doi:10.1016/j.eswa.2006.08.011 www.elsevier.com/locate/eswa Expert Systems with Applications 33 (2007) 1063–1075 Expert Systems with Applications Development of an expert system for fault diagnosis in scooter engine platform using fuzzy-logic inference Jian-Da Wu a,*, Yu-Hsuan Wang a, Mingsian R. Bai b a Graduate Institute of Vehicle Engineering, National Changhua University of Education, 1 Jin-De Road, Changhua City, Changhua 500, Taiwan, ROC b Department of Mechanical Engineering, National Chiao-Tung University, Taiwan, ROC Abstract In the present study, a fault diagnosis system using acoustic emission with an adaptive order tracking technique and fuzzy-logic inter- ference for a scooter platform is described. Order tracking of acoustic or vibration signal is a well-known technique that can be used for fault diagnosis of rotating machinery. Unfortunately, most of the conventional order-tracking methods are primarily based on Fourier analysis with the revolution of the machinery. Thus, the frequency smearing effect often arises in some critical conditions. In the present study, the order tracking problem is treated as the tracking of frequency-varying bandpass signals and the order amplitudes can be cal- culated with high resolution. The order amplitude figures are then used for creating the data bank in the proposed intelligent fault diag- nosis system. A fuzzy-logic inference is proposed to develop the diagnostic rules of the data base in the present fault diagnosis system. The experimental works are carried to evaluate the effect of the proposed system for fault diagnosis in a scooter platform under various operation conditions. The experimental results indicated that the proposed expert system is effective for increasing accuracy in fault diag- nosis of scooters. � 2006 Elsevier Ltd. All rights reserved. Keywords: Fault diagnosis; Fuzzy logic inference; Adaptive order tracking; Acoustic emission 1. Introduction The technique of early fault diagnosis is used to prevent serious damages in a mechanical system. Rotating machin- ery such as internal combustion engines, cooling fans and air compressors can have their vibration and acoustic emis- sion signals monitored for early fault diagnosis. Conven- tional fault diagnosis using vibration and acoustic emission signals already exists in the form of techniques for applying the time and frequency domain of signals, and analyzing the amplitude difference in signals (Peng & Chu, 2004; Zheng, Li, & Chen, 2002). However, the con- ventional methods are not always effective for application under certain critical conditions such as using a fixed sam- pling frequency for fast Fourier transform (FFT) analysis 0957-4174/$ - see front matter � 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2006.08.011 * Corresponding author. E-mail address: jdwu@cc.ncue.edu.tw (J.-D. Wu). in rapid fluctuation of the machinery speed. Order tracking is a well-known technique that can be used for fault diag- nosis of rotating machinery. Conventional order tracking technology is based on the frequency analysis, where nar- row band spectra of the frequency-varying signals utilize proper time-windowing, unfortunately, the smearing prob- lem that include spaced orders and crossing orders often arise critical conditions (Vold & Leuridan, 1993). In order to overcome this problem, a number of new techniques have been proposed, e.g. adaptive order tracking tech- niques (Bai, Huang, Hong, & Su, 2005; Bai, Jeng, & Chen, 2002), and adaptive wavelet analysis techniques (Lin & Zuo, 2003; Tse, Yang, & Tam, 2004). Most of the methods can extract the order of features embedded in the vibration and acoustic emission signals. In the present study, a high resolution adaptive order tracking technique is used to create different order ampli- tude figures of the scooter platform under various engine mailto:jdwu@cc.ncue.edu.tw 1064 J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 operation conditions as the data bank for the fault diagno- sis expert system (Wu, Huang, & Huang, 2004; Wu, Huang, & Chen, 2005). In the proposed technique, a more accurate description of signal feature can be drawn by con- verting frequency spectra into order spectra, and order is defined as the frequency normalized with