Structural Reliability Analysis Method Based On Chaotic Colliding Bodies Optimization Algorithm

The uncertainty existing in engineering structures often affects the performance of the structure and even leads to the failure of the structure,endangering personal safety.Therefore,it is of extremely importance to analyze structural reliability to ensure that the structure can work normally during normal service.Structural reliability analysis consists of two levels,namely,component reliability analysis and system reliability analysis.After decades of theoretical research and engineering practice by researchers,the component reliability analysis methods have been reaching maturity,such as the First order and second moment method(FORM),Monte Carlo simulation,and Response surface method.As engineering structures become more complex,structural performance functions tend to be highly nonlinear or can only be expressed in implicit functions.Furthermore,the traditional methods are difficult to balance between computational accuracy and efficiency in component reliability analysis.Thus,it is still of great practical significance to find an efficient and high-precision reliability analysis method that enable to adapt to highly nonlinear and implicit functional functions.The meta-heuristic optimization algorithm,also known as the swarm intelligence optimization algorithm,is not only enable to solve the global optimization problem effectively,but also proves to be an effective FORM solving algorithm in structural reliability analysis.Enhanced colliding body optimization(ECBO)is a swarm intelligent optimization method featured by implementation simplicity and relatively fast convergence speed.Nevertheless,there is still some instability in the randomness of particles when solving optimization problems.Chaos is characterized by ergodicity,pseudo-randomness and irregularity.This paper combines ECBO algorithm with chaos theory to replace random number sequence with chaotic sequence and proposes a new meta-heuristic optimization algorithm-Chaotic enhanced colliding bodies optimization algorithm(CECBO).The novel algorithm uses chaotic map to change the particle generation mode,accelerates the convergence speed of particles and improves the stability of convergence.Therefore,a stable and efficient FORM reliability analysis method on CECBO algorithm at component level is established by using the penalty function mechanism.The numerical results show that the method has the advantages of fast convergence speed and high accuracy.A structural system consists of multiple components is connected in different ways,which are mainly divided into three categories: series system,parallel system and mixed system.Failure probability estimation of structural system is an important problem in system reliability analysis.Existing engineering structures are often of multiple failure mode and may expressed in complex highly nonlinear functional functions.Traditional system reliability analysis methods are difficult to calculate system failure probabilities accurately or even cannot be effectively evaluated.The excellent performance of the CECBO algorithm in component reliability analysis suggests its great potential in structural system reliability analysis.Therefore,this paper proposes an efficient and accurate method for calculating the failure probability of parallel systems integrating the CECBO algorithm with the FORM,namely,the CECBO-based FORM parallel system reliability analysis method.The reliability evaluation model of the parallel system is established according to the failure criterion of the parallel system.The CECBO algorithm is utilized to solve the evaluation model to find the maximum likelihood point of the structural system.Thus,the linear approximation of the failure domain of the parallel system is obtained and the parallel system failure probability is also calculated.For the mixed system,the local parallel system is equivalent to a single component via the CECBO-based FORM parallel system reliability analysis method and also the reliability index vector and reliability index of the equivalent component are given.The equivalent plane method is employed to calculate the failure probability of the equivalent series system when the mixed system is converted into a series system.Therefore,a new structural system reliability analysis method on CECBO-based FORM algorithm is established.The results of the example show that the proposed method show superiority in convergence speed and computation accuracy when evaluating the failure probability of structural system as well as suggest excellent engineering application prospects.