Failure Diagnosis Using Quadratic Programming

This paper discusses the problem of determining which of a large set of possible but improbable malfunctions gave rise to a given set of measurements. The classes of systems under consideration generally lead to underdetermined sets of equations. Three methods of formulating and solving this class of problems are presented: 1) the pseudoinverse method: this leads to an easily-solved computational problem but it is not physically realistic and it tends to give poor results; 2) a pattern recognition approach based on a more realistic problem formulation: unfortunately, the computational problems associated with this formulation may be formoidable; and 3) a quadratic programming approack: this is based on minimization of a physically realistic objective function. A bmaosdification to eliminate discontinuities in the objetive function and a quasilinearization transform the original problem to an inequality-constrained quadratic minimization problem, which is readily solved by Lemke´s complementary pivoting method. A sequence of successive quasilinearizations and estimations is defilned which is proved to converge to a minimum of the original objective function. In tests this convergence occurred very fast. Examples are given; very general classes of problems are discussed which can be handled in this way.