Method for reliability model and analysis of multi-phase mission system

Abstract

The invention belongs to the technical field of system reliability. A reliability modeling and analysis method for multi-phase mission system is disclosed. Based on continuous-time Markov chain, a single-phase reliability model of multi-phase mission system is generated and solved. The reliability of the last phase is the reliability of the whole mission. The sparse matrix compression storage method is used to preprocess the single-stage Markov model. The generated Markov reliability model is solved based on the Krylov subspace computation method. By using the state mapping mechanism between stages, the single-stage model can be solved step by step. The idea of phase-by-phase modeling is adopted to avoid the problem of large scale caused by unified modeling. At that same time, compress storage based on sparse matrix and Krylov subspace method can effectively improve the spatial storage efficiency and computational efficiency of the model.

Description

technical field [0001] The invention belongs to the technical field of system reliability, and in particular relates to a multi-stage task system reliability modeling and analysis method. Background technique [0002] As modern systems become more and more complex and intelligent, the operation of the system is no longer a single process, but includes the transformation of multiple functional processes, or the process of forming a new system by reorganizing units at different stages. Taking the flight mission of a space vehicle as an example, it includes stages of takeoff, ascent, flight, landing, and landing. Each stage has different system configurations, mission success or failure criteria, and unit failure parameters. The above-mentioned system including multiple mission phases, and the system configuration and unit parameters change with the phases is a phased-mission system (phased-mission system, PMS). PMS is a common system in practical engineering applications, suc...

AI Technical Summary

Problems solved by technology

Relevant studies have pointed out that there is no method that can solve efficiently in all cases. At the same time, most of the existing methods are mainly for small and medium-sized matrices, and are not suitable for solving large-scale sparse matrices, because a large number of matrix power operations will lead to the disappearance of sparsity. , making the calculation inefficient

At present, the solution methods developed for large-scale environments include the iterative solution idea proposed by Reibman and Rauzy, which converts matrix operations into matrix and vector operations by deriving iterative formulas; Li et al. A solution algorithm based on Runge-Kutta is proposed. This method has high calculation accuracy, but the algorithm still consumes a lot of time when the matrix size is large.

[0006] To sum up, the problems existing in the reliability analysis technology of multi-stage system tasks based on Markov method are as follows: First, the lack of compressed storage processing for the model

The solution of the Markov reliability model involves the matrix exponential operation e tQ , when the size of the matrix is ​​large, its calculation is very difficult

Most of the existing solving algorithms are aimed at small and medium-scale matrices, and the efficiency is low when solving large-scale Markov models, especially some solving algorithms that include matrix power operations. After the power operation, the sparsity of the matrix gradually disappears, and its operation efficiency is even lower.

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