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Separation of combustion noise and piston-slap in diesel engine—Part I: Separation of combustion noise and piston-slap in diesel engine by cyclic Wiener filtering
ARTICLE IN PRESS Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing 19 (2005) 1209–1217 www.elsevier.com/locate/jnlabr/ymssp
Separation of combustion noise and piston-slap in diesel engine—Part I: Separation of combustion noise and piston-slap in diesel engine by cyclic Wiener filtering M. El. Badaouia,, J. Danie`rea, F. Guilleta, C. Servie`reb a
Laboratoire LASPI, IUT de Roanne, 20 Avenue de Paris, 42334 Roanne Cedex, France Laboratoire des Images et des Signaux (LIS), BP 46 38402 Saint-Martin d’He`res, France
b
Received 9 March 2005; received in revised form 10 August 2005; accepted 12 August 2005 Available online 5 October 2005
Abstract The main purpose of this study is to characterize the relative noise given out by a diesel engine, around the Top Dead Centre (TDC) by quantifying the proportions of ‘‘mechanical noise’’ originating mainly from piston-slap on the one hand and ‘thermal noise’’ originating from combustion on the other hand. Two different approaches are described here to solve this problem. In the first part of the paper, the cylinder pressure is measured and used as a reference in order to reconstruct the thermal noise. Next, we propose a method based on applying a cyclic Wiener filter to the measured cylinder pressure in order to separate the noises of mechanical and thermal origins. The final result is to reduce the engine resulting noise. The second part of the paper is devoted to blind source separation (BSS) methods applied on signals issued from accelerometers placed on one of the cylinders. It develops a BSS method based on a convolutive model of non-stationary mixtures and introduces a new method based on the joint diagonalization of time varying spectral matrices of the observations. Both methods are then applied to real data and the estimated sources are finally validated by several physical arguments. r 2005 Elsevier Ltd. All rights reserved. Keywords: Cyclic Wiener filter; Piston-slap; Combustion noise; Blind source separation
1. Introduction The purpose of this paper is to characterize the relative noise given out by a diesel engine, around the Top Dead Centre (TDC) by quantifying the proportions of ‘‘mechanical noise’’ (originating mainly from pistonslap) on the one hand and ‘‘thermal noise’’ originating from combustion on the other hand. Measurements are carried out by means of several accelerometers located on the engine. Retrieving such data has been for some years a major challenge for motorists because they can be used to reduce the resulting noise, e.g. by fixing the injection parameters or, better, to devise the best geometric piston features. Several approaches have been Corresponding author. Tel.: +33 4774 48928; fax: +33 4774 48921.
E-mail address: [email protected] (M.E. Badaoui). 0888-3270/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2005.08.010
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explored in the past to attempt to solve this difficult but fundamental problem [1–4]. However, no truly satisfactory solution has been found so far. The main difficulty of the problem is that the relevant causes of such noise are both spectrally and temporally overlapping. Therefore the separation methods, if they are to be efficient, must be based either on a priori knowledge of the noise—such as provided by a reference signal—or on the statistical independence of the noise sources—such as assumed in a blind procedure. This work was initiated within a collaboration between the laboratories LASPI (Roanne-France), LIS (Grenoble-France) and the company Metravib (Lyon-France). The two previous approaches have been explored by the LASPI and the LIS and they have been compared on real data issued of experiments carried out by Metravib. The paper is separated in two parts and presents the two types of noise separation. In the first part, the LASPI research team proposes a procedure taking a priori information into account. The supplementary information is provided by an additional pressure sensor. Typically, if the cylinder pressure is measured, it can be used as a reference in order to reconstruct the thermal acceleration. The transfer between pressure and acceleration issued of the combustion phenomenon is then estimated with a method based on a cyclic Wiener filtering approach [5]. Next, the thermal noise can be computed on each accelerometer and afterwards, the mechanical noise is obtained by subtraction. In the second part, blind source separation (BSS) methods are examined by the LIS research team. Basically, BSS recovers signals of different physical sources from the observation of several mixtures of them and in this case no reference signal is needed. This approach is usually used when the transfer from sources to sensors is too difficult to model. The lack of knowledge about mixtures and sources is then compensated by the strong hypothesis of mutual independence of the sources [6–9]. This second paper develops a BSS method based on a convolutive model of non-stationary mixtures. It introduces a method exploiting the joint diagonalization of time varying spectral matrices of the observation records and a new technique to handle the problem of permutation ambiguity in the frequency domain.
