Session: 01-10-01: Machine Learning, Artificial Intelligence, and Deep Learning in Dynamics, Vibrations, and Control

Paper Number: 164572

Reduced-Order Modeling of Structural Panels for Random Vibrations Using Proper Orthogonal Decomposition and Radial Basis Function Interpolation 

Structural panels in aerospace, automotive, and mechanical systems are often subjected to random vibrations due to unpredictable aerodynamic forces, acoustic excitations, and turbulent boundary layers. Accurately predicting these stochastic responses is crucial for ensuring the structural integrity and performance of these systems. While high-fidelity computational techniques such as finite element analysis (FEA) provide detailed insights into the dynamic behavior of such structures, they are computationally prohibitive for large-scale simulations, especially in applications requiring real-time analysis or extensive parametric studies. To address this challenge, this study develops a Reduced-Order Modeling (ROM) framework that integrates Proper Orthogonal Decomposition (POD) with Radial Basis Function (RBF) interpolation to efficiently analyze and predict the response of panels subjected to random excitations.

The methodology consists of two key components. First, POD is applied to extract the most significant spatial modes from high-fidelity numerical simulations, effectively reducing the dimensionality of the problem while preserving essential system dynamics. By retaining only a small number of dominant modes, POD enables a substantial reduction in computational complexity. Second, RBF interpolation is employed to reconstruct system responses across a range of stochastic loading conditions without requiring additional full-order simulations. This allows the model to generalize effectively and predict the structural response under varying excitation conditions with minimal computational effort.

To validate the performance of the proposed POD-RBF ROM framework, a series of computational experiments are conducted on aerospace-grade structural panels subjected to broadband random vibrations. The reference solutions obtained from full-scale finite element simulations serve as the training dataset for the reduced-order model. The results demonstrate that the POD-RBF method achieves a computational time reduction of approximately 90% compared to conventional FEA while maintaining high predictive accuracy. The error in spectral response predictions remains below 2%, indicating that the reduced-order model successfully captures the essential vibration characteristics of the panel. Furthermore, the framework is extended to evaluate the influence of design parameters such as material properties and geometric variations, showcasing its capability for rapid parametric analysis and optimization.

The key contribution of this study is the development of an efficient and adaptable reduced-order modeling approach for analyzing stochastic vibrations in structural panels. Unlike traditional ROM techniques that rely solely on modal truncation, the POD-RBF approach enhances flexibility and interpolation accuracy, making it well-suited for applications involving varying boundary conditions and uncertain loading environments. The ability to generate accurate response predictions in real time has significant implications for structural health monitoring, digital twin applications, and design optimization. By leveraging this ROM framework, engineers can perform rapid design iterations and uncertainty quantification without the computational expense associated with full-scale numerical simulations.

In conclusion, this study demonstrates that the POD-RBF reduced-order modeling framework provides a computationally efficient and highly accurate solution for predicting the random vibration response of structural panels. The significant reduction in computational requirements, combined with its predictive capabilities, positions this approach as a valuable tool for engineers working with large-scale dynamic systems. Future work will focus on extending this framework to incorporate nonlinear structural dynamics, multi-scale modeling, and experimental validation through laboratory testing on composite panels. Additionally, efforts will be made to integrate the ROM methodology into real-time adaptive control systems for aerospace and mechanical structures. The findings of this study highlight the potential of reduced-order modeling to revolutionize the analysis of vibration-prone structures, enabling faster, more efficient, and more robust design processes in modern engineering applications.

Presenting Author: Jean Michel dhainaut Embry-Riddle Aeronautical University

Presenting Author Biography: Full professor of mechanical engineering

Authors:

Spencer Armstrong Embry Riddle Aeronautical Engineering
Jean Michel dhainaut Embry-Riddle Aeronautical University