{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T20:51:53Z","timestamp":1778187113046,"version":"3.51.4"},"reference-count":20,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T00:00:00Z","timestamp":1585699200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/EMS\/00285\/2020"],"award-info":[{"award-number":["UID\/EMS\/00285\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/CEC\/00326\/2020"],"award-info":[{"award-number":["UID\/CEC\/00326\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["POCI-01-0145-FEDER-031243"],"award-info":[{"award-number":["POCI-01-0145-FEDER-031243"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["POCI-01-0145-FEDER-031216"],"award-info":[{"award-number":["POCI-01-0145-FEDER-031216"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Metals"],"abstract":"<jats:p>This work aims to compare the performance of various parametric and non-parametric metamodeling techniques when applied to sheet metal forming processes. For this, the U-Channel and the Square Cup forming processes were studied. In both cases, three steel grades were considered, and numerical simulations were performed, in order to establish a database for each combination of forming process and material. Each database was used to train and test the various metamodels, and their predictive performances were evaluated. The best performing metamodeling techniques were Gaussian processes, multi-layer perceptron, support vector machines, kernel ridge regression and polynomial chaos expansion.<\/jats:p>","DOI":"10.3390\/met10040457","type":"journal-article","created":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T15:37:21Z","timestamp":1585755441000},"page":"457","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Performance Comparison of Parametric and Non-Parametric Regression Models for Uncertainty Analysis of Sheet Metal Forming Processes"],"prefix":"10.3390","volume":"10","author":[{"given":"Armando E.","family":"Marques","sequence":"first","affiliation":[{"name":"CEMMPRE, Department of Mechanical Engineering, Univ Coimbra, 3030-788 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7650-9362","authenticated-orcid":false,"given":"Pedro A.","family":"Prates","sequence":"additional","affiliation":[{"name":"CEMMPRE, Department of Mechanical Engineering, Univ Coimbra, 3030-788 Coimbra, Portugal"}]},{"given":"Andr\u00e9 F. G.","family":"Pereira","sequence":"additional","affiliation":[{"name":"CEMMPRE, Department of Mechanical Engineering, Univ Coimbra, 3030-788 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8032-7262","authenticated-orcid":false,"given":"Marta C.","family":"Oliveira","sequence":"additional","affiliation":[{"name":"CEMMPRE, Department of Mechanical Engineering, Univ Coimbra, 3030-788 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3692-585X","authenticated-orcid":false,"given":"Jos\u00e9 V.","family":"Fernandes","sequence":"additional","affiliation":[{"name":"CEMMPRE, Department of Mechanical Engineering, Univ Coimbra, 3030-788 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9770-7672","authenticated-orcid":false,"given":"Bernardete M.","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"CISUC, Department of Informatics Engineering, Univ Coimbra, 3030-290 Coimbra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.commatsci.2007.07.014","article-title":"Optimization and tolerance prediction of sheet metal forming process using response surface model","volume":"42","author":"Wei","year":"2008","journal-title":"Comput. Mater. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1016\/j.matdes.2007.01.018","article-title":"Response surface methodology for the rapid design of aluminum sheet metal forming parameters","volume":"29","author":"Naceur","year":"2008","journal-title":"Mater. Des."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.finel.2012.04.012","article-title":"Variable fidelity design based surrogate and artificial bee colony algorithm for sheet metal forming process","volume":"59","author":"Sun","year":"2012","journal-title":"Finite Elem. Anal. Des."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s12289-012-1117-4","article-title":"Modeling and optimization of spring-back in bending process using multiple regression analysis and neural computation","volume":"7","author":"Teimouri","year":"2014","journal-title":"Int. J. Mater. Form."