2. Experimental device and modelling of the observations The signals have been acquired on a four-stroke and four-cylinder diesel engine. One of the cylinders was equipped with a pressure sensor whereas ten accelerometers sensors were placed around the instrumented cylinder. Signals issued from the accelerometers have been sampled at 25 600 Hz, synchronously to the rotation speed of the crankshaft. On each cycle of the signals, the signals have been truncated in the angular window [401, 801] of the crankshaft. In the processed window thermal and mechanical phenomena are temporally overlapping around the TDC, as well as spectrally overlapping. Consequently, an accelerometer measures an acceleration xðkÞ at discrete time k, as the addition of the thermal contribution xt ðkÞ and the mechanical one xm ðkÞ. The mechanical phenomenon is constituted by the piston-slap and by mechanical noises due to other cylinders. Concerning the thermal aspect, this engine is fitted with double injection: the pre-injection angle varies from a few degrees up to 301 before the TDC (according to the load), then the principal injection occurs in the vicinity the TDC. Thermal noises are evidently due to the pressure variations in the combustion chamber xt ðkÞ; some transfer functions therefore link the relationship between a ‘pðkÞ’ pressure at discrete time k that provides thermal noises at the sensor level [10]. In other words, the pressure sensor provides a reference signal of the combustion source which can perform the reconstruction of the thermal accelerations in each accelerometer signal. This separation method, using a pressure sensor as a reference, is presented in the first part of the paper. As thermal and mechanical noises are both spectrally and temporally overlapping, an accelerometer measures a signal xðkÞ ¼ xt ðkÞ þ xm ðkÞ. In a general model of propagation, the accelerations come from two types of sources st ðkÞ and sm ðkÞ by linear filtering where st ðkÞ represents the thermal source, and sm ðkÞ the mechanical source. So, the accelerometer signals are given by xðkÞ ¼ F ðst ðkÞÞ þ |fflfflfflffl{zfflfflfflffl} thermal noise
Hðsm ðkÞÞ |fflfflfflfflffl{zfflfflfflfflffl}
mechanical sources
þ nðkÞ,
(1)
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where xðkÞ is the observation vector and nðkÞ is additive noise, independent of the sources. Linear filters F (respectively H) model the propagation between each source st ðkÞ (respectively sm ðkÞ) and each accelerometer of vector xðkÞ. Sensors respond to vertical or horizontal ones, according to their positions. Therefore, some accelerometers are more sensitive to combustion noise whereas others receive more mechanical noise such as piston-slap. Nevertheless, all accelerometer signals are issued from convolutive mixtures of thermal and mechanical sources. If no reference signal is available, BSS methods can then be applied to accelerometer signals since they aim at the retrieval of independent sources (namely thermal and mechanical sources) only from linear mixtures of their responses. The BSS principle will be exposed more precisely in the second part of the paper and the results issued of the two approaches (blind or not) will be discussed therein. 3. Principle of the separation based on the pressure sensor Thermal noises are evidently due to pressure variations in the combustion chamber. For a given sensor measuring an acceleration: xðkÞ ¼ xt ðkÞ þ xm ðkÞ,
(2)
where xt ðkÞ and ym ðkÞ are, respectively, thermal and mechanical noises; the best transfer function capable of estimating xt ðkÞ from p(k) is provided by the Wiener gain formula: Gðf Þ ¼
Sxp ðf Þ , S pp ðf Þ
(3)
where S xp ðf Þ and Spp ðf Þ are, respectively, the cross-spectrum between acceleration and pressure and the autospectrum of pressure. Such filtering actually represents an estimation of pðkÞ from xðkÞ provided that the sources of thermal and mechanical noises are statistically uncorrelated, i.e. xm ðkÞ is orthogonal to pðkÞ. xm ðkÞ is then obtained by simple subtraction from xðkÞ (Fig. 1). The originality and the efficiency of this procedure reside in the construction method of the G filter that exploits the cyclostationary characteristics of the acceleration and pressure signals [4,11,12]. Data acquisition is recorded at given stationary operating points (medium speed, medium load, constant oil pressure and temperature). A pulse train is also acquired as issued from a magnetic sensor placed in front of a sprocket. In the course of this process all signals are sampled at a fixed frequency. Pressures and accelerations are then resampled by the pulse train with respect to the angular variable of the crankshaft. In this manner all engine cycles are defined by the same number of samples and are endowed with the same statistical features. As a consequence all re-sampled signals are then forced to be cyclostationary with a single cyclical period. Hence, all subsequent work can be restricted to only studying the engine cycle particularly around the TDC of the cylinder fitted with sensors.
Fig. 1. Principle of the separation.
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Fig. 2. Example of an accelerometer signal decomposed into different cyclic stochastic realizations after synchronous re-sampling. xðy; oÞ is the angular re-sampled signal as issued from the diesel engine, and xy ðy; Bi Þ is the ith angular signal realization.
