Leapfrog Filer Circuit

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Diagnostics of Incipient Faults in Analog Circuits

Li Min, Long Bing, Xian Weiming, Wang Houjun

School of Automation, University of Electronic Science and Technology of China (UESTC), Chengdu 611731,

ChinaPhone: +86-28-6183-0316, Fax: +86-28-6183-1310, E-mail: [email protected]

Abstract – Diagnosis of incipient faults for analog circuits isvery important, yet very difficult. A novel approach for

incipient faults in analog circuits is proposed. Firstly, the statistical property feature vector, which is composed of range,

mean, standard deviation, skewness, kurtosis, entropy andcentroid, is used to reflect the global property of outputresponse. Then, the least squares support vector machine(LSSVM) is used for diagnostics of the incipient faults inanalog circuits. Traditionally, multi-fault diagnosis for analogcircuits based on SVM usually uses a single feature vector totrain all binary SVM classifier. However, in fact, each binary

SVM classifier has different classification accuracy fordifferent feature vectors. Therefore, the Mahalanobis distance(MD) based on particle swarm optimization (PSO) is proposedto select a near-optimal feature vector and decrease thedimensions of the feature vector for each binary classifier. Theexperiment results show as following: (1) The accuracy usingthe near-optimal feature vectors is better than the accuracyusing a single vector; (2) The consuming time of the near-optimal feature vectors selected by MD based on PSO isreduced about 98% in comparison to the time of the optimal

feature vectors selected by the exhaustive method.

Keywords – analog circuits; diagnostics, incipient faults, least squares support vector machine, particle swarm optimization,Mahalanobis distance.

I. INTRODUCTION

More and more attention is being attached on the

performance degradation monitoring so that failure

can be predicted and prevented. This is referred as the

condition-based maintenance (CBM)[1]

. Thediagnosis of the incipient faults, such as shifts in

performance parameters, is crucial, yet very difficult.Xu et al. [2] has proposed to use the output voltage,

autoregressive-moving average (ARMA) coefficients,

and wavele t t ransform coeff ic ients as the

combinational feature vector whose dimensions werereduced by linear discriminant analysis (LDA) to train

hidden Markov model (HMM) for incipient fault

diagnosis of analog circuits. Deng et al. [3] has proposed to use the fault features extracted based on

the fractional correlation and the sub-band Volterra

series to train HMM for incipient fault diagnosis of

nonlinear analog circuits. The aforementionedincipient fault diagnosis methods are all based on

HMM, and the difference mainly lies in their ways ofextracting the feature. To improve the classification

accuracy, we propose to employ LSSVM as the

classifier. In addition, the extracting features of theaforementioned incipient fault diagnosis methods are

unfamiliar to the operator. Hence, the statistical property feature vector which is familiar to operator

and can reflect the global property of output response

is used in this paper.

Multi-fault diagnosis for analog circuits based onSVM is typically solved by combining many binary

SVM classifiers. Most researchers used a singlefeature vector to train all SVM binary classifiers [4].However, each SVM binary classifier has different

classification accuracy for different feature vectors.

On the other hand, to obtain the high classification

accuracy whilst reducing the physical size of featurevector, some form of feature selection that is capable

of selecting the most significant features of a featureset must be used. Xu et al. [2] used the LDA to

decrease the dimensions of the feature vector. Jack et

al. [5] proposed to use genetic algorithm (GA) to

select the most significant features from a large set of possible features in machine condition monitoring. By

considering that the evolutionary algorithm-particleswarm optimization (PSO) has many advantages, such

as simple concept, easy implementation, and quickconvergence [6] and the Mahalanobis distance (MD)

[7]-[8] is a useful way of determining similarity of an

unknown sample to a known one, the MD based onPSO is used to select a near-optimal feature vector for

each binary classifier.

This paper is organized as follows: Section II

describes the diagnostic procedure based on LSSVMfor analog circuits. Section III briefly presents the

statistical property feature vector of analog circuits.Section IV proposes the near-optimal feature vector

selected by MD based on PSO. Section V shows thesimulation results. Conclusions are drawn in Section

VI.

II. DIAGNOSTIC PROCEDURE BASED

ON LSSVM

A diagnostic procedure for analog circuits based on

LSSVM involves four phases: data collecting phase,

preprocessing phase, training phase, and diagnostic phase. Though data collecting is a time-consuming

work, it is not too difficult in technique. In the training

phase and diagnostic phase, a well-made LSSVM

The 11th IEEE International Conference on Electronic Measurement & Instruments ICEMI’2013

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toolbox, such as LSSVMlab toolbox, can be directly

used in the diagnosis of analog circuits. TheLSSVMlab toolbox can help us avoid duplicated work

and make the diagnostic program reliable. The

preprocessing is another key phase, which will focus

on how to define the feature vectors of CUTs and how

to select a near-optimal feature vector.