various shaft speeds. The technique focuses on adaptive filter based on the Kalman filter. The continuous acoustic emission signal is measured and analyzed using adaptive Kalman filtering order tracking that can eliminate noise and reconstruct the acoustic emission signal in this system. High resolution y(n) Kalman gain computer One-step pre Riccati equation solver G(n) 1Z I Initial condition K(1,0) Initial conditio K(n,n-1) Fig. 1. Block diagram of a Fig. 2. Signal-flow graph representa adaptive order tracking is also used to practically analyze and track the energy of order signal from the dynamic sig- nal. Meanwhile, the order tracking is formulated in terms of state space models. The multiple harmonics of acoustic emission signals have been used as different order ampli- tude figures of the scooter in this system. The amplitudes of different order can be calculated for extracting the fea- ture of the order figures. After processing signal analysis that obtained order features, the fuzzy-logic inference is used to classify the faults automatically. Many machinery fault diagnostic approaches use automatic diagnosis in x̂( | )nn y 0x̂(1 | y ) dictor F(n,n+1) nx̂( 1 | )n y+ K(n+1,n) n daptive Kalman filter. tion of adaptive order tracking. 0 1 a m em be rs hi p 0.5 0 1 a m em be rs hi p a -n S.D. a +n S.D. a -n S.D. a +n S.D. Fig. 3. Membership function: (a) triangular membership function and (b) p membership function. J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 1065 order to increase accuracy caused by subjective human determination. Fuzzy logic is a powerful tool for complex numerical analysis and knowledge modeling. (Huang, Table 1 Rules of fuzzy logic inference for the fault diagnosis system If Then 1X 2X � � � 7X 8X Normal Low 1 Low 2 � � � Low 1 Low 1 • Low 1 High 3 � � � Low 2 Low 2 High 2 High 1 � � � Low 2 Low 1 Low 3 High 2 � � � Low 2 Low 1 High 2 High 1 � � � Low 1 Low 1 Tachometer signals Order tracking Fuzz Infere Features Signal processing Knowledge base Infere rul Microphone signals Fig. 4. Experimental arrangemen Yang, & Huang, 1997) proposed a fuzzy logic system for the fault diagnosis system. (Mechefske, 1998) also pro- posed a fuzzy logic inference for fault classification by machinery vibration signal. In the present study, a fuzzy-logic inference is proposed to develop the diagnostic rules of the data base in an order tracking amplitude features. The fuzzy logic inference can calculate complex numerical analysis and use a member- ship value easily explained by human. The membership function establishes the inference rules and the knowledge base to systematize the post-processing procedure in this system. Both the p and the triangular membership function will be compared for fault diagnosis by using order ampli- tude figures of the scooter with normal and four fault con- ditions. The structure and principle of high resolution adaptive order tracking technique and fuzzy logic inference are described in the following sections. 2. Principle of adaptive order tracking technique In this section, an adaptive order tracking technique based on the Kalman filtering algorithm is described (Hay- kin, 1996). The analysis of the order tracking with the acoustic emission signal and shaft speed can be described as the amplitude of the frequency-modulated (Bai et al., 2002; Bai et al., 2005). The acoustic emission signal x(t) of the rotating machinery containing k orders is usually represented as Fault 1 Fault 2 Fault 3 Fault 4 • • • • Decision Operator y nce nce es t and fault diagnosis system. Fig. 5. Revolution of scooter in run-up test condition. Table 2 Membership value of consequence with p membership function at idle condition with pulley damaged Faults n (multiples of S.D.) 1 2 3 4 5 Normal 0.0030 0.0116 0.0243 0.0396 0.0562 Pulley 0.5665 0.8202 0.9078 0.9451 0.9639 Belt 0.0853 0.1826 0.2572 0.3187 0.3712 Air 0.0892 0.1185 0.1316 0.1430 0.1552 Clutch 0.0250 0.0780 0.1309 0.1752 0.2115 Table 3 True membership values in the fault diagnosis system Test faults The result of faults Normal Pulley Belt Air Clutch Normal 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 Pulley 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 Belt 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 Air 