MULTI-OBJECTIVES ROBUST COLLABORATIVE OPTIMIZATION BASED ON HYBRID SAPSO-SFLA FOR STRUCTURE WITH NON-NORMAL VARIABLES

To solve the reliability and its sensitivity for structural system whose implicit nonlinear performance function (PF) are complicated, changeable and of non-normal variables, the advantages of the saddlepoint approximation (SA) and line sampling (LS) are merged while the merits of dichotomy and the solution efficiency of the golden section method are combined to propose the saddlepoint approximation-line sampling method (SA-LS) based on the dichotomy of the golden section point. It is quick to find the zeropoint in PF corresponding to each sample along the important line sampling direction by the dichotomy above so that the structural failure probability can be transformed into the mean of a series linear PF failure probability, by which reliability sensitivity can be solved, thus the multi-objectives are inferred about the reliability sensitivity of failure probability with respect to the variables mean and variance and optimal economic indicator, such as volume. The collaborative optimization idea for multi-objectives is proposed to overcome the problem that it is difficult to converge for multi-objectives to be collaboratively optimized because of the errors when the RS is used as an objective function. To increase the convergence of the algorithm, the particle swarm optimization (PSO) algorithm and shuffled frog-leaping algorithm (SFLA) are hybridized after they are modified, and then the hybrid algorithm is applied to answer the foregoing multi-objectives. Examples show that: 1) the SPLSM based on the dichotomy of the golden section point is of high precision and fast velocity; 2) the convergence velocity of the proposed hybrid SAPSO-SFLA is superior to that of the modified PSO and SFLA, and its robustness can reduce the volume of the planet reducer gearbox in shield turning machine by 8.42%.