III. FEATURE VECTOR OF ANALOG

CIRCUITS

To determine the global properties of the responsecurve, the statistical property features which are

familiar to operator are proposed. Therefore, we

propose to use range, mean, standard deviation,skewness, kurtosis, entropy and centroid to constitute

a statistical feature vector. That is,

[ , , , , , , ] F w m v s k e n (1)

where , , , , , ,w m v s k e n are range, mean, standard

deviation, skewness, kurtosis, entropy, and centroid of

response signal respectively.

The range which is a measure of the maximumscope of the changes of the data is defined as follows:

max minw x x (2)

The mean value and standard deviation of signal x are defined as below:

( )m E x (3)

2var( ) ( )v x E x m (4)

The skewness which is a measure of the asymmetryof the data around the mean value is defined as

follows:3

3

[ ( )] E x m s

v

(5)

where v is the standard deviation.Kurtosis is defined in the zero-mean case by the

following equation:4 2 2( ) { } 3[ { }]kurt x E x E x (6)

Kurtosis is a measure of the heaviness of tails in

distribution of signal x and can be used to establish

an effective statistical test in identifying changes ofsignals.

Entropy is a fundamental concept of the

information theory. The entropy H of a random

variable x with density p(x) is defined as follows:

( ) ( ) log ( ) H x p x p x dx (7)However, during the analog circuit fault diagnosis,

it is very difficult to calculate the kurtosis and entropy

based on equation (6) and (7). Usually, the unbiased

estimate or approximation is used to obtain kurtosis

and entropy. Then, the equation (6) can be written asfollows:

4

4

1

2 22 2

1

( ){ }

( )[ { }]

( ( ))

M

n

M

n

x n E x

kurt x M E x

n

(8)

where M is the length of the signal. And the equation(7) can be approximated as follows:1 2 2 2

1 2( ) ( { ( )}) ( { ( )} 1/ 2) H x k E G x k E G x

(9)

where

1 36 /(8 3 9)k , 2 24 /(16 3 27)k ,

1 2( ) exp( / 2)G x x x ,

2 2( ) exp( / 2)G x x .

The centroid of the closed region which is formed

by the waveform of signal and axes can be obtained asfollows:

0

( )

( )

ug u du

u g u du

(10)

For a zero-mean discrete-valued signal, theequation (10) can be written as follows:

10

1

( )

( )

M

n

M

n

n x n

n

n

(11)

IV. FEATURE VECTOR SELECTION

A. Mahalanobis Distance

The MD methodology distinguishes multivariable

data groups by a univariate distance measure that iscalculated from the measurements of multiple

parameters [7-8].

The MD approach can provide a number forgauging similarity of an unknown sample set to a

known one. Generally, the two samples are more

similar, and more possible to belong to the same fault

class if their MD value is smaller. Thus, MD can beused to classify samples from two different fault

classes. Based on this idea, the feature vector withhigh recognition rate classified by MD is used to trainand test LSSVM classifier for any two fault classes of

analog circuits. But MD is just one kind of similarity

metrics and can not find an optimal feature vector forany data set. Therefore, the feature vector with high

recognition rate classified by MD is a near-optimal

vector, not an optimal one.

B. Particle Swarm Optimization

Its basic idea is that each solution of an

optimization problem is called a particle and a fitness



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function is defined to measure the degree of

superiority of every particle.The choice of fitness function is another primary

factor to influence the performance of the PSO

algorithm. To find a near-optimal feature vector, thefeature vector with high recognition rate classified by

MD should be selected. Therefore, the fitness functionis chosen as the maximum of recognition rate

classified by MD.It is known that the PSO algorithm adepts in real

number coding. In order to select the near-optimal

feature vectors easily, an additional step whichconverts a real number to a binary coding is added.

Based on equation (1), we use 7-bits to represent the

original feature vector sequentially. For example, ifthe binary string is 0010101, then the standard

deviation, kurtosis and centroid are selected.

Fig. 1. Flowchart of the near-optimal diagnostic program

based on LSSVM.

Fig. 2. Flowchart of the near-optimal feature vectorselected by MD based on PSO.

