Fault Diagnosis of Analog Circuit Based on PSO and BP Neural Network

JI Mengran,CHEN Gang,YANG Qing,ZHANG Jinge

( Shenyang Ligong University,Shenyang 110159,China )

Fault Diagnosis of Analog Circuit Based on PSO and BP Neural Network

JI Mengran,CHEN Gang,YANG Qing,ZHANG Jinge

( Shenyang Ligong University,Shenyang 110159,China )

In order to improve the speed and accuracy of analog circuit fault diagnosis,using Back Propagation Neural Network(BPNN),a new method is proposed based on Particle Swarm Optimization(PSO)to adjust weights of BP neural network.The model can not only overcome the limitations of the slow convergence and the local extreme values by basic BP algorithm,but also improve the learning ability and generalization ability with a higher precision.The response signals of analog circuit is preprocessed by Wavelet Packet Transform (WPT) as the fault feature．The simulation result shows that the proposed method has higher diagnostic accuracy and faster convergence speed,which is effective for fault location.

fault diagnosis;BP neural network;particle swarm optimization;analog circuit

Analog circuit fault diagnosis research since the nineteen sixties,has made a lot of achievements,researchers have proposed many fault diagnosis methods,such as fault dictionary method,parameter identification method and fault verification method.Since the discrete and nonlinear,diversity,element parameter fault phenomena,it is difficult for anology circuits′ fault diagnosis.The parameters identification method of components required to provide more diagnostic information needs a particular mathematical model,and mathematical operations time-consuming[1].While the neural network has the classification ability,learning and reasoning ability,strong robustness and self-adaptive ability,it can effectively solve the traditional pattern recognition methods which are difficult to solve,so,it provides an excellent solution for fault diagnosis[2].

The BP neural network is not only self-organizing,self-learning and adaptive ability,but also is simple principle,easy to implement,and it has been widely used in many fields.However,BP neural network has low learning efficiency,slow convergence and easy to fall into local optimum limitation,especially has great influence on the structure of the selected BP neural network learning ability and generalization ability of the network.This article combines the PSO algorithm with the BPNN,which is based on the error back-propagation.The PSO algorithm is introduced for adjusting the weights and thresholds of the BPNN[3].

1 FEATURE EXTRACTION OF WAVELET PACKET TRANSFOR

1.1 Wavelet Packet Transform

Wavelet Packet Transform(WPT)is a generalization of wavelet transform,which is based on the multi-resolution analysis,providing a more precise for signal analysis method[4].At present,in analog circuit fault diagnosis,wavelet packet technique as a powerful tool for information processing,so the method based on wavelet packet decomposition has been widely applied.

Take a three layer wavelet packet decomposition as an example,the wavelet packet decomposition tree shown in Figure 1,Sis the original signal,represents the low frequency[5],Drepresents high frequency end of the serial number indicates the number of layers of wavelet packet decomposition(i.e.the number of scales)is decomposed with the following relations:

S=AAA3+DAA3+ADA3+DDA3+AAD3+DAD3+ADD3+DDD3

(1)

Figure 1 Three layer wavelet packet decomposition

1.2 Wavelet Packet Energy Feature Extraction

Wavelet packet decomposition of the signal is the essence of multi-band-pass filter[6].It can be decomposed in the whole frequency band signal,obtained in different frequency bands of energy,it can regard as important information of a fault diagnosis.The circuit output signal wavelet packet decomposition,extract from low to high frequency signals all features[7],and reconstruction of wavelet packet decomposition coefficients to obtain the energy of each frequency band signal.

Here select the appropriate wavelet packet decomposition level fault feature extraction is crucial[8].If the decomposition level is too small,the resulting energy can not fully reflect the characteristics of the analog circuit fault;if the decomposition level is too high,redundant features will increase,which will affect the diagnostic accuracy and efficiency of diagnosis.Therefore,this wavelet packet layer is set to 3.Figure 2 is the schematic diagram of the wavelet packet decomposition.

Figure 2 Wavelet packet decomposition

2 PSO-BP MODEL FOR FAULT DIAGNOSIS

2.1 Particle Swarm Optimization

Particle Swarm Optimization′s[9]idea from artificial life and evolutionary computation theory,by simulating the behavior of birds for each particle habitat search optimum solution,and using these optimal solutions so that the whole swarm optimal,fitness function.

If the search targets a D-dimensional space,there is a group formed by the m particles,the vectorxi=(xi1,xi2,…,xiD),i=1,2,…,mindicates the position of thei-th particle,with a D-dimensional vectorvi=(vi1,vi2,…,viD,) indicates that the particle velocity,vectorpi=(pi1,pi2,…,piD) indicates that the particles are so far the best position to search,vectorpg=(pg1,pg2,…,pgD) represents the entire swarm optimal location of the search,particles update iteration formula is as follows:

vid(t+1)=ωvid(t)+c1r1(pid-xid(t))+c2r2(pgd-xid(t))

(2)

xid(t+1)=xid(t)+vid(t+1)

(3)

when,vid>Vmax,takevid=Vmax;

whenvid<-Vmax,takevid=-Vmax.

wherei=1,2,…,m,d=1,2,…,Dinertia weight coefficient expressed byω,acceleration constantsc1andc2with a non-negative constant representation,r1andr2are subject to [0,1] on the uniform distribution random number,xid(t) is ai-th particle′s current position,pidis a particleito present it to the optimal position for the search,pgdis a whole swarm able to search the optimal position,vidis ai-th particle′s current velocity,vid∈[Vmax,-Vmax],Vmaxis a maximum speed limit a nonnegative number.

