Digital signal processing of in-cylinder pressure for combustion diagnosis of internal combustion engines

ARTICLE IN PRESS Mechanical Systems and Signal Processing 24 (2010) 1767–1784

Contents lists available at ScienceDirect

Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/jnlabr/ymssp

Digital signal processing of in-cylinder pressure for combustion diagnosis of internal combustion engines F. Payri, J.M. Luja´n, J. Martı´n, A. Abbad  CMT-Motores Te´rmicos, Universidad Polite´cnica de Valencia Camino de Vera s/n, 46022 Valencia, Spain

a r t i c l e in fo

abstract

Article history: Received 24 November 2008 Received in revised form 19 November 2009 Accepted 8 December 2009 Available online 21 February 2010

In-cylinder pressure analysis is a key tool for engine research and diagnosis; however, it normally requires to process the experimental signal for providing valuable information. Usual four-step data processing consists on level correction, angle referencing, cycle averaging, and filtering. Concerning the last two issues, ad-hoc methods and experience-based algorithms are mostly used, and there is not a consensus in the scientific community about the optimal way to proceed. This paper presents a step-bystep approach to optimise the signal processing both for offline and online applications based on the characteristics of the signal. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Internal combustion engine Diesel engine In-cylinder pressure Piezoelectric sensor Filter Combustion diagnosis

1. Introduction The measurement of the in-cylinder pressure has been object of the study from the beginning of the internal combustion engine. The importance of this signal lies on the amount of information that it can provide such as peak pressure (which is a critical mechanical constraint), indicated mean effective pressure, pumping mean effective pressure or even it can allow some more complex calculations such as air mass flow estimation [1] or combustion diagnosis on the basis of the first law of thermodynamics [2,3]. Thus, in-cylinder pressure measurement is considered a very valuable source of information during the development and calibration stages of the engine. Moreover, many applications of in-cylinder pressure for control and diagnosis of both spark ignited and compression ignited engines can be found in literature. Although in-cylinder pressure is not still usual in production engines, many recent works have been focused on on-line combustion failure detection [4,5], cylinder trapped mass estimation [6,7], exhaust gas recirculation control [8,9], torque estimation [4], emissions control [10], noise control [11,12], etc. All these control strategies need of a reliable in-cylinder pressure signal in a real time basis, thus requiring efficient methodologies of signal processing. The earliest measurement methods of the in-cylinder pressure were based on completely mechanical systems, which provided a graphical representation of the pressure–volume cycle. A number of different methods [4] have been used from then, going from mechanical indicators of mean and peak pressure, systems based on the optical conversion of mechanical

 Corresponding author. Tel.: + 34 963877650; fax: + 34 963877659.

E-mail addresses: [email protected] (F. Payri), [email protected] (J.M. Luja´n), [email protected] (J. Martı´n), [email protected] (A. Abbad). URLS: http://www.CMT.UPV.es (F. Payri), http://www.CMT.UPV.es (J.M. Luja´n), http://www.CMT.UPV.es (J. Martı´n), http://www.CMT.UPV.es (A. Abbad). 0888-3270/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2009.12.011

ARTICLE IN PRESS 1768

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

indicator, electro-mechanical devices such as balanced-diaphragm indicators, to modern acquisition systems based on the use of piezoelectric crystals or optical sensors [13]. Piezoelectric transducer are based on the piezoelectric phenomenon consisting on the generation of electric charges when applying an external force or acceleration, on materials such as quartz (SiO2) or other synthetic materials [4]. They have the best technical specification regarding accuracy, bandwidth, thermal characteristics, robustness, durability and size [14], in addition they combine a high sensitivity with a wide amplitude measurement range [15] and they show a convenient frequency response. Thus, piezoelectric sensor have a temperature range (up to 620 K) much higher than piezoresistive (up to 423 K) and their accuracy is clearly higher to that of the new optical sensors [13]. Due to these reasons, nowadays piezoelectric transducer are being used almost exclusively for measuring in-cylinder pressures [8,14,16,17]; and so will be done in this work. Piezoelectric sensor signal is usually integrated and amplified with a charge amplifier (conditioner) with a linear response. The calibration of the sensor and conditioner can be done according to the following line: preal ¼ offset þ Ksens  pmeasured

ð1Þ

where Ksens is the sensor sensitivity constant and the offset depends on the operation conditions and some uncontrolled uncertainties, as mentioned below. The physical conception of the sensor is based on the measurement of the in-cylinder pressure variations rather than the pressure itself. Therefore, piezoelectric sensors do not provide absolute values of pressure and thus the correction of the pressure offset (pegging) in the Eq. (1) becomes a major problem when dealing with this kind of sensors. There are different strategies for the pressure pegging [14,18], which can be grouped according to two fundamental underlying ideas:

 Referencing the pressure signal on the basis of a known point using a pressure sensor in the inlet or exhaust manifold for providing the reference pressure during the intake [19] or exhaust [16] process.

 Modelling the compression stroke of the engine assuming a known heat transfer law or polytropic coefficient (which corresponds to fitting a exponential curve of the type pVn) [20–22]. The second problem when facing the in-cylinder pressure signal processing is derived from the fact that a precise angle phasing between pressure and chamber volume is required to carry out an accurate combustion and performance analyses. Both pressure and volume are dependant on crank angle. On the one hand the volume can be directly determined from the crankshaft position. On the other hand, for pressure measurement a crank angle domain acquisition (using encoders such as that described in the experimental set-up section) is usually preferred to the time domain acquisition. Hence, knowing the exact crank angle for each pressure sample is of vital importance. Several methodologies to set the angular absolute reference by detecting the top dead centre can be found in the literature [23,24]. Finally, despite of the good performance of the piezoelectric transducers, there are several sources of error that can affect the raw measured signal [25,26]. Typical sources of error include (along with the pressure pegging and crank angle phasing) inaccurate measurement system calibration, short-term and long-term drift due to thermal shock, mechanical vibration noise and electrical noise. Manufacturers of piezoelectric transducers and acquisition devices are aware of these problems and they have done important efforts to minimise them. In particular, the thermal shock can be reduced by special heat shields, coating of the transducer membrane, water cooling and temperature effect compensating design. For the sake of accuracy, some authors perform a signal processing to eliminate almost completely the thermal shock effect using empirical numerical corrections [27,28]. The mechanical vibration noise is minimised by means of acceleration compensated sensors and the electrical noise can be reduced using extremely high insulation of the system sensor-cablecharge amplifier. Finally if an accurate calibration of the system is regularly done, the error in the sensitivity of the system is kept the best. Most of the described technical solution are included in the high quality sensors used for research tasks, while the cheaper transducers usually used for monitoring show significant lower performance. The significance of each of these sources of errors will be dependent on the analysis to be performed. For example, indicated mean effective pressure is very sensitive to crank angle phasing and thermal shock but insensitive to random noise and absolute pressure referencing. On the other hand, heat release analysis, which is a main issue in this work, is sensitive to some extent to all the listed errors. Through optimum selection and maintenance of the instruments, measuring errors can be kept to a minimum. However, in any case experimental pressure signal requires to be processed for providing valuable information. Usual four-step data processing consists on level correction, angle referencing, cycle averaging and filtering. The last two issues are in the scope of this work. Different averaging and filtering techniques can be found in literature for smoothing the signal, thus allowing a precise combustion diagnosis. However, there is not a consensus in the scientific community about the optimal way to proceed and, in most cases, ad-hoc methods and experience-based algorithms are used. This work claims to be a contribution in response to current requirements of suitable tools for combustion analysis in state-of-the-art reciprocating engines. Thus, the main objective of this paper is to propose a general methodology to optimise the signal processing of in-cylinder pressure for combustion diagnosis, both for offline and online applications. The content of the paper is organised as follows. First, the step-by-step methodology is briefly described in Section 2, while a short description of the specific test equipment used to obtain the experimental data is given in Section 3. Following the steps proposed in the methodology,

