PROBLEMS OF DIFFERENTIAL AND TOPOLOGICAL DIAGNOSTICS. PART 4. THE CASE OF EXACT TRAJECTORIAL MEASUREMENTS

Abstract

Proposed work is the fourth in the cycle, therefore, the diagnostic problem is formulated for the case ofexact trajectorial measurements, the diagnostic theorem is stated and proved, and two diagnostic algorithmsthat follow from this theorem are presented. Techniques for an a priori counting of constants, which shouldbe stored in a program for the computer-aided diagnostics whenever the first diagnostic algorithm is used,and other algorithmic parameters are considered. If the second algorithm is applied, the constants should notbe stored; this algorithm is based on the search for the minimum value of the diagnostic functional amongthe values of this functional that were obtained in the process of diagnostics for the a priori chosen set ofreference malfunctions. Various extensions of the diagnostic theorem are considered, namely, the problem ofwhether the diagnostic algorithms thus obtained are applicable when the dimension of the diagnostic vectorbeing used is lower than that of the state vector or when the uninterrupted express-diagnostics with nochecking surface is carried out, the problem of selecting the minimum diagnostic time, the diagnostics ofmalfunctions occurring in the neighborhoods of reference non-degenerate malfunctions and not envisaged inthe a priori list. We consider other functionals solving the diagnostic problem. Finally, we state the extendeddiagnostic problem that is solved by using the proposed algorithms.