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Multivariate statistical analysis strategy for multiple misfire detection in internal combustion engines
Mechanical Systems and Signal Processing 25 (2011) 694–703
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/jnlabr/ymssp
Multivariate statistical analysis strategy for multiple misfire detection in internal combustion engines Chongqing Hu n, Aihua Li, Xingyang Zhao Xi’an Research Institute of Hi-Tech, Xi’an 710025, China
a r t i c l e i n f o
abstract
Article history: Received 19 July 2009 Received in revised form 23 March 2010 Accepted 27 August 2010 Available online 15 September 2010
This paper proposes a multivariate statistical analysis approach to processing the instantaneous engine speed signal for the purpose of locating multiple misfire events in internal combustion engines. The state of each cylinder is described with a characteristic vector extracted from the instantaneous engine speed signal following a three-step procedure. These characteristic vectors are considered as the values of various procedure parameters of an engine cycle. Therefore, determination of occurrence of misfire events and identification of misfiring cylinders can be accomplished by a principal component analysis (PCA) based pattern recognition methodology. The proposed algorithm can be implemented easily in practice because the threshold can be defined adaptively without the information of operating conditions. Besides, the effect of torsional vibration on the engine speed waveform is interpreted as the presence of super powerful cylinder, which is also isolated by the algorithm. The misfiring cylinder and the super powerful cylinder are often adjacent in the firing sequence, thus missing detections and false alarms can be avoided effectively by checking the relationship between the cylinders. Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.
Keywords: Internal combustion engine Speed fluctuation Multiple misfire detection Principal component analysis
1. Introduction Inspired by the on-board diagnostic (OBD) regulation, numerous successful approaches have been developed for engine misfire detection and faulty cylinder identification [1–5]. Since the instantaneous engine speed can be measured by the engine control system, the simplest and most cost-effective approach is to evaluate the engine speed fluctuation. This approach has been commonly used in engine mass production [6], but it is still difficult to detect multiple misfire events, especially under critical working conditions (at high speed and low loads). The misfire event can be detected by evaluating the engine speed waveform, which has been changed due to the lack of positive torque during the expansion stroke of the misfiring cylinder. The features of speed waveform extracted in time-domain [7], frequency-domain [8], or time–frequency-domain [9,10], are effective to identify misfiring cylinders when the engine is running at low-to-middle speed range. However, at high speed, the feature of misfire events may be masked by the following effects: the negligible drop of engine speed due to the misfire event, the low signal-to-noise ratio (SNR) of measured signal and the interference of torsional vibrations [11]. Another popular approach to misfire detection aims to estimate the indicated torque or in-cylinder pressure with a dynamic crankshaft model [12–15]. Although this method provides sufficient information about the engine combustion conditions, it is time-consuming and requires an accurate dynamic model. It would be more efficient to evaluate the n
Corresponding author. E-mail address: [email protected] (C. Hu).
0888-3270/$ - see front matter Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2010.08.010
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crankshaft kinetic energy variation caused by the combustions with the time periods, which are spent on the rotation of predefined angular sectors [16–18]. To distinguish misfire events from compression faults, two energy indices were extracted from an energy model of crankshaft [19]. However, the effect of torsional vibrations cannot be taken into account in these methods, because the crankshaft is often assumed to be a rigid body. Regarding multiple misfires, the engine speed oscillation induced by the first misfire event may still be present when the second misfire occurs, which makes the engine speed waveform more complicated. Hence, the location of multiple misfires is more difficult than that of single misfire event. To compensate the effect of torsional vibrations, different methods have been developed [20,21]. However, these methods require calculating and saving characteristic waveforms for various misfire patterns. Moreover, predefined threshold values are often indispensable to the identification of misfiring cylinders [8,16,20,21]; thus additional experiments should be carried out in advance. In this paper, misfire detection is implemented by processing the instantaneous engine speed with a multivariate statistical analysis algorithm. The state of each cylinder is described by the whole variation process of instantaneous engine speed during the corresponding expansion stroke, rather than some absolute values at particular positions. Thus, the threshold definition can be accomplished without the knowledge of engine speed and external loads. And the effect of torsional vibration can be interpreted as the presence of super powerful cylinders, which is useful to the location of misfiring cylinders. 2. Preprocessing of instantaneous engine speed The preprocessing procedure of instantaneous engine speed involves three steps: resampling, filtering and partitioning. 2.1. Resampling Normally, the instantaneous engine speed of an internal combustion (IC) engine is obtained by measuring the elapsed time between consecutive pulses, which are generated by the flywheel gear or other teethed disk mounted on the crankshaft and a simple inductive or Hall-effect transducer. The number of the teeth on the gear determines the number of samples of an engine cycle. If the gear has M teeth, the angle interval is 2p/M or the sampling interval is 360/M1, and the length of speed series for each engine cycle may be M (2-stroke engine) or 2M (4-stroke engine). The instantaneous engine speed at the center of each sampling interval is 60/MDT rpm, where DT is the time (in seconds) elapsed between two consecutive tooth edges. Thus, the instantaneous engine speed is the average velocity over its sampling interval, and the crankshaft can be supposed to rotate at constant velocity within each sampling interval. In each engine cycle, the cylinders dominate the output torque alternatively. For a N-cylinder, 4-stroke engine, cylinder i dominates the output torque in the crank angle interval (TDCi,TDCi +4p/N], where TDCi is the top dead center of cylinder i. Because the working capability of cylinder i can be described by the varying process of engine speed in (TDCi,TDCi + 4p/N], faulty cylinders can be isolated by comparing the trends of engine speed in these crank angle intervals. However, this requires that the instantaneous engine speed series in the N intervals have the same length, and their sampling position to the corresponding top dead center also be identical. So 2M should be an integral multiple of N. If this requirement is not satisfied, the engine speed can be resampled to modify the length of engine speed series using the following method. The rational length 2L is a multiple of N and closest to 2M. Fig. 1(a) shows the resampling strategy for the case L4M, while Fig. 2(b) is for the case LoM. In either case, the resampled speed is the average of the measured speed in the resampling
Fig. 1. Resampling strategy for the measured instantaneous engine speed: (a) L4M; (b) Lo M.
