The Bayesian network (BN) is an efficient tool for probabilistic modeling and causal inference, and it has gained considerable attentions in the field of reliability assessment. The common cause failure (CCF) is simultaneous failure of multiple elements in a system under a common cause, and it is a common phenomenon in engineering systems with dependent elements. Several models and methods have been proposed for modeling and assessment of complex systems with CCF. In this paper, a new reliability assessment method is proposed for the systems suffering from CCF in a dynamic environment. The CCF among components is characterized by a BN, which allows for bidirectional reasoning. A proportional hazards model is applied to capture the dynamic working environment of components and then the reliability function of the system is obtained. The proposed method is validated through an illustrative example, and some comparative studies are also presented.

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Wind power has been widely used in the past decade because of its safety and cleanness. Double fed induction generator (DFIG), as one of the most popular wind turbine generators, suffers from degradation. Therefore, reliability assessment for this type of generator is of great significance. The DFIG can be characterized as a multi-state system (MSS) whose components have more than two states. However, due to the limited data and/or vague judgments from experts, it is difficult to obtain the accurate values of the states and thus it inevitably contains epistemic uncertainty. In this paper, the fuzzy universal generating function (FUGF) method is utilized to conduct the reliability assessment of the DFIG by describing the states using fuzzy numbers. First, the fuzzy states of the DFIG system’s components are defined and the entire system state is calculated based the system structure function. Second, all components’ states are determined as triangular fuzzy numbers (TFN) according to experts’ experiences. Finally, the reliability assessment of the DFIG based on the FUGF is conducted.

This paper presents a novel algorithm for structural reliability analysis based on the finite step length and Armijo line search to remove the drawbacks of the Hasofer–Lind and Rakwitz–Fiessler (HL-RF) algorithm that may be subjected to non-convergence in the first-order reliability method (FORM). Initially, the sensitivity factor with finite step length is introduced for preventing the iterative process of the algorithm from entering a periodic loop. Subsequently, an optimization method based on the sufficient descent condition with the Armijo line search technique is proposed. With that, the initial step length and adjusting coefficient are optimized to enhance the applicability of the algorithm emphatically for highly nonlinear functions. A comparison analysis is carried out between the proposed algorithm and existing FORM-based algorithms to validate the robustness and efficiency of the proposed algorithm. The results of this demonstrate that the proposed algorithm is superior to the HL-RF algorithm in terms of robustness and surpass the other existing FORM-based algorithms in connection to efficiency.