# An Efficient Time-Variant Reliability Analysis Method with Mixed Uncertainties
## 1 Introduction
[28] proposed a new response approximation model for the time-dependent reliability analysis of uncertain structures under stochastic loads. Finally, the main objective of the quasi-static method is to change the time-variant reliability issue into a constant reliability issue. In this method, time-variant uncertain parameters are discretized to transform the complex time-variant reliability problem into a problem independent of time-variant parameters. In this regard, [PERSON] et al. [29] and [PERSON] et al. [30] transformed the time-variant reliability model into a static reliability model through representing the Gaussian process as multiple independent normal distributions. [PERSON] and [PERSON] [31] proposed the NEWREL method based on stochastic discretization method. [PERSON] et al. [10; 32] developed the reliability calculation method for discretizing time-variant uncertain parameters (TRPD) and extended it to system reliability. Subsequently, an improved version of TRPD [33] was proposed in which time-variant reliability analysis was performed only at the component level. This paper focuses on the TPRD approach. Known by references aforementioned, the majority of investigations in the field of time-variant reliability are confined to conventional structural reliability problems with random variables [34]. This kind of time-variant reliability analysis requires a large number of experimental samples to construct accurate probability distributions of random variables. However, experimental sample data is limited in many engineering applications. In this case, the boundary of the uncertain variable is easy to determine, and the uncertain variable is suitable to be described by the non-probabilistic interval variable. For reliability analysis problems with interval variables, non-probabilistic methods can be used to measure reliability [34]. There may be both random and non-probability interval-uncertain variables in structural systems. Therefore, it is necessary to develop effective methods to solve the mixed uncertainty problems [35; 36]. However, only a few researchers studied time-variantreliability problems of mixed variable structures. Specifically, a multi-layer nested analysis approach has been adopted to solve mixed time-variant reliability problems [29; 37]; the outer layer is used to discretize the stochastic process in the time-variant function, while the inner layer is nested optimized at each time step. Accordingly, the computational efficiency is extremely low, which adversely affects its practicability in industrial applications. To this end, it is vital to develop efficient algorithms to significantly decrease the computational burden of the time-variant reliability method with mixed variables. In the present study, it is intended to presented a novel approach to analyze the structural time-variant reliability with mixed variables. To this end, the existing time-variant reliability theory is combined with the interval uncertainty analysis. The rest of this paper is organized as follows: the structural time-variant reliability model with random variables is introduced in Section 2. Then, the structural time-variant reliability model with mixed variable and traditional solution method are discussed in Section 3. In Section 4, a new method is proposed to analyze the structural time-variant reliability. For evaluating the effectiveness of the presented approach, it is applied to several numerical and engineering case studies and then the obtained results are presented in Section 5. Finally, Section 6 summarizes the main results and conclusions of this study.