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Advanced Image Analysis for Learning Underlying Partial Differential Equations for Anomaly Identification

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Abstract

In this article, the authors adapt and utilize data-driven advanced image processing and machine learning techniques to identify the underlying dynamics and the model parameters for dynamic processes driven by partial differential equations (PDEs). Potential applications include non-destructive inspection for material crack detection using thermal imaging as well as real-time anomaly detection for process monitoring of three-dimensional printing applications. A neural network (NN) architecture is established that offers sufficient flexibility for spatial and temporal derivatives to capture the physical dependencies inherent in the process. Predictive capabilities are then established by propagating the process forward in time using the acquired model structure as well as individual parameter values. Moreover, deviations in the predicted values can be monitored in real time to detect potential process anomalies or perturbations. For concept development and validation, this article utilizes well-understood PDEs such as the homogeneous heat diffusion equation. Time series data governed by the heat equation representing a parabolic PDE is generated using high-fidelity simulations in order to construct the heat profile. Model structure and parameter identification are realized through a shallow residual convolutional NN. The learned model structure and associated parameters resemble a spatial convolution filter, which can be applied to the current heat profile to predict the diffusion behavior forward in time.
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Document Type: Research Article

Affiliations: 1: Department of Aerospace Engineering, The Pennsylvania State University, USA 2: Applied Research Lab, The Pennsylvania State University, USA

Publication date: March 1, 2020

This article was made available online on March 16, 2020 as a Fast Track article with title: "Advanced Image Analysis for Learning Underlying Partial Differential Equations for Anomaly Identification".

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  • The Journal of Imaging Science and Technology (JIST) is dedicated to the advancement of imaging science knowledge, the practical applications of such knowledge, and how imaging science relates to other fields of study. The pages of this journal are open to reports of new theoretical or experimental results, and to comprehensive reviews. Only original manuscripts that have not been previously published, nor currently submitted for publication elsewhere, should be submitted.

    IS&T's JIST-first publication option allows authors wishing to present their work at conferences, but have a journal citation for their paper, to submit a paper to JIST that follows the same rigorous peer-review vetting and publication process as traditional JIST articles, but with the benefit of a condensed time-to-publication time frame and guaranteed conference presentation slot.

    Please note: For purposes of its Digital Library content, IS&T defines Open Access as papers that will be downloadable in their entirety for free in perpetuity. Copyright restrictions on papers vary; see individual paper for details.

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