Crankshaft

ARTI AR TICLE CLE IN PR PRESS ESS Mechanical Systems and Signal Processing 24 (2010) 1529–1541

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

Model-based diagnosis of large diesel engines based on angular speed variations of the crankshaft $ M. Desbazeille a,

,1



, R.B. Randall b, F. Guillet a, M. El Badaoui a, C. Hoisnard c

a

´ de Lyon, F-42023, Saint Etienne, France; Universite´ de Saint-Etienne, Jean Monnet, F-42000, Saint-Etienne, France; LASPI, F-42334, IUT de Roanne, Universite France b School of Mechanical and Manufacturing Engineering, The University of New South Wales Sydney, 2052, Australia c EDF R&D Chatou, 78401 Chatou Cedex, France

a r t i c l e

i n f o

Article history: Received 17 July 2009 Received in revised form 14 December 2009 Accepted 17 December 2009 Available online 23 December 2009 Keywords: Large diesel engines Flexible crankshaft Angular speed variations Diagnosis Pattern recognition

a b s t r a c t

This work aims at monitoring large diesel engines by analyzing the crankshaft angular speed variations. It focuses on a powerful 20-cylinder diesel engine with crankshaft natural frequencies within the operating speed range. First, the angular speed variations are modeled at the crankshaft free end. This includes modeling both the crankshaft dynamical behavior and the excitation torques. As the engine is very large, the first cranks crankshaf haftt torsio torsional nal modes modes are in the low frequenc frequency y range range.. A model model with with the assumption of a flexible crankshaft is required. The excitation torques depend on the in-cylinde in-cylinderr pressure pressure curve. curve. The latter latter is modeled modeled with a phenomen phenomenologi ological cal model. Mechanical and combustion parameters of the model are optimized with the help of actual data. Then, an automated diagnosis based on an artificially intelligent system is propos proposed ed.. Neural Neural netwo networks rks are used used for patter pattern n recogn recogniti ition on of the angula angularr speed speed waveforms in normal and faulty conditions. Reference patterns required in the training phase phase are computed computed with with the model, model, calib calibrat rated ed using using a small small numbe numberr of actua actuall measurements. Promising results are obtained. An experimental fuel leakage fault is successfully diagnosed, including detection and localization of the faulty cylinder, as well as the approximation of the fault severity. & 2009 Elsevier Ltd. All rights reserved.

1. Introduc Introduction tion

Large diesel engines are widely used in many industrial applications such as the marine and power industries. It is a very important issue to ensure reliability of these engines, which are often of primary importance. Condition monitoring help predicting and therefore avoiding undesirable failures of such equipment. It consists in monitoring a parameter whose evolution is indicative of a developing failure. Many malfunctions of these engines are related to the combustion process. Indeed, the latter involves a lot of subsystems such as the timing system, e.g. valves and camshaft, the injection system, e.g. injectors and injection pumps, or the supercharging system, e.g. turbocharger. The in-cylinder gas pressure contains a lot of information about the combustion process. However, direct measurement of the in-cylinder gas pressure is impractical and uneconomical. A very expensive

$

This work was supported by EDF. Corres Correspon pondin ding g author author.. Tel.: Tel.: +33 4 7744 8155; fax: fax: + 33 4 77 1181 21. E-mail addresses: mathieu.desbazeille@uni mathieu.desbazeille@univ-st-etienne v-st-etienne.fr .fr (M. Desbazeille), Desbazeille) , [email protected] (R.B. Randall), Randall) , [email protected]@univ-st-etienne.fr etienne.fr (F. Guillet), Guillet), [email protected] (M. El Badaoui), [email protected] (C. Hoisnard). 1 ˆ Alpes. Held a doctoral fellowship from la Re´ Re´ gion Rhˆ Rhone 

0888-3270/ 0888-3270/$ $ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2009.12.004 doi:10.1016/j.ymssp.2009.12.004

ARTICLE IN PRESS M. Desbazeille et al. / Mechanical Systems and Signal Processing 24 (2010) 1529–1541

