{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T00:50:56Z","timestamp":1773708656892,"version":"3.50.1"},"reference-count":47,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T00:00:00Z","timestamp":1682467200000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U20A20287"],"award-info":[{"award-number":["U20A20287"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51905476"],"award-info":[{"award-number":["51905476"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010248","name":"Public Welfare Technology Application Research Project of Zhejiang Province","doi-asserted-by":"publisher","award":["LGG22E050008"],"award-info":[{"award-number":["LGG22E050008"]}],"id":[{"id":"10.13039\/501100010248","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010248","name":"Public Welfare Technology Application Research Project of Zhejiang Province","doi-asserted-by":"publisher","award":["2021Z110"],"award-info":[{"award-number":["2021Z110"]}],"id":[{"id":"10.13039\/501100010248","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,4,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>With light weight, high strength, and high performance, metal bent tubes have attracted increasing applications in aeronautics. However, the growing demand for customized tubular parts has led to a significant increase in the cost of conventional tube-bending processes, as they can only process tubes of a specific diameter. To this end, this paper proposes a variable diameter die (VDD) scheme which can bend tubes with a specific range of diameters. To investigate the formability of VDD-processed tubes for practical VDD applications, an accurate and reliable prediction method of cross-sectional distortion is imperative. Hence, we pioneer a novel intelligent model based on quantum-behaved particle swarm optimization (QPSO)-optimized back-propagation neural network (BPNN) to predict a rational cross-sectional distortion characterization index: average distortion rate. The adaptive adjustment of coefficients and the Gaussian distributed random vector are introduced to QPSO, which balance the search and enhance the diversity of the population, respectively. For further improvement in optimization performance, the informed initialization strategy is applied to QPSO. The efficiency of the proposed reinforced QPSO (RQPSO)-optimized BPNN model is evaluated by comparing the results with those of the BPNN, BPNN with Xavier initialization, several different particle swarm optimization variants-optimized BPNN models, and variants of popular machine learning models. The results indicated the superiority of RQPSO over other methods in terms of the coefficient of determination (${R}^2$), variance account for, root mean square error (MSE), mean absolute error, and standard deviation of MSE. Thus, the proposed novel algorithm could be employed as a reliable and accurate technique to predict the cross-sectional distortion of VDD-processed tubes.<\/jats:p>","DOI":"10.1093\/jcde\/qwad037","type":"journal-article","created":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T11:16:44Z","timestamp":1682507804000},"page":"1060-1079","source":"Crossref","is-referenced-by-count":32,"title":["Reinforced quantum-behaved particle swarm-optimized neural network for cross-sectional distortion prediction of novel variable-diameter-die-formed metal bent tubes"],"prefix":"10.1093","volume":"10","author":[{"given":"Caicheng","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University , Hangzhou 310027 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zili","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University , Hangzhou 310027 , China"},{"name":"Engineering Research Center for Design Engineering and Digital Twin of Zhejiang Province, Zhejiang University , Hangzhou 310027 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuyou","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University , Hangzhou 310027 , China"},{"name":"Ningbo Research Institute, Zhejiang University , Ningbo 315100 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaojian","family":"Liu","sequence":"additional","affiliation":[{"name":"Ningbo Research Institute, Zhejiang University , Ningbo 315100 , China"},{"name":"NingboTech University , Ningbo 315100 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianrong","family":"Tan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University , Hangzhou 310027 , China"},{"name":"Engineering Research Center for Design Engineering and Digital Twin of Zhejiang Province, Zhejiang University , Hangzhou 310027 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,4,25]]},"reference":[{"key":"2023061017403551500_bib1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.asoc.2021.107122","article-title":"Quantum inspired particle swarm optimization with guided exploration for function optimization","volume":"102","author":"Agrawal","year":"2021","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib2","article-title":"On feature selection using anisotropic general