Source-linked AI summary
Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks
Khemraj Shukla, Patricio Clark Di Leoni, James Blackshire, Daniel Sparkman, George Em Karniadakis
TL;DR
The paper addresses identifying and characterizing surface-breaking cracks from ultrasonic wavefield data when physical measurements are costly. It trains a physics-informed neural network using the acoustic wave equation and adaptive activation functions, recovering sound speed with 1% error and locating cracks through low-speed regions. The results also examine PCA preprocessing and data sub-sampling for this inverse problem.
Problem
The paper seeks to characterize surface-breaking cracks from ultrasonic surface acoustic wave data in an ill-posed setting where physical-system data can be costly to acquire.
Method
The study trains a PINN on laser-vibrometry wavefield data while constraining learning with the acoustic wave equation and adaptive activation functions.
Results
1% error was achieved in sound-speed estimation, while space-dependent sound speed identified crack regions; PCA filtering reduced relative error from 24.80% to 17.88%.
Takeaways & Limitations
The resulting PINN provides a promising neural-network model for ultrasonic crack characterization and ill-posed inverse problems, including with sub-sampled data.
Takeaways & Limitations
The study uses a time-domain acoustic wave equation; frequency-domain modeling would be more useful for examining near-field and far-field crack interactions.
Abstract
from arXiv · showhide
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.
1 Introduction
The paper motivates PINNs for ultrasonic wavefield imaging because physical-system data can be costly to acquire and unconstrained machine-learning mappings can fail. It applies PINNs to characterize cracks from ultrasonic surface acoustic wave data.
- High data-acquisition costs can hinder machine-learning analysis of physical and biological systems.
- PINNs use governing physical laws as regularization to reduce the space of admissible solutions.
- Wavefield imaging uses scanning laser vibrometry to measure surface motions generated by stationary ultrasonic excitation.
- This study uses PINNs to characterize incipient crack damage from ultrasonic surface acoustic wavefields rather than relying primarily on visualization or time-series analysis.The method learns spatially varying sound speed v(x, y), with low-speed regions indicating crack locations and extent.
2 Ultrasonic surface acoustic wave data
The study uses laser vibrometry to collect spatially sampled surface-displacement wavefields from a cracked aluminum-alloy reference specimen. Snapshots compare wave propagation with and without crack effects at incidence angles of 0°, 45°, and 90°.
- Wavefield imaging measures out-of-plane particle displacements caused by elastic waves at spatial positions on a material surface.A focused laser vibrometry beam detects surface motions produced by a contact transducer.
- The dataset contains 2D time snapshots of out-of-plane surface acoustic-wave displacements on a regularized (x, y) grid.
- Measurements were acquired at incidence angles of 0°, 45°, and 90° using a NIST surface-breaking crack reference standard in 7075-T651 aluminum alloy.
- Figure 1 pairs particle-displacement snapshots with and without crack effects for each of the three incidence angles.
3 Problem setup and Physics Informed Neural Network (PINN)
The paper formulates crack characterization as an inverse problem governed by the acoustic wave equation, using PINNs to infer spatially varying sound speed from wavefield measurements. The workflow combines neural-network modeling, physics-based residuals, adaptive activation functions, and PCA-based data filtering.
- Problem formulation: Crack characterization is posed as learning the spatially varying sound speed v(x, y) from measured wavefield solution u(t, x, y).PINNs address this inverse problem by computing unknown PDE parameters or functions while using the governing equation as prior information.
- PINN formulation: The PINN approximates u(t, x, y) with a deep neural network and forms a residual f(t, x) from the acoustic wave equation using automatic differentiation.The residual network shares parameters with the solution network, while the Laplacian produces a different activation-function dependence.
- Loss and optimization: Training minimizes a mean-squared data loss together with a physics residual loss that enforces the acoustic wave equation.MSEu corresponds to measurement data, whereas MSEf enforces the structure imposed by the PDE residual.
- Crack characterization: A second neural network learns v(x, y), which is then supplied to the PINN to represent spatially varying wave speed for crack characterization.The model identifies crack-related regions through reduced wave speed associated with attenuation and scattering.
- Adaptive activation function: The adaptive activation function learns a scalable parameter a jointly with network weights and biases, steepening tanh and accelerating convergence.The parameter is optimized through the loss function, with a scale factor n ≥ 1 introduced to accommodate the learning factor.
- Data preconditioning: PCA filtering removes insignificant components while preserving dominant variance; for 45° data, the first 45 components retain approximately 95% of the variance.The filtered traces are smoother than raw traces, and the 0° case requires 15 components compared with 45 for 45° and 20 for 90° data.
4 Results
The PINN reconstructed ultrasonic wavefields and inferred spatially varying wave speeds that marked the crack as a low-speed zone across incidence angles. PCA filtering and substantial data sub-sampling retained useful reconstruction and crack visualization.
- 0° incidence: 2.9 mm/µs: the recovered global sound speed converged during training, while crack sensitivity appeared as a local speed decrease.This result was obtained while modeling back-scattered events from the crack.
- 90° incidence: The 90° incidence experiment used 120 snapshots sampled at 20% of domain points to recover wavefields and spatial wave-speed variation.The supplied passages describe the figure contents but do not report a numerical outcome for this case.
- 45° incidence: A low-speed zone of 0.5 mm/µs represented the crack in the 45° incidence spatial speed map.The PINN traces showed very good agreement with real data, and the loss reduced to 1% using 10% of the data.
- Data sub-sampling: 10% and 20% data produced very similar convergence, wavefield reconstructions, and convincing crack images in the sub-sampling experiment.The two cases used the same network architecture and hyperparameters as Figure 6.
5 Summary
The study characterizes the crack through low sound-speed regions inferred from ultrasonic wavefields. It notes a frequency-domain acoustic-wave formulation as more useful for studying near-field and far-field interactions.
- Crack characterization: The crack was delineated by the zone marked by low sound speed.The study used 5 MHz data and attributes the decrease to near-field interactions between the wavefield and crack.
- Scope and formulation: A frequency-domain acoustic wave equation would be more useful for studying near-field and far-field interactions than the time-domain formulation used here.The authors also state that dispersion was not a concern for the aluminum alloy at 5 MHz, though it could matter at much higher frequencies.
A Python code snippet of PCA process
The PCA code selects enough components to capture a variance threshold, then transforms the data into that reduced representation and reconstructs filtered wavefields.
- Component selection: The routine fits PCA with 240 components and cumulatively evaluates the explained variance to choose the component count.The selection compares cumulative variance against 95% of the maximum cumulative variance.
- Data reconstruction: The filtering routine transforms the input data into PCA coordinates and applies the inverse transform to reconstruct filtered data.The number of retained components is obtained from the component-selection routine.
B PCA filtered data acquired at 0o and 900
PCA filtering retains a compact set of components for reconstructing wavefield data at different incidence angles. The required component count is lower at 0° than at 90°.
- 0° incidence: 15 components reconstruct the 0° wavefield data after insignificant components are zeroed out.The figure describes PCA-based filtering of the acquired wavefield.
- 90° incidence: 20 components reconstruct the 90° wavefield data after insignificant components are zeroed out.The figure describes PCA-based filtering of the acquired wavefield.