A gearbox fault diagnosis scheme based on near-field acoustic holography and spatial distribution features of sound field

Journal of Sound and Vibration 332 (2013) 2593–2610

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A gearbox fault diagnosis scheme based on near-field acoustic holography and spatial distribution features of sound field Wenbo Lu, Weikang Jiang n, Guoqing Yuan, Li Yan State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China

a r t i c l e i n f o

abstract

Article history: Received 1 May 2012 Received in revised form 2 December 2012 Accepted 4 December 2012 Handling Editor: K. Shin Available online 4 February 2013

Vibration signal analysis is the main technique in machine condition monitoring or fault diagnosis, whereas in some cases vibration-based diagnosis is restrained because of its contact measurement. Acoustic-based diagnosis (ABD) with non-contact measurement has received little attention, although sound field may contain abundant information related to fault pattern. A new scheme of ABD for gearbox based on near-field acoustic holography (NAH) and spatial distribution features of sound field is presented in this paper. It focuses on applying distribution information of sound field to gearbox fault diagnosis. A two-stage industrial helical gearbox is experimentally studied in a semianechoic chamber and a lab workshop, respectively. Firstly, multi-class faults (mild pitting, moderate pitting, severe pitting and tooth breakage) are simulated, respectively. Secondly, sound fields and corresponding acoustic images in different gearbox running conditions are obtained by fast Fourier transform (FFT) based NAH. Thirdly, by introducing texture analysis to fault diagnosis, spatial distribution features are extracted from acoustic images for capturing fault patterns underlying the sound field. Finally, the features are fed into multi-class support vector machine for fault pattern identification. The feasibility and effectiveness of our proposed scheme is demonstrated on the good experimental results and the comparison with traditional ABD method. Even with strong noise interference, spatial distribution features of sound field can reliably reveal the fault patterns of gearbox, and thus the satisfactory accuracy can be obtained. The combination of histogram features and gray level gradient co-occurrence matrix features is suggested for good diagnosis accuracy and low time cost. & 2013 Elsevier Ltd. All rights reserved.

1. Introduction Gearbox is one of the essential equipments in industrial machinery, and gearbox failure may lead to downtime loss even during some disastrous catastrophes. Fault diagnosis for gearbox is gaining in importance to prevent machine operating failure and even human casualties. Condition monitoring or fault diagnosis based on vibration signals has been well developed for some decades, and vibration signal analysis has been proven to be an effective approach for detecting gearbox faults. Over the past few years, many techniques including Fourier transform (FT), Hilbert–Huang transform, wavelet analysis and time–frequency distributions were employed to process vibration signals [1–6]. For gearbox fault diagnosis, many studies have been done based on vibration signal processing [1,4,7–9], including some common methodologies such as envelope spectrum, empirical mode decomposition, wavelet transform. However, generally vibration signals is acquired in a contact measurement way, so that vibration-based fault diagnosis was restrained in

n

Corresponding author. Tel./fax: þ86 21 34206332 820. E-mail address: [email protected] (W. Jiang).

