{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T15:57:04Z","timestamp":1772467024445,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2023,11,28]],"date-time":"2023-11-28T00:00:00Z","timestamp":1701129600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Key Research and Development Plan of Shandong Province","award":["2020CXGC011005"],"award-info":[{"award-number":["2020CXGC011005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Drastic changes in the random load of an electromechanical system bring about a reliability problem for the proportional solenoid valve based on a thermal effect. In order to accurately and effectively express the thermal load of a proportional solenoid valve under random load conditions and to meet the requirements of online acquisition, adaptive anomaly detection, and the missing substitution of thermal load data, a thermal load prediction model based on the Kalman filter algorithm is proposed. Taking the compound operation process of an excavator as the object and based on the field testing of an excavator and the independent testing experiment of a proportional solenoid valve in a non-installed state, a method of obtaining historical samples of the proportional solenoid valve\u2019s power and thermal load is given. The k-means clustering algorithm is used to cluster the historical samples of the power and thermal load corresponding to the working posture of a multi-tool excavator. The Grubbs criterion is used to eliminate the outliers in the clustering samples, and unbiased estimation is performed on the clustering samples to obtain the prediction model. The results show that the cross-validation of the sample data under the specific sample characteristics of the thermal load model was carried out. Compared with other methods, the prediction accuracy of the thermal load model based on the Kalman filter is higher, the adaptability is strong, and the maximum prediction deviation percentage is stable within 5%. This study has value as a reference for random cycle thermal load analyses of low-frequency electromechanical products.<\/jats:p>","DOI":"10.3390\/s23239474","type":"journal-article","created":{"date-parts":[[2023,11,28]],"date-time":"2023-11-28T11:43:16Z","timestamp":1701171796000},"page":"9474","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Thermal Load Model of a Proportional Solenoid Valve Based on Random Load Conditions"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-8181-6724","authenticated-orcid":false,"given":"Chenyu","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Tongji University, Shanghai 201804, China"}]},{"given":"Anlin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Tongji University, Shanghai 201804, China"}]},{"given":"Xiaotian","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Tongji University, Shanghai 201804, China"}]},{"given":"Xiaoxiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Tongji University, Shanghai 201804, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1186\/s10033-020-00446-2","article-title":"Research and Development of Electro-hydraulic Control Valves Oriented to Industry 4.0: A Review","volume":"33","author":"Xu","year":"2020","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_2","unstructured":"Lv, Z. (2011). Research on Cartridge Three-Way Proportional Pressure Reducing Valve. [Master\u2019s Thesis, Zhejiang University]."},{"key":"ref_3","first-page":"115","article-title":"Excavator dynamic performance test and its data wavelet processing method","volume":"42","author":"Wang","year":"2014","journal-title":"J. Tongji Univ. (Nat. Sci. Ed.)"},{"key":"ref_4","first-page":"128","article-title":"Anomaly detection model of energy consumption in copper tube production process based on PSO-BP algorithm","volume":"45","author":"Sun","year":"2016","journal-title":"Electro Mech. Eng. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3901\/JME.2003.11.001","article-title":"Multi-factor machine learning prediction model of building basic period","volume":"39","author":"Chen","year":"2022","journal-title":"Eng. Mech."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Brown, B.R. (2023). Engineering Intelligent Systems: Systems Engineering and Design with Artificial Intelligence, Visual Modeling, and Systems Thinking, Wiley.","DOI":"10.1002\/9781119665649"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"75","DOI":"10.9734\/jerr\/2021\/v20i617330","article-title":"Hybrid Based Artificial Intelligence Short\u2014Term Load Forecasting","volume":"20","author":"Adebunmi","year":"2021","journal-title":"J. Eng. Res. Rep."},{"key":"ref_8","first-page":"80","article-title":"Artificial neural network approach for electric load forecasting in power distribution company","volume":"6","author":"Hambali","year":"2017","journal-title":"e-Acad. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"107635","DOI":"10.1016\/j.epsr.2021.107635","article-title":"Applying load profiles propagation to machine learning based electrical energy forecasting","volume":"203","author":"Farah","year":"2022","journal-title":"Electr. Power Syst. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1049\/iet-gtd.2019.0797","article-title":"Mid-term electricity load forecasting by a new composite method based on optimal learning MLP algorithm","volume":"14","author":"Askari","year":"2020","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_11","unstructured":"Shi, S. (2014). Model Parameter Calibration of Hydraulic Excavator based on Experimental Data. [Master\u2019s Thesis, Tongji University]."},{"key":"ref_12","unstructured":"Pan, X. (2022). Research on Fuzzy Clustering Method and Feature Learning Technology for Complex Data. [Ph.D. Thesis, Jiangnan University]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"142894","DOI":"10.1109\/ACCESS.2019.2943916","article-title":"Sensor-Networked Underwater Target Tracking Based on Grubbs Criterion and Improved Particle Filter Algorithm","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wu, X., Hong, B., Peng, X., Wen, F., and Huang, J. (2011, January 6\u20139). Radial basis function neural network based short-term wind power forecasting with Grubbs test. Proceedings of the 2011 4th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT), Weihai, China.","DOI":"10.1109\/DRPT.2011.5994206"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Khashirunnisa, S., Chand, B.K., and Kumari, B.L. (2016, January 18\u201320). Performance analysis of Kalman filter, fuzzy Kalman filter and wind driven optimized Kalman filter for tracking applications. Proceedings of the 2016 2nd International Conference on Communication Control and Intelligent Systems (CCIS), Mathura, India.","DOI":"10.1109\/CCIntelS.2016.7878223"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kocadag, F., and Demirkol, A. (2015, January 19\u201320). Real time tracking of TV satellites on moving vehicles using Kalman filter. Proceedings of the 2015 2nd International Conference on Signal Processing and Integrated Networks (SPIN), Noida, India.","DOI":"10.1109\/SPIN.2015.7095286"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"106231","DOI":"10.1016\/j.engfailanal.2022.106231","article-title":"A critical review on the solenoid valve reliability, performance and remaining useful life including its industrial applications","volume":"136","author":"Angadi","year":"2022","journal-title":"Eng. Fail. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Tang, X., Peng, J., Chen, B., Jiang, F., Yang, Y., Zhang, R., Gao, D., Zhang, X., and Huang, Z. (2019, January 17\u201320). A parameter adaptive data-driven approach for remaining useful life prediction of solenoid valves. Proceedings of the 2019 IEEE International Conference on Prognostics and Health Management (ICPHM), San Francisco, CA, USA.","DOI":"10.1109\/ICPHM.2019.8819382"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"523","DOI":"10.3233\/JIFS-169608","article-title":"Application of particle filter technique to online prognostics for solenoid, valve","volume":"35","author":"Tang","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_20","first-page":"17","article-title":"Study on the efficacy and AUC of normality tests for Perfect and Imperfect Two-stage ordered Set Sampling","volume":"43","author":"Cai","year":"2023","journal-title":"Syst. Sci. Math."},{"key":"ref_21","first-page":"1408","article-title":"Comparison of normality test methods of geotechnical parameters based on pore pressure static cone penetration","volume":"51","author":"Lin","year":"2021","journal-title":"J. Jilin Univ. (Earth Sci. Ed.)"},{"key":"ref_22","first-page":"17","article-title":"A comparison of several normality testing methods based on Monte Carlo stochastic simulation","volume":"7","author":"Zhang","year":"2011","journal-title":"Stat. Decis. Mak."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Gupta, A., and Kumar, A. (2020, January 9\u201312). Mid Term Daily Load Forecasting using ARIMA, Wavelet-ARIMA and Machine Learning. Proceedings of the 2020 IEEE International Conference on Environment and Electrical Engineering and 2020 IEEE Industrial and Commercial Power Systems Europe (EEEIC\/I&CPS Europe), Madrid, Spain.","DOI":"10.1109\/EEEIC\/ICPSEurope49358.2020.9160563"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Du, Y. (2018, January 9\u201311). Application and analysis of forecasting stock price index based on combination of ARIMA model and BP neural network. Proceedings of the 2018 Chinese Control and Decision Conference (CCDC), Shenyang, China.","DOI":"10.1109\/CCDC.2018.8407611"},{"key":"ref_25","first-page":"45","article-title":"Prediction model of UAV engine flight parameters based on optimized VARIMA","volume":"41","author":"Wang","year":"2022","journal-title":"Army Autom."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/23\/9474\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:32:35Z","timestamp":1760131955000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/23\/9474"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,28]]},"references-count":25,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["s23239474"],"URL":"https:\/\/doi.org\/10.3390\/s23239474","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,28]]}}}