Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression
Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression
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DOI：
10.4208/cicp.oa-2020-0151
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Yixiang Deng;Guang Lin;Xiu Yang
中科院分区：
文献类型：
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作者：
Yixiang Deng;Guang Lin;Xiu Yang
提出一种基于多保真高斯过程回归（GPR）框架的数据融合方法。该方法将现有的感兴趣量（qi）数据及其梯度与不同保真度相结合，即梯度增强Cokriging方法（GE-Cokriging）。它同时提供了qi及其梯度的近似值和不确定性估计。我们将该方法与不使用梯度信息的传统多保真度Cokriging方法进行了比较，结果表明GE-Cokriging方法在预测qi及其梯度方面都具有更好的性能。此外，GE-Cokriging甚至在一些由于协方差矩阵的奇异性而导致Cokriging表现不佳的情况下显示出更好的泛化效果。我们展示了GE-Cokriging在几个实际案例中的应用，包括同时重建欠阻尼振荡器的轨迹和速度，以及研究大型电力系统中负载母线的功率因数对发电机母线输入功率变化的敏感性。我们还表明，虽然GE-Cokriging方法比Cokriging方法需要更高的计算成本，但精度比较的结果表明，这种成本通常是值得的。
We propose a data fusion method based on multi-fidelity Gaussian process regression (GPR) framework. This method combines available data of the quantity of interest (QoI) and its gradients with different fidelity levels, namely, it is a Gradient-enhanced Cokriging method (GE-Cokriging). It provides the approximations of both the QoI and its gradients simultaneously with uncertainty estimates. We compare this method with the conventional multi-fidelity Cokriging method that does not use gradients information, and the result suggests that GE-Cokriging has a better performance in predicting both QoI and its gradients. Moreover, GE-Cokriging even shows better generalization result in some cases where Cokriging performs poorly due to the singularity of the covariance matrix. We demonstrate the application of GE-Cokriging in several practical cases including reconstructing the trajectories and velocity of an underdamped oscillator with respect to time simultaneously, and investigating the sensitivity of power factor of a load bus with respect to varying power inputs of a generator bus in a large scale power system. We also show that though GE-Cokriging method requires a little bit higher computational cost than Cokriging method, the result of accuracy comparison shows that this cost is usually worth it.