0022-460X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jsv.2012.12.018

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some cases, especially for the testing components with irregular configuration surfaces or in the abominable testing environments like high-temperature, high-humidity or corrosion. By contrast, acoustic-based diagnosis (ABD) of machine has received little attention mainly due to noise contamination, although acoustic signals could be processed like vibration signals [10–13], and sound field around the machine may contain abundant fault-related information. Little literature is available on the application of audio frequency acoustic signals to gearbox fault diagnosis. By using the wavelet transform and Wigner–Ville distribution, Baydar and Ball [10,11] found that acoustic signals were very effective along vibration signals to detect various types of gear faults, such as tooth breakage, gear crack and localized wear, and could provide a powerful tool to indicate progressing faults in gearbox. The main advantage of ABD is that acoustic signal can be measured in a non-contact way while the machine is in operating condition, so that ABD is very useful in some inconvenient conditions. However, it was a difficult task to select proper measurement positions especially in the cases without enough prior knowledge. The selection of measurement positions was studied aiming at improving the traditional ABD technique [11], and no constructive suggestion had been given. Besides, in the traditional ABD technique only partial acoustic information was utilized due to single microphone measurement, so that the machine could be only locally diagnosed. These disadvantages can be overcome by employing the whole sound field information based on multi-channel synchronous measurement and processing. Gearbox conditions determine the transmission characteristics of vibration energy in its components, as well as that of acoustic energy, which directly result in the corresponding distribution of sound field. So, while a fault occurring in gearbox the spatial distribution information of sound field around the gearbox may contain some sensitive features highly related to fault pattern, and thus is probably applied to fault diagnosis. How to obtain the spatial distribution information of sound field is a key point to extract fault-related features from multi-channel acoustic signals. So far, however, there is little literature referring to this issue. Considering the good capability of sound field reconstruction, Lu et al. [14] applied near-field acoustic holography (NAH) technique to capturing spatial information of sound field for bearing fault diagnosis and obtained good results. NAH is one of hot techniques of visualizing sound field based on multi-channel synchronous measurement and processing, since it can reconstruct sound field at any observed surface [15–17] (that is to say, the whole sound field information). It was frequently used for source recognition and rarely applied to fault diagnosis. Recently, the feasibility and effectiveness of applying the NAH technique to machine fault diagnosis has been demonstrated on the experimental research [14]. Since the different running conditions of gearbox can result in corresponding distribution patterns of sound field, and different characteristic frequencies of gearbox have corresponding acoustic images (2-dimensional representation of sound field), it is possible that some fault-related features from these acoustic images can be extracted and applied to gearbox fault diagnosis. By FFT-based NAH technique, this research tries to utilize the spatial distribution characteristics of sound field for gearbox fault diagnosis. Texture analysis is a widely used technique for analyzing and classifying all types of images [18,19]. In order to obtain the spatial distribution characteristics of sound field, this research tries to extract textural features from acoustic images for classifying the different acoustic images depicting the corresponding gearbox condition patterns. Histogram of the intensity of images has been used extensively for recognition or retrieval of images [20–23], since histogram features are computationally efficient and robust to noise and small changes in images. However, histogram is only a global characterization of an image, and not adequate to effectively reflect the local changes of spatial relationship. The different texture features can be imaged well in the relative emplacement of pixels of different intensities. Due to the descriptive and easily computable nature, co-occurrence features describing differences in the spatial relationships of neighboring pixels have been widely used for classifying images, and co-occurrence matrix (CM) is an effective tool to describe co-occurrence features [24–27]. Here, gray level co-occurrence matrix (GLCM) and gray level gradient co-occurrence matrix (GLGCM) are investigated to extract spatial distribution features of sound field, respectively. For intelligent fault diagnosis, a pattern classifier with good discrimination and generalization capabilities is very important. Support vector machine (SVM) is a well-developed machine learning algorithm in the field of artificial intelligence for its high accuracy and favorable generalization capabilities [28–30]. In SVM, the structural risk minimization principle proposed by statistical learning theory is used to minimize an upper bound on the expected risk. In many practical applications of condition monitoring or fault diagnosis [31–34], the classification performance of SVM outperforms many traditional pattern recognition methods such as neural network. This research focuses on applying spatial distribution information of sound field to gearbox fault diagnosis and further validating a novel ABD scheme based on NAH technique. In this investigation, a two-stage industrial helical gearbox is experimentally studied in a semi-anechoic chamber and a lab workshop with complex background noise, respectively. The proposed fault diagnosis scheme is implemented according to the following procedure. Firstly, by multi-channel microphone array measurement, sound fields in different gearbox running conditions are reconstructed based on FFT-based NAH. Then, spatial distribution features are extracted from the corresponding acoustic images by texture analysis. Finally, Multi-SVM based pattern classification is conducted to identify various gearbox faults.

2. Sound field reconstruction by FFT-based NAH NAH is one of hot techniques of visualizing sound field, since it can reconstruct sound field on any observed surface based on sound pressure measurement near the source plane. All acoustic variables, such as sound pressure, particle

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Hologram (Measurement plane) y

(x, y, zc)

(x, y, zc) x

z Ss Sc

Sh

Sc

Source plane Backward reconstruction

Forward reconstruction

Fig. 1. Propagation of sound field.

velocity, sound intensity, etc., can be reconstructed by the sound pressure on the holographic measurement plane [16]. The propagation of sound field is illustrated in Fig. 1. FFT-based NAH is a simple frequency-domain method and can be easily implemented as follows. The holographic measurement plane Sh is chosen at z¼ zh, the reconstruction plane Sc at z¼zc, and the source plane Ss at z ¼zs. The sound pressures at the plane Sh and Sc are denoted as j(x, y, zh, f) and j(x, y, zc, f), respectively, where f is the reconstruction frequency. Given Green’s function GD(x, y, zh  zc, f) satisfying the Dirichlet boundary conditions, the generalized reconstruction equation can be expressed as [15,16]: h   1  i (1) jðx,y,zc ,f Þ ¼ F 1 j~ kx ,ky ,zh ,f G~ D kx ,ky ,zh zc ,f , 











(2)

j~ kx ,ky ,zc ,f ¼ F½jðx,y,zc ,f Þ,

(3)

  G~ D kx ,ky ,zh zc ,f ¼ F½GD ðx,y,zh zc ,f Þ,

(4)

j~ kx ,ky ,zh ,f ¼ F jðx,y,zh ,f Þ ,

where F denotes the 2-dimensional FFT, and the superscript  1 denotes the inverse transform. kx and ky are the spatial wavenumbers along the x and y directions, respectively. The 2-dimensional spatial Fourier transform of GD satisfying the homogeneous Dirichlet boundary conditions can be found analytically:  8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 2 > > kx þky r k , > exp jðzh zc Þ k kx ky , <   ~   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (5) G D kx ,ky ,zh zc ,f ¼ > 2 2 2 2 2 2 > > kx þky 4 k : : exp ðzh zc Þ kx þ ky k ,

3. Spatial distribution feature extraction by texture analysis Feature extraction plays a crucial role in fault diagnosis. Different types of fault in gearbox can generate different vibration characteristics, consequentially, which can result in corresponding distributions of the whole sound field. The spatial distribution characteristics of sound field can be imaged well in the texture information of acoustic images. Here, the spatial distribution features are extracted by texture analysis technique. Several typical texture feature extraction methods are investigated for capturing the spatial distribution information underlying the sound field.

