PhotoelastNet: a deep convolutional neural network for evaluating the stress field by using a single color photoelasticity image

Juan C. Briñez-de León; Juan C. Briñez-de León; Mateo Rico-García; Alejandro Restrepo-Martínez

doi:10.1364/AO.444563

Applied Optics
Vol. 61,
Issue 7,
pp. D50-D62
(2022)
•https://doi.org/10.1364/AO.444563

PhotoelastNet: a deep convolutional neural network for evaluating the stress field by using a single color photoelasticity image

Juan C. Briñez-de León, Mateo Rico-García, and Alejandro Restrepo-Martínez

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Juan C. Briñez-de León, Mateo Rico-García, and Alejandro Restrepo-Martínez, "PhotoelastNet: a deep convolutional neural network for evaluating the stress field by using a single color photoelasticity image," Appl. Opt. 61, D50-D62 (2022)

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About this Article
History
- Original Manuscript: October 1, 2021
- Revised Manuscript: December 9, 2021
- Manuscript Accepted: January 12, 2022
- Published: February 10, 2022
Virtual Issues
Applied Optics Artificial Intelligence and Machine Learning in Optical Information Processing (2022)

Abstract

Quantifying the stress field induced into a piece when it is loaded is important for engineering areas since it allows the possibility to characterize mechanical behaviors and fails caused by stress. For this task, digital photoelasticity has been highlighted by its visual capability of representing the stress information through images with isochromatic fringe patterns. Unfortunately, demodulating such fringes remains a complicated process that, in some cases, depends on several acquisitions, e.g., pixel-by-pixel comparisons, dynamic conditions of load applications, inconsistence corrections, dependence of users, fringe unwrapping processes, etc. Under these drawbacks and taking advantage of the power results reported on deep learning, such as the fringe unwrapping process, this paper develops a deep convolutional neural network for recovering the stress field wrapped into color fringe patterns acquired through digital photoelasticity studies. Our model relies on an untrained convolutional neural network to accurately demodulate the stress maps by inputting only one single photoelasticity image. We demonstrate that the proposed method faithfully recovers the stress field of complex fringe distributions on simulated images with an averaged performance of 92.41% according to the SSIM metric. With this, experimental cases of a disk and ring under compression were evaluated, achieving an averaged performance of 85% in the SSIM metric. These results, on the one hand, are in concordance with new tendencies in the optic community to deal with complicated problems through machine-learning strategies; on the other hand, it creates a new perspective in digital photoelasticity toward demodulating the stress field for a wider quantity of fringe distributions by requiring one single acquisition.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Method	Requirements	Characteristics
Phase shifting [9]	Six polariscope configurations	– Advantage: Capability of evaluating principal stress difference (isochromatic) and principal stress direction (isoclinic) – Disadvantage: several subprocesses for identifying the inconsistences, correcting the ambiguities, and unwrapping the phase ma.
Hybrid phase shifting [13]	Three polariscope configurations	– Advantage: Capability of evaluating principal stress difference (isochromatic) and principal stress direction (isoclinic) – Advantage: Half of the acquisitions compared with initial phase shifting method – Disadvantage: several subprocesses for identifying the inconsistences, correcting the ambiguities and unwrapping the phase map.
Load stepping [10]	Two polariscope configurations	– Advantage: Capability of evaluating principal stress difference (isochromatic) with a single polariscope configuration. Non inconsistencies or ambiguities – Disadvantage: Three load movements – Disadvantage: Tuning the load movements that produce appropriate phase shifts. Additional procedures for unwrapping the phase map.
Hybrid load stepping [36]	One polariscope configuration	– Advantage: Capability of evaluating principal stress difference (isochromatic) with a single polariscope configuration. Non-inconsistencies or ambiguities. – Advantage: Half of the acquisitions compared with initial load stepping method – Disadvantage: Three load movements – Disadvantage: Tuning the load movements that produce appropriate phase shifts. Additional procedures for unwrapping the phase map.
Twelve fringe photoelasticity [34]	One polariscope configuration	– Advantage: Capability of evaluating principal stress difference (isochromatic) with a single polariscope configuration. Non-inconsistencies or ambiguities. – Disadvantage: A color comparison chart is required per every experimental condition, introducing sensibility to experimental variations – Disadvantage: Color search strategies must be included
Regularized phase tracking [35]	One polariscope configuration	– Advantage: Capability of evaluating principal stress difference (isochromatic) with a single polariscope configuration. Non-inconsistencies or ambiguities. – Disadvantage: A seed point to start must be carefully introduced- Disadvantage: The fringe demodulation is obtaining by solving a cost function per every point – Disadvantage: Color search strategies must be included

