【作者】 范文亮； 盛向前； 李敏；

【Author】 Fan Wenliang;Sheng Qiang;Li Min;College of Civil Engineering, Chongqing University;Key Laboratory of Mountainous Urban Construction and New Technology, Ministry of Education, Chongqing University;Chengdu Housing and Urban-Rural Development Bureau;

【机构】 重庆大学土木工程学院； 重庆大学山地城镇建设与新技术教育部重点实验室； 成都市住房和城乡建设局；

【摘要】 响应面法是结构可靠性评估的一种重要方法。然而,对于极限状态函数具有高度非线性时,其失效概率不仅与验算点有关也与样本点的选取有关,因此响应面在选取样本点时,需要考虑实际的极限状态函数的非线性发展趋势。因此为了提高响应面的拟合精度,并且在重点关注验算点的区域的同时兼顾稍远区域的选点方法,进而发展一类改进的响应面法。首先确定验算点;其次,采用线性内插(或外插)的方式确定各轴离极限状态曲面较近的点和改进的验算点,这些点均为有效点;分别增加各轴离曲面较近点与改进验算点的中点,并且由中点和均值点插值获得离极限曲面更近的补充有效点;由有效点回归分析确定响应面函数;确定新的验算点并通过插值得到改进验算点,由新的改进验算点和上一次补充有效点确定中点,并经插值得到新的补充有效点;由所有有效点回归分析确定响应面函数;依次类推,逐步迭代,直至收敛。最后,通过算例验证了该方法的精度和效率。更多还原

【Abstract】 The response surface method is an important method for structural reliability assessment. However, when the limit state function is highly nonlinear, its failure probability is not only related to the checkpoint but also to the selection of the sample points. Therefore, when selecting the sample points, the response surface needs to consider the nonlinear development trend of the actual limit state function. Therefore, in order to improve the fitting precision of the response surface, and focus on the area of the checkpoint while taking into account the selection method of the slightly distant area, an improved response surface method is developed. First, the checkpoint is determined; secondly, linear interpolation(or extrapolation) is used to determine the point where each axis is closer to the limit state surface and the improved checkpoint, which are all effective points; respectively increase the axes closer to the surface Point and improve the midpoint of the checkpoint, and obtain the complementary effective point closer to the limit surface by interpolation of the midpoint and the meanpoint; determine the response surface function by effective point regression analysis; determine the new checkpoint and obtain the improved checkpoint by interpolation The midpoint is determined by the new improved checkpoint and the last supplemental effective point, and a new supplementary effective point is obtained by interpolation; the response surface function is determined by all effective point regression analysis; and so on, and iteratively iterative until convergence. Finally, the accuracy and efficiency of the method are verified by an example.更多还原