Uso do Algoritmo PARAFAC-EM para Preenchimento de Falhas em Séries Temporais de Velocidade do Vento na Região Nordeste do Brasil
DOI:
https://doi.org/10.26848/rbgf.v18.1.p077-094Keywords:
Data imputation, wind speed, PARAFAC-EM algorithmAbstract
This study evaluates the performance of a method for filling gaps in meteorological data time series, for wind speed data series, using the PARAFAC-EM algorithm. Hourly average wind speed data obtained from data collection platforms in the municipalities of Acopiara and Sobral in the state of Ceará/Brazil were used, totalling 8,640 records for each year in each region. Next, gaps were induced in the data series of 10%, 30% and 50%, which were filled in with PARAFAC-EM models to determine the rank with the best result. The performance of the proposed method was validated by calculating statistical metrics and applying Student's t-test. The results obtained showed that the proposed method with rank = 2 had the best performance in estimating the gaps in the data series, with statistical correlation classified as moderate in filling the gaps of 10%, 30% and 50% for the Acopiara/CE region, and from strong to very strong for the Sobral/CE region, with a significance level of 99%.
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Acar, E.; Dunlavy, D.M.; Kolda, T.G.; Morup, M. 2010. Scalable Tensor Factorizations with Missing Data. Chemometrics and Intelligent Laboratory Systems, v.106, p. 41-46. https://epubs.siam.org/doi/pdf/10.1137/1.9781611972801.61. DOI: https://doi.org/10.1016/j.chemolab.2010.08.004
Afrifa-Yamoah, E., Mueller. U.A., Taylor, S.M., Fisher, A.J. 2020. Missing data imputation of high-resolution temporal climate time series data. Meteorol Appl., 27, e1873. https://doi.org/10.1002/met.1873. DOI: https://doi.org/10.1002/met.1873
Ahn, H., Sun, K., Kim, K.P. 2022. Comparison of Missing Data Imputation Methods in Time Series Forecasting. Computers, Materials & Continua, 70 (1), 767-779. https://doi.org/10.32604/cmc. 2022.019369. DOI: https://doi.org/10.32604/cmc.2022.019369
Baraldi, A.N.; Enders, C.K. 2010. An introduction to modern missing data analyses. Journal of School Psychology, v.48, p.5-37. DOI: 10.1016/j.jsp.2009.10.001. DOI: https://doi.org/10.1016/j.jsp.2009.10.001
Bonfante, A.G.; Ventura, T.M.; Oliveira, A.G.; Marques, H.O.; Oliveira, R.S.; Martins, C.A.; Figueiredo, J.M. 2013. Uma abordagem computacional para preenchimento de falhas em dados micrometeorológicos. Revista Brasileira de Ciências Ambientais, v.27, p.61-70.
Brubacher, J. P., Oliveira, G. G., Guasselli, L. A. 2020. Preenchimento de Falhas e Espacialização de Dados Pluviométricos: Desafios e Perspectivas. Revista Brasileira de Meteorologia, 35(4), 615–629. https://doi.org/10.1590/0102-77863540067. DOI: https://doi.org/10.1590/0102-77863540067
Cai, M., Tian, Y., Li, A., Li, Y., Han, Y., Ji, W., Zhou, Q., Li, J., Li, W. (2023). Unraveling the evolution of dissolved organic matter in full-scale A/A/O wastewater treatment process using size exclusion chromatography with PARAFAC and nonnegative matrix factorization analysis, Water Research, vol. 235,119879. ISSN 0043-1354, https://doi.org/10.1016/j.watres.2023.119879. DOI: https://doi.org/10.1016/j.watres.2023.119879
Camargos, V.P.; César, C.C.; Caiaffa, W.T.; Xavier, C.C.; Proietti, F.A. 2011. Imputação múltipla e análise de casos completos em modelos de regressão logística: uma avaliação prática do impacto das perdas em covariáveis. Caderno de Saúde Pública, v.27, n.12, p.2299-2313.https://doi.org/10.1590/S0102311X2011001200003. DOI: https://doi.org/10.1590/S0102-311X2011001200003
Corbo, A.R., Santos, S.A.F., Bertolino, A.V.F.A., Pinto, A.B.S. 2024. Técnicas individuais e combinadas para preenchimento de falhas em dados diários de precipitação no município de São Gonçalo (RJ). Revista Brasileira de Climatologia, 35(20), 401–427. https://doi.org/10.55761/abclima.v35i20.1739. DOI: https://doi.org/10.55761/abclima.v35i20.17396
Devore, J. L. 2006. Probabilidade e Estatística para Engenharia e Ciência. Thomson Pioneira, São Paulo, Brasil.
