基于二参数寻优设计点的混合结构可靠性分析算法

Two-parameter Optimization Design Point-based Reliability Analysis Algorithm for Structures with Mixed Uncertainty

针对机械结构中既含随机变量又含区间变量的混合可靠性问题,提出一种基于二参数的混合可靠性分析算法。区间变量使可靠性分析问题变为双层优化问题,为降低双层优化模型对计算效率的影响,将其解耦为概率分析和区间分析高效循环序列迭代模型;在概率分析时,引入两个调整参数,分别控制搜索步长和搜索方向,以实现寻优设计点、保证收敛的稳定性及搜索效率;在区间分析时,将区间分析问题转化为方便求解的二次规划问题,并结合梯度投影法搜索区间最优点;通过两个案例分析,对所提算法的计算精度和效率进行验证。结果表明:该算法与蒙特卡洛抽样法相比,计算的最大失效概率相对误差均在5%以内,且函数调用次数在1 000次以内即可达到收敛;当功能函数非线性程度较高时,该算法同样具有较高的计算精度、效率及收敛稳定性。

A mixed reliability analysis algorithm based on two parameters is proposed for the mixed reliability problem of mechanical structure with random variables and interval variables. Interval variables make the reliability analysis problem become a double-loop optimization problem. In order to reduce the influence of double-loop optimization model on computational efficiency, it is decoupled into a high-efficiency sequence iterative model for probability and interval analysis. In order to optimize design point, two adjusting parameters are introduced to control the search step length and the search direction, respectively, in probability analysis, which ensures the convergence stability and the search efficiency. The interval analysis problem is transformed into a more solvable quadratic programming problem, and the gradient projection method is used to search for the interval optimum point. The analyzed results of two cases show that the relative error of maximun failure probability calculated by the proposed algorithm is within 5%, and the number of function calls can reach convergence within 1000 times compared with Monte Carlo sampling. When the performance function has a high degree of nonlinearity, the proposed algorithm also has high calculation accuracy, efficiency and convergence stability.