Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA
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MISFIRE INDEX DESIGN BY STATISTICAL SIGNAL PROCESSING IN HIGH PERFORMANCE ENGINES
Piero M. Azzoni., Davide Moro··, Carlo M. Porceddu-Cilione·, Giorgio Rizzoni u •
* ENEA, "Ezio Clementel", Bologna, Italy ** DIEM, University of Bologna, Italy *** Depart. of Mechanical Engineering, The Ohio State Univ.• USA Abstract: The present paper describes the application of statistical signal processing methods for the detection and identification of engine misfire in a high performance engine. The new environmental regulation in the Unites States requires the misftre detection because of its potential effect to decrease the effectiveness of the three way catalyst, at least resulting the irreversible destruction of the catalyst itself if the misfire presence is systematic. The method is based on compression and clustering of a data vector consisting of twelve Fourier components of the engine angular velocity signal. The paper describes the theory of the method and experimental results, illustrating the applicability of the method and its potential ability to solve a heretofore very challenging problem. 1. INTRODUCTION
This paper illustrates the application of a statistical signal processing method to the diagnosis of engine misfire in a 12-cylinder high-performance engine (5.7-litre Lamborghini engine). The misfire detection is solved in traditional four/six cylinder engine, with some different techniques. The difficulties to get the misfire detection in high performance engines are due to the high number of cylinders, that implies an increasing of the engine speed and a decreasing of the instantaneous crank-shaft fluctuation because of a more uniform torque development. The basic approach used in this study, that is, the analysis of fluctuations in engine angular velocity, is widely recognized as a viable approach (e.g. cf. Azzoni et al., 1994; Connolly and Rizzoni, 1994; Klenk et al., 1993; Ribbens and Park, 1993 and 1994; Ribbens and Rizzoni, 1993 and 1994). However, the particular application considered in this study, that is, a very high performance engine with many cylinders, has proven to be too challenging for the methods proposed in the above mentioned references. For this reason, the approach presented in this paper proposes the use of more advanced statistical signal processing techniques that result, as will be shown, in a promising diagnostic strategy. The effort described in this paper represents the continuation of ongoing work; earlier results have been reported by Azzoni et al. (1995, 1996).
angular velocity signal in the crank angle domain (that is, at equal crank angle increments). Each frequency domain data vector is computed over one engine cycle. Due to the complexity of the problem (see Azzoni et aI., 1995), an unstructured approach was employed, based simply on the statistical processing of the above mentioned vector of observations. Physical considerations are taken into account in the choice of the observation, and in the manner in which the data are generated. The reader may find a more complete explanation of the rationale for the pre-processing of the signal in Rizzoni (1989). The method described in this paper is divided into two phases: i) data compression; and ii) clustering.
The 24-dimensional observation vector (consisting of real and imaginary parts of the complex frequency components) is first reduced in dimension making use of a compression technique known as Principal Components Analysis. The resulting vector is a projection of the original vector onto a lower dimensional space. This operation is equivalent to performing a fonn of smoothing of the data, and extracts the statistically most relevant information contained in the observation. Next, clusters of data subsets are fonned to group the observations in a number of groups corresponding to each of the possible conditions (Le., nonnal combustion, misfire in cylinder n, n = 1,2, ... 12). The clustering approach is perhaps the more novel part of the method. Both phases are The method is based on the processing of a vector of described in detail later in the paper. observations consisting of the first twelve frequency components of the Fourier Series expansion of the measured Following a brief review of the theory underlying the engine angular velocity fluctuation signal. These order proposed method, experimental results are presented. The data frequency components are acquired by sampling the engine analyzed in the paper were acquired on a Lamborghini
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Automobili engine running in a test cell, and are representative of a class of high-performance engines. Only a small subset of the experiments conducted in collaboration with Lamborghini Automobili are illustrated in this paper due to space limitations. 2. THEORY OF METHOD 2.1 The Principal Component Analysis Approach
The Principal Components Analysis (PCA) method is a well known multi-variate statistical technique that permits analysis of complex data by providing the ability to compress large data sets into a lower dimensional representation. The data compression characteristics of PCA also make it suitable for the extraction of salient features from the data, and facilitate the solution of pattern recognition ad signature analysis problems. In this paper PCA is used in conjunction with clustering techniques to isolate the location of the misfiring cylinder. The real and imaginary parts of the first twelve frequency components of the engine angular velocity signal (excluding the DC component), form the initial data vector for PCA. As explained earlier, these frequency components are computed on a cycle by cycle basis. Let a sample data matrix be (1)
where i=1 .... ,/ is the engine cycle index andj=1 ..... 24. is the index of the real and imaginary parts of the twelve frequency components. Note that 1»24. and that Xi is the row vector corresponding to the ith engine cycle. The matrix X is typically generated by acquiring data at various engine speeds and loads. under nominally constant speed and load conditions. The Xi vectors can then be represented in 24-dimensional space. All the cycles related to the engine running under normal condition should fall in a single cluster. while the cycles with misfire are ideally grouped in 12 other clusters. each related to misfire occurrences in a single cylinder. Thus. in principle. it should be possible to identify the misfiring cylinder by recognizing the cluster to which the data most closely belongs. Unfortunately. to deal directly with the 24-dimensional data set would lead to a very unwieldy method and to the need to use high dimension hyperplanes to separate the clusters. due to the large dimension of each vector. In order to simultaneously reduce the noise influence and to reduce the required computation, the X data matrix is processed using the Principal Component Analysis technique (Rizzi. 1985). First. X is normalized in the following way:
z=
!