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crank angle interval. Also, the resampled speed is treated as the instantaneous engine speed at the center of the resampling crank angle interval. When the resampling is carried out, the speed waveform should not be changed. Since it is impossible to measure the instantaneous engine speed at the same crankshaft position with different sampling intervals simultaneously, the feasibility of the resampling strategy is proved by simulation results. Ideally, the instantaneous engine speed of an IC engine can be approximated by a sinusoidal function. The following equation describes the instantaneous engine speed of a 6-cylinder, 4-stroke engine, at a speed of 1200 rpm.
y_ ¼ 6:4cos 3y0:6cos 6y þ0:45cosð9yp=6Þ þ 0:26sinð12y þ p=3Þ þ 1200, y 2 ð0,4p
ð1Þ
If M =125, the mean engine speed in each sampling interval is 2p=M
y_ j ¼ R 2pj=M
2pðj1Þ=M
1=y_ dy
,
j ¼ 1,. . .,2M
ð2Þ
In this case, 2M is not a multiple of 6, and the target length 2L should be 252. The real instantaneous engine speed at the center of each resampling interval can be directly calculated with Eq. (1). Waveforms of the real speed and the resampled speed are shown in Fig. 2(a), while the difference between them is shown in Fig. 2(b). Apparently, these two waveforms almost coincide with each other. 2.2. Filtering The firing frequency in order domain for a four-stroke engine is the number of cylinders divided by two since each cylinder fires once every two revolutions of crankshaft. If all cylinders operate identically, the engine speed would be a periodic function of crank angle. In this case, the energy of engine speed waveform would just concentrate on the firing frequency and its harmonics [8]. The firing frequency and its harmonics are defined as the major orders. Therefore, in order domain, the components other than the major orders can be considered as the results of the difference among the operations of all cylinders [22,23]. Furthermore, the feature of misfire events can be enhanced by filtering out the major order components of the engine speed. This is accomplished by a discrete Fourier transform (DFT) based notch filter, which is shown in Fig. 3. The result of the filter is defined as the abnormal fluctuation signal denoted by o in the paper. The following example is presented to verify the availability of the notch filter. The speed signal used in this example was obtained from a 6135 G diesel engine, which was running at 800 rpm without loads. Also, misfires were stimulated in cylinder 2 and cylinder 5.The original fluctuation waveform of the engine speed and the abnormal fluctuation signal is
0.04 Real Speed Resampled Speed
1208
0.02
1204
Error (rpm)
Speed (rpm)
1206
1202 1200
0 −0.02
1198 1196
−0.04
1194 0
120
240 360 480 600 Crank Angle (deg.)
720
0
120
240 360 480 600 Crank Angle (deg.)
Fig. 2. Comparison between the resampled and real instantaneous engine speed.
Input instantaneous rotational speed series of an engine cycle
Compute the DFT
Compute the inverse DFT
Set coefficients of the major orders to 0
Fig. 3. Block diagram form of filtering algorithm.
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reported in Fig. 4. It can be noticed that o shows concave trends in (1201,2401] and (4801,6001], where the misfiring cylinders dominate the torque output. This is an important clue for misfire detection. Although this feature may not be evident under other operating conditions, it can be extracted by the methods introduced in the following sections.
2.3. Partitioning Since the length 2L of o is an integral multiple of N, the signal o can be partitioned into Z-dimensional vectors xi , i ¼ 1,. . .,N, where Z ¼ 2L=N:
ð3Þ
Each vector describes the abnormal fluctuation of instantaneous engine speed when the corresponding cylinder dominates the torque output. The vectors can be considered as measurement results of N procedure parameters for an engine cycle. In other words, they can be processed by multivariate statistical analysis methods.
3. Algorithm for misfire detection As mentioned before, the vector x represents the abnormal fluctuation of instantaneous engine speed when the corresponding cylinder dominates the torque output. If all cylinders are working uniformly, these vectors can be considered as the result of stochastic factors, such as measurement noise. For a misfiring cylinder, this vector presents a concave trend due to the fact that the indicated torque acting on the crankshaft is smaller than that under normal conditions. Contrarily, the trend of this vector will be a convex curve if the cylinder has super powerful working capability. In this context, convex or concave is defined as the polarity of a curve. The detection of misfire events and the isolation of faulty cylinders are implemented using the information contained in these vectors.
3.1. Occurrence determination Principal component analysis (PCA) is employed in our case, which is a powerful tool for multivariate statistics [24]. The application of PCA gives N principal components (PCs) Pi (i ¼ 1,. . .,N) and N eigenvalues li (i ¼ 1,. . .,N), where Pi is related to li by the covariance matrix of the vectors. How well the PC Pi explains the total variance of the vectors is measured by the relative proportion
l cj ¼ PN j
i¼1
li
,
j ¼ 1,. . .,N:
ð4Þ
The distribution of the variance shows the healthy condition of the engine. If all the cylinders operate absolutely identically, the abnormal fluctuation signal will be pure random noise, and the total variance will be distributed uniformly among the N PCs. Therefore, all the eigenvalues are equal and std(c), the standard deviation of c, will be 0. On the other hand, if misfire events have taken place, almost all of the variance will be explained by the first PCs. The extreme state of this condition is that the whole variance is explained only by the first PC. In this case
c ¼ ½1,0,. . .,0,
ð5Þ
15 ω
Speed Fluctuation (rpm)
Original waveform 10 5 0 −5 Cyl.1
−10 0
Cyl.5
120
Cyl.3
240
Cyl.6
360
Cyl.2
480
Cyl.4
600
Crank Angle (deg.) Fig. 4. Comparison between o and original fluctuation waveform of engine speed.
720
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and std(c) gets its biggest value smax v" ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi u # u 1 2 1 2 N1 t : =N ¼ smax ¼ 1 þ ðN1Þ 0 N N N
ð6Þ
Obviously 0 r stdðcÞ rsmax :
ð7Þ
The more uniformly the cylinders operate, the smaller the value of std(c). If 2stdðcÞ 4 smax :
ð8Þ
misfire events must have taken place in a great probability. So the occurrence of misfire events can be determined by the following criterion: stdðcÞ 4
1 smax , 2
or
2stdðcÞ 4 1: smax
ð9Þ
At the same time, the uniformity of the engine torque can be evaluated by the following index:
e¼
2stdðcÞ : smax
ð10Þ
The uniformity of the engine torque increases as index e decreases. 3.2. Faulty cylinder isolation The isolation of abnormal cylinders is accomplished by analyzing the correlation coefficients between x and the first PC P1 , which is defined by the following equation: covðxi ,P1 Þ ffi, ri,1 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi varðxi ÞvarðP1 Þ
ð11Þ
where covðxi ,P1 Þ ¼
varðxi Þ ¼
Z 1X ðo oi ÞðP1,k P1 Þ, Z k ¼ 1 i,k
Z 1X ðo oi Þ2 : Z k ¼ 1 i,k
ð12Þ
ð13Þ
P 2 2 Because N j ¼ 1 ri,j ¼ 1, ri,j can be considered as the proportion of variance of xi explained by Pj . Indeed, the PCs are orthogonal to each other, so that they can be seen as different trends extracted from the vectors. Furthermore, the first PC P1 explains most of the total variance, so it represents the most important trend contained in these vectors. Thus the big value of r2i,1 implies that the ith cylinder is working abnormally. However, whether the ith cylinder is the misfiring cylinder or the super powerful one is unknown, because the first PC P1 can be concave or convex arbitrarily, and the polarity of xi is also unknown. The polarity of P1 can be determined by calculating the correlation coefficient between P1 and any curve whose polarity is known. For example, a curve is represented by n ð14Þ xðnÞ ¼ cos 2p p , n ¼ 1,. . .,Z Z where Z is the dimension of xi . Apparently, x is convex. Let r be the correlation coefficient between x and P1 . If r 40, then P1 is a convex curve. Otherwise, P1 will be a concave curve. The polarity of xi can be determined by checking the sign of correlation coefficient. For simplicity, two indexes are defined as follows:
gi ¼ r2i,1 ,
ð15Þ
bi ¼ signðri,1 Þr2i,1 :
ð16Þ
If bi is positive, xi and P1 will have the same polarity. Contrarily, xi and P1 will have opposite polarities if bi is negative. The threshold value, which is requisite for the isolation of abnormal cylinders, is defined as stdðgÞ stdðgÞ, THR ¼ meanðgÞ 1 ð17Þ meanðgÞ where mean(g) and std(g) are the mean and standard deviation of g, respectively. This formula gives a threshold value for each engine cycle even if the average speed and the external load are fixed. So the cycle-to-cycle variation in the engine has been taken into account in the definition of threshold values.