regression neural network","volume-title":"Proceedings of the European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning","author":"Amato","year":"2020"},{"key":"2023061017403551500_bib4","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/j.asoc.2015.10.048","article-title":"Improved accelerated PSO algorithm for mechanical engineering optimization problems","volume":"40","author":"Ben\u00a0Guedria","year":"2016","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib5","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1109\/TEVC.2018.2885075","article-title":"Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions","volume":"23","author":"Cao","year":"2019","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"2023061017403551500_bib6","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.asoc.2015.10.020","article-title":"A combined neural network and genetic algorithm based approach for optimally designed femoral implant having improved primary stability","volume":"38","author":"Chanda","year":"2016","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib7","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1145\/1961189.1961199","article-title":"LIBSVM: A library for support vector machines","volume":"2","author":"Chang","year":"2011","journal-title":"ACM Transactions on Intelligent Systems and Technology"},{"key":"2023061017403551500_bib8","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1002\/srin.201000109","article-title":"Deformation analysis for the rotary draw bending process of circular tubes: Stress distribution and wall thinning","volume":"81","author":"Daxin","year":"2010","journal-title":"Steel Research International"},{"key":"2023061017403551500_bib9","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/MHS.1995.494215","article-title":"A new optimizer using particle swarm theory","volume-title":"MHS'95: Proceedings of the Sixth International Symposium on Micro Machine and Human Science","author":"Eberhart","year":"1995"},{"key":"2023061017403551500_bib10","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1016\/j.asoc.2018.09.013","article-title":"Optimizing long short-term memory recurrent neural networks using antalign=\u201ccenter\u201d colony optimization to predict turbine engine vibration","volume":"73","author":"ElSaid","year":"2018","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib11","doi-asserted-by":"crossref","first-page":"336","DOI":"10.4103\/0256-4602.64601","article-title":"A review of quantum-behaved particle swarm optimization","volume":"27","author":"Fang","year":"2010","journal-title":"IETE Technical Review"},{"key":"2023061017403551500_bib12","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.matdes.2022.110493","article-title":"Full-cross-section deformation characterization of Cu\/Al bimetallic tubes under rotary-draw-bending based on physics-driven B-spline curves fitting","volume":"215","author":"Fu","year":"2022","journal-title":"Materials & Design"},{"key":"2023061017403551500_bib13","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10994-006-6226-1","article-title":"Extremely randomized trees","volume":"63","author":"Geurts","year":"2006","journal-title":"Machine Learning"},{"key":"2023061017403551500_bib14","first-page":"249","article-title":"Understanding the difficulty of training deep feedforward neural networks","volume-title":"Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics","author":"Glorot","year":"2010"},{"key":"2023061017403551500_bib15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s00366-015-0400-7","article-title":"Prediction of seismic slope stability through combination of particle swarm optimization and neural network","volume":"32","author":"Gordan","year":"2016","journal-title":"Engineering with Computers"},{"key":"2023061017403551500_bib16","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.asoc.2020.106698","article-title":"An efficient model for predicting setting time of cement based on broad learning system","volume":"96","author":"Guo","year":"2020","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib17","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.asoc.2015.12.024","article-title":"Multi-objective design of state feedback controllers using reinforced quantum-behaved particle swarm optimization","volume":"41","author":"Hassani","year":"2016","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib18","doi-asserted-by":"crossref","first-page":"3221","DOI":"10.1007\/s00366-020-00997-x","article-title":"A novel approach for forecasting of ground vibrations resulting from blasting: Modified particle swarm optimization coupled extreme learning machine","volume":"37","author":"Jahed\u00a0Armaghani","year":"2021","journal-title":"Engineering with Computers"},{"key":"2023061017403551500_bib19","doi-asserted-by":"crossref","first-page":"3321","DOI":"10.1007\/s00366-021-01329-3","article-title":"A novel technique based on the improved firefly algorithm coupled with extreme learning machine (ELM-IFF) for predicting the thermal