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Normalization and source separation of acoustic emission signals for condition monitoring and fault detection of multi-cylinder diesel engines
Mechanical Systems and Signal Processing 64-65 (2015) 479–497
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Normalization and source separation of acoustic emission signals for condition monitoring and fault detection of multi-cylinder diesel engines Weiliang Wu a, Tian Ran Lin b, Andy C.C. Tan a,n a School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, 2 George St, Brisbane 4001, QLD, Australia b School of Mechanical Engineering, Qingdao Technological University, 11 Fushun Road Qingdao 266520, P.R. China
a r t i c l e i n f o
abstract
Article history: Received 2 September 2013 Received in revised form 12 March 2015 Accepted 19 March 2015 Available online 14 April 2015
A signal processing technique is presented in this paper to normalize and separate the source of non-linear acoustic emission (AE) signals of a multi-cylinder diesel engine for condition monitoring applications and fault detection. The normalization technique presented in the paper overcomes the long-existing non-linearity problem of AE sensors so that responses measured by different AE sensors can be quantitatively analysed and compared. A source separation algorithm is also developed in the paper to separate the mixture of the normalized AE signals produced by a multi-cylinder diesel engine by utilising the system parameters (i.e., wave attenuation constant and the arrival time delay) of AE wave propagation determined by a standard pencil lead break test on the engine cylinder head. It is shown that the source separation algorithm is able to separate the signal interference of adjacent cylinders from the monitored cylinder once the wave attenuation constant and the arrival time delay along the propagation path are known. The algorithm is particularly useful in the application of AE technique for condition monitoring of small-size diesel engines where signal interference from the neighbouring cylinders is strong. Crown Copyright & 2015 Published by Elsevier Ltd. All rights reserved.
Keywords: Acoustic emission Signal normalization Condition monitoring Diesel engines System parameter determination Pencil lead break test
1. Introduction Acoustic emissions are transient elastic waves produced by the rapid release of energy caused by dislocations or surface displacements in material. The phenomenon was first discovered in the early 1950s by Kaiser [1] who observed that a material under load emits ultrasonic waves when the previous maximum applied stress is exceeded. Since then, AE techniques have been adopted in many engineering applications, particularly in Non-Destructive-Testing (NDT) and Condition Monitoring (CM). For example, AE technique has been successfully employed to detect crack, fracture and property change in engineering materials [2,3], wear or leak of oil/gas in pipelines and high pressure vessels integrity evaluation [4,5]. The technique has also been applied in bearing defect detection [6,7]. It was found that AE technique is not only more effective than the conventional vibration technique in early bearing defect detection, it can also provide indications of the defected size and thus enable the monitoring of degradation rate of a damaged bearing [6]. Recently, AE n
Corresponding author. E-mail address: [email protected] (A.C.C. Tan).
http://dx.doi.org/10.1016/j.ymssp.2015.03.016 0888-3270/Crown Copyright & 2015 Published by Elsevier Ltd. All rights reserved.
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technique has been successfully employed for CM and fault detection of reciprocating machinery [8–11]. For instance, AE signals were used to identify the mechanical events such as valve movements, fuel injection and combustion in multicylinder diesel engines [8,12]. Nevertheless, the nonlinear frequency response of AE sensors remains a challenge in sensor calibration to provide a meaningful measurement. It also poses a problem in AE data analysis when multiple sensors are needed in a multi-cylinder diesel engine such as in Refs. [13–15]. Under such circumstances, extensive expert knowledge is needed to correctly interpret the information conveyed in the AE signals and the analysis of AE data can only be carried out in a qualitative manner. The drawbacks of AE technique often attract criticism from practitioners in the field which motivates the first half of the work presented in this paper. The accuracy of results obtained for direct comparison of AE signals from different (un-calibrated) sensors is always questionable since each AE sensor has the inherently unique nonlinear frequency response during the manufacturing process [16]. To overcome this problem, a simple signal processing technique is presented in this work where the nonlinear responses of AE sensors are normalized in the frequency domain based on the sensor calibration chart provided by the manufacturer. The signal processing approach normalizes the AE signals by linearizing their responses in the frequency domain. This process can be related to channel equalization in digital telecommunications. After this procedure, it not only enables the quantitative analysis of AE signals from different sensors but also enables a direct comparison of the signal amplitude in different frequency bands of a single AE sensor. The technique is thus particularly useful for source identification and separation of a complex system response where multiple AE events are present and several AE sensors are needed. AE root-mean-square (RMS) energy was successfully employed in the analysis of the AE signals for condition monitoring and fault detection of multi-cylinder diesel engines [10,17,18]. Comparing to raw AE data, AE RMS energy (termed as AEE in the later analysis) data is smaller in size and thus, requires less computer storage space and offers a faster data processing. Nevertheless, it was found that the AE signal produced by mechanical events of a cylinder of a small multi-cylinder diesel engine is often corrupted by signals generated from the adjacent cylinders due to the short time interval between sequential mechanical events and the small spatial distance between cylinders [18]. For instance, an AE sensor used to monitor AE events of a cylinder can also detect AE signals from the adjacent cylinders. The problem needs to be resolved for a better application of AE technique in condition monitoring of multi-cylinder diesel engines. To this end, a source separation algorithm is developed in the second half of this paper to minimize the signal interference of adjacent cylinders so that condition of a particular cylinder can be effectively monitored by an AE sensor mounted close to it. Blind source separation (BSS) algorithm is often employed to restore a set of hidden source signals from a set of observed signals. The word ‘blind’ implies that both source and the mixing process are unknown and only recordings of the mixtures are available [19]. However, it is impossible to uniquely estimate the original source signals without a prior knowledge of both sources and mixing process [20]. Furthermore, BSS algorithm also suffers from both scaling ambiguity and permutation indeterminacy after separation [21,22]. The drawbacks of BSS algorithm have thus far limited its application for CM and fault diagnosis of reciprocating machinery. The main challenges of applying BSS algorithms to AE signals of multi-cylinder diesel engines are three-folds: (1) the number and location of AE sources are undetermined during engine operation; (2) the propagation properties of AE waves along the engine structure are largely undetermined; and (3) the statistically independency of AE signals associated with different mechanical events of a diesel engine has not been studied. To overcome these challenges, a practical source separation algorithm analogically to the BSS process is presented in the second half of this paper to separate the mixture of AE signals from a multiple-cylinder diesel engine. Instead of restoring all the sources in the diesel engine, the proposed technique groups the sources within each cylinder as one source. Thus, the number of AE sensors required in a CM application equals to the number of cylinders, and if the condition changes or fault occurs in a particular cylinder it can be identified. A standard Pencil Lead Break (PLB) test is used to determine the parameters (i.e., the attenuation constant and arrival time delay) of AE wave propagation in the cylinder head required by the Source Separation (SS) algorithm. The layout for the rest of the paper is arranged as follows: Section 2 describes the diesel engine test rig and the experimental setup. Section 3 presents an elaboration of the signal normalization technique to normalize the AE data acquired from the diesel engine test rig. Effects of normalizing the AE signals and its implication on the signal analysis are also discussed in the section. A PLB test is conducted on the cylinder head of the diesel engine to determine the system parameters of AE wave propagation in Section 4. Section 5 describes the SS algorithm to separate the normalized AEE signals of the diesel engine for condition monitoring and engine fault detection. An error analysis is also presented in Section 5. The main findings of this study are summarized in Section 6. 2. A description of the diesel engine test rig An in-line four-cylinder diesel engine as shown in Fig. 1 was used in the experimental work presented in this paper. The engine generates a 15 kW of nominal power output at full load condition. The output shaft of the engine is coupled to an Olympian three-phase alternator. A three-phase, 15 kW industrial fan heater was connected to the generator to dissipate the power output of the diesel engine in the experiment. The fan heater has three heat settings, which can be adjusted for various engine loadings during the experiment. Four resonant-type, micro-30D AE sensors from Physical Acoustic Corporation (PAC) are mounted on the engine head close to each of the four cylinders to monitor the condition of the diesel engine as shown in Fig. 1. The AE signals are pre-
W. Wu et al. / Mechanical Systems and Signal Processing 64-65 (2015) 479–497
Cylinder4
Sensor 4
Cylinder 3
Sensor 3
Cylinder 2
Cylinder 1
Sensor 2
Sensor 1
481
Fig. 1. The four-cylinder diesel engine (Perkins 404C-22) and locations of the AE sensors used in the experimental study.
amplified by four matching PAC preamplifiers before being recorded by a National Instrument PXI data acquisition (DAQ) system. The DAQ system is capable of measuring up to 8 channels of data synchronously with 1 MHz sampling frequency. An optical TDC/encoder unit (attached onto the end of the crankshaft) is also used in the study to measure the TDC (top-deadcentre) of each cylinder during engine operation to enable the synchronization of AE signals with the engine mechanical events. Table 1 lists the specification and the static measurement of valve timing (in crank angles) of the diesel engine. It is note that the TDC in the table refers to the combustion TDC of each particular cylinder. 3. The AE signal normalization approach 3.1. Methodology As discussed earlier in Section 1, the signals measured by the four AE sensors from the diesel engine need to be normalized to overcome the nonlinear response of the sensors to enable a quantitative analysis in CM applications. A signal normalization technique is thus developed in this section. The original calibration charts (supplied by the manufacturer) of the four AE sensors are shown in Fig. 2. According to the manufacturer, each AE sensor was calibrated based on the surface wave calibration method developed by the US National Institute of Standards and Technology [23]. The dB values shown in the charts are based on the reference value of 1 V/mbar. The unique nonlinear characteristic of each AE sensor can be clearly observed in the calibration charts shown in Fig. 2. It is shown that the sensitivity of each AE sensor differs from one frequency to another frequency and drops substantially outside the designated resonant frequency band (0.1–0.35 MHz). The sensitivities of the sensors also differ from each other. This nonlinear property thus limits the quantitative analysis of AE signals measured by different sensors where results obtained by direct comparison of AE signals from different sensors are questionable. The calibration charts shown in Fig. 2 are digitized in this work to enable the signal normalization process of the AE data in digital domain. The calibration chart of each sensor was scanned and digitalized at a frequency interval of 0.01 MHz in the process based on the condition that variation of sensitivity value at the bounding frequencies (i.e., the lower and upper bound digital sampling lines) of each frequency band is less than 0.5 dB. The interval of the frequency band would be further refined in the digitizing process if the condition is not met. The average sensitivity of each frequency band (i.e., the average sensitivity value of the two bounding frequencies of the band) is used to represent the sensitivity of the band in the AE signal normalization process. The digitized calibration charts of the four AE sensors are shown and compared in Fig. 3. On the display, the original dB scale of the calibration charts was converted into the linear scale using A½
B ¼ 10
dB 20
V=μbar ;
ð1Þ
where B is the sensitivity of an AE sensor displayed in linear scale, A is the corresponding sensitivity displayed in dB scale with respect to the reference of 1 V/mbar. Once the sensitivity in each narrow frequency band of a sensor is determined, the measured raw AE signal from the sensor can be normalized and linearized by the normalization process described in Fig. 4. Four simple steps are required to transform a nonlinear raw AE signal (sðnÞ) to a normalized, linear AE signal (sðnÞ). In Step 1, a time domain raw AE data is transformed into the frequency domain (sðkÞ) using Fast Fourier Transform (FFT). This is followed by the bandpass filtering process in the frequency domain. In this study only the AE response within the designated working frequency band of an AE sensor is considered. A rectangular window (i.e., a window that has the value of 1 within the frequency band between 0.1 MHz and 0.35 MHz, and 0 outside this band) is chosen and applied to the
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Table 1 Perkins 404C-22 diesel engine specifications. Number of cylinders Arrangement Running speed Bore Stroke Displacement Compression ratio Firing order Injection Timing Default valve lash setting Exhaust valve—open Exhaust valve—close Inlet valve—open Inlet valve—close
4 In-line 1500 rpm 84.0 mm 100.0 mm 2.216 l 23.3:1 1-3-4-2 151 ( 7 11) before TDC 0.20 mm 1431 after TDC 3701 after TDC 3541 after TDC 5841 after TDC
Fig. 2. The calibration charts of the four AE sensors used to monitor the test engine (permission granted by PAC).
frequency spectrum to bandpass the AE signal in Step 2. Note that, multiplying a rectangular window filter in the frequency domain is equivalent to convolute its impulse response in the time domain [24]. The impulse response of a rectangular bandpass filter which has the cut-off frequency at f 1 and f 2 with the sampling frequency of f s is given by Eq. (2). hBP ðr Þ ¼
sin ðωc2 rÞ sin ðωc1 rÞ ; πr
where
ωc1 ¼
2π f 1 fs
and
ωc2 ¼
2π f 2 fs
1 or o 1
ð2Þ
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Fig. 3. Digitized calibration charts of the four AE sensors.
