{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T15:23:37Z","timestamp":1773674617355,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2016,9,15]],"date-time":"2016-09-15T00:00:00Z","timestamp":1473897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, we developed a model of combined streamflow forecasting based on cross entropy to solve the problems of streamflow complexity and random hydrological processes. First, we analyzed the streamflow data obtained from Wudaogou station on the Huifa River, which is the second tributary of the Songhua River, and found that the streamflow was characterized by fluctuations and periodicity, and it was closely related to rainfall. The proposed method involves selecting similar years based on the gray correlation degree. The forecasting results obtained by the time series model (autoregressive integrated moving average), improved grey forecasting model, and artificial neural network model (a radial basis function) were used as a single forecasting model, and from the viewpoint of the probability density, the method for determining weights was improved by using the cross entropy model. The numerical results showed that compared with the single forecasting model, the combined forecasting model improved the stability of the forecasting model, and the prediction accuracy was better than that of conventional combined forecasting models.<\/jats:p>","DOI":"10.3390\/e18090336","type":"journal-article","created":{"date-parts":[[2016,9,15]],"date-time":"2016-09-15T10:22:51Z","timestamp":1473934971000},"page":"336","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Combined Forecasting of Streamflow Based on Cross Entropy"],"prefix":"10.3390","volume":"18","author":[{"given":"Baohui","family":"Men","sequence":"first","affiliation":[{"name":"Renewable Energy Institute, North China Electric Power University, Beijing 102206, China"}]},{"given":"Rishang","family":"Long","sequence":"additional","affiliation":[{"name":"State Key Laboratory of New Energy Power System, North China Electric Power University, Beijing 102206, China"}]},{"given":"Jianhua","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of New Energy Power System, North China Electric Power University, Beijing 102206, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,15]]},"reference":[{"key":"ref_1","first-page":"22","article-title":"Decomposition of time series model in wulasitai River application of annual runoff prediction","volume":"17","author":"Zhang","year":"2006","journal-title":"J. Water Resour. Water Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/j.eswa.2006.10.003","article-title":"Predicting service request in support centers based on nonlinear dynamics ARMA modeling and neural networks","volume":"34","author":"Emili","year":"2008","journal-title":"Expert Syst. Appl."},{"key":"ref_3","first-page":"28","article-title":"GM (1,1) improved model for predicting annual runoff forecasting","volume":"24","author":"Li","year":"2006","journal-title":"Northeast Water Conserv. Hydroelect."},{"key":"ref_4","first-page":"263","article-title":"Projection pursuit auto regression model in predicting runoff of Yangtze River in application","volume":"37","author":"Yu","year":"2009","journal-title":"Hohai Univ. J."},{"key":"ref_5","first-page":"201","article-title":"The main stream of the Yellow River Runoff of transient components and frequency analysis and its prediction","volume":"23","author":"Zhou","year":"2003","journal-title":"Meteor. Sci."},{"key":"ref_6","first-page":"1","article-title":"Classification of runoff prediction model based on Markov Bayes","volume":"17","author":"Qiu","year":"2011","journal-title":"Water Conserv. Sci. Technol. Econ."},{"key":"ref_7","first-page":"19","article-title":"Application of BP neural network in the prediction of runoff and stream reservoir runoff forecast","volume":"23","author":"Wang","year":"2010","journal-title":"Environ. Protect. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1016\/j.ecoleng.2009.05.010","article-title":"Side-by-side comparison of horizontal surface flow and free water surface flow constructed wet lands and artificial neural network(ANN)modeling approach","volume":"35","author":"Muhsin","year":"2009","journal-title":"Ecol. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4144","DOI":"10.3390\/w7084144","article-title":"Daily Runoff Forecasting Model Based on ANN and Data Preprocessing Techniques","volume":"7","author":"Yun","year":"2015","journal-title":"Water"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jhydrol.2016.04.074","article-title":"A general framework for multivariate multi-index drought prediction based on Multivariate Ensemble Streamflow Prediction (MESP)","volume":"539","author":"Hao","year":"2016","journal-title":"J. Hydrol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1016\/j.jhydrol.2016.04.048","article-title":"Streamflow forecasting using functional regression","volume":"538","author":"Masselot","year":"2016","journal-title":"J. Hydrol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.advwatres.2015.08.014","article-title":"Parameter dimensionality reduction of a conceptual model for streamflow prediction in Canadian, snowmelt dominated ungauged basins","volume":"85","author":"Arsenault","year":"2015","journal-title":"Adv. Water Resour."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1057\/jors.1969.103","article-title":"The combination of forecast","volume":"20","author":"Bates","year":"1969","journal-title":"Oper. Res. Quart."},{"key":"ref_14","unstructured":"Gu, H.Y. (2008). Prediction of River Runoff. [Master\u2019s Thesis, Northeast Forestry University]."},{"key":"ref_15","first-page":"23","article-title":"Annual runoff combination forecasting method research and application","volume":"24","author":"Fan","year":"2006","journal-title":"North Water Conserv. Hydrol. Power"},{"key":"ref_16","first-page":"28","article-title":"Based on combination forecasting model of long-term forecasting of reservoir runoff","volume":"30","author":"Yin","year":"2008","journal-title":"People\u2019s Yellow River"},{"key":"ref_17","unstructured":"Su, X.H. (2005). Study on the Short-Term Load Forecasting Based on Artificial Neural Network. [Master\u2019s Thesis, Chongqing University]."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Singh, V.P. (2013). Entropy Theory and Its Applications in Environmental and Water Engineering, John Wiley.","DOI":"10.1002\/9781118428306"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1080\/00221686.2011.635889","article-title":"Entropy approach for 2D velocity distribution in open-channel flow","volume":"49","author":"Marini","year":"2011","journal-title":"J. Hydraul. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"988","DOI":"10.3390\/e15030988","article-title":"Experimental assessment of a 2-D entropy-based model for velocity distribution in open channel flow","volume":"15","author":"Fontana","year":"2013","journal-title":"Entropy"},{"key":"ref_21","first-page":"97","article-title":"A combination method for distribution transformer life prediction based on cross entropy theory","volume":"42","author":"Li","year":"2014","journal-title":"Power Syst. Protect. Control"},{"key":"ref_22","first-page":"29","article-title":"A Combination Method for Wind Power Predication Based on Cross Entropy Theory","volume":"32","author":"Chen","year":"2012","journal-title":"Proc. CSEE"},{"key":"ref_23","first-page":"5170","article-title":"Changes of rainfall runoff relationship and the reasons for the status quo analysis","volume":"38","author":"Liu","year":"2010","journal-title":"Anhui Agric. Sci."},{"key":"ref_24","unstructured":"Liu, H.W. (2010). The Feature Selection Algorithm Based on Information Entropy. [Master\u2019s Thesis, Jilin University]."},{"key":"ref_25","unstructured":"Box, G.E., and Jenkins, G.M. (1976). Time Series Analysis: Forecasting and Control, Holden Day. [revised ed.]."},{"key":"ref_26","first-page":"13","article-title":"The Gray Prediction Model of Equal Dimension and New Information and the Forecasting Precision\u2014Based on the Analysis and Prediction of the Pension Insurance for Urban Residents of China","volume":"12","author":"Si","year":"2008","journal-title":"Stat. Thinktank"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s10479-005-5724-z","article-title":"A Tutorial on the Cross-Entropy Method","volume":"134","author":"Kroese","year":"2005","journal-title":"Annal. Oper. Res."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/9\/336\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:31:00Z","timestamp":1760211060000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/9\/336"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,15]]},"references-count":27,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2016,9]]}},"alternative-id":["e18090336"],"URL":"https:\/\/doi.org\/10.3390\/e18090336","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,15]]}}}