This paper develops a method for the time-dependent reliability analysis of deteriorating structures using phase-type (PH) distributions. The deteriorating model consists of two aspects: the progressive deterioration posed by aging effects, and the shock deterioration caused by random shocks. Evaluating the distribution of the sum of random variables is a tough work in the model. For simplified problems that random variables follow specific distributions with the convolutions being derived analytically, it is effective to utilize semianalytical methods for the time-dependent reliability analysis. For other general problems (the distribution does not have additivity or is even unknown, only with limited datasets), the semianalytical method will no longer be applicable. In dealing with such problems, PH fitting is utilized in the proposed model, i.e., any distribution or general datasets are approximated as PH distributions using Expectation Maximization algorithms. Owing to the good properties in convolution of PH distributions, the time-dependent reliability can be evaluated conveniently. Numerical examples are given to demonstrate the efficiency of the model proposed, and its accuracy is verified by comparing the model results with those of Monte Carlo simulation. The interaction between the degradation process and the shock process is also modeled and displayed with an example and discussion.

Reliability analysis methods such as active learning Kriging surrogate model combined with simulation-based methods have been paid much attention in recent years. These techniques can reduce the computational cost to a certain extent. However, the computational burden may still be heavy for complex engineering problems. To address these issues, a Kriging-based important region sampling method is proposed for efficient reliability analysis. The new method is an improvement on the original active learning reliability method combining Kriging and Monte Carlo simulation (AK-MCS), and three strategies are developed to enhance the original method: 1) a new strategy, which is called the key point method, is utilized to define the initial design of experiment (DoE) instead of the Latin hypercube sampling; 2) the concept of dynamic important region/uncertain region and importance factor is proposed to avoid adding useless sample points to the DoE, which have little effect on the accuracy improvement of the Kriging model; 3) the redundant region is introduced to make the distance between the new and existed sample points be larger than a certain value and avoid the information redundancy caused by too close sample points. Five examples are utilized to demonstrate the efficiency and accuracy of this new method.

Performance and reliability of structures will deteriorate with the effects of loads, environment, and interior factors of materials. In this article, a novel cumulative damage model is developed for time-dependent reliability analysis of deteriorating structures. The deterioration is a combination of three stochastic processes: the gradual deterioration posed by aging effects, the sudden deterioration caused by transient loads, and the additional deterioration introduced by sustained loads. The aging effect is modeled as a gamma process, while the transient load is described by a Poisson process. The sustained load is modeled by a stationary binomial process and a Poisson square wave process, respectively. The load threshold for three different scenarios are all considered and applied to not only the transient loads but also the sustained loads. The time-dependent reliability of deteriorating structures is then evaluated based on this model via semi-analytical methods or numerical simulation methods. Three numerical examples and an example involving a natural gas pipeline are used to validate the effectiveness of the proposed model for computing the time-dependent reliability.