{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T03:09:03Z","timestamp":1784344143056,"version":"3.55.0"},"reference-count":35,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T00:00:00Z","timestamp":1726099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of P.R. China","award":["62272244"],"award-info":[{"award-number":["62272244"]}]},{"name":"National Natural Science Foundation of P.R. China","award":["62302232"],"award-info":[{"award-number":["62302232"]}]},{"name":"National Natural Science Foundation of P.R. China","award":["62372248"],"award-info":[{"award-number":["62372248"]}]},{"name":"National Natural Science Foundation of P.R. China","award":["62302236"],"award-info":[{"award-number":["62302236"]}]},{"name":"National Natural Science Foundation of P.R. China","award":["62102196"],"award-info":[{"award-number":["62102196"]}]},{"name":"National Natural Science Foundation of P.R. China","award":["22KJA520010"],"award-info":[{"award-number":["22KJA520010"]}]},{"name":"\u201c333\u201d Project of Jiangsu Province, and the Nature Science Research of Jiangsu Higher Education Institutions of China","award":["62272244"],"award-info":[{"award-number":["62272244"]}]},{"name":"\u201c333\u201d Project of Jiangsu Province, and the Nature Science Research of Jiangsu Higher Education Institutions of China","award":["62302232"],"award-info":[{"award-number":["62302232"]}]},{"name":"\u201c333\u201d Project of Jiangsu Province, and the Nature Science Research of Jiangsu Higher Education Institutions of China","award":["62372248"],"award-info":[{"award-number":["62372248"]}]},{"name":"\u201c333\u201d Project of Jiangsu Province, and the Nature Science Research of Jiangsu Higher Education Institutions of China","award":["62302236"],"award-info":[{"award-number":["62302236"]}]},{"name":"\u201c333\u201d Project of Jiangsu Province, and the Nature Science Research of Jiangsu Higher Education Institutions of China","award":["62102196"],"award-info":[{"award-number":["62102196"]}]},{"name":"\u201c333\u201d Project of Jiangsu Province, and the Nature Science Research of Jiangsu Higher Education Institutions of China","award":["22KJA520010"],"award-info":[{"award-number":["22KJA520010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With the development of the IoT, Wireless Rechargeable Sensor Networks (WRSNs) derive more and more application scenarios with diverse performance requirements. In scenarios where the energy consumption rate of sensor nodes changes dynamically, most existing charging scheduling methods are not applicable. The incorrect estimation of node energy requirement may lead to the death of critical nodes, resulting in missing events. To address this issue, we consider both the spatial imbalance and temporal dynamics of the energy consumption of the nodes, and minimize the Event Missing Rate (EMR) as the goal. Firstly, an Energy Consumption Balanced Tree (ECBT) construction method is proposed to prolong the lifetime of each node. Then, we transform the goal into Maximizing the value of the Evaluation function of each node\u2019s Energy Consumption Rate prediction (MEECR). Afterwards, the setting of the evaluation function is explored and the MEECR is further transformed into a variant of the knapsack problem, namely \u201cthe alternating backpack problem\u201d, and solved by dynamic programming. After predicting the energy consumption rate of the nodes, a charging scheduling scheme that meets the Dual Constraints of Nodes\u2019 energy requirements and MC\u2019s capability (DCNM) is developed. Simulations demonstrate the advantages of the proposed method. Compared to the baselines, the EMR was reduced by an average of 35.2% and 26.9%.<\/jats:p>","DOI":"10.3390\/s24185931","type":"journal-article","created":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T03:03:37Z","timestamp":1726196617000},"page":"5931","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Charging Scheduling Method for Wireless Rechargeable Sensor Networks Based on Energy Consumption Rate Prediction for Nodes"],"prefix":"10.3390","volume":"24","author":[{"given":"Songjiang","family":"Huang","sequence":"first","affiliation":[{"name":"School of Computer Science, Software and Cyberspace Security, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2347-2073","authenticated-orcid":false,"given":"Chao","family":"Sha","sequence":"additional","affiliation":[{"name":"School of Computer Science, Software and Cyberspace Security, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinyi","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Software and Cyberspace Security, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingwen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science, Software and Cyberspace Security, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruchuan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science, Software and Cyberspace