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Modal Decomposition and Identification for a Population of Structures Using Physics-Informed Graph Neural Networks and Transformers

Xudong Jian, Kiran Bacsa, Gregory Duthé, Eleni Chatzi

TL;DR

A novel deep learning framework that integrates graph neural networks, transformers, and a physics-informed loss function to achieve modal decomposition and identification across a population of structures is presented.

Abstract

Modal identification is crucial for structural health monitoring and structural control, providing critical insights into structural dynamics and performance. This study presents a novel deep learning framework that integrates graph neural networks (GNNs), transformers, and a physics-informed loss function to achieve modal decomposition and identification across a population of structures. The transformer module decomposes multi-degrees-of-freedom (MDOF) structural dynamic measurements into single-degree-of-freedom (SDOF) modal responses, facilitating the identification of natural frequencies and damping ratios. Concurrently, the GNN captures the structural configurations and identifies mode shapes corresponding to the decomposed SDOF modal responses. The proposed model is trained in a purely physics-informed and unsupervised manner, leveraging modal decomposition theory and the independence of structural modes to guide learning without the need for labeled data. Validation through numerical simulations and laboratory experiments demonstrates its effectiveness in accurately decomposing dynamic responses and identifying modal properties from sparse structural dynamic measurements, regardless of variations in external loads or structural configurations. Comparative analyses against established modal identification techniques and model variations further underscore its superior performance, positioning it as a favorable approach for population-based structural health monitoring.

Modal Decomposition and Identification for a Population of Structures Using Physics-Informed Graph Neural Networks and Transformers

TL;DR

A novel deep learning framework that integrates graph neural networks, transformers, and a physics-informed loss function to achieve modal decomposition and identification across a population of structures is presented.

Abstract

Modal identification is crucial for structural health monitoring and structural control, providing critical insights into structural dynamics and performance. This study presents a novel deep learning framework that integrates graph neural networks (GNNs), transformers, and a physics-informed loss function to achieve modal decomposition and identification across a population of structures. The transformer module decomposes multi-degrees-of-freedom (MDOF) structural dynamic measurements into single-degree-of-freedom (SDOF) modal responses, facilitating the identification of natural frequencies and damping ratios. Concurrently, the GNN captures the structural configurations and identifies mode shapes corresponding to the decomposed SDOF modal responses. The proposed model is trained in a purely physics-informed and unsupervised manner, leveraging modal decomposition theory and the independence of structural modes to guide learning without the need for labeled data. Validation through numerical simulations and laboratory experiments demonstrates its effectiveness in accurately decomposing dynamic responses and identifying modal properties from sparse structural dynamic measurements, regardless of variations in external loads or structural configurations. Comparative analyses against established modal identification techniques and model variations further underscore its superior performance, positioning it as a favorable approach for population-based structural health monitoring.
Paper Structure (21 sections, 11 equations, 15 figures, 3 tables)

This paper contains 21 sections, 11 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Our Contributions
  5. Methodology
  6. Problem Statement
  7. Feature Propagation
  8. Model Architecture
  9. Physics-Informed Loss Function
  10. Framework
  11. Numerical Experiments
  12. Dataset Description
  13. Implementation Details
  14. Experimental Results
  15. Comparison against Classic Modal Identification Methods
  16. ...and 6 more sections

Figures (15)

  • Figure 1: Architecture of the proposed model, in which the input and output are highlighted in red, hidden features in yellow, and deep learning blocks in blue.
  • Figure 2: An example of the graph dataset used in this study. A truss structure can be naturally represented by an attributed graph, where node acceleration and mode shapes are node features, and modal responses are graph (global) features.
  • Figure 3: Framework of using the GNN-based model for population-based structural modal identification
  • Figure 4: Visualization of the simulated dataset: (a) Geometric configuration designed to approximate a population of simply-supported truss; (b) Representative truss samples from the dataset, displaying only nodes and elements.
  • Figure 5: Probability histograms of the modal properties for the first six modes of the 100 trusses: (a) Natural frequencies; (b) Damping ratios.
  • ...and 10 more figures