{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T02:12:08Z","timestamp":1767665528382,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71671090"],"award-info":[{"award-number":["71671090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Joint research project of National Natural Science Foundation of China and Royal Society of UK","award":["71811530338"],"award-info":[{"award-number":["71811530338"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["NP2018466"],"award-info":[{"award-number":["NP2018466"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Qinglan Project for excellent youth or middle-aged academic leaders"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s00500-020-05521-3","type":"journal-article","created":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T14:02:18Z","timestamp":1612533738000},"page":"5209-5223","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Integral matching-based nonlinear grey Bernoulli model for forecasting the coal consumption in China"],"prefix":"10.1007","volume":"25","author":[{"given":"Lu","family":"Yang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7368-1746","authenticated-orcid":false,"given":"Naiming","family":"Xie","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,5]]},"reference":[{"key":"5521_CR1","volume-title":"Time series analysis: forecasting and control","author":"GE Box","year":"2015","unstructured":"Box GE, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: forecasting and control. Wiley, Hoboken"},{"issue":"6","key":"5521_CR2","doi-asserted-by":"publisher","first-page":"1194","DOI":"10.1016\/j.cnsns.2006.08.008","volume":"13","author":"CI Chen","year":"2008","unstructured":"Chen CI, Chen HL, Chen SP (2008) Forecasting of foreign exchange rates of Taiwan\u2019s major trading partners by novel nonlinear grey Bernoulli model NGBM(1,1). Commun Nonlinear Sci Numer Simul 13(6):1194\u20131204","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"5521_CR3","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/740272","author":"W Chia-Nan","year":"2015","unstructured":"Chia-Nan W (2015) An improved nonlinear grey Bernoulli model combined with Fourier series. Math Probl Eng. https:\/\/doi.org\/10.1155\/2015\/740272","journal-title":"Math Probl Eng"},{"issue":"1","key":"5521_CR4","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0771-050X(80)90013-3","volume":"6","author":"JR Dormand","year":"1980","unstructured":"Dormand JR, Prince PJ (1980) A family of embedded Runge\u2014Kutta formulae. J Comput Appl Math 6(1):19\u201326","journal-title":"J Comput Appl Math"},{"issue":"7","key":"5521_CR5","doi-asserted-by":"publisher","first-page":"1082","DOI":"10.1287\/mnsc.42.7.1082","volume":"42","author":"T Hill","year":"1996","unstructured":"Hill T, O\u2019Connor M, Remus W (1996) Neural network models for time series forecasts. Manag Sci 42(7):1082\u20131092","journal-title":"Manag Sci"},{"issue":"1\u20133","key":"5521_CR6","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1016\/j.cnsns.2015.03.006","volume":"27","author":"PH Hsin","year":"2015","unstructured":"Hsin PH, Chen CI (2015) Application of game theory on parameter optimization of the novel two-stage nash nonlinear grey Bernoulli model. Commun Nonlinear Sci Numer Simul 27(1\u20133):168\u2013174","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"6","key":"5521_CR7","doi-asserted-by":"publisher","first-page":"4318","DOI":"10.1016\/j.eswa.2009.11.068","volume":"37","author":"LC Hsu","year":"2010","unstructured":"Hsu LC (2010) A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry. Expert Syst Appl 37(6):4318\u20134323","journal-title":"Expert Syst Appl"},{"issue":"1","key":"5521_CR8","first-page":"1","volume":"1","author":"D Julong","year":"1989","unstructured":"Julong D (1989) Introduction to grey system theory. J Grey Syst 1(1):1\u201324","journal-title":"J Grey Syst"},{"issue":"2","key":"5521_CR9","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1108\/GS-01-2018-0005","volume":"8","author":"L Kong","year":"2018","unstructured":"Kong L, Ma X (2018) Comparison study on the nonlinear parameter optimization of nonlinear grey Bernoulli model (NGBM (1,1)) between intelligent optimizers. Grey Syst Theory Appl 8(2):210\u2013226","journal-title":"Grey Syst Theory Appl"},{"issue":"20","key":"5521_CR10","doi-asserted-by":"publisher","first-page":"25638","DOI":"10.1007\/s11356-020-08951-6","volume":"27","author":"Q Li","year":"2020","unstructured":"Li Q, Wang ZX, Zhang XY (2020) An improved gray Bernoulli model for estimating the relationship between economic growth and pollution emissions. Environ Sci Pollut Res 27(20):25638\u201325654","journal-title":"Environ Sci Pollut