{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T17:54:24Z","timestamp":1780422864204,"version":"3.54.1"},"reference-count":67,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T00:00:00Z","timestamp":1679529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The inverse finite element method (iFEM) is a model-based technique to compute the displacement (and then the strain) field of a structure from strain measurements and a geometrical discretization of the same. Different literature works exploit the error between the numerically reconstructed strains and the experimental measurements to perform damage identification in a structural health monitoring framework. However, only damage detection and localization are performed, without attempting a proper damage size estimation. The latter could be based on machine learning techniques; however, an a priori definition of the damage conditions would be required. To overcome these limitations, the present work proposes a new approach in which the damage is systematically introduced in the iFEM model to minimize its discrepancy with respect to the physical structure. This is performed with a maximum likelihood estimation framework, where the most accurate damage scenario is selected among a series of different models. The proposed approach was experimentally verified on an aluminum plate subjected to fatigue crack propagation, which enables the creation of a digital twin of the structure itself. The strain field fed to the iFEM routine was experimentally measured with an optical backscatter reflectometry fiber and the methodology was validated with independent observations of lasers and the digital image correlation.<\/jats:p>","DOI":"10.3390\/s23073406","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T03:16:46Z","timestamp":1679627806000},"page":"3406","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Towards Automatic Crack Size Estimation with iFEM for Structural Health Monitoring"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9169-6781","authenticated-orcid":false,"given":"Daniele","family":"Oboe","sequence":"first","affiliation":[{"name":"Politecnico di Milano, Mechanical Engineering Department, Via La Masa 1, 20156 Milano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9883-0517","authenticated-orcid":false,"given":"Dario","family":"Poloni","sequence":"additional","affiliation":[{"name":"Politecnico di Milano, Mechanical Engineering Department, Via La Masa 1, 20156 Milano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5511-8194","authenticated-orcid":false,"given":"Claudio","family":"Sbarufatti","sequence":"additional","affiliation":[{"name":"Politecnico di Milano, Mechanical Engineering Department, Via La Masa 1, 20156 Milano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marco","family":"Giglio","sequence":"additional","affiliation":[{"name":"Politecnico di Milano, Mechanical Engineering Department, Via La Masa 1, 20156 Milano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ymssp.2007.07.004","article-title":"Vibration-Based Structural Health Monitoring Using Output-Only Measurements under Changing Environment","volume":"22","author":"Deraemaeker","year":"2008","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Farrar, C.R., and Worden, K. (2012). Structural Health Monitoring: A Machine Learning Perspective, John Wiley and Sons.","DOI":"10.1002\/9781118443118"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"110675","DOI":"10.1016\/j.measurement.2021.110675","article-title":"Measurement Platform for Structural Health Monitoring Application of Large Scale Structures","volume":"190","author":"Lambinet","year":"2022","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.jcsr.2016.08.002","article-title":"Fatigue Cracking Detection in Steel Bridge Girders through a Self-Powered Sensing Concept","volume":"128","author":"Alavi","year":"2017","journal-title":"J. Constr. Steel Res."},{"key":"ref_5","first-page":"26","article-title":"A Computationally-Efficient Probabilistic Approach to Model-Based Damage Diagnosis","volume":"8","author":"Warner","year":"2017","journal-title":"Int. J. Progn. Health Manag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e1964","DOI":"10.1002\/stc.1964","article-title":"Optimization of an Artificial Neural Network for Fatigue Damage Identification Using Analysis of Variance","volume":"24","author":"Sbarufatti","year":"2017","journal-title":"Struct. Control Health Monit."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.ymssp.2013.06.003","article-title":"Performance Optimization of a Diagnostic System Based upon a Simulated Strain Field for Fatigue Damage Characterization","volume":"40","author":"Sbarufatti","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.cirpj.2020.02.002","article-title":"Characterising the Digital Twin: A Systematic Literature Review","volume":"29","author":"Jones","year":"2020","journal-title":"CIRP J. Manuf. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1109\/TII.2018.2873186","article-title":"Digital Twin in Industry: State-of-the-Art","volume":"15","author":"Tao","year":"2019","journal-title":"IEEE Trans. Ind. Informatics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"030901","DOI":"10.1115\/1.4046739","article-title":"Digital Twins: State-of-The-Art and Future Directions for Modeling and Simulation in Engineering Dynamics Applications","volume":"6","author":"Wagg","year":"2020","journal-title":"ASCE-ASME J. Risk Uncertain. Eng. Syst. Part B Mech. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"111728","DOI":"10.1016\/j.measurement.2022.111728","article-title":"Digital Twin for Rolling Bearings: A Review of Current Simulation and PHM Techniques","volume":"201","author":"Peng","year":"2022","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Glaessgen, E.H., and Stargel, D.S. (2012, January 23\u201326). The Digital Twin Paradigm for Future NASA and U.S. Air Force Vehicles. Proceedings of the 53rd AIAA\/ASME\/ASCE\/AHS\/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI, USA.","DOI":"10.2514\/6.2012-1818"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Seshadri, B.R., and Krishnamurthy, T. (2017, January 9\u201313). Structural Health Management of Damaged Aircraft Structures Using the Digital Twin Concept. Proceedings of the 25th AIAA\/AHS Adaptive Structures Conference, Grapevine, TX, USA.","DOI":"10.2514\/6.2017-1675"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Gockel, B.T., Tudor, A.W., Brandyberry, M.D., Penmetsa, R.C., and Tuegel, E.J. (2012, January 23\u201326). Challenges with Structural Life Forecasting Using Realistic Mission Profiles. Proceedings of the 53rd AIAA\/ASME\/ASCE\/AHS\/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI, USA.","DOI":"10.2514\/6.2012-1813"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"154798","DOI":"10.1155\/2011\/154798","article-title":"Reengineering Aircraft Structural Life Prediction Using a Digital Twin","volume":"2011","author":"Tuegel","year":"2011","journal-title":"Int. J. Aerosp. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Tuegel, E.J. (2012, January 23\u201326). The Airframe Digital Twin: Some Challenges to Realization. Proceedings of the 53rd AIAA\/ASME\/ASCE\/AHS\/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI, USA.","DOI":"10.2514\/6.2012-1812"},{"key":"ref_17","first-page":"95152","article-title":"On Digital Twin Condition Monitoring Approach for Drivetrains in Marine Applications","volume":"10","author":"Johansen","year":"2019","journal-title":"Proc. Int. Conf. Offshore Mech. Arct. Eng. OMAE"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107614","DOI":"10.1016\/j.ymssp.2021.107614","article-title":"Digital Twin, Physics-Based Model, and Machine Learning Applied to Damage Detection in Structures","volume":"155","author":"Ritto","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108087","DOI":"10.1016\/j.ymssp.2021.108087","article-title":"Online Condition Monitoring of Floating Wind Turbines Drivetrain by Means of Digital Twin","volume":"162","author":"Moghadam","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3563","DOI":"10.1007\/s00170-017-0233-1","article-title":"Digital Twin-Driven Product Design, Manufacturing and Service with Big Data","volume":"94","author":"Tao","year":"2018","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1016","DOI":"10.1016\/j.ifacol.2018.08.474","article-title":"Digital Twin in Manufacturing: A Categorical Literature Review and Classification","volume":"51","author":"Kritzinger","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"108978","DOI":"10.1016\/j.measurement.2021.108978","article-title":"Proposal of Digital Twin for Testing and Measuring of Transport Belts for Pipe Conveyors within the Concept Industry 4.0","volume":"174","author":"Fedorko","year":"2021","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"114512","DOI":"10.1016\/j.cma.2021.114512","article-title":"Structural Fatigue Life Prediction Considering Model Uncertainties through a Novel Digital Twin-Driven Approach","volume":"391","author":"Wang","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"107486","DOI":"10.1016\/j.ymssp.2020.107486","article-title":"A Smoothed IFEM Approach for Efficient Shape-Sensing Applications: Numerical and Experimental Validation on Composite Structures","volume":"152","author":"Kefal","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","unstructured":"Tessler, A., and Spangler, J.L. (2003). A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells, National Aeronautics and Space Administration, Langley Research Center; Langley Research Center Hampton. Virginia 2368 1-2 199; NASA\/TM-2003-212445."},{"key":"ref_26","unstructured":"Tessler, A., and Spangler, J. (2004, January 7\u20139). Inverse FEM for Full-Field Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells. Proceedings of the 2nd European Workshop on Structural Health Monitoring, Lancaster, Munich, Germany."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3100","DOI":"10.1016\/j.ijsolstr.2012.06.009","article-title":"Shape Sensing of 3D Frame Structures Using an Inverse Finite Element Method","volume":"49","author":"Gherlone","year":"2012","journal-title":"Int. J. Solids Struct."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Du, J., Bao, H., and Xu, Q. (2018). Optimal Sensor Placement Based on Eigenvalues Analysis for Sensing Deformation of Wing Frame Using IFEM. Sensors, 18.","DOI":"10.3390\/s18082424"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"045027","DOI":"10.1088\/0964-1726\/23\/4\/045027","article-title":"An Inverse Finite Element Method for Beam Shape Sensing: Theoretical Framework and Experimental Validation","volume":"23","author":"Gherlone","year":"2014","journal-title":"Smart Mater. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"109958","DOI":"10.1016\/j.measurement.2021.109958","article-title":"Shape Sensing of Timoshenko Beam Subjected to Complex Multi-Node Loads Using Isogeometric Analysis","volume":"184","author":"Chen","year":"2021","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"109881","DOI":"10.1016\/j.measurement.2021.109881","article-title":"Experimental Study of Pipeline Deformation Monitoring Using the Inverse Finite Element Method Based on the IBeam3 Element","volume":"184","author":"Wang","year":"2021","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"107656","DOI":"10.1016\/j.measurement.2020.107656","article-title":"Shape Sensing of Variable Cross-Section Beam Using the Inverse Finite Element Method and Isogeometric Analysis","volume":"158","author":"Zhao","year":"2020","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"109575","DOI":"10.1016\/j.measurement.2021.109575","article-title":"An Enhanced Inverse Beam Element for Shape Estimation of Beam-like Structures","volume":"181","author":"You","year":"2021","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.oceaneng.2015.11.032","article-title":"Displacement and Stress Monitoring of a Chemical Tanker Based on Inverse Finite Element Method","volume":"112","author":"Kefal","year":"2016","journal-title":"Ocean Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.oceaneng.2016.04.025","article-title":"Displacement and Stress Monitoring of a Panamax Containership Using Inverse Finite Element Method","volume":"119","author":"Kefal","year":"2016","journal-title":"Ocean Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"106944","DOI":"10.1016\/j.oceaneng.2020.106944","article-title":"Dent Damage Identification in Stiffened Cylindrical Structures Using Inverse Finite Element Method","volume":"198","author":"Li","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_37","first-page":"1299","article-title":"A Quadrilateral Inverse-Shell Element with Drilling Degrees of Freedom for Shape Sensing and Structural Health Monitoring","volume":"19","author":"Kefal","year":"2016","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.cma.2004.03.015","article-title":"A Least-Squares Variational Method for Full-Field Reconstruction of Elastic Deformations in Shear-Deformable Plates and Shells","volume":"194","author":"Tessler","year":"2005","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Oboe, D., Colombo, L., Sbarufatti, C., and Giglio, M. (2021). Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method. Sensors, 21.","DOI":"10.3390\/s21041388"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"110676","DOI":"10.1016\/j.measurement.2021.110676","article-title":"Shape Sensing of Plate Structures through Coupling Inverse Finite Element Method and Scaled Boundary Element Analysis","volume":"190","author":"Niu","year":"2022","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"108282","DOI":"10.1016\/j.measurement.2020.108282","article-title":"An Improved Inverse Finite Element Method for Shape Sensing Using Isogeometric Analysis","volume":"167","author":"Zhao","year":"2021","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2487","DOI":"10.1007\/s11012-015-0146-8","article-title":"Real-Time Displacement Monitoring of a Composite Stiffened Panel Subjected to Mechanical and Thermal Loads","volume":"50","author":"Cerracchio","year":"2015","journal-title":"Meccanica"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.ast.2017.07.005","article-title":"Health Structure Monitoring for the Design of an Innovative UAS Fixed Wing through Inverse Finite Element Method (IFEM)","volume":"69","author":"Papa","year":"2017","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1016\/j.ymssp.2018.10.041","article-title":"Definition of a Load Adaptive Baseline by Inverse Finite Element Method for Structural Damage Identification","volume":"120","author":"Colombo","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"107291","DOI":"10.1016\/j.oceaneng.2020.107291","article-title":"Structural Health Monitoring of an Offshore Wind Turbine Tower Using IFEM Methodology","volume":"204","author":"Li","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"106262","DOI":"10.1016\/j.oceaneng.2019.106262","article-title":"An Efficient Curved Inverse-Shell Element for Shape Sensing and Structural Health Monitoring of Cylindrical Marine Structures","volume":"188","author":"Kefal","year":"2019","journal-title":"Ocean Eng."