粒子群优化的Kriging近似模型及其在可靠性分析中的应用

Particle swarm optimized Kriging approximate model and its application to reliability analysis

将粒子群优化(PSO)算法引入Kriging建模过程,依靠PSO算法的群体搜索能力克服了模式搜索法单点序列搜索方式的局限性以及严重依赖于初猜解的缺点,保证了在任意初始条件下都能获取极大似然意义下的最优相关参数,从而有效确保了Kriging预测结果的最优无偏性.涡轮盘低循环疲劳可靠性分析实例表明,粒子群优化的Kriging(PSO-Kriging)近似模型对危险点周向应变变程的预测精度相对神经网络有数量级上的优势(最大误差由5.94%降低到0.09%),可不牺牲精度地代替有限元程序进行Monte Carlo模拟;同时PSO-Kriging建模与预测的总时间不及一次有限元分析的1/10.由于预测精度高(其最优无偏性由PSO算法保证)且计算开销不大,提出的PSO-Kriging对于实际工程结构的可靠性分析有一定应用价值.

Particle swarm optimization（PSO） algorithm was introduced into Kriging modeling process.By taking advantage of PSO’s multi-point search ability,the limits of pattern search method’s single-point search approach as well as its heavy dependence on the initial guess solution were overcome,so that the optimal correlation parameters in the maximum likelihood sense could be guaranteed under any initial conditions,and the optimal unbiased characteristic for the Kriging prediction could also be assured.A turbine disk low cycle fatigue（LCF）reliability analysis example indicates that the accuracy of the proposed PSO-Kriging in predicting the circumferential strain amplitude of the weakest point is higher than that of neural network on the order of magnitude,i.e.the maximum error decreases from 5.94% to 0.09%,so that it can replace the finite element program in Monte Carlo simulation without sacrificing the accuracy.Meanwhile,the time for PSO-Kriging’s modeling and predicting is less than 1/10 consumed by a single finite element run.Due to high-accuracy prediction（the optimal unbiased characteristic assured by PSO） and relative low expense,the proposed PSO-Kriging is valuable for the reliability analysis of real engineering structures.