Deep Generative Modeling of Infrared Images Provides Signature of Cracking in Cross-Linked Polyethylene Pipe

Abstract

Hyperspectral infrared (IR) images contain a large amount of highly spatially resolved information about the chemical composition of a sample. However, the analysis of hyperspectral IR imaging data for complex heterogeneous systems can be challenging because of the spectroscopic and spatial complexity of the data. We implement a deep generative modeling approach using a β-variational autoencoder to learn disentangled representations of the generative factors of variance in a data set of crosslinked polyethylene (PEX-a) pipe. We identify three distinct physicochemical factors of aging and degradation learned by the model and apply the trained model to high-resolution hyperspectral IR images of cross-sectional slices of unused virgin, used in-service, and cracked PEX-a pipe. By mapping the learned representations of aging and degradation to the IR images, we extract detailed information on the physicochemical changes that occur during aging, degradation, and cracking in PEX-a pipe. This study shows how representation learning by deep generative modeling can significantly enhance the analysis of high-resolution IR images of complex heterogeneous samples.

Deep Learning Analysis of the Propagation of Stabilizing Additive Hydrolysis in a Cross-Linked Polyethylene Pipe

“…The β-VAE loss function minimized by the neural network optimizer is the sum of two components: the mean squared error (MSE) of the reconstruction compared to the input and a scaled Kullback–Leibler (KL) divergence term, where the KL divergence measures the difference between two probability distributions − β _ VAE loss = MSE loss + β · KL divergence Typically, β > 1, which increases the weight of the KL divergence term in the loss function relative to that of the MSE loss term. , The balance between the two terms in eq is tuned by the choice of β. The most informative learned latent dimensions are identified as those with the largest KL divergence cost that produce the largest changes in the decoded spectra while holding the other latent dimensions constant …”

“…One of the challenging aspects of using IR microscopy to study the spatial distribution of IR spectra of different samples aged under different environmental conditions is understanding the large amount of data that is generated. Instead of using a univariate analysis to focus on specific IR absorption bands to interpret these large amounts of data as has been done in previous studies, ,− machine learning approaches such as deep or generative learning have been used recently in the field of materials science to provide new insights into the analysis of large amounts of spectroscopy and microscopy data. − Recently, we developed a deep learning β-variational autoencoder (β-VAE) model to analyze IR spectra of PEX-a pipe. , β-VAEs are a class of deep generative models that can learn disentangled (independent and interpretable) representations of the generative factors responsible for variance in data. − We previously trained our β-VAE model on a diverse data set of 25,000 IR spectra of PEX-a pipe exposed to different environmental conditions . We learned three informative latent dimensions corresponding to three physicochemical processes responsible for the variance in the IR microscopy data: the most informative latent dimension, L1, which describes the hydrolysis of a stabilizing additive; the second latent dimension, L2, which describes the oxidative degradation of amorphous polyethylene; and the third latent dimension, L3, which describes crack-specific degradation characterized by ketone carbonyl and conjugated alkene formation.…”

“…We learned three informative latent dimensions corresponding to three physicochemical processes responsible for the variance in the IR microscopy data: the most informative latent dimension, L1, which describes the hydrolysis of a stabilizing additive; the second latent dimension, L2, which describes the oxidative degradation of amorphous polyethylene; and the third latent dimension, L3, which describes crack-specific degradation characterized by ketone carbonyl and conjugated alkene formation. We have recently applied a pretrained β-VAE model to hyperspectral IR images of PEX-a pipe, which yielded high lateral spatial resolution maps of physicochemical changes to the pipe samples (latent variables L1, L2, and L3) produced by aging. This capability allowed us to characterize localized changes in the latent variables, e.g., line profiles of the stabilizing additive hydrolysis associated with L1 and the presence of cracks in the pipes associated with L3.…”

“…In the present study, we build on the success of our recent work , to apply our pretrained β-VAE model to line profiles of IR spectra measured across the wall thickness of PEX-a pipes that have been exposed to recirculating water at different fixed temperatures T for different aging times t . Exposure of the inner surface of the pipes to hot water causes hydrolysis of the ester linkages within the oligomeric stabilizing additive, and this leads to the propagation of the hydrolysis of a stabilizing additive from the inner pipe surface.…”

“…Exposure of the inner surface of the pipes to hot water causes hydrolysis of the ester linkages within the oligomeric stabilizing additive, and this leads to the propagation of the hydrolysis of a stabilizing additive from the inner pipe surface. Specifically, we track the L1 latent variable, which is due to the hydrolysis of the stabilizing additive, , with aging time t at different fixed aging temperatures T . By fitting the radial profiles of L1 to a sigmoidal function of the radial distance r , we interpret the propagation of the penetration depth δ of the hydrolysis as a simple one-dimensional diffusion process, which allows the determination of the activation energy for the diffusion process.…”