Test-Generation-Based Fault Detection in Analog ... - ETRI Journal

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Table 2. Opamp circuit results in one generation.TestPWL representationvector 0.0u 0.5u 1.0u 1.5u 2.0u 2.5u 3.0u 3.5u 4.0u 4.5u 5.0uFaultcoverage (%)1 0.5 1.0 0.0 -1.0 1.0 1.0 -0.5 -0.5 0.5 0.5 -0.5 86.672 0.0 1.0 -1.0 -1.0 1.0 0.5 1.0 0.0 0.5 1.0 1.0 1003 0.0 1.0 -0.5 -0.5 -1.0 1.0 0.5 0.5 -0.5 -1.0 -1.0 86.674 -0.5 -1.0 0.5 0.0 0.0 0.0 0.5 -1.0 0.0 -1.0 0.5 86.671345in2 xR1R6vnR2-Opamp+10791214116-2.5V+1315162117Fig. 4. Benchmark Opamp.R7R3R58-2.5V+C1-Opamp+1819R420vp292225C2Fig. 5. Benchmark state variable filter.28243027vo2326-outOpamp+ outcontinues until one of the stopping criteria is met.The IEEE benchmark circuits, operational amplifier(Opamp) shown in Fig. 4 and state variable filter (SVF) shownin Fig. 5 are taken as CUTs for the proposed test patterngeneration. The Opamp is used in non-inverting amplifiermode. The gain and bandwidth are taken as specifications forthe operational amplifier circuit, and 10% deviation is fixed asthe bound for each specification. The circuit is simulated withthese bounds and the limits for the parameters are fixed. Theresults obtained for the Opamp in one generation are shown inTable 2.IV. Proposed Fault Detection Method Using PWLSignalThe PWL stimulus generated by the genetic algorithmtechnique is used as a test stimulus and the circuits are tested.The IEEE benchmark circuits, Opamp, and SVF circuits aretaken as CUTs. In the proposed method, the bounds for theparameters are initially fixed based on thesatisfaction/violation of the specifications. Then, circuits aresimulated based on these bounds. The circuits are simulatedwith parametric variations using Monte Carlo simulation. Theoutput response is sampled and wavelet analysis is performed.Wavelet coefficients are obtained for fault-free and faultyresponses.value lies outside the threshold range, then the test signal isselected as a test signal detecting that particular fault. Thenumber of faults detected by this particular pattern determinesits fitness. The test pattern with the highest fitness value, that is,the pattern which detects the maximum number of faults, is thebest pattern for the current generation. This pattern will bepassed on to the next generation.Crossover is performed between the best pattern and anotherpattern in the population. This results in two children. Thefitness of each child is calculated as before. Of the two children,the one that is more fit is passed on to the next generation. Thus,the population for the next generation is obtained. This process1. Fault Detection Using Neural NetworksArtificial intelligence techniques are popularly used in manyVLSI problems. In many studies neural networks are used infault detection and classification problems. In previous works,a back propagation neural (BPN) net and a self organizing mapare [4] used for fault classification. In [5], a probabilistic neuralnetwork (PNN) is used for the detection of catastrophic faults,but AC current, AC voltage, DC current, and DC voltage arethe four measurements used for training the neural network. In[6] and [7], wavelet coefficients are used as preprocessors forthe data before the neural network is trained. In these works, aBPN network is used for classification and fault detection is212 Palanisamy Kalpana et al. ETRI Journal, Volume 31, Number 2, April 2009
Table 3. Classification results of operational amplifier using a PNNwith catastrophic faults.Minimumfractionvariance (PCA)1%2%5%SpreadDb1PNNCoif1%C %P %Q %C %P %Q0.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 1000.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 1000.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 100%C: percentage of correct fault-free classifications%P: percentage of correct faulty classifications%Q: average of the percentages of correct fault-free and faulty classificationsTable 4. Classification results of SVF using a PNN with catastrophicfaults.Minimumfractionvariance (PCA)1%2%5%SpreadDb1PNNCoif1%C %P %Q %C %P %Q0.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 1000.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 1000.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 100done only for parametric faults. In the pseudorandom signalbased testing method [8], a PNN produces better results thana BPN network. Therefore, a PNN is used in this proposedtesting method to detect both catastrophic and parametricfaults.V. Results and Discussion1. Catastrophic Fault DetectionAs discussed in section IV, the CUTs are tested for fault-freeand faulty conditions. Two wavelets Db1 and Coif1 are usedfor catastrophic fault detection and the results are tabulated inTable 5. Classification results of operational amplifier using a PNNwith parametric faults.Minimumfractionvariance (PCA)1%2%5%SpreadDb1PNNCoif1%C %P %Q %C %P %Q0.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 1000.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 1000.1 100 100 100 100 100 1000.2 100 100 100 100 100 1000.3 100 100 100 100 100 100Table 6. Classification efficiency of various wavelets in SVF.Wavelet %C %P %QDb1 85 100 92.5Db3 95 100 97.5Coif1 85 100 92.5Coif3 100 100 100Tables 3 and 4. The proposed test method used to detectcatastrophic faults achieves 100% fault coverage in bothcircuits.2. Parametric Fault DetectionThe Opmp circuit and SVF are simulated with parametricfaults. The wavelet coefficients obtained from the outputresponse are used in neural networks for parametric faultdetection. PNN is also used for parametric fault detection. Theresults for the operational amplifier using a PNN are tabulatedin Table 5.The classification efficiency of various wavelets for SVF istabulated in Table 6, and the classification results for SVF areshown in Table 7.The PWL-based method also achieves a classificationefficiency of 100% for parametric fault detection.The results obtained using the proposed PWL-based testingmethod are compared with the pseudorandom-based testingmethod [8]. The results are compared in Table 8. Both methodshave 100% fault coverage for catastrophic faults; however, theproposed method has higher fault coverage for parametricfaults than the pseudorandom method.ETRI Journal, Volume 31, Number 2, April 2009 Palanisamy Kalpana et al. 213
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