3.1. Histogram features Histogram is a simple and effective tool to extract texture features of an image. It represents the occurrence probabilities of gray levels and depicts the entire distribution of gray levels. Given a gray image A(x, y) with gray level ri, i¼ 1,2,y,L, where L is the quantized gray level, the histogram can be defined as Hðr i Þ ¼ ni =N,

(6)

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where ni is the number of pixel with gray level ri, and N is the total number of pixels. A histogram provides a global description of image characteristics. Here, 6 statistical features are extracted from the histogram and combined into one feature vector expressed as Hist: (1) mean

mm ¼

L X

iHðr i Þ,

(7)

i¼1

(2) variance

mv ¼

L  X

r i  mm

2

Hðr i Þ,

(8)

i¼1

(3) skewness

ms ¼

L  2 1 X r i  mm Hðr i Þ, 3=2

mv

(9)

i¼1

(4) kurtosis

mk ¼

L  4 1 X r i  mm Hðr i Þ3,

m2v i ¼ 1

(10)

(5) energy

me ¼

L X

Hðr i Þ2 ,

(11)

i¼1

(6) entropy

mn ¼ 

L X

Hðr i Þlog2 ½Hðr i Þ:

(12)

i¼1

3.2. GLCM features GLCM represents the conditional joint probabilities of all pair combinations of gray levels in the spatial window of interest with respect to two parameters: inter-pixel distance d and direction y. Given a gray image A(x, y) of size Nx pixels by Ny pixels, the spatial relationship of the pixel pair (i, j) with specified pair (d, y) is illustrated in Fig. 2(a). The joint probabilities measurement can be expressed as: P(i, j, d, y)¼{C(i, j)9(d, y)}, where C(i, j), the co-occurrence probabilities between gray level i and j, can be given by C ði,jÞ ¼ P ði,jÞ=

L X L X

P ði,jÞ,

(13)

i¼1j¼1

where L is the quantized gray level, and P(i, j) represents the number of co-occurrences of gray level i and j, as shown in Fig. 2(b) ( Pði,jÞ ¼ Cf½ððx1 ,y1 Þ,ðx2 ,y2 ÞÞ 2 ðLx  Ly Þ  ðLx  Ly Þ9f ðx1 ,y1 Þ ¼ i, f ðx2 ,y2 Þ ¼ jg, (14) x2 ¼ x1 þ Dx ¼ x1 þ dcos y, y2 ¼ y1 þ Dy ¼ y1 þ dsin y, i,j ¼ 1,2,:::,L, where G denotes the number of the pixel pairs (i, j) satisfying the conditions, and (x1, y1) is the coordinate with gray level i, (x2, y2) the coordinate with gray level j, Lx the horizontal spatial domain (1,2,y,Nx), Ly the vertical spatial domain (1,2,y,Ny). Before calculating GLCM, the reconstructed sound pressure level matrix p(x, y) is normalized to a gray level matrix F(x, y) by the quantized level L   pðx,yÞpmin ðL1Þ þ 1, Fðx,yÞ ¼ int (15) pmax pmin where int is the round operator, and pmax, pmin are the maximum and minimum value in p(x, y), respectively.

W. Lu et al. / Journal of Sound and Vibration 332 (2013) 2593–2610

1

…

2

…

Lx

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x

Nx

1 2

•

…

d

j Δy

Ly

θ

…

i•

Δx

Ny

y

1

…

2

L

1 2 …

L

Fig. 2. GLCM calculation: (a) spatial relationship of the pixel pair (i, j) and (b) GLCM with the quantized level L.

Four GLCMs with y ¼{01, 451, 901, 1351} and d ¼1 are usually used to extract second-order statistical features. Here, 12 statistical features suggested by Haralick et al. [24] are calculated from each GLCM. These features are angular second moment, contrast, correlation, entropy, variance, inverse difference moment, sum average, sum variance, sum entropy, difference average, difference variance and difference entropy, which are combined into one feature vector expressed as GLCM. To eliminate the effect from different directions and reduce the dimension of feature vector, GLCM features from four directions are averaged here.

3.3. GLGCM features Except for gray level, the change of neighbor gray levels (namely the gradient of gray level) can depict effectively the texture characteristics as well. GLGCM characterizes typically the spatial relationships of two basic elements of an image: gray and gradient. Given a gray image A(x, y), the gradient image g(x, y) can be defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @A @A gðx,yÞ ¼ : þ @x @y

(16)

By using Sobel operator, which is extensively used for edge detection in image processing, g(x, y) can be approximated as gðx,yÞ  2

3

1

0

1

6 Sx ¼ 4 2 1

0 0

7 2 5nAðx,yÞ, 1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sx 2 þ Sy 2 , 2

1

6 Sy ¼ 4 0 1

(17)

2 0 2

1

3

7 0 5nAðx,yÞ, 1

(18)

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where * denotes the convolution operation. The normalized gradient image G(x, y) can be obtained by the quantized gradient level L:   gðx,yÞg min ðL1Þ þ 1, (19) Gðx,yÞ ¼ int g max g min where gmax is the maximum value in g(x, y), and gmin is the minimum value in g(x, y). Similar to GLCM, the element P0 (i, j) of GLGCM (namely the number of co-occurrences of gray level i and gradient level j) can be obtained statistically:

           P 0 ði,jÞ ¼ C ½ x1 ,y1 , x2 ,y2 Þ 2 Lx  Ly  Lx  Ly F x1 ,y1 ¼ i, G x2 ,y2 ¼ j (20) where i, j ¼1,2,y,L, and (x1, y1) is the coordinate with gray level i, (x2, y2) the coordinate with gradient level j, and G, Lx, Ly, F(x, y) are the same as ones defined in Section 3.2. The co-occurrence probabilities between gray level i and gradient level j can be given by C 0 ði,jÞ ¼ P0 ði,jÞ=