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 Clutch 0 0 0 0 1 0 0 0 0 1 1066 J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 xðtÞ¼ A1 cos½hðtÞþ /1�þ A2 cos½2hðtÞþ /2�þ � � � � � � þ Ak cos½khðtÞþ /k�: ð1Þ Eq. (1) can be expanded as xðtÞ¼ A1I cos½hðtÞ�� A1Q sin½hðtÞ�þ �� �þ AkI cos½khðtÞ� � AkQ sin½khðtÞ�: ð2Þ By discrete time sampling, Eq. (2) can be represented as xðnÞ¼½cos½hðnÞ��sin½hðnÞ����cos½khðnÞ��sin½khðnÞ�� A1I A1Q .. . AkI AkQ 2 66666664 3 77777775 : ð3Þ The high-resolution order tracking based on Kalman filter has two equations. The first equation is called the process equation: Fig. 6. Order figures displayed for xðn þ 1Þ¼ Fðn þ 1; nÞxðnÞþ v1ðnÞ: ð4Þ engine speed at idle condition. Fig. 7. Performance of membership function versus the parameter n at idle condition: (a) triangular membership function and (b) p membership function. Fig. 8. Order amplitude figures of scooter acoustic emission in idle condition. A solid line depicts scooter without any fault; a dashed line depicts scooter with various faults: (a) pulley damaged, (b) belt damaged, (c) air leakage of intake and (d) clutch damaged. J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 1067 Meanwhile, the second equation is called the measurement equation: yðnÞ¼ CðnÞxðnÞþ v2ðnÞ ð5Þ The vectors v1(n) and v2(n) represent zero-mean and white noise. The noise vectors v1(n) and v2(n) are indi- vidually independent and E½v1ðnÞvH2 ðkÞ� ¼ 0 for all n and k. 1068 J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 The wave of the amplitude-modulated signal can track its frequency continually with respect to the fundamental and multiple frequencies in the rotating machinery. Using this form, the Kalman filtering algorithm is recommended to structure this model by the process and measurement equations. Measurement equation: yðnÞ� XN i¼�N AiðnÞexp½jhiðnÞ� ¼ v2ðnÞ: ð6Þ Process equation: r2AiðnÞ¼ v1ðnÞ: ð7Þ In common usage, Ai(n) can be assumed by the autoregres- sive (AR) model. HðzÞAiðzÞ¼ V 1ðzÞ: ð8Þ The state transition matrix and measurement matrix are described as Fig. 9. Order amplitude figures of scooter acoustic emission in 2000 rpm. A sol various faults: (a) pulley damaged, (b) belt damaged, (c) air leakage of intake Fðnþ1;nÞ¼ P 0 ��� 0 0 . . . 0 ��� 0 0 0 P 0 0 0 ��� 0 . . . 0 0 ��� 0 P 2 66666664 3 77777775 ; ð9Þ CðnÞ¼ exp½jhkðnÞ� 0 ��� exp½jh0ðnÞ� 0 ��� exp½jh�kðnÞ� 0½ �: ð10Þ The Kalman filtering procedure can be summarized as follows: GðnÞ¼ Fðn þ 1; nÞKðn; n � 1ÞCHðnÞ � ½CðnÞKðn; n � 1ÞCHðnÞþ Q2ðnÞ� �1 ; ð11Þ aðnÞ¼ yðnÞ� CðnÞx̂ðnjyn�1Þ; ð12Þ x̂ðn þ 1jynÞ¼ Fðn þ 1; nÞx̂ðnjyn�1Þþ GðnÞaðnÞ; ð13Þ Kðn þ 1; nÞ¼ Fðn þ 1; nÞKðnÞFHðn þ 1; nÞþ Q1ðnÞ: ð14Þ The representation of a block diagram in the Kalman filter is depicted in Fig. 1. The signal-flow graph of adap- tive order tracking and the identification of parameters by adaptive order tracking are represented in Fig. 2. By id line depicts scooter without any fault; a dashed line depicts scooter with and (d) clutch damaged. Fig. 10. Order amplitude figures of scooter acoustic emission in 2500 rpm. A solid line depicts scooter without any fault; a dashed line depicts scooter with various faults: (a) pulley damaged, (b) belt damaged, (c) air leakage of intake and (d) clutch damaged. J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 1069 adding the Kalman filtering algorithm we can eliminate noise and reconstruct the sound signals in this system. This proposed adaptive algorithm could increase the accuracy of the order amplitude figures and conveniently extract the features. 3. Fuzzy logic inference for fault diagnosis Fuzzy logic is a useful approach to simplify a complex system in engineering application. In the present study, a fuzzy-logic inference is used to calculate complex numerical analysis with a membership value easily interpreted by humans (Awad & Wafik, 1999). After extracting the fea- tures of the proposed adaptive order tracking amplitude figures, fuzzy logic is used to automatically diagnose the faults in the designed scooter experimental platform. The fuzzy-logic inference is proposed to establish the diagnostic rules of the data bank in this fault diagnosis system. The amplitudes of different order can be calculated for extract- ing the features of the order