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Abdollahzadeh, M.A., Kefal, A., and Yildiz, M. (2020). A Comparative and Review Study on Shape and Stress Sensing of Flat\/Curved Shell Geometries Using C0-Continuous Family of IFEM Elements. Sensors, 20.","DOI":"10.3390\/s20143808"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Kefal, A., and Yildiz, M. (2017). Modeling of Sensor Placement Strategy for Shape Sensing and Structural Health Monitoring of a Wing-Shaped Sandwich Panel Using Inverse Finite Element Method. Sensors, 17.","DOI":"10.3390\/s17122775"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"110031","DOI":"10.1016\/j.measurement.2021.110031","article-title":"A Combined Experimental\/Numerical Study on Deformation Sensing of Sandwich Structures through Inverse Analysis of Pre-Extrapolated Strain Measurements","volume":"185","author":"Abdollahzadeh","year":"2021","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"113431","DOI":"10.1016\/j.compstruct.2020.113431","article-title":"An Experimental Implementation of Inverse Finite Element Method for Real-Time Shape and Strain Sensing of Composite and Sandwich Structures","volume":"258","author":"Kefal","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.compstruct.2015.02.081","article-title":"A Novel Approach for Displacement and Stress Monitoring of Sandwich Structures Based on the Inverse Finite Element Method","volume":"127","author":"Cerracchio","year":"2015","journal-title":"Compos. Struct."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.compstruct.2017.07.078","article-title":"An Enhanced Inverse Finite Element Method for Displacement and Stress Monitoring of Multilayered Composite and Sandwich Structures","volume":"179","author":"Kefal","year":"2017","journal-title":"Compos. Struct."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Kefal, A., and Oterkus, E. (2020). Isogeometric IFEM Analysis of Thin Shell Structures. Sensors, 20.","DOI":"10.3390\/s20092685"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Li, T., Cao, M., Li, J., Yang, L., Xu, H., and Wu, Z. (2021). Structural Damage Identification Based on Integrated Utilization of Inverse Finite Element Method and Pseudo-Excitation Approach. Sensors, 21.","DOI":"10.3390\/s21020606"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"107163","DOI":"10.1016\/j.ymssp.2020.107163","article-title":"Shape Sensing and Damage Identification with IFEM on a Composite Structure Subjected to Impact Damage and Non-Trivial Boundary Conditions","volume":"148","author":"Colombo","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"113587","DOI":"10.1016\/j.compstruct.2021.113587","article-title":"Comparison of Strain Pre-Extrapolation Techniques for Shape and Strain Sensing by IFEM of a Composite Plate Subjected to Compression Buckling","volume":"262","author":"Oboe","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/0045-7825(94)90140-6","article-title":"A Variational Method for Finite Element Stress Recovery and Error Estimation","volume":"111","author":"Tessler","year":"1994","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0045-7825(85)90114-8","article-title":"A Three-Node Mindlin Plate Element with Improved Transverse Shear","volume":"50","author":"Tessler","year":"1985","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/S0045-7825(97)00135-7","article-title":"An Improved Variational Method for Finite Element Stress Recovery and a Posteriori Error Estimation","volume":"155","author":"Tessler","year":"1998","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/S0045-7825(96)01151-6","article-title":"C1-Continuous Stress Recovery in Finite Element Analysis","volume":"143","author":"Riggs","year":"1997","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"109167","DOI":"10.1016\/j.ymssp.2022.109167","article-title":"Physics-Based Strain Pre-Extrapolation Technique for Inverse Finite Element Method","volume":"177","author":"Oboe","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"110056","DOI":"10.1016\/j.ymssp.2022.110056","article-title":"Towards a Stochastic Inverse Finite Element Method: A Gaussian Process Strain Extrapolation","volume":"189","author":"Poloni","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"108545","DOI":"10.1016\/j.oceaneng.2020.108545","article-title":"Direct Damage Index Based on Inverse Finite Element Method for Structural Damage Identification","volume":"221","author":"Li","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"108289","DOI":"10.1016\/j.ymssp.2021.108289","article-title":"Structural Damage Identification Using Strain Mode Differences by the IFEM Based on the Convolutional Neural Network (CNN)","volume":"165","author":"Li","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"114520","DOI":"10.1016\/j.cma.2021.114520","article-title":"Coupling of Peridynamics and Inverse Finite Element Method for Shape Sensing and Crack Propagation Monitoring of Plate Structures","volume":"391","author":"Kefal","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"A49","DOI":"10.1115\/1.4008919","article-title":"Bearing Pressures and Cracks","volume":"6","author":"Westergaard","year":"1939","journal-title":"J. Appl. Mech."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/BF00191100","article-title":"On the Modified Westergaard Equations for Certain Plane Crag Problems","volume":"8","author":"Eftis","year":"1972","journal-title":"Int. J. Fract. Mech."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/7\/3406\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:01:53Z","timestamp":1760122913000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/7\/3406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,23]]},"references-count":67,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["s23073406"],"URL":"https:\/\/doi.org\/10.3390\/s23073406","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,23]]}}}