{"title":"A quantitative super-sensitivity photogrammetry method for full-field dynamic strain measurements","authors":"Guojian Cui , Shanwu Li , Yongchao Yang","doi":"10.1016/j.ymssp.2025.113379","DOIUrl":null,"url":null,"abstract":"<div><div>Full-field, high-precision strain measurements are critical for accurately characterizing structural dynamic behavior and local damage states. While traditional strain measurement techniques (e.g., strain gauges) typically provide only discrete point measurements, incoherent optical methods especially photogrammetry with digital image correlation and optical flows, provide a practical alternative to enable full-field strain estimation; however, their sensitivity remains insufficient for precise strain measurement applications. In this work, we quantitatively study the key influencing factors on the sensitivity limit of strain measurements and develop a <em>super-sensitivity</em> photogrammetry method for precise full-field dynamic strain measurement. Specifically, first, the developed method builds upon the recent advances in super-sensitivity optical flows that statistically exceeds the sensitivity limit for full-field displacement measurements. Then, it incorporates a Locally Estimated Scatterplot Smoothing (LOESS) algorithm to further suppress minor residual errors remaining in the obtained localized displacement field, coupled with higher pixel spatial resolution, to eventually achieve high-precision full-field strain measurements. Furthermore, a quantitative mathematical model of the <em>achievable</em> strain measurement sensitivity is theoretically derived based on uncertainty propagation theory, as <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mo>=</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mo>/</mo><mi>N</mi><mi>⋅</mi><mi>a</mi><mi>⋅</mi><mi>σ</mi><mo>/</mo><msqrt><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></msqrt><mi>⋅</mi><mn>1</mn><mo>/</mo><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>B</mi></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>b</mi></mrow></math></span>. This model elucidates the parametric dependence of strain measurement sensitivity on five key factors: imaging noise level (<span><math><mi>σ</mi></math></span>), number of effective spatial pixels (<span><math><msqrt><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></msqrt></math></span>), camera bit depth (<span><math><mi>B</mi></math></span>), pixel gauge length (<span><math><mi>N</mi></math></span>), and effect of displacement smoothing algorithm (<span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></math></span>). The effectiveness of the proposed method for full-field, high-precision strain measurement, and the derived quantitative theoretical model are validated through both numerical simulations and laboratory experiments on fundamental beam-type structures; notably, the developed method is found to be able to achieve a level of precision at <em>microstrain</em>, comparable to contact discrete strain gauge measurements. Moreover, observations on the parametric analysis of number of effective spatial pixels (<span><math><msqrt><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></msqrt></math></span>) and pixel gauge length (<span><math><mi>N</mi></math></span>) are consistent, quantitatively, with the derived mathematical model of the achievable strain measurement sensitivity. Thus, this work provides a novel quantitative super-sensitivity photogrammetry method for high-precision full-field dynamic strain estimation. Finally, remaining challenge associated with the fundamental mechanism of the strain measurement sensitivity is also discussed.</div></div>","PeriodicalId":51124,"journal":{"name":"Mechanical Systems and Signal Processing","volume":"240 ","pages":"Article 113379"},"PeriodicalIF":8.9000,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanical Systems and Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888327025010805","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Full-field, high-precision strain measurements are critical for accurately characterizing structural dynamic behavior and local damage states. While traditional strain measurement techniques (e.g., strain gauges) typically provide only discrete point measurements, incoherent optical methods especially photogrammetry with digital image correlation and optical flows, provide a practical alternative to enable full-field strain estimation; however, their sensitivity remains insufficient for precise strain measurement applications. In this work, we quantitatively study the key influencing factors on the sensitivity limit of strain measurements and develop a super-sensitivity photogrammetry method for precise full-field dynamic strain measurement. Specifically, first, the developed method builds upon the recent advances in super-sensitivity optical flows that statistically exceeds the sensitivity limit for full-field displacement measurements. Then, it incorporates a Locally Estimated Scatterplot Smoothing (LOESS) algorithm to further suppress minor residual errors remaining in the obtained localized displacement field, coupled with higher pixel spatial resolution, to eventually achieve high-precision full-field strain measurements. Furthermore, a quantitative mathematical model of the achievable strain measurement sensitivity is theoretically derived based on uncertainty propagation theory, as . This model elucidates the parametric dependence of strain measurement sensitivity on five key factors: imaging noise level (), number of effective spatial pixels (), camera bit depth (), pixel gauge length (), and effect of displacement smoothing algorithm (). The effectiveness of the proposed method for full-field, high-precision strain measurement, and the derived quantitative theoretical model are validated through both numerical simulations and laboratory experiments on fundamental beam-type structures; notably, the developed method is found to be able to achieve a level of precision at microstrain, comparable to contact discrete strain gauge measurements. Moreover, observations on the parametric analysis of number of effective spatial pixels () and pixel gauge length () are consistent, quantitatively, with the derived mathematical model of the achievable strain measurement sensitivity. Thus, this work provides a novel quantitative super-sensitivity photogrammetry method for high-precision full-field dynamic strain estimation. Finally, remaining challenge associated with the fundamental mechanism of the strain measurement sensitivity is also discussed.
期刊介绍:
Journal Name: Mechanical Systems and Signal Processing (MSSP)
Interdisciplinary Focus:
Mechanical, Aerospace, and Civil Engineering
Purpose:Reporting scientific advancements of the highest quality
Arising from new techniques in sensing, instrumentation, signal processing, modelling, and control of dynamic systems