ARTICLE IN PRESS F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

1769

different issues regarding the pressure acquisition and its treatment are dealt with in subsequent sections. Thus, the main results obtained in Section 4 allows to state that to optimise the signal processing for offline applications:

 It is interesting to select a limited number of cycles to be measured. An adaptive method to choose the optimal number  

of cycles is proposed in Section 4.1. It will be shown that acquiring more cycles than the optimal, do not provide extra accuracy in the averaged cycle. Due to cycle-to-cycle variability it is necessary to average several measured cycles to obtain an accurate heat release law. In Section 4.2, a simple method for averaging the signal is proposed. The method is based on the frequency domain analysis and it provides useful information regarding the signal-to-noise ratio. Filtering is a key issue because heat release law calculation uses in-cylinder pressure derivative signal and derivating increases the signal noise. An adaptive low-pass filter for removing the high frequency part of the signal is proposed in Section 4.3. The cutoff frequency is selected taking into account the characteristic signal-to-noise ratio of the signal.

In Section 4.4, the validation of the proposed signal processing for offline application is performed in terms of heat release law. Once the offline signal processing has been established and validated, the online signal is approached in Section 5. A finite impulse response (FIR) filter is proposed and design cutoff frequencies are selected accordingly to the offline filter. It is checked that both offline and online filtering provides similar results and filtering reduces the standard deviation of the raw signal, thus allowing a suitable combustion analysis. Finally, in Section 6, the most relevant conclusions extracted from the work are summarized. 2. Methodology When the characteristics of the methodology to process the in-cylinder pressure signal were considered, it was assumed that on the one hand it had be concise enough to establish each necessary step to follow and on the other hand it had to be general enough to be applied to different reciprocating engines. The proposal, is basically based on experimental analysis of the signal measurements at different operating conditions in a diesel engine. Despite the specific experimental configurations presented in the following section, the proposed methodology will allow an easy extension of the procedure, with minor changes, to different kinds of engines and measurement configurations. In any case, it has to be considered that the specific values of the averaging and filtering parameters can be tuned to different operating condition, as will be described. Accordingly to the aim of the work, simple theoretical tools have been used to analyse the experimental signals. In particular, statistical analysis of the signals has been performed in terms of standard deviation and frequency domain analysis has also been used. The methodology has been approached in two main phases:

 Signal processing for offline applications (Section 4). In this case, it is usual to measure several cycles because cycle-tocycle variability can be very important, particularly in the operating points with low combustion stability. Although the acquisition and processing time is by far less critical than in the online applications, it is worth to optimise the number of cycles to measure, so that time and memory requirements are minimised. Apart from the ‘quantitative’ aspect of the acquisition, the ‘qualitative’ issue of the processing is approached, specially from the filtering point of view. In fact, if pressure signal is not filtered (or filter parameters are incorrectly set), the signal noise can lead to very poor results in terms of heat release law. Taking into account these comments the following steps are proposed for the signal processing: 1. Determination of the optimal number of cycles to measure. An adaptive method based on the variation of the standard deviation of the signal is proposed. The proposed method takes into account that the higher the number of measured cycles is, the lower the standard deviation of pressure samples at each angle is. Thus, there is a point in which additional cycles do no provided extra information and consequently an objective criteria to select the number of cycles can be defined. 2. Signal averaging. For an accurate heat release law calculation it is usual to use mean average variables (air mass flow, fuel mass flow, engine speed, etc.) and thus it is necessary to average the in-cylinder pressures cycles so that a representative thermodynamic cycle can be analysed. Additionally, averaging diminishes point-to-point variation due to signal noise, thus improving combustion analysis. The frequency domain analysis is usually used for signal filtering but it also offers a powerful tool for averaging the signal. The proposed averaging method consist on discriminate between the content of the spectrum that corresponds to the mean cycle and the rest, which is due to signal noise. Although the numerical results of the method is equivalent to the conventional point-to-point averaging, its main advantage is that it provides interesting information concerning the signal-to-noise ratio. 3. Signal filtering. To carry out a good combustion analysis it is necessary to remove high frequency noise from measured pressure signal. This way, the useful physical information is conserved for the combustion analysis. Lowpass filters are suitable, however it is a key issue to select the cutoff frequency to discriminate what is signal and

ARTICLE IN PRESS 1770

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

what is noise. An adaptive filter is proposed, which cutoff frequency is selected so that high frequencies, in which it is not possible to differentiate between signal and noise, are eliminated. As this criterion is based on the signal characteristics, no experienced-based rule is necessary.



As the objective of the offline processing is to obtain a good combustion analysis in terms of heat release law, the standard deviation of the rate of heat release will be used as criterion to validate the proposed signal processing method. Depending on the operating point or requirements the limits can vary, however, as the criteria followed for choosing the optimal number of cycles and the cutoff frequency is based on the characteristics of the signal itself it can be extrapolated to different engines and operating conditions. The key issue was to state the steps to follow for the signal processing, thus in the sake of clarity and brevity only result obtained in one engine will be presented. However, the proposed methodology has been applied in several diesel engines (from 0.35 l to 2 l displacement volume) and hundreds of tests in the research group and the results were basically similar to those presented in this paper. Signal processing for online applications (Section 5). In this case, due to the time limitations it is not possible to measure and process several in-cylinder cycles as a whole, thus averaging it is not possible and special requirements for the filtering process must be considered. The offline filtering method will be used as the base for performing an online filtering that can provide a valid indication of chamber pressure for control strategies based on in-cylinder pressure.

3. Experimental set-up and tests A schema of the test cell layout with the basic instrumentation is shown in Fig. 1. The experimental measurements presented in this work were carried out in a high speed direct injection diesel engine with 2.0-l displacement. It is a currently in production engine produced by an European manufacturer. It is a four-cylinder turbo-charged engine equipped with a common rail injection system. Its main characteristics are given in Table 1. The engine was directly coupled to an electric dyno. With the purpose of keeping the vibration pattern of the block as close as possible to real-life operation, the gear box case was maintained assembled with the engine. Several mean variables (acquired at a constant sample frequency of 100 Hz) are necessary for controlling the engine operating point and also for the combustion diagnosis. An AVL tests system is used for this purpose; it collects the measurement signals of different instrumentation and controls the electric dynamometer. The most significant of these mean variables, along with the main characteristics of the devices to measure them have been included in Table 2. The in-cylinder pressure was measured in one of the cylinders by means of a Kistler 6055B glow-plug piezoelectric transducer, characterised by a wide measurement range (0–250 bar), sensitivity of  18.8 pC/bar and high natural frequency (130 kHz). The electrical charge yielded by piezoelectric transducers is converted into a proportional voltage signal by means of Kistler 5015 charge amplifiers. The pressure sensors were calibrated according to the traditional method [29] based on a quasi-steady calibration by means of a deadweight tester with NPL and NIST traceability. The use of this technique can be justified on the basis that the characteristic time of the measured signal is much longer than the response time of the transducers. In this way, a quasi-steady response of the transducer can be assumed when in-cylinder pressure fluctuations are measured. With these assumptions, the relative error obtained from the calibration of each transducer was 7 0:7%.