Type of Layer	Filter Size	Kernels	Input Size	Output Size	Act. Function
Input	—	—	$224 \times 224 \times 3$	—	—
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 3$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Maxpooling 2D	$2 \times 2$	—	$224 \times 224 \times 4$	$112 \times 112 \times 4$	—
Conv 2D	$3 \times 3$	8	$112 \times 112 \times 4$	$112 \times 112 \times 8$	SeLu
Conv 2D	$3 \times 3$	8	$112 \times 112 \times 8$	$112 \times 112 \times 8$	SeLu
Maxpooling 2D	$2 \times 2$	—	$112 \times 112 \times 8$	$56 \times 56 \times 8$	—
Conv 2D	$3 \times 3$	64	$56 \times 56 \times 8$	$56 \times 56 \times 64$	SeLu
Conv 2D	$3 \times 3$	64	$56 \times 56 \times 64$	$56 \times 56 \times 64$	SeLu
Maxpooling 2D	$2 \times 2$	—	$56 \times 56 \times 64$	$28 \times 28 \times 64$	—
Conv 2D	$3 \times 3$	256	$28 \times 28 \times 64$	$28 \times 28 \times 256$	SeLu
Conv 2D	$3 \times 3$	256	$28 \times 28 \times 256$	$28 \times 28 \times 256$	SeLu
Upsampling 2D	$2 \times 2$	—	$28 \times 28 \times 256$	$56 \times 56 \times 256$	—
Conv 2D	$3 \times 3$	64	$56 \times 56 \times 256$	$56 \times 56 \times 64$	SeLu
Conv 2D	$3 \times 3$	64	$56 \times 56 \times 64$	$56 \times 56 \times 64$	SeLu
Upsampling 2D	$2 \times 2$	—	$56 \times 56 \times 64$	$128 \times 128 \times 64$	—
Conv 2D	$3 \times 3$	8	$128 \times 128 \times 64$	$128 \times 128 \times 8$	SeLu
Conv 2D	$3 \times 3$	8	$128 \times 128 \times 8$	$128 \times 128 \times 8$	SeLu
Upsampling 2D	$2 \times 2$	—	$128 \times 128 \times 8$	$224 \times 224 \times 8$	—
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 8$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	1	$224 \times 224 \times 4$	$224 \times 224 \times 1$	SeLu
Output	—	—	—	$224 \times 224 \times 1$	—

	Metric Value	Standard Deviation
MSE	140.2428	371.7159
PSNR	37.2813	4.8545
SSIM	0.9241	0.0492