conductivity of soil","volume":"38","author":"Kardani","year":"2022","journal-title":"Engineering with Computers"},{"key":"2023061017403551500_bib20","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","article-title":"Particle swarm optimization","volume-title":"Proceedings of ICNN'95-International Conference on Neural Networks","author":"Kennedy","year":"1995"},{"key":"2023061017403551500_bib21","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1016\/j.ijmachtools.2006.09.001","article-title":"Role of mandrel in NC precision bending process of thin-walled tube","volume":"47","author":"Li","year":"2007","journal-title":"International Journal of Machine Tools & Manufacture"},{"key":"2023061017403551500_bib22","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.cja.2012.12.025","article-title":"\u2018Size effect\u2019 related bending formability of thin-walled aluminum alloy tube","volume":"26","author":"Li","year":"2013","journal-title":"Chinese Journal of Aeronautics"},{"key":"2023061017403551500_bib23","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.asoc.2020.106193","article-title":"Influence of initialization on the performance of metaheuristic optimizers","volume":"91","author":"Li","year":"2020","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib24","first-page":"12","article-title":"A quantum particle swarm optimization algorithm with teamwork evolutionary strategy","volume":"2019","author":"Liu","year":"2019","journal-title":"Mathematical Problems in Engineering"},{"key":"2023061017403551500_bib25","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.aei.2020.101089","article-title":"A novel axle temperature forecasting method based on decomposition, reinforcement learning optimization and neural network","volume":"44","author":"Liu","year":"2020","journal-title":"Advanced Engineering Informatics"},{"key":"2023061017403551500_bib26","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1007\/s00170-013-4983-0","article-title":"Experimental study on the effect of dies on wall thickness distribution in NC bending of thin-walled rectangular 3A21 aluminum alloy tube","volume":"68","author":"Liu","year":"2013","journal-title":"International Journal of Advanced Manufacturing Technology"},{"key":"2023061017403551500_bib27","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1109\/TCYB.2019.2925015","article-title":"A novel sigmoid-function-based adaptive weighted particle swarm optimizer","volume":"51","author":"Liu","year":"2021","journal-title":"IEEE Transactions on Cybernetics"},{"key":"2023061017403551500_bib28","doi-asserted-by":"crossref","DOI":"10.1016\/j.asoc.2020.106894","article-title":"QPSO algorithm based on Levy flight and its application in fuzzy portfolio","volume":"99","author":"Lu","year":"2021","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib29","first-page":"267","article-title":"Rotary draw bending of small diameter copper tubes: Predicting the quality of the cross-section","volume-title":"Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture","author":"Mentella","year":"2012"},{"key":"2023061017403551500_bib30","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s00366-019-00723-2","article-title":"Prediction of ultimate bearing capacity through various novel evolutionary and neural network models","volume":"36","author":"Moayedi","year":"2020","journal-title":"Engineering with Computers"},{"key":"2023061017403551500_bib31","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1007\/s00366-019-00894-y","article-title":"Research on deformation prediction of tunnel surrounding rock using the model combining firefly algorithm and nonlinear auto-regressive dynamic neural network","volume":"37","author":"Pan","year":"2021","journal-title":"Engineering with Computers"},{"key":"2023061017403551500_bib32","doi-asserted-by":"crossref","first-page":"5150","DOI":"10.1109\/TII.2019.2949355","article-title":"Tool wear prediction via multidimensional stacked sparse autoencoders with feature fusion","volume":"16","author":"Shi","year":"2020","journal-title":"IEEE Transactions on Industrial Informatics"},{"key":"2023061017403551500_bib33","first-page":"69","article-title":"A modified particle swarm optimizer","volume-title":"Proceedings of the IEEE International Conference on Evolutionary Computation","author":"Shi","year":"1998"},{"key":"2023061017403551500_bib34","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1162\/EVCO_a_00049","article-title":"Quantum-behaved particle swarm optimization: Analysis of individual particle behavior and parameter selection","volume":"20","author":"Sun","year":"2012","journal-title":"Evolutionary Computation"},{"key":"2023061017403551500_bib35","first-page":"325","article-title":"Particle swarm optimization with particles having quantum behavior","volume-title":"Proceedings of the 2004 Congress on Evolutionary Computation","author":"Sun","year":"2004"},{"key":"2023061017403551500_bib37","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1007\/11908029_76","article-title":"Enhancing