Fig. 4. Graphical description of the signal normalization process.
The use of rectangular bandpass filter in Step 2 is due to the consideration that a flat response of the window will not lead to any amplitude and phase distortion within the working frequency band. Nevertheless, it is worth noting that the flat rectangular bandpass filter is unrealizable in practical FIR filter design for real-time signal processing due to the infinite numbers of coefficients ðrÞ required to represent a rectangular window bandpass filter [25]. A time domain Hanning or Hamming window may be employed in real-time signal processing to overcome this limitation. However, these time domain windows do not provide a sharp cut-off as the rectangular window for the desired frequency band, and thus can cause amplitude distortion due to the trailing edges of the window and side lobes effects. 2 In Step 3, the bandpass filtered frequency spectrum of the AE signal ðs ðkÞÞ is normalized in each narrow frequency band by dividing the corresponding value in the digitized calibration chart of the sensor shown in Fig. 3 to obtain the normalized spectrum ðsðkÞÞ. An equalizer is the inverse filter response of the channel [26]. Therefore, Step 3 can be treated as channel equalization. After this, the dispersion effect of each AE sensor can be compensated. The final step of the normalization process is to inverse the normalized frequency response, sðkÞ, back to the time domain signal using inverse Fast Fourier transform (IFFT) to have the filtered and normalized time domain AE waveform, sðnÞ.
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Fig. 5. The signal normalization of an un-calibrated nonlinear AE signal: (a) original signal, (b) original frequency spectrum, (c) bandpassed frequency spectrum, (d) the time waveform of the bandpassed spectrum, (e) normalized frequency spectrum, and (f) normalized signal.
To better illustrate each step of the normalization process and its effect on the signal, the technique is applied to the raw AE data measured by Sensor 1 at the unload condition as shown in Fig. 5. The corresponding un-calibrated AE signal can be found by the solid blue line in Fig. 3. The major AE peaks shown in the raw AE signal (Fig. 5(a)) can be correlated to the major mechanical events of the diesel engine (i.e., combustion, valve opening and closing) as shown in [27]. Fig. 5(b) is the frequency spectrum of the time waveform shown in Fig. 5(a) and is calculated by means of FFT. Fig. 5(c) shows the bandpass spectrum of Fig. 5(b), and Fig. 5(e) is the normalized frequency spectrum that is calculated by dividing Fig. 5(c) to the digitized calibration chart given by Fig. 3. It clearly shows the change in the shape of the spectrum. Furthermore, the measured AE signal has also been converted to true physical quantity (mbar) representing the surface pressure in Fig. 5(e). The time waveforms of the bandpass signal and the normalized AE signals are shown in Fig. 5(d) and (f), respectively. These two time waveforms are similar to Fig. 5(a), but sharper in the transient response due to the removal of low frequency content in the bandpass process. The benefits of the signal normalization technique developed in this paper are two-folds: (1) it overcomes the inherent nonlinear response problem of AE sensors, and (2) it normalizes the AE response to enable a direct comparison as well as quantitatively analysis of AE signals measured by different sensors in both time and frequency domains. Furthermore, the AE signals after normalization can be displayed directly in the true physical unit rather than in arbitrary units or signal voltage as in the existing literatures [6,7,9–12,14,18]. The AE response of a system in different frequency bands can also be analysed quantitatively in the frequency domain after normalization. Therefore, only normalized AE data is analysed and discussed in the subsequent text of this paper.
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3.2. Application to diesel engine AE signals A typical application of the signal normalization technique is the comparison of signals measured by different AE sensors for condition monitoring of diesel engines. For a better clarification of displaying multiple AE signals in a single figure for comparison, AEE rather than the raw AE signals are used in the subsequent analysis. For a given raw AE signal, the corresponding AEE data is calculated by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn ¼ Nw þ ðm 1Þτ 2 Lr AEEðmÞ ¼ x ðnÞ; 1 r m r int ð3Þ ; 1 r n r Lr n ¼ ð m 1 Þ τ þ 1 Nw τ where x is the discrete time domain AE data, n is the index number of the raw data, N w is the moving window size used in the conversion, m is the sequential index of the moving window, Lr is the length of the original raw data, τ ¼ ð1 RÞ Nw is the number of non-overlapping data in the data integration, and R is the percentage of window overlapping. Note that, N w ¼ 100 and 80% data overlapping were used in the AEE conversion to ensure a smooth data transition and a good time resolution. Fig. 6 compares the AEE data from the four AE sensors shown in Fig. 1 measured when the engine was operated at the unload condition. The acronyms shown in Fig. 6, i.e., COMB, IVC, EVC represent combustion, inlet valve closing and exhaust valve closing of the diesel engine, respectively. The numerical index following these abbreviations refers to the cylinder where these mechanical events occur. Clear energy attenuation trend can be observed for AE sources originated from Cylinders 1 and 4, i.e., COMB1, IVC1 and IVC4 as shown in Fig. 6(b)–(d). For instance, Sensor 1 records the highest AE energy for the COMB1 event. This is followed by Sensors 2, 3 and 4. For these mechanical events, the signal energy decays proportionally to the distance along the propagation path away from the source cylinder. This type of AE sources can be easily identified by the observation of energy attenuation recorded by different sensors at different locations. On the other hand, the energy attenuation trend is not so obvious for AE sources originated from Cylinders 2 and 3 such as IVC2 and IVC3 (see Fig. 6(a) and (c)). For instance, Sensor 1 and Sensor 3 recorded higher or similar energy than Sensor 2 for the IVC2 event. Therefore, for sources originated from these two cylinders, source identification using direct energy attenuation analysis may not be suitable. The higher or similar signal energy recorded by sensors away from a source cylinder is due to the signal interference from the neighbouring cylinders and the reflecting boundaries of the small diesel engine. This will be examined further in a Pencil Lead Break (PLB) test conducted on the cylinder head of the diesel engine in the next section. 4. PLB test and system parameters determination In this section, a PLB test is conducted on the cylinder head of the diesel engine to better understand the characteristics of AE wave propagation on the complex engine head to provide an explanation of the interesting energy attenuation patterns of AE events shown in Fig. 6. The PLB test is also used to determine the AE wave propagation parameters of the engine head to be used in the source separation algorithm of next section. A schematic drawing of the valve positions on the cylinder head and the mounting positions of the four AE sensors (shown as S1, S2, S3 and S4) is shown in Fig. 7. Also shown in Fig. 7 is the schematic illustration of the direct wave propagation paths from the inlet valve of Cylinders 1 and 2 to the four AE sensors, and an illustration of how the boundary wave reflection affects the signals detected by Sensor 1. The PLB test was performed at the ten marked locations in sequence on each cylinder as shown in Fig. 8. The locations were chosen such that they are good representations of the source locations of combustion, valve closing and opening events during engine operation. The raw AE signals measured by the four sensors are normalized using the procedure described in Section 3. The normalized responses are converted into AEE data using Eq. (3) and averaged over the ten PLB test locations on each cylinder for comparison. The averaged AEE responses of the four sensors from the PLB test at each cylinder are shown and compared in Fig. 9. The AEE response of the sensor closest to the PLB source is plotted by thicker line in the figure. For simplicities, the sensor mounted next to the “source cylinder” is termed as the “source sensor” and the signal of the source sensor is termed as the “reference signal” in the following analysis. The other three sensors are termed as the “adjacent sensors” and the signals of these sensors are termed as the “adjacent signals”. It is shown in Fig. 9 that when the source occurs at Cylinder 1, the AEE amplitude of Sensor 1 is the largest. This is followed sequentially by Sensors 2, 3 and 4 (Fig. 9(a)). Similar observation can also be found for AE sources originated from Cylinder 4 (Fig. 9(d)). This observation agrees well with the wave propagation characteristics for sources originated from these two cylinders during engine operation where signal energy detected by the sensors depends on the distance between the sensors and the source. The result confirms that wave propagation of AE sources from these two cylinders is less affected by wave reflection and refraction at the boundaries for both dynamic and static tests as the two cylinders are the outer cylinders in the engine configuration (see Fig. 7). Similar to that in the dynamic case (engine running), no clear attenuation trend is observed for sources originated from the two inner cylinders (Cylinders 2 and 3) in the PLB test where adjacent signals can have higher or similar amplitude than the source signal (see Fig. 9(b) and (c)). This phenomenon is caused by the sensor proximity of the small test engine and the strong interference from the boundary wave reflection and refraction.
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Fig. 6. Comparison of the normalized AE data from the diesel engine at unload condition measured synchronously by four AE sensors and enlarged view of the combustion areas, (a) 0–901, (b) 180–2701, (c) 360–4501 and (d) 540-6301
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Fig. 7. Schematic drawing of the engine cylinder block and the sensor locations.
Fig. 8. Locations of PLB test at each cylinder head.
