Fault Diagnosis of Analog Circuits Using Extension ... - Semantic Scholar
Fault Diagnosis of Analog Circuits Using Extension Genetic Algorithm Meng-Hui Wang*, Kuei-Hsiang Chao, and Yu-Kuo Chung Department of Electrical Engineering National Chin-Yi University of Technology 35 Lane 215 Chung-Shan Rd. Sec. 1 Taiping City, Taichung County 411 Taiwan, R.O.C. [email protected]
Abstract. This paper proposed a new fault diagnosis method based on the extension genetic algorithm (EGA) for analog circuits. Analog circuits were difference at some node with the normal and failure conditions. However, the identification of the faulted location was not easily task due to the variability of circuit components. So this paper presented a novel EGA method for fault diagnosis of analog circuits, EGA is a combination of extension theory (ET) and genetic algorithm (GA). In the past, ET had to depend on experiences to set the classical domain and weight, but setting classical domain and weight were tedious and complicated steps in classified process. In order to improve this defect, this paper proposes an EGA to find the best parameter of classical domain and increase accuracy of the classification. The proposed method has been tested on a practical analog circuit, and compared with other classified method. The application of this new method to some testing cases has given promising results. Keywords: Analog circuit, Fault diagnosis, Extension genetic algorithm (EGA).
1 Introduction With the more complex of analog circuits and developed, test in analog circuits becoming an urgent task. The faults of Analog circuit are usually divided into two categories: hard faults and soft faults [1]. The hard faults are due to break of circuit component, and soft faults are due to a variation of one (or more) circuit component values over the tolerance range and deviation of about 50% of the faulty element from their nominal value [2-3]. The deviation of the component condition is complex, the poor fault models, component tolerances, nonlinear effects make the automatic fault diagnosis of analog circuits very complex[4-5], because soft faults do not change the circuit topology, but cause the circuit to operate outside its specifications. Hence, there were many fault diagnosis methods using artificial intelligence (AI) techniques to solve the problems in the past [6-7]. Cai originally created the concept of ET to solve contradictions and incompatibility problems in 1983 [8]. In recent years, ET has proposed practical applications on different applications for fault diagnosis [9-12]. The concept of an extension set is to *
Corresponding author.
Y. Tan, Y. Shi, and K.C. Tan (Eds.): ICSI 2010, Part I, LNCS 6145, pp. 453–460, 2010. © Springer-Verlag Berlin Heidelberg 2010
454
M.-H. Wang, K.-H. Chao, and Y.-K. Chung
extend the fuzzy logic value from [0,1] to (-∞,∞), which allows us to define any data in the domain and has given promising results in many fields. Extension clustering methods had depend on experiences to set the classical domain and weight, but setting classical domain and weight were tedious and complicated steps in clustering process. In order to overcome the defect of extension classified method, this paper using EGA searching characteristic of genetic algorithms to find the best parameter of classical domain in the Extension classified method. The fault diagnosis problem of an analog circuit is used to show the accuracy of the proposed method.
2 Extension Genetic Algorithm (EGA) This paper proposed classifying method involves the combination of extension theory and genetic algorithm. Extension theory provides a means of distance measurement for classification process, and genetic algorithm has the ability to search for an optimal solution in a wide space. EGA is a kind of supervised learning that finds out the best classical domain and gets better accuracy without adjusting weight [11]. 2.1 Outline of Extension Theory In the standard set, an element either belongs to or, so the range of the standard set is {0, 1}, which can be used to solve a two-valued problem. In contrast to the standard set, the fuzzy set allows for the description of concepts in which the boundary is not explicit. It concerns not only whether an element belongs to the set but also to what degree it belongs to. The range of a fuzzy set is [0, 1]. The extension set extends the fuzzy set from [0, 1] to (-∞, ∞). As a result, it allows us to define a set that includes any data in the domain. Extension theory tries to solve the incompatibility or contradiction problems by the transformation of the matter element. 