{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:38:54Z","timestamp":1760150334799,"version":"build-2065373602"},"reference-count":69,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T00:00:00Z","timestamp":1700006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ANID","award":["PFCHA\/DOCTORADO BECAS CHILE\/2021-21211486"],"award-info":[{"award-number":["PFCHA\/DOCTORADO BECAS CHILE\/2021-21211486"]}]},{"name":"Faculty of Engineering, Campus Curic\u00f3, University of Talca","award":["PFCHA\/DOCTORADO BECAS CHILE\/2021-21211486"],"award-info":[{"award-number":["PFCHA\/DOCTORADO BECAS CHILE\/2021-21211486"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Reducing the time spent on computational simulations is an active area in solid mechanics, and efforts are being made to implement novel techniques and apply them to time-sensitive areas in the industry and research. One of these techniques is called global\u2013local non-intrusive analysis, a methodology that enriches a local patch model using 3D elements with non-linear behavior (such as crack propagation), coupled with a linear, global 1D frame model that solves iteratively, thereby reducing overall times compared to a monolithic solution. However, engineers do not know the length of the local model (also known as the patch model) to be considered, which affects the convergence, computational time, and overall quality of the solution. Therefore, this study considered the use of categorical analyses for performing linear and quadratic discriminant solvers for a given set of simple cases with symmetric crack propagation within the local model and defining the convergence boundary with a certain probability of a successful convergence. In addition, a practical case was analyzed for different lengths of the local model, giving strong correlations to the results of the discriminant analysis. The solution of all the cases was also analyzed, considering the number of degrees of freedom, computational times, and the number of iterations for convergence. This aimed to establish a functional relation for engineering practice, enabling the determination of a suitable patch length for performing global\u2013local non-intrusive analysis with crack propagation in doubly symmetric steel sections.<\/jats:p>","DOI":"10.3390\/sym15112068","type":"journal-article","created":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T10:51:37Z","timestamp":1700045497000},"page":"2068","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Discriminant Analysis Based on the Patch Length and Crack Depth to Determine the Convergence of Global\u2013Local Non-Intrusive Analysis with 1D-to-3D Coupling"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7642-1644","authenticated-orcid":false,"given":"Mat\u00edas","family":"Jaque-Zurita","sequence":"first","affiliation":[{"name":"Engineering Systems Doctoral Program, Faculty of Engineering, Universidad de Talca, Campus Curic\u00f3, Curic\u00f3 3340000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8279-9703","authenticated-orcid":false,"given":"Jorge","family":"Hinojosa","sequence":"additional","affiliation":[{"name":"Industrial Technologies Department, Faculty of Engineering, University of Talca, Campus Curic\u00f3, Curic\u00f3 3340000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5268-4323","authenticated-orcid":false,"given":"Emilio","family":"Castillo-Ibarra","sequence":"additional","affiliation":[{"name":"Engineering Systems Doctoral Program, Faculty of Engineering, Universidad de Talca, Campus Curic\u00f3, Curic\u00f3 3340000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2046-7436","authenticated-orcid":false,"given":"Ignacio","family":"Fuenzalida-Henr\u00edquez","sequence":"additional","affiliation":[{"name":"Building Management and Engineering Department, Faculty of Engineering, University of Talca, Campus Curic\u00f3, Curic\u00f3 3340000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,15]]},"reference":[{"key":"ref_1","unstructured":"(2010). Specification for Structural Steel Buildings (Standard No. ANSI\/AISC 360\u201310)."},{"key":"ref_2","unstructured":"(2016). Seismic Provision for Structural Steel Buildings (Standard No. ANSI\/AISC 341\u201316)."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.prostr.2022.12.254","article-title":"Evaluation of Fatigue Crack Growth Rates in an IPE Beam Made of AISI 304 under Various Stress Ratios","volume":"43","author":"Miarka","year":"2023","journal-title":"Procedia Struct. Integr."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"115204","DOI":"10.1016\/j.engstruct.2022.115204","article-title":"Seismic behaviour of a self-centring steel connection with replaceable energy-dissipation components","volume":"274","author":"Lou","year":"2023","journal-title":"Eng. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.engstruct.2019.01.070","article-title":"Dynamic analysis of composite beam and floors with deformable connection using plate, bar and interface elements","volume":"184","author":"Machado","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1177\/0361198105192800108","article-title":"Review of steel bridges with fracture-critical elements","volume":"1928","author":"Dexter","year":"2005","journal-title":"Transp. Res. Rec."