{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T01:47:23Z","timestamp":1768441643088,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T00:00:00Z","timestamp":1704844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2021YFA1003501"],"award-info":[{"award-number":["2021YFA1003501"]}]},{"name":"National Key R&amp;D Program of China","award":["2021RD16"],"award-info":[{"award-number":["2021RD16"]}]},{"name":"National Key R&amp;D Program of China","award":["XLYC2002108"],"award-info":[{"award-number":["XLYC2002108"]}]},{"name":"National Key R&amp;D Program of China","award":["DUT22QN251"],"award-info":[{"award-number":["DUT22QN251"]}]},{"name":"Dalian city supports innovation and entrepreneurship projects for high-level talents","award":["2021YFA1003501"],"award-info":[{"award-number":["2021YFA1003501"]}]},{"name":"Dalian city supports innovation and entrepreneurship projects for high-level talents","award":["2021RD16"],"award-info":[{"award-number":["2021RD16"]}]},{"name":"Dalian city supports innovation and entrepreneurship projects for high-level talents","award":["XLYC2002108"],"award-info":[{"award-number":["XLYC2002108"]}]},{"name":"Dalian city supports innovation and entrepreneurship projects for high-level talents","award":["DUT22QN251"],"award-info":[{"award-number":["DUT22QN251"]}]},{"name":"Liaoning Province\u2019s Xing Liao Talents Program","award":["2021YFA1003501"],"award-info":[{"award-number":["2021YFA1003501"]}]},{"name":"Liaoning Province\u2019s Xing Liao Talents Program","award":["2021RD16"],"award-info":[{"award-number":["2021RD16"]}]},{"name":"Liaoning Province\u2019s Xing Liao Talents Program","award":["XLYC2002108"],"award-info":[{"award-number":["XLYC2002108"]}]},{"name":"Liaoning Province\u2019s Xing Liao Talents Program","award":["DUT22QN251"],"award-info":[{"award-number":["DUT22QN251"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2021YFA1003501"],"award-info":[{"award-number":["2021YFA1003501"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2021RD16"],"award-info":[{"award-number":["2021RD16"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["XLYC2002108"],"award-info":[{"award-number":["XLYC2002108"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["DUT22QN251"],"award-info":[{"award-number":["DUT22QN251"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Accurate and rapid thermal load identification based on limited measurement points is crucial for spacecraft on-orbit monitoring. This study proposes a stepwise identification method based on deep learning for identifying structural thermal loads that efficiently map the local responses and overall thermal load of a box structure. To determine the location and magnitude of the thermal load accurately, the proposed method segments a structure into several subregions and applies a cascade of deep learning models to gradually reduce the solution domain. The generalization ability of the model is significantly enhanced by the inclusion of boundary conditions in the deep learning models. In this study, a large simulated dataset was generated by varying the load application position and intensity for each sample. The input variables encompass a small set of structural displacements, while the outputs include parameters related to the thermal load, such as the position and magnitude of the load. Ablation experiments are conducted to validate the effectiveness of this approach. The results show that this method reduces the identification error of the thermal load parameters by more than 45% compared with a single deep learning network. The proposed method holds promise for optimizing the design and analysis of spacecraft structures, contributing to improved performance and reliability in future space missions.<\/jats:p>","DOI":"10.3390\/ma17020357","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T03:21:41Z","timestamp":1704943301000},"page":"357","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stepwise Identification Method of Thermal Load for Box Structure Based on Deep Learning"],"prefix":"10.3390","volume":"17","author":[{"given":"Hongze","family":"Du","sequence":"first","affiliation":[{"name":"State Key Laboratory of Structural Analysis for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Xu","sequence":"additional","affiliation":[{"name":"Ningbo Research Institute, Dalian University of Technology, Ningbo 315016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lizhe","family":"Jiang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Structural Analysis for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yufeng","family":"Bu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Structural Analysis for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenbo","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Structural Analysis for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Yan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Structural Analysis for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China"},{"name":"Ningbo Research Institute, Dalian University of Technology, Ningbo 315016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.ijimpeng.2013.08.005","article-title":"Impact Force Identification with Pseudo-Inverse Method on a Lightweight Structure for under-Determined, Even-Determined and over-Determined Cases","volume":"63","author":"Khoo","year":"2014","journal-title":"Int. J. Impact Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1080\/01495739.2014.937219","article-title":"Practical Algorithms for Online Thermal Stress Calculations and Heating Process Control","volume":"37","author":"Rusin","year":"2014","journal-title":"J. Therm. Stress."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"045004","DOI":"10.1088\/2631-8695\/abbb59","article-title":"Smart Wing Load Alleviation through Optical Fiber Sensing, Load Identification, and Deep Reinforcement Learning","volume":"2","author":"Wada","year":"2020","journal-title":"Eng. Res. Express"},{"key":"ref_4","first-page":"2088","article-title":"Inversion Research on Temperature Field with Nonlinear Multiple Heat Source Using I-DEAS","volume":"32","author":"Yong","year":"2011","journal-title":"J. Astronaut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"S603","DOI":"10.1088\/0264-9381\/21\/5\/032","article-title":"Structural, Thermal, Optical and Gravitational Modelling for LISA","volume":"21","author":"Merkowitz","year":"2004","journal-title":"Class. Quantum Grav."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1115\/1.3246912","article-title":"An Initial Value Approach to the Inverse Heat Conduction Problem","volume":"108","author":"Hensel","year":"1986","journal-title":"J. Heat Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1080\/174159799088027701","article-title":"Three-Dimensional Boundary Inverse Heat Conduction Problem for Regular Coordinate Systems","volume":"7","author":"Alifanov","year":"1999","journal-title":"Inverse Probl. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1115\/1.1751188","article-title":"Control-Oriented Modeling of Thermal Deformation of Machine Tools Based on Inverse Solution of Time-Variant Thermal Loads with Delayed Response","volume":"126","author":"Fraser","year":"2004","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/S0094-5765(98)00058-7","article-title":"Thermal Loads Identification Technique for Materials and Structures in Real Time","volume":"41","author":"Alifenov","year":"1997","journal-title":"Acta Astronaut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/s00466-005-0701-6","article-title":"An Inverse Estimation of Multi-Dimensional Load Distributions in Thermoelasticity Problems via Dual Reciprocity BEM","volume":"37","author":"Tanaka","year":"2005","journal-title":"Comput. Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1080\/10407798908944902","article-title":"Steady-State Two-Dimensional Inverse Heat Conduction","volume":"15","author":"Hensel","year":"1989","journal-title":"Numer. Heat Transf. Part B Fundam."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"124352","DOI":"10.1016\/j.ijheatmasstransfer.2023.124352","article-title":"A New Method to Identify Non-Steady Thermal Load Based on Element Differential Method","volume":"213","author":"Zhou","year":"2023","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1007\/s10778-008-0014-5","article-title":"Identification of the Thermal and Thermostressed States of a Two-Layer Cylinder from Surface Displacements","volume":"44","author":"Yasinskii","year":"2008","journal-title":"Int. Appl. Mech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1080\/01495739.2020.1775534","article-title":"An Inverse Meshfree Thermoelastic Analysis for Identification of Temperature-Dependent Thermal and Mechanical Material Properties","volume":"43","author":"Dadar","year":"2020","journal-title":"J. Therm. Stress."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.ast.2014.07.015","article-title":"Inverse Analysis for Transient Thermal Load Identification and Application to Aerodynamic Heating on Atmospheric Reentry Capsule","volume":"38","author":"Nakamura","year":"2014","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/S0045-7949(98)00085-6","article-title":"Application of Artificial Neural Networks to Load Identification","volume":"69","author":"Cao","year":"1998","journal-title":"Comput. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1007\/s10999-020-09505-x","article-title":"An Efficient Inverse Algorithm for Load Identification of Stochastic Structures","volume":"16","author":"Wang","year":"2020","journal-title":"Int. J. Mech. Mater. Des."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"084013","DOI":"10.1088\/1361-6501\/abe790","article-title":"Detection of Impact on Aircraft Composite Structure Using Machine Learning Techniques","volume":"32","author":"Ai","year":"2021","journal-title":"Meas. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1080\/17415970600573692","article-title":"The Inverse Determination of Aerodynamic Loading from Structural Response Data Using Neural Networks","volume":"14","author":"Trivailo","year":"2006","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1111\/j.1475-1305.2000.tb01175.x","article-title":"Impact location and quantification on a composite panel using neural networks and a genetic algorithm","volume":"36","author":"Worden","year":"2000","journal-title":"Strain"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Huang, D., Gao, Y., Yu, X., and Chen, L. (2022). The Feature Extraction of Impact Response and Load Reconstruction Based on Impulse Response Theory. Machines, 10.","DOI":"10.3390\/machines10070524"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"109621","DOI":"10.1016\/j.ymssp.2022.109621","article-title":"Structural Health Monitoring for Impact Localisation via Machine Learning","volume":"183","author":"Dipietrangelo","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.advengsoft.2018.01.007","article-title":"Static Load Estimation Using Artificial Neural Network: Application on a Wing Rib","volume":"125","author":"Cooper","year":"2018","journal-title":"Adv. Eng. Softw."},{"key":"ref_24","first-page":"287","article-title":"A Deep Learning-Based Computational Algorithm for Identifying Damage Load Condition: An Artificial Intelligence Inverse Problem Solution for Failure Analysis","volume":"117","author":"Ren","year":"2018","journal-title":"Comput. Model. Eng. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"151","DOI":"10.2322\/tjsass.62.151","article-title":"Investigation of inverse analysis and neural network approaches for identifying distributed load using distributed strains","volume":"62","author":"Wada","year":"2019","journal-title":"Trans. Jpn. Soc. Aeronaut. Space Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"103127","DOI":"10.1016\/j.wavemoti.2023.103127","article-title":"Localization of Low-Velocity Impact in CFRP Plate Using Time\u2013Frequency Features of Guided Wave and Convolutional Neural Network","volume":"119","author":"Feng","year":"2023","journal-title":"Wave Motion"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yang, H., Jiang, J., Chen, G., Mohamed, M.S., and Lu, F. (2021). A Recurrent Neural Network-Based Method for Dynamic Load Identification of Beam Structures. Materials, 14.","DOI":"10.3390\/ma14247846"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"106292","DOI":"10.1016\/j.ymssp.2019.106292","article-title":"Impact Load Identification of Nonlinear Structures Using Deep Recurrent Neural Network","volume":"133","author":"Zhou","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Rosafalco, L., Manzoni, A., Mariani, S., and Corigliano, A. (2021). An Autoencoder-Based Deep Learning Approach for Load Identification in Structural Dynamics. Sensors, 21.","DOI":"10.3390\/s21124207"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"075008","DOI":"10.1088\/1361-665X\/acd3c9","article-title":"A Thermal Load Identification Method Based on Physics-Guided Neural Network for Honeycomb Sandwich Structures","volume":"32","author":"Du","year":"2023","journal-title":"Smart Mater. Struct."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/2\/357\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:44:06Z","timestamp":1760103846000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/17\/2\/357"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,10]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["ma17020357"],"URL":"https:\/\/doi.org\/10.3390\/ma17020357","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,10]]}}}