1530

transducer is required for each cylinder, but these tend to have a limited lifetime. Instead, non-invasive measurements such as crankshaft speed [1–10] or engine block vibrations [11,12] are often employed. The drawback of engine block vibration-based methods is that a lot of instrumentation is required to be able to monitor all the cylinders especially in the case of large engines. Analysis of the crankshaft angular speed variations has drawn a lot of attention in past years [1]. Some methods directly analyze its periodic variations in the frequency domain [2]. Analysis of the lowest harmonics can even enable the identification of the faulty cylinder [3]. Other methods employ a dynamical model of the crankshaft to reconstruct the indicated torque, i.e. the torque due to the gas pressure, or the in-cylinder pressure curves [4–6]. However, most proposed methods are aimed at four- or six-cylinder engines with relatively rigid crankshafts. Little attention has been paid to larger engines [7]. High-count cylinder engines involve higher inertias, overlapping combustion events and torsional vibrations of the flexible crankshaft which strongly complicate the diagnostics. This work focuses on a powerful 20-cylinder diesel engine driving an emergency generator in a nuclear power plant. First, the angular speed variations are modeled at the crankshaft free end. This includes modeling both the crankshaft dynamical behavior and the excitation torques. Then, an automated diagnosis of combustion-related faults through the analysis of the crankshaft angular speed variations is proposed. Neural networks are used for pattern recognition of the angular speed waveforms in normal and faulty conditions. Previous works have already discussed exploiting pattern recognition to interpret crankshaft speed fluctuations in a similar way [8–10]. The knowledge bases of waveform patterns were obtained directly from experimental measurements. However, it is often not feasible to obtain sufficient data from faulty conditions for all possibilities. The originality of this work is the use of simulated examples generated with the above-mentioned model to train the neural networks.

2. Engine characteristics and experimental setup

As this study focuses on a specific diesel engine, its main characteristics are first presented.

2.1. Engine characteristics The main engine characteristics are reported in Table 1. It is a turbocharged direct-injection diesel engine designed by ¨ ¨ This 50 V-20 engine develops 4 MW at a speed of about 1500 rpm. The injection timing is not equally spaced. It is Warstil a. alternately 22 and 50 in crank angle. Its large number of cylinders and high speed mean that at least two cylinders are in expansion stroke at the same time. Fig. 1 shows a sketch of a power generator set. Cylinders are arranged in a 50 V in two separate banks (banks A and B). A damper (Paddle type [13]) is fixed at the crankshaft free end in order to reduce the crankshaft torsional vibrations. The damper is tuned according to a critical speed usually corresponding to the first crankshaft torsional resonance. A flywheel is fixed on the coupling between the diesel engine and the electrical generator in order to reduce the crankshaft angular speed variations at the coupling end. 3

3

3

3

Table 1 Engine characteristics.

Manufacturer Type Length  width  height ð mÞ Rated power (MW) Cylinder number Cylinder capacity (L) Rotating speed (rpm) Injection timing (deg in c.a. a) a

Wärstilä Diesel V 501 6  2:6  3:3 4 20 200 1500 22 and 50

Crank angle.

Coupling and flywheel

Crankshaft free end

Diesel engine

and damper Electrical

A1

A2

A3

A4

A5

A6

A7

B1

B2

B3

B4

B5

B6

B7

A8

A9

A10

B8

B9

B10

generator

Fig. 1. Power generator set.


1531

2.2. Experimental setup The crankshaft angular speed variations were measured at the crankshaft free end next to the damper. Measurements were carried out at 82% of the full load condition. The speed sensor was a laser rotational vibrometer (Polytec OFV-400 [14]). This kind of sensor directly measures angular speed variations by using two laser beams projected onto the shaft surface and the Doppler frequencies of the back-scattered beams [15]. Tests were conducted in 2005 and 2007 in normal and faulty conditions (see Table 2). In faulty condition, fuel leakages in the injection system were introduced. The injected fuel quantities of the cylinders A6 and A4 were respectively decreased to 80% and 50%.

3. Modeling of the crankshaft angular speed variations

3.1. Crankshaft modeling The crankshaft is modeled with a simple system which is equivalent dynamically. As the engine is very large, the assumption of a rigid crankshaft is no longer valid, so a model with a flexible crankshaft has been developed. It takes into consideration the relative torsional vibrations which cause twisting in the sections of the crankshaft. These torsional vibrations are superimposed on the rigid rotational motion of the crankshaft. This system consists of lumped inertias connected together by torsionally elastic springs (see Fig. 2). This kind of model has been widely used in mechanical engineering including crankshaft modeling [13,16,17]. The inertias respectively stand for the coupling and flywheel, the 10 cranks and the inner and outer parts of the damper. It is assumed that the angular speed variations of the electrical generator are null. As a consequence, the latter can be considered as a fixed node. The equivalent inertias and stiffnesses of the system were calculated from drawings, modeling of the crankshaft with a CAD (computer-aided design) software and finite element method. All these values are reported in Table 3. Table 2 Engine conditions.