global search ability of quantum-behaved particle swarm optimization by maintaining diversity of the swarm","volume-title":"Proceedings of the 5th International Conference on Rough Sets and Current Trends in Computing","author":"Sun","year":"2006"},{"key":"2023061017403551500_bib39","doi-asserted-by":"crossref","first-page":"3049","DOI":"10.1109\/ICSMC.2005.1571614","article-title":"Adaptive parameter control for quantum-behaved particle swarm optimization on individual level","volume-title":"Proceedings of the 2005 IEEE International Conference on Systems, Man and cybernetics","author":"Sun","year":"2005"},{"key":"2023061017403551500_bib40","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1016\/S0308-0161(00)00061-2","article-title":"Plastic-deformation analysis in tube bending","volume":"77","author":"Tang","year":"2000","journal-title":"International Journal of Pressure Vessels and Piping"},{"key":"2023061017403551500_bib41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijsolstr.2020.02.007","article-title":"A multi-fidelity competitive sampling method for surrogate-based stacking sequence optimization of composite shells with multiple cutouts","volume":"193","author":"Tian","year":"2020","journal-title":"International Journal of Solids and Structures"},{"key":"2023061017403551500_bib42","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s13042-013-0168-2","article-title":"Parallel quantum-behaved particle swarm optimization","volume":"5","author":"Tian","year":"2014","journal-title":"International Journal of Machine Learning and Cybernetics"},{"key":"2023061017403551500_bib43","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1007\/s00170-021-08051-w","article-title":"Spatial variable curvature metallic tube bending springback numerical approximation prediction and compensation method considering cross-section distortion defect","volume":"118","author":"Wang","year":"2022","journal-title":"International Journal of Advanced Manufacturing Technology"},{"key":"2023061017403551500_bib44","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1016\/S1003-6326(06)60344-0","article-title":"Effect of frictions on cross section quality of thin-walled tube NC bending","volume":"16","author":"Yang","year":"2006","journal-title":"Transactions of Nonferrous Metals Society of China"},{"key":"2023061017403551500_bib45","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.jmatprotec.2004.04.410","article-title":"Wrinkling analysis for forming limit of tube bending processes","volume":"152","author":"Yang","year":"2004","journal-title":"Journal of Materials Processing Technology"},{"key":"2023061017403551500_bib46","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.asoc.2020.106880","article-title":"Performance analysis and prediction of asymmetric two-level priority polling system based on BP neural network","volume":"99","author":"Yang","year":"2021","journal-title":"Applied Soft Computing"},{"key":"2023061017403551500_bib47","doi-asserted-by":"crossref","first-page":"3151","DOI":"10.1007\/s00170-020-06506-0","article-title":"Springback prediction model and its compensation method for the variable curvature metal tube bending forming","volume":"112","author":"Zhang","year":"2021","journal-title":"International Journal of Advanced Manufacturing Technology"},{"key":"2023061017403551500_bib48","first-page":"22","article-title":"Spring-back prediction of the bi-layered metallic tube under CNC bending considering neutral layer shifting extraction","volume":"10","author":"Zhang","year":"2020","journal-title":"Applied Sciences-Basel"},{"key":"2023061017403551500_bib49","doi-asserted-by":"crossref","first-page":"3847","DOI":"10.1007\/s00366-020-01267-6","article-title":"Improved Levenberg-Marquardt backpropagation neural network by particle swarm and whale optimization algorithms to predict the deflection of RC beams","volume":"38","author":"Zhao","year":"2021","journal-title":"Engineering with Computers"},{"key":"2023061017403551500_bib50","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1177\/0036850420984303","article-title":"Springback angle prediction of circular metal tube considering the interference of cross-sectional distortion in mandrel-less rotary draw bending","volume":"104","author":"Zhou","year":"2021","journal-title":"Science Progress"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwad037\/50098951\/qwad037.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/10\/3\/1060\/50569718\/qwad037.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/10\/3\/1060\/50569718\/qwad037.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,10]],"date-time":"2023-06-10T17:41:11Z","timestamp":1686418871000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/10\/3\/1060\/7143108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,25]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,4,29]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwad037","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,6]]},"published":{"date-parts":[[2023,4,25]]}}}