{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T05:14:01Z","timestamp":1767676441158,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T00:00:00Z","timestamp":1713657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Bruce Power LLP"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We develop decision support and automation for the task of ultrasonic non-destructive evaluation data analysis. First, we develop a probabilistic model for the task and then implement the model as a series of neural networks based on Conditional Score-Based Diffusion and Denoising Diffusion Probabilistic Model architectures. We use the neural networks to generate estimates for peak amplitude response time of flight and perform a series of tests probing their behavior, capacity, and characteristics in terms of the probabilistic model. We train the neural networks on a series of datasets constructed from ultrasonic non-destructive evaluation data acquired during an inspection at a nuclear power generation facility. We modulate the partition classifying nominal and anomalous data in the dataset and observe that the probabilistic model predicts trends in neural network model performance, thereby demonstrating a principled basis for explainability. We improve on previous related work as our methods are self-supervised and require no data annotation or pre-processing, and we train on a per-dataset basis, meaning we do not rely on out-of-distribution generalization. The capacity of the probabilistic model to predict trends in neural network performance, as well as the quality of the estimates sampled from the neural networks, support the development of a technical justification for usage of the method in safety-critical contexts such as nuclear applications. The method may provide a basis or template for extension into similar non-destructive evaluation tasks in other industrial contexts.<\/jats:p>","DOI":"10.3390\/a17040167","type":"journal-article","created":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T03:57:07Z","timestamp":1713758227000},"page":"167","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Evaluating Diffusion Models for the Automation of Ultrasonic Nondestructive Evaluation Data Analysis"],"prefix":"10.3390","volume":"17","author":[{"given":"Nick","family":"Torenvliet","sequence":"first","affiliation":[{"name":"Systems Design Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Zelek","sequence":"additional","affiliation":[{"name":"Systems Design Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.ijfatigue.2015.07.018","article-title":"Advanced ultrasonic \u201cProbability of Detection\u201d curves for designing in-service inspection intervals","volume":"86","author":"Carboni","year":"2016","journal-title":"Int. J. Fatigue"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cantero-Chinchilla, S., Wilcox, P.D., and Croxford, A.J. (2021). Deep learning in automated ultrasonic NDE\u2014Developments, axioms and opportunities. arXiv.","DOI":"10.1016\/j.ndteint.2022.102703"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hastie, T., Tibshirani, R., Friedman, J.H., and Friedman, J.H. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer.","DOI":"10.1007\/978-0-387-84858-7"},{"key":"ref_4","unstructured":"Liu, J., Shen, Z., He, Y., Zhang, X., Xu, R., Yu, H., and Cui, P. (2021). Towards out-of-distribution generalization: A survey. arXiv."},{"key":"ref_5","first-page":"24804","article-title":"Csdi: Conditional score-based diffusion models for probabilistic time series imputation","volume":"34","author":"Tashiro","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_6","unstructured":"Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., and Ganguli, S. (2015, January 7\u20139). Deep unsupervised learning using nonequilibrium thermodynamics. Proceedings of the International Conference on Machine Learning (PMLR), Lille, France."},{"key":"ref_7","first-page":"6840","article-title":"Denoising diffusion probabilistic models","volume":"33","author":"Ho","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_8","unstructured":"Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., and Poole, B. (2020). Score-based generative modeling through stochastic differential equations. arXiv."},{"key":"ref_9","unstructured":"Kong, Z., Ping, W., Huang, J., Zhao, K., and Catanzaro, B. (2020). Diffwave: A versatile diffusion model for audio synthesis. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015, January 5\u20139). U-net: Convolutional networks for biomedical image segmentation. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Munich, Germany.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_11","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, \u0141., and Polosukhin, I. (2017). Attention is all you need. Adv. Neural Inf. Process. Syst., 30, Available online: https:\/\/papers.nips.cc\/paper_files\/paper\/2017\/hash\/3f5ee243547dee91fbd053c1c4a845aa-Abstract.html."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.nucengdes.2017.09.029","article-title":"Automated sizing and classification of defects in CANDU pressure tubes","volume":"325","author":"Lardner","year":"2017","journal-title":"Nucl. Eng. Des."},{"key":"ref_14","unstructured":"Wallace, C., West, G., Zacharis, P., Dobie, G., and Gachagan, A. (2019, January 9\u201314). Experience, testing and future development of an ultrasonic inspection analysis defect decision support tool for CANDU reactors. Proceedings of the 11th Nuclear Plant Instrumentation, Control and Human-Machine Interface Technologies (NPIC & HMIT), Orlando, FL, USA."},{"key":"ref_15","unstructured":"Lardner, T., West, G.M., Dobie, G., and Gachagan, A. (2017, January 11\u201315). An expert-systems approach to automatically determining flaw depth within Candu pressure tubes. Proceedings of the 10th International Topical Meeting on Nuclear Plant Instrumentation, Control, and Human-Machine Interface Technologies (NPIC and HMIT), San Francisco, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1080\/00295450.2017.1421803","article-title":"Data-driven analysis of ultrasonic inspection data of pressure tubes","volume":"202","author":"Zacharis","year":"2018","journal-title":"Nucl. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/TUFFC.2021.3112078","article-title":"Using Deep Learning to Automate the Detection of Flaws in Nuclear Fuel Channel UT Scans","volume":"69","author":"Hammad","year":"2022","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S0022-3115(02)00880-2","article-title":"Delayed hydride cracking in Zr\u20132.5 Nb pressure tube material","volume":"304","author":"Singh","year":"2002","journal-title":"J. Nucl. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bengio, Y. (2013). Deep Learning of Representations: Looking Forward. arXiv.","DOI":"10.1007\/978-3-642-39593-2_1"},{"key":"ref_20","unstructured":"Higgins, I., Matthey, L., Pal, A., Burgess, C., Glorot, X., Botvinick, M., Mohamed, S., and Lerchner, A. (2024, April 14). Beta-Vae: Learning Basic Visual Concepts with a Constrained Variational Framework. Available online: https:\/\/openreview.net\/forum?id=Sy2fzU9gl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1561\/2200000056","article-title":"An Introduction to Variational Autoencoders","volume":"12","author":"Kingma","year":"2019","journal-title":"Found. Trends\u00ae Mach. Learn."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Torenvliet, N., Liu, Y., and Zelek, J. (2023, January 18\u201320). Automating Safety Critical Ultrasonic Data Analysis with a Variational Auto-Encoder. Proceedings of the 2023 IEEE Sensors Applications Symposium (SAS), Ottawa, ON, Canada.","DOI":"10.1109\/SAS58821.2023.10254105"},{"key":"ref_23","unstructured":"Nachmani, E., Roman, R.S., and Wolf, L. (2024, April 14). Denoising Diffusion Gamma Models. Available online: https:\/\/arxiv.org\/abs\/2110.05948."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/4\/167\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:31:56Z","timestamp":1760106716000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/4\/167"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,21]]},"references-count":23,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["a17040167"],"URL":"https:\/\/doi.org\/10.3390\/a17040167","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2024,4,21]]}}}