goal. Addressing the key issue from the root is to design an adaptive filter motivated by the particular feature of the fault in the encoder signal. Deconvolution methods which could adaptively design an FIR filter by iteratively choose the filter coefficients to maximize the prespecified objective [29] provide an alternative to solve the problem. Actually, DMs have been extensively studied and successfully employed in vibration analysis for machinery fault diagnosis. In 2006, minimum entropy deconvolution (MED) which used kurtosis value of the signal as the objective is firstly introduced to enhance the fault feature of the vibration signal [30]. Since then, improvements and applications of MED have attracted considerable attention. McDonald et al. [31] found the preference of the MED algorithm is to deconvolve the independent impulse, then proposed a new method named the maximum correlated kurtosis deconvolution (MCKD) which can overcome the 8
Journal Pre-proof shortcoming of MED by introducing correlated kurtosis (CK) as the new objective. Yet, the efficiency of MCKD exceedingly relies on the prior period [32]. In view of this, multipoint optimal minimum entropy deconvolution (MOMED) [33] and improved maximum correlated kurtosis deconvolution (IMCKD) [34] are proposed successively. These works make a great contribution for the theory expansion of DMs. However, some drawbacks still limit the performance of DMs. On the one hand, MED, MCKD and its variants are susceptible to the effect of filtered signal and the discontinuity point. It is easy to make these methods lose efficacy [33]. On the other hand, the filter length as the most critical parameter affects the effectiveness of DM. Till now, the selection of the filter length just relies on the experience [34]. In this paper, IMCKDA is proposed to overcome these disadvantages of the traditional DMs and used for fault detection of wind turbine gear based on the encoder signal. Firstly, using the convolution adjustment, the proposed method can be free from the interference of the discontinuity point and the effect of the filtered signal. Then a new index, CG, is structured and combined with a specific selection strategy, to adaptively select the appropriate filter length. Finally, the proposed IMCKDA is verified to be more suitable for processing of the encoder signal than the existing state-of-the-art DMs and an alternative tool for the fault diagnosis of wind turbine gear by the real experimental cases. The main contributions of this paper are summarized as follows: (1) The analysis based on built-in encoder signal is firstly used for gearbox fault detection in wind turbines. It provides a new alternative tool for addressing the bottle neck issue of wind turbine gear fault diagnosis. (2) The adaptive filtering method is initially applied for denoising of encoder signal in this paper. Benefiting from the superiority of proposed method, a better result with high SNR can be obtained which will make the diagnosis decision easy to give. (3) Compared with the traditional DMs, the proposed IMCKDA has more merits: ① It can be applied 9
Journal Pre-proof without any prior knowledge and the least input parameters; ② The proposed method is free from the interference of the discontinuity point and the effect of filtered signal; ③ It can adaptively choose the filter length. The rest of this article is organized as follows. Section 2 makes a brief review of the deconvolution theory. In Section 3, the proposed method is introduced in detail from 3 subsections. Section 4 displays the application framework of the proposed method for the fault diagnosis of wind turbine gearbox. Section 5 further validates the robustness of the proposed method by three real datasets from the gearbox, containing root crack, corrosion fault and two worn teeth fault of the planet gear. Finally, the conclusion is drawn in Section 6.
2. Deconvolution theory Analogous to vibration signal, encoder signal could be viewed as a mixed signal. After transmission path effect, encoder signal is compounded by the components caused by the fault and other noise. It can be defined: x(t ) g (t ) n(t ) * h(t )
(1)
where x(t), g(t) and n(t) are the measured signal, fault component and noise, respectively. h(t) is the response of the transmission path effect. * denotes the convolution operation. The idea of DMs is to design an FIR filter to make the filtered signal restore the fault component by maximizing the objective function. The process can be represented as shown in Fig. 1:
y (t ) x(t ) * f (l ) g (t )
(2)
10
Journal Pre-proof n (t )
hn
g (t )
hg
x(t )
f (l )
y (t ) g (t )
FIR filter
Fig. 1. The process of the deconvolution. In the field of machinery fault diagnosis, different filter methods, including wavelet transform [35], the intelligent filter method [36], decomposition methods [37] and the filter methods based on 1/3-binary tree filter bank, such as kurtogram [38] and its variants [39-41] have been successfully applied. However, different from the filter methods based on the fixed filter bank, DMs can adaptively design the shape and the position of the filter by iteratively updating the filter coefficients. Therefore, the filtered results of DMs are more accurate and informative when the selection of the objective function and the filter parameters is appropriate. To process the fault signal under different scenarios, numerous of indexes, such as kurtosis, CK etc., are used as the objective function in the traditional DMs. The description about the traditional DMs can be referred in Appendix A. As one of the most widely used adaptive filtering methods, DMs had achieved much in terms of machine diagnosis with the vibration signal, especially in the denoising of the complex signal. However, the selection of filter length, the susceptibility to discontinuity point and the effect from filtered signal still seriously undermine the usefulness of the existing DMs. Furthermore, in the analysis of encoder signal, the adaptive filtering methods are still the unexplored territory. Therefore, to overcome these drawbacks, IMCKDA is proposed in this paper.