Method	Requirements	Characteristics
Phase shifting [9]	Six polariscope configurations	– Advantage: Capability of evaluating principal stress difference (isochromatic) and principal stress direction (isoclinic) – Disadvantage: several subprocesses for identifying the inconsistences, correcting the ambiguities, and unwrapping the phase ma.
Hybrid phase shifting [13]	Three polariscope configurations	– Advantage: Capability of evaluating principal stress difference (isochromatic) and principal stress direction (isoclinic) – Advantage: Half of the acquisitions compared with initial phase shifting method – Disadvantage: several subprocesses for identifying the inconsistences, correcting the ambiguities and unwrapping the phase map.
Load stepping [10]	Two polariscope configurations	– Advantage: Capability of evaluating principal stress difference (isochromatic) with a single polariscope configuration. Non inconsistencies or ambiguities – Disadvantage: Three load movements – Disadvantage: Tuning the load movements that produce appropriate phase shifts. Additional procedures for unwrapping the phase map.
Hybrid load stepping [36]	One polariscope configuration	– Advantage: Capability of evaluating principal stress difference (isochromatic) with a single polariscope configuration. Non-inconsistencies or ambiguities. – Advantage: Half of the acquisitions compared with initial load stepping method – Disadvantage: Three load movements – Disadvantage: Tuning the load movements that produce appropriate phase shifts. Additional procedures for unwrapping the phase map.
Twelve fringe photoelasticity [34]	One polariscope configuration	– Advantage: Capability of evaluating principal stress difference (isochromatic) with a single polariscope configuration. Non-inconsistencies or ambiguities. – Disadvantage: A color comparison chart is required per every experimental condition, introducing sensibility to experimental variations – Disadvantage: Color search strategies must be included
Regularized phase tracking [35]	One polariscope configuration	– Advantage: Capability of evaluating principal stress difference (isochromatic) with a single polariscope configuration. Non-inconsistencies or ambiguities. – Disadvantage: A seed point to start must be carefully introduced- Disadvantage: The fringe demodulation is obtaining by solving a cost function per every point – Disadvantage: Color search strategies must be included

Type of Layer	Filter Size	Kernels	Input Size	Output Size	Act. Function
Input	—	—	$224 \times 224 \times 3$	—	—
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 3$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Maxpooling 2D	$2 \times 2$	—	$224 \times 224 \times 4$	$112 \times 112 \times 4$	—
Conv 2D	$3 \times 3$	8	$112 \times 112 \times 4$	$112 \times 112 \times 8$	SeLu
Conv 2D	$3 \times 3$	8	$112 \times 112 \times 8$	$112 \times 112 \times 8$	SeLu
Maxpooling 2D	$2 \times 2$	—	$112 \times 112 \times 8$	$56 \times 56 \times 8$	—
Conv 2D	$3 \times 3$	64	$56 \times 56 \times 8$	$56 \times 56 \times 64$	SeLu
Conv 2D	$3 \times 3$	64	$56 \times 56 \times 64$	$56 \times 56 \times 64$	SeLu
Maxpooling 2D	$2 \times 2$	—	$56 \times 56 \times 64$	$28 \times 28 \times 64$	—
Conv 2D	$3 \times 3$	256	$28 \times 28 \times 64$	$28 \times 28 \times 256$	SeLu
Conv 2D	$3 \times 3$	256	$28 \times 28 \times 256$	$28 \times 28 \times 256$	SeLu
Upsampling 2D	$2 \times 2$	—	$28 \times 28 \times 256$	$56 \times 56 \times 256$	—
Conv 2D	$3 \times 3$	64	$56 \times 56 \times 256$	$56 \times 56 \times 64$	SeLu
Conv 2D	$3 \times 3$	64	$56 \times 56 \times 64$	$56 \times 56 \times 64$	SeLu
Upsampling 2D	$2 \times 2$	—	$56 \times 56 \times 64$	$128 \times 128 \times 64$	—
Conv 2D	$3 \times 3$	8	$128 \times 128 \times 64$	$128 \times 128 \times 8$	SeLu
Conv 2D	$3 \times 3$	8	$128 \times 128 \times 8$	$128 \times 128 \times 8$	SeLu
Upsampling 2D	$2 \times 2$	—	$128 \times 128 \times 8$	$224 \times 224 \times 8$	—
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 8$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	4	$224 \times 224 \times 4$	$224 \times 224 \times 4$	SeLu
Conv 2D	$3 \times 3$	1	$224 \times 224 \times 4$	$224 \times 224 \times 1$	SeLu
Output	—	—	—	$224 \times 224 \times 1$	—

Abstract

Data Availability

Cited By

Figures (11)

Tables (13)

Equations (10)

Applied Optics