The signals corresponding to every cycle are considered as the realization of the same stochastic process (Fig. 2), consequently the statistical features can be assessed in a general and efficient manner using the ‘synchronous averaging’ method. Fig. 2 displayed one example of an accelerometer sensor decomposed into different stochastic cyclic realizations as provided from synchronous re-sampling. One can use the overall average of those cycles as a consistent statistical estimator of the signal mean (i.e. the so-called time or synchronous average). The Wiener filter is constructed from the residues of the pressure signal and the accelerations, (i.e. from their realizations from which the synchronous averages have been subtracted). Therefore it only uses properties related to second-order statistics. The efficiency of such filtering enables to benefit from the fact that: (1) The residues have a broader frequency band than the averages, and are therefore better suited to the problem of identifying a filter. (2) The fundamental hypothesis on which the principle of separation rests is the statistical uncorrelation of mechanical and thermal noises, which is certainly easier to meet for the residues than for the raw signals with their synchronous averages. The only drawback is that only a minor part of the power produced by the residual signal is used and this must be balanced by the use of a larger number of cycles. As many filters as accelerometers are required, and filtering is applied to the original signals (while taking into account their synchronous averages). From the so-obtained results we will not only be able to deduce the position of the piston and the extent of the shocks occurring between the piston and the liner, but also to
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qualify the piston as an average of the percentage of mechanical noise (PMN). Such averages are performed on all available cycles and all chosen sensors in a given angular window and in a given frequency window. It is necessary to note however that Wiener filtering the pressure only allows the extraction of the noise of thermal origin. It is not possible therefore to separate piston-slap from other mechanical noises. Identifying the shocks between the piston and the liner is obviously more difficult. 4. Experimental device The signals have been acquired on a four-stroke and four-cylinder diesel engine. One of the cylinders is equipped with a pressure sensor. Ten accelerometers sensors are placed around the cylinder fitted with sensors. Three sensors, named after their numbers 1, 3 and 7, have been used for this study. Sensor 1 responds to vertical moves, positioned at the top of the combustion chamber whereas sensors 3 and 7 have a horizontal position on both sides of the liner. The engine has been equipped with a set of pistons which are particularly noisy. Some acquisitions have been made at several speeds and under several loads. Results are presented are for a speed of 2500 rpm with a couple of 6 Da N ms. As previously mentioned, the engine is fitted with a double injection system, so that an angular window as large as [401 801] was used, the TDC corresponding to 01. Every acquisition includes about 140 engine cycles. For the last 20 cycles, the injection in the piston fitted with sensor has been cancelled to allow for measures of the absolute power of mechanical noises in decibels. It is therefore also possible to rank the pistons and compare the results to those obtained by the PMN. Such cycles when no injection takes places have been coined ‘‘dead cycles’’. 5. Experimental results First, we compare the total power measured on each sensor, for the active and the dead cycles. It provides us with an accurate evaluation of the shock positions on the piston liner and with their consequences in relation to the combustion, therefore making it possible to assess the efficiency of our separation methods. Figs. 3, 4 and 5 display the powers measured, respectively, by sensors 3, 7 and 1. The power has been normalized to be equal to unity in the processed window. The top figure includes combustion; the bottom one
Fig. 3. Powers on sensor 3 with and without combustion.
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Fig. 4. Powers on sensor 7 with and without combustion.
Fig. 5. Powers on sensor 1 with and without combustion.
does not but rather includes the measured pressures and the injection control pulses. It is seen in Fig. 3 that sensor 3 only registers piston noise and is insensitive to the combustion process. The maximum power is located at 18110 when combustion occurs and 18180 when no combustion takes place. Considering Fig. 4, it is noticeable that sensor 7 registers three important shocks at 20150 , 231 and 271 when combustion takes places, whereas similar shocks are observed 0150 further in the absence of combustion.
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A shock at 2120 is also noticeable. Combustion is noticeable between 101 and 201, including the position of the main shock and the pre-combustion effect between 121 and 01. Fig. 5 shows that sensor 1 is more sensitive to combustion. It can be seen indeed that pre-combustion spreads will between 221 and 41 and that the main combustion takes places between 81 and 351. Mechanical shocks take place at 211, 23180 , 28180 , 421 and 451. The first two shocks may coincide with those observed on sensor 7, while the last two shocks cannot be piston liner induced considering their respective position. We applied the proposed cyclic Wiener filtering procedure on these different sensors. Figs. 6, 7 and 8 show the estimated powers relating, respectively, to combustion and mechanical noises on sensors 1, 3 and 7. The power of each contribution is averaged over the cycle index and has been normalized by the maximum power of the corresponding sensor. On sensor 1—Fig. 6—the main combustion is registered between 61 and 201 and pre-combustion between— 121 and 41. The power of combustion is to be compared to that of the first separated source as obtained from the BSS method of part II (Fig. 4 of part II). It appears that both methods provide similar results although the pre-combustion cannot be accurately found by means of the BSS method solely. Concerning the estimated power of mechanical noises, peaks are well noticeable at 28180 , 421 and 451 with are the same plus 11 with those previously identified when no combustion took place. This estimated power is also to be compared to the sum of the powers of the last two sources as obtained from the BSS method of part II. The analysis of sensor 3,—Fig. 7—results in similar conclusions: the estimated power of mechanical noise is very similar to that previously recorded when no combustion took place—Fig. 3 (with the same difference in degree)—and it is about one-hundredth of the mechanical noise power. Much similarity is also to be noticed between the estimated power of combustion on Fig. 7 and the power of the first separated source on sensor 3 as provided by the BSS method of part II (Fig. 5 part II), and also between the estimated power of mechanical noises and the power of the second source (with an approximate shift of 21). The results of Fig. 8 also confirm the comments that have been made about Fig. 4 on sensor 7, i.e. that this sensor is more sensitive to piston-liner shocks than to combustion: a factor of more than ten between the powers of these two sources is found. The power of mechanical noises is similar enough to the power obtained without combustion on Fig. 4 (with more than 11 difference) and other shocks located at 21 can also be found by this method. One can also say
Thermal noise
1 0.8 0.6 0.4 0.2 0 -40
-20
0
20 Degree
40
60
80
-20
0
20 Degree
40
60
80
Mechanical noise
1 0.8 0.6 0.4 0.2 0 -40
Fig. 6. Estimated powers of combustion and mechanical noise after separation on the sensor 1.