2005 1. Normal condition 2. Faulty fuel pumps (A6 and A4) 2007 1. Normal condition

Coupling and flywheel j 1

Cranks j2

j2

j2

j2

j3

j3

j2

j2

Damper j2

j2

j4

j5

Electrical generator k 1

Degree of freedom (dof): 1

k 2

k 3

2

k 3

3

k 3

4

k 3

5

k 4

6

k 3

7 8

k 3

k 3

9

k 3

k 5

10 11

Fig. 2. Crankshaft modeling. Table 3 Inertias and stiffnesses.

Inertia (kg m2 )

Stiffness (106 Nmrad1 )

j1 ¼ 140 j2 ¼ 7:5 j3 ¼ 8 j4 ¼ 0:75 j5 ¼ 23:7

k1 ¼ 0:5 k2 ¼ 36 k3 ¼ 24 k4 ¼ 15 k5 ¼ 8 k6 ¼ 2

k 6

12

13


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To determine the natural frequencies and mode shapes, the following system of equations was employed: ð1Þ

Jy ðt Þ þ Cy ðt Þ þ Kyðt Þ ¼ T ðt Þ €

_

with, J ¼ diag ð½ j1    j5 Þ

K¼

2 66 64

k1 þ k2 k2

k2

k2 &

k5 þ k6

k6

k6

k6

3 77 75

yðt Þ ¼ ½ y1 ðt Þ    y13 ðt ÞT T ðt Þ ¼ ½0 T 1 ðt Þ    T 10 ðt Þ 0 0T

J is the inertia matrix, C is the damping matrix and K is the torsional stiffness matrix. All matrices are 13  13. y ðt Þ is the torsional vibration amplitude vector and T ðt Þ is the excitation torque vector. All vectors are 13  1. The damping is complex, but modeled as proportional viscous damping, i.e. C is a linear combination of J and K. There is a long tradition for doing this, meaning that it has been found to give a good representation of crankshaft behavior [16]. The main departure from the assumed model is probably that the major damping along the crankshaft, from friction between the pistons and cylinders, is closer to Coulomb than viscous friction. However, it would be very close to proportional as being distributed in the same way as the inertias and springs. A modal analysis can be performed in order to determine the undamped natural frequencies and the associated mode shapes of the system. The first four modes are represented in Fig. 3 and the corresponding frequencies are reported in Table 4 (second column). The first mode is said to be the crankshaft rigid body mode. The second mode is the damper mode. The next modes are the crankshaft torsional modes.

1

2

3

4

5 6

7

8

9 10 11 12 13

1

2

3 4

Degree of freedom

1

2

3

4

5 6

7

8

5

6

7

8

9 10 11 12 13

Degree of freedom

9 10 11 12 13

1

2

3 4

Degree of freedom

5

6

7

8

9 10 11 12 13

Degree of freedom Fig. 3. The first four mode shapes.


1533

Table 4 Estimated and observed torsional resonance frequencies.

Mode

Estimated frequency (Hz)

Observed frequency (Hz)

1 2 3 4 5

7.2 32.6 61.7 127.9 202.6

9.5 37.3 51.8 119.5 210.5

−30 2 3

−35 ) B d (

1

−40

m u r t c e p S −45

4

5 −50

−55 0

50

100

150

200

250

Frequency (Hz) Fig. 4. Spectrum of the angular speed variations during a run-up in speed.

Analysis of a run-up in speed enables detection of the critical speeds. Fig. 4 shows a spectrum of the angular speed variations during a run-up in speed. The first five torsional resonance frequencies of the model seem to be visible. The estimated and observed frequencies are compared in Table 4. These frequencies are quite close. The crankshaft dynamical behavior can be represented by mathematical functions such as the mobility functions [18]. The latter represent the transfer functions between the torque excitations applied to the crankshaft and the crankshaft angular velocity responses. These functions are a linear weighted combination of the modes and have the following expressions: n