Due to the close similarities of AE wave propagation in both dynamic and static cases, it is reasonable to assume that the wave propagation constant and time delays obtained from the PLB test can be used to describe the parameters of wave propagation of AE sources generated by mechanical events of the diesel engine during operation. To calculate the attenuation constant and the Arrival Time Delay (ATD) of an AE wave after emitting from a source, the amplitude relationship between the AE signals at two different locations away from a source in an infinite medium given by Nivesrangsan et al. [14] is re-visited here as Ai ðtÞ ¼ αij Aj ðtÞ;
ð4Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ηðr i r j Þ is the attenuation where Ai ðtÞ and Aj ðtÞ are the amplitude of the continuous AE signals 1 at locations i and j, αij ¼ e constant from location j to i, η is the wave attenuation factor m , ri and rj are the distance away from the source for location i and j. Eq. (4) can be re-written in digital form, and to incorporate the Arrival Time Delay (ATD) between two discrete AE signals measured at two sensor locations as Ai ðnÞ ¼ αij Aj ðn ΔnÞ;
1 r n r L;
ð5Þ
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Fig. 9. Averaged AEE responses of the PLB test at each cylinder; (a) Cylinder 1; (b) Cylinder 2; (c) Cylinder 3; and (d) Cylinder 4.
where n is the data index of a discrete AE signal of length L, Δn ¼ Δt=T is the data sample difference corresponding to the arrival time difference Δt between the two sensor locations. T ¼ 1=f s is the sampling interval. An analogy equation to Eq. (5) can also be written to describe the relationship between the AEE data at two sensor locations as Ei ðmÞ ¼ αij Ej ðm βij Þ;
ð6Þ
where Ei ðmÞ and Ej ðmÞ are the digitised AEE data corresponding to Ai and Aj , m is the data index, β ij ¼ intðΔn=τÞ represents the ATD between the two sensor locations. Eq. (6) can be used to determine the relationship between the source signal and any adjacent signals from the PLB test (see Fig. 9). A least squares (LS) algorithm is further employed to optimize the results of attenuation constant ðαij Þ and ATD ðβij Þ calculated from Eq. (6) to describe the relationship of any two AEE data: 2 Xm ¼ L Ei ðmÞ αij Ej m βij ; 1 r m r L; ð7Þ LS ¼ m¼1 where Ej is the reference AEE data and Ei is the AEE data from one of the adjacent sensors. Fig. 10 shows an example of the optimisation process in determining the two wave propagation parameters between the reference AEE data of Sensor 1 and the adjacent AEE data of Sensor 2 shown in Fig. 9(a). The saddle point in the figure represents the optimised parameters (i.e.,α21 ¼ 0:64 and β21 ¼ 2) that can lead to minimum estimation error. The process is repeated for all the AEE responses obtained from the PLB test on the four cylinders. A 4 4 attenuation constant matrix and a 4 4 ATD matrix can then be obtained for the test engine as 2 3 1 1 0:63 0:28 6 0:64 1 0:81 0:41 7 7 α¼6 ð8aÞ 6 7; 4 0:44 0:95 1 0:66 5 0:29
0:62
0:94
1
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489
Fig. 10. 3D plot of evaluating the optimized attenuation and ATD parameters.
and 2
0 6 2 6 β¼6 4 5 13
2
6
0
1
0 5
0 1
11
3
7 7 7 7; 2 5
ð8bÞ
0
where each element αij , in α represents the attenuation constant from source sensor j to adjacent sensor i, each element βij in β represents the ATD from Sensor j to Sensor i. For instance, the first column of α display the attenuation constants of the estimated adjacent signals of Sensors 2, 3 and 4 using the reference signal of Sensor 1 are 0.64, 0.44 and 0.29, respectively. It is shown in Eqs. (8a) and (8b) that both attenuation and ATD matrices are slightly asymmetric caused by noise interference and experimental errors in the experiment. The parameters, αij and βij from Eqs. (8a) and (8b) are substituted back into Eq. (6) to estimate each of the adjacent signal (E~ ijj ) using the reference signal (Ej ), which is then compared to the measured adjacent signal (Ei ) to evaluate the errors of this parameter estimation. The percentage of squared error between the estimated and measured signals of each adjacent sensor i using the reference signal of source sensor j is calculated by: 2 P Ei E~ ijj εij ¼ 100 0=0 ; ð9Þ P 2 Ei which then yields a 4 4 estimation error matrix 2 3 0 1:82 5:28 14:16 6 2:19 0 2:08 4:90 7 7 ε¼6 6 7: 4 3:73 2:54 0 2:23 5 11:14
7:64
4:01
ð10Þ
0
It is shown that the estimation error increases monotonously as the distance between the adjacent sensor and the source increases. For example, the estimation errors of the adjacent signals (Sensors 2, 3 and 4) using the reference signal from Sensor 1 are 2.19%, 3.73% and 11.14%, respectively. The maximum estimation error shown in the error matrix is 14.16%. Inherited from the errors presented in the attenuation and ATD matrices, the error matrix given here is also slightly asymmetric. Fig. 11 compares the measured and the estimated signals of the three adjacent sensors for the PLB test on Cylinder 1. It is shown that the estimated AEE responses match well with the measured AEE responses of Sensors 2 and 3 not only along the rising edge but also on the falling edge (see Fig. 11(a) and (b)). A larger error is induced between the estimated and the measured AEE responses of Sensor 4 as shown in Fig. 11(c). Results shown in Fig. 11 agree with the values in the first column of the error matrix where the estimation error increases as the distance between the sensor location and the source increases. Fig. 11 also confirms that the adjacent signals on an engine head can be estimated with a small error once the reference signal and wave propagation parameters are known. 5. A source separation technique for diesel engine CM signals Results obtained from the dynamic and static tests of the diesel engine in Sections 3 and 4 showed that sources from adjacent cylinders can have strong signal interference to the AE signals of a monitored cylinder, particularly for the two inner cylinders. To overcome this problem, a Source Separation (SS) algorithm is presented in this section. The algorithm
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Fig. 11. Comparison of the measured and estimated AEE responses from the PLB test at Cylinder 1, (a) Sensor 2, (b) Sensor 3, and (c) Sensor 4.
differs from the conventional BSS algorithm by utilizing the pre-determined AE wave propagation properties of the diesel engine to minimize the reconstituted error in the source separation. As shown in Fig. 6, the EVC event of a cylinder occurs in the combustion region of another cylinder and thus causing substantial interference of the signal produced by the COMB events. Therefore, the resultant AEE data from the four sensors are mixture of the reference signal from the monitored cylinder and the adjacent signals from the neighbouring cylinders. If the interference can be separated, the mechanical events of each cylinder can be monitored independently by a single AE sensor. The separation process can be difficult without a prior knowledge of the mixing process and the statistical independent of the sources when sources from multiple cylinders are present simultaneously in a signal. Torkkola [28] presented a BSS algorithm by assuming that the outputs are mixtures of convoluted independent sources and no noise is present. The adaptive algorithm for updating the filter coefficients described in Ref. [28] can be simplified by utilising the pre-determined system parameters. This is indeed the case for the SS algorithm presented in this study where the attenuation constant and ATD from the PLB test are employed. Therefore, the algorithm is no longer ‘blind’ where the convolution process is simplified to a pure attenuation and delay process with no noise present. Fig. 12 depicts the flow chart of the source separation process developed in this work. Based on the AEE conversion algorithm given by Eq. (3), the engine specification and the valve timing given in Table 1 and the sampling frequency (1 MHz) used in AE data acquisition, it requires at least 100 AEE data points in a data segment (corresponding to 20 CA degrees) to fully embrace two mechanical events. Therefore, the resultant AEE data matrix, U, is divided into N segmental matrices with a fix data length of 100 in Step I of the SS process. Assuming that the data in any two rows of the segmental AEE matrix, Un , are generated by two AE sources in Cylinders i and j, the data of each row can be described by Uni ðmÞ ¼ aii Si ðm βii Þ þaij Sj ðm βij Þ;
1 r m r 100;
1 r ir 4;
1 r jr 4; ia j
ð11Þ
Unj ðmÞ ¼ aji Si ðm βji Þ þajj Sj ðm βjj Þ;
1 r m r 100;
1 r ir 4;
1 r jr 4;
ð12Þ
j ai
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491
Start
Step I: Divide the AEE data U into N segmental matrix, Un, 1 ≤
≤
Unew = empty matrix of size U
= 1
False
<
Exit Return Unew
True Step II: Perform Source Separation for the nth segment of AEE data, Un
=
+ 1
Fig. 12. Flow chart of the source separation (SS) algorithm.
where Uni and Unj represent the row i and j in Un (i.e., AEE data from Sensors i and j), Si and Sj are the reference AEE data from row i and j to represent the intrinsic AE sources in Cylinders i and j. The coefficients aii and αjj are the diagonal terms, αij and αji are the off-diagonal terms in the attenuation matrix α. βii , βjj , βij and βji are the diagonal and off-diagonal terms of the ATD matrix, β. The complex convolutive mixing process in time domain can be solved by converting it into instantaneous mixing process in frequency domain in Step II of the SS process given by the flowchart in Fig. 13. The time domain data described by Eqs. (11) and (12) are transformed into the frequency domain by means of Fast Fourier Transform (FFT) as Uni ðkÞ ¼ aii Si ðkÞe
j0 2π mkβii 100
j0 2π mkβji
þaij Sj ðkÞe
j0 2π mkβij 100
;
ð13Þ
j0 2π mkβjj
Unj ðkÞ ¼ aji Si ðkÞe 100 þajj Sj ðkÞe 100 pffiffiffiffiffiffiffiffi where j0 ¼ 1 represents the imaginary number. Given both α and β and from Eqs. (13) and (14), the frequency domain reference AEE data can be obtained by
ð14Þ
Si ðkÞ ¼ ðwii Uni ðkÞ þwij Unj ðkÞÞ=GðkÞ;
1 rk r 100;
1 r ir 4;
1 r jr 4;
ia j
ð15Þ
Sj ðkÞ ¼ ðwji Uni ðkÞ þwjj Unj ðkÞÞ=GðkÞ;
1 rk r 100;
1 r ir 4;
1 r jr 4;
ja i
ð16Þ
j0 2π mkðβ þ β Þ 1 j0 2π mkβ j0 2π mkβ ij ji ij ji , wji ¼ αji exp . The time, wii ¼ wjj ¼ 1, wij ¼ αij exp where GðkÞ ¼ 1 aij aji exp 100 100 100 domain reference AEE data can also be obtained by inverting Si ðkÞ and Sj ðkÞusing inverse FFT (IFFT). Because the SS algorithm developed here does not have the capacity to provide the exact source information in each AEE data segment, a trial and error strategy is then adopted to derive this information from the resultant AEE data, U. Based on the chosen data length and from Fig. 6, we can assume that there are maximum two mechanical events in each data segment,Un , whose source can be from either one or two cylinders. Therefore, there are ten possible combinations of the source cylinders for the resultant AEE data which are listed in Table 2. At each data segment, the algorithm evaluates the constituted error of all ten possible combinations. It then solves for the ~ based on the following two assumptions: reference AEE signal(s) and estimates the four channels of new AEE data, U, (1) If the conditional statement i ¼ j in Fig. 13 is true, the source is considered to be from one cylinder. The AEE data ðUni Þ from the corresponding sensor is then used as the reference AEE ðSi Þ to estimate the other three adjacent AEE data using ~ the parameter matrices α and β to estimate the reconstituted AEE data, U.