Res"},{"issue":"484","key":"5521_CR11","doi-asserted-by":"publisher","first-page":"1570","DOI":"10.1198\/016214508000000797","volume":"103","author":"H Liang","year":"2008","unstructured":"Liang H, Wu H (2008) Parameter estimation for differential equation models using a framework of measurement error in regression models. Publ Am Statal Assoc 103(484):1570\u20131583","journal-title":"Publ Am Statal Assoc"},{"key":"5521_CR12","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.cam.2019.03.048","volume":"360","author":"X Liu","year":"2019","unstructured":"Liu X, Xie N (2019) A nonlinear grey forecasting model with double shape parameters and its application. Appl Math Comput 360:203\u2013212","journal-title":"Appl Math Comput"},{"key":"5521_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-10-1841-1","volume-title":"Grey data analysis","author":"S Liu","year":"2017","unstructured":"Liu S, Yang Y, Forrest J (2017) Grey data analysis. Springer, Berlin"},{"key":"5521_CR14","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1016\/j.neucom.2015.11.032","volume":"177","author":"J Lu","year":"2016","unstructured":"Lu J, Xie W, Zhou H, Zhang A (2016) An optimized nonlinear grey Bernoulli model and its applications. Neurocomputing 177:206\u2013214","journal-title":"Neurocomputing"},{"key":"5521_CR15","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.cam.2018.07.044","volume":"347","author":"X Ma","year":"2019","unstructured":"Ma X, Liu Z, Wang Y (2019) Application of a novel nonlinear multivariate grey Bernoulli model to predict the tourist income of China. J Comput Appl Math 347:84\u201394","journal-title":"J Comput Appl Math"},{"key":"5521_CR16","volume-title":"Numerical optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal J, Wright S (2006) Numerical optimization. Springer, Berlin"},{"key":"5521_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-7190-9","volume-title":"Dynamic data analysis","author":"J Ramsay","year":"2017","unstructured":"Ramsay J, Hooker G (2017) Dynamic data analysis. Springer, Berlin"},{"key":"5521_CR18","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1111\/j.1467-9868.2007.00610.x","volume":"69","author":"JO Ramsay","year":"2007","unstructured":"Ramsay JO, Hooker G, Campbell D, Cao JG (2007) Parameter estimation for differential equations: a generalized smoothing approach. J R Stat Soc Stat Methodol B 69:741\u2013796","journal-title":"J R Stat Soc Stat Methodol B"},{"key":"5521_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.spc.2020.07.009","volume":"25","author":"U \u015eahin","year":"2021","unstructured":"\u015eahin U (2021) Future of renewable energy consumption in France, Germany, Italy, Spain, Turkey and UK by 2030 using optimized fractional nonlinear grey Bernoulli model. Sustain Prod Consump 25:1\u201314","journal-title":"Sustain Prod Consump"},{"issue":"109","key":"5521_CR20","first-page":"948","volume":"138","author":"U \u015eahin","year":"2020","unstructured":"\u015eahin U, \u015eahin T (2020) Forecasting the cumulative number of confirmed cases of COVID-19 in Italy, UK and USA using fractional nonlinear grey Bernoulli model. Chaos Solitons Fractals 138(109):948","journal-title":"Chaos Solitons Fractals"},{"key":"5521_CR21","volume-title":"Linear regression analysis","author":"GA Seber","year":"2012","unstructured":"Seber GA, Lee AJ (2012) Linear regression analysis, vol 329. Wiley, Hoboken"},{"key":"5521_CR22","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1016\/j.energy.2017.09.037","volume":"140","author":"F Shaikh","year":"2017","unstructured":"Shaikh F, Ji Q, Shaikh PH, Mirjat NH, Uqaili MA (2017) Forecasting China\u2019s natural gas demand based on optimised nonlinear grey models. Energy 140:941\u2013951","journal-title":"Energy"},{"issue":"3","key":"5521_CR23","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1023\/B:STCO.0000035301.49549.88","volume":"14","author":"AJ Smola","year":"2004","unstructured":"Smola AJ, Sch\u00f6lkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199\u2013222","journal-title":"Stat Comput"},{"issue":"7\u20138","key":"5521_CR24","doi-asserted-by":"publisher","first-page":"1416","DOI":"10.1016\/j.mcm.2008.11.015","volume":"49","author":"TL Tien","year":"2009","unstructured":"Tien TL (2009) A new grey prediction model FGM(1,1). Math Comput Model 49(7\u20138):1416\u20131426","journal-title":"Math Comput Model"},{"issue":"3","key":"5521_CR25","doi-asserted-by":"publisher","first-page":"780","DOI":"10.1016\/j.cie.2012.12.010","volume":"64","author":"ZX Wang","year":"2013","unstructured":"Wang ZX (2013) An optimized nash nonlinear grey Bernoulli model for forecasting the main economic indices of high technology enterprises in China. Comput Ind Eng 64(3):780\u2013787","journal-title":"Comput Ind Eng"},{"issue":"1","key":"5521_CR26","first-page":"169","volume":"51","author":"ZX