H ij ðoÞ ¼ jo 

Aijr 2 2 ðor o Þ þ 2 jer oor r ¼ 1

X

ð2Þ

Indices i and j respectively denote the response and the excitation dof. n is the number of excited modes. o is the frequency in radians per second. o r and e r are respectively the natural frequency and the damping ratio associated with the mode r . Aijr is a scalar whose magnitude depends on the location of the response dof i and the excitation dof j with respect to nodes and anti-nodes of the mode r . The closer the response dof i or the excitation dof j are to a node the lower is its magnitude. These functions are computed using the first five modes at the response dof 12 corresponding to the crankshaft free end dof. The observed resonance frequencies are used instead of the estimated ones. The damping ratios were estimated by using the spectrum of the run-up in speed and the half-power bandwidth method [19]. Fig. 5 shows two examples of mobility functions. The excitation dof is either the dof 3 (the second crank) or the dof 10 (the eighth crank). As the coupling end is close to a node, the strength of the modes, i.e. the residues, are low in the first case. As a consequence, cylinders close to the coupling will have less contribution to the crankshaft angular speed variations. 3.2. In-cylinder pressure curve modeling The main excitations applied to the crankshaft are the gas torque T g and the inertia torque T i . The simplified expressions of these torques are [13] T ðaÞ ¼ T g ðaÞ þ T i ðaÞ

ð3Þ

with, sinð2aÞ T g ðaÞ ¼ SRP ðaÞ sinðaÞ þ 2l






1534

−60 H123 H1210

−70 ) B d ( −80 e d u t i n g −90 a M

−100

−110 0

50

100

150

200

250

Frequency (Hz) Fig. 5. Examples of mobility functions.

2

2

T i ðaÞ ¼ W rec R O



sinðaÞ

4l

sin ð2aÞ 3sinð3aÞ sin ð4aÞ þ þ þ 2l 4l 4l2



a is the crankshaft angle, P ðaÞ is the in-cylinder gas pressure and O is the mean speed in radians per second. S , R and W rec are respectively the piston surface, the crank radius and the reciprocating mass. l is the ratio between the connecting rod length L and the crank radius R. All these parameters are known except for the in-cylinder pressure. The in-cylinder pressure P ðaÞ is the superposition of the compression pressure P m ðaÞ and the combustion pressure P c ðaÞ: P ðaÞ ¼ P m ðaÞþ P c ðaÞ

ð4Þ

3.2.1. Compression contribution The compression contribution can easily be estimated by considering a polytropic process: P m ðaÞ ¼ P intake

V intake V ðaÞ

g

 

ð5Þ

P intake and V intake are respectively the pressure and the volume at the end of the intake stroke. g is the polytropic index of the fluid (fuel/air mixture). Its value is typically in the range of 1.3–1.4 [20]. The volume V is the volume of the cylinder chamber depending on the crankshaft position a and on mechanical geometries: V ðaÞ ¼

2 4

0 s ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 1 @ A

Cu 1cosðaÞ þ l 1 2

2

1

sin ðaÞ 2

l

þ

2

3 5

ð6Þ

r1

Cu is the piston swept volume and r is the compression ratio.

3.2.2. Combustion contribution Modeling of the combustion contribution is more delicate. Phenomenological models are widely used because of their simplicity. These models are zero dimensional models. It is assumed that the in-cylinder pressure is spatially uniform. These models are based on predicting the rate of heat released (RoHR) with predefined functions. Wiebe’s function is one of the best known [21]. The single Wiebe’s function model has the following expression: 1 dQ ðaÞ ¼ Q tot 6:908ðmv þ 1Þ ymv exp 6:908 ymv þ 1 da Dac



with y ¼



ð7Þ

aasc Dac

Q tot is the total heat released. Dac and asc are respectively the combustion duration and the start of the combustion in crank angle. m v is a Wiebe’s function parameter. The total heat released depends on the injected fuel mass quantity m inj and the lower heating value of the fuel LHV : Q tot ¼ minj LHV

ð8Þ


1535

Superimposition of several Wiebe’s functions may be required in order to reproduce the RoHR closely as several stages are usually observed during the combustion process (premixed and mixing-controlled phases for example) [22,23]. However, for simplicity reasons, only a single Wiebe’s function is used. Then, the in-cylinder pressure can be computed step by step with a well-known thermodynamic relation between heat Q , pressure P and volume V and finite differences:

g1 ðg þ 1ÞV ðaÞgV ða þ DaÞ P c ða þ DaÞ ¼ dQ ðaÞþ P c ðaÞ V ðaÞ g1





ð9Þ

This model requires the estimation of four parameters: 1. 2. 3. 4.

the ignition delay (interval between the start of the injection and the start of the combustion), the combustion duration, Wiebe’s function shape parameter ( mv ), and the polytropic index g .

These parameters were determined by curve-fitting with an actual measurement of the in-cylinder pressure provided by the manufacturer. The pressure curve was measured at 75% of the full load condition and averaged over 30 cycles. Results are presented in Table 5 and in Fig. 6. A quite good match is obtained.

