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Uncertainty Aware Deep Neural Network for Multistatic Localization with Application to Ultrasonic Structural Health Monitoring

Ishan D. Khurjekar, Joel B. Harley

TL;DR

This paper uses an uncertainty-aware deep neural network framework to learn robust localization models and represent uncertainty, and uses mixture density networks to generate damage location distributions based on training data uncertainty.

Abstract

Guided ultrasonic wave localization uses spatially distributed multistatic sensor arrays and generalized beamforming strategies to detect and locate damage across a structure. The propagation channel is often very complex. Methods can compare data with models of wave propagation to locate damage. Yet, environmental uncertainty (e.g., temperature or stress variations) often degrade accuracies. This paper uses an uncertainty-aware deep neural network framework to learn robust localization models and represent uncertainty. We use mixture density networks to generate damage location distributions based on training data uncertainty. This is in contrast with most localization methods, which output point estimates. We compare our approach with matched field processing (MFP), a generalized beamforming framework. The proposed approach achieves a localization error of 0.0625 m as compared to 0.1425 m with MFP when data has environmental uncertainty and noise. We also show that the predictive uncertainty scales as environmental uncertainty increases to provide a statistically meaningful metric for assessing localization accuracy.

Uncertainty Aware Deep Neural Network for Multistatic Localization with Application to Ultrasonic Structural Health Monitoring

TL;DR

This paper uses an uncertainty-aware deep neural network framework to learn robust localization models and represent uncertainty, and uses mixture density networks to generate damage location distributions based on training data uncertainty.

Abstract

Guided ultrasonic wave localization uses spatially distributed multistatic sensor arrays and generalized beamforming strategies to detect and locate damage across a structure. The propagation channel is often very complex. Methods can compare data with models of wave propagation to locate damage. Yet, environmental uncertainty (e.g., temperature or stress variations) often degrade accuracies. This paper uses an uncertainty-aware deep neural network framework to learn robust localization models and represent uncertainty. We use mixture density networks to generate damage location distributions based on training data uncertainty. This is in contrast with most localization methods, which output point estimates. We compare our approach with matched field processing (MFP), a generalized beamforming framework. The proposed approach achieves a localization error of 0.0625 m as compared to 0.1425 m with MFP when data has environmental uncertainty and noise. We also show that the predictive uncertainty scales as environmental uncertainty increases to provide a statistically meaningful metric for assessing localization accuracy.

Paper Structure

This paper contains 17 sections, 17 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Methodology: Uncertainty aware damage localization
  3. Localization Input Uncertainties
  4. Challenges with DNN-based Localization
  5. Addressing Challenges using Mixture Density Networks
  6. Damage Localization Mixture Density Network
  7. Matched Field Processing Comparison
  8. Simulation Setup
  9. Data Setup
  10. UR-Net implementation
  11. MFP Setup
  12. Results and Discussion
  13. Performance comparison at varying levels of noise
  14. Performance comparison at varying levels of uncertainty
  15. Representing predictive uncertainty with UR-net
  16. ...and 2 more sections

Figures (13)

  • Figure 1: Illustration of a Lamb wave impulse response, as defined by \ref{['lambwave']} for a distance $r$ = 0.5407 m. The function $\kappa_n(\omega)$ is defined by the solution of the Rayleigh-Lamb equation tian2014lamb for a 1 m by 1 m aluminum plate.
  • Figure 2: Ambiguity heatmap produced by MFP in presence of: (a) no uncertainty and (b) uncertainty in velocity (wavenumber distortion = 0.15) + 5dB noise
  • Figure 3: Damage localization example with a traditional DNN
  • Figure 4: Mixture density network
  • Figure 5: UR-Net Framework
  • ...and 8 more figures