2.2 Basic of Genetic Algorithm The genetic algorithm (GA) is the most well-known, and it is always to combine with other algorithm for optimized problems. Genetic algorithm is transposed the notions of evolution in nature to computers and imitate natural evolution [13]. Basically, they find solution to a problem by maintaining a population of possible solutions according to the “survival of the fittest” principle. Genetic algorithm constitutes a class of search algorithms especially suited to solving complex optimization problems. In addition to parameter optimization, genetic algorithm is also suggested for solving problems in creative design, such as combining components in a novel creative way. In general, the major advantage of using the GA is that the optimal solution is obtained globally [14]. The genetic algorithm generally includes the following five parts: (1) gene coding, (2) fitness function, (3) selection mechanism, and (4) crossover and mutation mechanism. 2.3 The Computing Method of EGA This section will present the mathematical description of EGA. The extension method would be found out at the paper of the author [9], so it isn’t necessary to be explained here. Before using the algorithm, we define several variables. First, the training patterns
Fault Diagnosis of Analog Circuits Using Extension Genetic Algorithm
455
are set to be patterns = [X1,X2,…,Xn], where the total number of training patterns is Nn. The i-th pattern is Xik = {X1,X2,…,XNc}, where the total number of features is Nc, and k is the category of i-th pattern. To evaluate the objectives of convergence, Nm is the total mistake number, then the total mistake rate ET, it can be defined by: ET =
Nm Nn
(1)
The learning algorithm of the proposed EGA is shown as follows: Step1: Choose values of the classical domains. The range of classical domains can be directly obtained from previous experience, or determined from training data as follows:
VkjL = min{ X kj }
(2)
VkjU = max{ X kj }
(3)
j = 1,2,..., Nc
(4)
The k is the category of patterns. Step2: Calculate the initial cluster centers for every classical domain.
V
c kj
=
V kjL + V kjU
(5)
2
c Vkc = { Vkc1 ,Vkc2 ,...,VkNc }
(6)
In which Vk = VkjL ,VkjU , j is the total number of a matter element model’s features. The
VkjL is the upper limits of VP , and VkjL is the lower limits of VP. Step3: Classical domain of the upper and lower limits of the length of the gene is
(
)
(7)
2 n 2 < VkU − Vkc × d ≤ 2 m 2
(
)
(8)
Gene kL = m1 (bits)
(9)
GeneUk = m 2 (bits)
(10)
2 n1 < Vkc − VkL × d ≤ 2 m1
In the Eq. (15) and (16), d is the resolution by user defined, and is set to 10000 in this paper. The m1 and m2 is the length of the gene. Step4: Combine all the genes to the chromosome of sequence 0 and 1.
456
M.-H. Wang, K.-H. Chao, and Y.-K. Chung
Step5: Result in a population from binary coding randomly to be the parents that include N groups of chromosome and then turn it into decimal.
chrom
10
= chromosome 2 × (
sk − rk ) + rk 2m − 1
(11)
In which N is the number by user defined, and it is set to 20 in this paper. Step6: Build the pro-generation model. ⎡ N, c1 , ⎢ c2 , ⎢ Rk = ⎢ # ⎢ c Nc , ⎢⎣
v1L ,v1U ⎤ ⎥ v 2L ,v U2 ⎥ ⎥ # ⎥ L U v Nc ,v Nc ⎥⎦
(12)
Step7: Read the first training patterns. Step8: Calculate the correlation of matter-element. ⎧ − 2 ρ ( vtj ,Vij ) , if vtj ∈ Vij ⎪ Vij ⎪ K ij ( vtj ) = ⎨ ρ ( vtj ,Vij ) ⎪ ⎪ ρ ( v ,V ′ ) − ρ ( v ,V ) , if vtj ∉ Vij tj pj tj ij ⎩
(13)
Where |Vij| is obtained from sp-rp. N
λi = ∑ Wij K ij , i = 1,2,..., m
(14)
2λ − λmin − λmax , i = 1,2,...,m λmax − λmin
(15)
j =1
λi′ =
If ( λk′ =1) THEN (the fault type is k)
(16)
Step9: Repeat step7-step8 until the entire pattern is completed and then goes to next step. Step10: Calculate the accuracy rate of the chromosome (individual). Step11: Repeat step7-step10 until the all chromosomes have been processed, and then go to next step. Step12: Calculate the fitness of every chromosome. Fitness = S H The S is the total correct number. H is the total number of training patterns.
(17)
Fault Diagnosis of Analog Circuits Using Extension Genetic Algorithm
457
Step13: Choose parental chromosome to execute crossover by roulette wheel selection. The rate of the chosen parents is: Pk =
Fk N
∑F
(18)
i
i =1
The Fk is the fitness of an individual. Pk is the percentage of the selected Step14: Set the chosen filial generation which is obtained from step13 into the mating pool, and makes mutation. Step15: Repeat step7-step14 until the propagation of the last generation or convergence, then the training epoch is finished.