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If the occurrence of misfire events has been determined, the misfiring cylinder can be identified by checking the parameters of each cylinder with the following criteria: (1) P1 is convex, gi 4THR, and bi o 0; or (2) P1 is concave, gi 4 THR, and bi 40. Similarly, the super powerful cylinder also can be identified using the following criteria: (1) P1 is convex, gi 4THR, and bi 40; or (2) P1 is concave, gi 4THR, and bi o0.
3.3. Error correction operation (ECO) In order to reduce the risk of false alarms and missing detections, the effect of torsional vibration on the engine speed waveform should be interpreted properly. After the occurrence of a misfire event, the engine speed will decrease suddenly, and the next healthy cylinder should do more work to resume the initialized speed. Consequently, the engine will be accelerated sharply during the expansion stroke of the healthy cylinder, which results in an overshot speed waveform. Therefore, the engine speed shows damped oscillation during its adjustment process. This will affect the diagnostic results, since the state of each cylinder is described with the variation process of the engine speed. However, it can also be used to revise the diagnostic results. In other words, if a cylinder shows super powerful working capability, the previous one can be taken as the misfiring cylinder. Contrarily, if a cylinder is taken as a faulty cylinder and the next one is taken as a normal cylinder, it can be considered as a false alarm.
4. Experimental tests Some experimental tests have been conducted on a 6135 G diesel engine, which is the driver of a power plant, to validate the misfire detection methodology presented in the previous sections. The major specifications of the engine are summarized in Table 1. The engine is connected to an electric dynamometer, so that different loads can be applied to it. In order to stress the potentiality of the proposed algorithm, numerous tests are carried out at the rated speed of the diesel engine, since it is more difficult to isolate the misfiring cylinders at high speed and low loads. Meanwhile, tests are also conducted to show the adaptability of the proposed algorithm to middle speed conditions. Two different multiple misfire patterns, as described in Table 2, are stimulated in the experiments: separated misfire events (cylinder 2 and cylinder 5) and adjacent misfire events (cylinder 5 and cylinder 3). To simulate a faulty cylinder, the nut, which connects the high-pressure fuel line to the corresponding element of the injection pump, is slightly unscrewed and a leakage is introduced in the fuel supply of the cylinder. In this way, both partial misfires and absolute misfires can be stimulated in the cylinders. Two magnetic pickups are used, one mounted in front of the camshaft pulley to generate a cycle reference signal, another one facing the flywheel teeth. After conditioning, the output signals from the above sensors are transmitted to a PXI6052E data acquisition card. The instantaneous engine speed is determined by measuring the time between two consecutive teeth with a digital timer of 20 MHz. The photograph of the experiment scene is shown in Fig. 5. Table 1 Test engine specifications. Total displacement Architecture Fuel system Injection system Injection type Bore Stroke Compression ratio Number of valves Idle speed Rated speed Maximum power Firing sequence Flywheel teeth number
12 L L6 B-type injection pump Sequential speed-density multipoint Direct 135 mm 140 mm 16.5:1 4 per cylinder 500 rpm 1500 rpm 75 kW at 1500 rpm 1-5-3-6-2-4 125
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Table 2 Experimental tests. Test number
Engine speed (rpm)
Faults
1 2 3 4 5 6 7 8
800 800 1500 1500 1500 1500 1500 1500
Cyl.2 Cyl.2 Cyl.2 Cyl.2 Cyl.3 Cyl.3 Cyl.2 Cyl.2
Load (N m)
30% misfueled disconnected 30% misfueled disconnected disconnected disconnected 30% misfueled 30% misfueled
Cyl.5 Cyl.5 Cyl.5 Cyl.5 Cyl.5 Cyl.5 Cyl.5 Cyl.5
40% misfueled disconnected 40% misfueled disconnected 40% misfueled disconnected 40% misfueled 40% misfueled
0 0 0 0 0 0 95 239
Fig. 5. Photograph of the experiment scene.
Table 3 Performance of the proposed algorithm for the tests in Table 2.
Detectable ratio before ECO (%) False alarms before ECO (%) Detectable ratio after ECO (%) False alarms after ECO (%)
No. 1
No. 2
No. 3
No. 4
No. 5
No. 6
No. 7
No. 8
97.0 1.27 97.75 0
100 0 100 0
47.75 2.05 95.5 0
98.75 1.0 100 0
79.25 27.62 79.25 1.55
98.25 23.09 98.25 2.72
50 0 96.5 0
88.75 0 92.5 0
5. Results and discussion In each test, the engine speed signal of 200 consecutive cycles is collected and processed with the proposed diagnostic method. For comparison purposes, the diagnostic results before ECO are also recorded. Table 3 summarizes the results obtained in terms of detectable ratio and false alarm percentage under different operating conditions before and after ECO. The detectable ratio is the proportion of correctly isolated misfire events to the total misfire events, and the percentage of false alarms is the proportion of false alarms to the number of detected events.
5.1. Availability of ECO Both the missing detections and the false alarms can be reduced effectively if the misfiring cylinders are not adjacent in the firing sequence, as can be seen in Table 3. The detectable ratios of the tests nos. 3 and 7, in particular, are quite different before and after ECO. In Fig. 6, the diagnostic results of these two tests before ECO are reported according to the firing sequence. It can be observed that simple threshold checking is not effective for the identification of faulty cylinders, because the feature of partial misfires under critical operating conditions is so obscure that many false alarms will arise if a smaller threshold is adopted. However, most of missing detections can be retrieved successfully by ECO, since cylinder 3 and cylinder 4 have been taken as the super powerful cylinders, which follow cylinder 5 and cylinder 2, respectively, in the firing sequence. Meanwhile, false alarms in test no. 3 can be totally eliminated. If the faulty cylinders do not work
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1 β
0.5 0 −0.5 20
40 60 80 Combustion Events (6 per engine cycle)
100
120
20
40 60 80 Combustion Events (6 per engine cycle)
100
120
1 β
0.5 0 −0.5
Fig. 6. Diagnostic results of tests no. 3 (a) and no. 7 (b) before ECO (m: super powerful combustions; .: misfire events; K: normal combustions; —: threshold).