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Fig. 13. Flow chart for the detailed SS algorithm. Table 2 Possible source cylinder combinations of a resultant AEE data segment. Single cylinder
Two cylinders
Cylinder Cylinder Cylinder Cylinder
Cylinder Cylinder Cylinder Cylinder Cylinder Cylinder
1 2 3 4
1&2 1&3 1&4 2&3 2&4 3&4
and and and and and and
Cylinder Cylinder Cylinder Cylinder Cylinder Cylinder
2&1 3&1 4&1 3&2 4&2 4&3
(2) If the conditional statement i ¼ j is false, the sources are considered to be from two of the cylinders. The resultant AEE data (Uni ,Unj ) from the two corresponding source sensors are used in Eqs. (11) and (12) to calculate the reference AEE data (Si ,Sj ). This is then used to solve for the frequency domain reference AEE (Si ðkÞ, Sj ðkÞ) using Eqs. (15) and (16). Each ~ i and U ~ j . The final reconstituted AEE data, U, ~ in this case are reference AEE is used to calculate the estimated AEE data, U the sum of the two estimated data. ~ is used to calculate the percentage of squared error matrix ε' from the The newly obtained reconstituted AEE data, U original AEE data, Un : 2 P4 P100 n ~ i ðmÞ Ui ðmÞ U i ¼ 1 m ¼ 1 ε0 ¼ 100ð%Þ; 1 r i r4 ð17Þ 2 P4 P100 n i¼1 m ¼ 1 Ui ðmÞ
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From this calculation, a symmetric matrix ε0 of size 4 4 can be obtained for each set of data segment, Un . An example of the error matrix for a given AEE data segment is given below: 2 3 15:63 45:79 15:42 6:53 6 45:79 15:32 65:19 20:67 7 7 ε0 ¼ 6 ð18Þ 6 7 4 15:42 65:19 48:54 89:68 5 6:53
20:67
89:68
170:24
Each element, ε0ij , in ε0 represents the estimation error by assuming that the sources are from Cylinders i and j. The offdiagonal terms are equal in pairs, such that ε0ij ¼ ε0ji . This is due to the assumption that sources from Cylinders i and j can be considered as the same for sources from Cylinders j and i. In Step III, the algorithm chooses one out of the ten possible source combinations leading to the minimum reconstituted error to identify the source cylinder(s) in each AEE data segment. A new reference AEE data segment Unnew is returned after knowing the correct combination. The SS algorithm stops and returns a separated AEE data matrix, Unew , after completing N iterations. 5.1. Separation of the diesel engine CM data The SS algorithm developed in the previous section is applied to separate the four channels of AEE data shown in Fig. 6. The separation result is presented in Fig. 14. It is shown that the reference AEE signal(s) from the mechanical event(s) of the source cylinder(s) are successfully separated from the adjacent AEE signals after applying the SS algorithm. For example, Fig. 14(a) clearly shows the reference AEE signal of EVC1 at 101 CA recorded by Sensor 1, and the COMB4 signal of Cylinder 4 starts from about 21 to 401 CA recorded by Sensor 4. More significantly, the sources originated from Cylinders 2 and 3 are also separated successfully by the algorithm, for instance, the signal from IVC2 at about 411 CA recorded by Sensor 2 (Fig. 14(a)), the signal from IVC3 at 4021 CA recorded by Sensor 3 (see Fig. 14(c)). The source separation result also clearly indicates a maximum surface pressure produced by different mechanical events of the engine, e.g., 80 mbar by EVC1, 45 mbar by COMB4 and 70 mbar by IVC2. It should be noted that the algorithm did not work as well in separating sources from the two inner cylinders (Cylinders 2 and 3) when the mechanical events of these two cylinders co-existed in the same data segment (see Fig. 14(b) and (d)). This is due to the small spatial distance between these two cylinders of the small test engine causing the AEE signals generated by the two cylinders to be seriously overlapped. For example, it is shown in Fig. 14(b) that the AEE energy of EVC3 overlaps with the AE signal of COMB2 (between 190 and 2001 CA), and has a larger amplitude. The algorithm then misinterprets that the AEE signal is generated by the EVC3 event only causing the incorrect separation of the resultant AEE signal. 5.2. Error analysis An error analysis is presented in this section to evaluate the effectiveness and error tolerance of the SS algorithm developed in this work. It is shown in the previous analysis that errors can be induced in estimating the system parameters of the engine though it is not known how such estimation error affects the accuracy and effectiveness of the SS technique in separating the mixture of AE signals. Incorrect estimation of the engine system parameters may lead to poor separation results. Therefore, the error tolerance of the algorithm needs to be examined. A 10% error and 1 step delay error are assumed for the off-diagonal elements in the attenuation constant (α), and ATD (β) matrices obtained from the PLB test in the following analysis as: 2 3 1 0:9 0:69 0:31 6 0:58 1 0:73 0:41 7 7 α0 ¼ 6 ð19aÞ 6 7; 4 0:48 0:86 1 0:73 5 0:32
0:56
0:85
1
and 2
10
3
0 6 1 β0 ¼ 6 6 4 4
2
4
0
0
1
0
9 7 7 7: 3 5
12
4
1
0
ð19bÞ
The new system parameters are then used in the SS algorithm, and the result is shown in Fig. 15. Comparing Fig. 15 with Fig. 14, it is found that small errors (say, 10%) in the system parameter estimation will not have a much effect on the accuracy of the source separation. To evaluate this further, the error for the off-diagonal elements of the attenuation matrix (α) is increased to 20% as shown in Eq. (20) and the time delay error is kept to be the same as in the last case. These system parameters are used in the SS algorithm and the result is shown in Fig. 16. It is shown that the algorithm failed to accurately separate the sources from a mixture of cylinders. For example, the IVC2 (40–501 CA) is incorrectly separated as the
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Fig. 14. Comparison of the normalized AEE data from the diesel engine at normal and unload condition after separation and the enlarged views for the combustion regions: (a) 0–901, (b) 180–2701, (c) 360–4501, and (d) 540–6301.
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Fig. 15. The separated AEE data of unload condition with 10% error and 1 step delay error in attenuation and ATD, respectively and enlarged view for combustion regions: (a) 0–901, and (b) 180–2701.
combination of mechanical events in Cylinders 1 and 4 while IVC3 (400–4101 CA) is incorrectly separated as the combination of mechanical events in Cylinders 1 and 4 instead of mechanical events from Cylinders 2 & 3. 2 3 1 0:8 0:5 0:22 6 0:77 1 0:65 0:36 7 7 α″ ¼ 6 ð20Þ 6 7; 4 0:53 0:76 1 0:79 5 0:23
0:5
0:75
1
6. Concluding remarks A signal normalization and source separation technique is presented in this paper to normalize the nonlinear response problem of AE sensors, and to separate the sources detected by multiple AE sensors for condition monitoring applications of diesel engines. A four-step signal normalization approach was outlined in the paper to process the un-calibrated nonlinear AE signals based on the sensor calibration chart. The technique is easy to implement in practical AE signal analysis. It was employed in this study to normalize the CM data measured by four AE sensors on a diesel engine so that the measured responses by the sensors can be compared directly for a quantitative analysis. It was shown in the study that AE signals originated from the
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Fig. 16. The separated AEE data of unload condition with 20% error and 1 step delay error in attenuation and ATD, respectively and enlarged view for combustion regions (a) 0–901, and (b) 360–4501.
outer cylinders of the in-line four-cylinder diesel engine demonstrate a clear energy attenuation pattern. For such sources, the AE energy measured by a sensor is proportional to the distance between the sensor and the source cylinder. On the contrary, the energy decaying trend of the AE signals originated from the two inner cylinders of the four-cylinder engine is not so obvious due to the strong interference from the boundary wave reflection and refraction of the small engine block. A source separation technique was developed to overcome this problem so that the operation condition of an engine cylinder of a multi-cylinder diesel engine can be monitored effectively by an AE sensor mounted close to it. A standard PLB test was conducted on the cylinder head of the engine to determine the attenuation constant and the ATD for various AE wave propagation paths (the propagation paths from each cylinder to each sensor) required in the source separation. It is noted that the property of AE attenuation pattern of the PLB test at each cylinder follows the same pattern as that of the source generated by the mechanical events of each cylinder. This implies that the AE wave attenuation and ATD determined by the static PLB test can be utilized to determine the interferences to adjacent sensors once the reference signal produced by the mechanical events is known. It was shown that the source separation process improves the source identification ability by reducing/eliminating the interferences from adjacent cylinders. Therefore, each cylinder of a diesel engine can be monitored separately. Furthermore, combining with the normalization process of the AE signals, the valve activities and combustion process of each cylinder can be quantitatively monitored.
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Acknowledgments This paper was developed within the CRC for Infrastructure and Engineering Asset Management, established and supported under the Australian Government’s Cooperative Research Centres Programme. The authors gratefully acknowledge the financial support provided by the CRC. Financial supports from ASC Pty Ltd., the CRC’s industry sponsor for the purchase of the diesel engine test rig used in this research is also acknowledged. References [1] J. Kaiser, An Investigation into the Occurrence of Noises in Tensile Tests, or a Study of Acoustic Phenomena in Tensile tests, Tech. Hochsch. Munchen, Munich, Germany, 1950 Ph.D. Thesis. [2] A. Carpinteri, G. Lacidogna, N. Pugno, Structural damage diagnosis and life-time assessment by acoustic emission monitoring, Eng. Fract. Mech. 74 (1) (2007) 273–289. [3] T. Chotard, et al., Application of the acoustic emission technique to characterise liquid transfer in a porous ceramic during drying, J. Eur. Ceram. Soc. 26 (7) (2006) 1075–1084. [4] M.F. Shehadeh, Monitoring of Long Steel Pipes using Acoustic Emission. 2006. [5] L. Sun, et al., Study on acoustic emission detection for pipeline leakage based on EMD signal analysis method, J. Vib. Shock 26 (10) (2007) 161–164. [6] A.M. Al-Ghamd, D. Mba, A comparative experimental study on the use of acoustic emission and vibration analysis for bearing defect identification and estimation of defect size, Mech. Syst. Signal Process. 20 (7) (2006) 1537–1571. [7] S. Al-Dossary, R.I.R. Hamzah, D. Mba, Observations of changes in acoustic emission waveform for varying seeded defect sizes in a rolling element bearing, Appl. Acoust. 70 (1) (2009) 58–81. [8] T.L. Fog et al. On condition monitoring of exhaust valves in marine diesel engines, in: Neural Networks for Signal Processing IX, 1999. Proceedings of the 1999 IEEE Signal Processing Society Workshop, 1999. [9] N.H. Pontoppidan, S. Sigurdsson, J. Larsen, Condition monitoring with mean field independent components analysis, Mech. Syst. Signal Process. 19 (6) (2005) 1337–1347. [10] R. Douglas, J. Steel, R. Reuben, A study of the tribological behaviour of piston ring/cylinder liner interaction in diesel engines using acoustic emission, Tribol. Int. 39 (12) (2006) 1634–1642. [11] N.H. Pontoppidan J. Larsen. Unsupervised condition change detection in large diesel engines, in: IEEE 13th Workshop on Neural Networks for Signal Processing, 2003: NNSP’03, 2003. [12] D.P. Lowe, et al., Diesel engine problems, acoustic emission signals and simulated misfire faults, Eng. Asset Manage. Infrastruct. Sustainability (2012) 587–598. [13] P. Nivesrangsan, J.A. Steel, R.L. Reuben, AE mapping of engines for spatially located time series, Mech. Syst. Signal Process. 19 (5) (2005) 1034–1054. [14] P. Nivesrangsan, J.A. Steel, R.L. Reuben, Acoustic emission mapping of diesel engines for spatially located time series—Part II: Spatial reconstitution, Mech. Syst. Signal Process. 21 (2) (2007) 1084–1102. [15] P. Nivesrangsan, J.A. Steel, R.L. Reuben, Source location of acoustic emission in diesel engines, Mech. Syst. Signal Process. 21 (2) (2007) 1103–1114. [16] J.Z. Sikorska, D. Mba, Challenges and obstacles in the application of acoustic emission to process machinery, Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 222 (1) (2008) 1–19. [17] E.Y. Kim, A.C.C. Tan, B.S. Yang, Acoustic emission for diesel engine monitoring: a review and preliminary analysis, Eng. Asset Manage. Infrastruct. Sustainability (2012) 489–499. [18] W. Wu, A.C.C. Tan, E. Kim. Enhancing acoustic emission signals from multi-cylinder diesel engine, in: Proceedings of the Sixth Australasian Congress on Applied Mechanics, Engineers Australia, 2010. [19] M.S. Pedersen, et al., A Survey of Convolutive Blind Source Separation Methods, Springer, 2007. [20] G.R. Naik, An overview of independent component analysis and its applications, 2011. [21] J. Antoni, Blind separation of vibration components: principles and demonstrations, Mech. Syst. Signal Process. 19 (6) (2005) 1166–1180. [22] A. Hyvarinen, E. Oja, Independent component analysis: algorithms and applications, Neural Netw. 13 (4–5) (2000) 411–430. [23] MISTRAS Group Inc. Acoustic Emission Sensors: Their Selection and Calibration. [Cited 2013 11 Jan.]; Available from: 〈http://www.pacndt.com/index. aspx?go=products&focus=/sensors/selection_and_calibration.htm〉. [24] A.A. Khan, Digital Signal Processing Fundamentals, Da Vinci Engineering Press, Hingham, Massachusetts, 2005. [25] S.K. Mitra, Digital Signal Proessing: A Computer-based Approach, fourth ed. McGraw-Hill Companies, Inc, New York, NY, 2011. [26] A. Das, Digital Communication: Principles and System Modelling, Springer, Berlin Heidelberg, 2010. [27] T.R. Lin, A.C.C. Tan. Characterizing the signal pattern of a four-cylinder diesel engine using acoustic emission and vibration analysis, in: Proceedings of World Conference on Acoustic Emission-2011, Chinese Society for Non-destructive Testing, 2011. [28] K. Torkkola, Blind separation of convolved sources based on information maximization, in: Neural Networks for Signal Processing [1996] VI. IEEE Proceedings of the 1996 IEEE Signal Processing Society Workshop, 1996.