3. Proposed method 11
Journal Pre-proof To clearly describe the proposed method, three subsections are organized as follows. Firstly, the derivation process of IMCKDA using the convolution adjustment definition is elaborated in Section 3.1. Secondly, through algorithm introduction and performance analysis, Sections 3.2 and 3.3 respectively illustrate the solution for the selection of prior period and filter length in the proposed method. 3.1. Convolution Adjustment Definition for the Derivation The ultimate goal of DMs is to find the optimal filter coefficients. With the objective function method, the expression of the filter can be deduced. Similarly, IMCKDA chooses CK as the objective function. Since the performance of the proposed method does not rely on the order of shift, M =1 is fixed in the objective function, that is N
max CK1 (Ts ) max f
f
(y y n 1
n
n T s
N 2 yn n 1
)2 (3)
2
where f [ f1 , f 2 ,..., f L ]T is an FIR filter with the length L. By the derivation of (4), the expression of the filter can be deduced.
d CK1 (Ts ) 0, k 1, 2,..., L df k
(4)
Generally, the convolution definition of the filter process is given: L
yn ∑ fl xn l 1 , n 1, 2,..., N
(5)
l 1
Then, by taking the derivatives of the optimization function (4) and taking the inverse filtering expression (5) into consideration, the final iterative expression of optimal filter can be obtained. Yet, numerous examples have verified DMs are sensitive to discontinuity point and the filtered signal by the derivation above [31, 33]. To overcome the weakness, a new convolution adjustment definition as shown in (6) is introduced to 12
Journal Pre-proof replace of the traditional one in this paper. Through making a delay in the input signal, the preference to deconvolve the spurious impulse can be avoided. L
yn ∑ fl xn L l , n 1, 2,..., N L 1
(6)
l 1
Firstly, by taking the derivatives of the numerator portions, the expression can be presented: d d CK1 (Ts ) Numerator df k df k
N
n 1
yn yn Ts
2
N
N
n 1
n 1
2 xn L l yn yn2Ts 2 xn Ts L l yn Ts yn2
(7)
Similarly, the derivative of denominator can be presented: 2
d d N 2 N 2 N CK1 (Ts ) Denominator y 4 n yn yn xn L l df k df k n 1 n 1 n 1
(8)
Then, the expression (4) can be deduced: 2
N N N 2 N 2 2 y 2 x y y 2 x y y 4 yn yn Ts n n L l n n T n T L l n T n s s s n 1 n 1 n 1 n 1
2
N 2 yn n 1
3 N
y x n 1
n n L l
0
(9)
For the sake of conciseness, the expression (9) is denoted: 2
2
2 β 2 X0 y y 2 ( X0α 0 XTs α1 ) xL t 0 where Xt 0 ... 0
(10)
xL 1t
xL 2 t
...
xL t 0 ... 0
xL 1t xL t ... 0
... ... ... ...
xN t xN 1t xN 2 t ; ... xN L t 1 LbyN L 1
α 0 [ y1 y12Ts , y2 y22Ts ,..., yN yN2 Ts ]T ; α1 [ y1Ts y12 , y2Ts y22 ,..., yN Ts yN2 ]T ; β [ y1 y1Ts , y2 y2Ts ,..., yN yN Ts ]T . And the symbol T denotes the transposition operation,
.2
is defined as
the Euclidian norm. The expression for inverse filtering (6) can be simplified: y XT0 f
(11)
Finally, the expression of IMCKDA filter is given: 13
Journal Pre-proof f
y 2β
2 2 2
X X 0
T 1 0
( X0α 0 XTs α1 )
(12)
2
3.2. Update of Iterative Period As mentioned above, the key of the methods based on CK lies in the accurate period provided. However, the fault period is very difficult to be accurately estimated in real world applications. Due to random slip of rollers, the bearing fault impulses are generated with not exactly equal intervals even under the stationary scenario [34]. Different from the bearing fault, the impulses caused by gear fault are exactly period without the effect from the random slip. Even so, it is hard to ensure the performance of DMs based on CK, since the speed and operation variation will bring the fluctuation of the period. With the advantage of the iteration algorithm, Miao et al. [34] proposed an estimation method of iteration period according to the filtered signal. Without any prior knowledge, the proposed method could update the iterative period to ensure the updated period converge to the fault period. The procedure can be described as follows:
x%(n) x(n) j Hilbert x(n)
(13)
N Ts arg max x (t )x (t )dt , min( ) , N t 1 N r ( ) x (t )x (t )dt 0
(14) (15)
t 1
Firstly, the analytic signal of the input signal or the filtered signal is obtained by Hilbert transform by (13). Secondly, through calculating the autocorrelation of the analytic signal according to (14), the maximum of the autocorrelation is chosen as the candidate of the period for the iteration. It worth mentioning here the range of the candidate does not contain the part of 0 to the first point which makes the autocorrelation equal to 0, just shown in (15). Based on the description above, the algorithm of IMCKDA is illustrated in Table І.
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Journal Pre-proof TABLE I IMCKDA ALGORITHM Input:
x- the raw signal or the iterated signal; L-the filter length; n-the number of iterations;
Output:
y-the filtered signal.
