基于多变量高斯过程模型的贝叶斯建模与稳健参数设计

针对模型预测偏差和波动的稳健参数设计问题,在多变量高斯过程(multivariate Gaussian process,MGP)建模的框架下,结合质量损失函数和非线性优化约束方法构建一个新的多响应优化模型.首先,利用成对估计方法获得超参数近似值,构建多变量高斯模型;其次,结合MGP模型特征,构造充分考虑响应波动因素的质量损失函数.利用蒙特卡罗模拟方法,获得响应落入指定区间的期望概率;然后,以期望概率为约束,结合本文所提质量损失函数建立优化模型;最后,利用全局优化算法进行寻优,获得考虑响应期望概率的优化结果.实际案例和软件仿真表明,该方法综合权衡了预测偏差和预测波动引起的不确定性对优化结果的影响.获得了兼顾质量损失和期望概率最优均衡解,从而实现稳健参数设计.

Bayesian modeling and robust parameter design based on multivariate Gaussian process model

For the robust parameter design problem of prediction deviation and variability, a new optimization model is constructed by combining the quality loss and Bayesian posterior estimation method under the framework of multivariate Gaussian process (MGP) modeling. Firstly, the hyperparameters are obtained by using the pairwise estimation method, and the MGP is constructed. Secondly, Monte Carlo simulation method is used to obtain the expected probability that the responses fall within the specified intervals. Then, the optimization model is established by using the quality loss function proposed in this paper with the expected probability as the constraint. Finally, the global optimization algorithm is used to perform global optimization, and the optimization results considering the expected probability are obtained. The example shows that proposed method comprehensively considers the impact of prediction deviation and variability on the optimization result. The optimal considering quality loss and expected probability is obtained, and realizing robust parameter design.