{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T13:45:17Z","timestamp":1790948717551,"version":"4.1.0"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,23]],"date-time":"2020-03-23T00:00:00Z","timestamp":1584921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010193","name":"Korea Electric Power Corporation","doi-asserted-by":"publisher","award":["R18XA05"],"award-info":[{"award-number":["R18XA05"]}],"id":[{"id":"10.13039\/501100010193","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2019M3F2A1073179"],"award-info":[{"award-number":["2019M3F2A1073179"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>For efficient and effective energy management, accurate energy consumption forecasting is required in energy management systems (EMSs). Recently, several artificial intelligence-based techniques have been proposed for accurate electric load forecasting; moreover, perfect energy consumption data are critical for the prediction. However, owing to diverse reasons, such as device malfunctions and signal transmission errors, missing data are frequently observed in the actual data. Previously, many imputation methods have been proposed to compensate for missing values; however, these methods have achieved limited success in imputing electric energy consumption data because the period of data missing is long and the dependency on historical data is high. In this study, we propose a novel missing-value imputation scheme for electricity consumption data. The proposed scheme uses a bagging ensemble of multilayer perceptrons (MLPs), called softmax ensemble network, wherein the ensemble weight of each MLP is determined by a softmax function. This ensemble network learns electric energy consumption data with explanatory variables and imputes missing values in this data. To evaluate the performance of our scheme, we performed diverse experiments on real electric energy consumption data and confirmed that the proposed scheme can deliver superior performance compared to other imputation methods.<\/jats:p>","DOI":"10.3390\/s20061772","type":"journal-article","created":{"date-parts":[[2020,3,24]],"date-time":"2020-03-24T07:16:08Z","timestamp":1585034168000},"page":"1772","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":69,"title":["Bagging Ensemble of Multilayer Perceptrons for Missing Electricity Consumption Data Imputation"],"prefix":"10.3390","volume":"20","author":[{"given":"Seungwon","family":"Jung","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9524-5729","authenticated-orcid":false,"given":"Jihoon","family":"Moon","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sungwoo","family":"Park","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1936-6785","authenticated-orcid":false,"given":"Seungmin","family":"Rho","sequence":"additional","affiliation":[{"name":"Department of Software, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sung Wook","family":"Baik","sequence":"additional","affiliation":[{"name":"Department of Software, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0418-4092","authenticated-orcid":false,"given":"Eenjun","family":"Hwang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ain, Q.-U., Iqbal, S., Khan, S.A., Malik, A.W., Ahmad, I., and Javaid, N. (2018). IoT Operating System Based Fuzzy Inference System for Home Energy Management System in Smart Buildings. Sensors, 18.","DOI":"10.3390\/s18092802"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.egyr.2014.10.001","article-title":"Consumer energy management system with integration of smart meters","volume":"1","author":"Pereira","year":"2015","journal-title":"Energy Rep."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.rser.2016.10.054","article-title":"Data quality of electricity consumption data in a smart grid environment","volume":"75","author":"Chen","year":"2017","journal-title":"Renew. Sust. Energ. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kim, T., Ko, W., and Kim, J. (2019). Analysis and Impact Evaluation of Missing Data Imputation in Day-ahead PV Generation Forecasting. Appl. Sci., 9.","DOI":"10.3390\/app9010204"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.enbuild.2019.04.034","article-title":"Recurrent inception convolution neural network for multi short-term load forecasting","volume":"194","author":"Kim","year":"2019","journal-title":"Energy Build."},{"key":"ref_6","unstructured":"Ardakanian, O., Koochakzadeh, N., Singh, R.P., Golab, L., and Keshav, S. (2014, January 28). Computing Electricity Consumption Profiles from Household Smart Meter Data. Proceedings of the Workshops of the EDBT\/ICDT 2014 Joint Conference (EDBT\/ICDT 2014), Athens, Greece."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Peppanen, J., Zhang, X., Grijalva, S., and Reno, M.J. (2016, January 6\u20139). Handling bad or missing smart meter data through advanced data imputation. Proceedings of the 2016 IEEE Power & Energy Society, Innovative Smart Grid Technologies Conference (ISGT), Minneapolis, MN, USA.","DOI":"10.1109\/ISGT.2016.7781213"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kim, M., Park, S., Lee, J., Joo, Y., and Choi, J.K. (2017). Learning-Based Adaptive Imputation Method with kNN Algorithm for Missing Power Data. Energies, 10.","DOI":"10.3390\/en10101668"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.trc.2011.12.006","article-title":"The retrieval of intra-day trend and its influence on traffic prediction","volume":"22","author":"Chen","year":"2012","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1016\/j.compenvurbsys.2012.08.005","article-title":"Non-parametric regression for space\u2013time forecasting under missing data","volume":"36","author":"Haworth","year":"2012","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"042025","DOI":"10.1088\/1757-899X\/490\/4\/042025","article-title":"Missing Data estimation with a bi-dimensional adaptive weighted method for power grid data","volume":"490","author":"Wang","year":"2019","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5820","DOI":"10.1109\/TSG.2017.2697440","article-title":"A hierarchical framework for smart grid anomaly detection using large-scale smart meter data","volume":"9","author":"Moghaddass","year":"2017","journal-title":"IEEE Trans. Smart Grid."