3 Experiment Results and Discuss The circuit under test (CUT) was used to illustrate our method as shown in Fig. 1, it is a low-pass filter that passes low-signals but attenuates signals with frequencies higher than the cutoff frequency. In this paper, the DC gain of the filter is set to 1 and the cutoff frequency is set to 1 kHz. Node 1 and 2 are the testing node where voltage can be measured or simulated. The nominal values and the tolerances of the components are summarized in Table 1.
Fig. 1. The second-order low-pass filter Table 1. The nominal value of low-pass filter Components R1 R2 Ri Rf C1 C2
Nominal values 100KΩ 85KΩ 2.2MΩ 0.1KΩ 5nF 2nF
Tolerance (%) ±5 ±5 ±5 ±5 ±5 ±5
458
M.-H. Wang, K.-H. Chao, and Y.-K. Chung
3.1 Testing the Ability to Training The CUT was simulated both at normal and all faulty conditions by using PSPICE software, the tolerance rang of normal was selected deviation of about ±5% of the nominal values, and soft fault was deviation of about ±20%. By analyzing sensitivity of the CUT, R1, R2, C1 and C2 are selected to be the fault components, consequently, 13 fault classes are definite, and Table 2 shows the typical circuit signal for 9 kinds of faults. In this research was discovered that the transient voltage (V1, V2) and phase spectrum (P1, P2) were different between normal and other faults condition at nodes, the RMS value of transient voltage and phase spectrum can made the pattern of CUT in the training stage, every fault is produced 50 sets with the Monte-Carlo method, there are total 450 sets of training data. In addition, this paper is produced another 30 sets for each fault to test the stability of the fault diagnostic system, hence there are total 270 sets of testing data. In the paper, the parameter of EGA is setting the tolerance of error rate to be 0.01, the crossover rate is 0.8, and the mutation rate is 0.1. The learning times are set to 100 epochs that can give convergence result. In the training stage, the rate of highest accuracy is 98.4%. Fig. 2 shows the training curve of the rate of highest accuracy for each epoch. When the training stage of the EGA has been completed, then the identifying stages of the proposed method can be started for fault diagnosis, so this paper design a user interface of fault diagnosis window for this analog circuit by the Microsoft Visual Basic (VB), it can diagnose fault quickly by analyzing 4 circuit signals and to show what kind of fault in the analog circuit. For example, Fig. 3 shows a diagnostic fault in R2 and also shown in the fault displayed window by a twinkling red light to alert user which one circuit element was happening fault. Table 2. The typical circuit data with different fault types (Partial samples) Cases V1
V2
P1
P2
Faults no.
Actual fault type
20
7.749
14.434
-93.204
-151.301
1
Normal
70
9.923
16.691
-97.915
-156.404
2
R1 over nominal
120
9.924
16.691
-88.829
-147.318
3
R1 below nominal
187
7.531
16.560
-91.174
-156.134
4
R2 over nominal
236
7.685
11.709
-96.250
-143.379
5
R2 below nominal
285
7.143
13.658
-101.683
-159.625
6
C1 over nominal
335
7.5005
13.853
-84.7055
-142.6476
7
C1 below nominal
383
7.527
14.353
-87.139
-152.612
8
C2 over nominal
429
7.983
13.980
-102.364
-149.876
9
C2 below nominal
Fault Diagnosis of Analog Circuits Using Extension Genetic Algorithm
459
Fig. 2. The minimum error rate of training Fig. 3. User interface of fault diagnosis system curve
3.2 Testing Results Table 3 shows the accuracy by using the multilayer neural network (MNN), k-means, ET, and the proposed EGA based method to diagnosis the soft fault of tested circuit. The maximum testing accuracy is 92.3% in the MNN, 84.67% in the k-means based method and 92% in the traditional extension method. The testing accuracy of proposed method is 96.2%. It is clearly to show the proposed EGA-based diagnosis method to be better than other methods in the both training and testing stages. Moreover, the training times of proposed method is also less than the MNN. Table 3. Diagnosis performances of different methods Methods Proposed method Extension method K-means MNN(4-7-9) MNN(4-8-9) MNN(4-9-9)
Training times (Epochs) 100 N/A N/A 1000 1000 1000
Training accuracy (%) 98.6% N/A N/A 86.2% 87.6% 95.8%
Testing accuracy (%) 96.2% 92% 84.67% 84.6% 85.7% 92.3%
4 Conclusions This paper presents a novel fault diagnosis method based on EGA for analog circuits. Compared with other traditional AI methods, the proposed EGA-based method can achieve the higher accuracy. The calculation of the proposed diagnosis algorithm is also fast and simple. It is feasible to implement the proposed method in a Microcomputer for portable fault detecting devices. This new approach merits more attention, because EGA deserves serious consideration as a tool in diagnosis or classified problems. We hope this paper will lead to further investigation for industrial applications.
