# Internal Combustion Engine Fault Identification Based on FBG Vibration Sensor and Support Vector Machines Algorithm

Authors: Faye Zhang; Mingshun Jiang; Lei Zhang; Shaobo Ji; Qingmei Sui; Chenhui Su; Shanshan Lv
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

State monitoring and fault diagnosis of an internal combustion engine are critical for complex machinery safety. In the present study, a high-frequency vibration system was proposed based on Fiber Bragg Grating (FBG) cantilever sensor and intelligent algorithm. Structural vibration signal containing fault information of engine valves and oil nozzle was identified by FBG sensors and preprocessed using wavelet decomposition and reconstruction. Moreover, vibration energy was taken as fault characteristics. Subsequently, a fault identification model was built based on multiclassυ-support vector classification (υ-SVC). Experimental tests on the valve fault and fuel injection advance angle fault were performed and presented to verify the efficacy of the proposed approach. The results here reveal that the proposed method exhibits excellent fault detection performance for ICE fault identification. Furthermore, the proposed method can achieve higher performance than other methods in the fault identification accuracy.


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## Body

## 1. Introduction

The working state of valve or oil nozzle is an important condition for engines, covering all petrol engines and diesel engines. Any defect in valves or oil nozzle will lead to the loss of engine power and even cause permanent damage. Thus, to avoid fatal failure of valves or oil nozzle and to reduce the secondary damage caused by breakdowns, it is urgently required to detect valve or oil nozzle defects quickly and accurately [1, 2].Vibration analysis is one of the techniques that have been used for engine condition monitoring and fault diagnosis successfully. While engine is operating with different faults, the corresponding vibration signal will change, as reflected in the resonant frequency component changes [3, 4]. With the advancement of fiber optic sensing technology, a novel principle and method has been provided for condition monitoring and diagnosis of machinery. FBG sensors exhibit compact structure, good insulation, easy installation, high reliability, easy to build sensor networks, and other prominent advantages [5, 6]. Accordingly, FBG sensors are considered an ideal choice for detecting engine vibration [7–9].With the improvement in the precision of the engine, automatic intelligent diagnosis technology with accurate recognition and prediction results is urgently required. Thus far, numerous studies have been conducted on fault diagnosis algorithms, e.g., expert systems [10–12], artificial neural networks (ANN) [13–15], and fuzzy logic [16–18]. Expert system refers to the use of computer storage of human knowledge, which imitates the reasoning of solving a particular problem by human expert. ANN requires a huge amount of learning to build a fault model, which is employed to perform fault diagnosis. Fuzzy logic requires considerable system input and output signal characteristics to build a model of the membership function of various variables. However, these methods need many samples for training, thereby limiting the popularization and the application of the algorithm. Support vector machine (SVM) [19] is preferred for fault diagnosis for its high accuracy and good generalization even with small samples. Thus, the algorithm has been an effective method for diagnosing mechanical faults, e.g., bearing [20], gearbox [21], and centrifugal pump [22].In this study, a high-frequency system was presented based on Fiber Bragg Grating (FBG) cantilever sensor and edge filter demodulation scheme to collect vibration signals of engine valves and oil nozzle. The signals were subsequently preprocessed by wavelet decomposition and reconstruction, and vibration energy was proposed to extract fault features. Next, a multifault diagnosis model based onυ-SVC was built and verified on an internal combustion engine (ICE) by valve and fuel injection advance angle fault identification. The results reveal that the proposed method can achieve high predictive accuracy than the SOM neural network-based method, which was up to 95%.


