Diagnosability of Nonlinear Circuits and Systems—Part I: The dc Case

A theory for the diagnosabilty of nonlinear dc circuits (memoryless systems) is developed. Based on an input-output model, a necessary and sufficient condition for the local diagnosability of the system, which is a rank test on a matrix, is derived. Various ways of reducing the computational complexity of this test are indicated. A sufficient condition for single fault diagnosability, which is much weaker than the necessary and sufficient condition for local diagnosability, is also derived. It is also shown that for diagnosable systems, it is possible to to pick a finite number of test inputs that are sufficient to diagnose the system. An illustrative example is presented.

[1]  T. Trick,et al.  A note on single fault detection in positive resistor circuits , 1978 .

[2]  T. Trick,et al.  Calculation of parameter values from node voltage measurements , 1979 .

[3]  R. Berkowitz.  Conditions for Network-Element-Value Solvability , 1962 .

[4]  J. Dieudonne.  Foundations of Modern Analysis , 1969 .

[5]  G. Roussas,et al.  A first course in mathematical statistics , 1976 .

[6]  G. Stewart,et al.  Rank degeneracy and least squares problems , 1976 .

[7]  E. Polak.  On The Global Stabilization of Locally Convergent Algorithms for Optimization and Root Finding , 1975 .

[8]  N. Navid,et al.  A theory and an algorithm for analog circuit fault diagnosis , 1979 .

[9]  T. Rothenberg.  Identification in Parametric Models , 1971 .

[10]  R. Saeks,et al.  A search algorithm for the solution of the multifrequency fault diagnosis equations , 1979 .

[11]  Robert K. Brayton,et al.  The Sparse Tableau Approach to Network Analysis and Design , 1971 .

[12]  J. Munkres,et al.  Calculus on Manifolds , 1965 .

[13]  Neeraj Sen,et al.  Fault diagnosis for linear systems via multifrequency measurements , 1979 .

[14]  E. Polak,et al.  NEWTON DERIVED METHODS FOR NONLINEAR EQUATIONS AND INEQUALITIES , 1975 .

[15]  R. Saeks,et al.  Fault isolation via components simulation , 1972 .

[16]  John W. Bandler,et al.  Multiple-fault location of analog circuits , 1981 .

[17]  Albert E. Ruehli,et al.  The modified nodal approach to network analysis , 1975 .

[18]  Ruey-Wen Liu,et al.  Sequentially linear fault diagnosis: Part I-Theory , 1979 .