Wang","year":"2017","unstructured":"Wang ZX (2017) A weighted non-linear grey Bernoulli model for forecasting non-linear economictime series with small data sets. Econ Comput Econ Cybern Stud Res 51(1):169\u2013186","journal-title":"Econ Comput Econ Cybern Stud Res"},{"key":"5521_CR27","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.eswa.2019.06.053","volume":"136","author":"B Wei","year":"2019","unstructured":"Wei B, Xie N, Yang Y (2019) Data-based structure selection for unified discrete grey prediction model. Expert Syst Appl 136:264\u2013275","journal-title":"Expert Syst Appl"},{"key":"5521_CR28","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.renene.2019.03.006","volume":"140","author":"W Wu","year":"2019","unstructured":"Wu W, Ma X, Zeng B, Wang Y, Cai W (2019a) Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model. Renew Energy 140:70\u201387","journal-title":"Renew Energy"},{"key":"5521_CR29","first-page":"1","volume":"2019","author":"WZ Wu","year":"2019","unstructured":"Wu WZ, Zhang T, Zheng C (2019b) A novel optimized nonlinear grey Bernoulli model for forecasting China\u2019s GDP. Complexity 2019:1\u201310","journal-title":"Complexity"},{"key":"5521_CR30","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1016\/j.apm.2020.04.006","volume":"84","author":"W Wu","year":"2020","unstructured":"Wu W, Ma X, Zeng B, Lv W, Wang Y, Li W (2020) A novel grey Bernoulli model for short-term natural gas consumption forecasting. Appl Math Model 84:393\u2013404","journal-title":"Appl Math Model"},{"key":"5521_CR31","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1016\/j.apm.2017.07.010","volume":"51","author":"X Xiao","year":"2017","unstructured":"Xiao X, Yang J, Mao S, Wen J (2017) An improved seasonal rolling grey forecasting model using a cycle truncation accumulated generating operation for traffic flow. Appl Math Model 51:386\u2013404","journal-title":"Appl Math Model"},{"issue":"2","key":"5521_CR32","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1007\/s11069-014-1200-x","volume":"74","author":"N Xie","year":"2014","unstructured":"Xie N, Pearman AD (2014) Forecasting energy consumption in china following instigation of an energy-saving policy. Nat Hazards 74(2):639\u2013659","journal-title":"Nat Hazards"},{"issue":"2","key":"5521_CR33","doi-asserted-by":"publisher","first-page":"1173","DOI":"10.1016\/j.apm.2008.01.011","volume":"33","author":"N Xie","year":"2009","unstructured":"Xie N, Liu S (2009) Discrete grey forecasting model and its optimization. Appl Math Model 33(2):1173\u20131186","journal-title":"Appl Math Model"},{"key":"5521_CR34","doi-asserted-by":"publisher","first-page":"97839","DOI":"10.1109\/ACCESS.2020.2995974","volume":"8","author":"W Xie","year":"2020","unstructured":"Xie W, Pu B, Pei C, Lee SJ, Kang Y (2020) A novel mutual fractional grey Bernoulli model with differential evolution algorithm and its application in education investment forecasting in China. IEEE Access 8:97839\u201397850","journal-title":"IEEE Access"},{"key":"5521_CR35","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.automatica.2014.10.126","volume":"52","author":"C Young Peter","year":"2015","unstructured":"Young Peter C (2015) Refined instrumental variable estimation: maximum likelihood optimization of a unified Box\u2013Jenkins model. Automatica 52:35\u201346","journal-title":"Automatica"},{"issue":"1","key":"5521_CR36","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/S0169-2070(97)00044-7","volume":"14","author":"G Zhang","year":"1998","unstructured":"Zhang G, Patuwo BE, Hu MY (1998) Forecasting with artificial neural networks: the state of the art. Int J Forecast 14(1):35\u201362","journal-title":"Int J Forecast"},{"issue":"2","key":"5521_CR37","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.amc.2008.10.045","volume":"207","author":"J Zhou","year":"2009","unstructured":"Zhou J, Fang R, Li Y, Zhang Y, Peng B (2009) Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization. Appl Math Comput 207(2):292\u2013299","journal-title":"Appl Math Comput"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-020-05521-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-020-05521-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-020-05521-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T22:27:21Z","timestamp":1698618441000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-020-05521-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,5]]},"references-count":37,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["5521"],"URL":"https:\/\/doi.org\/10.1007\/s00500-020-05521-3","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2021,2,5]]},"assertion":[{"value":"5 February 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}