## 2. Description of Proposed Algorithm

### 2.1. FBG High-Frequency Vibration Sensor Design

The sensor structure is shown in Figure1. The sensor is composed of three parts, namely, an equi-intensity cantilever beam of dimensions L×b×h, a fixed support, and an FBG adhered on the cantilever.Figure 1
The architecture of FBG high-frequency vibration sensor.Given the centroid of the equi-intensity cantilever beam with no-load locating at positionL/3, the eigenfrequency is expressed as (1)f=12πkm=12πmgω∙L3∙1m=12π486Eh243ρL4.The parameters of the sensor were set as listed in Table1. The natural frequency is 14.8kHz, which is given by (1).Table 1
The parameters of FBG vibration sensor.
number parameters value 1 E 195GPa 2 ρ 8000kg/m3 3 h 3.5 mm 4 L 25.0 mm 5 b 5.0 mmA finite element model of the first order was built to explore the harmonic response frequency characteristics of the sensor by ANSYS (Figure2). The natural frequency is 8.9kHz, lower than the theoretical value caused by lateral vibration of the beam end. Besides, to the best of our knowledge, the papers on FBG vibration sensor with higher natural frequency have been rarely published.Figure 2
The finite element model.


### 2.2. FBG Demodulation System

The structure diagram of the demodulation system is given in Figure3. The system consists of an ASE light source without flat processing, a circulator, a photoelectric conversion and amplification circuit, an FBG vibration sensor, and a data processing unit as well as a computer. The ASE light source offers the system a light source, and its spectral linear segment serves as an edge filter. The circulator provides an optical signal loop, while its unidirectional feature can prevent the transmission of the reflected light into the light source. The FBG vibration sensor converts the valve vibration signal into a light intensity signal. The intensity signal, which is collected by the data processing unit, is converted into a voltage signal by the photoelectric conversion circuit. The computer displays the voltage signal. The demodulation system works as follows: when reflection peak of FBG vibration sensors shifts ∆λ, caused by engine structure failure vibration signals, its intensity will vary owing to the modulation effect of ASE source hypotenuse filter. This change is converted to a voltage signal by photoelectric conversion and amplification circuit. Afterwards, the voltage will be collected by the data processing unit and displayed by computer.Figure 3
The structure diagram of FBG demodulation system.The peak sample frequency of the system is 200 kHz, and its demodulation precision is 2.5mV/pm. The wavelength of FBG sensor was set ranging from 1533 nm to 1536 nm, which is the maximum slope position of the ASE light source spectral curve. Given the intensity of vibration signals, the wavelength was selected to be 1534 nm and stretched to 1534.570 nm by preloading.


### 2.3. Fault Diagnosis Formulation

The process of building the model, based onυ-support vector classification (υ-SVC) technology [23], is illustrated as follows.To diagnose the fault, the convex optimization problem solved byυ-SVC is defined as(2)minw,b,ξ,ρ⁡12wTw-νρ+1l∑i=1lξis.t.yiw∙ϕxi+b≥ρ-ξiξi≥0,i=1,…,l,ρ≥0.l denotes the training sample count; xi∈Rn,i=1,…,l is the extracted fault features; n is feature dimension. yi∈1,-1 is category label. w is normal vector; ξi is slack variable; 0<ν≤1 is a hyperparameter that denotes an upper bound on the fraction of training errors and a lower bound of the fraction of support vectors; ϕ refers to a nonlinear function that maps the input space into a higher dimensional space, and ρ is threshold. The solution of (2) is obtained by its dual Lagrange equation(3)maxα⁡Tα=-12∑i=1l∑j=1lyiyjαiαjϕxi,ϕxjs.t.∑i=1Nαiyi=00≤αi≤1N∑i=1Nαi≥ν.α = α 1 , α 2 , … , α N refer to Lagrange multipliers. kxi,yj=ϕxi,ϕyj is kernel function, which is taken as(4)kxi,xj=exp-γxi-xj,whereγ denotes the nuclear wide. By solving (3) with (4), the final υ-SVC model can be expressed as(5)fx=sgn⁡∑i=1lαiyikxi,x+b=sgn⁡∑i=1lαiyiexp-γxi-x+b.Equation (5) is the υ-SVC classifier model. If fx≥0, the fault state belongs to fault type i and if fx<0. Thus, it does not belong to fault type i.To solve multiclassification problems, multiclassifier based on directed acyclic graph (DAG) [24] and υ-SVC was proposed. Considering an example of p fault type, a total of pp+1/2 υ-SVC classifiers were built, and the fault diagnosis model based on υ-SVC and DAG is shown in Figure 4. The fault diagnosing process is as follows: when identifying any of the fault samples, first, start from 01vsp; if the recognition result is fault 1, enter the right to 01vsp-1; otherwise, enter the left to 02vsp. Repeat the mentioned process until arriving one node of the last layers of the model, which is the fault to be identified.Figure 4
The fault type identification model.