C. Near-Optimal Feature Vector Selected By MD

Based on PSO

Since the feature vector with high recognition rate

classified by MD may differ among every two fault

classes, multiple binary LSSVM classifiers are used.The classification accuracy for the feature vector with

high recognition rate classified by MD does not

always have the optimal accuracy, but it is better than

most of the feature vectors. Though it is not anoptimal feature selection method, it provides an easy,



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effective approach to select a near-optimal feature

vector, which is useful for automatic testing anddiagnosis of analog circuits.

The flowchart of the near-optimal diagnostic

program based on LSSVM using the feature vectorwith high recognition rate classified by MD is shown

in Fig.1. And, the flowchart of the near-optimalfeature vector selected by MD based on PSO is shown

in Fig. 2. To evaluate the performance of our proposedmethod, we have also implemented an optimal

diagnostic procedure using an exhaustive method

based on LSSVM classifier.

V. SIMULATION RESULTS

The experimental circuit is a leapfrog filter (Fig.3),

which is a benchmark circuit of ITC97[9]

. Thetolerance of the resistors and capacitors are set to 5%

and 10% respectively. There are many components inthe filter, and some components such as R1, R2, R3,

R4, R8 and C2 that are more sensitive to the test

signal than the other components, are selected as the

potential faulty components. For each of the faultycomponents, two soft-fault classes are shown as

follows: a class for the component values larger than

the nominal one (labeled by) and the other for thecomponent values smaller than the nominal one

(labeled by). Therefore, 12 fault classes, in addition to

the fault-free condition, are simulated, and output of

the leapfrog filter is used as the test node.

Fig. 3. Schematic diagram of a leapfrog filer circuit.

To identify the incipient faults of the leapfrog filter

circuit, the fault interval for each faulty component is

set to near its normal tolerance range.

The fault intervals for all faulty components arelisted in Table 1. Traditionally, during simulation, the

fault value of the faulty components was usually set to

be a fixed value, and as a result, the fault dictionaryestablished through this method is incomplete and has

substantial deviation from the actual situation. To

solve this problem, the mean value with tolerance

method which is named as MVT is proposed. Faultycomponent R1 is used as an example to illustrate the

basic idea of MVT. According to Fig.3 and Table 1,the fault interval is [10.5K, 11.5K] when the fault

value of R1 becomes larger. Then, the mean value of

the fault interval is calculated as m=

(10.5+11.5)/2=11K. After that, the tolerance of the

mean value needs to be found. It is found that the

tolerance should be set to 4.5% owing to the following:11*(1+4.5%) =11.495K, 11*(1-4.5%) =10.505K.

Therefore, the fault value of the faulty components can

no longer be set to a fixed value, and then, based on

Monte Carlo analysis, the complete and reasonablefault dictionary can be established. Based on the idea

of MVT, the fault values of the leapfrog filter’s

components are shown in Table 2. In our work, onlysingle incipient fault has been considered.

Table 1. Fault intervals for all faulty components.

Faulty

Component

R1 [1.05Yna1.15Yn] [0.85Yn0.95Yn]

R2 [1.05Yn1.15Yn] [0.85Yn0.95Yn]

R3 [1.05Yn1.15Yn] [0.85Yn0.95Yn]

R4 [1.05Yn1.15Yn] [0.85Yn0.95Yn]

R8 [1.05Yn1.15Yn] [0.85Yn0.95Yn]

C2 [1.10Yn1.20Yn] [0.80Yn0.90Yn]aYn is the nominal value.

Table 2. Nominal and fault value with tolerance.

Fault

ID

Fault

Class

Nominal

Value

Fault

Value

Tolerance

F0 NF

F1 R 10K 11K 4.5%

F2 R 10K 9K 5.5%

F3 R 10K 11K 4.5%

F4 R 10K 9K 5.5%

F5 R 10K 11K 4.5%

F6 R 10K 9K 5.5%

F7 R 10K 11K 4.5%

F8 R 10K 9K 5.5%

F9 R 10K 11K 4.5%

F10 R 10K 9K 5.5%

F11 C2 20nF 23nF 4.5%

F12 C2 20nF 20nF 5.5%

To obtain the simulation fault data according to thefault classes in Table 2, a time-domain transient

analysis and a Monte Carlo analysis method inOrCAD/Pspice 10.5 software are used. In the time-

domain transient analysis, run-to-time and maximum

step size are set as 3 ms and 1us respectively. In the

Monte Carlo analysis, number of runs and usedistribution are set to 600 and Gaussian respectively.

