Gradient-Based Optimization Method for Experimental Modal Parameter Estimation with Finite Element Model

Abstract

This paper presents a novel gradient-based optimization algorithm for improving the accuracy of experimentally estimated modal parameters with the assistance of finite element models. Initially, we recast the discrete vibration response equation into a matrix form and formulate the parameter estimation problem in modal analysis as an optimization problem. Then the problem is solved with a gradient-based iterative algorithm, which explicitly exhibits the closed form of gradients used in optimization. Initial values for this iteration are parameters derived from finite element models, since every important engineering structure should be analyzed with a finite element model before it is constructed. Subsequently, the performance of this algorithm is validated by both pure numerical experiments, which simulate the physical world, and experiments using real measurement data gathered by sensors in the real physical world. The algorithm’s performance is further enhanced by incorporating gradient clipping and an adaptive iteration threshold. As a comparison, a discussion on classical least-squares time-domain method for the problem is provided. For practical applications, the Shi–Tomasi corner detection and Lucas–Kanade optical flow methods are deployed to detect corner points from videos taken during the vibration of a structure and track the motion of these points in the videos.