## 2.1. FBG High-Frequency Vibration Sensor Design

The sensor structure is shown in Figure1. The sensor is composed of three parts, namely, an equi-intensity cantilever beam of dimensions L×b×h, a fixed support, and an FBG adhered on the cantilever.Figure 1
The architecture of FBG high-frequency vibration sensor.Given the centroid of the equi-intensity cantilever beam with no-load locating at positionL/3, the eigenfrequency is expressed as (1)f=12πkm=12πmgω∙L3∙1m=12π486Eh243ρL4.The parameters of the sensor were set as listed in Table1. The natural frequency is 14.8kHz, which is given by (1).Table 1
The parameters of FBG vibration sensor.
number parameters value 1 E 195GPa 2 ρ 8000kg/m3 3 h 3.5 mm 4 L 25.0 mm 5 b 5.0 mmA finite element model of the first order was built to explore the harmonic response frequency characteristics of the sensor by ANSYS (Figure2). The natural frequency is 8.9kHz, lower than the theoretical value caused by lateral vibration of the beam end. Besides, to the best of our knowledge, the papers on FBG vibration sensor with higher natural frequency have been rarely published.Figure 2
The finite element model.


## 2.2. FBG Demodulation System

The structure diagram of the demodulation system is given in Figure3. The system consists of an ASE light source without flat processing, a circulator, a photoelectric conversion and amplification circuit, an FBG vibration sensor, and a data processing unit as well as a computer. The ASE light source offers the system a light source, and its spectral linear segment serves as an edge filter. The circulator provides an optical signal loop, while its unidirectional feature can prevent the transmission of the reflected light into the light source. The FBG vibration sensor converts the valve vibration signal into a light intensity signal. The intensity signal, which is collected by the data processing unit, is converted into a voltage signal by the photoelectric conversion circuit. The computer displays the voltage signal. The demodulation system works as follows: when reflection peak of FBG vibration sensors shifts ∆λ, caused by engine structure failure vibration signals, its intensity will vary owing to the modulation effect of ASE source hypotenuse filter. This change is converted to a voltage signal by photoelectric conversion and amplification circuit. Afterwards, the voltage will be collected by the data processing unit and displayed by computer.Figure 3
The structure diagram of FBG demodulation system.The peak sample frequency of the system is 200 kHz, and its demodulation precision is 2.5mV/pm. The wavelength of FBG sensor was set ranging from 1533 nm to 1536 nm, which is the maximum slope position of the ASE light source spectral curve. Given the intensity of vibration signals, the wavelength was selected to be 1534 nm and stretched to 1534.570 nm by preloading.