figures. The energy of order figure amplitude is calculated by using root-mean-square (rms) as the input values: W ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 H XH h¼1 YðhÞ !vuut ð15Þ where W is the rms value of order amplitude, Y is an order amplitude, and H is the number of the order amplitude. After obtaining the order feature of the order figures, the data analysis includes finding the mean value and standard deviation of each order after the extracting feature proce- dure has finished. The decision of the membership function is also a key point and especially punctilious for fuzzy-logic inference. The fuzzy membership function has represented variable sets that include S, p, triangular and gauss. In the present study, the triangular and p membership function will be used to develop the fuzzy logic inference (Mech- efske, 1998). The triangular and p membership functions are established as shown in Fig. 3. The equation of p mem- bership function can be described as 1070 J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 pðz; a; bÞ¼ 1 1 þðz�a b Þ2 ; ð16Þ where a is the mean value of each order, b is the n times the standard deviation (S.D.) in each order. The membership function establishes the inference rules and the knowledge base under fault decision conditions. The rules of fuzzy logic inference are defined as ±n times the standard deviation of each condition at each order. Those are used for the higher and lower limits of the fuzzy logic member- ship domain. The rules have been defined an inference rule variable x in universe of the discourse, and the equation follows as: ðA1 \ A2 \�� �\ AnÞðxÞ¼ minfA1ðxÞ; A2ðxÞ:::AnðxÞg; for all x 2 X ; ð17Þ where A(x) is a rule of the membership function. Eq. (17) can be represented the Table 1. The processing procedure must be systematized with the inference rules in this system. Fig. 11. Order amplitude figures of scooter acoustic emission in 3000 rpm. A so various faults: (a) pulley damaged, (b) belt damaged, (c) air leakage of intake The fuzzy membership domain is defined with various strength ranges from 0 to 1. The condition of maximal probability will be inferred according to the knowledge base and evaluation of the inference rules. The fuzzy logic inference could increase the efficiency of diagnosing faults in the present system. 4. Experimental investigation of fault diagnosis system In the experimental investigation, the scooter acoustic emission signals were analyzed to verify the proposed fuzzy logic inference fault diagnosis system. The fault diagnosis system consists of the signal analysis and the fault infer- ence. In the signal analysis, the adaptive order tracking with Kalman filter for extracting the order feature of acoustic emission signal is used, and fault inference utilizes a fuzzy logic approach to classify faults under different operating conditions. Experimental arrangement and the fuzzy logic system of the scooter defect diagnosis system lid line depicts scooter without any fault; a dashed line depicts scooter with and (d) clutch damaged. J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 1071 is shown Fig. 4. A scooter with an electronic fuel injection system, single-cylinder, four-stroke, 0.125-l internal com- bustion engine is used in this application. The sound emis- sion signal is measured using a condenser microphone (PCB 130D20) located close to the scooter engine transmis- sion. A fiber optical sensor (PW-PH02) is utilized to detect the revolution signal and angular displacement of the engine as reference signals of the order tracking procedures in the diagnostic system. The sampling frequency is chosen to be 20 kHz with the data record system (Hardware: NI 6024E; Software: Lab-view). In the present study, five conditions of the scooter are used in the experimental work. These include without fault, pulley damage, belt damage, air leakage of the intake man- ifold and clutch damage. In the experimental work, there are 10 pieces of data in each fault condition to establish the fuzzy-logic inference. The engine is operated in an idling condition (1700 rpm), 2000 rpm, 2500 rpm, 3000 rpm, 3500 rpm and run-up test conditions. The engine revolution of the run-up condition is shown as Fig. 5. In Fig. 12. Order amplitude