1
β
0.5 0 −0.5 −1 20
40 60 80 Combustion Events (6 per engine cycle)
100
120
1 β
0.5 0 −0.5 20
40 60 80 Combustion Events (6 per engine cycle)
100
120
20
40 60 80 Combustion Events (6 per engine cycle)
100
120
1
β
0.5 0 −0.5
Fig. 7. Diagnostic results of tests no. 1 (a), no. 4 (b) and no. 8 (c) before ECO (m: super powerful combustions; .: misfire events; K: normal combustions; —: threshold).
absolutely or the external load is high, most of the misfire events can be located correctly without ECO. Nevertheless, ECO is also helpful for the reduction of missing detections and false alarms, as can be observed in Fig. 7. In the case of adjacent misfire events, only false alarms can be effectively eliminated by ECO. The diagnostic results of tests nos. 5 and 6 before ECO are presented in Fig. 8. Although cylinder 2 is often improperly taken as the misfiring cylinder, cylinder 4 is not taken as the super powerful cylinder in most cases. Therefore, the majority of false alarms can be eliminated. But it is helpless for the rediscovery of undetected misfire events, because the first misfire may be shadowed by the next one.
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Moreover, the introduction of ECO makes it easier to define threshold for the identification of faulty cylinders. As can be seen in Figs. 6–8, the feature of super powerful cylinders is more evident than that of the misfiring cylinders. Hence, a larger threshold is also suitable for the isolation of faulty cylinders, especially for the case of separated misfire events.
5.2. Risk of missing detection The risk of missing detections mainly comes from the occurrence determination of misfire events with Eq. (9). Even if misfire events have taken place, the parameter e also can be smaller than 1, as can be seen in Fig. 9. The improper determination is probably caused by the randomness of torsional vibrations. In the case of e o1, all cylinders are determined to be healthy, and then the next two steps of the diagnostic algorithm will be skipped.
5.3. Limitations The proposed methodology is only suitable for the misfire detection under steady-state operating conditions. As described in Sections 2 and 3, the index b is a relative quantity for evaluating the working capability of the cylinders. Under transient working conditions, this index could get distinct values even if all cylinders are working normally.
1 β
0.5 0 −0.5 20
40 60 80 Combustion Events (6 per engine cycle)
100
120
20
40 60 80 Combustion Events (6 per engine cycle)
100
120
1 β
0.5 0 −0.5
1.08
1.06
1.07
1.05
1.06
1.04
1.05
1.03
1.04
1.02 ε
ε
Fig. 8. Diagnostic results of tests no. 5 (a) and no. 6 (b) before ECO (m: super powerful combustions; .: misfire events; K: normal combustions; —: threshold).
1.03
1.01
1.02
1
1.01
0.99
1
0.98
0.99
0.97 0
10
20
30
Engine Cycles
40
50
0
10
20
30
Engine Cycles
Fig. 9. Parameter e evaluated for test no. 3 (a) and no. 8 (b).
40
50
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6. Conclusions In this paper we proposed an original algorithm to process the engine speed signal for multiple misfire detections in IC engines. The proposed method is relatively easy to be implemented in practice, because the threshold can be defined adaptively with the measured signal. Besides, the effect of torsional vibration on the engine speed waveform is interpreted as the presence of super powerful cylinders. Since the super powerful cylinder always follows a misfiring one in the firing sequence, and the super powerful cylinder often can be identified correctly, both missing detections and false alarms can be reduced effectively by checking the relationship between the cylinders. The efficiency of the proposed algorithm has been verified through the experimental results obtained from a 6135 G diesel engine. More than 90% of separated partial misfire events can be located correctly even at high speed and low loads. In contrast, it is more difficult to identify adjacent misfiring cylinders, because the first misfire event may be shadowed by the second one. The proposed algorithm also can be applied to identify the single misfire event, even though it is designed for multiple misfire detections.
Acknowledgements The authors would like to thank Dr. Xiaojing Yuan for his great assistance. The anonymous reviewers are sincerely appreciated for their valuable suggestions to improve the paper. References [1] J. Williams, An overview of misfiring cylinder engine diagnostic techniques based on crankshaft angular velocity measurements, SAE Paper 960039, 1996. [2] Y. Ohashi, M. Kuoiwa, K. Okamura, A. Ueda, The application of ionic current detection system for the combustion condition control, SAE Paper 199901-0550, 1999. [3] Y. Chung, C. Bae, S. Choi, K. Yoon, Application of a wide range oxygen sensor for the misfire detection, SAE Paper 1999-01-1485, 1999. [4] P. Bogus, J. Merkisz, Misfire detection of locomotive diesel engine by non-linear analysis, Mechanical Systems and Signal Processing 19 (2005) 881–899. [5] J. Jiang, F. Gu, R. Gennish, D.J. Moore, G. Harris, A.D. Ball, Monitoring of diesel engine combustions based on the acoustic source characterisation of the exhaust system, Mechanical Systems and Signal Processing 22 (2008) 1465–1480. [6] J. Merkisz, P. Bogus, R. Grzeszczyk, Overview of engine misfire detection methods used in on board diagnostics, Journal of KONES—Internal Combustion Engines 8 (2002) 326–341. [7] J. Yang, L. Pu, Z. Wang, Y. Zhou, X. Yan, Fault detection in a diesel engine by analysing the instantaneous angular speed, Mechanical Systems and Signal Processing 15 (2001) 549–564. [8] D. Taraza, N.A. Henein, W. Bryzik, The frequency analysis of the crankshaft’s speed variation a reliable tool for diesel engine diagnosis, Journal of Engineering for Gas Turbines and Power 123 (2001) 428–432. [9] N. Cavina, E. Corti, G. Minelli, G. Serra, Misfire detection based on engine speed time-frequency analysis, SAE Paper 2002-01-0480, 2002. [10] F. Ponti, Instantaneous engine speed time-frequency analysis for onboard misfire