L X L X

P0 ði,jÞ:

(21)

i¼1j¼1

Then 15 statistical features [27] from the GLGCM are calculated: small gradient advantage, large gradient advantage, gray distribution homogeneity, gradient distribution homogeneity, energy, gray average, gradient average, gray standard deviation, gradient standard deviation, correlation, gray entropy, gradient entropy, hybrid entropy, difference moment and inverse difference moment, which are combined into one feature vector expressed as GLGCM. 4. Pattern classification by multi-SVM Fault diagnosis is essentially a kind of pattern recognition or classification. SVM has gained great acceptance in fault diagnosis of machinery [35–38], due to its capability of providing high classification accuracy over small training sets and nice generalization. In this research SVM as a pattern classifier is employed to recognize various types of gearbox fault. SVM was proposed initially for 2-classification, whereas the multi-class problems are usually encountered in fault diagnosis. Here multi-SVM is employed by applying one-against-one strategy [39]. For k-class pattern classification, this strategy constructs k(k  1)/2 SVMs where each one is trained on data from two classes. For training data xt from ith and the jth classes, each 2-classification problem is solved as follows: 8  T ij ij > wij Fðxt Þ þ b Z 1xt , if yt ¼ i, > > < X T  ij T 1 ij T ij ij ij (22) ðw Þ w þC xijt ðwij Þ , s:t: min w Fðxt Þ þ b r 1þ xt , if yt ¼ j, ij > 2 wij ,b , xij > t > : xij Z0, i ¼ 1,. . .,k, j ¼ 1,. . .,k, t ¼ 1,. . .,kðk1Þ=2, t where xt are mapped to linearly separable space with a higher dimension from original input pattern space by a kernel ij function F, and wij defines the boundary between two different classes. yt is the output class of xt, xt a slack factor, bij a scalar threshold, C a penalty parameter, which controls the trade-off between margin maximization and error minimization [40]. To illustrate the classification principle, a 2D example shown in Fig. 3 is used without any loss of generality. In this figure, SVM attempts to place a line (the solid line: H) between the two different classes (circles represent ith class, and squares represent jth class) and orientates it in such a way that the margin of the two boundaries (the dotted line: Hi and Hj) is maximized. The data locating at the boundaries is called support vector (SV). After all k(k 1)/2 SVMs are constructed, the ‘‘Max Wins’’ voting strategy is used as following. If x is judged as in the ith ij class based on the decision function sgnððwij ÞT FðxÞ þ b Þ where sgn is the sign function, the vote for the ith class is added by one. Otherwise, the jth is increased by one. Then x is predicted in the class with the largest vote. 5. Gearbox fault diagnosis This study focuses on applying the spatial distribution information of sound field to diagnosing gearbox faults based on the FFT-based NAH. The proposed diagnosis scheme is implemented according to the following procedure as shown in Fig. 4. 1) To sample synchronously acoustic signals at the measurement plane Sh in different running conditions of gearbox by a microphone array, respectively. 2) To reconstruct sound fields at the reconstruction plane Sc close to the sound source plane Ss by the FFT-based NAH and acquire acoustic images at the chosen characteristic frequencies. 3) To extract spatial distribution features from the acoustic images by texture analysis. 4) To train classifiers and diagnose gearbox by multi-SVM.

W. Lu et al. / Journal of Sound and Vibration 332 (2013) 2593–2610

xj

ij

Φ (xj)

Φ (□) Φ (□)

Φ (●)

2599

Φ (□)

Φ (□) Φ (■)

H

xi

.Φ

=

.Φ

1

ij

)+ (x t

b

=

)+ (x t

0

ij

b

=

-1

Φ (○) Φ (○) Φ (●) Φ (○) Φ (○) Φ (○) w

Φ (■)

n rgi ma

Hi

ij

w

)+ (x t

ij

Φ (□) Φ (□)

ij

w

.Φ

b

SV

Hj

Φ (○) Φ (xi)

Fig. 3. An illustration for SVM classification principle.

FFT-based NAH algorithm Microphone array

Acoustic signals Acoustic images

Texture analysis

Training and recognition

…

Gearbox

Diagnosis result

Multi-SVM classifiers

Spatial distribution features

Fig. 4. Gearbox fault diagnosis flow.