Contents lists available at ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Normalization and source separation of acoustic emission signals for condition monitoring and fault detection of multi-cylinder diesel engines Weiliang Wu a, Tian Ran Lin b, Andy C.C. Tan a,n a School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, 2 George St, Brisbane 4001, QLD, Australia b School of Mechanical Engineering, Qingdao Technological University, 11 Fushun Road Qingdao 266520, P.R. China
a r t i c l e i n f o
abstract
Article history: Received 2 September 2013 Received in revised form 12 March 2015 Accepted 19 March 2015 Available online 14 April 2015
A signal processing technique is presented in this paper to normalize and separate the source of non-linear acoustic emission (AE) signals of a multi-cylinder diesel engine for condition monitoring applications and fault detection. The normalization technique presented in the paper overcomes the long-existing non-linearity problem of AE sensors so that responses measured by different AE sensors can be quantitatively analysed and compared. A source separation algorithm is also developed in the paper to separate the mixture of the normalized AE signals produced by a multi-cylinder diesel engine by utilising the system parameters (i.e., wave attenuation constant and the arrival time delay) of AE wave propagation determined by a standard pencil lead break test on the engine cylinder head. It is shown that the source separation algorithm is able to separate the signal interference of adjacent cylinders from the monitored cylinder once the wave attenuation constant and the arrival time delay along the propagation path are known. The algorithm is particularly useful in the application of AE technique for condition monitoring of small-size diesel engines where signal interference from the neighbouring cylinders is strong. Crown Copyright & 2015 Published by Elsevier Ltd. All rights reserved.
Keywords: Acoustic emission Signal normalization Condition monitoring Diesel engines System parameter determination Pencil lead break test
1. Introduction Acoustic emissions are transient elastic waves produced by the rapid release of energy caused by dislocations or surface displacements in material. The phenomenon was first discovered in the early 1950s by Kaiser [1] who observed that a material under load emits ultrasonic waves when the previous maximum applied stress is exceeded. Since then, AE techniques have been adopted in many engineering applications, particularly in Non-Destructive-Testing (NDT) and Condition Monitoring (CM). For example, AE technique has been successfully employed to detect crack, fracture and property change in engineering materials [2,3], wear or leak of oil/gas in pipelines and high pressure vessels integrity evaluation [4,5]. The technique has also been applied in bearing defect detection [6,7]. It was found that AE technique is not only more effective than the conventional vibration technique in early bearing defect detection, it can also provide indications of the defected size and thus enable the monitoring of degradation rate of a damaged bearing [6]. Recently, AE n
Corresponding author. E-mail address: [email protected] (A.C.C. Tan).
http://dx.doi.org/10.1016/j.ymssp.2015.03.016 0888-3270/Crown Copyright & 2015 Published by Elsevier Ltd. All rights reserved.
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technique has been successfully employed for CM and fault detection of reciprocating machinery [8–11]. For instance, AE signals were used to identify the mechanical events such as valve movements, fuel injection and combustion in multicylinder diesel engines [8,12]. Nevertheless, the nonlinear frequency response of AE sensors remains a challenge in sensor calibration to provide a meaningful measurement. It also poses a problem in AE data analysis when multiple sensors are needed in a multi-cylinder diesel engine such as in Refs. [13–15]. Under such circumstances, extensive expert knowledge is needed to correctly interpret the information conveyed in the AE signals and the analysis of AE data can only be carried out in a qualitative manner. The drawbacks of AE technique often attract criticism from practitioners in the field which motivates the first half of the work presented in this paper. The accuracy of results obtained for direct comparison of AE signals from different (un-calibrated) sensors is always questionable since each AE sensor has the inherently unique nonlinear frequency response during the manufacturing process [16]. To overcome this problem, a simple signal processing technique is presented in this work where the nonlinear responses of AE sensors are normalized in the frequency domain based on the sensor calibration chart provided by the manufacturer. The signal processing approach normalizes the AE signals by linearizing their responses in the frequency domain. This process can be related to channel equalization in digital telecommunications. After this procedure, it not only enables the quantitative analysis of AE signals from different sensors but also enables a direct comparison of the signal amplitude in different frequency bands of a single AE sensor. The technique is thus particularly useful for source identification and separation of a complex system response where multiple AE events are present and several AE sensors are needed. AE root-mean-square (RMS) energy was successfully employed in the analysis of the AE signals for condition monitoring and fault detection of multi-cylinder diesel engines [10,17,18]. Comparing to raw AE data, AE RMS energy (termed as AEE in the later analysis) data is smaller in size and thus, requires less computer storage space and offers a faster data processing. Nevertheless, it was found that the AE signal produced by mechanical events of a cylinder of a small multi-cylinder diesel engine is often corrupted by signals generated from the adjacent cylinders due to the short time interval between sequential mechanical events and the small spatial distance between cylinders [18]. For instance, an AE sensor used to monitor AE events of a cylinder can also detect AE signals from the adjacent cylinders. The problem needs to be resolved for a better application of AE technique in condition monitoring of multi-cylinder diesel engines. To this end, a source separation algorithm is developed in the second half of this paper to minimize the signal interference of adjacent cylinders so that condition of a particular cylinder can be effectively monitored by an AE sensor mounted close to it. Blind source separation (BSS) algorithm is often employed to restore a set of hidden source signals from a set of observed signals. The word ‘blind’ implies that both source and the mixing process are unknown and only recordings of the mixtures are available [19]. However, it is impossible to uniquely estimate the original source signals without a prior knowledge of both sources and mixing process [20]. Furthermore, BSS algorithm also suffers from both scaling ambiguity and permutation indeterminacy after separation [21,22]. The drawbacks of BSS algorithm have thus far limited its application for CM and fault diagnosis of reciprocating machinery. The main challenges of applying BSS algorithms to AE signals of multi-cylinder diesel engines are three-folds: (1) the number and location of AE sources are undetermined during engine operation; (2) the propagation properties of AE waves along the engine structure are largely undetermined; and (3) the statistically independency of AE signals associated with different mechanical events of a diesel engine has not been studied. To overcome these challenges, a practical source separation algorithm analogically to the BSS process is presented in the second half of this paper to separate the mixture of AE signals from a multiple-cylinder diesel engine. Instead of restoring all the sources in the diesel engine, the proposed technique groups the sources within each cylinder as one source. Thus, the number of AE sensors required in a CM application equals to the number of cylinders, and if the condition changes or fault occurs in a particular cylinder it can be identified. A standard Pencil Lead Break (PLB) test is used to determine the parameters (i.e., the attenuation constant and arrival time delay) of AE wave propagation in the cylinder head required by the Source Separation (SS) algorithm. The layout for the rest of the paper is arranged as follows: Section 2 describes the diesel engine test rig and the experimental setup. Section 3 presents an elaboration of the signal normalization technique to normalize the AE data acquired from the diesel engine test rig. Effects of normalizing the AE signals and its implication on the signal analysis are also discussed in the section. A PLB test is conducted on the cylinder head of the diesel engine to determine the system parameters of AE wave propagation in Section 4. Section 5 describes the SS algorithm to separate the normalized AEE signals of the diesel engine for condition monitoring and engine fault detection. An error analysis is also presented in Section 5. The main findings of this study are summarized in Section 6. 2. A description of the diesel engine test rig An in-line four-cylinder diesel engine as shown in Fig. 1 was used in the experimental work presented in this paper. The engine generates a 15 kW of nominal power output at full load condition. The output shaft of the engine is coupled to an Olympian three-phase alternator. A three-phase, 15 kW industrial fan heater was connected to the generator to dissipate the power output of the diesel engine in the experiment. The fan heater has three heat settings, which can be adjusted for various engine loadings during the experiment. Four resonant-type, micro-30D AE sensors from Physical Acoustic Corporation (PAC) are mounted on the engine head close to each of the four cylinders to monitor the condition of the diesel engine as shown in Fig. 1. The AE signals are pre-
W. Wu et al. / Mechanical Systems and Signal Processing 64-65 (2015) 479–497
Cylinder4
Sensor 4
Cylinder 3
Sensor 3
Cylinder 2
Cylinder 1
Sensor 2
Sensor 1
481
Fig. 1. The four-cylinder diesel engine (Perkins 404C-22) and locations of the AE sensors used in the experimental study.