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Mechanical noise
Thermal noise
1216
0.01 0.008 0.006 0.004 0.002 0 -40
-20
0
20 Degree
40
60
80
1 0.8 0.6 0.4 0.2 0 -40
-20
0
20 Degree
40
60
80
Fig. 7. Estimated powers of combustion and mechanical noise after separation on sensor 3.
Thermal noise
0.1 0.08 0.06 0.04 0.02 0 -40
-20
0
20 Degree
40
60
80
-20
0
20 Degree
40
60
80
Mechanical noise
1 0.8 0.6 0.4 0.2 0 -40
Fig. 8. Estimated powers of combustion and mechanical noise after separation on sensor 7.
that the sum of the powers of the second and third sources obtained by BSS (Fig. 6, part II) is very similar to the power estimated by the cyclic Wiener filter. It is worthwhile to note that the results of the BSS method and those of the Wiener filter are somewhat different relative to the separated piston-slap source. Actually in order to obtain comparable results it is necessary to add the sources 2 and 3 returned by the BSS method, because it is the combined effect of these two sources which corresponds to the mechanical noise estimated from the Wiener filter. On source 2 part of the piston-slap is retrieved that corresponds to an impact point of the piston on the liner, and on source 3 the piston-slap corresponding to another impact point on the liner is also measured. The points of impact being different it is then natural that two different piston-slap phenomena are returned by BSS are assigned to different sources, because they are considered as statistically independent. Moreover, the propagation between sensors and sources is also different as the points of impact are distinct. Therefore, the two piston-slap phenomena act as two different sources in the mixing model. The separation by Wiener filtering gives two
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uncorrelated signals: the combustion noise and the mechanical noise, in which one recovers the piston-slap but also all other phenomena uncorrelated with the combustion. 6. Conclusion We have shown that the Wiener filtering of the pressure measured inside the cylinder constitutes a simple means of evaluation of the part of the combustion power on accelerometer sensors. The filter is estimated from the pressure signal and the accelerometer sensors only from second-order statistics under the cyclostationary hypothesis. The Wiener filter makes it possible to estimate the contribution of combustion noise in the accelerometer signal and, by subtraction, to also estimate the noise due to mechanical sources. The result of the separation has been corroborated by those obtained from the BSS method presented in part II of this paper. The results of the two separation methods have been found coherent in terms of instantaneous power on all tested sensors. It would be interesting to carry out a more detailed study of the impact points on the liner by the BSS methods in order to better isolate piston-slap which is not feasible by the Wiener filter method. Acknowledgements The authors wish to thank the Re´gion Rhoˆne Alpes and the Metravib company (France) for their financial support. Also, we acknowledge the anonymous reviewers for their help in improving this paper. References [1] E.E. Ungar, D. Ross, Vibration noise due to piston-slap in reciprocating machinery, Journal of Sound and Vibration 2 (2) (1965) 132–146. [2] S.N.Y. Gerges, J.C. Luca, N. Labor, A literature review of diesel engine noise with emphasis on piston slap, International Journal of Acoustics and Vibration 5 (2000) 37–45. [3] S.M. Cho, S.T. Ahn, Y.H. Kim, A simple model to estimate impact force inducted by piston slap, Journal of Sound and Vibration 255 (2) (2002) 229–242. [4] J. Antoni, Apport de l’e´chantillonnage angulaire et de la cyclostationnarite´ au diagnostic par analyse vibratoire des moteurs thermiques, Ph.D. Thesis, INP Grenoble, 2000. [5] J. Antoni, F. Bonnardot, A. Raad, M. El Badaoui, Cyclostationary modelling of rotating machine vibration signals, Mechanical Systems and Signal Processing 18 (6) (2004) 1285–1314. [6] P. Comon, Independent component analysis, a new concept, Signal Processing 36 (3) (1994) 287–314. [7] J.F. Cardoso, Blind signal separation statistical principle, Proceedings of the IEEE 86 (1998) 2009–2025. [8] J. He´rault, C. Jutten, Blind separation of sources, I. An adaptive algorithm based on neuromimetic architecture, Signal Processing 24 (1) (1991) 1–10. [9] A. Hyvarinen, Survey on independent component analysis, Neural Computing Surveys 2 (1999) 94–128. [10] H. Kanda, M. Okubo, T. Yonezawa, Analysis of noise sources and their transfer paths in diesel engines, SAE Paper No. 900014, 1990, pp. 34–41. [11] Y. Gao, R.B. Randall, Reconstruction of diesel engine cylinder pressure using a time domain smoothing technique, Mechanical Systems and Signal Processing 13 (5) (1999). [12] W.A. Gardner, Cyclostationarity in Communication and Signal Processing, IEEE Press, New York, 1994.
