Regularizing Algorithms for Diagnosing

In this work several approaches of a stable method for construction of the diagnostic matrix for gas turbine engine are being researched, when initial data are given inexactly, and their maximal deviation estimation is known. The essence of the problem is the following: the equations in minor deviations describing the gas turbine engine give us system of linear algebraic equations AC=B, where the matrix C is called a diagnostic matrix, the matrix A components comprise the coefficients of the calculated parameters, and the matrix B components comprise the coefficients of measured parameters. However, as a rule the matrix A is sparse and ill-conditioned matrix, so there is a problem of stable inversion, as a result the problem becomes ill-posed. Therefore, methods of ill-posed problem theory are used: normal pseudosolution is searched instead of an exact solution (it is important to note that normal pseudosolution is not always approximates to the exact one) using classical Tikhonov's regularization method, however, that method causes inherent obstacles, which possible solutions are discovered. There are described 3 approaches of finding the regularization parameter.

Sergey A. Andreyev, Transport and Telecommunication Institute, Latvia. Specialist in computer sciences, mathematical modelling, reliability and fault diagnosis of complicated objects and systems.Sharif E. Guseynov, Liepaja University, Latvia. Specialist in mathematical modelling, ill-posed and inverse problems, PDF, theory of optimization.