基于切平面布点的一种改进响应面方法

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。

AN ADAPTIVE RESPONSE SURFACE METHOD BASED ON THE SELECTION OF EXPERIMENTAL POINTS USING TANGENT PLANE

An improved response surface method is proposed based on a reasonable selection of experimental points. The experimental points are selected in a tangent plane through the design point, and these experimental points are moved along the normal vector of the tangent plane. The reinforced experimental points are selected by using the information of the design point and the experimental point selected previously. The experimental points of the proposed method focus on the design point and consider the trend of the limit state function (LSF) around the region of a design point, so that the fitting precision of a response surface function (RSF) to the LSF around the region of the design point is increased. In the process of the fitting of RSF, in order to improve the evaluation accuracy of failure probability, the proposed method can guarantee that there is no error between the RSF and LSF at the design point. Examples given have demonstrated the efficiency and the accuracy of the proposed method for both numerical and implicit LSFs.