Separation of combustion noise and piston-slap in diesel engine—Part I: Separation of combustion noise and piston-slap in diesel engine by cyclic Wiener filtering M. El. Badaouia,, J. Danie`rea, F. Guilleta, C. Servie`reb a
Laboratoire LASPI, IUT de Roanne, 20 Avenue de Paris, 42334 Roanne Cedex, France Laboratoire des Images et des Signaux (LIS), BP 46 38402 Saint-Martin d’He`res, France
b
Received 9 March 2005; received in revised form 10 August 2005; accepted 12 August 2005 Available online 5 October 2005
Abstract The main purpose of this study is to characterize the relative noise given out by a diesel engine, around the Top Dead Centre (TDC) by quantifying the proportions of ‘‘mechanical noise’’ originating mainly from piston-slap on the one hand and ‘thermal noise’’ originating from combustion on the other hand. Two different approaches are described here to solve this problem. In the first part of the paper, the cylinder pressure is measured and used as a reference in order to reconstruct the thermal noise. Next, we propose a method based on applying a cyclic Wiener filter to the measured cylinder pressure in order to separate the noises of mechanical and thermal origins. The final result is to reduce the engine resulting noise. The second part of the paper is devoted to blind source separation (BSS) methods applied on signals issued from accelerometers placed on one of the cylinders. It develops a BSS method based on a convolutive model of non-stationary mixtures and introduces a new method based on the joint diagonalization of time varying spectral matrices of the observations. Both methods are then applied to real data and the estimated sources are finally validated by several physical arguments. r 2005 Elsevier Ltd. All rights reserved. Keywords: Cyclic Wiener filter; Piston-slap; Combustion noise; Blind source separation
1. Introduction The purpose of this paper is to characterize the relative noise given out by a diesel engine, around the Top Dead Centre (TDC) by quantifying the proportions of ‘‘mechanical noise’’ (originating mainly from pistonslap) on the one hand and ‘‘thermal noise’’ originating from combustion on the other hand. Measurements are carried out by means of several accelerometers located on the engine. Retrieving such data has been for some years a major challenge for motorists because they can be used to reduce the resulting noise, e.g. by fixing the injection parameters or, better, to devise the best geometric piston features. Several approaches have been Corresponding author. Tel.: +33 4774 48928; fax: +33 4774 48921.
E-mail address: [email protected] (M.E. Badaoui). 0888-3270/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2005.08.010
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explored in the past to attempt to solve this difficult but fundamental problem [1–4]. However, no truly satisfactory solution has been found so far. The main difficulty of the problem is that the relevant causes of such noise are both spectrally and temporally overlapping. Therefore the separation methods, if they are to be efficient, must be based either on a priori knowledge of the noise—such as provided by a reference signal—or on the statistical independence of the noise sources—such as assumed in a blind procedure. This work was initiated within a collaboration between the laboratories LASPI (Roanne-France), LIS (Grenoble-France) and the company Metravib (Lyon-France). The two previous approaches have been explored by the LASPI and the LIS and they have been compared on real data issued of experiments carried out by Metravib. The paper is separated in two parts and presents the two types of noise separation. In the first part, the LASPI research team proposes a procedure taking a priori information into account. The supplementary information is provided by an additional pressure sensor. Typically, if the cylinder pressure is measured, it can be used as a reference in order to reconstruct the thermal acceleration. The transfer between pressure and acceleration issued of the combustion phenomenon is then estimated with a method based on a cyclic Wiener filtering approach [5]. Next, the thermal noise can be computed on each accelerometer and afterwards, the mechanical noise is obtained by subtraction. In the second part, blind source separation (BSS) methods are examined by the LIS research team. Basically, BSS recovers signals of different physical sources from the observation of several mixtures of them and in this case no reference signal is needed. This approach is usually used when the transfer from sources to sensors is too difficult to model. The lack of knowledge about mixtures and sources is then compensated by the strong hypothesis of mutual independence of the sources [6–9]. This second paper develops a BSS method based on a convolutive model of non-stationary mixtures. It introduces a method exploiting the joint diagonalization of time varying spectral matrices of the observation records and a new technique to handle the problem of permutation ambiguity in the frequency domain.