ENGINE

Angle encoder

In-cylinder pressure

Piezoelectric sensor (Kistler 6055B)

1/rev (trigger) n/rev

Charge amplifier (Kistler 5015)

Mean variables AVL test system Dyno control

Mean variables measurement and control system Fig. 1. Engine test cell layout.

Real time acquisition and procesing system (3 configurations)

ARTICLE IN PRESS F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

1771

Table 1 Main engines characteristics. Displaced volume Cylinders Bore Stroke Connecting rod length Crank length Compression ratio Maximum power

2.0 4 84 90 143.5 45 16:1 125

(l) (mm) (mm) (mm) (mm) (kW)

Table 2 Mean variables measurement characteristics. Variable

Device

Error

Speed Torque _ fÞ Fuel mass flow rate ðm _ aÞ Air mass flow rate ðm Inlet pressure (pin) Exhaust pressure (pex) Inlet temperature (Tin) Exhaust temperature (Tex)

Magnetic sensor Load cell AVL 733S fuel balance Sensyflow hot-film anemometers Kistler 4045A5 piezoresistive sensor Kistler 4045A5 piezoresistive sensor Type K class B thermocouple Type K class B thermocouple

7 1 rpm 7 1 Nm 71 7 1% 7 1% 7 1% 72 K 72 K

Two different signals supplied by an optical encoder are used for the in-cylinder acquisition:

 The first is a pulse each crankshaft revolution which is used as trigger signal, so that all instantaneous signals 

acquisition can be started at the same crankshaft position. This signal is necessary for the angular absolute reference of the pressure, as commented. The second is an external clock used as sampling signal for the instantaneous acquisition systems, so that in-cylinder pressure evolution can be measured synchronised with the crankshaft angle. For this work an angular resolution of 0:53 was used.

both signals are fed to the acquisition system. Accordingly with the methodology described in the previous section, two kinds of analyses are going to be performed: offline and online analysis; to acquire the in-cylinder pressure three different acquisition systems were used: For the offline analysis (see paragraph 4) the following configuration was used:

 Configuration 1: Yokogawa DL708E oscillographic recorder with a A/D converter module with a resolution of 16 bits. For the online analysis (see paragraph 5) two different configurations were used:

 Configuration 2: PXI platform from National Instruments with a RT8170 embedded real time controller with a 850 MHz clock processor. The A/D conversion have a resolution of 16 bits.

 Configuration 3: it consists of a 150 MHz digital signal processor (DSP) from Texas Instruments using an A/D converter of 14 bits. The experimental results that are going to be presented in this work, were obtained from a experimental test matrix covering usual engine operation points. The main characteristics of the tests that were carried out are shown in Table 3. 4. Offline processing of the in-cylinder pressure The in-cylinder pressure signal measurement is affected by several effects that make it necessary to be filtered before it is used for control or diagnosis purposes. On the one hand, it must be considered the existence of signal noise due to the pressure conversion (thermal effects, sensor resonance, lack of linearity in the sensor, vibrations, etc.), signal transmission (electrical effects, bad connections, etc.) and analog–digital conversion; finally there can be combustion chamber resonance [11], which is not interesting from the thermodynamic analysis point of view. On the other hand, even when the engine is operating in steady conditions, cycle-to-cycle variations can appear. This effect is very important in spark ignition engines and it is nonnegligible in diesel engines. This scattering is caused by variations in the amount of fuel supplied [30], the injection timing, the exhaust gas recirculation repartition [31], the

ARTICLE IN PRESS 1772

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

Table 3 Experimental tests. Test

1 (motoring) 2 3 4 5 6 7 8 9 10

Speed (rpm)

Torque (Nm)

_ f =m _a m 103 (kg/s)

pin/p ex 100 (kPa)

Tin/ Tex (K)

1000 1000 1300 1500 1500 2000 3000 3000 3500 4000

 25 160 210 95 90 314 159 365 83 123

0/6.7 1.2/19.1 2.1/29.9 0.99/28.1 0.95/27.9 4.3/70.2 3.3/89.0 7.0/135.3 2.3/75.6 3.7/99.0

0.99/1.05 1.21/1.46 1.44/1.54 1.12/1.16 1.08/1.13 2.33/2.93 1.96/2.28 2.8/3.1 1.41/1.96 1.56/2.44

331/332 298/776 312/851 322/673 322/663 322/981 330/778 320/973 322/701 322/817

Presure (x100kPa)

150

100 75 50 25 0 -25 -180 10

dp (x100kPa/deg)

Minimum values Maximum values Mean of 10 cycles

125

-120

-60

0

60

120

180

Minimum values Maximum values

5

Mean of 10 cycles

0 -5 -10 -180

-120

-60

0

60

120

180

Crank angle (deg) Fig. 2. Minimum, maximum and mean pressure (top) and pressure derivative (bottom) for 10 consecutive measured cycles (Test 3).

trapped air mass and composition, and the movement of air in the cylinder; these effects can also affect the combustion process, which amplifies the small variations. The stated effects can be seen in Fig. 2. In the top, the minimum, maximum and mean pressure cycles show a not negligible variation near the maximum pressure. Although the effect of the signal noise can not be clearly seen in the pressure, when the pressure derivative is calculated (bottom part of Fig. 2) both the cyclical variations and noise are well seen. It is necessary to remark that the pressure derivative is used for thermodynamic analysis and thus the rate of heat release would show similar cycle-to-cycle variations and noise. In the sake of clarity, it must be stated that plots in Fig. 2 intend to illustrate the effect of cycle-to-cycle variation and thus a number of 10 cycles has been arbitrarily chosen for both pressure and derivative plots. As it is dealt in the following section, this is not the definite number cycles proposed, however similar results would have been obtained with any other number of cycles. To reduce the effects of noise and cycle-to-cycle variation it is necessary to measure several cycles and then filtering the signal, as it is described in the following sections.

4.1. On the number of cycles to be processed To minimise the problem of the cycle-to-cycle variation, several consecutive cycles of pressure are usually measured, since one chosen at random may not be representative of the steady operating conditions of the engine. There is no

ARTICLE IN PRESS F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

1773

Table 4 Number of averaged cycles from different authors. Authors

N cycles

Engine

Comments

Armas [32] Cartwright and Fleck [33] Lancaster et al. [22] Macian [34] Randolph [35] Brunt and Emtage [36] Lancaster et al. [22]

20 35–40 40 110 300 300 300

4S-Diesel 2S-Spark 2S-Spark 2S-Spark Spark 2S-Spark 4S-2S-Spark

Stabilized engine Stabilized engine Stabilized engine Unstable engine Study on long term drift Unstable engine Unstable engine

consensus on the optimum number of cycles required to be measured. Table 4 shows a summary of proposals from several authors [22,32–36]. At a first glance, the range presented in Table 4 can be incoherent because of the important divergences between authors. However, if a deeper analysis of the works is done this discrepancy between authors can be justified because the optimal number of cycles to be averaged depends on the engine type, but also on the unit tested, the acquisition system, and the operating point [34,36]. In general all the authors agree that the engine stability is the key issue to determine the number of cycles. Taking into account these comments it can be stated that:

 In general, lower number of cycles are needed in diesel engines due to its lower cycle-to-cycle dispersion (with respect to a spark ignition engine). The reason can be found in the fact that its thermo-fluid dynamic processes are more stable.

