# A Multi-Head Attention Network for Fast Prediction of Ultrasonic Guided Wave Dispersion Under Coupled Temperature and Stress

## TL;DR

A new deep learning model predicts ultrasonic wave behavior under temperature and stress changes, enabling faster and more reliable sensor monitoring in extreme conditions.

## Contribution

The D-MHAN model offers a fast and accurate alternative to traditional methods for predicting ultrasonic wave dispersion under coupled temperature and stress.

## Key findings

- The D-MHAN model achieves a Pearson correlation coefficient of 0.9999 in predicting dispersion curves.
- The model is 30 times faster than SAFE and 168 times faster than WFEM methods.
- The model enables real-time compensation for environmental effects in ultrasonic sensors.

## Abstract

What are the main findings?
A Multi-Head Attention Network (D-MHAN) is proposed to accurately map eleven physical parameters to guided wave dispersion curves under coupled temperature–stress conditions, achieving a Pearson correlation coefficient of 0.9999.The deep learning model achieves computational speeds approximately 30 and 168 times faster than the Semi-Analytical Finite Element (SAFE) and Wave Finite Element Method (WFEM) approaches, respectively.

A Multi-Head Attention Network (D-MHAN) is proposed to accurately map eleven physical parameters to guided wave dispersion curves under coupled temperature–stress conditions, achieving a Pearson correlation coefficient of 0.9999.

The deep learning model achieves computational speeds approximately 30 and 168 times faster than the Semi-Analytical Finite Element (SAFE) and Wave Finite Element Method (WFEM) approaches, respectively.

What are the implications of the main findings?
The millisecond-level prediction capability overcomes the computational bottleneck of traditional methods, enabling real-time environmental effect compensation and calibration for ultrasonic sensors.The quantified parameter sensitivity analysis provides a theoretical basis for selecting optimal sensor wave modes to enhance monitoring robustness in extreme environments.

The millisecond-level prediction capability overcomes the computational bottleneck of traditional methods, enabling real-time environmental effect compensation and calibration for ultrasonic sensors.

The quantified parameter sensitivity analysis provides a theoretical basis for selecting optimal sensor wave modes to enhance monitoring robustness in extreme environments.

Ultrasonic guided wave sensors are widely employed for structural health monitoring; yet, their signal interpretation reliability is frequently compromised in extreme environments where coupled temperature and stress induce significant nonlinear drifts in dispersion characteristics. To overcome the computational bottleneck of conventional numerical methods that hinders real-time sensor calibration, this paper proposes a Dispersion Multi-Head Attention Network (D-MHAN) that directly maps eleven raw physical parameters to full-band dispersion responses. By adopting a non-normalized input strategy to internalize underlying physical laws, the model enables robust out-of-distribution extrapolation even when material properties exceed the training manifold. It was validated against a high-fidelity dataset spanning temperatures from −250 °C to 100 °C and stresses from 0 to 150 MPa generated by the Semi-Analytical Finite Element (SAFE) method. The proposed D-MHAN achieves a Pearson correlation coefficient of 0.9999 and provides computational speeds approximately 30 and 168 times faster than SAFE and the Wave Finite Element Method (WFEM). The model’s practical utility is further corroborated by cryogenic experiments on an aerospace storage tank. This work establishes a critical foundation for real-time parameter sensitivity analysis and environmental effect compensation in practical ultrasonic sensing applications.