Security, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, H., Wang, X., Ge, B., Zhang, T., and Zhu, Z. (2023). A Multi-Strategy Improved Sparrow Search Algorithm for Coverage Optimization in a WSN. Sensors, 23.","DOI":"10.3390\/s23084124"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Orfanos, V.A., Kaminaris, S.D., Papageorgas, P., Piromalis, D.D., and Kandris, D. (2023). A Comprehensive Review of IoT Networking Technologies for Smart Home Automation Applications. J. Sens. Actuator Netw., 12.","DOI":"10.3390\/jsan12020030"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1109\/TCE.2020.2987433","article-title":"Congestion Free Routing Mechanism for IoT-Enabled Wireless Sensor Networks for Smart Healthcare Applications","volume":"66","author":"Chanak","year":"2020","journal-title":"IEEE Trans. Consum. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.asoc.2018.11.022","article-title":"Periodic charging planning for a mobile WCE in wireless rechargeable sensor networks based on hybrid PSO and GA algorithm","volume":"75","author":"Lyu","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3135","DOI":"10.1109\/TVT.2019.2962877","article-title":"Research on Cost-Balanced Mobile Energy Replenishment Strategy for Wireless Rechargeable Sensor Networks","volume":"69","author":"Sha","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2649","DOI":"10.1109\/JIOT.2020.3020134","article-title":"A Periodic and Distributed Energy Supplement Method Based on Maximum Recharging Benefit in Sensor Networks","volume":"8","author":"Sha","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chen, T.-S., Chen, J.-J., Gao, X.-Y., and Chen, T.-C. (2022). Mobile Charging Strategy for Wireless Rechargeable Sensor Networks. Sensors, 22.","DOI":"10.3390\/s22010359"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"17585","DOI":"10.1109\/JIOT.2023.3277667","article-title":"Optimizing Energy Consumption and Provisioning for Wireless Charging and Data Collection in Large-Scale WRSNs with Mobile Elements","volume":"10","author":"Ijemaru","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"13699","DOI":"10.1109\/JSEN.2024.3373664","article-title":"Deep Reinforcement Learning-Based Joint Sequence Scheduling and Trajectory Planning in Wireless Rechargeable Sensor Networks","volume":"24","author":"Jiang","year":"2024","journal-title":"IEEE Sens. J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Simitha, K.M., and Raj, S. (2019, January 12\u201314). IoT and WSN Based Water Quality Monitoring System. Proceedings of the 2019 3rd International Conference on Electronics, Communication and Aerospace Technology (ICECA), Coimbatore, India.","DOI":"10.1109\/ICECA.2019.8821859"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1109\/TMC.2017.2732979","article-title":"Combining Solar Energy Harvesting with Wireless Charging for Hybrid Wireless Sensor Networks","volume":"17","author":"Wang","year":"2018","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1741","DOI":"10.1109\/TVT.2019.2959808","article-title":"Energy-Efficient UAV Routing for Wireless Sensor Networks","volume":"69","author":"Baek","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"101401","DOI":"10.1016\/j.pmcj.2021.101401","article-title":"EMPC: Energy-Minimization Path Construction for data collection and wireless charging in WRSN","volume":"73","author":"Zhong","year":"2021","journal-title":"Pervasive Mob. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3888","DOI":"10.1109\/JSEN.2020.3023301","article-title":"J-RCA: A Joint Routing and Charging Algorithm with WCE Assisted Data Gathering in Wireless Rechargeable Sensor Networks","volume":"21","author":"Lu","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/JIOT.2020.3005598","article-title":"Dynamic Charging Scheme Problem with Actor\u2013Critic Reinforcement Learning","volume":"8","author":"Yang","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2478","DOI":"10.1109\/TNET.2021.3095280","article-title":"Minimizing Charging Delay for Directional Charging","volume":"29","author":"Lin","year":"2021","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"93731","DOI":"10.1109\/ACCESS.2022.3203410","article-title":"Multimobile Charger Charging Strategy Based on Dual Partitioning Model for Wireless Rechargeable Sensor Networks","volume":"10","author":"Jia","year":"2022","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3526090","article-title":"DMCP: A Distributed Mobile Charging Protocol in Wireless Rechargeable Sensor Networks","volume":"19","author":"Kaswan","year":"2022","journal-title":"ACM Trans. Sens. Netw."