detection and cylinder isolation in a V12 high-performance engine, Journal of Engineering for Gas Turbines and Power 130 (2008) 012805. [11] S. Naik, Advanced misfire detection using adaptive signal processing, International Journal of Adaptive Control and Signal Processing 18 (2004) 181–198. [12] U. Kiencke, Engine misfire detection, Control Engineering Practice 7 (1997) 203–208. [13] S.X. Chen, J.J. Moskwa, Application of non-linear sliding-mode observers for cylinder pressure reconstruction, Control Engineering Practice 5 (1997) 1115–1121. [14] Y.H. Zweiri, L.D. Seneviratne, Diesel engine indicated and load torque estimation using a non-linear observer, Proceedings of the Institution of Mechanical Engineers Part D: Journal of Automobile Engineering 220 (2006) 775–785. [15] Y. Wang, F. Chu, Real-time misfire detection via sliding mode observer, Mechanical Systems and Signal Processing 19 (2005) 900–912. [16] M. Klenk, W. Moser, W. Muller, W. Wimmer, Misfire detection by evaluating crankshaft speed—a means to comply with OBDII, SAE Paper 930399, 1993. [17] D. Moro, F. Ponti, G. Cipolla, M. Mammetti, L. Poggio, An approach for misfire diagnosis in critical zones of the operating range of a high-performance engine, SAE Paper 2003-01-1058, 2003. [18] N. Cavina, G. Cipolla, F Marcigliano, D. Moro, L. Poggio, A methodology for increasing the signal to noise ratio for the misfire detection at high speed in a high performance engine, Control Engine Practice 14 (2006) 243–250. [19] F.V. Tinaut, A. Melgar, H. Laget, J.I. Dominguez, Misfire and compression fault detection through the energy model, Mechanical Systems and Signal Processing 21 (2007) 1521–1535. [20] N. Cavina, F. Ponti, Engine torque nonuniformity evaluation using instantaneous crankshaft speed signal, Journal of Engineering for Gas Turbines and Power 125 (2003) 1050–1058. [21] F. Ponti, Development of a torsional behavior powertrain model for multiple misfire detection, Journal of Engineering for Gas Turbines and Power 130 (2008) 022803. [22] A.W. Osburn, T.M. Kostek, M.A. Franchek, Residual generation and statistical pattern recognition for engine misfire diagnostics, Mechanical Systems and Signal Processing 20 (2006) 2232–2258. [23] M. Montani, N. Speciale, N. Cavina, Misfire detection by a wavelet based analysis of crankshaft speed fluctuation, in: Proceedings of the IASTED International Conference on Circuits, Signals and Systems, Clearwater Beach, Florida, USA, 2004, pp. 15–20. [24] W. Hardle, L. Simar, Applied Multivariate Statistical Analysis, Springer, NY, USA, 2003.
Contents lists available at ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/jnlabr/ymssp
Multivariate statistical analysis strategy for multiple misfire detection in internal combustion engines Chongqing Hu n, Aihua Li, Xingyang Zhao Xi’an Research Institute of Hi-Tech, Xi’an 710025, China
a r t i c l e i n f o
abstract
Article history: Received 19 July 2009 Received in revised form 23 March 2010 Accepted 27 August 2010 Available online 15 September 2010
This paper proposes a multivariate statistical analysis approach to processing the instantaneous engine speed signal for the purpose of locating multiple misfire events in internal combustion engines. The state of each cylinder is described with a characteristic vector extracted from the instantaneous engine speed signal following a three-step procedure. These characteristic vectors are considered as the values of various procedure parameters of an engine cycle. Therefore, determination of occurrence of misfire events and identification of misfiring cylinders can be accomplished by a principal component analysis (PCA) based pattern recognition methodology. The proposed algorithm can be implemented easily in practice because the threshold can be defined adaptively without the information of operating conditions. Besides, the effect of torsional vibration on the engine speed waveform is interpreted as the presence of super powerful cylinder, which is also isolated by the algorithm. The misfiring cylinder and the super powerful cylinder are often adjacent in the firing sequence, thus missing detections and false alarms can be avoided effectively by checking the relationship between the cylinders. Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.
Keywords: Internal combustion engine Speed fluctuation Multiple misfire detection Principal component analysis
1. Introduction Inspired by the on-board diagnostic (OBD) regulation, numerous successful approaches have been developed for engine misfire detection and faulty cylinder identification [1–5]. Since the instantaneous engine speed can be measured by the engine control system, the simplest and most cost-effective approach is to evaluate the engine speed fluctuation. This approach has been commonly used in engine mass production [6], but it is still difficult to detect multiple misfire events, especially under critical working conditions (at high speed and low loads). The misfire event can be detected by evaluating the engine speed waveform, which has been changed due to the lack of positive torque during the expansion stroke of the misfiring cylinder. The features of speed waveform extracted in time-domain [7], frequency-domain [8], or time–frequency-domain [9,10], are effective to identify misfiring cylinders when the engine is running at low-to-middle speed range. However, at high speed, the feature of misfire events may be masked by the following effects: the negligible drop of engine speed due to the misfire event, the low signal-to-noise ratio (SNR) of measured signal and the interference of torsional vibrations [11]. Another popular approach to misfire detection aims to estimate the indicated torque or in-cylinder pressure with a dynamic crankshaft model [12–15]. Although this method provides sufficient information about the engine combustion conditions, it is time-consuming and requires an accurate dynamic model. It would be more efficient to evaluate the n
Corresponding author. E-mail address: [email protected] (C. Hu).
