[论文解读] Sensitivity analysis using the Metamodel of Optimal Prognosis

Thomas Most, Johannes Will|arXiv (Cornell University)|Aug 7, 2024

Fault Detection and Control Systems被引用 40

一句话总结

本论文提出 Metamodel of Optimal Prognosis (MOP)，一种将多项式回归与 Moving Least Squares 相结合、并使用 Coefficient of Prognosis (CoP) 的模型选择框架，自动识别全局敏感性分析和鲁棒性分析的最优子空间与元模型。

ABSTRACT

In real case applications within the virtual prototyping process, it is not always possible to reduce the complexity of the physical models and to obtain numerical models which can be solved quickly. Usually, every single numerical simulation takes hours or even days. Although the progresses in numerical methods and high performance computing, in such cases, it is not possible to explore various model configurations, hence efficient surrogate models are required. Generally the available meta-model techniques show several advantages and disadvantages depending on the investigated problem. In this paper we present an automatic approach for the selection of the optimal suitable meta-model for the actual problem. Together with an automatic reduction of the variable space using advanced filter techniques an efficient approximation is enabled also for high dimensional problems. This filter techniques enable a reduction of the high dimensional variable space to a much smaller subspace where meta-model-based sensitivity analyses are carried out to assess the influence of important variables and to identify the optimal subspace with corresponding surrogate model which enables the most accurate probabilistic analysis. For this purpose we investigate variance-based and moment-free sensitivity measures in combination with advanced meta-models as moving least squares and kriging.

研究动机与目标

• Motivate sensitivity analysis as a tool to reduce design variables and assess CAE solver behavior in industrial optimization.
• Introduce variance-based sensitivity measures and limitations of traditional meta-models in high dimensions.
• Propose the MOP framework to automatically select important inputs and suitable metamodels (polynomial or MLS).
• Show how CoP guides model quality assessment and subspace selection for robust optimization.

提出的方法

• Scan the input space using Monte Carlo or optimized Latin Hypercube Sampling to generate discrete realizations.
• Compare variance-based sensitivity indices (first order and total effect) and classical correlation metrics, highlighting limitations in high dimensions.
• Develop and employ polynomial regression and Moving Least Squares (MLS) metamodels, with CoD/Adjusted CoD and Coefficient of Prognosis (CoP) to assess fit.
• Introduce the Metamodel of Optimal Prognosis (MOP) that selects optimal variable subsets based on CoP and uses the chosen subspace with either polynomial or MLS basis.
• Compute total-effect sensitivity indices within the MOP to quantify variable importance, including interactions.
• Validate MOP via analytical nonlinear function and NVH automotive robustness case study; visualize 2D/3D subspace dependencies.

实验结果

研究问题

• RQ1 How can sensitivity analysis be performed efficiently in high-dimensional engineering problems without prohibitive sampling costs?
• RQ2 Can a model-independent quality measure (CoP) be used to automatically select the most relevant input subset and the suitable metamodel?
• RQ3 How does the MOP perform relative to Kriging, SVR, and ANN in terms of approximation quality under dimensionality increase?
• RQ4 What insights can CoP-derived subspaces provide for understanding solver behavior and robustness in industrial applications?

主要发现

• Variance-based methods require many simulations; meta-modeling aids reduce computational effort.
• MOP identifies an optimal subset of important variables and the best metamodel (polynomial or MLS) for accurate approximation.
• For the analytical test function, MLS with the three major variables achieved higher CoP than other combinations, demonstrating effective variable reduction.
• Compared to Kriging, SVR, and ANN, polynomial/MLS-based MOP generally avoids the curse of dimensionality and maintains higher approximation quality when focusing on important variables.
• In the NVH application, early convergence shows CoP around 90–97% with as few as 100 samples, and including additional variables improves the capture of interactions from ~5% to ~11%.
• MOP subspace visualizations help reveal nonlinear interactions and solver behavior, and CoP serves as an indicator for solver noise and model reliability.