2. Experimental device and modelling of the observations The signals have been acquired on a four-stroke and four-cylinder diesel engine. One of the cylinders was equipped with a pressure sensor whereas ten accelerometers sensors were placed around the instrumented cylinder. Signals issued from the accelerometers have been sampled at 25 600 Hz, synchronously to the rotation speed of the crankshaft. On each cycle of the signals, the signals have been truncated in the angular window [401, 801] of the crankshaft. In the processed window thermal and mechanical phenomena are temporally overlapping around the TDC, as well as spectrally overlapping. Consequently, an accelerometer measures an acceleration xðkÞ at discrete time k, as the addition of the thermal contribution xt ðkÞ and the mechanical one xm ðkÞ. The mechanical phenomenon is constituted by the piston-slap and by mechanical noises due to other cylinders. Concerning the thermal aspect, this engine is fitted with double injection: the pre-injection angle varies from a few degrees up to 301 before the TDC (according to the load), then the principal injection occurs in the vicinity the TDC. Thermal noises are evidently due to the pressure variations in the combustion chamber xt ðkÞ; some transfer functions therefore link the relationship between a ‘pðkÞ’ pressure at discrete time k that provides thermal noises at the sensor level [10]. In other words, the pressure sensor provides a reference signal of the combustion source which can perform the reconstruction of the thermal accelerations in each accelerometer signal. This separation method, using a pressure sensor as a reference, is presented in the first part of the paper. As thermal and mechanical noises are both spectrally and temporally overlapping, an accelerometer measures a signal xðkÞ ¼ xt ðkÞ þ xm ðkÞ. In a general model of propagation, the accelerations come from two types of sources st ðkÞ and sm ðkÞ by linear filtering where st ðkÞ represents the thermal source, and sm ðkÞ the mechanical source. So, the accelerometer signals are given by xðkÞ ¼ F ðst ðkÞÞ þ |fflfflfflffl{zfflfflfflffl} thermal noise
Hðsm ðkÞÞ |fflfflfflfflffl{zfflfflfflfflffl}
mechanical sources
þ nðkÞ,
(1)
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where xðkÞ is the observation vector and nðkÞ is additive noise, independent of the sources. Linear filters F (respectively H) model the propagation between each source st ðkÞ (respectively sm ðkÞ) and each accelerometer of vector xðkÞ. Sensors respond to vertical or horizontal ones, according to their positions. Therefore, some accelerometers are more sensitive to combustion noise whereas others receive more mechanical noise such as piston-slap. Nevertheless, all accelerometer signals are issued from convolutive mixtures of thermal and mechanical sources. If no reference signal is available, BSS methods can then be applied to accelerometer signals since they aim at the retrieval of independent sources (namely thermal and mechanical sources) only from linear mixtures of their responses. The BSS principle will be exposed more precisely in the second part of the paper and the results issued of the two approaches (blind or not) will be discussed therein. 3. Principle of the separation based on the pressure sensor Thermal noises are evidently due to pressure variations in the combustion chamber. For a given sensor measuring an acceleration: xðkÞ ¼ xt ðkÞ þ xm ðkÞ,
(2)
where xt ðkÞ and ym ðkÞ are, respectively, thermal and mechanical noises; the best transfer function capable of estimating xt ðkÞ from p(k) is provided by the Wiener gain formula: Gðf Þ ¼
Sxp ðf Þ , S pp ðf Þ
(3)
where S xp ðf Þ and Spp ðf Þ are, respectively, the cross-spectrum between acceleration and pressure and the autospectrum of pressure. Such filtering actually represents an estimation of pðkÞ from xðkÞ provided that the sources of thermal and mechanical noises are statistically uncorrelated, i.e. xm ðkÞ is orthogonal to pðkÞ. xm ðkÞ is then obtained by simple subtraction from xðkÞ (Fig. 1). The originality and the efficiency of this procedure reside in the construction method of the G filter that exploits the cyclostationary characteristics of the acceleration and pressure signals [4,11,12]. Data acquisition is recorded at given stationary operating points (medium speed, medium load, constant oil pressure and temperature). A pulse train is also acquired as issued from a magnetic sensor placed in front of a sprocket. In the course of this process all signals are sampled at a fixed frequency. Pressures and accelerations are then resampled by the pulse train with respect to the angular variable of the crankshaft. In this manner all engine cycles are defined by the same number of samples and are endowed with the same statistical features. As a consequence all re-sampled signals are then forced to be cyclostationary with a single cyclical period. Hence, all subsequent work can be restricted to only studying the engine cycle particularly around the TDC of the cylinder fitted with sensors.
Fig. 1. Principle of the separation.
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Fig. 2. Example of an accelerometer signal decomposed into different cyclic stochastic realizations after synchronous re-sampling. xðy; oÞ is the angular re-sampled signal as issued from the diesel engine, and xy ðy; Bi Þ is the ith angular signal realization.
