分片响应面法在随机振动响应分析中的应用

在分析结构的随机振动响应时,响应面法(Response Surface Method)可有效地降低随机仿真的计算代价。然而,当随机变量存在大变异系数时,传统的响应面法无法满足所要求的精度。分片响应面基于对随机变量变异系数进行合理分块的原则,缩小响应面的近似范围,并对分割后的响应面进行独立分析,从而提高了响应面在该空间的近似精度。首先采用分块响应面法结合蒙特卡洛MC抽样技术,以单质点振子模型的随机振动响应为算例,对分块响应面法的正确性进行验证。计算结果表明,在随机变量的变异系数不大时,分片响应面法的计算精度不低于传统响应面法,而当随机变量具有大变异系数时,分片响应面法的近似精度远高于传统响应面法。此外,以随机地震动作用下的桥墩随机振动为背景,将该方法进行了进一步地推广及应用。

The application of the slicing response surface method in stochastic vibration analysis

A hybrid method,which combining response surface method with Monte Carlo method,could reduce the computational cost of analysis of stochastic response of system.When the coefficient of variation is huge enough,the established response surface could not satisfy the requirement of calculation.The slicing technology is adopted to handle this situation.The section of responses can separate into several sub-sections,and every sub-section is solved independently.In this paper,some cases are computed.The accuracy of slicing response surface method is verified.The calculation results show that when the coefficient of variation of the random variable is small,the calculation accuracy of the piecewise response surface method is not lower than that of the traditional response surface method,and when the random variable has a large coefficient of variation,the approximate accuracy of the piecewise response surface method is much higher.In addition,based on the random vibration of the bridge pier under random ground motion as the background,the method is further popularized and applied.