Therefore, the simulated data for each fault class

(including F0) are 600 sets. In each set, there are 3000

points in the time-domain transient response curve.To obtain the high classification accuracy for each

binary classifier whilst reducing the physical size of



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The classification accuracy for each fault class

(including F0) is shown in Table 3.

Table 3. Classification accuracy for each fault class.

Fault ID Fault

Class

Accuracy (%)

F0 NF 92.50

F1 R 98.00

F2 R 98.00

F3 R 95.00

F4 R 96.00

F5 R 96.33

F6 R 90.83

F7 R 98.67

F8 R 96.33

F9 R 100.00

F10 R 92.40

F11 C2 88.50F12 C2 93.20

Average 95.06

VI. CONCLUSIONS

A near-optimal feature vector selected by MD based on PSO has been proposed for diagnostics of

the incipient faults in analog circuits using LSSVM.

Through the simulation results for the three filterswith parametric faults, we can draw the following

conclusions:

The accuracy using the near-optimal feature

vectors is better than the accuracy using a single vector.The consuming time of the near-optimal feature

vectors selected by MD based PSO is reduced about

98% in comparison to the time of the optimal feature

vectors selected by the exhaustive methodThe proposed method provides a tradeoff between

diagnostic accuracy and time for diagnostics of theincipient faults in analog circuits, which is beneficial

for analog IC or circuits testing and diagnosis.

ACKNOWLEDGMENT

This work was supported in part by National NaturalScience Foundation of China under Grants 61071029,60934002, 61271035 and 61201009, and in part by theFundamental Research Funds for the Central Universities

under Grants ZYGX2012J088.

REFERENCES

[1] DAI J, DAS D, PECHT M. Prognostic-based riskmitigation for telecom equipment under free air coolingconditions[J]. Energy, v2012,99(4):423-429.

[2] XU L, HUANG J, WANG H, et al. A novel method forthe diagnosis of the incipient faults in analog circuits

based on LDA and HMM[J]. Circuit, Systems, and SignalProcessing,2010,29(4):577-600.

[3] DENG Y, SHI Y B, ZHANG W. Diagnostic of incipientfaults in nonlinear analog circuits[J]. Metrology andMeasurement Systems, 2012,19(2):203-218.

[4] ZHANG Y, WEI X Y, JIANG H F. One-class classifier based on SBT for analog circuit fault diagnosis[J].

Measurement, 2008,41(4): 371-380.[5] JACK L B, NANDI A K. Genetic algorithms for feature

selection in machine condition monitoring with vibrationsignals[C]. IEE Proceedings-Vision, Image and SignalProcessing, 2000,147(3):.205-212.

[6] KENNEDY J, EBERHART R. Particle swarmoptimization[C]. IEEE International Conference on Neural

Networks, 1995:1942-1948.[7] MAHALANOBIS P C. On the generalized distance in

statistics[C]. in Proceedings of the national institute ofscience of India,1936:49-55.

[8] KUMAR S, CHOW T W S, PECHT M. Approach to faultidentification for electronic products using Mahalanobisdistance[J]. IEEE Transactions on Instrumentation andMeasurement, 2010,59(8):2055-2064.

[9] KONDAGUNTURI R, BRADLEY E, MAGGARD K, etal. Benchmark circuits for analog and mixed-signaltesting[C]. Southeastcon, 1999:217-220.

AUTHOR BIOGRAPHY

Li Min: PhD candidate in the University of ElectronicScience and Technology of China (UESTC). His currentresearch interests include diagnostics, prognostics for circuitsand systems.

Long Bing : received MS from Harbin EngineeringUniversity in 2002, and PhD from Harbin Institute ofTechnology in 2005, respectively. Now he is an associate

professor at the University of Electronic Science andTechnology of China (UESTC). He served as a generalsecretary & publication chair in IEEE ICTD09. In recent years,he has published more than 60 scholarly papers, and reported 8

patent declarations in China. His current research interestsinclude failure analysis, automatic testing, diagnostics,

prognostics and health management, and testability design andanalysis for circuits and systems.

Xian Weiming: MS candidate in the University ofElectronic Science and Technology of China (UESTC). Hiscurrent research interests include diagnostics, prognostics forcircuits and systems.

Wang Houjun: received MS and PhD in information andsignal processing from the University of Electronics Scienceand Technology of China (UESTC) in 1985 and 1992,respectively. He is currently a professor and has been a vice

president of UESTC from 2005. His research interests includetime domain measurement and signal processing, design fortestability of complex systems, architecture of auto test systems,and fault diagnosis.


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