 In the same engine there can be important variations because different operating point show different stability, thus



engines behaves in a more steady way at high speed and load, being idle conditions specially critical. The operating points used by the authors to propose the highest values in Table 4 are very unstable: near the misfire limit [22], low speed and load [36] or literally the ’operating point with the highest dispersion’ [34]. Apart from the engine and operating point stability, the acquisition system can influence the optimal number of cycle to measure as Randolph [35] shows in his work on long term thermal stability.

In addition, besides the inherent variability in the data, another factor that must be taken into account when determining the number of cycles to record is the most critical or demanding application to which the data will be subjected [22]. To illustrate this statement it can be said that the optimal number of cycles to analyse the indicated mean effective pressure or the heat release law is not necessarily the same. In most cases authors do not perform an specific statistical or sensitivity study to determine the optimal number of cycles but they apply experience-based rules which are difficult to export to different situations. In this section a methodology for determining the optimal number of cycles to be measured is proposed. Accordingly to the previous comments, it must be highlighted that this work is aimed to determine a general methodology to select the optimal number of cycles in terms of obtaining a good heat release calculation, however this number can vary at different experimental conditions (engine, operating point y), as justified. As starting point,a number of cycles N, as high as possible was acquired. N= 500 cycles have been measured because it exceeded clearly the maximum number in Table 4. Then, a set of mean cycles, for different number (nc) of averaged cycles, was calculated in the following way: p nc;i ðaÞ ¼

þ nc 1 iX p ðaÞ nc j ¼ i j

ð2Þ

being pj the in-cylinder pressure during the j-th cycle, which is a function of the crankangle ðaÞ. For each nc, Eq. (2) provides a set of N nc+1 averaged pressure signals fp nc;i ðaÞg. For each one of these sets, standard deviation can be obtained as follows:

snc ðaÞ ¼ snc ðfp nc;i ðaÞgÞ

ð3Þ

Fig. 3 shows the evolution of the standard deviation for a given number of cycles (nc =5); in the sake of comprehension, the maximum and minimum envelope has also been represented. It can be clearly seen that the standard deviation shows an important point-to-point variations which is dependent on the crank angle; particularly an important increase appears during the combustion. As shown in Fig. 4, there is a high correlation between the standard deviation calculated from averaged signals with nc =25, and the rate of heat release, dHRL (calculated according to [3]). Although it is out of the aim of this work, it is interesting to see the potential of using the cycle-to-cycle standard deviation as a simplified (and fast) indirect method for combustion evaluation. Thus, start and end of combustion can be easily estimated, and also some of the dHRL characteristics such as maximum dHRL location and premixed combustion dHRL peak. This simplified technique can also be used even when no mean variable (air mass flow, fuel mass, exhaust gas recirculation, etc.) is available, and thus, dHRL calculation is not possible.

ARTICLE IN PRESS 1774

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

3.5 Minimum envelope curve Maximum envelope curve Mean of 5 averaged cycles

Standard deviation (x100kPa)

3

2.5

2

1.5

1

0.5

0 -50

-25

0

25

50

75

Crank angle (deg) Fig. 3. Standard deviation and its envelopes curves (series of 5 averaged cycles)—Test 3.

Maximum

75

0.5

Standard deviation dHRL

dHRL (J/deg)

50 0.3

0.2 25

Standard deviation (x100kPa)

0.4

0.1

0 0

-50

-25

0

25

50

75

100

Crank angle (deg) Fig. 4. Standard deviation evolution calculated with nc = 25 (right) and dHRL (left)—Test 7.

The stated remarkable increase of the standard deviation is due to cycle-to-cycle variation of the combustion process which leads to affect the sensor and combustion chamber resonances. The scattering during the combustion process is derived from slight variations in the injection process, change in the chamber conditions, etc. which usually lead to changes in the angle of start of combustion, instantaneous rate of heat release and hence important cycle-to-cycle variations. If the number of averaged cycles is considered, it can be concluded that the higher the number of averaged cycles is, the closer the maximum and minimum envelopes are, as shown in Fig. 5. However, there is a point (in this case about nc= 22)

ARTICLE IN PRESS F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

Standard deviation (x100kPa)

4

1775

Envelope σ of 4 cycles averaged Envelope σ of 5 cycles averaged Envelope σ of 15 cycles averaged Envelope σ of 20 cycles averaged Envelope σ of 25 cycles averaged

3

2

1

0 -45

-30

-15

0 15 Crank angle (deg)

30

45

60

Fig. 5. Standard deviation of average cycles related to the number of averaged cycles (Test 3).

4 3.5

Maximum (σmax - σmin)

3 2.5 2 1.5 1 0.5 0 0

10

20 30 Number of cycles to average

40

50

Fig. 6. Evolution of the maximum difference between the maximum and minimum envelope of the standard deviation when varying the number of averaged cycles nc.

in which increasing the number of cycles does not diminishes the variation of the standard deviation. Beyond this point, including additional cycles does not improve the precision of the averaged value. This is due to the fact that it is difficult to ensure steady conditions during many cycles because of low frequency variations in the system. Hence, this number of cycles can be then considered as a rough estimate of optimum number of cycles; in the example it was considered nc=25, slightly higher to 22. To illustrate the method, Fig. 6 shows the evolution of the maximum difference, between the maximum and minimum envelope of the standard deviation, when varying nc. The optimal point (when the improvement in the standard deviation