amplified by four matching PAC preamplifiers before being recorded by a National Instrument PXI data acquisition (DAQ) system. The DAQ system is capable of measuring up to 8 channels of data synchronously with 1 MHz sampling frequency. An optical TDC/encoder unit (attached onto the end of the crankshaft) is also used in the study to measure the TDC (top-deadcentre) of each cylinder during engine operation to enable the synchronization of AE signals with the engine mechanical events. Table 1 lists the specification and the static measurement of valve timing (in crank angles) of the diesel engine. It is note that the TDC in the table refers to the combustion TDC of each particular cylinder. 3. The AE signal normalization approach 3.1. Methodology As discussed earlier in Section 1, the signals measured by the four AE sensors from the diesel engine need to be normalized to overcome the nonlinear response of the sensors to enable a quantitative analysis in CM applications. A signal normalization technique is thus developed in this section. The original calibration charts (supplied by the manufacturer) of the four AE sensors are shown in Fig. 2. According to the manufacturer, each AE sensor was calibrated based on the surface wave calibration method developed by the US National Institute of Standards and Technology [23]. The dB values shown in the charts are based on the reference value of 1 V/mbar. The unique nonlinear characteristic of each AE sensor can be clearly observed in the calibration charts shown in Fig. 2. It is shown that the sensitivity of each AE sensor differs from one frequency to another frequency and drops substantially outside the designated resonant frequency band (0.1–0.35 MHz). The sensitivities of the sensors also differ from each other. This nonlinear property thus limits the quantitative analysis of AE signals measured by different sensors where results obtained by direct comparison of AE signals from different sensors are questionable. The calibration charts shown in Fig. 2 are digitized in this work to enable the signal normalization process of the AE data in digital domain. The calibration chart of each sensor was scanned and digitalized at a frequency interval of 0.01 MHz in the process based on the condition that variation of sensitivity value at the bounding frequencies (i.e., the lower and upper bound digital sampling lines) of each frequency band is less than 0.5 dB. The interval of the frequency band would be further refined in the digitizing process if the condition is not met. The average sensitivity of each frequency band (i.e., the average sensitivity value of the two bounding frequencies of the band) is used to represent the sensitivity of the band in the AE signal normalization process. The digitized calibration charts of the four AE sensors are shown and compared in Fig. 3. On the display, the original dB scale of the calibration charts was converted into the linear scale using A½
B ¼ 10
dB 20
V=μbar ;
ð1Þ
where B is the sensitivity of an AE sensor displayed in linear scale, A is the corresponding sensitivity displayed in dB scale with respect to the reference of 1 V/mbar. Once the sensitivity in each narrow frequency band of a sensor is determined, the measured raw AE signal from the sensor can be normalized and linearized by the normalization process described in Fig. 4. Four simple steps are required to transform a nonlinear raw AE signal (sðnÞ) to a normalized, linear AE signal (sðnÞ). In Step 1, a time domain raw AE data is transformed into the frequency domain (sðkÞ) using Fast Fourier Transform (FFT). This is followed by the bandpass filtering process in the frequency domain. In this study only the AE response within the designated working frequency band of an AE sensor is considered. A rectangular window (i.e., a window that has the value of 1 within the frequency band between 0.1 MHz and 0.35 MHz, and 0 outside this band) is chosen and applied to the
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Table 1 Perkins 404C-22 diesel engine specifications. Number of cylinders Arrangement Running speed Bore Stroke Displacement Compression ratio Firing order Injection Timing Default valve lash setting Exhaust valve—open Exhaust valve—close Inlet valve—open Inlet valve—close
4 In-line 1500 rpm 84.0 mm 100.0 mm 2.216 l 23.3:1 1-3-4-2 151 ( 7 11) before TDC 0.20 mm 1431 after TDC 3701 after TDC 3541 after TDC 5841 after TDC
Fig. 2. The calibration charts of the four AE sensors used to monitor the test engine (permission granted by PAC).
frequency spectrum to bandpass the AE signal in Step 2. Note that, multiplying a rectangular window filter in the frequency domain is equivalent to convolute its impulse response in the time domain [24]. The impulse response of a rectangular bandpass filter which has the cut-off frequency at f 1 and f 2 with the sampling frequency of f s is given by Eq. (2). hBP ðr Þ ¼
sin ðωc2 rÞ sin ðωc1 rÞ ; πr
where
ωc1 ¼
2π f 1 fs
and
ωc2 ¼
2π f 2 fs
1 or o 1
ð2Þ
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483
Fig. 3. Digitized calibration charts of the four AE sensors.
Fig. 4. Graphical description of the signal normalization process.
The use of rectangular bandpass filter in Step 2 is due to the consideration that a flat response of the window will not lead to any amplitude and phase distortion within the working frequency band. Nevertheless, it is worth noting that the flat rectangular bandpass filter is unrealizable in practical FIR filter design for real-time signal processing due to the infinite numbers of coefficients ðrÞ required to represent a rectangular window bandpass filter [25]. A time domain Hanning or Hamming window may be employed in real-time signal processing to overcome this limitation. However, these time domain windows do not provide a sharp cut-off as the rectangular window for the desired frequency band, and thus can cause amplitude distortion due to the trailing edges of the window and side lobes effects. 2 In Step 3, the bandpass filtered frequency spectrum of the AE signal ðs ðkÞÞ is normalized in each narrow frequency band by dividing the corresponding value in the digitized calibration chart of the sensor shown in Fig. 3 to obtain the normalized spectrum ðsðkÞÞ. An equalizer is the inverse filter response of the channel [26]. Therefore, Step 3 can be treated as channel equalization. After this, the dispersion effect of each AE sensor can be compensated. The final step of the normalization process is to inverse the normalized frequency response, sðkÞ, back to the time domain signal using inverse Fast Fourier transform (IFFT) to have the filtered and normalized time domain AE waveform, sðnÞ.
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Fig. 5. The signal normalization of an un-calibrated nonlinear AE signal: (a) original signal, (b) original frequency spectrum, (c) bandpassed frequency spectrum, (d) the time waveform of the bandpassed spectrum, (e) normalized frequency spectrum, and (f) normalized signal.
To better illustrate each step of the normalization process and its effect on the signal, the technique is applied to the raw AE data measured by Sensor 1 at the unload condition as shown in Fig. 5. The corresponding un-calibrated AE signal can be found by the solid blue line in Fig. 3. The major AE peaks shown in the raw AE signal (Fig. 5(a)) can be correlated to the major mechanical events of the diesel engine (i.e., combustion, valve opening and closing) as shown in [27]. Fig. 5(b) is the frequency spectrum of the time waveform shown in Fig. 5(a) and is calculated by means of FFT. Fig. 5(c) shows the bandpass spectrum of Fig. 5(b), and Fig. 5(e) is the normalized frequency spectrum that is calculated by dividing Fig. 5(c) to the digitized calibration chart given by Fig. 3. It clearly shows the change in the shape of the spectrum. Furthermore, the measured AE signal has also been converted to true physical quantity (mbar) representing the surface pressure in Fig. 5(e). The time waveforms of the bandpass signal and the normalized AE signals are shown in Fig. 5(d) and (f), respectively. These two time waveforms are similar to Fig. 5(a), but sharper in the transient response due to the removal of low frequency content in the bandpass process. The benefits of the signal normalization technique developed in this paper are two-folds: (1) it overcomes the inherent nonlinear response problem of AE sensors, and (2) it normalizes the AE response to enable a direct comparison as well as quantitatively analysis of AE signals measured by different sensors in both time and frequency domains. Furthermore, the AE signals after normalization can be displayed directly in the true physical unit rather than in arbitrary units or signal voltage as in the existing literatures [6,7,9–12,14,18]. The AE response of a system in different frequency bands can also be analysed quantitatively in the frequency domain after normalization. Therefore, only normalized AE data is analysed and discussed in the subsequent text of this paper.
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3.2. Application to diesel engine AE signals A typical application of the signal normalization technique is the comparison of signals measured by different AE sensors for condition monitoring of diesel engines. For a better clarification of displaying multiple AE signals in a single figure for comparison, AEE rather than the raw AE signals are used in the subsequent analysis. For a given raw AE signal, the corresponding AEE data is calculated by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn ¼ Nw þ ðm 1Þτ 2 Lr AEEðmÞ ¼ x ðnÞ; 1 r m r int ð3Þ ; 1 r n r Lr n ¼ ð m 1 Þ τ þ 1 Nw τ where x is the discrete time domain AE data, n is the index number of the raw data, N w is the moving window size used in the conversion, m is the sequential index of the moving window, Lr is the length of the original raw data, τ ¼ ð1 RÞ Nw is the number of non-overlapping data in the data integration, and R is the percentage of window overlapping. Note that, N w ¼ 100 and 80% data overlapping were used in the AEE conversion to ensure a smooth data transition and a good time resolution. Fig. 6 compares the AEE data from the four AE sensors shown in Fig. 1 measured when the engine was operated at the unload condition. The acronyms shown in Fig. 6, i.e., COMB, IVC, EVC represent combustion, inlet valve closing and exhaust valve closing of the diesel engine, respectively. The numerical index following these abbreviations refers to the cylinder where these mechanical events occur. Clear energy attenuation trend can be observed for AE sources originated from Cylinders 1 and 4, i.e., COMB1, IVC1 and IVC4 as shown in Fig. 6(b)–(d). For instance, Sensor 1 records the highest AE energy for the COMB1 event. This is followed by Sensors 2, 3 and 4. For these mechanical events, the signal energy decays proportionally to the distance along the propagation path away from the source cylinder. This type of AE sources can be easily identified by the observation of energy attenuation recorded by different sensors at different locations. On the other hand, the energy attenuation trend is not so obvious for AE sources originated from Cylinders 2 and 3 such as IVC2 and IVC3 (see Fig. 6(a) and (c)). For instance, Sensor 1 and Sensor 3 recorded higher or similar energy than Sensor 2 for the IVC2 event. Therefore, for sources originated from these two cylinders, source identification using direct energy attenuation analysis may not be suitable. The higher or similar signal energy recorded by sensors away from a source cylinder is due to the signal interference from the neighbouring cylinders and the reflecting boundaries of the small diesel engine. This will be examined further in a Pencil Lead Break (PLB) test conducted on the cylinder head of the diesel engine in the next section. 4. PLB test and system parameters determination In this section, a PLB test is conducted on the cylinder head of the diesel engine to better understand the characteristics of AE wave propagation on the complex engine head to provide an explanation of the interesting energy attenuation patterns of AE events shown in Fig. 6. The PLB test is also used to determine the AE wave propagation parameters of the engine head to be used in the source separation algorithm of next section. A schematic drawing of the valve positions on the cylinder head and the mounting positions of the four AE sensors (shown as S1, S2, S3 and S4) is shown in Fig. 7. Also shown in Fig. 7 is the schematic illustration of the direct wave propagation paths from the inlet valve of Cylinders 1 and 2 to the four AE sensors, and an illustration of how the boundary wave reflection affects the signals detected by Sensor 1. The PLB test was performed at the ten marked locations in sequence on each cylinder as shown in Fig. 8. The locations were chosen such that they are good representations of the source locations of combustion, valve closing and opening events during engine operation. The raw AE signals measured by the four sensors are normalized using the procedure described in Section 3. The normalized responses are converted into AEE data using Eq. (3) and averaged over the ten PLB test locations on each cylinder for comparison. The averaged AEE responses of the four sensors from the PLB test at each cylinder are shown and compared in Fig. 9. The AEE response of the sensor closest to the PLB source is plotted by thicker line in the figure. For simplicities, the sensor mounted next to the “source cylinder” is termed as the “source sensor” and the signal of the source sensor is termed as the “reference signal” in the following analysis. The other three sensors are termed as the “adjacent sensors” and the signals of these sensors are termed as the “adjacent signals”. It is shown in Fig. 9 that when the source occurs at Cylinder 1, the AEE amplitude of Sensor 1 is the largest. This is followed sequentially by Sensors 2, 3 and 4 (Fig. 9(a)). Similar observation can also be found for AE sources originated from Cylinder 4 (Fig. 9(d)). This observation agrees well with the wave propagation characteristics for sources originated from these two cylinders during engine operation where signal energy detected by the sensors depends on the distance between the sensors and the source. The result confirms that wave propagation of AE sources from these two cylinders is less affected by wave reflection and refraction at the boundaries for both dynamic and static tests as the two cylinders are the outer cylinders in the engine configuration (see Fig. 7). Similar to that in the dynamic case (engine running), no clear attenuation trend is observed for sources originated from the two inner cylinders (Cylinders 2 and 3) in the PLB test where adjacent signals can have higher or similar amplitude than the source signal (see Fig. 9(b) and (c)). This phenomenon is caused by the sensor proximity of the small test engine and the strong interference from the boundary wave reflection and refraction.