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Grigoras, G., Cartina, G., Bobric, E.C., and Barbulescu, C. (July, January 28). Missing data treatment of the load profiles in distribution networks. Proceedings of the 2009 IEEE Bucharest PowerTech, Bucharest, Romania.","DOI":"10.1109\/PTC.2009.5282021"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Huang, Z., and Zhu, T. (December, January 29). Real-time data and energy management in microgrids. Proceedings of the 2016 IEEE Real-Time Systems Symposium (RTSS), Porto, Portugal.","DOI":"10.1109\/RTSS.2016.017"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Turrado, C., S\u00e1nchez Lasheras, F., Calvo-Roll\u00e9, J., Pi\u00f1\u00f3n-Pazos, A.J., Melero, M., and de Cos Juez, F. (2016). A Hybrid Algorithm for Missing Data Imputation and Its Application to Electrical Data Loggers. Sensors, 16.","DOI":"10.3390\/s16091467"},{"key":"ref_16","unstructured":"Raki\u0107evi\u0107, J., Savi\u0107, G., and Bulaji\u0107, M. (2016). Selecting an Appropriate Method for Missing Data Imputation: A Case of Countries Ranking. Symposium proceedings-XV International symposium Symorg 2016: Reshaping the Future through Sustainable Business Development and Entrepreneurship, University of Belgrade, Faculty of Organizational Sciences."},{"key":"ref_17","unstructured":"Mohammadi, F., and Zheng, C. (2018, January 4). A Precise SVM Classification Model for Predictions with Missing Data. Proceedings of the 4th National Conference on Applied Research in Electrical, Mechanical Computer and IT Engineering, Shiraz, Iran."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"31069","DOI":"10.3390\/s151229842","article-title":"A New Missing Data Imputation Algorithm Applied to Electrical Data Loggers","volume":"15","year":"2015","journal-title":"Sensors"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.3390\/en7041935","article-title":"Short-term electrical peak demand forecasting in a large government building using artificial neural networks","volume":"7","author":"Grant","year":"2014","journal-title":"Energies"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hosein, S., and Hosein, P. (2017, January 23\u201326). Load forecasting using deep neural networks. Proceedings of the 2017 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), Washington DC, USA.","DOI":"10.1109\/ISGT.2017.8085971"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Nguyen, H.H., Harbi, N., and Darmont, J. (2011, January 21\u201323). An efficient local region and clustering-based ensemble system for intrusion detection. Proceedings of the 15th Symposium on International Database Engineering & Applications, Lisboa, Portugal.","DOI":"10.1145\/2076623.2076647"},{"key":"ref_22","first-page":"2821","article-title":"Smoothing forecast ensembles with fitted probability distributions","volume":"128","author":"Wilks","year":"2002","journal-title":"Q. J. R. Meteorolog. Soc. A J. Atmos. Sci. Appl. Meteorol. Phys. Oceanogr."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Son, M., Moon, J., Jung, S., and Hwang, E. (2018, January 26\u201328). A Short-Term Load Forecasting Scheme Based on Auto-Encoder and Random Forest. Proceedings of the International Conference on Applied Physics, System Science and Computers, Dubrovnik, Croatia.","DOI":"10.1007\/978-3-030-21507-1_21"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Park, S., Moon, J., and Hwang, E. (2019, January 9\u201312). 2-Stage Electric Load Forecasting Scheme for Day-Ahead CCHP Scheduling. Proceedings of the IEEE International Conference on Power Electronics and Drive System (PEDS), Toulouse, France.","DOI":"10.1109\/PEDS44367.2019.8998960"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Kane, M.J., Price, N., Scotch, M., and Rabinowitz, P. (2014). Comparison of ARIMA and Random Forest time series models for prediction of avian influenza H5N1 outbreaks. BMC Bioinform., 15.","DOI":"10.1186\/1471-2105-15-276"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.enbuild.2017.04.038","article-title":"Trees vs. Neurons: Comparison between random forest and ANN for high-resolution prediction of building energy consumption","volume":"147","author":"Ahmad","year":"2017","journal-title":"Energy Build."},{"key":"ref_28","unstructured":"Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., and Isard, M. (2016, January 2\u20134). TensorFlow: A System for Large-Scale Machine Learning. Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI \u201916), Savannah, GA, USA."},{"key":"ref_29","first-page":"2825","article-title":"Scikit-learn: Machine learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016, January 13\u201317). XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_31","unstructured":"Yoon, J., Jordon, J., and Van Der Schaar, M. (2018, January 10\u201315). Gain: Missing data imputation using generative adversarial nets. Proceedings of the International Conference on Machine Learning, Stockholm Sweden."},{"key":"ref_32","unstructured":"Nair, V., and Hinton, G.E. (2010, January 21\u201324). Rectified linear units improve restricted Boltzmann machines. Proceedings of the 27th international conference on machine learning (ICML-10), Haifa, Israel."},{"key":"ref_33","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_34","first-page":"714","article-title":"Approximating number of hidden layer neurons in multiple hidden layer BPNN architecture","volume":"3","author":"Karsoliya","year":"2012","journal-title":"Int. J. Eng. Trends. Technol."},{"key":"ref_35","unstructured":"Heaton, J. (2008). Introduction to Neural Networks with Java, Heaton Research, Inc."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Moon, J., Kim, Y., Son, M., and Hwang, E. (2018). Hybrid Short-Term Load Forecasting Scheme Using Random Forest and Multilayer Perceptron. Energies, 11.","DOI":"10.3390\/en11123283"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Huang, N., Lu, G., and Xu, D. (2016). A permutation importance-based feature selection method for short-term electricity load forecasting using random forest. Energies, 9.","DOI":"10.3390\/en9100767"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/6\/1772\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:10:49Z","timestamp":1760173849000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/6\/1772"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,23]]},"references-count":37,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["s20061772"],"URL":"https:\/\/doi.org\/10.3390\/s20061772","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,23]]}}}