{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T07:58:21Z","timestamp":1781683101242,"version":"3.54.5"},"reference-count":41,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T00:00:00Z","timestamp":1764028800000},"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":["62401429, 62401445, and 62425113"],"award-info":[{"award-number":["62401429, 62401445, and 62425113"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2024M761178 and 2025M771739"],"award-info":[{"award-number":["2024M761178 and 2025M771739"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postdoctoral Fellowship Program of CPSF","award":["GZC20241332, GZC20232048 and GZC20251207"],"award-info":[{"award-number":["GZC20241332, GZC20232048 and GZC20251207"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["ZYTS25144"],"award-info":[{"award-number":["ZYTS25144"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>System reliability, which is essential for the normal operation of satellites in orbit, is decisively governed by the performance of solar array, making accurate temperature forecasting of solar array imperative. Reliable solar array temperature forecasting is essential for predictive maintenance and autonomous power-system management. Forecasting relies on temperature telemetry data, which provide comprehensive thermal information. This task remains challenging due to the high-dimensional, long-horizon temperature sequences with inherent cross-variable coupling, whose dynamics exhibit nonlinear and non-stationary behaviors owing to orbital transitions and varying operational modes. In this context, multi-step forecasting is essential, as it better characterizes long-term dynamics of temperature and provides forward-looking trends that are beyond the capability of single-step forecasting. To tackle these issues, we propose a solar array temperature multivariate trend forecasting method based on Cross-Attention Patch Time Series Transformer (CA-PatchTST). Specifically, we decompose temperature variables into trend and residual components using a moving average filter to suppress noise and highlight the dominant component. In addition, the PatchTST model extracts local features and long-term dependencies of the trend and residual components separately through the patching encoders and channel-independent mechanisms. The cross-attention mechanism is designed to capture the correlation between temperature variables of different devices in solar array. Extensive experiments on the real solar array temperature dataset demonstrate that the CA-PatchTST surpasses mainstream baselines in root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), with ablation studies further confirming the complementary roles of sequence decomposition and cross-attention.<\/jats:p>","DOI":"10.3390\/s25237199","type":"journal-article","created":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T16:31:54Z","timestamp":1764088314000},"page":"7199","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Solar Array Temperature Multivariate Trend Forecasting Method Based on the CA-PatchTST Model"],"prefix":"10.3390","volume":"25","author":[{"given":"Yunhai","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of Electronic Information Countermeasure and Simulation Technology of Ministry of Education, Xidian University, Xi\u2019an 710071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4636-2966","authenticated-orcid":false,"given":"Xiaoran","family":"Shi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronic Information Countermeasure and Simulation Technology of Ministry of Education, Xidian University, Xi\u2019an 710071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6297-623X","authenticated-orcid":false,"given":"Zhenxi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronic Information Countermeasure and Simulation Technology of Ministry of Education, Xidian University, Xi\u2019an 710071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Aerospace Science and Technology, Xidian University, Xi\u2019an 710071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nwankwo, V.U., Jibiri, N.N., and Kio, M.T. 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