ARTICLE IN PRESS 1776

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

is below a prefixed threshold) can be clearly selected. Finally, in order to consider the effect of the operating point, this procedure could be repeated in several characteristic operating points and then, the maximum optimal nc should be selected. If the values were very different, a scheduled approach can be used for different operating points. 4.2. Signal averaging In order to analyse the effect of averaging, a frequency analysis was performed by calculating the discrete Fourier transform (DFT). Fig. 7 shows the spectrum corresponding to the original 25 cycles (marks) and to the averaged pressure signal (solid grey) for motored conditions (top plot) and combustion operating points (bottom plot). Due to the different number of samples processed, npc for the averaged signal and npc  nc for the original signal, there is a different frequency scale (a factor of nc must be used). Beyond that, there is a good coherence between both signal when only k  nc harmonics are compared: in fact the spectrum of the averaged signal can be obtained considering only the harmonics multiple of nc as it is shown in Fig. 8. This issue can be straightforward derived from the DFT definition [37], and small differences in the graph correspond to numerical errors. As a conclusions, it can be said that cycle averaging correspond to neglect the harmonics which are not multiples of k  nc. This raises two methods of calculating the average cycle of nc cycles: either through the application of Eq. (2), or through the DFT, being both methods equivalent in terms of final result. However, the spectrum representation shows additional details about signal-to-noise ratio (which can be calculated from the harmonics in the spectrum which are not multiples of nc). Spectrum in Figs. 7 and 8 also denote the important differences between combustion and motored conditions. In the case of the motored cycle, there is only a low frequency band where information exists, while combustion is presented in mean and high frequencies. Note that when higher frequencies are considered, the signal-to-noise ratio diminishes and this is a key issue when the derivative of the pressure is processed (this can be done after the inverse DFT is calculated or in the frequency domain multiplying by j  2p  f ) because derivation amplifies the high frequency band. Hence, some kind of low-pass filter must be applied for removing the high frequency part of the signal. The filter must eliminate noise (very high frequency) without losing information from the physical phenomenon of combustion (mid and high frequencies). In many cases it is really difficult to establish a strict limit between the two components. 4.3. Signal filtering Digital filters are widely used for smoothing the in-cylinder pressure [38,39]; digital filtering techniques are bandsensitive and allow a selective effect on different frequency ranges. For the offline application, direct modification of the spectrum is possible allowing a zero-phase effect (i.e. all frequencies keep their original phase and then signal is not

100 Amplitud Peak

25

25 cycles

50 75

Mean of 25 cycles

1 0.01 0.0001 1.E-06 1

10

100

1000

10000

100000

100 Amplitud Peak

25

25 cycles

50 75

Mean of 25 cycles

1 0.01 0.0001 1.E-06 1

10

100

1000

10000

Harmonic Fig. 7. Original spectrum of nc cycles pressure (marks) and of the averaged cycle (solid grey) in motored (up) and combustion (down) tests—Tests 1 and 7-.

ARTICLE IN PRESS F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

10

Selected harmonics from 25 cycles

1 Amplitud Peak

1777

Mean of 25 cycles

0.1 0.01 0.001 0.0001 1E-05 1.E-06 1

5

10

50

100

500

1000

Selected harmonics from 25 cycles

10 Amplitud Peak

100

Mean of 25 cycles

1 0.1 0.01 0.001 0.0001 1

5

10

50 Harmonic

100

500

1000

Fig. 8. Spectrum of the averaged cycle (solid grey) and considering only the nc multiples of the original spectrum of nc cycles (marks). Motored (up)— Test 1- and combustion (down)—Test 7-.

Table 5 Cutoff and stopband edge harmonics depending of engine speed n for motored and full load. Motored All n Cutoff harmonic (kc) Stopband edge harmonic (kstop) a

55 65

a

Full load no 1250

1250 o no 4000

n 4 4000

240 300

283:6250:0349  n kc +60

144 204

n is the engine speed in (rpm).

distorted in phase). However, the direct elimination of the high-frequency band can cause overshoots in the pressure signal (the well known Gibbs effect), which causes nonnegligible problems in the dHRL calculation. This can be mitigated by smoothing the transition (increasing the roll-off) using window-sync filters with smooth band transition, through Hanning function for example [40]. A key issue is the selection of the cutoff and stopband edge frequencies. Armas [32] and Martı´n [41] use the values of cutoff harmonic (kc) and stopband edge harmonic (kstop) shown in Table 5. The values for motoring conditions were obtained evaluating the plausibility of the heat transfer to the walls calculated from the polytropic coefficient [42], which is a very sensitive parameter to the pressure quality, as it uses the pressure derivative for the calculation. In the case of the combustion tests, the main consideration to set the cutoff frequency and the transition band is the quality of the rate of heat release. Values in Table 5 have been proved to be adequate for several engines and various types of sensors, with satisfactory results. However, depending on the sensor assembly (flush mounted [33], with a connecting duct [33,40] or using an adapted glow plug [10,13,43]) the phenomenon of the adapter resonance, along with the chamber resonance, can alter the quality of results. It is very recommendable to review the spectrum in each case prior to filtering, to detect possible irregularities and to ensure the suitability of the filter. Here, a method based on the characteristics of the signal spectrum, instead of a experience-based rule, is proposed. For that, first a motored cycle is analysed (top plots in Figs. 7 and 8). The cutoff harmonic in Table 5 roughly corresponds to the place where the average cycle harmonics converges with the non-cyclic harmonics, which have been attributed to signal noise and cycle-to-cycle variations. On the basis of the spectrum of the non-averaged signal (nc consecutive cycles), it is easy to calculate the difference between the content in harmonic k  nc and the mean content in harmonics k  nc þ 1 to k  ðnc þ 1Þ1. This is represented for

ARTICLE IN PRESS F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

Difference Normalized

1778

100 Test 8 (full load 3000 rpm) Test 10 (mid load 4000 rpm) Test 1 (motored 1000 rpm)

75 50 25 0 5

10

50

100

500

1000

Difference

1.0E-02 Recommended cutoff

7.5E-03 5.0E-03 2.5E-03 0.0E+00 -2.5E-03 100

150

200

250

300

350

Difference

2.0E-02 1.5E-02 1.0E-02 5.0E-03 0.0E+00 350

400

450

500

550 Harmonic

600

650

700

Fig. 9. Difference of the k-th harmonic amplitude and the mean of the following nc  1 (Test 1, 8 and 10).

motoring and combustion tests in Fig. 9, where it is shown how it decays when the frequency increases, although some peaks are obtained in the mid and high frequency range. Three main zones can be identified: the first corresponds to the pressure changes due to mechanical work, combustion and heat transfer (top plot), the second (with peaks about k= 150–350) is due mainly to resonance effects in the combustion chamber [11] (centre plot) and the third, with very high frequencies ðk4 500Þ, in which the sensor resonance takes place (bottom plot). To obtain the cutoff harmonic, a margin of difference that eliminates the second and third zone is taken. This way, similar values as proposed in Table 5 (for the corresponding engine speed) are obtained with the stated procedure. However, the general methodology that have been proposed is based directly on the signal spectrum whence it have two main advantages with respect to the proposal in Table 5:

 Implicitly, it takes into account the effect of the load which can be important as shown in the following paragraph.  It can be easily extended to other engine and operating point. Once kc and kstop are defined, the proposed filter stands as follows: Pkfilt ¼ Pk  yk

ð4Þ

being 8 > > 1 > > > >  1 2 3 0  > > kstop > > > k kc  <1 6 7 B C 2 7 B  pC 6 yk ¼ 4cos@ A þ 15 k 2 > stop > > > > > > > > > > :0

kstop if k o kc  2 kstop kstop if kc  o ko kc þ 2 2 if k o kc þ

ð5Þ

kstop 2

where Pk is the content of the averaged pressure signal at harmonic k and Pfilt k is the filtered value of the spectrum. To get the averaged and filtered pressure in the temporal domain, inverse DFT is used. Fig. 10 presents the results of the various stages of signal processing in combustion conditions.

ARTICLE IN PRESS F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

Pressure (x100kPa)

55

1cycle Mean (25 cycles) Mean filtered

50 45 40 35 30 25 -10

Derivative pressure (x100kPa)

1779

0

10

2

20

30

40

50

1cycle Mean (25cycles) Mean filtered

1 0 -1 -2 -25

0

25 50 Crank angle (deg)

75

100

Fig. 10. Example of measured, averaged and filtered pressure (Test 4).