Initialization: f = [0 1 0 0 …]T
x Ts according to (13)-(15);
Start:
x, Ts X0 , X0 XT0 , XTs ; 1
y xf ;
Loop:
Update y Ts according to (13)-(15); Update x, Ts X0 , X0 X0T , XTs ; 1
y , Ts β, α 0 , α1 ; y , β, X0 XT0 , X0 , α 0 , XTs , α1 f according to (12); 1
End Loop Obtain filtered signal y. End Compared with IMCKD proposed in [34], the proposed IMCKDA has two merits. Firstly, IMCKDA is free from the interference of the discontinuity point and the filter operation by the convolution adjustment. Secondly, it can adaptively select the appropriate filter length under different scenarios. 3.3. Selection of Filter Length In this section, a selection strategy of filter length is introduced. Firstly, a new index, CG, is structured based the definition of Gini index. Actually, Gini index was originally introduced in economics and used 15
Journal Pre-proof to measure the wealth inequality or sparsity [42]. Benefiting from its remarkable performance in the evaluation of the sparsity, Gini index has been widely applied in field of signal process [43-45]. The definition of Gini index is given as follows: N
Gini index 1 2 n 1
1 xn N n 2 x1 N
(16)
where x=[x1 , x2 ,..., xN ] and its elements are sorted in ascent order, that is x1 x2 ... xN . . and . 1 are the absolute value and L1 norm, respectively. Fig. 2 shows the 2-dimensional (2D) distribution of kurtosis and Gini index. Note that Gini index is only applied to the distribution with the positive. Therefore, the 2D distribution is constructed by symmetry operation from the part of (0,1] with x1 = 0 and x2 = 0 as the symmetry axis. It can be seen that both of kurtosis and Gini index are scale invariant, but they have the different gradients according to the change of color. Through the analysis of the curve lines, Gini index has a better consistency with the change of amplitude than kurtosis. Making full use of the advantage, CG is originally structured as shown in (17) to guide the selection of filter length. N
CG ( x) 1 2 n 1
1 xn N n 2 x1 N
(17)
where x =[ x1 x1Ts , x2 x2Ts ,..., xN xN Ts ] .
16
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Fig. 2. Distribution of kurtosis (a) and Gini index (b) in the 2D coordinate. Just like CK in (A.2), the period is inset into the definition of Gini index to generate CG. To verify the feasibility of the new index and compare their performance, a simulated de-trended encoder signal with gear fault as shown in (18), is used in the numerical test. e(t ) g (t iT )
(18)
i
where g (t ) A exp(t 2 / 2 2 ) , T is the period of transient impulses caused by gear fault, A and are the amplitude and width of g(t), respectively. They can be used to control the landscape of the transient impulse. In the simulated mode, suppose a localized defect occurs on the planet gear of 20 teeth. The other parameters of simulated encoder signal are listed in Table II. TABLE II PARAMETERS OF THE SIMULATED DE-TRENDED ENCODER SIGNAL A(degree)
(s)
T(s)
0.05
0.001
0.1
By increasing the SNR of the tested signal from -15 to 25 dB, the results are investigated as shown in Fig. 3. First and most importantly, they have a rising tendency with the increase of SNR. In other words, both could measure the fault information quantificationally. Yet, the difference is that CG has a better consistency with the change of SNR than CK. It is significantly important for accurately evaluating the 17
Journal Pre-proof efficiency of the filtering operation. 10-4 0.8
3
0.6
2
1
-15
Correlated Gini index
Correlated Kurtosis
CK CG
0.4
-10
-5
0
5
10
15
20
25
SNR [dB]
Fig. 3. The trend of CG and CK with the change of SNR. It has been reported that a priori estimation of the optimal FIR filter length is not possible [46]. However, the dominant effect of the filter length for the efficiency of the IMCKDA could be attenuated. Since the proposed method has a synthetically consideration for the fault feature, both the impulsiveness and periodicity, the appropriate filter length which makes the proposed method obtain a satisfactory result is easy to be screened from a definite range. The selection strategy of filter length can be concluded in Table III.
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Journal Pre-proof TABLE III SELECTION STRATEGY OF FILTER LENGTH Initialization: The range of filter length L [20, 300] Start: Loop:
i=1; n=1; Run IMCKDA from L = 20; cg(i) = CG(y); i+1; if i>=10; cgm(n)=mean(cg); n+1; i=1; if cgm(n+1)<= cgm(n); break;
End Loop L arg max[CG(IMCKDA(y , L))], L [20,10* n] L
End The selection strategy introduced above provided an alternative scheme for the denoising of encoder signal using IMCKDA and its strong practicability will be validated by the real experimental cases.
