Reliability Control of Complex Technical Systems Based on the Modified Method of the Shortest Descent

Abstract

When creating highly reliable technical systems, including objects of space technology, it is necessary to determine the technical characteristics taking into account the loading conditions already at the design stage. This allows to provide a given level of reliability of the technical system while reducing the amount of testing. When solving this problem for the created technical systems of small batches at the design stage, there is no data for a priori statistical analysis and, as a rule, it is not possible to determine all the set of possible disturbances (destabilizing factors or loads) that can lead to abnormal situations. In addition, at the stage of developing a complex technical system, it is not possible to conduct the whole complex of tests in order to collect the necessary information. Getting approximate solutions makes it necessary to conduct additional tests of the technical system to refine the limit values of the parameters, which is associated with significant costs. With these factors in mind, it is important to increase the accuracy of the applied mathematical methods and reduce the number of iterations when searching for optimal (best) solutions. In this paper, a modified method for steepest descent based on its conjugation with an algorithm for accelerated search is proposed. The algorithm of accelerated search is based on the determination of such an initial iteration from the solution region of the steepest descent method, at which the current error in the distribution density of the controlled parameter will not exceed a given error. The proposed approach makes it possible to reduce the number of iterations while maintaining the required accuracy of the parameters of the technical system and, by introducing the regularization parameters, increase the stability of the solution to the reliability management problem.