Initial health state assessment method under non-parameterized probability box and random variables

Theinitial health state assessment of a system under uncertain parameters is of significant importance for prognostics and health management (PHM) research of transmission systems. The probability box (P-box) model is an effective quantification tool that can handle both aleatory and epistemic uncertainties. In this paper, a new initial health state assessment method is proposed for a mixed system consisting of a single random variable and a single non-parametric P-box variable, which can accurately and quickly solve the initial health state index boundary. The new method improves the sampling-based method by discretizing the cumulative distribution function of the P-box variable and assigning corresponding weight coefficients to the discretized intervals using the idea of importance sampling. Second, the sample is weighted using the sampling method, and the problem of repeated optimization is transformed into two optimization problems with con straints, in order to obtain the initial health state index boundary. Finally, the accuracy and effectiveness of the proposed method are verified through two numerical examples.