利用矩点估计法简化响应面可靠度指标的计算

针对响应面可靠度指标计算方法的缺陷,将罗森布鲁斯统计矩点估计法引入到经典响应面方法中对其进行改进。改进后响应面方法,考虑基本随机变量偏态情况,改变了模拟试验中随机变量抽样值的计算方法;直接采用了统计矩计算可靠度指标,使可靠度指标的计算在真实极限状态曲面的某些特殊点上进行;在计算过程中不需拟合近似极限状态曲面和对非线性方程进行线性化处理,不产生迭代误差和累积误差,计算过程简洁明了。最后分别利用改进的响应面方法和经典响应面方法分析了某一矿山大型工程的稳定可靠性,并以蒙特卡洛法计算结果作为准精确解进行了比较,计算结果满足工程要求。

SIMPLIFIED CALCULATION OF RELIABILITY INDEX IN RESPONSE SURFACE METHOD BY POINT ESTIMATION OF PROBABILITY MOMENT

To improve some deficiency of calculation of reliability index in response surface method (RSM), point estimation of probability moment deduced by Resonbluth was introduced into response surface method. Improved response surface method (IRSM) can take into account the departure degree for probability density curve of basic random variables when sampling. Calculation formula for the sample values of random variables was changed and the reliability degree index was calculated through probability moment in improved RSM. Some special points of real limit state curve surface was adopted when calculating reliability degree index in the IRSM. There are no need for linearization and fitting of approximate limit state function while calculating reliability degree index. Iterative and cumulate error of reliability degree index does not arise. Principle and calculation process of IRSM is much simpler than RSM. Stability reliability degree for surrounding rock of a large underground engineering was analyzed by ISRM and RSM and Monte-Carlo method respectively. Result calculated by Monte-Carlo was taken as a standard solution to show the accuracy of solution of IRSM. Comparison between the solutions of IRSM and RSM shows that result calculated by IRSM is more accurate than that of RSM. Accuracy of IRSM can meet engineering requirement. IRSM has both theoretical and practical value.