0888-3270/$ - see front matter Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2010.08.010
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crankshaft kinetic energy variation caused by the combustions with the time periods, which are spent on the rotation of predefined angular sectors [16–18]. To distinguish misfire events from compression faults, two energy indices were extracted from an energy model of crankshaft [19]. However, the effect of torsional vibrations cannot be taken into account in these methods, because the crankshaft is often assumed to be a rigid body. Regarding multiple misfires, the engine speed oscillation induced by the first misfire event may still be present when the second misfire occurs, which makes the engine speed waveform more complicated. Hence, the location of multiple misfires is more difficult than that of single misfire event. To compensate the effect of torsional vibrations, different methods have been developed [20,21]. However, these methods require calculating and saving characteristic waveforms for various misfire patterns. Moreover, predefined threshold values are often indispensable to the identification of misfiring cylinders [8,16,20,21]; thus additional experiments should be carried out in advance. In this paper, misfire detection is implemented by processing the instantaneous engine speed with a multivariate statistical analysis algorithm. The state of each cylinder is described by the whole variation process of instantaneous engine speed during the corresponding expansion stroke, rather than some absolute values at particular positions. Thus, the threshold definition can be accomplished without the knowledge of engine speed and external loads. And the effect of torsional vibration can be interpreted as the presence of super powerful cylinders, which is useful to the location of misfiring cylinders. 2. Preprocessing of instantaneous engine speed The preprocessing procedure of instantaneous engine speed involves three steps: resampling, filtering and partitioning. 2.1. Resampling Normally, the instantaneous engine speed of an internal combustion (IC) engine is obtained by measuring the elapsed time between consecutive pulses, which are generated by the flywheel gear or other teethed disk mounted on the crankshaft and a simple inductive or Hall-effect transducer. The number of the teeth on the gear determines the number of samples of an engine cycle. If the gear has M teeth, the angle interval is 2p/M or the sampling interval is 360/M1, and the length of speed series for each engine cycle may be M (2-stroke engine) or 2M (4-stroke engine). The instantaneous engine speed at the center of each sampling interval is 60/MDT rpm, where DT is the time (in seconds) elapsed between two consecutive tooth edges. Thus, the instantaneous engine speed is the average velocity over its sampling interval, and the crankshaft can be supposed to rotate at constant velocity within each sampling interval. In each engine cycle, the cylinders dominate the output torque alternatively. For a N-cylinder, 4-stroke engine, cylinder i dominates the output torque in the crank angle interval (TDCi,TDCi +4p/N], where TDCi is the top dead center of cylinder i. Because the working capability of cylinder i can be described by the varying process of engine speed in (TDCi,TDCi + 4p/N], faulty cylinders can be isolated by comparing the trends of engine speed in these crank angle intervals. However, this requires that the instantaneous engine speed series in the N intervals have the same length, and their sampling position to the corresponding top dead center also be identical. So 2M should be an integral multiple of N. If this requirement is not satisfied, the engine speed can be resampled to modify the length of engine speed series using the following method. The rational length 2L is a multiple of N and closest to 2M. Fig. 1(a) shows the resampling strategy for the case L4M, while Fig. 2(b) is for the case LoM. In either case, the resampled speed is the average of the measured speed in the resampling
Fig. 1. Resampling strategy for the measured instantaneous engine speed: (a) L4M; (b) Lo M.
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crank angle interval. Also, the resampled speed is treated as the instantaneous engine speed at the center of the resampling crank angle interval. When the resampling is carried out, the speed waveform should not be changed. Since it is impossible to measure the instantaneous engine speed at the same crankshaft position with different sampling intervals simultaneously, the feasibility of the resampling strategy is proved by simulation results. Ideally, the instantaneous engine speed of an IC engine can be approximated by a sinusoidal function. The following equation describes the instantaneous engine speed of a 6-cylinder, 4-stroke engine, at a speed of 1200 rpm.
y_ ¼ 6:4cos 3y0:6cos 6y þ0:45cosð9yp=6Þ þ 0:26sinð12y þ p=3Þ þ 1200, y 2 ð0,4p
ð1Þ
If M =125, the mean engine speed in each sampling interval is 2p=M
y_ j ¼ R 2pj=M
2pðj1Þ=M
1=y_ dy
,
j ¼ 1,. . .,2M
ð2Þ
In this case, 2M is not a multiple of 6, and the target length 2L should be 252. The real instantaneous engine speed at the center of each resampling interval can be directly calculated with Eq. (1). Waveforms of the real speed and the resampled speed are shown in Fig. 2(a), while the difference between them is shown in Fig. 2(b). Apparently, these two waveforms almost coincide with each other. 2.2. Filtering The firing frequency in order domain for a four-stroke engine is the number of cylinders divided by two since each cylinder fires once every two revolutions of crankshaft. If all cylinders operate identically, the engine speed would be a periodic function of crank angle. In this case, the energy of engine speed waveform would just concentrate on the firing frequency and its harmonics [8]. The firing frequency and its harmonics are defined as the major orders. Therefore, in order domain, the components other than the major orders can be considered as the results of the difference among the operations of all cylinders [22,23]. Furthermore, the feature of misfire events can be enhanced by filtering out the major order components of the engine speed. This is accomplished by a discrete Fourier transform (DFT) based notch filter, which is shown in Fig. 3. The result of the filter is defined as the abnormal fluctuation signal denoted by o in the paper. The following example is presented to verify the availability of the notch filter. The speed signal used in this example was obtained from a 6135 G diesel engine, which was running at 800 rpm without loads. Also, misfires were stimulated in cylinder 2 and cylinder 5.The original fluctuation waveform of the engine speed and the abnormal fluctuation signal is
0.04 Real Speed Resampled Speed
1208
0.02
1204
Error (rpm)
Speed (rpm)
1206
1202 1200
0 −0.02
1198 1196
−0.04
1194 0
120
240 360 480 600 Crank Angle (deg.)
720
0
120
240 360 480 600 Crank Angle (deg.)
Fig. 2. Comparison between the resampled and real instantaneous engine speed.
Input instantaneous rotational speed series of an engine cycle
Compute the DFT
Compute the inverse DFT
Set coefficients of the major orders to 0
Fig. 3. Block diagram form of filtering algorithm.
720
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reported in Fig. 4. It can be noticed that o shows concave trends in (1201,2401] and (4801,6001], where the misfiring cylinders dominate the torque output. This is an important clue for misfire detection. Although this feature may not be evident under other operating conditions, it can be extracted by the methods introduced in the following sections.
2.3. Partitioning Since the length 2L of o is an integral multiple of N, the signal o can be partitioned into Z-dimensional vectors xi , i ¼ 1,. . .,N, where Z ¼ 2L=N:
ð3Þ
Each vector describes the abnormal fluctuation of instantaneous engine speed when the corresponding cylinder dominates the torque output. The vectors can be considered as measurement results of N procedure parameters for an engine cycle. In other words, they can be processed by multivariate statistical analysis methods.
3. Algorithm for misfire detection As mentioned before, the vector x represents the abnormal fluctuation of instantaneous engine speed when the corresponding cylinder dominates the torque output. If all cylinders are working uniformly, these vectors can be considered as the result of stochastic factors, such as measurement noise. For a misfiring cylinder, this vector presents a concave trend due to the fact that the indicated torque acting on the crankshaft is smaller than that under normal conditions. Contrarily, the trend of this vector will be a convex curve if the cylinder has super powerful working capability. In this context, convex or concave is defined as the polarity of a curve. The detection of misfire events and the isolation of faulty cylinders are implemented using the information contained in these vectors.
3.1. Occurrence determination Principal component analysis (PCA) is employed in our case, which is a powerful tool for multivariate statistics [24]. The application of PCA gives N principal components (PCs) Pi (i ¼ 1,. . .,N) and N eigenvalues li (i ¼ 1,. . .,N), where Pi is related to li by the covariance matrix of the vectors. How well the PC Pi explains the total variance of the vectors is measured by the relative proportion
l cj ¼ PN j
i¼1
li
,
j ¼ 1,. . .,N:
ð4Þ
The distribution of the variance shows the healthy condition of the engine. If all the cylinders operate absolutely identically, the abnormal fluctuation signal will be pure random noise, and the total variance will be distributed uniformly among the N PCs. Therefore, all the eigenvalues are equal and std(c), the standard deviation of c, will be 0. On the other hand, if misfire events have taken place, almost all of the variance will be explained by the first PCs. The extreme state of this condition is that the whole variance is explained only by the first PC. In this case
c ¼ ½1,0,. . .,0,
ð5Þ
15 ω
Speed Fluctuation (rpm)
Original waveform 10 5 0 −5 Cyl.1
−10 0
Cyl.5
120
Cyl.3
240
Cyl.6
360
Cyl.2
480
Cyl.4
600
Crank Angle (deg.) Fig. 4. Comparison between o and original fluctuation waveform of engine speed.