3.3. Simulation of the angular speed variations The crankshaft angular speed variations y i at a response dof i (i ¼ 12 at the free end) are defined as the convolution between the torques T Ak and T Bk applied to the cranks k on both banks of the crankshaft (banks A and B) and the mobility transfer function h ij (expressed in the angle domain a ¼ Ot Þ: _

11

y i ðaÞ ¼ _

X

11

hij ðaÞ  T A j1 þ

j ¼ 2

X

hij ðaÞ  T B j1

ð10Þ

j ¼ 2

with, T Ak ¼ T g ðaf Ak Þþ T i ðaf Ak Þ Table 5 Wiebe’s function parameters.

Ignition delay (deg) Combustion duration (deg) Wiebe’s function shape parameter Polytropic index

19 115 0.45 1.34

120 measurement model

100 80 ] r a b [ e r 60 u s s e r P 40 20

−360

−270

−180

−90

0

90

180

Crankshaft angle [°] Fig. 6. In-cylinder pressure curve-fitting.

270

360


1536

Table 6 Optimization of the natural frequencies f r and damping ratios e r .

Mode

Initial values

2 3 4 5

Optimized values

f r (Hz)

er (%)

f r (Hz)

er (%)

37.3 51.8 119.5 210.5

0.13 0.07 0.07 0.07

37.9 52.3 125.8 209.4

0.06 0.10 0.05 0.07

25 measurement simulation

20 ) m 15 p r ( s 10 n o i t 5 a i r a v 0 d e e p −5 s r a −10 l u g n A −15

−20 −25 0

90

180

270

360

450

540

630

720

Crankshaft angle (°) Fig. 7. Simulation of the angular speed variations at the crankshaft free end (continuous line) compared to the actual measurement (dashed line).

T Bk ¼ T g ðafBk Þþ T i ðafBk Þ

f Ak and f Bk are angular shifts which depend on the injection timing (not equally spaced). The angular speed variations at the crankshaft free end were simulated and compared to the actual measurement. Nevertheless, the model error was quite significant. In order to obtain a better match, the natural frequencies f r and damping ratios e r were optimized by curve-fitting according to the crankshaft angular response. Results are presented in Table 6 and in Fig. 7. A very good match is obtained. Errors were initially committed on the estimation of the damping ratios since the spectrum of the run-up in speed does not really reflect the natural response of the structure.

4. An automated diagnosis based on pattern recognition

4.1. Motivations The crankshaft angular speed responses can be decomposed into a sum of individual contributions corresponding to the crankshaft responses to each cylinder excitation. Fig. 8 shows the contributions of different cylinders to the simulated angular speed variations at the crankshaft free end. Each cylinder has a specific signature which depends on its location with respect to nodes and anti-nodes of the modes. As a consequence, any faulty cylinder in combustion stroke will distort the angular speed waveform in a specific way. The comprehension of these distortions is complex since they depend both on the system mode shapes and on the faulty cylinder. This is the reason why an automated diagnosis based on pattern recognition is proposed. Neural networks are used for pattern recognition of the crankshaft angular speed waveforms in normal and faulty conditions. A separate neural network is trained for each of the following stages: 1. detection of a combustion-related fault (detection phase), 2. identification of the faulty cylinder (localization phase), 3. and determination of the fault severity (quantification phase).


20

20 rms = 3.3 rpm

rms = 3.6 rpm

A2

) 10 m p r ( 0 d e e p S

1537

A4

) 10 m p r ( 0 d e e p S

−10

−10

−20

−20 0

180

360

540

720

0

Crankshaft angle (°) 20

360

540

720

Crankshaft angle (°) 20

rms = 4.7 rpm

180

rms = 5.7 rpm

A6

) 10 m p r ( 0 d e e p S

A8

) 10 m p r ( 0 d e e p S

−10

−10

−20

−20 0

180

360

540

Crankshaft angle (°)

720

0

180

360

540

720

Crankshaft angle (°)

Fig. 8. Contributions of different cylinders to the simulated angular speed variations at the crankshaft free end. The abbreviation rms denotes the root mean square value.

