Initial Values Estimation and Solution Finding for Inverse Problem of Reliability Evaluation Using Deep Neural Network

Correct values of component reliability parameters are crucial to the success of overall reliability evaluation (RE). Inverse problem of RE (IPRE) is the process of obtaining the unknown reliability parameters (URPs) from given system (or bus) reliability indices. Solution finding of the IPRE is a great challenge because of its high nonlinearity. This paper proposes an efficient combination method to find valid initial values and true values of the URPs based on the deep forward neural network (DFNN) techniques. Good nonlinear approximation performance of the DFNN is exploited to provide the proper initial values for the URPs considering the characteristics of the IPRE. The main work is as follows. Firstly, the analytical formulas of reliability indices with respect to variable reliability parameters are given based on the Monte Carlo simulation (MCS). Then, the nonlinear equation set for the IPRE is constructed based on the analytical formulas and then a large number of training samples are generated conveniently. Next, the DFNN is trained to estimate reliable initial values. Last, the true values of the URPs are obtained from their initial values by the continuation method. The effectiveness of the proposed method has been verified on the RBTS, IEEE-RTS system.