720
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and std(c) gets its biggest value smax v" ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi u # u 1 2 1 2 N1 t : =N ¼ smax ¼ 1 þ ðN1Þ 0 N N N
ð6Þ
Obviously 0 r stdðcÞ rsmax :
ð7Þ
The more uniformly the cylinders operate, the smaller the value of std(c). If 2stdðcÞ 4 smax :
ð8Þ
misfire events must have taken place in a great probability. So the occurrence of misfire events can be determined by the following criterion: stdðcÞ 4
1 smax , 2
or
2stdðcÞ 4 1: smax
ð9Þ
At the same time, the uniformity of the engine torque can be evaluated by the following index:
e¼
2stdðcÞ : smax
ð10Þ
The uniformity of the engine torque increases as index e decreases. 3.2. Faulty cylinder isolation The isolation of abnormal cylinders is accomplished by analyzing the correlation coefficients between x and the first PC P1 , which is defined by the following equation: covðxi ,P1 Þ ffi, ri,1 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi varðxi ÞvarðP1 Þ
ð11Þ
where covðxi ,P1 Þ ¼
varðxi Þ ¼
Z 1X ðo oi ÞðP1,k P1 Þ, Z k ¼ 1 i,k
Z 1X ðo oi Þ2 : Z k ¼ 1 i,k
ð12Þ
ð13Þ
P 2 2 Because N j ¼ 1 ri,j ¼ 1, ri,j can be considered as the proportion of variance of xi explained by Pj . Indeed, the PCs are orthogonal to each other, so that they can be seen as different trends extracted from the vectors. Furthermore, the first PC P1 explains most of the total variance, so it represents the most important trend contained in these vectors. Thus the big value of r2i,1 implies that the ith cylinder is working abnormally. However, whether the ith cylinder is the misfiring cylinder or the super powerful one is unknown, because the first PC P1 can be concave or convex arbitrarily, and the polarity of xi is also unknown. The polarity of P1 can be determined by calculating the correlation coefficient between P1 and any curve whose polarity is known. For example, a curve is represented by n ð14Þ xðnÞ ¼ cos 2p p , n ¼ 1,. . .,Z Z where Z is the dimension of xi . Apparently, x is convex. Let r be the correlation coefficient between x and P1 . If r 40, then P1 is a convex curve. Otherwise, P1 will be a concave curve. The polarity of xi can be determined by checking the sign of correlation coefficient. For simplicity, two indexes are defined as follows:
gi ¼ r2i,1 ,
ð15Þ
bi ¼ signðri,1 Þr2i,1 :
ð16Þ
If bi is positive, xi and P1 will have the same polarity. Contrarily, xi and P1 will have opposite polarities if bi is negative. The threshold value, which is requisite for the isolation of abnormal cylinders, is defined as stdðgÞ stdðgÞ, THR ¼ meanðgÞ 1 ð17Þ meanðgÞ where mean(g) and std(g) are the mean and standard deviation of g, respectively. This formula gives a threshold value for each engine cycle even if the average speed and the external load are fixed. So the cycle-to-cycle variation in the engine has been taken into account in the definition of threshold values.
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If the occurrence of misfire events has been determined, the misfiring cylinder can be identified by checking the parameters of each cylinder with the following criteria: (1) P1 is convex, gi 4THR, and bi o 0; or (2) P1 is concave, gi 4 THR, and bi 40. Similarly, the super powerful cylinder also can be identified using the following criteria: (1) P1 is convex, gi 4THR, and bi 40; or (2) P1 is concave, gi 4THR, and bi o0.
3.3. Error correction operation (ECO) In order to reduce the risk of false alarms and missing detections, the effect of torsional vibration on the engine speed waveform should be interpreted properly. After the occurrence of a misfire event, the engine speed will decrease suddenly, and the next healthy cylinder should do more work to resume the initialized speed. Consequently, the engine will be accelerated sharply during the expansion stroke of the healthy cylinder, which results in an overshot speed waveform. Therefore, the engine speed shows damped oscillation during its adjustment process. This will affect the diagnostic results, since the state of each cylinder is described with the variation process of the engine speed. However, it can also be used to revise the diagnostic results. In other words, if a cylinder shows super powerful working capability, the previous one can be taken as the misfiring cylinder. Contrarily, if a cylinder is taken as a faulty cylinder and the next one is taken as a normal cylinder, it can be considered as a false alarm.
4. Experimental tests Some experimental tests have been conducted on a 6135 G diesel engine, which is the driver of a power plant, to validate the misfire detection methodology presented in the previous sections. The major specifications of the engine are summarized in Table 1. The engine is connected to an electric dynamometer, so that different loads can be applied to it. In order to stress the potentiality of the proposed algorithm, numerous tests are carried out at the rated speed of the diesel engine, since it is more difficult to isolate the misfiring cylinders at high speed and low loads. Meanwhile, tests are also conducted to show the adaptability of the proposed algorithm to middle speed conditions. Two different multiple misfire patterns, as described in Table 2, are stimulated in the experiments: separated misfire events (cylinder 2 and cylinder 5) and adjacent misfire events (cylinder 5 and cylinder 3). To simulate a faulty cylinder, the nut, which connects the high-pressure fuel line to the corresponding element of the injection pump, is slightly unscrewed and a leakage is introduced in the fuel supply of the cylinder. In this way, both partial misfires and absolute misfires can be stimulated in the cylinders. Two magnetic pickups are used, one mounted in front of the camshaft pulley to generate a cycle reference signal, another one facing the flywheel teeth. After conditioning, the output signals from the above sensors are transmitted to a PXI6052E data acquisition card. The instantaneous engine speed is determined by measuring the time between two consecutive teeth with a digital timer of 20 MHz. The photograph of the experiment scene is shown in Fig. 5. Table 1 Test engine specifications. Total displacement Architecture Fuel system Injection system Injection type Bore Stroke Compression ratio Number of valves Idle speed Rated speed Maximum power Firing sequence Flywheel teeth number
12 L L6 B-type injection pump Sequential speed-density multipoint Direct 135 mm 140 mm 16.5:1 4 per cylinder 500 rpm 1500 rpm 75 kW at 1500 rpm 1-5-3-6-2-4 125
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Table 2 Experimental tests. Test number
Engine speed (rpm)
Faults
1 2 3 4 5 6 7 8
800 800 1500 1500 1500 1500 1500 1500
Cyl.2 Cyl.2 Cyl.2 Cyl.2 Cyl.3 Cyl.3 Cyl.2 Cyl.2
Load (N m)
30% misfueled disconnected 30% misfueled disconnected disconnected disconnected 30% misfueled 30% misfueled
Cyl.5 Cyl.5 Cyl.5 Cyl.5 Cyl.5 Cyl.5 Cyl.5 Cyl.5
40% misfueled disconnected 40% misfueled disconnected 40% misfueled disconnected 40% misfueled 40% misfueled
0 0 0 0 0 0 95 239
Fig. 5. Photograph of the experiment scene.
