Wavelet Decomposition Enhances Nonlinear Finite Element Model Updating for Structural Dynamics

A newly developed nonlinear finite element model updating method based on the wavelet decomposition of acceleration time history responses achieves satisfactory updating accuracy and robust noise tolerance, enabling the precise prediction of nonlinear structural dynamic behavior. While finite element models serve as standard computational tools for predicting structural dynamic behavior within structural health monitoring programs, real-world engineering structures frequently exhibit pronounced nonlinearities. These inherent nonlinear characteristics present substantial challenges to the fidelity and reliability of conventional linear or baseline finite element models.

To overcome the limitations of traditional updating approaches, the research introduces a specialized nonlinear finite element model updating framework that extracts robust dynamic response features directly from measured acceleration time histories using wavelet decomposition. By systematically processing the time history records, the method isolates and extracts low-frequency wavelet coefficients that serve as compact, representative features of nonlinear dynamic structural responses. This feature extraction strategy provides multiple simultaneous advantages for the updating procedure: it effectively compresses extensive sensor datasets to reduce overall data dimensionality, significantly enhances updating efficiency, and provides strong robustness against the ambient noise commonly encountered in structural measurements.

Addressing the formidable computational demands associated with repetitive finite element simulations during model updating, the proposed methodology incorporates a surrogate-assisted optimization strategy. Global sensitivity analysis using the Sobol method is first deployed to screen the system parameters and identify the specific nonlinear structural parameters that exert the greatest influence on the response features. Once the most sensitive nonlinear parameters are determined, they are integrated with the extracted low-frequency wavelet features to train and construct a Kriging surrogate model. This surrogate model acts as an accurate, computationally efficient substitute, effectively replacing the high-cost finite element model throughout the iterative nonlinear finite element model updating calculations.

The practical feasibility, computational performance, and noise tolerance of the proposed framework were systematically evaluated through comprehensive numerical studies on two distinct structural configurations. Numerical investigations were conducted on a simply supported beam as well as a multi-degree-of-freedom five-story reinforced concrete frame structure, with both benchmark models subjected to noisy response conditions. In the five-story reinforced concrete frame evaluation, the updating results were compared directly against an established reference method. This comparative analysis clearly demonstrated the superior performance of the wavelet-based updating method, confirming its ability to accurately identify nonlinear parameters and capture complex structural responses despite significant noise corruption.

To establish practical applicability beyond idealized numerical simulations, the authors conducted physical experimental validation on a laboratory three-story frame structure. The experimental testing demonstrated that the proposed method maintains satisfactory updating accuracy and noise robustness under real-world physical testing conditions. By successfully integrating wavelet-based acceleration decomposition, Sobol parameter sensitivity analysis, and Kriging surrogate modeling, the framework reliably updates structural parameters and enables the accurate prediction of nonlinear structural behavior in practical structural health monitoring and engineering vibration applications.

Subject of Research: Nonlinear finite element model updating in structural health monitoring

Article Title: Nonlinear model updating method based on wavelet decomposition of acceleration time history response

Article References: Cao, M., Peng, Z., Gu, J., & Hua, L. (2026). Nonlinear model updating method based on wavelet decomposition of acceleration time history response. Earthquake Engineering and Engineering Vibration, 25(4), 1137-1154. https://doi.org/10.1007/s11803-026-2425-x

Image Credits: AI Generated

DOI: 10.1007/s11803-026-2425-x

Keywords: finite element model updating, wavelet decomposition, acceleration time history, nonlinear dynamics, Sobol sensitivity analysis, Kriging surrogate model, structural health monitoring, noise robustness, Nonlinear, model, updating, method