Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks (2005.03596v1)

Abstract: We introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the learning process by adding the residuals of a system of Partial Differential Equations to the loss function. Our PINN is supervised with realistic ultrasonic surface acoustic wave data acquired at a frequency of 5 MHz. The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry. The PINN is physically informed by the acoustic wave equation and its convergence is sped up using adaptive activation functions. The adaptive activation function uses a scalable hyperparameter in the activation function, which is optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The usage of adaptive activation function significantly improves the convergence, notably observed in the current study. We use PINNs to estimate the speed of sound of the metal plate, which we do with an error of 1\%, and then, by allowing the speed of sound to be space dependent, we identify and characterize the crack as the positions where the speed of sound has decreased. Our study also shows the effect of sub-sampling of the data on the sensitivity of sound speed estimates. More broadly, the resulting model shows a promising deep neural network model for ill-posed inverse problems.

• The paper introduces a physics-informed neural network (PINN) that integrates acoustic wave equations with ultrasonic data for non-destructive quantification of surface-breaking cracks.
• The PINN uses adaptive activation functions and a two-network structure to estimate wave speeds with high accuracy, achieving roughly 1% error in experiments.
• This PINN method significantly reduces data requirements (10-20%) while maintaining reliability, offering a robust tool for non-destructive testing in material science.

Overview of Physics-Informed Neural Networks for Ultrasonic Crack Quantification

The paper introduces an effective application of Physics-Informed Neural Networks (PINNs) tailored for the non-destructive quantification of surface-breaking cracks in metal plates using ultrasonic waves. This paper focuses on the innovative use of PINNs, which integrate data-driven models with physical equations to enhance learning efficiency in identifying cracks through ultrasonic measurements. The datasets employed consist of realistic surface wave data for an aluminum alloy captured at a 5 MHz frequency and analyzed through laser vibrometry techniques.

PINNs, as discussed in this paper, leverage the acoustic wave equation to incorporate physical laws directly within the loss function. This integration ensures that the learning model remains grounded in real-world physics while processing the ultrasonic data. The central aim is to map variations in the speed of sound through space to detect zones where fractures cause significant attenuation, effectively revealing the crack location and characteristics.

Technical Insights

The implementation of PINNs in this paper is characterized by several sophisticated methodologies:

1. Adaptive Activation Functions: Adaptive activation functions are used to dynamically alter the loss function's topology, which accelerates convergence. This approach provides a notable improvement in training efficiency compared to traditional activation functions.
2. Learning Framework: Two neural networks are employed wherein one estimates the spatially-dependent wave speed while the other models ultrasonic wave propagation. The composite structure allows the model to accurately detect regions of reduced sound speed indicative of fractures.
3. Data Processing: Innovative data preconditioning using Principal Component Analysis (PCA) efficiently isolates the essential components of ultrasonic data, effectively reducing noise and leading to a more precise modeling process.
4. Inverse Problem Approach: The identification of cracks is treated as an inverse problem. The model leverages the relationship between partial differential equations and the ultrasonic dataset to deduce the material's internal structure without entirely relying on extensive data acquisition.

Results

The experiments conducted with PINNs display exceptional accuracy in estimating wave speeds, with an error margin limited to roughly 1%. This precision underscores the model's robustness in tackling ill-posed problems. Moreover, the paper reports substantial effectiveness even with a reduced dataset, with data requirements minimized to 10-20% of the total available. This reduction in data intensity translates to significant logistical and financial savings while maintaining reliability in output.

The ability of the proposed PINN framework to reveal the location and extent of surface-breaking cracks through ultrasonic data opens new avenues in material science, particularly in non-destructive testing applications. The findings demonstrate the potential of PINNs as superior alternatives to traditional imaging or time-series analysis methods traditionally used in this domain.

Implications and Future Prospects

The overall contribution of this work lies in its ability to seamlessly combine data-driven frameworks with robust physical constraints, thereby reducing ambiguity and increasing model interpretability within a practical framework. This approach equips researchers with an expeditious tool for material analysis, potentially transforming practices in fields such as aerospace material evaluation and structural health monitoring.

Future developments might involve extending the PINN application to a broader range of materials or incorporating additional physical laws for more complex systems. Furthermore, enriching the model's versatility by integrating machine learning strategies that cater to fully three-dimensional data representations could yield even greater accuracy and insight into subsurface discontinuities.

This research serves as a robust foundation for employing PINNs in challenging inverse problems, highlighting their versatility and promising potential in delivering comprehensive solutions for non-destructive evaluation techniques.