figures of scooter acoustic emission in 3500 rpm. A so various faults: (a) pulley damaged, (b) belt damaged, (c) air leakage of intake particular, the run-up test is emphasized in this research because the adaptive order tracking can accurately track the energy of the order signal from the dynamic signal. After recording the signals, they would be used in order tracking analysis to track the energy of the order amplitude signal. Acoustic emission signal features could be drawn by converting the frequency spectrum into order spectrum, and order is defined as the frequency normalized with various shaft speeds. The first eight orders of the amplitude figures with adaptive Kalman filter under the idle condition without any fault in the scooter platform are shown as Fig. 6. The amplitudes of the order figures can be calcu- lated for the feature as input for fuzzy logic inference. After extracting the features, the fuzzy logic inference approach is used in the proposed fault diagnosis. First, the mean and the standard deviation of each condition at each order are estimated, and the higher and lower limits of the fuzzy logic membership domain as the fuzzy infer- ence rules are defined. There are eight orders in one fault condition which means there are eight inference rules in lid line depicts scooter without any fault; a dashed line depicts scooter with and (d) clutch damaged. Fig. 13. Order amplitude figures of scooter acoustic emission in run-up condition. A solid line depicts scooter without any fault; a dashed line depicts scooter with various faults: (a) pulley damaged, (b) belt damaged, (c) air leakage of intake and (d) clutch damaged. 1072 J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 the system. After calculation by the inference rules and knowledge base, the results have been represented by mem- bership values. The membership value of the fault diagno- sis system is between 0 and 1, where 0 means impossible and 1 means possible. When the membership value is close to 1, this means the condition is true. The inference rules and knowledge base have been established based on the membership function. In this research, the triangular and p membership functions are proposed to develop the fuzzy-logic inference. The triangular membership function applies when tolerance of fault is large and the p member- ship function is applied in critical conditions. Table 4 The optimum n values with two different membership function under various n Value Engine operation conditions Membership function Idle 2000 rpm 2500 rpm Triangular 4 3 3 p 2 2 2 Besides the membership function, choosing the opti- mum inference error versus n value could also increase the resolution of system. With fuzzy logic inference, the membership value of consequence with p membership function in the idling condition with pulley damage are cal- culated and summarized in Table 2. When the n is larger the membership domain is wider. The membership value of the accurate classification increases with an increasing n value. Nevertheless, the membership value of fault classi- fication also increases with an increasing n value. Defining optimum inference error versus n value is necessary. The optimum inference error versus n value is determined by: operation conditions 3000 rpm 3500 rpm Run-up 4 4 2 2 2 1 Table 5 Faults classification under various engine operation conditions with triangular membership function Engine operation Test faults Membership value of faults Normal Pulley Belt Air Clutch Idle Normal 0.7746 0.0413 0.1220 0.1953 0.0598 Pulley 0 0.7709 0.1412 0.1047 0.0462 Belt 0.1315 0.3227 0.8087 0.0929 0.1845 Air 0.1163 0.1629 0.0494 0.8626 0.1210 Clutch 0.1733 0.1653 0.1248 0.2085 0.6836 2000 rpm Normal 0.7258 0.0273 0.0991 0.1997 0.1155 Pulley 0 0.8760 0 0.0766 0.1163 Belt 0.1006 0.1474 0.7555 0.0380 0.2292 Air 0.1983 0.1846 0 0.7205 0.0187 Clutch 0.0975 0.1452 0.1899 0.0056 0.7119 2500 rpm Normal 0.7703 0.0676 0.0836 0.1122 0.2659 Pulley 0 0.6470 0.0640 0.2315 0 Belt 0.0805 0.2228 0.7233 0.1323 0.2442 Air 0 0.1207 0.0555 0.7630 0.0584 Clutch 0.2621 0.0715 0.2556 0.0744 0.7270 3000 rpm Normal 0.7551 0 0.0651 0 0.3291 Pulley 0 0.8143 0.1052 0.1298 0.0825 Belt 0 0.0972 0.7559 0.1223 0.3124 Air 0 0.1642 0.1134 0.8489 0.2022 Clutch 0.0341 0 0.2208 