Sensitivity analysis using the Metamodel of Optimal Prognosis

TL;DR

The paper tackles the challenge of performing global sensitivity analysis with expensive CAE simulations in high-dimensional design spaces. It introduces the Metamodel of Optimal Prognosis (MOP), a framework that automatically selects an optimal subspace and surrogate model (e.g., Polynomial or Moving Least Squares) by optimizing the Coefficient of Prognosis (CoP) quality metric, and uses advanced sampling (LHS) to robustly explore inputs. By combining CoP-based model selection with subspace filtering, MOP yields accurate sensitivity estimates (via $S_T^{MOP}$ and $CoP$) even in high dimensions and can visualize dependencies in 2D/3D subspaces, smoothing solver noise when needed. The NVH automotive example demonstrates practical benefits: identifying a small set of influential thicknesses among 46 parameters with relatively few simulations, outperforming traditional polynomial or MLS approaches, and providing actionable insights for robust design.

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.

Figures (12)

• Figure 1: Dimension reduction for a nonlinear function with five inputs based on Latin Hypercube Sampling (left) with 100 samples and full factorial design (right) with $3^5=243$ samples
• Figure 2: Subspace plot of the investigated nonlinear function and convergence of the CoD measures with increasing number of support points
• Figure 3: Local weighting of support point values (left) and influence of the influence radius $D$ on the smoothing of the MLS approximation function (right)
• Figure 4: Convergence of the CoP measure by using MLS approximation compared to the polynomial CoD measure
• Figure 5: CoP values of different input variable combinations and approximation methods obtained with the analytical nonlinear function