4.4. Validation of signal processing. effect on dHRL To verify the good performance of the proposed signal processing, a number of N= 500 cycles of in-cylinder pressure, at different stationary operating points, were acquired. In each operating point, it was took as representatives cycles the averages of 1, 4, 7, 10, 15 and 20 consecutive cycles; the stated procedure for averaging and filtering was applied to obtain the mean filtered cycles. Then the standard deviation of dH RL (at each crank angle) for each number of averaged cycles was studied. Three of these operating points (Tests 2, 6 and 9 in Table 3) are presented in Fig. 11. It can be seen that at a first glance, the trend in the standard deviation of dHRL shows a similar behaviour to that of the in-cylinder pressure shown in Fig. 5: the higher the numbers of averaged cycles is the lower the variability of the dH RL standard deviation is. A deeper analysis shows that differently to the pressure, the dHRL standard deviation does not show a clear minimum limit when nc increases. Anyway, it is also clear that similarly to pressure, the effect of the cycles number gets lower as it increases and thus an asymptotic trend similarly to that presented in Fig. 6 is expected. The main reason of this different behaviour is the fact that the calculation of dHRL is not linear with dp. To illustrate this statement, Eq. (6) shows the expression of the apparent net heat release rate [17] dHRL ¼

g 1  p dV þ  Vdp g1 g1

ð6Þ

where g is the adiabatic coefficient and V is the instantaneous in-cylinder volume. The expression of dHRL includes both p and dp (also V and dV, but these variables are analytically calculated from crank angle and hence they show no noise) and thus it presents a relative lower sensitivity to cycle-to-cycle dispersion and noise due to the ‘cumulative’ effect of p. Additional effect of the signal filtering helps to diminish dH RL standard deviation. Having in mind that the main objective of the proposed signal processing is to reach a high quality combustion diagnosis, by the calculation of dHRL, it is a key issue to obtain a low level of noise in this signal. As can be seen in Fig. 11, for the same number of measured cycles, the higher the engine load (higher torque) is the higher the standard deviation is. This behaviour is derived from the stated relationship between the combustion process and the cycle-to-cycle variation: as the torque increases the amount of injected fuel increases whence more intense combustion process take place. Besides the maximal standard deviation approximately corresponds to the points of dHRL maximums. With the proposed number of measured cycles nc=25 stated in Section 4.1, a dHRL standard deviation lower to 1 J/deg (this is the maximum value obtained at Test 6 2000 rpm and 314 Nm—when averaging 20 consecutive cycles) would be reached at any operating point. Of course, this threshold can be modified if a less restrictive limits is desired, while a more

ARTICLE IN PRESS

dHRL standard deviation (J/deg)

18 Test 6: 2000 rpm 314 Nm 16 14 12 10 8 6 4 2 0 -20 0 20 -40

40

60

dHRL standard deviation (J/deg)

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

dHRL standard deviation (J/deg)

1780

3 Test 9: 3500 rpm 83 Nm

2.5 2 1.5 1 0.5 0 -40

-20

0 20 40 Crank angle (deg)

60

5 Test 2 : 1000 rpm 160 Nm

4 3

1 cycle 4 cycles 10 cycles 15 cycles 20 cycles

2 1 0 -40

-20

0 20 40 Crank angle (deg)

60

Fig. 11. Example of the effect of signal processing on the standard deviation of dHRL calculated (Tests 6 -top left-, 9 -top right- and 2-down-).

restrictive limits would lead to take a great amount of additional cycles due to the commented asymptotic trend in both pressure and dHRL. At this point it has to be highlighted that a number of cycles nc= 7 and 15 would have been enough to maintain the dHRL standard deviation lower than 1 J/deg at the Test 9  3500 rpm and 83 Nm- and 2  1000 rpm and 160 Nm, respectively. This work is focused on establishing the methodology to select the number of cycles more than to setting its definite number; thus, as commented in Section 4.1, the researcher have to chose if the cycles number must be optimised at any operating point or a constant value (selected from the most restrictive operating condition) is used. From the authors experience, if there is no memory restriction for the acquisition, it is better to always use a constant number of cycles because it simplifies the acquisition devices configuration and extra measured cycles are available for additional analysis. Anyway, it has been shown that they have no significant benefit on the combustion diagnosis. The presented results validate the procedure to select the cycles number and filtering methodology that have been used to obtain an adequate and repetitive combustion analysis. Once the offline signal processing has been established and validated, the online signal treatment can be approached. 5. Online in-cylinder pressure filtering The filtering method proposed in the last section is suitable for offline application. However, for control-oriented applications it is not valid for the following reasons:

 nc cycles must be acquired before they are processed, thus causing an important delay from the data acquisition.  Steady operation during nc cycles is required, which is not the case during normal accelerations and decelerations in automotive engines [44,45].

 The size of memory needed to store the samples corresponding to the nc cycles is quite large. As an example, using 1440 

samples per cycle (i.e. 0.5 crank angle degrees resolution), 25 cycles and 16 bit resolution, about 72 KB memory is needed. Finally, DFT-based filter calculation is quite time consuming.

When addressing offline filtering, a particular filter used for pressure signals is the moving average [46]. However, Shi [40] suggests that the use of the moving average has a number of problems such as its ability to smooth depends on the sampling interval, and can not properly eliminate problems as duct resonances while sharp variations in the pressure due to premixed combustion are distorted. On the other hand, the filter for the offline treatment provides a basis for designing filters that can be run in real time.

ARTICLE IN PRESS F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

5000

1781

3500 rpm 2750 rpm

Passband edge frequency (Hz)

4000 2000 rpm

3000

1500 rpm

67%

100%

33%

2000

1000 Motored

0 50

100

150 200 Cutoff harmonic

250

300

Fig. 12. Cutoff frequency map.

Considering the cutoff harmonics as proposed for offline analysis, the cutoff frequency (passband edge frequency) map shown in Fig. 12, for different engine loads and speeds, was obtained. A similar plot can be obtained for the stopband edge frequency. The conversion from harmonic (k) to frequency (f) requires the sampling frequency fs (which depends on the speed in case of crank angle domain acquisition) and the number of samples per cycle npc. Then f¼