The signals corresponding to every cycle are considered as the realization of the same stochastic process (Fig. 2), consequently the statistical features can be assessed in a general and efficient manner using the ‘synchronous averaging’ method. Fig. 2 displayed one example of an accelerometer sensor decomposed into different stochastic cyclic realizations as provided from synchronous re-sampling. One can use the overall average of those cycles as a consistent statistical estimator of the signal mean (i.e. the so-called time or synchronous average). The Wiener filter is constructed from the residues of the pressure signal and the accelerations, (i.e. from their realizations from which the synchronous averages have been subtracted). Therefore it only uses properties related to second-order statistics. The efficiency of such filtering enables to benefit from the fact that: (1) The residues have a broader frequency band than the averages, and are therefore better suited to the problem of identifying a filter. (2) The fundamental hypothesis on which the principle of separation rests is the statistical uncorrelation of mechanical and thermal noises, which is certainly easier to meet for the residues than for the raw signals with their synchronous averages. The only drawback is that only a minor part of the power produced by the residual signal is used and this must be balanced by the use of a larger number of cycles. As many filters as accelerometers are required, and filtering is applied to the original signals (while taking into account their synchronous averages). From the so-obtained results we will not only be able to deduce the position of the piston and the extent of the shocks occurring between the piston and the liner, but also to
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qualify the piston as an average of the percentage of mechanical noise (PMN). Such averages are performed on all available cycles and all chosen sensors in a given angular window and in a given frequency window. It is necessary to note however that Wiener filtering the pressure only allows the extraction of the noise of thermal origin. It is not possible therefore to separate piston-slap from other mechanical noises. Identifying the shocks between the piston and the liner is obviously more difficult. 4. Experimental device The signals have been acquired on a four-stroke and four-cylinder diesel engine. One of the cylinders is equipped with a pressure sensor. Ten accelerometers sensors are placed around the cylinder fitted with sensors. Three sensors, named after their numbers 1, 3 and 7, have been used for this study. Sensor 1 responds to vertical moves, positioned at the top of the combustion chamber whereas sensors 3 and 7 have a horizontal position on both sides of the liner. The engine has been equipped with a set of pistons which are particularly noisy. Some acquisitions have been made at several speeds and under several loads. Results are presented are for a speed of 2500 rpm with a couple of 6 Da N ms. As previously mentioned, the engine is fitted with a double injection system, so that an angular window as large as [401 801] was used, the TDC corresponding to 01. Every acquisition includes about 140 engine cycles. For the last 20 cycles, the injection in the piston fitted with sensor has been cancelled to allow for measures of the absolute power of mechanical noises in decibels. It is therefore also possible to rank the pistons and compare the results to those obtained by the PMN. Such cycles when no injection takes places have been coined ‘‘dead cycles’’. 5. Experimental results First, we compare the total power measured on each sensor, for the active and the dead cycles. It provides us with an accurate evaluation of the shock positions on the piston liner and with their consequences in relation to the combustion, therefore making it possible to assess the efficiency of our separation methods. Figs. 3, 4 and 5 display the powers measured, respectively, by sensors 3, 7 and 1. The power has been normalized to be equal to unity in the processed window. The top figure includes combustion; the bottom one
Fig. 3. Powers on sensor 3 with and without combustion.
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Fig. 4. Powers on sensor 7 with and without combustion.
Fig. 5. Powers on sensor 1 with and without combustion.
does not but rather includes the measured pressures and the injection control pulses. It is seen in Fig. 3 that sensor 3 only registers piston noise and is insensitive to the combustion process. The maximum power is located at 18110 when combustion occurs and 18180 when no combustion takes place. Considering Fig. 4, it is noticeable that sensor 7 registers three important shocks at 20150 , 231 and 271 when combustion takes places, whereas similar shocks are observed 0150 further in the absence of combustion.
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A shock at 2120 is also noticeable. Combustion is noticeable between 101 and 201, including the position of the main shock and the pre-combustion effect between 121 and 01. Fig. 5 shows that sensor 1 is more sensitive to combustion. It can be seen indeed that pre-combustion spreads will between 221 and 41 and that the main combustion takes places between 81 and 351. Mechanical shocks take place at 211, 23180 , 28180 , 421 and 451. The first two shocks may coincide with those observed on sensor 7, while the last two shocks cannot be piston liner induced considering their respective position. We applied the proposed cyclic Wiener filtering procedure on these different sensors. Figs. 6, 7 and 8 show the estimated powers relating, respectively, to combustion and mechanical noises on sensors 1, 3 and 7. The power of each contribution is averaged over the cycle index and has been normalized by the maximum power of the corresponding sensor. On sensor 1—Fig. 6—the main combustion is registered between 61 and 201 and pre-combustion between— 121 and 41. The power of combustion is to be compared to that of the first separated source as obtained from the BSS method of part II (Fig. 4 of part II). It appears that both methods provide similar results although the pre-combustion cannot be accurately found by means of the BSS method solely. Concerning the estimated power of mechanical noises, peaks are well noticeable at 28180 , 421 and 451 with are the same plus 11 with those previously identified when no combustion took place. This estimated power is also to be compared to the sum of the powers of the last two sources as obtained from the BSS method of part II. The analysis of sensor 3,—Fig. 7—results in similar conclusions: the estimated power of mechanical noise is very similar to that previously recorded when no combustion took place—Fig. 3 (with the same difference in degree)—and it is about one-hundredth of the mechanical noise power. Much similarity is also to be noticed between the estimated power of combustion on Fig. 7 and the power of the first separated source on sensor 3 as provided by the BSS method of part II (Fig. 5 part II), and also between the estimated power of mechanical noises and the power of the second source (with an approximate shift of 21). The results of Fig. 8 also confirm the comments that have been made about Fig. 4 on sensor 7, i.e. that this sensor is more sensitive to piston-liner shocks than to combustion: a factor of more than ten between the powers of these two sources is found. The power of mechanical noises is similar enough to the power obtained without combustion on Fig. 4 (with more than 11 difference) and other shocks located at 21 can also be found by this method. One can also say
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Fig. 6. Estimated powers of combustion and mechanical noise after separation on the sensor 1.
