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Featured Application: The present study can provide an efficient sampling method for candidate points in the iteration process of active learning reliability analysis. In active learning reliability methods, an approximation of limit state function (LSF) with high precision is the key to accurately calculating the failure probability (Pf). However, existing sampling methods cannot guarantee that candidate samples can approach the LSF actively, which lowers the accuracy and stability of the results and causes excess computational effort. In this paper, a novel candidate samples-generating algorithm was proposed, by which a group of evenly distributed candidate points on the predicted LSF of performance function (either the real one or the surrogate model) could be obtained. In the proposed method, determination of LSF is considered as an optimization problem in which the absolute value of performance function was considered as objective function. After this, a normal search particle swarm optimization (NSPSO) was designed to deal with such problems, which consists of a normal search pattern and a multi-strategy framework that ensures the uniform distribution and diversity of the solution that intends to cover the optimal region. Four explicit performance functions and two engineering cases were employed to verify the effectiveness and accuracy of NSPSO sampling method. Four state-of-the-art multi-modal optimization algorithms were used as competitive methods. Analysis results show that the proposed method outperformed all competitive methods and can provide candidate samples that evenly distributed on the LSF. [ABSTRACT FROM AUTHOR]

In active learning reliability methods, an approximation of limit state function (LSF) with high precision is the key to accurately calculating the failure probability (Pf). However, existing sampling methods cannot guarantee that candidate samples can approach the LSF actively, which lowers the accuracy and stability of the results and causes excess computational effort. In this paper, a novel candidate samples-generating algorithm was proposed, by which a group of evenly distributed candidate points on the predicted LSF of performance function (either the real one or the surrogate model) could be obtained. In the proposed method, determination of LSF is considered as an optimization problem in which the absolute value of performance function was considered as objective function. After this, a normal search particle swarm optimization (NSPSO) was designed to deal with such problems, which consists of a normal search pattern and a multi-strategy framework that ensures the uniform distribution and diversity of the solution that intends to cover the optimal region. Four explicit performance functions and two engineering cases were employed to verify the effectiveness and accuracy of NSPSO sampling method. Four state-of-the-art multi-modal optimization algorithms were used as competitive methods. Analysis results show that the proposed method outperformed all competitive methods and can provide candidate samples that evenly distributed on the LSF.

Motivated by the limit state curve (LSC) finding problem in reliability analysis, a new category of optimization problems referred to as the regional-modal optimization problems (RMOPs) was investigated in this paper. The most distinguishing feature of RMOPs is the continuity of its solutions. Existing optimization methods are not capable of capturing this feature and thus cannot produce acceptable results for RMOPs. Therefore, based on niching PSO a normal search particle swarm optimization (NSPSO) algorithm that can provide discrete optimal solutions for a continuous optimal region with arbitrary pre-specified density was developed. NSPSO is consisting of a normal search pattern and a multi-strategy fusion. Normal searching is the core of NSPSO, in which each particle is guided by the normal vector of the region composed of its several best neighborhoods. Normal searching prevents the particles from clustering and thus provide a basis for the solution diversity. Further, a multi-strategy framework with three components was introduced to improve the performance of NSPSO. It includes a dynamic particle repulsion strategy that improve the solution diversity, a particle memory strategy to prevent local optimum, and an elite breeding strategy that was developed to increase the efficiency of the method. This framework gives NSPSO the ability to maintain the balance between exploitation and exploration and thereby to realize the uniform distribution and high coverage and diversity of the algorithm. Furthermore, the key parameters involved in NSPSO were analyzed thoroughly. The NSPSO is compared with ten state-of-the-art multi-mode optimization algorithms in terms of twenty typical test functions with different properties that were constructed in this study. The experimental results demonstrate the superiority of our proposed algorithm over the state-of-the-art algorithms in solving RMOPs. [ABSTRACT FROM AUTHOR]