0.0749 0.7573 3500 rpm Normal 0.7441 0 0.1331 0.2122 0.2880 Pulley 0 0.7746 0.1247 0 0 Belt 0.0824 0.0886 0.8140 0.0324 0.4255 Air 0.1327 0 0.1542 0.7590 0.3111 Clutch 0.0644 0 0.2380 0.2244 0.8184 Run-up Normal 0.7265 0.0517 0.1525 0.2855 0.1209 Pulley 0.0118 0.4940 0.2737 0.1444 0.1097 Belt 0.1121 0.3728 0.6823 0.1996 0.1259 Air 0.1577 0.2550 0.2338 0.6522 0.0454 Clutch 0.1678 0.2025 0.1815 0.2047 0.7268 J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 1073 error ¼ Xl i¼1 Xm j¼1 ðd ij � d̂ ijÞ 2 ; ð18Þ where dij is the membership value of the ith calculation re- sult that is inferred to the jth fault. d̂ ij is the true member- ship value of the ith practical data relative to the jth fault. The parameters l and m are the numbers of the fault con- dition and test data, respectively. Assuming every fault condition has three data to establish a knowledge base, the membership values of the true consequence form d̂ ij in this system are summarized in Table 3. The optimum n value is the minimum error in estimation of the knowl- edge base. Fig. 7(a) is the performance of membership function versus the parameter n with the triangular mem- bership function under the idling engine operation condi- tion. The definition of optimum inference error versus n value with the p membership function under the idling operation condition is shown as Fig. 7(b). In the figure, the optimum n = 2 is relative to Table 2. When n = 2 the results of fault conditions have a higher resolution with the p membership function at an idling engine oper- ation schedule system. 5. Results and discussion This section will describe the results of the proposed fault diagnosis system in a scooter platform under various operating conditions. A conventional adaptive order track- ing fault diagnosis technique is carried out using visual inspection of the order amplitude figure under different fault conditions. Obviously, different faults in the mechan- ical system occur with different amplitudes in order figures. Unfortunately, the conventional inspection is not a precise approach for damage diagnosis. In the present study, the order amplitude figures of scooter acoustic emission are used for the data bank in the proposed fuzzy-logic infer- ence for the intelligent fault diagnosis system. The order amplitude figures of scooter acoustic emission in the idling condition with various faults in the platform are shown as Fig. 8. Although by observing Fig. 8(a), we can infer normal conditions and pulley damage conditions using visual comparison, however, for other fault conditions such as belt damage, air leakage of intake and clutch dam- aged as shown in Fig. 8(b)–(d), there are too many order figures to infer the fault conditions using only visual 1074 J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 comparison. Therefore, the fuzzy-logic inference is used to automatically increase the accuracy of the classification faults in the intelligent fault diagnosis system. The data bank also includes other amplitude figures of order track- ing under various operating conditions shown in Figs. 9– 13, which includes 2000 rpm, 2500 rpm, 3000 rpm, 3500 rpm and run-up engine operating conditions. Therefore, this research employs fuzzy-logic inference to establish data bank verification of the synthetic system under various operating conditions. The different data banks organize the inference rules and knowledge base of fuzzy logic infer- ence respectively. Estimating the optimum inference error versus n value can increase the resolution of the diagnostic system. Under various operating conditions with two different membership functions, inference rules evaluate the optimum n values which are summarized in Table 5. According to the results of Table 4, the membership values are calculated with fuzzy logic inference accurately and conveniently. Meanwhile, the triangular and p membership functions are compared in the fuzzy-logic inference under various engine operating conditions. The results of faults classifica- tion under various engine operating conditions using the triangular and p membership functions are summarized Table 6 Faults classification under various engine operation conditions with p membe Engine operation Test faults Membership value of fau Normal