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wessing, S., Rudolph, G., Turck, S., Klimmek, C., Sch\u00e4fer, S.C., Schneider, M., and Lehmann, U. (2012). Replacing FEA for sheet metal forming by surrogate modeling. Cogent Eng., 1.","DOI":"10.1080\/23311916.2014.950853"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s12289-015-1276-1","article-title":"Innovative metamodelling-based process design for manufacturing: an application to Incremental Sheet Forming","volume":"10","author":"Ambrogio","year":"2017","journal-title":"Int. J. Mater. Form."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4265","DOI":"10.1007\/s00170-019-04477-5","article-title":"Optimization of variable blank holder force in deep drawing based on support vector regression model and trust region","volume":"105","author":"Feng","year":"2019","journal-title":"Int. J. Adv. Manuf."},{"key":"ref_8","unstructured":"Lin, J.D., Huang, L., and Zhou, H.B. (2017, January 28\u201330). Forming defects prediction for sheet metal forming using Gaussian process regression. Proceedings of the 29th Chinese Control and Decision Conference, Chongqing, China."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.jmatprotec.2013.08.008","article-title":"Effects of material scatter on the plastic behavior and stretchability in sheet metal forming","volume":"214","author":"Wiebenga","year":"2014","journal-title":"J. Mater. Process. Technol."},{"key":"ref_10","unstructured":"Blatman, G. (2009). Adaptive Sparse Polynomial Chaos Expansions for Uncertainty Propagation and Sensitivity Analysis. [Ph.D. Thesis, Universit\u00e9 Blaise Pascal]."},{"key":"ref_11","unstructured":"Kaur, D., Wilson, D., Forrest, M., and Feng, L. (2005, January 26\u201328). Regression tree and neuro-fuzzy approach to system identification of laser lap welding. Proceedings of the 2005 Annual Meeting of the North American Fuzzy Information Processing Society, Detroit, MI, USA."},{"key":"ref_12","unstructured":"Segal, M.R. (2004). Machine Learning Benchmarks and Random Forest Regression. UCSF: Center for Bioinformatics and Molecular Biostatistics, Available online: https:\/\/escholarship.org\/uc\/item\/35x3v9t4."},{"key":"ref_13","unstructured":"Cook, B., and Huber, M. (2019, January 19\u201322). Balanced k-Nearest Neighbors. Proceedings of the Thirty-Second International Flairs Conference, Florida, FL, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/B:STCO.0000035301.49549.88","article-title":"A tutorial on support vector regression","volume":"14","author":"Smola","year":"2004","journal-title":"Stat. Comput."},{"key":"ref_15","unstructured":"Welling, M. (2020, January 30). Kernel ridge regression. Max Welling\u2019s Classnotes in Machine Learning. Available online: https:\/\/www.ics.uci.edu\/~welling\/classnotes\/papers_class\/Kernel-Ridge.pdf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/S0924-0136(99)00345-3","article-title":"Three-dimensional numerical simulation of the deep-drawing process using solid finite elements","volume":"97","author":"Menezes","year":"2000","journal-title":"J. Mater. Process. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s11831-015-9159-7","article-title":"Surface Smoothing Procedures in Computational Contact Mechanics","volume":"24","author":"Neto","year":"2017","journal-title":"Arch. Comput. Meth. Eng."},{"key":"ref_18","unstructured":"Alves, J.L. (2003). Simula\u00e7\u00e3o Num\u00e9rica do Processo de Estampagem de Chapas Met\u00e1licas. [Ph.D. Thesis, University of Minho]."},{"key":"ref_19","unstructured":"(2020, January 22). GPy: A Gaussian Process Framework in Python. Available online: http:\/\/github.com\/SheffieldML\/GPy."},{"key":"ref_20","first-page":"2825","article-title":"Scikit-learn: machine learning in python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."}],"container-title":["Metals"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-4701\/10\/4\/457\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:14:15Z","timestamp":1760174055000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-4701\/10\/4\/457"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,1]]},"references-count":20,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["met10040457"],"URL":"https:\/\/doi.org\/10.3390\/met10040457","relation":{},"ISSN":["2075-4701"],"issn-type":[{"value":"2075-4701","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,1]]}}}