5.1. Experimental rig and acoustic signal acquisition A two-stage industrial helical reduction gearbox with different local faults is experimentally studied in a semi-anechoic chamber. The experimental rig, as shown in Fig. 5, consists of an alternating motor, a gearbox, a magnetic powder brake, a tension controller, microphones and a data record system. The gearbox and the motor, joined together with a flexible coupling, are fixed firmly on the rig. The tension controller adjusts magnetizing current and keeps it at a constant value, by which the magnetic powder brake provides the gearbox with a constant load in the whole experimental process. The structure and parameters of the gearbox are shown in Fig. 6. When the motor runs at its rated speed 1500 rpm, the running frequencies of three rotating shafts (f1, f2, f3) and two mesh pairs (f12, f34) are shown in Table 1. The linear microphone array with 17 elements can be moved on the overall hologram plane step by step, and the number of scanning steps is 23. Each scanning step distance is 0.05 m. The distance between adjoining microphones in the linear array is 0.05 m. The distance from the holography plane Sh to the source plane Ss is zh  zs ¼0.05 m. The reconstruction plane Sc is chosen at Ss. The signals from scanning measurement are not temporal synchronous, so the reference microphones are mounted near the gearbox to reserve the phase information. To get gearbox local fault conditions, a mild pitting, a moderate pitting, a severe pitting and a tooth breakage fault are made artificially, respectively, as shown in Fig. 7. All of faults are made on the gear Z3. In this way, five running conditions of gearbox are simulated. In order to keep coherent dynamic conditions and get relatively pure fault-related signals, some points while measuring are considered. Firstly, the gearbox cover and the gaskets are pre-processed, so that the gearbox can be easily disassembled and reassembled, and thus the installation errors can be minimized. Secondly, the gears and their shafts are firmly fixed in the gearbox all the time and the faults are directly machined on the gear by a hand electro drill for avoiding installation tolerances of the gear shafts and bearings. Thirdly, after producing the gear faults the gearbox cover is assembled carefully and the mounting bolts are installed in a sequence. Moreover, for all of the mounting bolts the tightening torque values keep the same by using a torque-indicating wrench. ¨ A 32 channel data record system Muller-BBM PAK is used for synchronously sampling acoustic signals from the microphone array and references. All signals are sampled at 4096 Hz. In this way, 12 samples are collected for each condition.

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Tension controller Microphone array Magnetic powder brake Reference 5 Reference 3 Reference 2 Loudspeaker

Motor Reference 4

Record system

Gearbox Reference 1 Fig. 5. Experimental rig of gearbox fault diagnosis in semi-anechoic room.

5.2. Acoustic image acquisition and feature extraction In NAH techniques, reconstruction frequencies should be determined at first. To investigate the fault patterns in acoustic images at different characteristic frequencies, here the fundamental mesh frequency (246 Hz) and its side frequencies (232.3 Hz and 259.7 Hz) are chosen as the reconstruction frequencies. According to the FFT-based NAH technique and measurement parameters presented above, for all testing samples the sound fields are reconstructed respectively. The acoustic images at different characteristic frequencies in different gearbox running conditions are shown in Fig. 8. As illustrated in Fig. 8, it can be found that the different characteristic frequencies have their corresponding acoustic images. For different conditions at the same characteristic frequencies, the acoustic images are very similar and the sound source locations hardly change, but the corresponding energy distributions have some differences depending on the different conditions. So, the spatial distribution information may be applied to identifying the different types of gearbox fault. Furthermore, the distributions of acoustic images at the mesh frequency are more stable than that at the side frequencies. In order to capture the spatial distribution characteristics underlying the sound field, the texture features introduced in Section 3 are extracted from acoustic images for identifying the different fault patterns of gearbox. The feature extraction algorithms are programmed based on Matlab, and conducted on the personal computer with Pentium CPU 2.6 GHz and memory 2 GB.

5.3. Fault pattern identification and diagnosis results In the construction of multi-SVM model, 5-fold cross validation with grid research is conducted to determine the model parameters. For each validation, 5  12 original samples are randomly partitioned into 5 subsamples. Of the 5 subsamples, a single subsample is retained as the validation data for testing the multi-SVM model, and the remaining 4 subsamples are used as training data. The cross-validation process is then repeated 5 times (namely 5-folds), with each of the 5 subsamples used exactly once as the validation data. The 5 results from the folds then can be averaged to produce a single estimation as the final testing accuracy rate. After the texture features are fed into the multi-SVM classifiers, pattern identification can be implemented for fault diagnosis. To investigate the capability of diagnosing gearbox faults based on spatial distribution features at different characteristic frequencies, the acoustic images at the mesh frequency and its side frequencies are utilized respectively. For different feature extraction methods, the diagnosis accuracy rates based on the mesh frequency 246 Hz are shown in Table 2, where the accuracy is expressed as a percentage. Tables 3 and 4 show the diagnosis accuracy rates based on the side frequency 232.3 Hz and 259.7 Hz, respectively. Table 5 shows the CPU time for extracting features from all samples based on different feature extraction methods. It can be observed in Table 2 both CM methods can get good diagnosis accuracy, and the Hist method shows the worst results due to its inability to reflect the small changes of local spatial distribution. However, the combination of Hist and

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Z4

Z2

Z3

Z1

2601

Z4=81

Output

Z2=64 f34 f2

f12

Z3=18 Input

f1

Z1=35

230 mm Fig. 6. The structure and parameters of gearbox.

540 mm

f3

2602

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Table 1 Running frequencies of the gearbox. Label

f1

f2

f3

f12

f34

Frequency (Hz)

25

13.7

3

875

246

Fig. 7. Gearbox faults: (a) mild pitting in gear Z3, (b) moderate pitting in gear Z3, (c) severe pitting in gear Z3 and (d) tooth breakage in gear Z3.