4.2. Neural networks Artificial neural networks (ANNs) have the capability to learn complex functions from observations. These have a large variety of architectures [24] and a large variety of applications such as classification or pattern recognition [25]. The most widely used network is the multilayer perceptron (MLP). Multilayer perceptrons with one hidden layer and sigmoid activation functions are used for classification purposes of the diesel engine conditions. The inputs to the networks (features) are the Fourier coefficients of the crankshaft angular speed variations. Real and imaginary parts are both considered. In detection phase, two classes are possible (normal and faulty conditions). The network output is a scalar equal to zero or one depending on the condition. In localization phase, 20 classes are possible (one for each cylinder). The network output is a vector composed of 20 elements. One element is equal to one indicating the faulty cylinder and the others are equal to zero. The number of neurons in the hidden layer was determined using a trial and error procedure. This number was set to eight. 4.3. Training data The generation of training data is an important step in the development of artificial neural networks. The training data should be as representative as possible of the engine conditions. Training of the networks is usually realized with experimental examples. In this work, simulated examples are used instead because it is not economically viable to experience or experimentally simulate the number of fault conditions and locations required to train the networks. Previous works have already shown the benefits of using simulated feature vectors for bearing or gearbox diagnostics [26,27]. Only a relatively small amount of actual data are required to calibrate and update the simulation model, and give a measure of the amount of random variation in measurements for a given condition (healthy or faulty). These considerations are reinforced in the case of large diesel engines with a high number of cylinders. Indeed, the experimental tests would require at least as many engine conditions as cylinders, multiplied by the number of degrees of severity to be distinguished for each fault. The procedure for data generation is illustrated in Fig. 9. Data are generated at a unique operating point, i.e. constant mean speed and constant load. The crankshaft angular speed variations are simulated both in normal and faulty conditions. A modeling correction, corresponding to the difference observed between the model and the actual signal in normal condition (see Fig. 7), is added to the signal. The latter is then decomposed by Fourier series. A Gaussian noise is added to each feature. Thus, different realizations can be produced at the same condition. Standard deviations were set by analysis of two actual measurements recorded at different dates (2005 and 2007) in normal condition. These two measurements give an estimate of the expected variability of the crankshaft angular speed variations for each Fourier coefficient. Deviations up to one rpm were observed between the two measurements.


1538

Faulty cylinder Fault level

Model

Fourier series

Modeling corection

Feature vector

Gaussian noise

Fig. 9. Training data.

100 Accuracy

95 ) % ( s n o i t a c i f i s s a l c t c e r r o C

90 85 80 75 70 65 60 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fault level (β) Fig. 10. Total percentage of correct classifications (accuracy) in detection phase.

Simulated faults are related to the combustion process. Torques applied to the crankshaft depend on the in-cylinder gas pressure P ðaÞ. Faults are introduced by decreasing the maximum peak pressure: P ðaÞ ¼ P m ðaÞ þð1bÞP c ðaÞ

ð11Þ

b is a fault level. A fault level equal to unity means no combustion at all. The way faults are introduced is quite similar to a fuel leakage fault. All the features (real and imaginary parts of the Fourier coefficients) may have different sensitivities to the engine conditions. Only some of them may carry useful information. It is a very important issue to select the best feature set. The performance of the classification process strongly depends on this selection. Generalization ability is improved by eliminating insensitive features. Moreover, feature selection reduces the size of the network and therefore decreases the computing time in the training phase. From a geometrical point of view, the classification process can be seen as the division of an observation space into distinct regions corresponding to the different engine conditions (classes). From this consideration, a feature selection based on two geometrical criteria is adopted [28]. These two criteria give a measure of the distance between classes. The more the features are grouped in distinct clusters, the greater the ease of the classification process. In this application, the best set is composed of the first (12.5 Hz) and fourth (50 Hz) orders. 4.4. Results 4.4.1. Detection phase The detection phase aims at determining if the engine is operating in normal or in faulty condition. It requires the choice of a fault detection threshold. The latter corresponds to the lowest fault ( bmin ) that could be detected with sufficient accuracy. This is a compromise between the rate of false alarm and the detection sensitivity. Simulations were conducted in order to determine a fault detection threshold. Networks were trained at different fault levels b from 10% to 100%. At a given fault level, 100 healthy examples and 100 faulty examples (five for each cylinder) were computed. The training examples were then divided into two sets: 75% were used for training and 25% were used for validation. Training is stopped when the best validation performance occurs, i.e. the network becomes over trained on the training set. Another independent set was computed in order to test the network generalization ability. Because they were presented to the network in a random manner, the sequence of the training examples is different during each training. This can lead to varying results of the network performance. This is the reason why training of the network was repeated several times. The best result obtained was selected. Fig. 10 shows the total percentage of correct classifications (accuracy) according to the fault level. As expected, the higher the fault level, the higher the percentage of correct classifications. The latter remains higher than 95% as long as the


100

1539

Cylinder A2 Cylinder A8

90 ) % ( s n o i t a c i f i s s a l c t c e r r o C

80 70 60 50 40 30 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fault level (β) Fig. 11. Percentage of examples with faulty cylinders A2 and A8 correctly classified in detection phase.