Table 3 Performance of the proposed algorithm for the tests in Table 2.
Detectable ratio before ECO (%) False alarms before ECO (%) Detectable ratio after ECO (%) False alarms after ECO (%)
No. 1
No. 2
No. 3
No. 4
No. 5
No. 6
No. 7
No. 8
97.0 1.27 97.75 0
100 0 100 0
47.75 2.05 95.5 0
98.75 1.0 100 0
79.25 27.62 79.25 1.55
98.25 23.09 98.25 2.72
50 0 96.5 0
88.75 0 92.5 0
5. Results and discussion In each test, the engine speed signal of 200 consecutive cycles is collected and processed with the proposed diagnostic method. For comparison purposes, the diagnostic results before ECO are also recorded. Table 3 summarizes the results obtained in terms of detectable ratio and false alarm percentage under different operating conditions before and after ECO. The detectable ratio is the proportion of correctly isolated misfire events to the total misfire events, and the percentage of false alarms is the proportion of false alarms to the number of detected events.
5.1. Availability of ECO Both the missing detections and the false alarms can be reduced effectively if the misfiring cylinders are not adjacent in the firing sequence, as can be seen in Table 3. The detectable ratios of the tests nos. 3 and 7, in particular, are quite different before and after ECO. In Fig. 6, the diagnostic results of these two tests before ECO are reported according to the firing sequence. It can be observed that simple threshold checking is not effective for the identification of faulty cylinders, because the feature of partial misfires under critical operating conditions is so obscure that many false alarms will arise if a smaller threshold is adopted. However, most of missing detections can be retrieved successfully by ECO, since cylinder 3 and cylinder 4 have been taken as the super powerful cylinders, which follow cylinder 5 and cylinder 2, respectively, in the firing sequence. Meanwhile, false alarms in test no. 3 can be totally eliminated. If the faulty cylinders do not work
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1 β
0.5 0 −0.5 20
40 60 80 Combustion Events (6 per engine cycle)
100
120
20
40 60 80 Combustion Events (6 per engine cycle)
100
120
1 β
0.5 0 −0.5
Fig. 6. Diagnostic results of tests no. 3 (a) and no. 7 (b) before ECO (m: super powerful combustions; .: misfire events; K: normal combustions; —: threshold).
1
β
0.5 0 −0.5 −1 20
40 60 80 Combustion Events (6 per engine cycle)
100
120
1 β
0.5 0 −0.5 20
40 60 80 Combustion Events (6 per engine cycle)
100
120
20
40 60 80 Combustion Events (6 per engine cycle)
100
120
1
β
0.5 0 −0.5
Fig. 7. Diagnostic results of tests no. 1 (a), no. 4 (b) and no. 8 (c) before ECO (m: super powerful combustions; .: misfire events; K: normal combustions; —: threshold).
absolutely or the external load is high, most of the misfire events can be located correctly without ECO. Nevertheless, ECO is also helpful for the reduction of missing detections and false alarms, as can be observed in Fig. 7. In the case of adjacent misfire events, only false alarms can be effectively eliminated by ECO. The diagnostic results of tests nos. 5 and 6 before ECO are presented in Fig. 8. Although cylinder 2 is often improperly taken as the misfiring cylinder, cylinder 4 is not taken as the super powerful cylinder in most cases. Therefore, the majority of false alarms can be eliminated. But it is helpless for the rediscovery of undetected misfire events, because the first misfire may be shadowed by the next one.
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Moreover, the introduction of ECO makes it easier to define threshold for the identification of faulty cylinders. As can be seen in Figs. 6–8, the feature of super powerful cylinders is more evident than that of the misfiring cylinders. Hence, a larger threshold is also suitable for the isolation of faulty cylinders, especially for the case of separated misfire events.
5.2. Risk of missing detection The risk of missing detections mainly comes from the occurrence determination of misfire events with Eq. (9). Even if misfire events have taken place, the parameter e also can be smaller than 1, as can be seen in Fig. 9. The improper determination is probably caused by the randomness of torsional vibrations. In the case of e o1, all cylinders are determined to be healthy, and then the next two steps of the diagnostic algorithm will be skipped.
5.3. Limitations The proposed methodology is only suitable for the misfire detection under steady-state operating conditions. As described in Sections 2 and 3, the index b is a relative quantity for evaluating the working capability of the cylinders. Under transient working conditions, this index could get distinct values even if all cylinders are working normally.
1 β
0.5 0 −0.5 20
40 60 80 Combustion Events (6 per engine cycle)
100
120
20
40 60 80 Combustion Events (6 per engine cycle)
100
120
1 β
0.5 0 −0.5
1.08
1.06
1.07
1.05
1.06
1.04
1.05
1.03
1.04
1.02 ε
ε
Fig. 8. Diagnostic results of tests no. 5 (a) and no. 6 (b) before ECO (m: super powerful combustions; .: misfire events; K: normal combustions; —: threshold).
1.03
1.01
1.02
1
1.01
0.99
1
0.98
0.99
0.97 0
10
20
30
Engine Cycles
40
50
0
10
20
30
Engine Cycles
Fig. 9. Parameter e evaluated for test no. 3 (a) and no. 8 (b).
40
50
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6. Conclusions In this paper we proposed an original algorithm to process the engine speed signal for multiple misfire detections in IC engines. The proposed method is relatively easy to be implemented in practice, because the threshold can be defined adaptively with the measured signal. Besides, the effect of torsional vibration on the engine speed waveform is interpreted as the presence of super powerful cylinders. Since the super powerful cylinder always follows a misfiring one in the firing sequence, and the super powerful cylinder often can be identified correctly, both missing detections and false alarms can be reduced effectively by checking the relationship between the cylinders. The efficiency of the proposed algorithm has been verified through the experimental results obtained from a 6135 G diesel engine. More than 90% of separated partial misfire events can be located correctly even at high speed and low loads. In contrast, it is more difficult to identify adjacent misfiring cylinders, because the first misfire event may be shadowed by the second one. The proposed algorithm also can be applied to identify the single misfire event, even though it is designed for multiple misfire detections.
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