4. Application framework It has been mentioned that the signal directly recorded by rotary encoder is the position series. As shown in Fig. 7, intuitively, it is a gradient straight line. It is impossible to detect any fault information from the raw encoder signal. Therefore, this section introduces the application framework of the proposed method for the fault diagnosis of wind turbine gearbox. To excavate the rich fault information from the encoder signal, it is necessary to transfer the raw position series into more meaningful kinetic variables. IAA is believed to directly reflect the torsional vibration introduced by faults and it can be obtained easily by the second-order difference of the position series. Therefore, IAA is considered to be the suitable variables for the fault diagnosis [16]. In addition, noise inevitably exists in the measured signals because of the interference and computational error, which often hinders the feature extraction from the different signal styles [47-49]. 19
Journal Pre-proof Comb filtering, also known as time synchronous averaging, is the effective tool for the enhancement of synchronous components and the elimination of asynchronous components by taking the ensemble average of the segments with the specified period. Especially for the gear fault, the fault period is fixed when the rotating speed is constant. This process can be denoted as follows [50]: s ( n)
1 K
K 1
s(n kT ) k 0
(19)
s
where s(n) is the IAA signal. K denotes the number of periods being averaged. Generally, in the diagnosis of gearbox fault, K≥ 3 is chosen for the measurement of periodicity. In this paper, K = 5 is applied in all simulation and experiments. Due to the period fluctuation caused by the speed and operation variation, the comb filtering just provides a coarse filter operation. Therefore, a more reliable filter should be designed for the extraction of fault feature. To meet the requirements driven by the advancement of industrial engineering, large-scale and high-complex modern equipment, such as wind turbine, is being widely used. Numerous synchronous and asynchronous interference highly complicate the signal even with comb filtering. It has been mentioned that the existing DMs did not gain any benefit from the filtered signal. In view of this, IMCKDA is proposed to overcome the disadvantage by using convolution adjustment definition. Therefore, the fault feature can be further enhanced for the diagnosis. To verify the effectiveness of the proposed method, the real experiment of the gear fault is carried out in the following subsections. To further highlight the superiority of IMCKDA in process of IAA after comb filtering, other three existing state-of-the-art DMs, i.e., MED [30], MEDA [33] and MOMEDA [33], are used in the comparative study. Without loss of generality, all methods use the same number of iterations n=30 and the same selection strategy of filter length in Table III. In addition, the fault period is provided in MOMEDA.
20
Journal Pre-proof 5. Case study 5.1. Experimental setup In this subsection, three experimental cases are employed to further compare with the proposed IMCKDA and the traditional DMs. Fig. 4(a) illustrates the experimental bench which reflects the operation condition of the real wind turbine gearbox and Fig. 4(b) elaborates the schematic diagram of the experimental bench. The planetary gearbox is driven by an AC motor. By controlling the motor, different conditions with different speeds can be simulated. The magnetic break is used to model the wind loading for the fun. Two rotary encoders (Heidenhain ERN100) are mounted on the input and output shaft of the planetary gearbox, respectively. The resolution is 5000 pulses/ revolution. As shown in Fig. 5, the encoder signal is measured by an IK220 counter card with 5000 Hz sampling rate. The data acquisition system is integrated into the PC. Through data transformation and pretreatment, the measured signal can be analyzed using the proposed method in this paper. Additionally, the configuration with detailed parameters of the planetary gearbox is shown in Fig. 4(c). One can see that the motion of the planet gear is most complicated, since it couples the autorotation and revolution around the sun gear. The interference from the complex motion could undermine the fault feature. Furthermore, several main fault styles of the wind turbine gearbox, including root crack, corrosion fault and two worn teeth fault of the planet gear as shown in Fig. 6, are considered. Root crack and corrosion fault belong to the weak and early fault. Therefore, the fault feature is rather weak and easily buried by noise. The signal with two worn teeth fault contains more fault information and the distribution discipline of the impulses is more complex. It will make the methods based on periodicity puzzled easily. To highlight the superiority of IMCKDA, these challenging experimental cases are tested in this paper.
21
Journal Pre-proof (a)
(b)
Magnetic Break
Motor
Output Planetary Input Encoder Gearbox Encoder
Input encoder
Driving Motor
Output encoder Break
Planetary gearbox Wind fan
(c) Planet gear Zp = 31 Np = 3
Sun gear Zs = 20 Ring gear Zr = 82
Fig. 4. (a) Experimental bench, (b) its schematic diagram and (c) schematic view of the planetary gearbox.
22
Journal Pre-proof Encoder Heidenhain ERN100
Planetary gearbox
Heidenhain IK220
200 100
Data acquisition system
0 -100
0
20
40
60
80
position [tooth]
Signal Analysis
Fig. 5. The process of the data acquisition and analysis.
Fig. 6. Physical maps of different planetary gear faults. 5.2. Case 1: Root Crack The experimental case with root crack is firstly carried out. Raw encoder signal from the output encoder is presented in Fig. 7. By the operations of converting and comb filtering, the IAA signal is depicted in Fig. 8. Although the synchronous components are enhanced by comb filtering, the obvious periodic impulses are difficult to be detected. Compared with the simulation model, the signal from the industrial field is more complicated. Contrasting the results of MED and MEDA, it can be inferred that the two sharp peaks with red dotted line in Fig. 9(a) caused by the effect of the sensibility of MED for the filtered signal. Obviously, the fatal drawback makes MED completely lose the inspection ability for the 23
Journal Pre-proof fault. Overcoming the weakness of MED, the periodic impulses are highlighted in the filtered signal in Fig. 9(b). A fixed interval with 31 teeth indicates the fault of the planetary gear. Yet, the impulses with1
Amplitude [deg]
tooth fixed interval enhanced by MOMEDA in Fig. 9(c) which means MOMEDA fails to detect the fault.
4000 2000 0
0.5
1
1.5
2
2.5
3
Time [s]
104
2
Amplitude [rev/s ]
Fig. 7. Measured encoder signal with root crack fault.