## 2.3. Fault Diagnosis Formulation

The process of building the model, based onυ-support vector classification (υ-SVC) technology [23], is illustrated as follows.To diagnose the fault, the convex optimization problem solved byυ-SVC is defined as(2)minw,b,ξ,ρ⁡12wTw-νρ+1l∑i=1lξis.t.yiw∙ϕxi+b≥ρ-ξiξi≥0,i=1,…,l,ρ≥0.l denotes the training sample count; xi∈Rn,i=1,…,l is the extracted fault features; n is feature dimension. yi∈1,-1 is category label. w is normal vector; ξi is slack variable; 0<ν≤1 is a hyperparameter that denotes an upper bound on the fraction of training errors and a lower bound of the fraction of support vectors; ϕ refers to a nonlinear function that maps the input space into a higher dimensional space, and ρ is threshold. The solution of (2) is obtained by its dual Lagrange equation(3)maxα⁡Tα=-12∑i=1l∑j=1lyiyjαiαjϕxi,ϕxjs.t.∑i=1Nαiyi=00≤αi≤1N∑i=1Nαi≥ν.α = α 1 , α 2 , … , α N refer to Lagrange multipliers. kxi,yj=ϕxi,ϕyj is kernel function, which is taken as(4)kxi,xj=exp-γxi-xj,whereγ denotes the nuclear wide. By solving (3) with (4), the final υ-SVC model can be expressed as(5)fx=sgn⁡∑i=1lαiyikxi,x+b=sgn⁡∑i=1lαiyiexp-γxi-x+b.Equation (5) is the υ-SVC classifier model. If fx≥0, the fault state belongs to fault type i and if fx<0. Thus, it does not belong to fault type i.To solve multiclassification problems, multiclassifier based on directed acyclic graph (DAG) [24] and υ-SVC was proposed. Considering an example of p fault type, a total of pp+1/2 υ-SVC classifiers were built, and the fault diagnosis model based on υ-SVC and DAG is shown in Figure 4. The fault diagnosing process is as follows: when identifying any of the fault samples, first, start from 01vsp; if the recognition result is fault 1, enter the right to 01vsp-1; otherwise, enter the left to 02vsp. Repeat the mentioned process until arriving one node of the last layers of the model, which is the fault to be identified.Figure 4
The fault type identification model.


## 3. Experiments and Analysis

To validate the proposed fault diagnosis method, the valve and fuel injection advance angle fault experiment were performed.


### 3.1. Experiment Setup

The experimental setup used for valve fault diagnosis is shown in Figure5. The test system consists of a H195 diesel engine, an FBG acceleration sensor, and a fiber grating demodulator as well as a computer. The FBG acceleration sensor attached on cylinder head by epoxy adhesive sensed the vibration changes of engine structure and converted them into FBG wavelength changes. The wavelength changes were captured by the fiber grating demodulator and then transferred to computer via network.Figure 5
The engine vibration testing system.In this case, nine types of fault types under no-load condition (e.g., normal state), shown in Tables2 and 3, were involved in the experiment. The vibration signals were continuously acquired by the FBG vibration sensor, while keeping engine speed varied from 800 rpm to 1200 rpm at 200 rpm steps per min. 243 samples for fault type were acquired in the tests, while the sampling point was set to 40000. The waveforms of the nine operating states at 1200rmp in time domain are shown in Figure 6.Table 2
Experimental conditions set of valve experiment.
fault type intake gap (mm) outlet gap (mm) load rate (%) engine speed (rpm) number of experiments I 0.3 0.5 0 800 9 1000 9 1200 9 II 0.3 0.7 0 800 9 1000 9 1200 9 III 0.3 0.9 0 800 9 1000 9 1200 9 IV(normal state) 0.3 0.4 0 800 9 1000 9 1200 9 V 0.5 0.4 0 800 9 1000 9 1200 9 VI 0.7 0.4 0 800 9 1000 9 1200 9Table 3
Experimental conditions set of fuel injection advance angle experiment.
fault type Fuel injection advance angle (°) load rate (%) engine speed (rpm) number of experiments VII 16 0 800 9 1000 9 1200 9  VIII(normal state) 20 0 800 9 1000 9 1200 9  IX 24 0 800 9 1000 9 1200 9Figure 6
Time domain waveforms of the nine operating states: (a) fault type I, (b) fault type II, (c) fault type III, (d) fault type IV (normal state), (e) fault type V, (f) fault type VI, (g) fault type VII, (h) fault type VIII, and (i) fault type IX.
(a) (b) (c) (d) (e) (f) (g) (h) (i)Figure6 suggests that the dynamic signals were accurately detected by FBG acceleration sensor, which reveals that FBG sensor can be used for engine structural fault identification. However, the figure also suggests that it was hard to distinguish their fault state depending on the time domain vibration signals individually.To find the differences between different fault types, the vibration signals collected at different valve clearance in time domain and frequency domain were analyzed. Normal state with valve clearance 0.4mm, intake valve clearance 0.3mm (s.t fault type IV), and abnormal state with intake valve clearance 0.7mm (s.t fault type VI) were taken as an example. The results are shown in Figure7, showing that there were significant differences in frequency domain at 900 Hz~1400Hz and 1650 Hz~1850Hz.Figure 7
Comparison of time domain and frequency domain characteristics. (a) Time domain diagram of normal state signal, (b) frequency diagram of normal state signal, (c) time domain diagram of abnormal state signal, and (d) frequency diagram of abnormal state signal.
(a) (b) (c) (d)


