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Reduced Sampling For construction Of Quadratic response Surface Approximations using Adaptive Experimental Design

机译：使用自适应实验设计减少构造二次响应曲面逼近的采样

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Purpose - To reduce the computational complexity per step from O(n~2) to O(n) for optimization based on quadratic surrogates, where n is the number of design variables. Design/methodology/approach - Applying nonlinear optimization strategies directly to complex multidisciplinary systems can be prohibitively expensive when the complexity of the simulation codes is large. Increasingly, response surface approximations (RSAs), and specifically quadratic approximations, are being integrated with nonlinear optimizers in order to reduce the CPU time required for the optimization of complex multidisciplinary systems. For evaluation by the optimizer, RSAs provide a computationally inexpensive lower fidelity representation of the system performance. The curse of dimensionality is a major drawback in the implementation of these approximations as the amount of required data grows quadratically with the number n of design variables in the problem. In this paper a novel technique to reduce the magnitude of the sampling from O(n~2) to O(n) is presented. Findings - The technique uses prior information to approximate the eigenvectors of the Hessian matrix of the RSA and only requires the eigenvalues to be computed by response surface techniques. The technique is implemented in a sequential approximate optimization algorithm and applied to engineering problems of variable size and characteristics. Results demonstrate that a reduction in the data required per step from O(n~2 ) to O(n) points can be accomplished without significantly compromising the performance of the optimization algorithm. Originality/value - A reduction in the time (number of system analyses) required per step from O(n~2) to O(n) is significant, even more so as n increases. The novelty lies in how only O(n) system analyses can be used to approximate a Hessian matrix whose estimation normally requires O(n~2) system analyses.
机译：目的-将阶跃运算的运算复杂度从O（n〜2）降低到O（n），以便基于二次代理进行优化，其中n是设计变量的数量。设计/方法/方法-当模拟代码的复杂性很大时，直接将非线性优化策略应用于复杂的多学科系统可能会非常昂贵。为了减少复杂多学科系统的优化所需的CPU时间，越来越多地将响应面近似（RSA）（特别是二次近似）与非线性优化器集成在一起。为了由优化程序进行评估，RSA提供了系统性能的计算成本低廉的低保真度表示。维度的诅咒是实现这些近似值的主要缺点，因为所需数据量随着问题中设计变量的数量n呈二次方增长。本文提出了一种将采样量从O（n〜2）减小到O（n）的新技术。结果-该技术使用先验信息来近似RSA的Hessian矩阵的特征向量，并且仅需要通过响应面技术来计算特征值。该技术在顺序近似优化算法中实现，并应用于可变大小和特征的工程问题。结果表明，在不显着影响优化算法性能的情况下，可以将每步所需的数据从O（n〜2）减少到O（n）点。创意/价值-从O（n〜2）到O（n）每步所需的时间（系统分析次数）的减少是显着的，甚至随着n的增加而减少。新颖之处在于，只有O（n）系统分析才能用于近似估计其估计通常需要O（n〜2）系统分析的Hessian矩阵。

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