Improved response surface method of reliability analysis based on efficient search method
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摘要:
针对结构可靠性计算中广泛应用的响应面法计算量大、迭代效率低等问题，提出了一种基于样本点混合加权和可靠性指标变向搜索的改进响应面法。首先，在传统响应面法的权数选取策略基础上，构建一种考虑样本点与设计点距离和样本点极限状态函数值大小的混合加权方法。然后，对每次响应面迭代求解过程中，由于传统一次二阶矩方法求解效率低等问题，基于变向搜索算法，实现对每一次响应面迭代过程中设计点的有效搜索。算例表明，在一定的计算精度下，所提方法具有很好的收敛性，且大幅减少迭代次数，可以获取高精度的最大失效点和可靠性指标。
Abstract:Aimed at the problems of large amount of calculation and low iteration efficiency of response surface method which is widely used in structural reliability calculation, an improved response surface method based on hybrid weighting of sample points and variable-direction search of reliability index is proposed. Firstly, based on the weight selection strategy of the traditional response surface function, a hybrid weighting method considering not only the distance between the sample point and the design point but also the limit-state-function value of the sample point is constructed. Secondly, due to the inefficiency problem of the traditional first-order second-moment method in each iteration of response surface, an effective search of design points based on the variable-direction search algorithm in each iteration process of response surface is realized. The numerical examples show that the method has good convergence and greatly reduces the number of iterations under certain calculation accuracy. And the maximum failure point and reliability index can be obtained accurately.
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图 1 实验点权值计算示意图
Figure 1. Schematic diagram of weight calculation of experimental point
图 4 改进响应面法求解迭代过程(算例1)
Figure 4. Solving iterative process of improved response surface method in Example 1
图 5 失效概率计算结果比较(算例1)
Figure 5. Comparison of failure probability calculation results in Example name-style="western"
图 6 改进响应面法求解迭代过程(算例2)
Figure 6. Solving iterative process of improved response surface method in Example 2
图 7 失效概率计算结果比较(算例2)
Figure 7. Comparison of failure probability calculation results in Example 2
图 9 改进后响应面法求解迭代过程(算例3)
Figure 9. Solving iterative process of improved response surface method in Example 3
图 10 失效概率计算结果比较(算例3)
Figure 10. Comparison of failure probability calculation results in Example 3
表 1 算例1计算结果比较
Table 1. Comparison of calculation results in Example 1
方法 失效概率 误差/% 调用极限状态函数次数 计算时间/s 直接蒙特卡罗法 0.007 575 3 0 传统响应面法 不收敛 单权值改进响应面法 0.007 575 3 0 10 0.027 本文方法 0.007 575 3 0 10 0.026 
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表 2 算例2中随机变量统计信息
Table 2. Statistic information of random variables in Example 2
变量 分布形式 均值 标准差 x1 对数正态 120 12 x2 对数正态 120 12 x3 对数正态 120 12 x4 对数正态 120 12 x5 对数正态 50 15 x6 对数正态 40 12
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表 3 算例2计算结果比较
Table 3. Comparison of calculation results in Example 2
方法 失效概率 误差/% 调用极限状态函数次数 计算时间/s 直接蒙特卡罗法 0.012 22 0 传统响应面法 0.012 066 1.26 364 0.156 单权值改进响应面法 0.011 66 4.58 351 0.164 本文方法 0.012 325 0.86 286 0.119
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表 4 算例3计算结果比较
Table 4. Comparison of calculation results in Example 3
方法 失效概率 误差/% 调用极限状态函数次数 计算时间/s 直接蒙特卡罗法 0.836 27 0 传统响应面法 0.836 41 0.016 74 196 0.052 单权值改进响应面法 0.838 17 0.022 72 28 0.036 本文方法 0.836 32 0.005 98 49 0.039
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