### 3.2. Feature Extraction

To extract fault characteristics, the collected signals were decomposed by wavelet decomposition and reconstruction. Besides, the vibration energy was calculated by the processed formula, which was defined as follows.Continuous vibration signals are denoted as functionft, which meet the following conditions within the range of real numbers:(6)∫-∞+∞fx2dx<+∞.Given the time seriesF=fT,f2T,…,fnT obtained by sampling, the vibration energy is expressed as(7)E=12N2-N1∑i=N1N2fiT-fT02.N 1 = 0 , 1,2 , … , n ,   N 2 = 1,2 , … , n, and N2≥N1. T denotes the sample Interval; n is the total sampling points. fT0 is the initial state of the vibration signal.The vibration signal of fault type I at 1000 rpm processed by wavelet decomposition and reconstruction with DB4 wavelet function is shown in Figure8. Subsequently, the vibration energy of processed signals is calculated by (5). Three samples of each fault type were taken as examples. The results, used as feature vectors, are listed in Table 4.Table 4
Feature vector based on Wavelet decomposition and reconstruction.
Operating state No. vibration energy feature vector E a 41 E d 41 E d 31 E d 21 E d 11 1 29171.56 125.61 419.31 190.47 916.02 Fault type I 2 28467.95 314.92 536.79 310.96 615.85 3 29162.03 657.91 1198.32 743.29 1532.70  1 34728.80 157.96 446.43 203.43 305.95 Fault type II 2 37501.9 442.93 787.90 364.83 757.68 3 41248.90 604.38 1035.80 783.93 1459.29  1 51984.62 2601.75 2774.43 440.82 774.74 Fault type III 2 66161.88 3606.90 4286.53 2143.04 3459.64 3 55689.37 10129.43 4527.10 3965.93 7854.19  Fault type IV 1 86067.38 133.12 327.000 195.39 288.40 (Normal) 2 84843.81 267.18 464.92 343.86 844.38 3 84297.88 542.58 1182.75 710.60 2152.55  1 70662.03 155.80 281.01 201.87 520.20 Fault type V 2 70043.63 302.41 671.87 496.92 1467.39 3 70177.78 611.64 1671.62 703.10 1696.39  1 66528.25 338.03 491.06 398.17 1325.69 Fault type VI 2 66243.20 673.17 1596.44 839.55 1802.04 3 67345.94 956.43 1467.58 1159.19 2497.36  Fault type VII 1 187.27 824.61 876.71 328.32 4278.87 2 176.31 387.19 104.38 477.13 4155.92 3 208.67 741.50 100.80 341.36 3565.39  Fault type VIII 1 115.19 304.61 353.27 367.06 4727.75 2 173.00 608.37 891.72 459.13 3843.63 3 136.02 962.09 780.94 932.79 4177.78  Fault type IX 1 275.42 163.24 194.65 550.57 5338.03 2 200.03 109.90 118.59 400.76 4896.44 3 231.09 130.74 178.99 557.56 6101.87Figure 8
The decomposed vibration signals of fault type I.To conclude the relationship between the vibration energy and the engine fault directly, the first feature vector of each fault type was normalized and plotted in the same coordinate system, as shown in Figure9.Figure 9
The characteristics of different fault feature vector: (a) fault type I, (b) fault type II, (c) fault type III, (d) fault type IV, (e) fault type V, (f) fault type VI, (g) fault type VII, (h) fault type VIII, and (i) fault type IX.
(a) (b) (c) (d) (e) (f) (g) (h) (i)Figure9 shows that all faults have different feature vectors. Accordingly, the vibration energy of decomposed vibration signals can be extracted as the fault characteristic.