k  fs npc

ð7Þ

For the online filter design constant phase shift finite impulse response (FIR) filter was selected, which has the following form:    X m m1 hðjÞ  p½ij; i ¼ m; m þ 1; . . . ; npc ð8Þ pf i þ ¼ 2 j¼1 where m is the filter order, and h(n) the filter coefficients, which are symmetrical (i.e. h(n)= h(m  n)) for ensuring the constant phase response. Filtered pressure is shifted (m  1)/2 samples for correcting the constant phase shift caused by the filter. Cutoff frequencies according to Fig. 12 were selected for the online filter, stopband was fixed in 1 KHz, while ensuring a ripple of 0.001 dB in the passband and 60 dB in the stopband. Remez algorithm [47] was used for obtaining the filter order and coefficients. Fig. 13 shows the filter coefficients and filter order (XY plane) for different engine speeds obtained at full load (it corresponds with the 100% load line in Fig. 12). As expected, the higher the engine speed is the higher the filter order is. Similar trend was obtained (not shown) when the engine load increases. The maximum value of the filter coefficients for each engine speed is plot at the YZ plane in Fig. 13. Finally, Fig. 14 shows the frequency and the step response of one of the filters in Fig. 13. In order to check the online operation of the filters, they were tested in the two different control platforms detailed in the experimental set-up section: the embedded real time controller (PXI) and the digital signal processor (DSP). Execution time of the maximum order filter, acquiring 1440 samples per cycle, was 0.5 and 1.7 ms, respectively. When operating at 6000 rpm one engine cycle lasts for 20 ms, hence processing time was judged enough for real time operation. Fig. 15 shows some results obtained in the Test 5 of Table 3, in which 500 consecutive cycles were measured. First of all, it must be noted that as real time operation does not permit a 25 cycle averaging of the signal, the averaging process has been omitted. Thus, cycle by cycle analysis have been applied in both the online and offline processing so that the comparison between them can be done. Top part of Fig. 15 shows the mean pressure of 25 non-filtered averaged cycles, one non-filtered cycle and the same cycle filtered with the online filter. It is interesting to see that a first glance the three pressure traces have a very similar evolution, however if the difference between the two single cycles (non-filtered and online filtered) and the mean cycle is considered, it can be appreciated some instantaneous variation (mid part of Fig. 15). As expected, the filtered signal shows a lower peaks values. The bottom part of Fig. 15 shows cycle-to-cycle standard deviation of the non-filtered average cycles and the same for online filtered cycles. In the sake of clarity, the offline filtered

ARTICLE IN PRESS 1782

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

0.865 Max.coefficients

Filter coefficients map

0.619

0.394

Order of filter

0.5

0.333

0.289

0.25

1000 1500 2000 Y = 2500 Sp ee 3000 d[ rpm 3500 4000 ]

51 61 71 79 89 99 109 119 129 137 147 157 125

150

0

Z = Filter coefficients (h (n))

0.75

0.481

-0.25 25

50 75 100 t (n) X = Coefficien

0

Fig. 13. Map of filter coefficients at full load operating conditions.

Amplitude (dB)

0

Cutoff frequency

Magnitude

-25 -50

Stopband edge frequency

-75 -100 Frequency 1 Step reponse

Gain

0.75 0.5 0.25 0

Filter order /2

Samples Fig. 14. Frequency and step response for a given filter from Fig. 13; normalized frequency and sample axis have been used.

cycles deviation have been omitted from this plot because if it was included, no appreciable difference with the online filtered signal can be seen. Thus, it is concluded that both offline and online filtering of one single cycle provides a very similar results, as desirable. In addition, it can be stated that the filtering process (both online or offline) reduces the standard deviation of the signal by up to 50%. Some residual dispersion will always remain because, although noise can be eliminated by filtering, some cycle-to-cycle dispersion will remain due to physical effects, as commented.

ARTICLE IN PRESS

50

1 non filtered cycle Mean of 25 cycles 1 filtered cycle

40 30 20 10 0

1 non filtered cycle

-50

Standard deviation

1783

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -50

-25

1 filtered cycle

0

25 50 Crank angle (deg)

75

1.5 1 0.5 0 -0.5 -1 100

Difference (x100kPa)

Pressure (x100kPa)

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

Mean of 25 cycles 1 filtered cycle

-25

0

25

50

75

100

Crank angle (deg) Fig. 15. Pressure and cycle-to-cycle standard deviation (Test 5). Top: mean pressure (25 averaged cycles), one non-filtered cycled and the same cycle filtered. Mid: pressure difference between non-filtered cycle and online filtered cycle respect to the mean cycle. Bottom: cycle-to-cycle standard deviation of the filtered mean cycle (25 averaged cycles) and online filtered cycles (500 consecutive cycles).

6. Conclusions A step-by-step methodology to process the in-cylinder pressure signal for combustion diagnosis has been presented. The methodology is aimed to the filter design for online applications, however the step-by-step approach has allowed to address in detail the complete in-cylinder pressure processing for both offline and online analysis. The main conclusions regarding the offline analysis are:

 The decision of the number of cycles to be measured is performed on the basis of the cycle-to-cycle standard deviation of the signal. In the tested engine and operating points an optimal number of 25 measured cycles has been found.

 A simple averaging method based on the frequency domain analysis has been presented. The method provides mean in 

cylinder pressure traces numerically equivalent to the conventional time domain averaging, but additional information regarding the signal-to-noise ratio is available. Spectrum analysis allows the definition of cutoff frequencies for the filter design, thus avoiding experienced-based rules. A zero-phase DFT filtering has been proposed for offline applications. The main conclusions regarding the online analysis are:

 Due to time and memory limitations it is not possible to measure and process several in-cylinder pressure cycles as it is done in the offline analysis.

 A FIR filter has been proposed for online applications. The filter parameters have been obtained on the basis of the cutoff frequencies proposed for the offline applications.

 The proposed online filtering have been tested with two real time acquisition and processing platforms. The calculation time of the proposed signal processing is adequate for real time operation. In addition, the results compares very similar between offline and online processing.

Acknowledgements This work has been supported by Ministerio de Ciencia y Tecnologı´a through Project PLANUCO no. TRA2006-15620C02-02. The authors would like to thank C. Guardiola for his valuable contribution.

