Structural reliability assessment by salp swarm algorithm–based FORM

Abstract

The first-order reliability method (FORM) is well recognized as an efficient approach for reliability analysis. Rooted in considering the reliability problem as a constrained optimization of a function, the traditional FORM makes use of gradient-based optimization techniques to solve it. However, the gradient-based optimization techniques may result in local convergence or even divergence for the highly nonlinear or high-dimensional performance function. In this paper, a hybrid method combining the Salp Swarm Algorithm (SSA) and FORM is presented. In the proposed method, a Lagrangian objective function is constructed by the exterior penalty function method to facilitate meta-heuristic optimization strategies. Then, SSA with strong global optimization ability for highly nonlinear and high-dimensional problems is utilized to solve the Lagrangian objective function. In this regard, the proposed SSA-FORM is able to overcome the limitations of FORM including local convergence and divergence. Finally, the accuracy and efficiency of the proposed SSA-FORM are compared with two gradient-based FORMs and several heuristic-based FORMs through eight numerical examples. The results show that the proposed SSA-FORM can be generally applied for reliability analysis involving low-dimensional, high-dimensional, and implicit performance functions. KEYWORDS first-order reliability method, high-dimensional problem, meta-heuristic algorithm, reliability analysis, Salp Swarm Algorithm 1224

Breadth-First Search Multi-Dimensional Binary Search Tree based Algorithms for Structural

“…Compared to methods following the three afore-mentioned three clues, methods emphasize on searching algorithms seem more efficient and accurate, which are realized by regulating the sampling process strategically through some algorithms. The family of searching algorithms for structural reliability is board and varied, in which some of the heuristic ones are directional divisions [34][35][36][37], swarm algorithms [38,39], genetic algorithms [40][41][42], gradient or difference-based algorithms [43,44], etc. Yet, further improvements on searching algorithms with respect to the following aspects are always welcomed: 1, maximizing computational efficiency by minimizing the number of redundant samplings; 2, increasing robustness by adapting to a board type range of PFs; 3, stabilization of the convergence rate; 4, customization for different engineering cases according to the requirement of accuracy.…”

An improved reliability index based on regional equivalent conversion

“…Reliability solving is converted into computing probability distribution of the function composed of these variables. As a classic reliability model, the mathematical expression of probabilistic reliability model is a multi‐integrals as follows 2 : $$\begin{equation} {P_f} = \mathop \int \limits_{g( x ) \le 0} {f_X}( {x,{\theta _x}} )dx \end{equation}$$where $${P_f}$$ represents the probability of failure, $$x = ( {{x_1},{x_2}, \ldots ,{x_n}} )$$ is the basic variable. $${\theta _x}$$ is its distribution parameter, and the random uncertainty of the basic variable is described by the probability density function $${f_X}( {x,{\theta _x}} )$$.…”

“…For problems with highly nonlinear limit state function, meta‐heuristic algorithms are often used to solve the FORM. For example, Zhong et al 2,20 . proposed FORM combining Harris Hawks Optimization (HHO‐FORM) 21 and FORM combining Salp Swarm Algorithm (SSA‐FORM) to realize the effective solution of high‐dimensional problems.…”

“…Reliability solving is converted into computing probability distribution of the function composed of these variables. As a classic reliability model, the mathematical expression of probabilistic reliability model is a multi-integrals as follows 2 :…”

“…For problems with highly nonlinear limit state function, meta-heuristic algorithms are often used to solve the FORM. For example, Zhong et al 2,20 proposed FORM combining Harris Hawks Optimization (HHO-FORM) 21 and FORM combining Salp Swarm Algorithm (SSA-FORM) to realize the effective solution of high-dimensional problems. Hasofer-Lind 22 proposed AFOSM, which expands the point with the largest probability of failure, namely the Most Probable Point (MPP) through Taylor's formula and take a linear approximation.…”