### 3.3. Model Training and Verifying

The engine valve fault identification experiment was stratified into two parts, namely, building the fault identification model by model training and verifying the constructed model by model testing.For model training, the experiments were performed 3 times on ZH195 diesel engine by keeping the engine speed from 800 rpm to 1200 rpm at 200 rpm steps under no-load condition. Thus, 9 groups of vibration signals were obtained, and the fault features were extracted. Subsequently, the engine state shifted from fault II to fault IX, and the same experiments were performed. 81 groups of vibration signals were detected, and the fault features were extracted. Finally, the fault detection model based on multiclassυ-SVC was trained. In this study, hyperparameter γ was set as 4, and hyperparameter υ was set as 32 using the cross validation. The training result is shown in Figure 10. It is found that the multiclassification υ-SVC method identified different fault type accurately.Figure 10
The training results of the fault type identification.When the model was built, further experiments were performed from fault I to fault IX, and the experiment count was set as 162. Thus, 162 groups of vibration signals and their relevant fault feature were extracted to verify the correctness of the model. The result is shown in Figure11, showing that the average accuracy of fault identification reached 96.3%. The result here reveals that the proposed fault identification method can be effectively used for diagnosing the engine fault.Figure 11
The verifying results of the fault type identification.The fault identification performance of the built model based onυ-SVC was compared with the results of SOM (Self-Organization feature Map) neural network. The SOM neural network refers to a self-organizing, self-learning network consisting of a fully connected array of neurons [25]. It is preferred for fault classification for its high accuracy even with small samples. The number of competitive layer neurons was set as 36, and the number of training steps was set as 500. The identification results are listed in Table 5, showing that the fault model based on υ-SVC achieved higher fault identification rates.Table 5
Identification results.
Method Identification accuracy Fault Type Number ofsamples Correct identification number Accuracy (%) Average accuracy (%) υ-SVC I 18 18 100.0 96.3 II 18 18 100.0 III 18 17 94.4 IV 18 18 100.0 V 18 17 94.4 VI 18 18 100.0 VII 18 17 94.4 VIII 18 17 94.4 IX 18 16 88.9  SOM neural network I 18 17 94.4 88.9 II 18 17 94.4 III 18 16 88.9 IV 18 17 94.4 V 18 17 94.4 VI 18 16 88.9 VII 18 16 88.9 VIII 18 16 88.9 IX 18 15 83.3


## 3.1. Experiment Setup

The experimental setup used for valve fault diagnosis is shown in Figure5. The test system consists of a H195 diesel engine, an FBG acceleration sensor, and a fiber grating demodulator as well as a computer. The FBG acceleration sensor attached on cylinder head by epoxy adhesive sensed the vibration changes of engine structure and converted them into FBG wavelength changes. The wavelength changes were captured by the fiber grating demodulator and then transferred to computer via network.Figure 5
The engine vibration testing system.In this case, nine types of fault types under no-load condition (e.g., normal state), shown in Tables2 and 3, were involved in the experiment. The vibration signals were continuously acquired by the FBG vibration sensor, while keeping engine speed varied from 800 rpm to 1200 rpm at 200 rpm steps per min. 243 samples for fault type were acquired in the tests, while the sampling point was set to 40000. The waveforms of the nine operating states at 1200rmp in time domain are shown in Figure 6.Table 2
Experimental conditions set of valve experiment.
fault type intake gap (mm) outlet gap (mm) load rate (%) engine speed (rpm) number of experiments I 0.3 0.5 0 800 9 1000 9 1200 9 II 0.3 0.7 0 800 9 1000 9 1200 9 III 0.3 0.9 0 800 9 1000 9 1200 9 IV(normal state) 0.3 0.4 0 800 9 1000 9 1200 9 V 0.5 0.4 0 800 9 1000 9 1200 9 VI 0.7 0.4 0 800 9 1000 9 1200 9Table 3
Experimental conditions set of fuel injection advance angle experiment.
fault type Fuel injection advance angle (°) load rate (%) engine speed (rpm) number of experiments VII 16 0 800 9 1000 9 1200 9  VIII(normal state) 20 0 800 9 1000 9 1200 9  IX 24 0 800 9 1000 9 1200 9Figure 6
Time domain waveforms of the nine operating states: (a) fault type I, (b) fault type II, (c) fault type III, (d) fault type IV (normal state), (e) fault type V, (f) fault type VI, (g) fault type VII, (h) fault type VIII, and (i) fault type IX.
(a) (b) (c) (d) (e) (f) (g) (h) (i)Figure6 suggests that the dynamic signals were accurately detected by FBG acceleration sensor, which reveals that FBG sensor can be used for engine structural fault identification. However, the figure also suggests that it was hard to distinguish their fault state depending on the time domain vibration signals individually.To find the differences between different fault types, the vibration signals collected at different valve clearance in time domain and frequency domain were analyzed. Normal state with valve clearance 0.4mm, intake valve clearance 0.3mm (s.t fault type IV), and abnormal state with intake valve clearance 0.7mm (s.t fault type VI) were taken as an example. The results are shown in Figure7, showing that there were significant differences in frequency domain at 900 Hz~1400Hz and 1650 Hz~1850Hz.Figure 7
Comparison of time domain and frequency domain characteristics. (a) Time domain diagram of normal state signal, (b) frequency diagram of normal state signal, (c) time domain diagram of abnormal state signal, and (d) frequency diagram of abnormal state signal.
(a) (b) (c) (d)


