{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T16:14:03Z","timestamp":1770135243226,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:00:00Z","timestamp":1769817600000},"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":["52302460"],"award-info":[{"award-number":["52302460"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["ZCLQN25E0502"],"award-info":[{"award-number":["ZCLQN25E0502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Accurate reconstruction of train collision accidents is essential for understanding impact conditions, assessing crashworthiness, and supporting safety improvements. This study proposes a surrogate-based optimization framework for reconstructing structural damage in train collisions from post-accident observations. The pre-impact kinematic state, expressed by a six-dimensional vector of relative offsets, rotations, and impact velocity, is formulated as an inverse problem in which a Sum of Squared Relative Deviations (SSRD) between measured and simulated residual deformations serves as the objective function. A reduced two-vehicle finite element (FE) model is developed to capture the dominant impact dynamics, an Optimal Latin Hypercube Design is used to sample the parameter space, and a Kriging surrogate model is constructed to approximate the response. A simulated annealing algorithm is applied to search for the global minimum. The framework is demonstrated on a real high-speed rear-end collision of electric multiple units. The Kriging model achieves a coefficient of determination of about 0.85, and the optimized kinematic state yields FE-predicted residual deformations that agree with field measurements at key locations to within about 5%. The results show that the method can efficiently reconstruct physically plausible collision scenarios and provide insight into parameter sensitivity and identifiability for railway safety analysis.<\/jats:p>","DOI":"10.3390\/systems14020156","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T09:48:08Z","timestamp":1770025688000},"page":"156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Surrogate-Based Reconstruction of Structural Damage in Train Collisions: A Systematic Optimization Framework"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-2933-749X","authenticated-orcid":false,"given":"Hui","family":"Zhao","sequence":"first","affiliation":[{"name":"Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dehong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Guangzhou EMU Depot, China Railway Guangzhou Group Co., Ltd., Guangzhou 511483, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory for Track Traffic Safety of Ministry of Education, Central South University, Changsha 410075, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107495","DOI":"10.1016\/j.aap.2024.107495","article-title":"Investigation on the Dynamic Characteristic of Occupant During the Frontal Collision Between High-Speed Train and Obstacle","volume":"199","author":"Yao","year":"2024","journal-title":"Accid. 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