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Fig. 8. Estimated powers of combustion and mechanical noise after separation on sensor 7.
that the sum of the powers of the second and third sources obtained by BSS (Fig. 6, part II) is very similar to the power estimated by the cyclic Wiener filter. It is worthwhile to note that the results of the BSS method and those of the Wiener filter are somewhat different relative to the separated piston-slap source. Actually in order to obtain comparable results it is necessary to add the sources 2 and 3 returned by the BSS method, because it is the combined effect of these two sources which corresponds to the mechanical noise estimated from the Wiener filter. On source 2 part of the piston-slap is retrieved that corresponds to an impact point of the piston on the liner, and on source 3 the piston-slap corresponding to another impact point on the liner is also measured. The points of impact being different it is then natural that two different piston-slap phenomena are returned by BSS are assigned to different sources, because they are considered as statistically independent. Moreover, the propagation between sensors and sources is also different as the points of impact are distinct. Therefore, the two piston-slap phenomena act as two different sources in the mixing model. The separation by Wiener filtering gives two
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uncorrelated signals: the combustion noise and the mechanical noise, in which one recovers the piston-slap but also all other phenomena uncorrelated with the combustion. 6. Conclusion We have shown that the Wiener filtering of the pressure measured inside the cylinder constitutes a simple means of evaluation of the part of the combustion power on accelerometer sensors. The filter is estimated from the pressure signal and the accelerometer sensors only from second-order statistics under the cyclostationary hypothesis. The Wiener filter makes it possible to estimate the contribution of combustion noise in the accelerometer signal and, by subtraction, to also estimate the noise due to mechanical sources. The result of the separation has been corroborated by those obtained from the BSS method presented in part II of this paper. The results of the two separation methods have been found coherent in terms of instantaneous power on all tested sensors. It would be interesting to carry out a more detailed study of the impact points on the liner by the BSS methods in order to better isolate piston-slap which is not feasible by the Wiener filter method. Acknowledgements The authors wish to thank the Re´gion Rhoˆne Alpes and the Metravib company (France) for their financial support. Also, we acknowledge the anonymous reviewers for their help in improving this paper. References [1] E.E. Ungar, D. Ross, Vibration noise due to piston-slap in reciprocating machinery, Journal of Sound and Vibration 2 (2) (1965) 132–146. [2] S.N.Y. Gerges, J.C. Luca, N. Labor, A literature review of diesel engine noise with emphasis on piston slap, International Journal of Acoustics and Vibration 5 (2000) 37–45. [3] S.M. Cho, S.T. Ahn, Y.H. Kim, A simple model to estimate impact force inducted by piston slap, Journal of Sound and Vibration 255 (2) (2002) 229–242. [4] J. Antoni, Apport de l’e´chantillonnage angulaire et de la cyclostationnarite´ au diagnostic par analyse vibratoire des moteurs thermiques, Ph.D. Thesis, INP Grenoble, 2000. [5] J. Antoni, F. Bonnardot, A. Raad, M. El Badaoui, Cyclostationary modelling of rotating machine vibration signals, Mechanical Systems and Signal Processing 18 (6) (2004) 1285–1314. [6] P. Comon, Independent component analysis, a new concept, Signal Processing 36 (3) (1994) 287–314. [7] J.F. Cardoso, Blind signal separation statistical principle, Proceedings of the IEEE 86 (1998) 2009–2025. [8] J. He´rault, C. Jutten, Blind separation of sources, I. An adaptive algorithm based on neuromimetic architecture, Signal Processing 24 (1) (1991) 1–10. [9] A. Hyvarinen, Survey on independent component analysis, Neural Computing Surveys 2 (1999) 94–128. [10] H. Kanda, M. Okubo, T. Yonezawa, Analysis of noise sources and their transfer paths in diesel engines, SAE Paper No. 900014, 1990, pp. 34–41. [11] Y. Gao, R.B. Randall, Reconstruction of diesel engine cylinder pressure using a time domain smoothing technique, Mechanical Systems and Signal Processing 13 (5) (1999). [12] W.A. Gardner, Cyclostationarity in Communication and Signal Processing, IEEE Press, New York, 1994.