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, N., Wu, J., and Dai, H. (2019, January 7\u201310). Bundle Charging: Wireless Charging Energy Minimization in Dense Wireless Sensor Networks. Proceedings of the 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS), Dallas, TX, USA.","DOI":"10.1109\/ICDCS.2019.00085"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2345","DOI":"10.1109\/TNET.2023.3248088","article-title":"Energy Cost Minimization in Wireless Rechargeable Sensor Networks","volume":"31","author":"Jia","year":"2023","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"11796","DOI":"10.1109\/JIOT.2021.3132015","article-title":"Joint Scheduling and Trajectory Optimization of Charging UAV in Wireless Rechargeable Sensor Networks","volume":"9","author":"Liu","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Dai, H., Wang, X., Xu, L., Dong, C., Liu, Q., Meng, L., and Chen, G. (2020, January 3\u20136). Area Charging for Wireless Rechargeable Sensors. Proceedings of the 2020 29th International Conference on Computer Communications and Networks (ICCCN), Honolulu, HI, USA.","DOI":"10.1109\/ICCCN49398.2020.9209664"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"108573","DOI":"10.1016\/j.comnet.2021.108573","article-title":"Charging UAV deployment for improving charging performance of wireless rechargeable sensor networks via joint optimization approach","volume":"201","author":"Liang","year":"2021","journal-title":"Comput. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3512888","article-title":"Optimal Charging Oriented Sensor Placement and Flexible Scheduling in Rechargeable WSNs","volume":"18","author":"Wu","year":"2022","journal-title":"ACM Trans. Sens. Netw. (TOSN)"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1109\/TNET.2022.3199389","article-title":"Robust Wireless Rechargeable Sensor Networks","volume":"31","author":"Yang","year":"2023","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3518","DOI":"10.1109\/JSYST.2020.2977984","article-title":"A Periodic Multinode Charging and Data Collection Scheme with Optimal Traveling Path in WRSNs","volume":"14","author":"Lyu","year":"2020","journal-title":"IEEE Syst. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1109\/TGCN.2021.3080918","article-title":"A Novel Joint Optimization Method Based on Mobile Data Collection for Wireless Rechargeable Sensor Networks","volume":"5","author":"Boukerche","year":"2021","journal-title":"IEEE Trans. Green Commun. Netw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1863","DOI":"10.1109\/TGCN.2023.3305026","article-title":"RECO: On-Demand Recharging and Data Collection for Wireless Rechargeable Sensor Networks","volume":"7","author":"Wedaj","year":"2023","journal-title":"IEEE Trans. Green Commun. Netw."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1109\/TNET.2022.3220927","article-title":"Maximizing Energy Efficiency of Period-Area Coverage with a UAV for Wireless Rechargeable Sensor Networks","volume":"31","author":"Lin","year":"2023","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/TMC.2018.2887381","article-title":"CHASE: Charging and Scheduling Scheme for Stochastic Event Capture in Wireless Rechargeable Sensor Networks","volume":"19","author":"Dai","year":"2020","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Aloqaily, O.I., Flocchini, P., and Santoro, N. (2020, January 20\u201322). Achieving Immortality in Wireless Rechargeable Sensor Networks Using Local Learning. Proceedings of the 2020 International Symposium on Networks, Computers and Communications (ISNCC), Montreal, QC, Canada.","DOI":"10.1109\/ISNCC49221.2020.9297268"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3993","DOI":"10.1109\/JSYST.2021.3109056","article-title":"Coverage and Connectivity Aware Energy Charging Mechanism Using Mobile Charger for WRSNs","volume":"16","author":"Kan","year":"2022","journal-title":"IEEE Syst. J."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Yang, J., Bai, J.-S., and Xu, Q. (2020). An Online Charging Scheme for Wireless Rechargeable Sensor Networks Based on a Radical Basis Function. Sensors, 20.","DOI":"10.3390\/s20010205"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Chen, Z., Jia, X., Wei, Z., and Wang, J. (June, January 28). Age of Information and its Distribution Properties in Energy Harvesting WSN. Proceedings of the ICC 2023\u2014IEEE International Conference on Communications, Rome, Italy.","DOI":"10.1109\/ICC45041.2023.10279831"},{"key":"ref_35","unstructured":"Heinzelman, W.B., Chandrakasan, A., and Balakrishnan, H. (2000, January 4\u20137). Energy-efficient communication protocol for wireless microsensor networks. Proceedings of the 33rd Annual Hawaii International Conference on System Sciences, Maui, HI, USA."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/18\/5931\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:55:08Z","timestamp":1760111708000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/18\/5931"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,12]]},"references-count":35,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["s24185931"],"URL":"https:\/\/doi.org\/10.3390\/s24185931","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,12]]}}}