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该文建立了分析大坝可靠度的计算方法。首先,使用Monte-Carlo法得到服从一定分布的随机参数,运用复合失效准则建立不同的功能函数,从而得出相应的功能函数的样本点。然后,采用二次多项式拟合相应的响应面。运用拉格朗日乘数法,将在响应面约束下求解设计验算点的非线性的约束最优化问题转化为解线性方程组问题,使用Jacobi迭代法求解线性方程组进行迭代。最后,使用二分法通过迭代得出拉格朗日乘子,反推出设计验算点,从而得出复合失效准则下大坝各个单元可靠度。取大坝各个单元可靠度的最小值作为其最终的可靠度。与常规求大坝各个单元可靠度的方法相比,该方法有其优点:一是中间过程不用求梯度,适用范围广;二是将非线性问题转化为线性问题进行求解,可以用于极限状态方程非线性程度较高的可靠度分析。
This paper establishes a method of calculating dam reliability. First, Monte-Carlo method is used to obtain random parameters which are subject to a certain distribution. Different composite functional criteria are established by using composite failure criteria, and the sample points of the corresponding functional functions are obtained. Then, the second order polynomial fit the corresponding response surface. The Lagrange multiplier method is used to transform the nonlinear constrained optimization problem solving the design checkpoint under the response surface constraint into a solution to the system of linear equations. Jacobi iterative method is used to solve the linear equations iteration. Finally, by using the dichotomy method, the Lagrange multiplier is obtained through iteration, and the design checkpoint is deduced to obtain the reliability of each unit of the dam under the composite failure criterion. Take the minimum reliability of each dam unit as its final reliability. Compared with the conventional method of obtaining the reliability of each unit of the dam, this method has its advantages: one is that the gradient is not required for the intermediate process and the application is wide; the other is that the nonlinear problem is transformed into a linear problem and can be used for the limit state Reliability Analysis of Higher Nonlinearity of Equations.