Pulle Idle Normal 0.8098 0.01 Pulley 0.1437 0.82 Belt 0.1846 0.18 Air 0.2287 0.11 Clutch 0.1379 0.07 2000 rpm Normal 0.8385 0.13 Pulley 0.0144 0.94 Belt 0.1183 0.32 Air 0.2941 0.30 Clutch 0.1246 0.30 2500 rpm Normal 0.8726 0.14 Pulley 0.0065 0.77 Belt 0.1143 0.35 Air 0.0785 0.23 Clutch 0.3635 0.19 3000 rpm Normal 0.7920 0.03 Pulley 0.0046 0.85 Belt 0.0319 0.15 Air 0.0175 0.20 Clutch 0.0762 0.04 3500 rpm Normal 0.7912 0.05 Pulley 0.0019 0.82 Belt 0.1065 0.16 Air 0.2133 0.06 Clutch 0.1153 0.07 Run-up Normal 0.7671 0.13 Pulley 0.0550 0.52 Belt 0.1757 0.43 Air 0.1740 0.28 Clutch 0.2276 0.34 in Tables 5 and 6. The data showed that both the triangular and p membership functions are effective for fault classifi- cation in various fault conditions. In particular, the run- up operation schedule is emphasized in this research, the scooter engine can be operated by running up or casting down under practical condition. The run-up operation schedule has fine result by inferring the faults successfully. The triangular membership function is applied when tol- erance of fault is large and the p membership function is applied in certain condition. From Table 4, we can find the p membership function with the same various engine operations has smaller n values than the triangular mem- bership function. This is because the features of adaptive order tracking have critical tolerance of faults in the same fault conditions. From Tables 5 and 6, the p membership function has higher membership values of accurate classifi- cation than the triangular membership function at each fault condition under the idling engine operation. In other operations, the p membership function also has high reso- lution. The p membership function is more capable of han- dling the qualities for this experimental work than the triangular membership function. But the results of the two membership functions provide evidence that fuzzy logic inference is a useful fault diagnosis system. rship function lts y Belt Air Clutch 16 0.1478 0.1391 0.2003 02 0.3903 0.2634 0.2757 26 0.8476 0.0968 0.2021 85 0.1092 0.9104 0.2538 80 0.2120 0.1643 0.7143 34 0.1617 0.3303 0.1933 57 0.0693 0.1061 0.1523 64 0.8637 0.0897 0.3306 46 0.0992 0.8417 0.1157 66 0.3683 0.1004 0.8129 40 0.1532 0.2633 0.3881 55 0.1146 0.3110 0.0321 65 0.8353 0.2370 0.2992 26 0.1079 0.8817 0.1158 09 0.3511 0.1980 0.8430 21 0.0997 0.0374 0.4237 55 0.1441 0.1634 0.1047 51 0.7932 0.1680 0.3456 44 0.1544 0.8962 0.2562 07 0.2520 0.1149 0.8030 91 0.1843 0.2560 0.3564 08 0.1609 0.0086 0.0330 53 0.8705 0.0828 0.4825 46 0.2111 0.8044 0.3707 62 0.3251 0.2481 0.8724 95 0.2233 0.2603 0.1850 06 0.2954 0.1866 0.2206 17 0.7016 0.2116 0.2671 49 0.3192 0.7006 0.1295 14 0.2555 0.2922 0.7214 J.-D. Wu et al. / Expert Systems with Applications 33 (2007) 1063–1075 1075 6. Conclusions In the present study, a prototype of an expert system for fault diagnosis in scooters platform using fuzzy-logic inter- ference with adaptive order tracking technique is devel- oped. The adaptive order tracking based on Kalman filter extracts the order features of the scooter test platform. They then are used for creating the data bank in the pro- posed intelligent fault diagnosis system. Fuzzy logic infer- ence is used for fault classification in the proposed system. The experimental results indicated that the pro- posed system is effective for increasing the accuracy of fault diagnosis under various operation conditions. Acknowledgement The study was supported by the National Science Coun- cil of Taiwan, the Republic of China, under project number NSC-94-2218-E-018-001. References Awad, S. H., & Wafik, B. L. (1999). A fuzzy logic approach to the selection of cranes. Automation in Construction, 8(5), 597–608. Bai, M., Huang, J., Hong, M., & Su, F. (2005). 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Gear fault diagnosis based on continuous wavelet transform. Mechanical Systems and Signal Pro- cessing, 16(2–3), 447–457. Development of an expert system for fault diagnosis in scooter engine platform using fuzzy-logic inference Introduction Principle of adaptive order tracking technique Fuzzy logic inference for fault diagnosis Experimental investigation of fault diagnosis system Results and discussion Conclusions Acknowledgement References