Uncertainty Quantification Methods for Optimal Excitation Design in Parameter Identification

TL;DR

This paper introduces two uncertainty quantification-based methods for designing optimal system excitations to improve parameter identification in complex engineering models, validated through vehicle dynamics experiments.

Contribution

It develops an intrusive polynomial chaos expansion and a non-intrusive Wasserstein distance-based approach for efficient optimal excitation design.

Findings

Both methods significantly reduce computational costs.

Demonstrated improved parameter identification in vehicle models.

Validated effectiveness through experimental tests on a test vehicle.

Abstract

Parameter identification is crucial in virtual engineering processes, yet determining appropriate system excitations for identifying specific parameters remains challenging. In practice, extensive experimental programs often fail to generate data with sufficient information content for reliable parameter estimation. This work presents a systematic approach for deriving optimal excitations by maximizing the global sensitivity of target parameters across the space of possible excitation functions. To address the computational challenge of sensitivity evaluation during optimization, we develop two complementary approaches based on uncertainty quantification (UQ) methods. For systems with known mathematical structure, we present an intrusive polynomial chaos expansion (PCE) method that constructs deterministic surrogate models, enabling rapid sensitivity computation. For black-box models where intrusive approaches are not feasible, we introduce a novel non-intrusive method based on optimal transport theory, specifically using Wasserstein distances to quantify sensitivity measures without requiring knowledge of internal system dynamics. Both methods significantly reduce computational costs, making optimal excitation design practical for complex engineering systems. We demonstrate the effectiveness of both approaches on vehicle dynamics models, showing substantial improvements in parameter identification capability. The benefit for parameter identification is further validated experimentally on a test vehicle and compared to the state of the art.