Efficient Response Surface Modeling by Using Moving Least-Squares Method and Sensitivity
Efficient Response Surface Modeling by Using Moving Least-Squares Method and Sensitivity
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DOI：
10.2514/1.12366
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发表时间：
2005-11
期刊：
影响因子：
2.5
通讯作者：
Chwail Kim;Semyun Wang;K. Choi
中科院分区：
文献类型：
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作者：
Chwail Kim;Semyun Wang;K. Choi
响应面法（RSM）目前已成为较知名的元建模技术之一。然而，它的近似误差对设计者施加了一些限制，因为经典的响应面法使用最小二乘法（LSM）从给定的函数数据中找到最佳拟合的近似模型。讨论了如何利用移动最小二乘法结合敏感性信息高效、准确地构建遥感模型。推导了采用MLSM的灵敏度公式。该方法在构造响应面时需要确定多个参数。对这些参数进行了参数研究和优化。但是，由于优化的不连续性问题，采用遗传算法。相关系数用于函数和梯度误差之间的归一化比较。此外，还应用倒数条件数来避免病态近似。给出了在逼近过程中的几个难点及相应的解决方法，并通过数值算例验证了该方法的精度和效率。如果每个采样点的灵敏度可以通过利用廉价的计算有效地计算，所提出的方法被认为是非常有效和准确的。
The response surface method (RSM) has currently become one of the better-known meta-modeling techniques. However, its approximation errors have placed several restrictions on designers as classical RSM uses the leastsquares method (LSM) to find the best-fitting approximation models from the given function data. We discuss how to construct RS models efficiently and accurately using the moving least-squares method (MLSM) combined with sensitivity information. The formulations for incorporating the sensitivity using the MLSM are derived. With this method, several parameters should be determined during the construction of response surfaces. The parametric study and optimization for these parameters are performed. However, because of the discontinuity problem of the optimization, a genetic algorithm is adopted. The correlation coefficient is used for the normalized comparison between the function and gradient errors. Also, the reciprocal condition number is applied to avoid illconditioned approximations. Several difficulties and their respective solutions during the approximation processes are described, and the numerical examples are then demonstrated to verify the accuracy and the efficiency of this method. If the sensitivity of each sampling point can be calculated efficiently by utilizing a cheap computation, the proposed method is recognized as very efficient and accurate.