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Fig. 6. Comparison of the normalized AE data from the diesel engine at unload condition measured synchronously by four AE sensors and enlarged view of the combustion areas, (a) 0–901, (b) 180–2701, (c) 360–4501 and (d) 540-6301
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Fig. 7. Schematic drawing of the engine cylinder block and the sensor locations.
Fig. 8. Locations of PLB test at each cylinder head.
Due to the close similarities of AE wave propagation in both dynamic and static cases, it is reasonable to assume that the wave propagation constant and time delays obtained from the PLB test can be used to describe the parameters of wave propagation of AE sources generated by mechanical events of the diesel engine during operation. To calculate the attenuation constant and the Arrival Time Delay (ATD) of an AE wave after emitting from a source, the amplitude relationship between the AE signals at two different locations away from a source in an infinite medium given by Nivesrangsan et al. [14] is re-visited here as Ai ðtÞ ¼ αij Aj ðtÞ;
ð4Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ηðr i r j Þ is the attenuation where Ai ðtÞ and Aj ðtÞ are the amplitude of the continuous AE signals 1 at locations i and j, αij ¼ e constant from location j to i, η is the wave attenuation factor m , ri and rj are the distance away from the source for location i and j. Eq. (4) can be re-written in digital form, and to incorporate the Arrival Time Delay (ATD) between two discrete AE signals measured at two sensor locations as Ai ðnÞ ¼ αij Aj ðn ΔnÞ;
1 r n r L;
ð5Þ
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Fig. 9. Averaged AEE responses of the PLB test at each cylinder; (a) Cylinder 1; (b) Cylinder 2; (c) Cylinder 3; and (d) Cylinder 4.
where n is the data index of a discrete AE signal of length L, Δn ¼ Δt=T is the data sample difference corresponding to the arrival time difference Δt between the two sensor locations. T ¼ 1=f s is the sampling interval. An analogy equation to Eq. (5) can also be written to describe the relationship between the AEE data at two sensor locations as Ei ðmÞ ¼ αij Ej ðm βij Þ;
ð6Þ
where Ei ðmÞ and Ej ðmÞ are the digitised AEE data corresponding to Ai and Aj , m is the data index, β ij ¼ intðΔn=τÞ represents the ATD between the two sensor locations. Eq. (6) can be used to determine the relationship between the source signal and any adjacent signals from the PLB test (see Fig. 9). A least squares (LS) algorithm is further employed to optimize the results of attenuation constant ðαij Þ and ATD ðβij Þ calculated from Eq. (6) to describe the relationship of any two AEE data: 2 Xm ¼ L Ei ðmÞ αij Ej m βij ; 1 r m r L; ð7Þ LS ¼ m¼1 where Ej is the reference AEE data and Ei is the AEE data from one of the adjacent sensors. Fig. 10 shows an example of the optimisation process in determining the two wave propagation parameters between the reference AEE data of Sensor 1 and the adjacent AEE data of Sensor 2 shown in Fig. 9(a). The saddle point in the figure represents the optimised parameters (i.e.,α21 ¼ 0:64 and β21 ¼ 2) that can lead to minimum estimation error. The process is repeated for all the AEE responses obtained from the PLB test on the four cylinders. A 4 4 attenuation constant matrix and a 4 4 ATD matrix can then be obtained for the test engine as 2 3 1 1 0:63 0:28 6 0:64 1 0:81 0:41 7 7 α¼6 ð8aÞ 6 7; 4 0:44 0:95 1 0:66 5 0:29
0:62
0:94
1
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Fig. 10. 3D plot of evaluating the optimized attenuation and ATD parameters.
and 2
0 6 2 6 β¼6 4 5 13
2
6
0
1
0 5
0 1
11
3
7 7 7 7; 2 5
ð8bÞ
0
where each element αij , in α represents the attenuation constant from source sensor j to adjacent sensor i, each element βij in β represents the ATD from Sensor j to Sensor i. For instance, the first column of α display the attenuation constants of the estimated adjacent signals of Sensors 2, 3 and 4 using the reference signal of Sensor 1 are 0.64, 0.44 and 0.29, respectively. It is shown in Eqs. (8a) and (8b) that both attenuation and ATD matrices are slightly asymmetric caused by noise interference and experimental errors in the experiment. The parameters, αij and βij from Eqs. (8a) and (8b) are substituted back into Eq. (6) to estimate each of the adjacent signal (E~ ijj ) using the reference signal (Ej ), which is then compared to the measured adjacent signal (Ei ) to evaluate the errors of this parameter estimation. The percentage of squared error between the estimated and measured signals of each adjacent sensor i using the reference signal of source sensor j is calculated by: 2 P Ei E~ ijj εij ¼ 100 0=0 ; ð9Þ P 2 Ei which then yields a 4 4 estimation error matrix 2 3 0 1:82 5:28 14:16 6 2:19 0 2:08 4:90 7 7 ε¼6 6 7: 4 3:73 2:54 0 2:23 5 11:14
7:64
4:01
ð10Þ
0
It is shown that the estimation error increases monotonously as the distance between the adjacent sensor and the source increases. For example, the estimation errors of the adjacent signals (Sensors 2, 3 and 4) using the reference signal from Sensor 1 are 2.19%, 3.73% and 11.14%, respectively. The maximum estimation error shown in the error matrix is 14.16%. Inherited from the errors presented in the attenuation and ATD matrices, the error matrix given here is also slightly asymmetric. Fig. 11 compares the measured and the estimated signals of the three adjacent sensors for the PLB test on Cylinder 1. It is shown that the estimated AEE responses match well with the measured AEE responses of Sensors 2 and 3 not only along the rising edge but also on the falling edge (see Fig. 11(a) and (b)). A larger error is induced between the estimated and the measured AEE responses of Sensor 4 as shown in Fig. 11(c). Results shown in Fig. 11 agree with the values in the first column of the error matrix where the estimation error increases as the distance between the sensor location and the source increases. Fig. 11 also confirms that the adjacent signals on an engine head can be estimated with a small error once the reference signal and wave propagation parameters are known. 5. A source separation technique for diesel engine CM signals Results obtained from the dynamic and static tests of the diesel engine in Sections 3 and 4 showed that sources from adjacent cylinders can have strong signal interference to the AE signals of a monitored cylinder, particularly for the two inner cylinders. To overcome this problem, a Source Separation (SS) algorithm is presented in this section. The algorithm
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Fig. 11. Comparison of the measured and estimated AEE responses from the PLB test at Cylinder 1, (a) Sensor 2, (b) Sensor 3, and (c) Sensor 4.
differs from the conventional BSS algorithm by utilizing the pre-determined AE wave propagation properties of the diesel engine to minimize the reconstituted error in the source separation. As shown in Fig. 6, the EVC event of a cylinder occurs in the combustion region of another cylinder and thus causing substantial interference of the signal produced by the COMB events. Therefore, the resultant AEE data from the four sensors are mixture of the reference signal from the monitored cylinder and the adjacent signals from the neighbouring cylinders. If the interference can be separated, the mechanical events of each cylinder can be monitored independently by a single AE sensor. The separation process can be difficult without a prior knowledge of the mixing process and the statistical independent of the sources when sources from multiple cylinders are present simultaneously in a signal. Torkkola [28] presented a BSS algorithm by assuming that the outputs are mixtures of convoluted independent sources and no noise is present. The adaptive algorithm for updating the filter coefficients described in Ref. [28] can be simplified by utilising the pre-determined system parameters. This is indeed the case for the SS algorithm presented in this study where the attenuation constant and ATD from the PLB test are employed. Therefore, the algorithm is no longer ‘blind’ where the convolution process is simplified to a pure attenuation and delay process with no noise present. Fig. 12 depicts the flow chart of the source separation process developed in this work. Based on the AEE conversion algorithm given by Eq. (3), the engine specification and the valve timing given in Table 1 and the sampling frequency (1 MHz) used in AE data acquisition, it requires at least 100 AEE data points in a data segment (corresponding to 20 CA degrees) to fully embrace two mechanical events. Therefore, the resultant AEE data matrix, U, is divided into N segmental matrices with a fix data length of 100 in Step I of the SS process. Assuming that the data in any two rows of the segmental AEE matrix, Un , are generated by two AE sources in Cylinders i and j, the data of each row can be described by Uni ðmÞ ¼ aii Si ðm βii Þ þaij Sj ðm βij Þ;
1 r m r 100;
1 r ir 4;
1 r jr 4; ia j
ð11Þ
Unj ðmÞ ¼ aji Si ðm βji Þ þajj Sj ðm βjj Þ;
1 r m r 100;
1 r ir 4;
1 r jr 4;
ð12Þ
j ai
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Start
Step I: Divide the AEE data U into N segmental matrix, Un, 1 ≤
≤
Unew = empty matrix of size U
= 1
False
<
Exit Return Unew
True Step II: Perform Source Separation for the nth segment of AEE data, Un
=
+ 1
Fig. 12. Flow chart of the source separation (SS) algorithm.
where Uni and Unj represent the row i and j in Un (i.e., AEE data from Sensors i and j), Si and Sj are the reference AEE data from row i and j to represent the intrinsic AE sources in Cylinders i and j. The coefficients aii and αjj are the diagonal terms, αij and αji are the off-diagonal terms in the attenuation matrix α. βii , βjj , βij and βji are the diagonal and off-diagonal terms of the ATD matrix, β. The complex convolutive mixing process in time domain can be solved by converting it into instantaneous mixing process in frequency domain in Step II of the SS process given by the flowchart in Fig. 13. The time domain data described by Eqs. (11) and (12) are transformed into the frequency domain by means of Fast Fourier Transform (FFT) as Uni ðkÞ ¼ aii Si ðkÞe
j0 2π mkβii 100
j0 2π mkβji
þaij Sj ðkÞe
j0 2π mkβij 100
;
ð13Þ
j0 2π mkβjj
Unj ðkÞ ¼ aji Si ðkÞe 100 þajj Sj ðkÞe 100 pffiffiffiffiffiffiffiffi where j0 ¼ 1 represents the imaginary number. Given both α and β and from Eqs. (13) and (14), the frequency domain reference AEE data can be obtained by
ð14Þ
Si ðkÞ ¼ ðwii Uni ðkÞ þwij Unj ðkÞÞ=GðkÞ;
1 rk r 100;
1 r ir 4;
1 r jr 4;
ia j
ð15Þ
Sj ðkÞ ¼ ðwji Uni ðkÞ þwjj Unj ðkÞÞ=GðkÞ;
1 rk r 100;
1 r ir 4;
1 r jr 4;
ja i
ð16Þ
j0 2π mkðβ þ β Þ 1 j0 2π mkβ j0 2π mkβ ij ji ij ji , wji ¼ αji exp . The time, wii ¼ wjj ¼ 1, wij ¼ αij exp where GðkÞ ¼ 1 aij aji exp 100 100 100 domain reference AEE data can also be obtained by inverting Si ðkÞ and Sj ðkÞusing inverse FFT (IFFT). Because the SS algorithm developed here does not have the capacity to provide the exact source information in each AEE data segment, a trial and error strategy is then adopted to derive this information from the resultant AEE data, U. Based on the chosen data length and from Fig. 6, we can assume that there are maximum two mechanical events in each data segment,Un , whose source can be from either one or two cylinders. Therefore, there are ten possible combinations of the source cylinders for the resultant AEE data which are listed in Table 2. At each data segment, the algorithm evaluates the constituted error of all ten possible combinations. It then solves for the ~ based on the following two assumptions: reference AEE signal(s) and estimates the four channels of new AEE data, U, (1) If the conditional statement i ¼ j in Fig. 13 is true, the source is considered to be from one cylinder. The AEE data ðUni Þ from the corresponding sensor is then used as the reference AEE ðSi Þ to estimate the other three adjacent AEE data using ~ the parameter matrices α and β to estimate the reconstituted AEE data, U.