## 3.2. Feature Extraction

To extract fault characteristics, the collected signals were decomposed by wavelet decomposition and reconstruction. Besides, the vibration energy was calculated by the processed formula, which was defined as follows.Continuous vibration signals are denoted as functionft, which meet the following conditions within the range of real numbers:(6)∫-∞+∞fx2dx<+∞.Given the time seriesF=fT,f2T,…,fnT obtained by sampling, the vibration energy is expressed as(7)E=12N2-N1∑i=N1N2fiT-fT02.N 1 = 0 , 1,2 , … , n ,   N 2 = 1,2 , … , n, and N2≥N1. T denotes the sample Interval; n is the total sampling points. fT0 is the initial state of the vibration signal.The vibration signal of fault type I at 1000 rpm processed by wavelet decomposition and reconstruction with DB4 wavelet function is shown in Figure8. Subsequently, the vibration energy of processed signals is calculated by (5). Three samples of each fault type were taken as examples. The results, used as feature vectors, are listed in Table 4.Table 4
Feature vector based on Wavelet decomposition and reconstruction.
Operating state No. vibration energy feature vector E a 41 E d 41 E d 31 E d 21 E d 11 1 29171.56 125.61 419.31 190.47 916.02 Fault type I 2 28467.95 314.92 536.79 310.96 615.85 3 29162.03 657.91 1198.32 743.29 1532.70  1 34728.80 157.96 446.43 203.43 305.95 Fault type II 2 37501.9 442.93 787.90 364.83 757.68 3 41248.90 604.38 1035.80 783.93 1459.29  1 51984.62 2601.75 2774.43 440.82 774.74 Fault type III 2 66161.88 3606.90 4286.53 2143.04 3459.64 3 55689.37 10129.43 4527.10 3965.93 7854.19  Fault type IV 1 86067.38 133.12 327.000 195.39 288.40 (Normal) 2 84843.81 267.18 464.92 343.86 844.38 3 84297.88 542.58 1182.75 710.60 2152.55  1 70662.03 155.80 281.01 201.87 520.20 Fault type V 2 70043.63 302.41 671.87 496.92 1467.39 3 70177.78 611.64 1671.62 703.10 1696.39  1 66528.25 338.03 491.06 398.17 1325.69 Fault type VI 2 66243.20 673.17 1596.44 839.55 1802.04 3 67345.94 956.43 1467.58 1159.19 2497.36  Fault type VII 1 187.27 824.61 876.71 328.32 4278.87 2 176.31 387.19 104.38 477.13 4155.92 3 208.67 741.50 100.80 341.36 3565.39  Fault type VIII 1 115.19 304.61 353.27 367.06 4727.75 2 173.00 608.37 891.72 459.13 3843.63 3 136.02 962.09 780.94 932.79 4177.78  Fault type IX 1 275.42 163.24 194.65 550.57 5338.03 2 200.03 109.90 118.59 400.76 4896.44 3 231.09 130.74 178.99 557.56 6101.87Figure 8
The decomposed vibration signals of fault type I.To conclude the relationship between the vibration energy and the engine fault directly, the first feature vector of each fault type was normalized and plotted in the same coordinate system, as shown in Figure9.Figure 9
The characteristics of different fault feature vector: (a) fault type I, (b) fault type II, (c) fault type III, (d) fault type IV, (e) fault type V, (f) fault type VI, (g) fault type VII, (h) fault type VIII, and (i) fault type IX.
(a) (b) (c) (d) (e) (f) (g) (h) (i)Figure9 shows that all faults have different feature vectors. Accordingly, the vibration energy of decomposed vibration signals can be extracted as the fault characteristic.