2.2 BP Neural Network

BP neural network structure is the most typical three-tier network architecture,namely input layer,hidden layer and output layer[10].The structure shows in Figure 3.

Figure 3 BP Neural Network Structure

BP neural network algorithm consists of two phases:

1)Forward propagation input information through the input layer and hidden layer and layer by layer by the process and calculating the actual output value of each unit.

2)Back-propa-gation process.If the output layer can not obtain a desired output value,layer by layer recursively calculate the actual output and the desired output of the difference(error),the difference is adjusted according to the weights.Repeated use of these two processes,making the smallest error signal when the error reaches the desired requirements,the network learning process is over.

2.3 PSO to Optimize BP Neural network strategy

PSO-BP neural network model algorithm as follows:

1)Construct BP neural network and initalize network weights and threshold:use net=newff(minmax(P),[8,1],{′tansig′,′purelin′},′traincgf′) to construct BP neural network.Random initialization swarm,each group is the connection weights and threshold initial value;

2)Calculated for each particle(connection weights and threshold)of the fitness function;

3) Compare the current particle fitness function value and the previous best fitness value,whichever is greater value to the current particle′s best fitness value;

4) Select all the particles in one of the best fitness value,as a global optimal solution;

5)For each particle,to calculate its forward speed:

vi(t+1)=ωvi(t)+c1r1(pi-xi(t))+c2r2(pg-xi(t))

(4)

6)Calculates the position of the particle after forward:

xi(t+1)=xi(t)+vi(t+1)

(5)

7)According to equation(4)reduces inertia weightω:

ω=ωmax-(ωmax-ωmin)/itermaxiter

(6)

8) Change the acceleration factorc1,c2:

c1=c1max(c1max-c1min)/itermaxiter

(7)

c2=c2max(c2max-c2min)/itermaxiter

(8)

9) If the algorithm to meet the convergence criteria or the maximum number of iterations,then exit the PSO algorithm,step 10,otherwise return to step 2;

10)Use of BP neural network algorithm to continue training,if the training results are better than PSO training results,BP neural network output,otherwise the output PSO trained neural network.Among them,c1,c2are the learning factors,c1max、c2max、c1min、c2minare learning factorc1,c2of the maximum and minimum;r1、r2are random numbers on [0,1].ωis a coefficient of inertia weight,ωmax、ωminare inertia weight factors,respectively the maximum and minimum;iter、itermaxare PSO algorithm iterations and the maximum number of iterations;vi(t) is a particle velocity I;pi(t) is the optimal solution of the individual particles;pg(t) is the global optimum particle;xi(t) is the position of the particle.

3 CASE STUDY

In order to verify the effectiveness and feasibility of the proposed method to a center frequency of 25 kHz bandpass filter instance as a diagnostic[11],Circuit shows in Figure 4.Figure tolerance of resistors and capacitors were±5%and±10%of the components to be diagnosed isC1,C2,R2andR3.

Experimental set fault type shows in Table I.↑ indicates that the corresponding failure mode corresponding to the tolerance interval is set to [Normal tolerance,50%],↓ indicates that the corresponding failure modes corresponding tolerance interval is set to [-50%,the normal tolerance].Figure 4 also shows the fault location.

When experiment,the circuit is applied to an amplitude of 5 V,the time is 10us pulse voltage.The output voltage signal will be sampled after three wavelet packet decomposition,extracted from low frequency to high frequency signal characteristic of all,and the coefficients of the wavelet packet decomposition reconstructed,the energy band structure having eight feature vector,and its normalized.

Using Multisim different fault conditions on the circuit for Monte Carlo analysis,the data 150 obtained as a sample,whichever is the 75 training samples,and the other group as a test sample 75.Some of the sample data samples shown in Table 2.

Figure 4 25 kHz Sallerl-Key bandpass filter

Table 1 FAULT TYPES TABLES

To test based on PSO-BP neural network learning ability,you can set training precision of 0.001,the error curve is shown in Figure 5.

Test results as shown in Figure 6.This paper shows that the proposed method is better than the traditional BP method.That is because the use of particle swarm algorithm improves the optimal parameters of the BP neural network efficiency,it also solves the problem of low BP learning efficiency,and it also improves the network convergence speed and classification speed.

Table 2 DATA SAMPLES

Figure 5 PSO optimized BP network training error graph

Figure 6 Training test results

4 CONCLUTION

This paper presents an approach based on PSO-BP neural network and wavelet packet decomposition combining analog circuit fault diagnosis method. The PSO optimization algorithm and BP neural network combined with improved network learning ability and generalization ability.Simulation results show that the use of PSO-BP neural network and wavelet packet decomposition of analog circuit fault diagnosis method is effective,this method accelerates network convergence speed and classification speed,improve the accuracy of fault diagnosis and fault location accuracy.

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馬金發(fā))

date： 2013-12-18

This work is supported the Science and Technology Research Project of Liaoning Provincial Department of Education.

Biography： JI Mengran(1989—)，female,graduate candidate；Corresponding author：CHEN Gang(1962—)，female，professor，Research direction：fault diagnosis of analog circuit.

1003-1251(2014)05-0090-05

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