1 0 -1 0
50
100
150
position [tooth]
2
Amplitude [rev/s ]
Fig. 8. IAA after comb filtering in the experiment case 1.
(a)
(b)
MED
5000 0
2
Amplitude [rev/s ]
-5000 0
50
100
150
position [tooth]
(c)
2000 0 -2000 -4000
MEDA
31 teeth 0
50
(d)
MOMEDA
0.02 0.01 0 -0.01 50
100
150
150
IMCKDA
31 teeth
4000 2000 0 -2000 0
100
position [tooth]
0
50
position [tooth]
100
150
position [tooth]
Fig. 9. Results of MED (a), MEDA(b), MOMEDA(c) and IMCKDA(d) in the experiment case 1.
24
0.32 0.31 0.3 0.29 0.28 20
CG Maximum point Mean value
30
Sample Number
Correlated Gini index
Journal Pre-proof 1000
2*Ts Ts
800 600 400 200 5
40
10
15
20
25
30
Iteration
Filter Length
(a)
(b)
Fig. 10. IMCKDA: (a) Selection of the filter length and (b) the change of iterative period in the experiment case 1. The filtered signal of IMCKDA is presented in Fig. 9(d). Similarly, the periodic impulses indicate the fault of the planetary gear. However, it obviously has a higher SNR compared with the filtered signal of MEDA. Fig. 10 displays the selection of the filter length and the change of iterated period in the filtering of IMCKDA. Using the selection strategy, L = 49 is chosen as the filter length as shown in Fig. 10(a). From Fig. 10(b), one can see the true fault period is identified from the 5th iteration, which verifies the advantage that IMCKDA can automatically adjust iterative period to close the true period. 5.3. Case 2: Corrosion Fault In this subsection, a corrosion fault is artificially rooted on the planetary gear by wire-electrode cutting. After converting and comb filtering, IAA signal is generated as displayed in Fig. 11. Obviously, the serried impulses with single tooth interval highlight the effect from the gear meshing. Due to the sensibility of MED for the filtered signal, the landscape of the filtered signals is dominated by two sharp peaks in Fig. 12(a). Even without the abnormal peaks, the impulses are barely visible from the filtered signals of MEDA and MOMEDA from Fig. 12(b) and (c). This may be attributed to the fact that the weak change caused by the corrosion fault in the IAA is difficult to be detected. By contrast, without any prior knowledge, IMCKDA can enhance the weak fault information from the 25
Journal Pre-proof result in Fig. 12(d). With the selected filter length L = 34, the true fault period is locked from the 4th iteration from Fig. 13. The clear impulses with 31 teeth interval manifest the feasibility and effectiveness of the proposed method in denoising of encoder signal. 2
Amplitude [rev/s ]
104 1 0 -1 -2
0
50
100
150
position [tooth] Fig. 11. IAA after comb filtering in the experiment case 2.
2
Amplitude [rev/s ]
2
Amplitude [rev/s ]
(a)
(b)
MED
5000
0
0
-2000
-5000 0
50
100
150
position [tooth]
(c) 0.06 0.04 0.02 0 -0.02 -0.04
MEDA
2000
0
100
IMCKDA
1000 0 -1000 -2000 -3000 0
50
100
150
position [tooth]
(d)
MOMEDA
50
150
31 teeth 0
position [tooth]
50
100
150
position [tooth]
0.24 0.22 CG Maximum point Mean value
0.2 0.18 20
40
Sample Number
Correlated Gini index
Fig. 12. Results of MED (a), MEDA(b), MOMEDA(c) and IMCKDA(d) in the experiment case 2.
60
600 400
2*Ts Ts
200 5
Filter Length
10
15
20
Iteration
(a)
(b) 26
25
30
Journal Pre-proof Fig. 13. IMCKDA: (a) Selection of the filter length and (b) the change of iterative period in the experiment case 2. 5.4. Case 3: Two Worn Teeth Fault It has been mentioned that two worn teeth fault on the planetary gear is rather challenging. Firstly, the distribution discipline of the impulses caused by fault is more intricate than the single fault. Secondly, the determination of the relative positions of two worn teeth fault is necessary for the diagnosis of gear fault. Despite this fact, this task which needs to accurately restore all fault impulses without any deviation is a
104
2
Amplitude [rev/s ]
challenge for all filtered methods.
2 0 -2 0
50
100
150
position [tooth]
(a)
0
50
100
position [tooth]
2
MOMEDA
0.02 0 -0.02
0
MEDA
5000 0 -5000 -10000
5000 0 -5000 -10000 -15000
(c) Amplitude [rev/s ]
(b)
MED
2
Amplitude [rev/s ]
Fig. 14. IAA after comb filtering in the experiment case 3.