Table 7 Actual and predicted conditions with actual data in detection phase.

Actual

Predicted Normal condition

Normal condition (2005) Normal condition (2007) Faulty fuel pumps

Faulty condition

| | |

fault level is higher than 25% and strongly decreases below 30%. A detection threshold of 25% is proposed. Fig. 11 shows the percentage of examples with faulty cylinders A2 and A8 that were correctly classified according to the fault level. Cylinder A2 is located next to the coupling whereas cylinder A8 is located next to the crankshaft free end. At a fault level equal to 25%, the percentage of misclassifications is up to 5% for the former compared with 0% for the latter. It is obvious that detection at low fault level is more accurate for cylinders next to the crankshaft free end. Indeed, the contributions of these cylinders to the crankshaft angular speed variations are higher, especially for the fourth order. It means that these cylinders strongly distort the angular speed waveform when operating in faulty condition in comparison to those located at the opposite end. The trained network at a fault level of 25% well classifies the actual data (see Table 7). Faults were introduced by decreasing the injected fuel quantities in cylinders A6 and A4 up to 80% and 50% respectively.

4.4.2. Localization and quantification phases It is known that the engine is operating in faulty condition. The localization phase aims at identifying which cylinder has a fault. A network was trained for localization of the faulty cylinder. Faulty examples were randomly computed at different fault levels from 25% to 100% (10 examples for each cylinder). As previously, the training examples were divided into two sets, a training set and a validation set. The training was stopped before over-training of the training set. Another independent set was computed to evaluate the network performances. The training was repeated several times and the best result obtained was selected. The percentage of correct classification is higher than 98%. Simulations give very good performances. The actual data are correctly classified. Cylinder A6 is identified as faulty. In reality, two fuel pumps were disturbed in that case. Fuel leakage faults were introduced in cylinder A6 and cylinder A4. However, it seems that the signature of the former is predominant. Indeed the injected fuel quantities were decreased by 80% in cylinder A6 compared with 50% in cylinder A4. Moreover, cylinder A6 is closer to the crankshaft free end. Contribution of this cylinder to the crankshaft angular speed variation is higher. Another network can be used in order to quantify the fault severity. Examples were computed with faulty cylinder A6 at different fault levels, 25%, 50%, 75% and 100%. The fault severity is then predicted to 75% which is very close to the actual


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10 simulation measurement

) m 5 p r ( s n o i t a i r a 0 v d e e p s r a l u −5 g n A

−10 0

180

360

540

720

Crankshaft angle (°) Fig. 12. Measured and simulated angular speed differences between normal and faulty conditions.

disturbance. Fig. 12 shows the measured and simulated angular speed differences between normal and faulty conditions. The signal waveforms are quite similar especially in the low frequencies. 5. Conclusion

