Diagnosis of Analog Circuits: The Problem of Ambiguity of Test Equation Solutions

Abstract

Diagnosis of analog electronic circuits is a crucial issue in computer-aided design. During the diagnosis, solving a test equation to identify the values of faulty parameters is usually necessary. The equation is nonlinear to the parameters, even for linear circuits. The nonlinearity of the equation implies the possibility of multiple solutions. No method exists that guarantees the determination of all the solutions of the test equation. However, even information about more than one existing solution is essential for the designer. It allows for the selection of another test at the design step and helps to obtain an unambiguous solution during the diagnosis. Information about the possibility of additional solutions is essential for simulation after test methods (e.g., identification and verification methods) and for simulation before test methods, so-called dictionary methods, especially those targeting multiple fault classification. The paper deals with the problem of multiple solutions of the test equation for nonlinear DC circuits and proposes a method for identifying the solutions using a deflation technique. The outcomes are compared with the results obtained using standard and adaptively damped Newton–Raphson iterative methods. The methods use randomly selected initial guesses to find multiple solutions. The effectiveness of all the methods for identifying multiple solutions was verified numerically and via laboratory tests.