50
100
150
0
(d) 3000 2000 1000 0 -1000 150 0
position [tooth]
50
1
100
150
teeth position [tooth] 13 31 teeth IMCKDA 31 teeth 1
2
2
50
3
3
4
100
4
5
5
150
position [tooth]
Fig. 15. Results of MED (a), MEDA(b), MOMEDA(c) and IMCKDA(d) in the experiment case 3. 27
0.3 0.25 CG Maximum point Mean value
0.2 0.15 20
40
60
Sample Number
Correlated Gini index
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80
800
2*Ts Ts
600 400 200 5
10
15
20
25
30
Iteration (b)
Filter Length (a)
Fig. 16. IMCKDA: (a) Selection of the filter length and (b) the change of iterative period in the experiment case 3. Fig. 14 shows the IAA signal after comb filtering. The distinct impulses depict the dominant function of the gear meshing in the encoder signal. Without the sharp peak in the filtered signal of MED from Fig. 15(a), it can be explained that the impulse components bury the effect from sensibility of MED for the filtered signal. Intuitively, MEDA and MOMEDA just further enhance the impulses caused by the gear meshing, from which one cannot find any fault information from Fig. 15(b) and (c). The result of IMCKDA is displayed in Fig. 15(d). The impulses are clearly extracted. To present a better visual display, different marks are added on the figure of the filtered signal. It can be observed that the interval of the impulses with same color and adjacent numbers is 31 teeth which indicates two faults on the planetary gear. The interval of the impulses with same number and different colors is 13 teeth which indicates the relative position of the two faults. From Fig. 16(a), it is clear that L = 50 should be chosen as the filter length. From the change of iterative period in Fig. 16(b), IMCKDA also locks a specified sampling number which is exactly the number of sampling points during the planetary gear period Ts. With the same iterated period, the impulses caused by different faults are enhanced simultaneously. This can be explained by the envelope spectrum analysis in Fig. 17. Note that the characteristic frequency of planetary gear fault and its harmonics are the main components. Essentially, 28
Journal Pre-proof the different planetary gear faults have the same fault period which meets the requirements of IMCKDA
2
Amplitude [rev/s ]
to deconvolute the impulses with same feature.
2fs/Ts
300
fs/Ts 3fs/Ts
200 100 0
0
50
100
150
200
Frequency [Hz] Fig. 17. The envelope spectrum of the filtered signal of IMCKDA in the experiment case 3.
6. Conclusion Due to the harsh operation environment, gearboxes as the key part of the wind turbine are prone to damage. However, the difficulty from both the measurement and analysis is undermining the superiorities and usefulness of these existing methods based on the vibration and acoustic emission. In contrast, encoder signal carries rich diagnostic information which may be considered as an alternative tool for the wind turbine condition monitoring. To the denoising of encoder signal for the wind turbine gear fault diagnosis, a novel adaptive filtering method, IMCKDA, is initially introduced in this paper. By the convolution adjustment definition, the drawbacks of the sensibility to the filtered signal and the discontinuity point, are overcome. Moreover, CG is originally proposed to guide the selection of the filter length. Combined with the selection strategy, the appropriate candidate is easy to be screened from a definite range which makes the proposed method converge to a satisfactory result. Benefiting from these superiorities, IMCKDA becomes the alternative tool for denoising of encoder signal. The feasibility and effectiveness of IMCKDA are verified by the experimental cases with the existing state-of-the-art DMs, containing MED, MEDA and MOMEDA used in the comparative study. In addition, this study can be considered as the first investigative step since it concerns a single 29
Journal Pre-proof application of the method to specific type of gear failure modes and to unique specimen and therefore its effectiveness has to be proved with further investigations.
Acknowledgment This work is supported by the National Natural Science Foundation of China (No. 51421004, 91860205 and 51905017) and the Defense Industrial Technology Development Program (Grant No. JCKY2018601C013), which are highly appreciated by the authors.
Appendix A. Brief review of Deconvolution methods By using kurtosis in (A.1) as the objective function, MED [30] can enhance the impulse components caused by fault. Kurtosis is verified to be a measured index for the impulsiveness of the signal. As a result, MED is considerably susceptible to the random impulse noise. The reason for the result may attribute to that kurtosis just highlights the impulsiveness of the signal, but ignores the periodicity. Motivated by this, McDonald et al. [31] incorporated the period into the definition of kurtosis and proposed CK as shown in (A.2). By maximizing CK of filtered signal, MCKD is generated. To resolve the problem of MCKD which depends on the prior period, multipoint kurtosis in (A.4) is proposed by adding a constant vector t to the definition of kurtosis. And then, MOMED is proposed [33].
Kurtosis
1 N 1 N
N
y
4
y
n 1 N
y y
n 1
2
(A.1)
2
where y and N are the mean and length of signal y, respectively.
CK M (Ts )
N
M
n 1
m0 N
( ynmTs )2
(A.2)
( y ) n 1
2 M 1 n
30
Journal Pre-proof where M is the order of shift. Ts is the sampling number that can be denoted:
Ts f s T
(A.3)
where fs is the sampling frequency and T is the period.
Multiponit kurosis t
1 N 1 N
N
y n 1 N
y n 1
4
y
2
y
(A.4)
2
where t is a constant vector, which is used to define the locations and weightings of the goal impulses to be deconvolved.