## 3.3. Model Training and Verifying

The engine valve fault identification experiment was stratified into two parts, namely, building the fault identification model by model training and verifying the constructed model by model testing.For model training, the experiments were performed 3 times on ZH195 diesel engine by keeping the engine speed from 800 rpm to 1200 rpm at 200 rpm steps under no-load condition. Thus, 9 groups of vibration signals were obtained, and the fault features were extracted. Subsequently, the engine state shifted from fault II to fault IX, and the same experiments were performed. 81 groups of vibration signals were detected, and the fault features were extracted. Finally, the fault detection model based on multiclassυ-SVC was trained. In this study, hyperparameter γ was set as 4, and hyperparameter υ was set as 32 using the cross validation. The training result is shown in Figure 10. It is found that the multiclassification υ-SVC method identified different fault type accurately.Figure 10
The training results of the fault type identification.When the model was built, further experiments were performed from fault I to fault IX, and the experiment count was set as 162. Thus, 162 groups of vibration signals and their relevant fault feature were extracted to verify the correctness of the model. The result is shown in Figure11, showing that the average accuracy of fault identification reached 96.3%. The result here reveals that the proposed fault identification method can be effectively used for diagnosing the engine fault.Figure 11
The verifying results of the fault type identification.The fault identification performance of the built model based onυ-SVC was compared with the results of SOM (Self-Organization feature Map) neural network. The SOM neural network refers to a self-organizing, self-learning network consisting of a fully connected array of neurons [25]. It is preferred for fault classification for its high accuracy even with small samples. The number of competitive layer neurons was set as 36, and the number of training steps was set as 500. The identification results are listed in Table 5, showing that the fault model based on υ-SVC achieved higher fault identification rates.Table 5
Identification results.
Method Identification accuracy Fault Type Number ofsamples Correct identification number Accuracy (%) Average accuracy (%) υ-SVC I 18 18 100.0 96.3 II 18 18 100.0 III 18 17 94.4 IV 18 18 100.0 V 18 17 94.4 VI 18 18 100.0 VII 18 17 94.4 VIII 18 17 94.4 IX 18 16 88.9  SOM neural network I 18 17 94.4 88.9 II 18 17 94.4 III 18 16 88.9 IV 18 17 94.4 V 18 17 94.4 VI 18 16 88.9 VII 18 16 88.9 VIII 18 16 88.9 IX 18 15 83.3


## 4. Conclusions

In the present study, a novel ICE fault identification method combining FBG vibration sensor and SVM was proposed. The experimental tests on the valve fault and fuel injection advance angle fault were performed and presented to verify the efficacy of the newly proposed approach. The experimental case studies reveal that the proposed method exhibit excellent fault detection performance for ICE fault identification. Compared with SOM neural network-based method, the proposed method can achieve higher fault identification rates. Thus, this study provided a practical and effective device for ICE fault identification in future research.



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*Source: 8469868-2019-05-16.xml*