GLGCM (HistþGLGCM) outperforms other methods, which indicates it can effectively capture different fault patterns underlying the sound field from the global and local spatial distribution characteristics. Although two CM methods can get comparable accuracy, from Table 5, the CPU time based on GLGCM is far less than that based on GLCM especially for large quantized levels. So, in view of the diagnosis accuracy and time cost, the Hist þGLGCM method is more effective and advisable for practical application. Tables 3 and 4 indicate the spatial distribution features based on the side frequencies cannot effectively diagnose the gearbox faults. The main reason is that spectrum amplitudes at the side frequencies are often unstable due to the nonlinearity and modulation in gearbox system, and thus the features extracted from acoustic images are not reliable for recognizing the fault patterns underlying sound field. According to traditional diagnosis scheme, the mesh frequency and its side frequencies are usually chosen together as characteristic frequencies. Table 6 shows the diagnosis accuracy rates based on the mesh frequency 246 Hz, the side frequency 232.3 Hz and 259.7 Hz. Obviously, the accuracy is not better than that in Table 2, which further indicates the side frequencies as characteristic frequencies are not advisable for our proposed diagnosis scheme and only the mesh frequency is enough. To compare with the traditional ABD method, the acoustic signals in Refs. [1–3] are respectively utilized for gearbox fault diagnosis based on single measurement point. 6 time-domain statistical features (mean, rms, kurtosis, crest factor, skewness, entropy) and 3 amplitude features at the frequency 246 Hz, 232.3 Hz and 259.7 Hz from power spectrum are extracted to recognize the five gearbox conditions. The sample number for each condition is 12. The diagnosis accuracy rates expressed as a percentage are shown in Table 7. The results are worse than that in Table 2 and depend on the different measurement points. For practical application, however, it is not easy to determine the appropriate measurement point.

W. Lu et al. / Journal of Sound and Vibration 332 (2013) 2593–2610

dB 90

-0.4

75

0.2 60 -0.4 -0.2

0 x/m

0.2

dB 90

0.2 60 -0.4 -0.2

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-0.2

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-0.4 -0.2

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-0.4

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60

60 0 0.2 x/m

-0.4

0.2 -0.4 -0.2

75

-0.4 -0.2 dB 90

-0.4

y/m

75

0

0.4

60

0.4

-0.2

0

dB 90

0.2

-0.4 -0.2 dB 90

-0.4

0.4

-0.2

0

0.4

60 0 0.2 x/m

-0.4

0.2

0.4

75

-0.4 -0.2

0.4

-0.4

0.2

0

0.4

60

0.4

y/m

75

dB 90

0.2

-0.2

0

0.4

-0.4

y/m

75

-0.4 -0.2 dB 90

-0.4

0 0.2 x/m

-0.2

0

0.4

60 -0.4 -0.2

0.2

0.4

y/m

0.4

-0.4

y/m

y/m

75

75

0.4

60 0 0.2 x/m

-0.2

0

0 0.2

-0.4 -0.2

-0.2

y/m

75

0.4

0.4

-0.4

y/m

0 0.2

0.4

0.4

-0.2 y/m

0

dB 90

-0.4

-0.2 y/m

y/m

-0.2

dB 90

-0.4

2603

60

0.4 -0.4 -0.2

0 x/m

0.2

0.4

0.4

60 -0.4 -0.2

0 0.2 x/m

0.4

Fig. 8. Acoustic images in different gearbox running conditions: (a)–(e) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 246 Hz, respectively, (f)–(j) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 232.3 Hz, respectively, and (k)–(o) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 259.7 Hz, respectively.

5.4. Influence of noise interference In order to study the influence of noise interference, random noise with signal-to-noise ratio (SNR) 0 dB is made by a loudspeaker located at a distance 0.6 m from the gearbox as shown in Fig. 5. Signal acquisition, sample collection, fault

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Table 2 Accuracy based on the meshing frequency 246 Hz. Feature extraction method

Quantized level (L)

Hist GLCM GLGCM GLCMþ GLGCM Histþ GLGCM

8

16

32

64

128

75.0 76.7 90.0 91.7 90.0

78.3 90.0 86.7 86.7 86.7

81.7 81.7 91.7 93.3 97.3

78.3 81.7 91.7 91.7 93.3

81.7 83.3 85.0 88.3 93.3

8

16

32

64

128

36.7 60.0 58.3 56.7 55.0

36.7 58.3 60.0 63.3 58.3

40.0 60.0 58.3 58.3 56.7

41.3 61.7 63.3 61.7 63.3

40.0 60.0 58.3 61.7 60.0

8

16

32

64

128

53.3 65.0 65.0 68.3 76.7

50.0 68.3 73.3 78.3 76.7

50.0 71.7 68.3 68.3 75.0

51.7 71.7 65.0 68.3 70.0

51.7 70.0 70.0 71.7 78.3

Table 3 Accuracy based on the side frequency 232.3 Hz. Feature extraction method

Quantized level (L)

Hist GLCM GLGCM GLCMþ GLGCM Histþ GLGCM

Table 4 Accuracy based on the side frequency 257.9 Hz. Feature extraction method

Hist GLCM GLGCM GLCMþ GLGCM Histþ GLGCM

Quantized level (L)

Table 5 CPU time for feature extraction (s). Feature extraction method

Hist GLCM GLGCM

Quantized level (L) 8

16

32

64

128

0.05 1.5 0.1

0.05 5.3 0.2

0.05 21.3 0.5

0.05 104.3 1.5

0.1 875.4 5.7

Table 6 Accuracy based on the meshing frequency 246 Hz, the side frequency 232.3 Hz and 259.7 Hz. Feature extraction method