References
[1] Z. Li, Y. Jiang, Q. Guo, C. Hu, Z. Peng, Multi-dimensional variational mode decomposition for bearing-crack detection in wind turbines with large driving-speed variations, Renewable Energy, 116 (2018) 55-73. [2] T.E.W.E.A. (EWEA), https://windeurope.org/, 2015. [3] Y. Feng, Y. Qiu, C.J. Crabtree, H. Long, P.J. Tavner, Monitoring wind turbine gearboxes, Wind Energy, 16 (2013) 728-740. [4] S.T. Kandukuri, A. Klausen, H.R. Karimi, K.G. Robbersmyr, A review of diagnostics and prognostics of low-speed machinery towards wind turbine farm-level health management, Renewable and Sustainable Energy Reviews, 53 (2016) 697-708. [5] F.P. García Márquez, A.M. Tobias, J.M. Pinar Pérez, M. Papaelias, Condition monitoring of wind turbines: Techniques and methods, Renewable Energy, 46 (2012) 169-178. [6] G. He, K. Ding, W. Li, X. Jiao, A novel order tracking method for wind turbine planetary gearbox vibration analysis based on discrete spectrum correction technique, Renewable Energy, 87 (2016) 364-375. [7] J. Chen, J. Pan, Z. Li, Y. Zi, X. Chen, Generator bearing fault diagnosis for wind turbine via empirical wavelet transform using measured vibration signals, Renewable Energy, 89 (2016) 80-92. [8] J. Chen, J. Pan, C. Zhang, X. Luo, Z. Zhou, B. Wang, Specialization improved nonlocal means to detect periodic impulse feature for generator bearing fault identification, Renewable Energy, 103 (2017) 448-467. [9] Y. Kong, T. Wang, F. Chu, Meshing frequency modulation assisted empirical wavelet transform for fault diagnosis of wind turbine planetary ring gear, Renewable Energy, 132 (2019) 1373-1388. [10] W. Teng, X. Ding, H. Cheng, C. Han, Y. Liu, H. Mu, Compound faults diagnosis and analysis for a wind turbine gearbox via a novel vibration model and empirical wavelet transform, Renewable Energy, 136 (2019) 393-402. [11] S. Shanbr, F. Elasha, M. Elforjani, J. Teixeira, Detection of natural crack in wind turbine gearbox, Renewable Energy, 118 (2018) 172-179. [12] J. Tang, S. Soua, C. Mares, T.-H. Gan, An experimental study of acoustic emission methodology for in service condition monitoring of wind turbine blades, Renewable Energy, 99 (2016) 170-179. 31
Journal Pre-proof [13] Y. Zhang, W. Lu, F. Chu, Planet gear fault localization for wind turbine gearbox using acoustic emission signals, Renewable Energy, 109 (2017) 449-460. [14] P. Guo, D. Infield, X. Yang, Wind Turbine Generator Condition-Monitoring Using Temperature Trend Analysis, IEEE Transactions on Sustainable Energy, 3 (2012) 124-133. [15] M. Elforjani, E. Bechhoefer, Analysis of extremely modulated faulty wind turbine data using spectral kurtosis and signal intensity estimator, Renewable Energy, 127 (2018) 258-268. [16] M. Zhao, J. Lin, Health Assessment of Rotating Machinery Using a Rotary Encoder, IEEE Transactions on Industrial Electronics, 65 (2018) 2548-2556. [17] B. Li, X. Zhang, J. Wu, New procedure for gear fault detection and diagnosis using instantaneous angular speed, Mechanical Systems and Signal Processing, 85 (2017) 415-428. [18] W. Qiao, D. Lu, A Survey on Wind Turbine Condition Monitoring and Fault Diagnosis—Part I: Components and Subsystems, IEEE Transactions on Industrial Electronics, 62 (2015) 6536-6545. [19] Z. Liu, L. Zhang, A review of failure modes, condition monitoring and fault diagnosis methods for large-scale wind turbine bearings, Measurement, (2019) 107002. [20] J. Jiao, M. Zhao, J. Lin, J. Zhao, A multivariate encoder information based convolutional neural network for intelligent fault diagnosis of planetary gearboxes, Knowledge-Based Systems, 160 (2018) 237-250. [21] W. Moustafa, O. Cousinard, F. Bolaers, K. Sghir, J. Dron, Low speed bearings fault detection and size estimation using instantaneous angular speed, Journal of Vibration and Control, 22 (2016) 3413-3425. [22] F. Gu, I. Yesilyurt, Y. Li, G. Harris, A. Ball, An investigation of the effects of measurement noise in the use of instantaneous angular speed for machine diagnosis, Mechanical Systems and Signal Processing, 20 (2006) 1444-1460. [23] L. Renaudin, F. Bonnardot, O. Musy, J.B. Doray, D. Rémond, Natural roller bearing fault detection by angular measurement of true instantaneous angular speed, Mechanical Systems and Signal Processing, 24 (2010) 1998-2011. [24] M. Zhao, J. Jiao, J. Lin, A Data-Driven Monitoring Scheme for Rotating Machinery Via Self-Comparison Approach, IEEE Transactions on Industrial Informatics, 15 (2019) 2435-2445. [25] T.R. Lin, A.C. Tan, L. Ma, J. Mathew, Condition monitoring and fault diagnosis of diesel engines using instantaneous angular speed analysis, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229 (2015) 304-315. [26] S.K. Roy, A.R. Mohanty, C.S. Kumar, Fault detection in a multistage gearbox by time synchronous averaging of the instantaneous angular speed, Journal of Vibration and Control, 22 (2016) 468-480. [27] B. Li, X. Zhang, A new strategy of instantaneous angular speed extraction and its application to multistage gearbox fault diagnosis, Journal