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Fig. 13. Flow chart for the detailed SS algorithm. Table 2 Possible source cylinder combinations of a resultant AEE data segment. Single cylinder
Two cylinders
Cylinder Cylinder Cylinder Cylinder
Cylinder Cylinder Cylinder Cylinder Cylinder Cylinder
1 2 3 4
1&2 1&3 1&4 2&3 2&4 3&4
and and and and and and
Cylinder Cylinder Cylinder Cylinder Cylinder Cylinder
2&1 3&1 4&1 3&2 4&2 4&3
(2) If the conditional statement i ¼ j is false, the sources are considered to be from two of the cylinders. The resultant AEE data (Uni ,Unj ) from the two corresponding source sensors are used in Eqs. (11) and (12) to calculate the reference AEE data (Si ,Sj ). This is then used to solve for the frequency domain reference AEE (Si ðkÞ, Sj ðkÞ) using Eqs. (15) and (16). Each ~ i and U ~ j . The final reconstituted AEE data, U, ~ in this case are reference AEE is used to calculate the estimated AEE data, U the sum of the two estimated data. ~ is used to calculate the percentage of squared error matrix ε' from the The newly obtained reconstituted AEE data, U original AEE data, Un : 2 P4 P100 n ~ i ðmÞ Ui ðmÞ U i ¼ 1 m ¼ 1 ε0 ¼ 100ð%Þ; 1 r i r4 ð17Þ 2 P4 P100 n i¼1 m ¼ 1 Ui ðmÞ
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From this calculation, a symmetric matrix ε0 of size 4 4 can be obtained for each set of data segment, Un . An example of the error matrix for a given AEE data segment is given below: 2 3 15:63 45:79 15:42 6:53 6 45:79 15:32 65:19 20:67 7 7 ε0 ¼ 6 ð18Þ 6 7 4 15:42 65:19 48:54 89:68 5 6:53
20:67
89:68
170:24
Each element, ε0ij , in ε0 represents the estimation error by assuming that the sources are from Cylinders i and j. The offdiagonal terms are equal in pairs, such that ε0ij ¼ ε0ji . This is due to the assumption that sources from Cylinders i and j can be considered as the same for sources from Cylinders j and i. In Step III, the algorithm chooses one out of the ten possible source combinations leading to the minimum reconstituted error to identify the source cylinder(s) in each AEE data segment. A new reference AEE data segment Unnew is returned after knowing the correct combination. The SS algorithm stops and returns a separated AEE data matrix, Unew , after completing N iterations. 5.1. Separation of the diesel engine CM data The SS algorithm developed in the previous section is applied to separate the four channels of AEE data shown in Fig. 6. The separation result is presented in Fig. 14. It is shown that the reference AEE signal(s) from the mechanical event(s) of the source cylinder(s) are successfully separated from the adjacent AEE signals after applying the SS algorithm. For example, Fig. 14(a) clearly shows the reference AEE signal of EVC1 at 101 CA recorded by Sensor 1, and the COMB4 signal of Cylinder 4 starts from about 21 to 401 CA recorded by Sensor 4. More significantly, the sources originated from Cylinders 2 and 3 are also separated successfully by the algorithm, for instance, the signal from IVC2 at about 411 CA recorded by Sensor 2 (Fig. 14(a)), the signal from IVC3 at 4021 CA recorded by Sensor 3 (see Fig. 14(c)). The source separation result also clearly indicates a maximum surface pressure produced by different mechanical events of the engine, e.g., 80 mbar by EVC1, 45 mbar by COMB4 and 70 mbar by IVC2. It should be noted that the algorithm did not work as well in separating sources from the two inner cylinders (Cylinders 2 and 3) when the mechanical events of these two cylinders co-existed in the same data segment (see Fig. 14(b) and (d)). This is due to the small spatial distance between these two cylinders of the small test engine causing the AEE signals generated by the two cylinders to be seriously overlapped. For example, it is shown in Fig. 14(b) that the AEE energy of EVC3 overlaps with the AE signal of COMB2 (between 190 and 2001 CA), and has a larger amplitude. The algorithm then misinterprets that the AEE signal is generated by the EVC3 event only causing the incorrect separation of the resultant AEE signal. 5.2. Error analysis An error analysis is presented in this section to evaluate the effectiveness and error tolerance of the SS algorithm developed in this work. It is shown in the previous analysis that errors can be induced in estimating the system parameters of the engine though it is not known how such estimation error affects the accuracy and effectiveness of the SS technique in separating the mixture of AE signals. Incorrect estimation of the engine system parameters may lead to poor separation results. Therefore, the error tolerance of the algorithm needs to be examined. A 10% error and 1 step delay error are assumed for the off-diagonal elements in the attenuation constant (α), and ATD (β) matrices obtained from the PLB test in the following analysis as: 2 3 1 0:9 0:69 0:31 6 0:58 1 0:73 0:41 7 7 α0 ¼ 6 ð19aÞ 6 7; 4 0:48 0:86 1 0:73 5 0:32
0:56
0:85
1
and 2
10
3
0 6 1 β0 ¼ 6 6 4 4
2
4
0
0
1
0
9 7 7 7: 3 5
12
4
1
0
ð19bÞ
The new system parameters are then used in the SS algorithm, and the result is shown in Fig. 15. Comparing Fig. 15 with Fig. 14, it is found that small errors (say, 10%) in the system parameter estimation will not have a much effect on the accuracy of the source separation. To evaluate this further, the error for the off-diagonal elements of the attenuation matrix (α) is increased to 20% as shown in Eq. (20) and the time delay error is kept to be the same as in the last case. These system parameters are used in the SS algorithm and the result is shown in Fig. 16. It is shown that the algorithm failed to accurately separate the sources from a mixture of cylinders. For example, the IVC2 (40–501 CA) is incorrectly separated as the
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Fig. 14. Comparison of the normalized AEE data from the diesel engine at normal and unload condition after separation and the enlarged views for the combustion regions: (a) 0–901, (b) 180–2701, (c) 360–4501, and (d) 540–6301.
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Fig. 15. The separated AEE data of unload condition with 10% error and 1 step delay error in attenuation and ATD, respectively and enlarged view for combustion regions: (a) 0–901, and (b) 180–2701.
combination of mechanical events in Cylinders 1 and 4 while IVC3 (400–4101 CA) is incorrectly separated as the combination of mechanical events in Cylinders 1 and 4 instead of mechanical events from Cylinders 2 & 3. 2 3 1 0:8 0:5 0:22 6 0:77 1 0:65 0:36 7 7 α″ ¼ 6 ð20Þ 6 7; 4 0:53 0:76 1 0:79 5 0:23
0:5
0:75
1
6. Concluding remarks A signal normalization and source separation technique is presented in this paper to normalize the nonlinear response problem of AE sensors, and to separate the sources detected by multiple AE sensors for condition monitoring applications of diesel engines. A four-step signal normalization approach was outlined in the paper to process the un-calibrated nonlinear AE signals based on the sensor calibration chart. The technique is easy to implement in practical AE signal analysis. It was employed in this study to normalize the CM data measured by four AE sensors on a diesel engine so that the measured responses by the sensors can be compared directly for a quantitative analysis. It was shown in the study that AE signals originated from the
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Fig. 16. The separated AEE data of unload condition with 20% error and 1 step delay error in attenuation and ATD, respectively and enlarged view for combustion regions (a) 0–901, and (b) 360–4501.
outer cylinders of the in-line four-cylinder diesel engine demonstrate a clear energy attenuation pattern. For such sources, the AE energy measured by a sensor is proportional to the distance between the sensor and the source cylinder. On the contrary, the energy decaying trend of the AE signals originated from the two inner cylinders of the four-cylinder engine is not so obvious due to the strong interference from the boundary wave reflection and refraction of the small engine block. A source separation technique was developed to overcome this problem so that the operation condition of an engine cylinder of a multi-cylinder diesel engine can be monitored effectively by an AE sensor mounted close to it. A standard PLB test was conducted on the cylinder head of the engine to determine the attenuation constant and the ATD for various AE wave propagation paths (the propagation paths from each cylinder to each sensor) required in the source separation. It is noted that the property of AE attenuation pattern of the PLB test at each cylinder follows the same pattern as that of the source generated by the mechanical events of each cylinder. This implies that the AE wave attenuation and ATD determined by the static PLB test can be utilized to determine the interferences to adjacent sensors once the reference signal produced by the mechanical events is known. It was shown that the source separation process improves the source identification ability by reducing/eliminating the interferences from adjacent cylinders. Therefore, each cylinder of a diesel engine can be monitored separately. Furthermore, combining with the normalization process of the AE signals, the valve activities and combustion process of each cylinder can be quantitatively monitored.
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Acknowledgments This paper was developed within the CRC for Infrastructure and Engineering Asset Management, established and supported under the Australian Government’s Cooperative Research Centres Programme. The authors gratefully acknowledge the financial support provided by the CRC. Financial supports from ASC Pty Ltd., the CRC’s industry sponsor for the purchase of the diesel engine test rig used in this research is also acknowledged. References [1] J. Kaiser, An Investigation into the Occurrence of Noises in Tensile Tests, or a Study of Acoustic Phenomena in Tensile tests, Tech. Hochsch. Munchen, Munich, Germany, 1950 Ph.D. Thesis. [2] A. Carpinteri, G. Lacidogna, N. Pugno, Structural damage diagnosis and life-time assessment by acoustic emission monitoring, Eng. Fract. Mech. 74 (1) (2007) 273–289. [3] T. Chotard, et al., Application of the acoustic emission technique to characterise liquid transfer in a porous ceramic during drying, J. Eur. Ceram. Soc. 26 (7) (2006) 1075–1084. 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