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Frangopol, D.M., and Soliman, M. (2019). Structures and Infrastructure Systems, Routledge.","DOI":"10.1201\/9781351182805"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1002\/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J","article-title":"A finite element method for crack growth without remeshing","volume":"46","author":"Dolbow","year":"1999","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1002\/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S","article-title":"Elastic crack growth in finite elements with minimal remeshing","volume":"45","author":"Belytschko","year":"1999","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Khoei, A.R. (2014). Extended Finite Element Method: Theory and Applications, John Wiley & Sons.","DOI":"10.1002\/9781118869673"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1061\/(ASCE)ST.1943-541X.0000054","article-title":"Nonlocal Damage Formulation for a Flexibility-Based Frame Element","volume":"135","author":"Valipour","year":"2009","journal-title":"J. Struct. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1002\/nme.1620320604","article-title":"Method of finite element tearing and interconnecting and its parallel solution algorithm","volume":"32","author":"Roux","year":"1991","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1016\/0045-7949(91)90334-I","article-title":"Iterative global\/local finite element analysis","volume":"40","author":"Whitcomb","year":"1991","journal-title":"Comput. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1615\/IntJMultCompEng.v6.i3.50","article-title":"A Nonlinear Dual-Domain Decomposition Method: Application to Structural Problems with Damage","volume":"6","author":"Pebrel","year":"2008","journal-title":"Int. J. Multiscale Comput. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.advengsoft.2013.12.010","article-title":"Domain decomposition methods with nonlinear localization for the buckling and post-buckling analyses of large structures","volume":"70","author":"Hinojosa","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1360","DOI":"10.1016\/j.compstruc.2006.08.085","article-title":"A two-scale approach with homogenization for the computation of cracked structures","volume":"85","author":"Guidault","year":"2007","journal-title":"Comput. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s00466-009-0378-3","article-title":"A three-scale domain decomposition method for the 3D analysis of debonding in laminates","volume":"44","author":"Kerfriden","year":"2009","journal-title":"Comput. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1007\/s00466-017-1444-x","article-title":"A non-invasive implementation of a mixed domain decomposition method for frictional contact problems","volume":"60","author":"Oumaziz","year":"2017","journal-title":"Comput. Mech."},{"key":"ref_19","unstructured":"Allix, O., and Gosselet, P. (2020). Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids, Springer."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s11831-014-9132-x","article-title":"Non-intrusive Coupling: Recent Advances and Scalable Nonlinear Domain Decomposition","volume":"23","author":"Duval","year":"2016","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1007\/s00466-013-0882-3","article-title":"Local\/global non-intrusive crack propagation simulation using a multigrid X-FEM solver","volume":"52","author":"Passieux","year":"2013","journal-title":"Comput. Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"112744","DOI":"10.1016\/j.cma.2019.112744","article-title":"An adaptive global\u2013local approach for phase-field modeling of anisotropic brittle fracture","volume":"361","author":"Noii","year":"2020","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.finel.2019.01.003","article-title":"Space\/time global\/local noninvasive coupling strategy: Application to viscoplastic structures","volume":"156","author":"Blanchard","year":"2019","journal-title":"Finite Elem. Anal. Des."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1007\/s00466-021-02124-z","article-title":"Global-Local non intrusive analysis with robin parameters: Application to plastic hardening behavior and crack propagation in 2D and 3D structures","volume":"69","author":"Oumaziz","year":"2022","journal-title":"Comput. Mech."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Jaque-Zurita, M., Hinojosa, J., and Fuenzalida-Henr\u00edquez, I. (2023). Global\u2013Local Non Intrusive Analysis with 1D to 3D Coupling: Application to Crack Propagation and Extension to Commercial Software. Mathematics, 11.","DOI":"10.3390\/math11112540"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/j.cma.2007.08.017","article-title":"Analysis and applications of a generalized finite element method with global-local enrichment functions","volume":"197","author":"Duarte","year":"2008","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.enganabound.2020.05.019","article-title":"2-D Crack propagation analysis using stable generalized finite element method with global-local enrichments","volume":"118","author":"Fonseca","year":"2020","journal-title":"Eng. Anal. Bound. Elem."