460
M.-H. Wang, K.-H. Chao, and Y.-K. Chung
Acknowledgments The author gratefully acknowledges the support of the National Science Council, Taiwan, ROC, under the grant no. NSC-98-2221-E-167-028.
References 1. Yongkui, S., Guangju, C., Hui, L.: Analog Circuits Fault Diagnosis Using Support Vector Machine. In: International Conf. Communications, Circuits and Systems, ICCCAS 2007, pp. 1003–1006 (2007) 2. Catelani, M., Fort, A., Alippi, C.: A Fuzzy Approach for Soft Fault Detection in Analog Circuits. Meas. 32, 73–83 (2002) 3. Slamani, M., Kaminska, B.: Fault Observability Analysis of Analog Circuits in Frequency Domain. IEEE Trans. Circuits Systems II, Analog and Digital Signal Proc., 134–139 (1996) 4. Tadeusiewicz, M., Halgas, S., Korzybski, M.: An Algorithm for Soft-Fault Diagnosis of Linear and Nonlinear Circuits. IEEE Trans. Circuits Systems, Fundamental Theory and Applications 49(11), 1648–1653 (2002) 5. Catelani, M., Fort, A.: Soft Fault Detection and Isolation in Analog Circuits: some Results and a Comparison between a Fuzzy Approach and Radial Basis Function Networks. IEEE Trans. Instrumentation and Meas. 51, 196–202 (2002) 6. Yanghong, T., Yigang, H., Chun, C., Guanyuan, Q.: A Novel Method for Analog Fault Diagnosis Based on Neural Networks and Genetic Algorithms. IEEE Trans. Nstrumentation and Meas. 57(11), 2631–2639 (2008) 7. Spina, R., Upadhyaya, S.: Linear Circuit Fault Diagnosis Using Neuron Morphed Analyzers. IEEE Trans. Circuits Systems II, Analog Digital Signal Proc. 44(3), 188–196 (1997) 8. Cai, W.: The Extension Set and Incompatibility Problem. J. of Scientific Exploration 1, 81–93 (1983) 9. Wang, M.H.: A Novel Extension Method for Transformer Fault Diagnosis. IEEE Trans. Power Delivery 18(1), 164–169 (2002) 10. Wang, M.H.: Application of Extension Theory to Vibration Fault Diagnosis of Generator Sets. IEE Proc. Generation, Transmission and Distribution 151(4), 503–508 (2004) 11. Wang, M.H., Tseng, Y.F., Chen, H.C., Chao, K.H.: A novel clustering algorithm based on the extension theory and genetic algorithm. Expert Systems With Applications 36(4), 8269–8276 (2009) 12. Wang, M.H., Ho, C.Y.: Application of Extension Theory to PD Pattern Recognition of High Voltage Current Transformers. IEEE Trans. Power Delivery 20(3), 1939–1946 (2005) 13. Renner, G., Ekárt, A.: Genetic algorithms in computer aided design. Computer-Aided Design 35(8), 709–726 (2003) 14. Hwang, S.F., He, R.S.: A hybrid real-parameter genetic algorithm for function optimization. Advanced Engineering Informatics 20(1), 7–21 (2006)
Abstract. This paper proposed a new fault diagnosis method based on the extension genetic algorithm (EGA) for analog circuits. Analog circuits were difference at some node with the normal and failure conditions. However, the identification of the faulted location was not easily task due to the variability of circuit components. So this paper presented a novel EGA method for fault diagnosis of analog circuits, EGA is a combination of extension theory (ET) and genetic algorithm (GA). In the past, ET had to depend on experiences to set the classical domain and weight, but setting classical domain and weight were tedious and complicated steps in classified process. In order to improve this defect, this paper proposes an EGA to find the best parameter of classical domain and increase accuracy of the classification. The proposed method has been tested on a practical analog circuit, and compared with other classified method. The application of this new method to some testing cases has given promising results. Keywords: Analog circuit, Fault diagnosis, Extension genetic algorithm (EGA).
