{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T04:10:48Z","timestamp":1773202248734,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,23]],"date-time":"2020-01-23T00:00:00Z","timestamp":1579737600000},"content-version":"vor","delay-in-days":0,"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":["U1737207"],"award-info":[{"award-number":["U1737207"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The entropy evaluation method of assembly stress has become a hot topic in recent years. However, the current research can only evaluate the maximum stress magnitude and stress magnitude uniformity, and it cannot evaluate the stress position distribution. In this paper, an evaluation method of stress distribution characterized by strain energy density distribution is proposed. In this method, the relative entropy is used as the evaluation index of the stress distribution difference between the error model and the ideal model. It can evaluate not only the stress magnitude, but also the stress position. On this basis, an optimization method of the precise assembly process which takes the relative entropy as the optimization objective is proposed. The stress distributions of the optical lens are evaluated, and the assembly angle of the spacer in the process of the optical lens system assembly is optimized. By comparing the stress distribution of the optimized model and the ideal model, the validity of this method is proved.<\/jats:p>","DOI":"10.3390\/e22020137","type":"journal-article","created":{"date-parts":[[2020,1,23]],"date-time":"2020-01-23T10:36:02Z","timestamp":1579775762000},"page":"137","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["An Optimization Method of Precision Assembly Process Based on the Relative Entropy Evaluation of the Stress Distribution"],"prefix":"10.3390","volume":"22","author":[{"given":"Zifu","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhijing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Klein, B., and Mannewitz, F. (1993). Statistische Tolerierung, Vieweg+Teubner Verlag.","DOI":"10.1007\/978-3-663-20230-1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1007\/s00170-017-0936-3","article-title":"A novel modelling method of geometric errors for precision assembly","volume":"94","author":"Zhang","year":"2018","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cao, Z., and Ma, S. (2009, January 11\u201312). Research on Scheduling and Simulation of Production for the Mixed Model General Automotive Assembly Process, Measuring Technology and Mechatronics Automation. Proceedings of the Measuring Technology and Mechatronics Automation, Zhangjiajie, China.","DOI":"10.1109\/ICMTMA.2009.314"},{"key":"ref_4","unstructured":"Singh, I., Qin, I., Hui, X., and Huynh, C. (June, January 29). Pd-coated Cu wire bonding technology: Chip design, process optimization, production qualification and reliability test for high reliability semiconductor devices. Proceedings of the Electronic Components and Technology Conference, San Diego, CA, USA."},{"key":"ref_5","first-page":"130","article-title":"Online Control Threshold Optimization for Complex Mechanical Products Assembly Process Based on Hybrid Genetic Particle Swarm Optimization","volume":"52","author":"Wang","year":"2016","journal-title":"J. Mech. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Jiao, S., Zhang, C., Liu, G., Lu, J., and Tang, S. (2017). Experimental investigation of residual stress distribution during turning of weak stiffness revolving parts. AIP Conference Proceedings, AIP Publishing LLC.","DOI":"10.1063\/1.4993025"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.compgeo.2018.06.002","article-title":"Internal stress distribution and cracking around flaws and openings of rock block under uniaxial compression: A particle mechanics approach","volume":"102","author":"Xiang","year":"2018","journal-title":"Comput. Geotech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1067\/mva.2000.103971","article-title":"Wall stress distribution on three-dimensionally reconstructed models of human abdominal aortic aneurysm","volume":"31","author":"Raghavan","year":"2000","journal-title":"J. Vasc. Surg."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/S0109-5641(01)00042-2","article-title":"Effect of adhesive layer properties on stress distribution in composite restorations\u2014A 3D finite element analysis","volume":"18","author":"Ausiello","year":"2002","journal-title":"Dent. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00477-014-0959-3","article-title":"Comparison between Shannon and Tsallis entropies for prediction of shear stress distribution in open channels","volume":"29","author":"Bonakdari","year":"2015","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.physa.2017.08.023","article-title":"Formulating the shear stress distribution in circular open channels based on the Renyi entropy","volume":"490","author":"Khozani","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_12","first-page":"340","article-title":"The application of an improved particle swarm algorithm based on the information entropy in truss structure optimization design","volume":"19","author":"Zhou","year":"2012","journal-title":"Chin. J. Eng. Des."},{"key":"ref_13","first-page":"20","article-title":"Evolution Analysis of Rock System State Based on Stress Field Entropy","volume":"29","author":"Zhang","year":"2009","journal-title":"Min. Metall. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Fang, Y., Jin, X., Huang, C., and Zhang, Z. (2017). Entropy-Based Method for Evaluating Contact Strain-Energy Distribution for Assembly Accuracy Prediction. Entropy, 19.","DOI":"10.3390\/e19020049"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chen, X., Jin, X., Shang, K., and Zhang, Z. (2019). Entropy-Based Method to Evaluate Contact-Pressure Distribution for Assembly-Accuracy Stability Prediction. Entropy, 21.","DOI":"10.3390\/e21030322"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Alberto, B., Matteo, G., and Alessandro, T. (2017). Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation. Entropy, 19.","DOI":"10.3390\/e19070301"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Shang, Y. (2016). Bounding Extremal Degrees of Edge-Independent Random Graphs Using Relative Entropy. Entropy, 18.","DOI":"10.3390\/e18020053"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_19","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, The MIT Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0010-4485(99)00028-7","article-title":"Representation and interpretation of geometric tolerances for polyhedral objects. II.: Size, orientation and position tolerances","volume":"31","author":"Roy","year":"1999","journal-title":"Comput. Aided Des."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/TASE.2005.853583","article-title":"A scheme for mapping tolerance specifications to generalized deviation space for use in tolerance synthesis and analysis","volume":"3","author":"Wang","year":"2006","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s00170-010-2839-4","article-title":"Simulation of variational compliant assemblies with shape errors based on morphing mesh approach","volume":"53","author":"Franciosa","year":"2011","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1007\/s00170-018-2305-2","article-title":"Deviation modeling of manufactured surfaces from a perspective of manufacturing errors","volume":"98","author":"Wu","year":"2018","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1016\/j.procir.2016.01.031","article-title":"Physics-driven Shape Variation Modelling at Early Design Stage","volume":"41","author":"Das","year":"2016","journal-title":"Procedia CIRP"},{"key":"ref_25","first-page":"62","article-title":"A Spectroscopic Method for Measuring Stress of Optical Glass","volume":"24","author":"Yao","year":"2010","journal-title":"J. Chang. Inst. Technol."},{"key":"ref_26","first-page":"40","article-title":"Autotesting of the Optical Glass Stress","volume":"33","author":"Yong","year":"2005","journal-title":"Glass Enamel"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhang, L.J., Yi, T., and Bai, T.Z. (2007, January 11). Research on a system and method of automated whole-field measurement of optical glass stress. Proceedings of the SPIE\u2014The International Society for Optical Engineering, Beijing, China.","DOI":"10.1117\/12.760237"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"F\u00e1tima, G., Rub\u00e9n, L., Marina, B., and Rub\u00e9n, G. (2017). Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method. Materials, 10.","DOI":"10.3390\/ma10101116"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"\u00cd\u00f1iguez-Macedo, S., Lostado-Lorza, R., Escribano-Garc\u00eda, R., and Mart\u00ednez-Calvo, M.\u00c1. (2019). Finite Element Model Updating Combined with Multi-Response Optimization for Hyper-Elastic Materials Characterization. Materials, 12.","DOI":"10.3390\/ma12071019"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/137\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:08:24Z","timestamp":1760364504000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,23]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["e22020137"],"URL":"https:\/\/doi.org\/10.3390\/e22020137","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,23]]}}}