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ModeConv: A Novel Convolution for Distinguishing Anomalous and Normal Structural Behavior

Melanie Schaller, Daniel Schlör, Andreas Hotho

TL;DR

ModeConv introduces a modal graph convolutional layer that learns eigenmode representations from sensor-network data by using a complex-valued, SVD-based convolution coupled with modal transformation. Grounded in structural dynamics and PSD/covariance analysis, it aims to separate intrinsic structural modes from external disturbances for robust anomaly detection while reducing computational cost. Across two large SHM datasets, ModeConv variants (ModeConvFast and ModeConvLaplace) demonstrate strong anomaly-detection performance and favorable runtimes compared to standard GNN baselines and wrappers. The work highlights practical potential for real-time SHM and suggests broader applicability to vibration-driven domains beyond civil engineering.

Abstract

External influences such as traffic and environmental factors induce vibrations in structures, leading to material degradation over time. These vibrations result in cracks due to the material's lack of plasticity compromising structural integrity. Detecting such damage requires the installation of vibration sensors to capture the internal dynamics. However, distinguishing relevant eigenmodes from external noise necessitates the use of Deep Learning models. The detection of changes in eigenmodes can be used to anticipate these shifts in material properties and to discern between normal and anomalous structural behavior. Eigenmodes, representing characteristic vibration patterns, provide insights into structural dynamics and deviations from expected states. Thus, we propose ModeConv to automatically capture and analyze changes in eigenmodes, facilitating effective anomaly detection in structures and material properties. In the conducted experiments, ModeConv demonstrates computational efficiency improvements, resulting in reduced runtime for model calculations. The novel ModeConv neural network layer is tailored for temporal graph neural networks, in which every node represents one sensor. ModeConv employs a singular value decomposition based convolutional filter design for complex numbers and leverages modal transformation in lieu of Fourier or Laplace transformations in spectral graph convolutions. We include a mathematical complexity analysis illustrating the runtime reduction.

ModeConv: A Novel Convolution for Distinguishing Anomalous and Normal Structural Behavior

TL;DR

ModeConv introduces a modal graph convolutional layer that learns eigenmode representations from sensor-network data by using a complex-valued, SVD-based convolution coupled with modal transformation. Grounded in structural dynamics and PSD/covariance analysis, it aims to separate intrinsic structural modes from external disturbances for robust anomaly detection while reducing computational cost. Across two large SHM datasets, ModeConv variants (ModeConvFast and ModeConvLaplace) demonstrate strong anomaly-detection performance and favorable runtimes compared to standard GNN baselines and wrappers. The work highlights practical potential for real-time SHM and suggests broader applicability to vibration-driven domains beyond civil engineering.

Abstract

External influences such as traffic and environmental factors induce vibrations in structures, leading to material degradation over time. These vibrations result in cracks due to the material's lack of plasticity compromising structural integrity. Detecting such damage requires the installation of vibration sensors to capture the internal dynamics. However, distinguishing relevant eigenmodes from external noise necessitates the use of Deep Learning models. The detection of changes in eigenmodes can be used to anticipate these shifts in material properties and to discern between normal and anomalous structural behavior. Eigenmodes, representing characteristic vibration patterns, provide insights into structural dynamics and deviations from expected states. Thus, we propose ModeConv to automatically capture and analyze changes in eigenmodes, facilitating effective anomaly detection in structures and material properties. In the conducted experiments, ModeConv demonstrates computational efficiency improvements, resulting in reduced runtime for model calculations. The novel ModeConv neural network layer is tailored for temporal graph neural networks, in which every node represents one sensor. ModeConv employs a singular value decomposition based convolutional filter design for complex numbers and leverages modal transformation in lieu of Fourier or Laplace transformations in spectral graph convolutions. We include a mathematical complexity analysis illustrating the runtime reduction.
Paper Structure (28 sections, 22 equations, 10 figures, 12 tables, 1 algorithm)

This paper contains 28 sections, 22 equations, 10 figures, 12 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model categorisation within GNN taxonomy
  4. Benchmarking models
  5. Additional Benchmarking Models
  6. Physical Background
  7. Datasets
  8. Simulated Smart Bridge Dataset
  9. Luxemburg Dataset
  10. Data Preprocessing
  11. ModeConv Method
  12. Data Input
  13. Signal Block
  14. PDE Building Block
  15. Convolution Block
  16. ...and 13 more sections

Figures (10)

  • Figure 1: Visualization of ModeConv Concept: In the upper part starting from the left to the right the installed Sensor Network is showcased as a graph with sensors as nodes and the connections between them as edges; all nodes get the overlapping signal of free vibrations and external vibrations as input signal (showcased with two sinus curves in different frequencies here); these mixed signals are used as input for the covariance matrix; the covariance of signals is further used to calculate the Power Spectral Density (PSD) and the PSD matrix. In the lower part of the image starting from the left to the right again, the sensornodes are represented as mass points with a certain stiffness and damping, these parameters are used as input for the equation of motion in structural dynamics to calculate the matrix of frequency response functions; Then these two matrices are used together with the PSD matrix as input for the ModeConv Convolutional filter for complex numbers with the imaginary part as first dimension and the real part as second dimension. This filter is designed to automatically learn the Eigenmodes, which are the inherent free vibrations and filters out the external effects, that are not relevant to detect anomalies in the the structural behaviour.
  • Figure 2: Side view of the measurement cross sections freundt2020-09-30kuenstliche-messdaten.
  • Figure 3: Measurement cross-section of the simulated bridge structure freundt2020-09-30kuenstliche-messdaten.
  • Figure 4: Overview of the measurement setup in side view (upper view) and top viewer (lower part) with a, accelerometers in red; b, displacement sensors in green; c, temperature sensors in blue and d, shakers in yellow, schommer2017damage.
  • Figure 5: Overview over ModeConv building blocks with its A, ODE Block, B, Signal Block and C, Convolutional Block.
  • ...and 5 more figures