{'fraction_non_alphanumeric': 0.01195219123505976, 'fraction_numerical': 0.0, 'mean_word_length': 5.659090909090909, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A probabilistic approach for estimating defect size and density considering detection uncertainties and measurement errors

Every structural component has some form and amount of hidden defects, however small it might be. These defects should be detected and characterized in order to ensure reliability of safety-critical structures. Test equipment is often used to inspect and gather data from probable defect sites in structural components during in-service inspections for maintenance purposes. This data is then analyzed and processed to measure the defect size and density. In-service inspection data may be highly uncertain in nature owing to detection uncertainties and measurement errors typically associated with the testing and evaluation process. These uncertainties and errors, if not properly accounted for, can result in defect size and density estimates not representative of the true state of degradations. In this article we first provide a description of the detection uncertainties and measurement errors in the context of nondestructive testing and evaluation. We then propose a Bayesian approach that updates prior knowledge of defect size and density with uncertain nondestructive evaluation data, accounting for detection uncertainties, measurement errors, and other associated uncertainties, to infer the posterior estimates of true size and number of defects. An example application of the proposed approach is then presented for estimating true defect size and density in nuclear reactor piping welds using ultrasonic evaluation data. The Bayesian approach presented in this article fills a critical gap in health management and reliability prognosis of structures, thereby enhancing the overall structural safety and operability.