结构可靠度计算的非均匀离散化发生函数法
Calculating Structural Reliability with Generation Function Method Based on Non-uniform Discretization

发生函数法是结构可靠性分析和多状态系统性能评估的重要工具，现有发生函数法存在计算效率低、计算精度差的问题。在发生函数法中提出非均匀离散化方法和近似项合并技术，即运用最优化方法求解安全裕度函数最危险点（最小值），以最危险点为中心对各变量按幂函数进行非均匀离散化，采取非等距直方图法计算各变量发生函数，检验离散效果是否达到最佳，最后计算系统可靠度值。发生函数的非均匀离散化方法在系统性能状态个数不变的情况下，提高了计算精度和效率，避免了增加系统性能状态个数带来的组合爆炸问题。新方法充分考虑了结构可靠度计算的误差形成机理和MATLAB编程的可行性，为涉及多变量非线性极限状态函数的结构可靠度快速、高效计算提供有效工具。
The generation function method is an important tool for structural reliability analysis and performance assessment of a multi-state system, but its computational efficiency and accuracy are poor. The non-uniform discretization method and the approximate merger technique are put forward. Firstly, the most dangerous point (minimum) of the safety margin function is obtained with the optimization method. Secondly, with the most dangerous point being at the center, each variable is non-uniformly discretized in accordance with the power function. Thirdly, variable generation functions are calculated by adopting the non-equidistant histogram method to test whether the discretization effect is optimal. Finally, the structural reliability is calculated. The generation function method not only improves its accuracy and efficiency but also avoids the combinatorial explosion under the condition that the number of the multi-state system's performance statuses does not change. The new method takes into consideration the error formation mechanism in calculating structural reliability and the MATLAB programming feasibility. It also provides an effective tool for the fast and efficient computation of the multi-variable nonlinear structural reliability with the finite-limit state function