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1007\/s00466-016-1318-7","article-title":"Well-conditioning global\u2013local analysis using stable generalized\/extended finite element method for linear elastic fracture mechanics","volume":"58","author":"Malekan","year":"2016","journal-title":"Comput. Mech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.istruc.2022.02.003","article-title":"Machine learning for structural engineering: A state-of-the-art review","volume":"38","author":"Thai","year":"2022","journal-title":"Structures"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"110501","DOI":"10.1016\/j.engstruct.2020.110501","article-title":"Neural network-based formula for shear capacity prediction of one-way slabs under concentrated loads","volume":"211","author":"Abambres","year":"2020","journal-title":"Eng. Struct."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"497","DOI":"10.12989\/sss.2015.16.3.497","article-title":"Fuzzy modelling approach for shear strength prediction of RC deep beams","volume":"16","author":"Mohammadhassani","year":"2015","journal-title":"Smart Struct. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"04015002","DOI":"10.1061\/(ASCE)CP.1943-5487.0000466","article-title":"Shear strength prediction in reinforced concrete deep beams using nature-inspired metaheuristic support vector regression","volume":"30","author":"Chou","year":"2016","journal-title":"J. Comput. Civ. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.engstruct.2017.04.048","article-title":"Assessment of RC exterior beam-column Joints based on artificial neural networks and other methods","volume":"144","author":"Kotsovou","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"113497","DOI":"10.1016\/j.engstruct.2021.113497","article-title":"Predicting bearing capacity of double shear bolted connections using machine learning","volume":"251","author":"Sarothi","year":"2022","journal-title":"Eng. Struct."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1016\/j.jcsr.2003.09.006","article-title":"Neural network modeling of the load-carrying capacity of eccentrically-loaded single-angle struts","volume":"60","author":"Sakla","year":"2004","journal-title":"J. Constr. Steel Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1007\/s13296-019-00276-6","article-title":"Artificial neural networks (ANN) based compressive strength prediction of afrp strengthened steel tube","volume":"20","author":"Djerrad","year":"2020","journal-title":"Int. J. Steel Struct."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2755","DOI":"10.1016\/j.istruc.2021.06.030","article-title":"Design of cold-formed stainless steel circular hollow section columns using machine learning methods","volume":"33","author":"Xu","year":"2021","journal-title":"Structures"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.engstruct.2017.02.047","article-title":"An Artificial Neural Networks model for the prediction of the compressive strength of FRP-confined concrete circular columns","volume":"140","author":"Cascardi","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1016\/j.istruc.2020.10.010","article-title":"Prediction of axial load-carrying capacity of GFRP-reinforced concrete columns through artificial neural networks","volume":"28","author":"Raza","year":"2020","journal-title":"Structures"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"112836","DOI":"10.1016\/j.engstruct.2021.112836","article-title":"Explainable extreme gradient boosting tree-based prediction of load-carrying capacity of FRP-RC columns","volume":"245","author":"Bakouregui","year":"2021","journal-title":"Eng. Struct."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"109637","DOI":"10.1016\/j.engstruct.2019.109637","article-title":"An efficient artificial neural network for damage detection in bridges and beam-like structures by improving training parameters using cuckoo search algorithm","volume":"199","author":"Khatir","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/j.acme.2016.11.005","article-title":"Detection of fatigue cracking in steel bridge girders: A support vector machine approach","volume":"17","author":"Hasni","year":"2017","journal-title":"Arch. Civ. Mech. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"100767","DOI":"10.1016\/j.jobe.2019.100767","article-title":"Classification of in-plane failure modes for reinforced concrete frames with infills using machine learning","volume":"25","author":"Huang","year":"2019","journal-title":"J. Build. Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.1177\/1475921720923081","article-title":"Detecting structural damage under unknown seismic excitation by deep convolutional neural network with wavelet-based transmissibility data","volume":"20","author":"Lei","year":"2021","journal-title":"Struct. Health Monit."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.engfailanal.2019.04.047","article-title":"Classification of failure modes in ductile and non-ductile concrete joints","volume":"103","author":"Naderpour","year":"2019","journal-title":"Eng. Fail. Anal."