Zjj
= Xjj -.fTXj} sj"vI
(2)
where: and
(3)
and where .}. factor makes the Z T Z matrix equivalent to the correlation matrix. Once a normalized data matrix exists, it becomes possible to define a new orthonormal basis, Uh U2 •... , UJ. The Ul axis is determined in such a way that the square distances between vectors Zj and the ul axis are minimized. This is analogous to maximizing the square projections of the vectors zi on U1. Summing up these square projections, the variance of the random vectors Zj is obtained. The u2 axis is found following the same procedure with the supplementary constraint of its orthogonality with u1. The U3 axis is defined in the same way adding the orthogonality to U1 and U2. and so on. This procedure is effectively the same that is followed in computing the eigenvalues and eigenvectors of the following equation: Z T ZU=UD) (4) where Z TZ is a symmetrical correlation matrix. D) is a (24 x 24) diagonal matrix of the real and positive eigenvalues and U={ Uj, u2, ...• uJ } is the orthogonal eigenvector matrix. The projection of the ith cycle vectors onto the new basis is calculated by means of the transformation matrix U: F=Uij}={fj}=ZU (5) where F is a (l x 24) matrix. called the factor matrix. The fj={/ij} columns (the Principal Components) contain the projections of all the 1 points onto the Uj axis. The next step is to order the J columns fi. according to the decreasing value of the variance on the Uj axis. Taking into account only the most significant Principal Components the dimension of the F matrix is reduced from (1 x 24) to (1 x A). where A is the number of columns which contain over the 80% of the whole data set information. so reducing the computing time, without a substantial loss of information. When data from a new cycle is processed according to this method, the 24-vector of Fourier components, x*. is transfonned according to
--;:::rr
*_!*_xj-Xj} Zj
Z -
(6)
J
where Xj and Sj are the same mean and standard deviation previously computed from the X data matrix. The coordinates of the Z* vector in the new reference system are given by (7) f*=Z*U 2.2 Cluster analysis The object of cluster analysis is to group data sets into homogeneous clusters, such that each statistical subgrouping in the set is uniquely assigned to one cluster. In the specific case of this study we refer to the individual misfiring conditions, i.e., each of the cylinders plus normal operation thirteen clusters in all. Two targets for the application considered in this paper are: i) make the clustering procedure independent of the starting point to arrive at a small number of stable groups; ii) examine the formation of the stable clusters to determine the true number of clusters occurring in the data set.
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velocita angolare" Proc. of MISMAC III - Metodi di Sperimentazione nelle Macchine, pp. 1-9, Dipartimento
Of course, this is a only partial validation of the misfire diagnostic procedure, because only the cylinders I, 5, 8 and 12 have been considered.
di Ingegneria Meccanica, Univ. di Cagliari, Cagliari, ltalia, October 7, 1994.