ARTICLE IN PRESS 1784

F. Payri et al. / Mechanical Systems and Signal Processing 24 (2010) 1767–1784

References [1] J.M. Desantes, J. Galindo, C. Guardiola, V. Dolz, Air mass flow estimation in turbocharged diesel engines from in-cylinder pressure measurement, Experimental Thermal and Fluid Science 34 (2010) 37–47. [2] M.F.J. Brunt, H. Rai, A.L. Emtage, The calculation of heat release energy from engine cylinder pressure data, SAE Paper 981052, 1998. [3] M. Lapuerta, O. Armas, J.J. Herna´ndez, Diagnosis of DI Diesel combustion from in cylinder pressure signal by estimation of mean thermodynamic properties of the gas, Applied Thermal Engineering 19 (1999) 513–529. [4] Y. Shimasaki, M. Kobayashi, H. Sakamoto, M. Ueno, M. Hasegawa, S. Yamaguchi, T. Suzuki, Study on engine management system using chamber pressure sensor integrated with spark plug, SAE Paper 2004-01-0519, 2004. ¨ [5] S. Leonhardt, N. Muller, R. Isermann, Methods for engine supervision and control based on cylinder pressure information, IEEE/ASME Transactions on Mechatronic 4 (1999) 235–245. [6] J. Worm. An evaluation of several methods for calculating transient trapped mass with emphasis on the Delta P approach, SAE paper 2005-01-0990, 2005. ¨ ¨ [7] R. Muller, M. Hart, A. Truscott, A. Noble, G. Krotz, M. Eickhoff, C. Cavalloni, M. Gnielka, Combustion pressure based engine management system, SAE paper 2000-01-0928, 2000. [8] M.C. Sellnau, F.A. Matekunas, P.A. Battiston, C. Chang, D.R. Lancaster, Cylinder-pressure-based engine control using pressure-ratio-management and lowcost non-intrusive cylinder pressure sensors, SAE paper 2000-01-0932, 2000. [9] M. Hasegawa, Y. Shimasaki, S. Yamaguchi, M. Kobayashi, H. Sakamoto, N. Kitayama, T. Kanda, Study on ignition timing control for diesel engines using in-cylinder pressure sensor, SAE paper 2006-01-0180, 2006. [10] M. Beasley, R. Cornwell, P. Fussey, R. King, A. Noble, T. Salamon, A. Truscott, Reducing diesel emissions dispersion by coordinated combustion feedback control, SAE Paper 2006-01-0186, 2006. [11] F. Payri, A. Broatch, B. Tormos, V. Marant, New methodology for in-cylinder pressure analysis in direct injection diesel engines—application to combustion noise, Measurement Science and Technology 16 (2005) 540–547. [12] A. Albrecht, P. Moulin, O. Grondin, G. Corde, Control design for HCCI combustion engine based on virtual engine simulator: from control development to real time calibration, in: THIESEL 2006 Conference on Thermo- and Fluid Dynamic Processes in Diesel Engines, Valencia, Spain, 2006, pp. 471–489. [13] M.T. Wlodarcyk, High accuracy glow plug-integrated cylinder pressure sensor for closed loop engine control, SAE Paper 2006-01-0184, 2006. [14] M.F.J. Brunt, C.R. Pond, Evaluation of techniques for absolute cylinder pressure correction, SAE Paper 9700369, 1997. [15] E. Rosseel, R. Sierens, Evaluating piezo-electric transducer response to thermal shock from in-cylinder pressure data, SAE Paper 1999-01-0935, 1999. [16] G.H. Neo, N. Collings, Pressure data analysis of formula one racing engines, SAE Paper 970061, 1997. [17] M.F.J. Brunt, C.P. Kieron, Calculation of heat release in direct injection diesel engines, SAE Paper 1999-01-0187, 1999. [18] A.L. Randolph, Cylinder-pressure-based combustion analysis in race engines, SAE Paper 942487, 1994. [19] S.C. Homsy, A. Atreya, An experimental heat release rate analysis of a diesel engine operating under steady conditions, SAE Paper 970889, 1997. [20] J. Ghojel, D. Honnery, Heat release model for the combustion of diesel oil emulsions in DI diesel engines, Applied Thermal Engineering 25 (2005) 2072–2085. [21] G. Hohenberg, Experimentelle Erfassung der Wandwarme in Kolbenmotoren (Experimental acquisition of the wall heat in piston engines), Ph.D. Thesis, Technical University of Graz, Graz, Austria, 1980. [22] D.R. Lancaster, R.B. Krieger, J.H. Lienesch, Measurements and analysis of engine pressure data, SAE Paper 750026, 1975. [23] M. Morishita, T. Kushiyama, An improved method for determining the TDC position in a pV-diagram, SAE Paper 980625, 1998. [24] M.J. Stas, An universally applicable thermodynamic method for TDC determination, SAE Paper 2000-01-0561, 2000. [25] R.S. Davis, G.J. Paterson, Cylinder pressure data quality checks and procedures to maximize data accuracy, SAE Paper 2006-01-1346, 2006. [26] D.T. Hountalas, A. Anestis, Effect of pressure transducer position on measured cylinder pressure diagram of high speed diesel engines, Energy Conversion and Management 39 (1998) 589–607. [27] H.S. Rai, M.F.J. Brunt, C.P. Loader, Quantification and reduction of IMEP errors resulting from pressure transducer thermal shock in a SI engine, SAE Paper 1999-01-1329, 1999. [28] S. Lee, C. Bae, R. Prucka, G. Fernandes, Z.S. Filipi, D.N. Assanis, Quantification of thermal shock in a piezoelectric pressure transducer, SAE Paper 2005-01-2092, 2005. [29] J. Tichy, G. Gautschi, Piezo-Elektrische Meßtechnik, Springer, Berlin, 1980. [30] F. Payri, J. Luja´n, C. Guardiola, G. Rizzoni, Injection diagnosis through common-rail pressure measurement, Proceedings of the I MECH E Part D Journal of Automobile Engineering 220 (2006) 347–357. [31] J.M. Luja´n, J. Galindo, J.R. Serrano, B. Pla, A methodology to identify the intake charge cylinder to cylinder distribution in turbocharged direct injection diesel engines, Measurement Science and Technology 19 (2008) No. 065401. [32] O. Armas, Diagnostico experimental del proceso de combustio´n en motores Diesel de inyeccio´n directa, Ph.D. Thesis, Universidad Polite´cnica de Valencia, Valencia, Spain, 1998. [33] A. Cartwight, R. Fleck, Cylinder pressure analysis in high performance two stroke engines, SAE Paper 962535, 1996. [34] V. Macian, Contribucio´n al estudio de la influencia del movimiento del ruido sobre la dispersio´n cı´clica y su caracterizacio´n, Ph.D. Thesis, Universidad Politecnica de Valencia, Valencia, Spain, 1984. [35] A.L. Randolph, Methods of processing cylinder-pressure transducer signals to maximize data accuracy, SAE Paper 900170, 1990. [36] M.F.J. Brunt, A.L. Emtage, Evaluation of IMEP routines and analysis errors, SAE Paper 960609, 1996. [37] F.J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform, Proceedings of the IEEE 66 (1978) 51–83. ¨ [38] R. Sonntag, S. BrechbAuhl, M. Schnepf, P. Wolfer, New ways to measure pressure inside Diesel engines without the use of individual bore holes, in: THIESEL 2002 Conference on Thermo- and Fluid Dynamic Processes in Diesel Engines, Valencia, Spain, 2002, pp. 569–578. [39] T.E. Alberts, S. Liu, R.W. Lally, Investigation of an inexpensive piezoelectric pressure sensor for internal combustion engine spark timing control, SAE Paper 2006-01-0183, 2006. [40] S.X. Shi, H.Z. Sheng, Numerical simulation and digital signal processing in measurements of cylinder pressure of internal combustion engines, IMechE C20/87 (1987) 211–218. [41] J. Martı´n. Aportacio´n al diagno´stico de la combustio´n en motores Diesel de inyeccio´n directa, Ph.D, Thesis, Universidad Politecnica de Valencia, Valencia, Spain, 2007. [42] M. Lapuerta, O. Armas, S. Molina, Study of the compression cycle of a reciprocating engine through the polytropic coefficient, Applied Thermal Engineering 23 (2003) 313–323. [43] F. Payri, S. Molina, J. Martı´n, O. Armas, Influence of measurement errors and estimated parameters on combustion diagnosis, Applied Thermal Engineering 26 (2006) 226–236. [44] J. Galindo, V. Bermudez, J.R. Serrano, J.J. Lopez, Cycle to cycle diesel combustio´n characterization during engine transient operation, SAE Transactions 01ATT-366 (2002) 2056–2070. [45] J. Galindo, J.M. Lujan, J.R. Serrano, L. Hernandez, Combustion simulation of turbochargers HSDI diesel engines during transient operation using neuronal networks, Applied Thermal Engineering 25 (2005) 877–898. [46] R. Douglas, R.J. Kee, B.P. Carberry, Analysis of chamber pressure data in two stroke engines, SAE Paper 972792, 1997. [47] G. Phillips, P. Taylor, Theory and Applications of Numerical Analysis, second ed, Elsevier Academic Press, London, 1996.