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/S0045-7949(02)00451-0","article-title":"Neural networks applications in concrete structures","volume":"81","author":"Hadi","year":"2003","journal-title":"Comput. Struct."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1016\/S0143-974X(01)00105-5","article-title":"Optimum design of cold-formed steel space structures using neural dynamics model","volume":"58","author":"Tashakori","year":"2002","journal-title":"J. Constr. Steel Res."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"113156","DOI":"10.1016\/j.engstruct.2021.113156","article-title":"Accurate prediction of cyclic hysteresis behaviour of RBS connections using deep learning neural networks","volume":"247","author":"Horton","year":"2021","journal-title":"Eng. Struct."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"102825","DOI":"10.1016\/j.advengsoft.2020.102825","article-title":"A robust method for safety evaluation of steel trusses using Gradient Tree Boosting algorithm","volume":"147","author":"Truong","year":"2020","journal-title":"Adv. Eng. Softw."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"101816","DOI":"10.1016\/j.jobe.2020.101816","article-title":"Machine learning applications for building structural design and performance assessment: State-of-the-art review","volume":"33","author":"Sun","year":"2021","journal-title":"J. Build. Eng."},{"key":"ref_51","unstructured":"Murphy, K.P. (2012). Machine Learning: A Probabilistic Perspective, MIT Press."},{"key":"ref_52","unstructured":"Ghojogh, B., and Crowley, M. (2019). Linear and quadratic discriminant analysis: Tutorial. arXiv."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1080\/15376494.2020.1759164","article-title":"Classification and prediction of multidamages in smart composite laminates using discriminant analysis","volume":"29","author":"Khan","year":"2022","journal-title":"Mech. Adv. Mater. Struct."},{"key":"ref_54","first-page":"012022","article-title":"Classification-based damage localization in composite plate using strain field data","volume":"1106","author":"Janeliukstis","year":"2018","journal-title":"J. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.jsv.2016.06.046","article-title":"Machinery fault diagnosis using joint global and local\/nonlocal discriminant analysis with selective ensemble learning","volume":"382","author":"Yu","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Angra, S., and Ahuja, S. (2017, January 23\u201325). Machine learning and its applications: A review. Proceedings of the 2017 International Conference on Big Data Analytics and Computational Intelligence (ICBDAC), Chirala, India.","DOI":"10.1109\/ICBDACI.2017.8070809"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Castillo-Ibarra, E., Alsina, M.A., Astudillo, C.A., and Fuenzalida-Henr\u00edquez, I. (2023). PFA-Nipals: An Unsupervised Principal Feature Selection Based on Nonlinear Estimation by Iterative Partial Least Squares. Mathematics, 11.","DOI":"10.3390\/math11194154"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"James, G., Witten, D., Hastie, T., and Tibshirani, R. (2021). An Introduction to Statistical Learning: With Applications in R, Springer.","DOI":"10.1007\/978-1-0716-1418-1"},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Ledoit, O., and Wolf, M. (2003). Honey, I Shrunk the Sample Covariance Matrix. SSRN Electron. J.","DOI":"10.2139\/ssrn.433840"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Jombart, T., Devillard, S., and Balloux, F. (2010). Discriminant analysis of principal components: A new method for the analysis of genetically structured populations. BMC Genet., 11.","DOI":"10.1186\/1471-2156-11-94"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support-vector networks","volume":"20","author":"Cortes","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TIT.1967.1053964","article-title":"Nearest neighbor pattern classification","volume":"13","author":"Cover","year":"1967","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_63","unstructured":"Alpaydin, E. (2010). Introduction to Machine Learning, The MIT Press. [2nd ed.]."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer.","DOI":"10.1007\/978-0-387-84858-7"},{"key":"ref_66","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Tada, H., Paris, P.C., and Irwin, G.R. (2000). The Stress Analysis of Cracks Handbook, ASME Press. [3rd ed.].","DOI":"10.1115\/1.801535"},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Anderson, T.L. (2017). FRACTURE MECHANICS: Fundamentals and Applications, CRC Press. [4th ed.].","DOI":"10.1201\/9781315370293"},{"key":"ref_69","unstructured":"EDF (2017). Code Aster\/Salome-Meca Module 2: Advanced Training, EDF."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/11\/2068\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:23:20Z","timestamp":1760131400000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/11\/2068"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,15]]},"references-count":69,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["sym15112068"],"URL":"https:\/\/doi.org\/10.3390\/sym15112068","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,11,15]]}}}