1 Introduction With the more complex of analog circuits and developed, test in analog circuits becoming an urgent task. The faults of Analog circuit are usually divided into two categories: hard faults and soft faults [1]. The hard faults are due to break of circuit component, and soft faults are due to a variation of one (or more) circuit component values over the tolerance range and deviation of about 50% of the faulty element from their nominal value [2-3]. The deviation of the component condition is complex, the poor fault models, component tolerances, nonlinear effects make the automatic fault diagnosis of analog circuits very complex[4-5], because soft faults do not change the circuit topology, but cause the circuit to operate outside its specifications. Hence, there were many fault diagnosis methods using artificial intelligence (AI) techniques to solve the problems in the past [6-7]. Cai originally created the concept of ET to solve contradictions and incompatibility problems in 1983 [8]. In recent years, ET has proposed practical applications on different applications for fault diagnosis [9-12]. The concept of an extension set is to *
Corresponding author.
Y. Tan, Y. Shi, and K.C. Tan (Eds.): ICSI 2010, Part I, LNCS 6145, pp. 453–460, 2010. © Springer-Verlag Berlin Heidelberg 2010
454
M.-H. Wang, K.-H. Chao, and Y.-K. Chung
extend the fuzzy logic value from [0,1] to (-∞,∞), which allows us to define any data in the domain and has given promising results in many fields. Extension clustering methods had depend on experiences to set the classical domain and weight, but setting classical domain and weight were tedious and complicated steps in clustering process. In order to overcome the defect of extension classified method, this paper using EGA searching characteristic of genetic algorithms to find the best parameter of classical domain in the Extension classified method. The fault diagnosis problem of an analog circuit is used to show the accuracy of the proposed method.
2 Extension Genetic Algorithm (EGA) This paper proposed classifying method involves the combination of extension theory and genetic algorithm. Extension theory provides a means of distance measurement for classification process, and genetic algorithm has the ability to search for an optimal solution in a wide space. EGA is a kind of supervised learning that finds out the best classical domain and gets better accuracy without adjusting weight [11]. 2.1 Outline of Extension Theory In the standard set, an element either belongs to or, so the range of the standard set is {0, 1}, which can be used to solve a two-valued problem. In contrast to the standard set, the fuzzy set allows for the description of concepts in which the boundary is not explicit. It concerns not only whether an element belongs to the set but also to what degree it belongs to. The range of a fuzzy set is [0, 1]. The extension set extends the fuzzy set from [0, 1] to (-∞, ∞). As a result, it allows us to define a set that includes any data in the domain. Extension theory tries to solve the incompatibility or contradiction problems by the transformation of the matter element. 2.2 Basic of Genetic Algorithm The genetic algorithm (GA) is the most well-known, and it is always to combine with other algorithm for optimized problems. Genetic algorithm is transposed the notions of evolution in nature to computers and imitate natural evolution [13]. Basically, they find solution to a problem by maintaining a population of possible solutions according to the “survival of the fittest” principle. Genetic algorithm constitutes a class of search algorithms especially suited to solving complex optimization problems. In addition to parameter optimization, genetic algorithm is also suggested for solving problems in creative design, such as combining components in a novel creative way. In general, the major advantage of using the GA is that the optimal solution is obtained globally [14]. The genetic algorithm generally includes the following five parts: (1) gene coding, (2) fitness function, (3) selection mechanism, and (4) crossover and mutation mechanism. 2.3 The Computing Method of EGA This section will present the mathematical description of EGA. The extension method would be found out at the paper of the author [9], so it isn’t necessary to be explained here. Before using the algorithm, we define several variables. First, the training patterns
Fault Diagnosis of Analog Circuits Using Extension Genetic Algorithm
455
are set to be patterns = [X1,X2,…,Xn], where the total number of training patterns is Nn. The i-th pattern is Xik = {X1,X2,…,XNc}, where the total number of features is Nc, and k is the category of i-th pattern. To evaluate the objectives of convergence, Nm is the total mistake number, then the total mistake rate ET, it can be defined by: ET =
Nm Nn
(1)
The learning algorithm of the proposed EGA is shown as follows: Step1: Choose values of the classical domains. The range of classical domains can be directly obtained from previous experience, or determined from training data as follows:
VkjL = min{ X kj }
(2)
VkjU = max{ X kj }
(3)
j = 1,2,..., Nc
(4)
The k is the category of patterns. Step2: Calculate the initial cluster centers for every classical domain.
