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基于合理选择试验点的位置,该文提出一种改进响应面方法。该方法首先在经过设计点的切平面上布置试验点,然后沿切平面法向量方向移动试验点,并利用设计点和先前试验点的信息布置加强试验点。所布置的试验点既对设计点附近区域给予足够重视,同时又考虑极限状态函数在设计点附近区域的变化趋势,进而提高响应面函数在设计点附近区域的拟合精度。在响应面函数的拟合过程中,该文方法能够保证响应面函数在设计点处是无误差的,进一步提高失效概率的评估精度。算例表明,对于显式和隐式极限状态函数,该方法均具有较好的效率和精度。
Based on the reasonable choice of the location of test points, this paper proposes an improved response surface method. The method first arranges the test point on the tangent plane passing through the design point, then moves the test point along the normal direction of the tangent plane and uses the information of the design point and the previous test point to arrange the reinforcement test point. The designed test points not only pay enough attention to the area around the design point, but also consider the trend of the limit state function in the area near the design point, and then improve the fitting accuracy of the response surface function in the area near the design point. In the process of fitting the response surface function, this method can ensure that the response surface function is error-free at the design point and further improve the evaluation accuracy of the failure probability. The example shows that this method has good efficiency and precision for the explicit and implicit limit state functions.