This paper has dealt with the diagnosis of large diesel engines by analyzing the crankshaft angular speed variations measured at a single point. It focused on a powerful 20-cylinder diesel engine. Combustion-related faults were considered. It was shown that diagnosis through the analysis of the angular speed fluctuations is conceivable even in the case of large engines with a high number of cylinders. Due to the crankshaft flexibility, torsional vibrations are superimposed on the rigid rotational motion of the crankshaft and complicate the analysis. Cylinders have different contributions to the crankshaft angular speed variations and do not distort these variations in the same manner when operating in faulty condition. The extraction of relevant parameters on the engine condition without any knowledge of the system is difficult. A model capable of simulating the crankshaft torsional response was desirable. Neural networks were used for pattern recognition of the angular speed waveforms in normal and faulty conditions. Reference patterns were computed with the model using a small number of measurements to calibrate the simulation model and the amount of random variation to include in the simulations for a given condition. Promising results were obtained. An experimental fuel leakage fault was correctly diagnosed, including detection and localization of the faulty cylinder and an indication of the severity of the fault. It was also shown that detection of faulty cylinders next to the coupling end (where dynamic response is low) is harder in comparison to the opposite end. More actual data, especially in faulty condition, would be required to fully confirm the obtained results. References [1] J. Williams, An overview of misfiring cylinder engine diagnostic techniques based on crankshaft angular velocity measurements, SAE Paper No. 960039, 1996, pp. 31–37. [2] M. Geveci, A.W. Osburn, M.A. Franchek, An investigation of crankshaft oscillations for cylinder health diagnostics, Mechanical Systems and Signal Processing 19 (2005) 1107–1134. [3] D. Taraza, N.A. Henein, W. Bryzik, The frequency analysis of the crankshaft’s speed variation: a reliable tool for diesel engine diagnosis, Journal of Engineering for Gas Turbines and Power 123 (2) (2001) 428–432. [4] S. Citron, J. O’Higgins, L. Chen, Cylinder by cylinder engine pressure and pressure torque determination utilizing speed fluctuations, SAE Paper No. 890486, 1989. [5] H. Fehrenbach, Model-based combustion pressure computation through crankshaft angular acceleration analysis, in: 22nd International Symposium on Automotive Technology and Automation, 1990. [6] F. Ostman, H. Toivonen, Active torsional vibration control of reciprocating engines, Control Engineering Practice 16 (1) (2008) 78–88. [7] P. Charles, J.K. Sinha, F. Gu, L. Lidstone, A.D. Ball, Detecting the crankshaft torsional vibration of diesel engines for combustion related diagnosis, Journal of Sound and Vibration 321 (2009) 1171–1185. [8] A.K. Sood, C.B. Friedlander, A.A. Fahs, Engine fault analysis: part I —statistical methods, IEEE Transactions on Industrial Electronics 32 (4) (1985) 294–300. [9] T.S. Brown, W.S. Neill, Determination of engine cylinder pressures from crankshaft speed fluctuations, SAE Paper No. 920463, 1992. [10] S. Leonhardt, C. Ludwig, R. Schwarz, Real-time supervision for diesel engine injection, Control Engine Practice 3 (7) (1995) 1003–1010. [11] J. Antoni, J. Daniere, F. Guillet, Effective vibration analysis of IC engines using cyclostationarity. Part I —a methodology for condition monitoring, Journal of Sound and Vibration 257 (2002) 815–837. [12] J. Antoni, J. Dani ere, F. Guillet, Effective vibration analysis of IC engines using cyclostationarity. Part II —new results on the reconstruction of the cylinder pressures, Journal of Sound and Vibration 257 (2002) 839–856. [13] C.M. Harris, A.G. Piersol, Harris’s Shock and Vibration Handbook, fifth ed., McGraw-Hill, New York, 2002. [14] Polytec GmbH, Basics of rotational vibration sensing, Waldbronn, Germany. 

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[15] N.A. Halliwell, The laser torsional vibrometer: a step forward in rotating machinery diagnostics, Journal of Sound and Vibration 190 (3) (1996) 199–418. [16] P.R. Johnston, L.M. Shusto, Analysis of diesel engine crankshaft torsional vibrations, SAE Paper No. 870870, 1994. [17] A.S. Mendes, P.S. Meirelles, D.E. Zampieri, Analysis of torsional vibration in internal combustion engines: modeling and experimental validation, Proceeding of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 222 (2) (2008) 155–178. [18] D.J. Ewins, Modal Testing: Theory Practice and Application, second ed., Research Studies Press, 2001. [19] A.D. Nashif, D.I.G. Jones, J.P. Henderson, Vibration Damping, Wiley Interscience, New York, 1985. [20] J.B. Heywood, Internal Combustion Engine Fundamentals, McGraw-Hill, New York, 1988. [21] I.T. Vibe, Brennverlauf und Kreisprozess von Verbrennungsmotoren, VEB-Verlag Technik, Berlin, 1970. [22] N. Miyamoto, T. Chikahisa, T. Murayama, R. Sawyer, Description and analysis of diesel engine rate of combustion and performance using Vibe’s functions, SAE Paper No. 850107, 1985. [23] H. Yasar, H. Soyhan, H. Walmley, B. Head, C. Sorusbay, Double-Wiebe function: an approach for single-zone HCCI engine modeling, Applied Thermal Engineering 28 (2008) 1284–1290. [24] J.M. Zurada, Introduction to Artificial Neural Systems, West Publishing Company, 1992. [25] C.G. Looney, Pattern Recognition Using Neural Networks: Theory and Algorithms for Engineers and Scientists, Oxford University Press, New York, 1997. [26] R.B. Randall, Training neural networks for bearing diagnostics using simulated feature vectors, in: AI-MECH Symposium, Gliwice, Poland, 14–16 November 2001. [27] R.B. Randall, The application of fault simulation to machine diagnostics and prognostics, ICSV16, Krakow, Poland, 5–9 July 2009. [28] J. Dybala, S. Radkowski, Geometrical method of selection of features of diagnostic signals, Mechanical Systems and Signal Processing 21 (2007) 761–779.

Crankshaft

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