V
c kj
=
V kjL + V kjU
(5)
2
c Vkc = { Vkc1 ,Vkc2 ,...,VkNc }
(6)
In which Vk = VkjL ,VkjU , j is the total number of a matter element model’s features. The
VkjL is the upper limits of VP , and VkjL is the lower limits of VP. Step3: Classical domain of the upper and lower limits of the length of the gene is
(
)
(7)
2 n 2 < VkU − Vkc × d ≤ 2 m 2
(
)
(8)
Gene kL = m1 (bits)
(9)
GeneUk = m 2 (bits)
(10)
2 n1 < Vkc − VkL × d ≤ 2 m1
In the Eq. (15) and (16), d is the resolution by user defined, and is set to 10000 in this paper. The m1 and m2 is the length of the gene. Step4: Combine all the genes to the chromosome of sequence 0 and 1.
456
M.-H. Wang, K.-H. Chao, and Y.-K. Chung
Step5: Result in a population from binary coding randomly to be the parents that include N groups of chromosome and then turn it into decimal.
chrom
10
= chromosome 2 × (
sk − rk ) + rk 2m − 1
(11)
In which N is the number by user defined, and it is set to 20 in this paper. Step6: Build the pro-generation model. ⎡ N, c1 , ⎢ c2 , ⎢ Rk = ⎢ # ⎢ c Nc , ⎢⎣
v1L ,v1U ⎤ ⎥ v 2L ,v U2 ⎥ ⎥ # ⎥ L U v Nc ,v Nc ⎥⎦
(12)
Step7: Read the first training patterns. Step8: Calculate the correlation of matter-element. ⎧ − 2 ρ ( vtj ,Vij ) , if vtj ∈ Vij ⎪ Vij ⎪ K ij ( vtj ) = ⎨ ρ ( vtj ,Vij ) ⎪ ⎪ ρ ( v ,V ′ ) − ρ ( v ,V ) , if vtj ∉ Vij tj pj tj ij ⎩
(13)
Where |Vij| is obtained from sp-rp. N
λi = ∑ Wij K ij , i = 1,2,..., m
(14)
2λ − λmin − λmax , i = 1,2,...,m λmax − λmin
(15)
j =1
λi′ =
If ( λk′ =1) THEN (the fault type is k)
(16)
Step9: Repeat step7-step8 until the entire pattern is completed and then goes to next step. Step10: Calculate the accuracy rate of the chromosome (individual). Step11: Repeat step7-step10 until the all chromosomes have been processed, and then go to next step. Step12: Calculate the fitness of every chromosome. Fitness = S H The S is the total correct number. H is the total number of training patterns.
(17)
Fault Diagnosis of Analog Circuits Using Extension Genetic Algorithm
457
Step13: Choose parental chromosome to execute crossover by roulette wheel selection. The rate of the chosen parents is: Pk =
Fk N
∑F
(18)
i
i =1
The Fk is the fitness of an individual. Pk is the percentage of the selected Step14: Set the chosen filial generation which is obtained from step13 into the mating pool, and makes mutation. Step15: Repeat step7-step14 until the propagation of the last generation or convergence, then the training epoch is finished.
3 Experiment Results and Discuss The circuit under test (CUT) was used to illustrate our method as shown in Fig. 1, it is a low-pass filter that passes low-signals but attenuates signals with frequencies higher than the cutoff frequency. In this paper, the DC gain of the filter is set to 1 and the cutoff frequency is set to 1 kHz. Node 1 and 2 are the testing node where voltage can be measured or simulated. The nominal values and the tolerances of the components are summarized in Table 1.
