Study On Volterra Models And Feature Extraction In Fault Diagnosis For Nonlinear Analog Circuit

With the rapid development of electronic industries and technologies, the problemto diagnose faults in nonlinear analog circuits has become the bottleneck in faultdiagnosis of circuits. Since the nonlinear analog circuits are very complicated, if thediagnosis methods of linear circuits are used to analyze the nonlinear analog circuits, thediagnosis results are not satisfactory. Using the Volterra series can establish the faultmodels of common nonlinear analog circuits accurately. Some domestic and foreignresearchers have made use of the models to solve the problems of fault diagnosis ofnonlinear analog circuits and obtained certain achievements. However, since thedimensional disaster problem exists in the Volterra series, only limited lower-orderitems can be used in application, which makes the fault features be difficult to extractand the diagnosis results be decreased. This dissertation aims at the problem ofextracting fault features from nonlinear analog circuits and tries to use lower-orderitems of the Volterra series to improve the capability of detecting and locating soft andhard faults in weak nonlinear analog circuits. From the fullband Volterra series, subbandVolterra series, fractional Volterra series, non-parametric Volterra series, the faultfeatures of nonlinear analog circuits are extracted. The main works and contributions ofthe dissertation are as follows:(1) Considering the problem of fault diagnosis of nonlinear analog circuits, theapproach that extracts the fault features from the fullband Volterra series is studieddeeply. Combined with the hidden Markov model (HMM), the fault features are used todiagnose faults to verify the effectivenss of the fault features. Firstly, the fullbandVolterra series and the HMM are described. Then, the fullband Volterra series faultmodels of nonlinear analog circuits are derived accurately. From the model, the faultfeatures are extracted. Detailed analysis about computational complexity is made.Finally, the experiment is implemented to compare with other fault diagnosis methodsin the fault recognition capability and diagnosis cost.(2) Considering the problem of soft fault location using the fullband Volterraseries to extract fault features, the approach of extracting fault features from the subband Volterra series is studied deeply. Detailed discussions are made in theprinciples, mathematical models and practical executive steps. Firstly, the wavelettransform (WT) are described. Then, the subband Volterra series models of nonlinearcircuits are derived accurately. From the model, the fault features are extracted. Detailedanalysis about computational complexity is made. Finally, the experiments areimplemented to compare with other fault diagnosis methods in the fault recognitioncapability and diagnosis cost.(3) To improve the fault diagnosis capability of nonlinear analog circuits further,the approach from the fractional Volterra series and the approach from the fractionalcorrelation analysis to extract fault features are studied deeply. Detailed discussions aremade about the principles, mathematical models and practical executive steps. Firstly,the fractional transform and the fractional correlation are described. Then, the fractionalVolterra series fault models and the model of the fractional Volterra series correlationfunction are derived accurately. From the models, the fault features are extracted.Detailed analysis about computational complexity is made. Finally, the experiments areimplemented to compare with other fault diagnosis methods in the fault recognitioncapability and diagnosis cost.(4) Considering the problem of the computational complexity using parametricVolterra series, the method of non-parametric Volterra series is studied deeply. Firstly,the optimized excited signals are obtained by the theory of optimal search. Based on thefeatures of nonlinear systems and the optimized excited signals, the non-parametricVolterra series fault models of nonlinear analog circuits are derived accurately. From themodel, the fault features are extracted. Then, detailed analysis about computationalcomplexity is made. Finally, the experiments are implemented to compare the methodwith other fault diagnosis methods in the fault recognition capability and diagnosis cost.