4. CONCLUSION AND FUTURE WORK The results presented in this paper show a marked improvement in the ability to detect misfire and to identify the misfiring cylinder with respect to earlier studies (Azzoni et al., 1995). Experimental tests verified the ability to detect and isolate the occurrence of isolated misfires corresponding to very low rates (less than 0.3%), at each of the operating conditions tested. For the experiments reported in this paper, no false alarms were issued. There are still some problems, however, in detecting misfire at very high engine speed, because of torsional resonances which makes the diagnostic signal noisy in the frequency range selected for the misfire identification. Extension of the method to higher engine speeds is currently being studied. In the future, we plan to apply the same methodology to data acquired during road tests. The experimental test have already been performed in the high speed annular circuit of Nardo (Lecce, Italy) with the Lamborghini Diablo because of the necessity to reach high load condition that can be obtained with the car running at 240 kmIh. Among the road tests that have been carried out are: occasional and systematic misftre at low and high constant engine speed; operation in different gear, with the car in acceleration and in a normal city trip.
ACKNOWLEDGMENTS The authors wish to thank Lamborghini Automobili S.p.A. for the invaluable collaboration in the experimental studies. In addition, we also wish to thank Messrs. G. Cantoni and S. Rebottini for their assistance in acquiring and processing the data. A special acknowledgment goes to Prof. G. Minelli and to Ing. M. Ceccarani for their expert advice.
California Air Resources Board "Technical Status Update and Proposed Revisions to Malfunction and Diagnostic System Requirements Applicable to 1994 and Subsequent California Passenger Cars, Light-Duty Trucks, and Medium-Duty Vehicles - (OBD 11)" CARB Staff Report, 1991. Connolly, F. G. Rizzoni, "Real Time Estimation of Engine Torque for the Detection of Engine MisfIreS" Tmusactioo of the ASME. Journal of Dynamic Systems Measurement and Control. Vol. 116, No. 2, Dec.1994. Klenk, M., W. Moser, W. Muller and W. Wimmer, "Misfire Detection by Evaluating Crankshaft Speed - a Means to Comply with OBD 11", SAE paper 930399, presented at
1993 SAE International Congress and Exposition. Plapp, G. M. Klenk, W. Moser, "Methods of On-Board Misfire Detection", SAE Technical paper 900232, presented at 1990 SAE International Congress and
Exposition. Porceddu-Cilione, C. M., "L'application en temps r~l des methodes de discrimination h des donn~es industrielles"; Cahiers de l'analyse des donnoos.l.2. 111-122; 1987. Ribbens W. B., Park J., "Road Test Results of an IC Engine Misfire Detection System" SAE Technical Paper 930398, presented at 1993 SAE International Congress and
Exposition. Ribbens W. B., Park J., "Road Test of a MisfIre Detection System" SAE Technical Paper 940975, presented at 1994
SAE International Congress and Exposition. REFERENCES Azzoni, P.M., D. Moro, C.M. Porceddu-Cilione, G. Rizzoni, "Misfire detection in a high performance engine by the Principal Components Analysis Approach". SAE Technical paper nO 960622, presented at 1996 SAE
International Congress and Exposition. Azzoni, P.M. , G. Cantoni, M. Ceccarani, S. Mazzetti, G. Minelli, D. Moro, G. Rizzoni, "Measurement of Engine Misfire in a Lamborghini V -12 Engine Using Crankshaft Speed Auctuations", SAE Technical paper nO 950837, presented at 1995 SAE International Congress and
Exposition .. Azzoni P. M., Cantoni G., Minelli G., Moro D., "Individuazione di difetti di combustione in un motore ad accensione comandata tramite la misura delle variazioni di
Ribbens W. B., Rizzoni G., Engine Misfire Detection Utilizing Angular Velocity Fluctuations, United States Patents: 5,200,899, April 6, 1993; 5,239,473, August 24, 1993; and 5,278,760, January 11, 1994. Rizzi, A. "Analisi dei dati. Applicazioni dell'informatica alIa statistica", NIS La Nuova Italia Scientifica, Roma, Italy (1985). Rizzoni G., "Estimate of Indicated Torque from Crankshaft Speed Fluctuations: A Model for the Dynamics of the IC Engine", IEEE Transactions on Yehicular Tecbnolo&y, Vol. 38, No. 3, pp. 168-179, August 1989. Rizzoni, G., "A Passenger Vehicle Onboard Computer System for Engine Fault Diagnosis, Performance Measurement and Control," Proc. of 37th IEEE Veh. Technol. Co'!f" pp. 450-457, Tampa, FL, June 1987, pp. 450-457.
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