Fig. 1. The second-order low-pass filter Table 1. The nominal value of low-pass filter Components R1 R2 Ri Rf C1 C2
Nominal values 100KΩ 85KΩ 2.2MΩ 0.1KΩ 5nF 2nF
Tolerance (%) ±5 ±5 ±5 ±5 ±5 ±5
458
M.-H. Wang, K.-H. Chao, and Y.-K. Chung
3.1 Testing the Ability to Training The CUT was simulated both at normal and all faulty conditions by using PSPICE software, the tolerance rang of normal was selected deviation of about ±5% of the nominal values, and soft fault was deviation of about ±20%. By analyzing sensitivity of the CUT, R1, R2, C1 and C2 are selected to be the fault components, consequently, 13 fault classes are definite, and Table 2 shows the typical circuit signal for 9 kinds of faults. In this research was discovered that the transient voltage (V1, V2) and phase spectrum (P1, P2) were different between normal and other faults condition at nodes, the RMS value of transient voltage and phase spectrum can made the pattern of CUT in the training stage, every fault is produced 50 sets with the Monte-Carlo method, there are total 450 sets of training data. In addition, this paper is produced another 30 sets for each fault to test the stability of the fault diagnostic system, hence there are total 270 sets of testing data. In the paper, the parameter of EGA is setting the tolerance of error rate to be 0.01, the crossover rate is 0.8, and the mutation rate is 0.1. The learning times are set to 100 epochs that can give convergence result. In the training stage, the rate of highest accuracy is 98.4%. Fig. 2 shows the training curve of the rate of highest accuracy for each epoch. When the training stage of the EGA has been completed, then the identifying stages of the proposed method can be started for fault diagnosis, so this paper design a user interface of fault diagnosis window for this analog circuit by the Microsoft Visual Basic (VB), it can diagnose fault quickly by analyzing 4 circuit signals and to show what kind of fault in the analog circuit. For example, Fig. 3 shows a diagnostic fault in R2 and also shown in the fault displayed window by a twinkling red light to alert user which one circuit element was happening fault. Table 2. The typical circuit data with different fault types (Partial samples) Cases V1
V2
P1
P2
Faults no.
Actual fault type
20
7.749
14.434
-93.204
-151.301
1
Normal
70
9.923
16.691
-97.915
-156.404
2
R1 over nominal
120
9.924
16.691
-88.829
-147.318
3
R1 below nominal
187
7.531
16.560
-91.174
-156.134
4
R2 over nominal
236
7.685
11.709
-96.250
-143.379
5
R2 below nominal
285
7.143
13.658
-101.683
-159.625
6
C1 over nominal
335
7.5005
13.853
-84.7055
-142.6476
7
C1 below nominal
383
7.527
14.353
-87.139
-152.612
8
C2 over nominal
429
7.983
13.980
-102.364
-149.876
9
C2 below nominal
Fault Diagnosis of Analog Circuits Using Extension Genetic Algorithm
459
Fig. 2. The minimum error rate of training Fig. 3. User interface of fault diagnosis system curve
3.2 Testing Results Table 3 shows the accuracy by using the multilayer neural network (MNN), k-means, ET, and the proposed EGA based method to diagnosis the soft fault of tested circuit. The maximum testing accuracy is 92.3% in the MNN, 84.67% in the k-means based method and 92% in the traditional extension method. The testing accuracy of proposed method is 96.2%. It is clearly to show the proposed EGA-based diagnosis method to be better than other methods in the both training and testing stages. Moreover, the training times of proposed method is also less than the MNN. Table 3. Diagnosis performances of different methods Methods Proposed method Extension method K-means MNN(4-7-9) MNN(4-8-9) MNN(4-9-9)
Training times (Epochs) 100 N/A N/A 1000 1000 1000
Training accuracy (%) 98.6% N/A N/A 86.2% 87.6% 95.8%
Testing accuracy (%) 96.2% 92% 84.67% 84.6% 85.7% 92.3%
4 Conclusions This paper presents a novel fault diagnosis method based on EGA for analog circuits. Compared with other traditional AI methods, the proposed EGA-based method can achieve the higher accuracy. The calculation of the proposed diagnosis algorithm is also fast and simple. It is feasible to implement the proposed method in a Microcomputer for portable fault detecting devices. This new approach merits more attention, because EGA deserves serious consideration as a tool in diagnosis or classified problems. We hope this paper will lead to further investigation for industrial applications.
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M.-H. Wang, K.-H. Chao, and Y.-K. Chung
Acknowledgments The author gratefully acknowledges the support of the National Science Council, Taiwan, ROC, under the grant no. NSC-98-2221-E-167-028.
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