of Sound and Vibration, 396 (2017) 340-355. [28] Y. Zhou, T. Tao, X. Mei, G. Jiang, N. Sun, Feed-axis gearbox condition monitoring using built-in position sensors and EEMD method, Robotics and Computer-Integrated Manufacturing, 27 (2011) 785-793. [29] R.B. Randall, J. Antoni, Rolling element bearing diagnostics—A tutorial, Mechanical Systems and Signal Processing, 25 (2011) 485-520. [30] H. Endo, R.B. Randall, Enhancement of autoregressive model based gear tooth fault detection technique by the use of minimum entropy deconvolution filter, Mechanical Systems and Signal Processing, 21 (2007) 906-919. [31] G.L. McDonald, Q. Zhao, M.J. Zuo, Maximum correlated Kurtosis deconvolution and application on gear tooth chip fault detection, Mechanical Systems and Signal Processing, 33 (2012) 237-255. [32] Y. Miao, M. Zhao, J. Lin, X. Xu, Sparse maximum harmonics-to-noise-ratio deconvolution for weak fault signature detection in bearings, Measurement Science and Technology, 27 (2016) 105004. [33] G.L. McDonald, Q. Zhao, Multipoint Optimal Minimum Entropy Deconvolution and Convolution Fix: Application to vibration fault detection, Mechanical Systems and Signal Processing, 82 (2017) 461-477. [34] Y. Miao, M. Zhao, J. Lin, Y. Lei, Application of an improved maximum correlated kurtosis deconvolution method for fault diagnosis of rolling element bearings, Mechanical Systems and Signal Processing, 92 (2017) 173-195. [35] J. Chen, Z. Li, J. Pan, G. Chen, Y. Zi, J. Yuan, B. Chen, Z. He, Wavelet transform based on inner product in fault 32
Journal Pre-proof diagnosis of rotating machinery: A review, Mechanical Systems and Signal Processing, 70-71 (2016) 1-35. [36] J. Zarei, M.A. Tajeddini, H.R. Karimi, Vibration analysis for bearing fault detection and classification using an intelligent filter, Mechatronics, 24 (2014) 151-157. [37] Y. Miao, M. Zhao, J. Lin, Identification of mechanical compound-fault based on the improved parameter-adaptive variational mode decomposition, ISA Transactions, 84 (2019) 82-95. [38] J. Antoni, Fast computation of the kurtogram for the detection of transient faults, Mechanical Systems and Signal Processing, 21 (2007) 108-124. [39] Y. Lei, J. Lin, Z. He, Y. Zi, Application of an improved kurtogram method for fault diagnosis of rolling element bearings, Mechanical Systems and Signal Processing, 25 (2011) 1738-1749. [40] J. Antoni, The infogram: Entropic evidence of the signature of repetitive transients, Mechanical Systems and Signal Processing, 74 (2016) 73-94. [41] A. Moshrefzadeh, A. Fasana, The Autogram: An effective approach for selecting the optimal demodulation band in rolling element bearings diagnosis, Mechanical Systems and Signal Processing, 105 (2018) 294-318. [42] C. Gini, Measurement of inequality of incomes, The Economic Journal, 31 (1921) 124-126. [43] D. Zonoobi, A.A. Kassim, Y.V. Venkatesh, Gini Index as Sparsity Measure for Signal Reconstruction from Compressive Samples, IEEE Journal of Selected Topics in Signal Processing, 5 (2011) 927-932. [44] Y. Miao, M. Zhao, J. Lin, Improvement of kurtosis-guided-grams via Gini index for bearing fault feature identification, Measurement Science and Technology, 28 (2017) 125001. [45] C.A. Loza, J.C. Principe, Transient model of EEG using Gini Index-based matching pursuit,
2016 IEEE International
Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016, pp. 724-728. [46] M. Buzzoni, J. Antoni, G. D'Elia, Blind deconvolution based on cyclostationarity maximization and its application to fault identification, Journal of Sound and Vibration, 432 (2018) 569-601. [47] S.T. Kandukuri, J.S.L. Senanayaka, V.K. Huynh, H.R. Karimi, K.G. Robbersmyr, Current signature based fault diagnosis of field-oriented and direct torque–controlled induction motor drives, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 231 (2017) 849-866. [48] Y. Wang, Z. He, Y. Zi, Enhancement of signal denoising and multiple fault signatures detecting in rotating machinery using dual-tree complex wavelet transform, Mechanical Systems and Signal Processing, 24 (2010) 119-137. [49] M. Zhao, X. Jia, J. Lin, Y. Lei, J. Lee, Instantaneous speed jitter detection via encoder signal and its application for the diagnosis of planetary gearbox, Mechanical Systems and Signal Processing, 98 (2018) 16-31. [50] S. Braun, The synchronous (time domain) average revisited, Mechanical Systems and Signal Processing, 25 (2011) 1087-1102.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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Highlights 1. The built-in encoder signal as a new alternative tool is firstly used for gearbox fault detection in wind turbines. 2. An improved MCKDA is proposed to denoise the encoder signal without any prior knowledge and the least input parameters. 3. Compared with the traditional DMs, the proposed IMCKDA is more suitable for fault diagnosis based on the encoder signal. 4. The proposed method can expand the application to the vibration, sound and current etc. other data styles.
1