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A matrix-T approach to the sequential design of optimization experiments

机译：矩阵T方法用于优化实验的顺序设计

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摘要

A new approach to the sequential design of experiments for the rapid optimization of multiple response, multiple controllable factor processes is presented. The approach is Bayesian and is based on an approximation of the cost to go of the underlying dynamic programming formulation. The approximation is based on a matrix T posterior predictive density for the predicted responses over the length of the experimental horizon that allows the responses to be cross-correlated and/or correlated over time. The case of an unknown variance is addressed; the assumed models are linear in the parameters but can be nonlinear in the factors. It is shown that the proposed approach has dual-control features, initially probing the process to reduce the parameter uncertainties and eventually converging to the desired solution. The convergence of the proposed method is numerically studied and convergence conditions discussed. Performance comparisons are given with respect to a known-parameters controller, the efficient global optimization algorithm, popular in sequential optimization of deterministic engineering metamodels, and with respect to the classical use of response surface designs followed by an optimization step.
机译：提出了一种用于快速优化多响应，多可控因子过程的实验顺序设计的新方法。该方法是贝叶斯方法，是基于基本动态编程公式的运行成本的近似值。该近似基于在实验视野的长度上的预测响应的矩阵T后验预测密度，其允许响应随时间互相关和/或相关。解决了未知方差的情况；假设的模型在参数上是线性的，但在因子上可以是非线性的。结果表明，所提出的方法具有双重控制功能，首先探测该过程以减少参数不确定性，最后收敛到所需的解决方案。数值研究了该方法的收敛性，并讨论了收敛条件。针对已知参数控制器，有效的全局优化算法（在确定性工程元模型的顺序优化中流行）以及相对于响应面设计的经典用法（随后是优化步骤）进行了性能比较。

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