Hist GLCM GLGCM GLCMþ GLGCM Histþ GLGCM

Quantized level (L) 8

16

32

64

128

65.0 81.7 81.7 83.3 83.3

68.3 76.7 86.7 88.3 90.0

66.7 78.3 90.0 88.3 90.0

65.0 76.7 88.3 88.3 91.7

66.7 78.3 83.3 85.0 83.3

simulation, sound field reconstruction and feature extraction are the same as before. Acoustic images at the mesh frequency 246 Hz, the side frequency 232.3 Hz and 259.7 Hz in different gearbox running conditions are shown in Fig. 9. Compared with Fig. 8, the acoustic images at the mesh frequency are very similar, whereas the energy distributions in

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Table 7 Accuracy based on single measurement point. Measurement position

dB 90

-0.4

76.0

79.7

dB 90

-0.2

0

75

0.4

0 0.2 x/m

dB 90

0

75

-0.4 -0.2

0 0.2 x/m

0.4

-0.4 -0.2 dB 90

-0.4

0 0.2 x/m

dB 90

0

75

60

0.4 -0.4 -0.2

0 0.2 x/m

-0.4 -0.2 dB 90

-0.4

0 0.2 x/m

dB 90

0

75

0.4

60

0.4 -0.4 -0.2

0 0.2 x/m

dB 90

-0.4

0 0.2 x/m

0.4

0

75

60

0.4 -0.4 -0.2

0 0.2 x/m

0.4

dB 90

0

75

0.2

0.2

0.2

0.4

-0.2 y/m

y/m

75

60 0 0.2 x/m

-0.4

-0.2

0

75

-0.4 -0.2 dB 90

-0.4

-0.2

0

0.4

60 -0.4 -0.2

0.4

dB 90

0.2

0.2

0.2

0.4

-0.2 y/m

y/m

75

60 0 0.2 x/m

-0.4

-0.2

0

75

-0.4 -0.2

0.4

-0.4

-0.2

0

0.4

60

0.4

0.4

dB 90

0.2

0.2

0.2

0.4

-0.2 y/m

y/m

75

60 0 0.2 x/m

-0.4

-0.2

0

75

-0.4 -0.2

0.4

-0.4

-0.2

0

0.4

60

0.4

60

0.4

dB 90

0.2

0.2

0.2

0.4

-0.2 y/m

y/m

75

0 0.2 x/m

-0.4

-0.2

0

60 -0.4 -0.2

0.4

-0.4

-0.2

75

0.4

60 -0.4 -0.2

dB 90

-0.4

0 0.2

0.4

60 0 0.2 x/m

dB 90

-0.4

0.2

-0.4 -0.2

y/m

77.3

y/m

75

y/m

y/m

0

0.4

y/m

Ref. [3]

-0.2

0.2

y/m

Ref. [2]

-0.4

-0.2

y/m

Ref. [1]

0.4

60 -0.4 -0.2

0 0.2 x/m

0.4

0.4

60 -0.4 -0.2

0 0.2 x/m

0.4

Fig. 9. Acoustic images in different gearbox running conditions with random noise interference: (a)–(e) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 246 Hz, respectively, (f)–(j) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 232.3 Hz, respectively, and (k)–(o) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 259.7 Hz, respectively.

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Table 8 Accuracy based on the meshing frequency 246 Hz with random noise interference. Feature extraction method

Quantized level (L)

Hist GLCM GLGCM GLCMþ GLGCM Histþ GLGCM

8

16

32

64

128

61.7 75.0 76.7 78.3 80.0

68.3 83.3 81.7 85.0 86.7

71.7 80.0 80.0 85.0 85.0

70.0 81.7 78.3 86.7 83.3

70.0 83.3 83.3 86.7 86.7

Microphone array Scanning testing shelf Air compressor Reference 3 Reference 1

Reference 2

Reference 4

Reference 5

Fig. 10. Experimental rig of gearbox fault diagnosis in lab workshop.

acoustic images at the side frequencies become more stochastic. For different feature extraction methods, the diagnosis accuracy rates based on the mesh frequency 246 Hz are shown in Table 8. It can be seen that with the influence of strong noise interference, the Hist þGLGCM method can still get satisfactory results, even though the accuracy become a little lower. To further validate the effectiveness and reliability of the proposed diagnosis scheme in practical working environment, the experimental rig in Fig. 5 is moved to a lab workshop with complex background noise. As shown in Fig. 10, the experimental rig is located at a distance 1.8 m from the wall, and an air compressor is set close to the wall and with a distance 4.2 m from the rig. While only air compressor working, only gearbox working (in normal condition), and both air compressor and gearbox working (in normal condition), the spectra of acoustic signals in Ref. [3] are shown in Fig. 11(a)–(c), respectively. SNR within the frequency range 200 Hz–300 Hz from Ref. [3] is 1.7 dB. In complex environment, acoustic signal is more likely to be contaminated, and thus fault pattern recognition is more difficult for the traditional ABD. So, it is quite necessary to explore a new ABD scheme. According to our proposed scheme, while air compressor and gearbox working, signal acquisition, sample collection, fault simulation, sound field reconstruction and feature extraction are the same as before. Acoustic images at the mesh

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Amplitude / dB

100

80 X: 245.5 Y: 62.05

60

40 0

200

Amplitude / dB

100

400 600 Frequency / Hz

800

1000

400 600 Frequency / Hz

800

1000

X: 245.8 Y: 84.75

80

60

40 0

200

Amplitude / dB

100

X: 246 Y: 86.75

80

60

40 0

200

400

600

800

1000

Frequency / Hz Fig. 11. Spectrums of acoustic signal at Ref. [3]: (a) only air compressor working, (b) only gearbox working (in normal condition), and (c) both air compressor and gearbox working (in normal condition).

frequency 246 Hz, the side frequency 232.3 Hz and 259.7 Hz in different gearbox running conditions are shown in Fig. 12. The main energy in acoustic images at the mesh frequency turns to the right side due to the influence of the air compressor and wall. For different feature extraction methods, the diagnosis accuracy rates based on the mesh frequency 246 Hz are shown in Table 9. The satisfactory accuracy can be still obtained. The acoustic signals at Ref. [1–3] are respectively utilized for the traditional ABD method based on single measurement point. 6 time-domain statistical features (mean, rms, kurtosis, crest factor, skewness, entropy) and 3 amplitude features at the frequency 246 Hz, 232.3 Hz and 259.7 Hz from power spectrum are extracted. The sample number for each condition is 12. The diagnosis accuracy rates expressed as a percentage are shown in Table 10. Obviously, the results are unacceptable for practical application. Athough the characteristics of acoustic signal from single point are not stable for identifying fault patterns due to the interference and contamination, the spatial distribution characteristics from the whole sound field can keep good stability. So, the proposed ABD scheme is suggested especially for complex background environment. 6. Conclusions A gearbox fault diagnosis scheme based on NAH technique and spatial distribution features of sound field is proposed. For a faulty gearbox, the sound field contains abundant information for fault pattern identification. By multi-channel microphone array measurement, the whole sound field information can be reconstructed based on FFT-based NAH. Acoustic images at the characteristic frequencies are obtained for depicting the corresponding sound field. By applying texture analysis, spatial distribution features are extracted from acoustic images for capturing fault patterns underlying the sound field. Gearbox fault diagnosis is experimentally studied in a semi-anechoic chamber and a lab workshop,

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dB 90

-0.4

0.4 0 0.2 x/m

0.4

75

dB 90

0.4 0 x/m

0.2

0

0.4

75

60 0 x/m

0.2

0.2

dB 90

60 -0.4 -0.2

0 x/m

0.2

75

0 x/m

0.2

0.2 60 -0.4 -0.2

0 x/m

0.2

y/m

75

0 x/m

0.2

0.2 0 x/m

0.2

0.4

60

0.2

0.4 dB 90

-0.4

75

y/m

0

0.4

60 0 x/m

-0.2 0

75

0.2

0.2 -0.4 -0.2

75

-0.4 -0.2 dB 90

-0.4

y/m

75

0

0.4

-0.2

0

dB 90

0.4

60 -0.4 -0.2

-0.2

0.4

0.2

0.4

dB 90

-0.4

0.2

-0.2

0

0.4

60 0 x/m

-0.4

0.2

0.4

75

-0.4 -0.2 dB 90

-0.4

y/m

75

0

0.4

-0.2

0

dB 90

0.4

60 -0.4 -0.2

-0.2

0.4

0.2

0.4

dB 90

-0.4

0.2

-0.2

0

0.4

0 x/m

-0.4

0.2

0.4

60 -0.4 -0.2

y/m

y/m

75

75

0.4

-0.2

0

0

0.4

-0.4

-0.2

dB 90

0.2

-0.4 -0.2 dB 90

-0.4

0.4

-0.2

0.4

60 -0.4 -0.2

0 0.2 x/m

-0.4

0.2

0.2

60 -0.4 -0.2

y/m

0

75

0.4

0.4

-0.2 y/m

y/m

60 0 0.2 x/m

-0.4

-0.2

0 0.2

-0.4 -0.2 dB 90

-0.4

y/m

75

0.4

60 -0.4 -0.2

y/m

0 0.2

0.2

y/m

-0.2 y/m

75

y/m

y/m

0

dB 90

-0.4

-0.2

-0.2

0.4

dB 90

-0.4

-0.4 -0.2

0 x/m

0.2

0.4

60

0.4

-0.4 -0.2

0 x/m

0.2

0.4

60

Fig. 12. Acoustic images in different gearbox running conditions while air compressor and gearbox working: (a)–(e) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 246 Hz, respectively, (f)–(j) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 232.3 Hz, respectively, and (k)–(o) normal, mild pitting, moderate pitting, severe pitting and tooth breakage fault at 259.7 Hz, respectively.

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Table 9 Accuracy based on the meshing frequency 246 Hz with air compressor noise interference. Feature extraction method

Hist GLCM GLGCM GLCM þ GLGCM Hist þGLGCM

Quantized level (L) 8

16

32

64

128

70.0 80.7 76.7 85.0 83.3

60.0 88.3 81.7 85.0 83.3

68.3 86.7 88.3 88.3 88.3

75.0 85.0 83.3 86.7 85.7

73.0 85.0 86.7 88.3 88.3

Table 10 Accuracy based on single measurement point. Measurement position Ref. [1]

Ref. [2]

Ref. [3]

68.7

68.3

70.3

respectively. The satisfactory experimental results demonstrate that the proposed scheme is feasible and effective for diagnosing multi-class faults of gearbox even with the influence of strong noise interference, and the comparison with the traditional ABD method further validates its effectiveness. Besides, in view of diagnosis accuracy and time cost, the combination of histogram method and GLGCM method is suggested for practical application.

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