Donders, A.R.T. et al. Review: 2006. A gentle introduction to imputation of missing values. Journal of Clinical Epidemiology, v.59, p.1087-1091. 10.1016/j.jclinepi.2006.01.014. DOI: https://doi.org/10.1016/j.jclinepi.2006.01.014
Giovanella, T.H., Oliveira, F.C., Marchi, V. A. A., Tluszcz, J. 2021. Desempenho de Métodos de Preenchimento de Falhas em Dados de Evapotranspiração de Referência para Região Oeste do Paraná. Revista Brasileira de Meteorologia, 36(3), 415–422. https://doi.org/10.1590/0102-77863630001. DOI: https://doi.org/10.1590/0102-77863630001
Harshman, R.A. 1970. Foundations of Parafac procedure: Models and conditions of an “explanatory” multi-model facor analysis. UCLA, Working papers in phonetics. pp.1-84.
Hitichcock, F.L. The Expression of a Tensor or a Polyadic as Sum of Products. 1927. Journal of Mathematics and Physics, vol. 6, pp. 164-189. DOI: https://doi.org/10.1002/sapm192761164
Huang, G.; Paes, A. T. 2009. Posso usar o teste t de Student quando preciso comparar três ou mais grupos? Einstein: Educação Continuada em Saúde, v.7, n.2, p.63-64.
Junninen, H.; Niska, H.; Tuppurainem, K.; Ruuskanen, J. 2004. Methods for imputation of missing values in air quality data sets. Atmospheric Environment, v.38, p.2895-2907. DOI: 10.1016/j.atmosenv.2004.02.026. DOI: https://doi.org/10.1016/j.atmosenv.2004.02.026
Kolda, T.; Bader, B. 2009. Tensor Decompositions and Applications. SIAM Publication Library, vol.51, n.3, p.455-500. DOI: https://doi.org/10.1137/07070111X. DOI: https://doi.org/10.1137/07070111X
Larson, R.; Farber, B. 2010. Estatística Aplicada. Prentice Hall, 4˚Edição, São Paulo: Pearson.
Lira, M.A.T.; Silva, E.M.; Brabo, J.M. 2011. Estimativas dos Recursos Eólicos no Litoral Cearense usando a Teoria da Regressão Linear. 2007. Revista Brasileira de Meteorologia, vol.26, n.3, p.349-366. DOI: https://doi.org/10.1590/S010277862011000300003. DOI: https://doi.org/10.1590/S0102-77862011000300003
Lira, M.A.T.; Silva, E.M.; Alves, J.M.B.; Veras, G.V.O. 2014. Estimation of wind resources in the coast of Ceará, Brazil, using the linear regression theory. Renewable & Sustainable Energy Reviews, v.39, p.509-529. DOI: https://doi.org/10.1016/j.rser.2014.07.097. DOI: https://doi.org/10.1016/j.rser.2014.07.097
Lima, F.J.P.; Cavalcanti, E.P.; Souza, E.P.; Silva, E.M. 2012. Evalution of the Wind Power in the State of Paraíba Using the Mesoscale Atmospheric Model Brazilian Developments on the Regional Atmospheric Modelling System. ISRN Renewable Energy. Article ID 847356. https://doi.org/10.5402/2012/847356. DOI: https://doi.org/10.5402/2012/847356
Miao, X., Wu, Y., Wang, J., Gao, Y., Mao, X., & Yin, J. 2021. Generative Semi-supervised Learning for Multivariate Time Series Imputation. Proceedings of the AAAI Conference on Artificial Intelligence, 35(10), 8983-8991. https://doi.org/10.1609/aaai. v35i10.17086. DOI: https://doi.org/10.1609/aaai.v35i10.17086
Mongomery, D. C.; Runger, G.C. 2009. Estatística aplicada e probabilidade para engenheiros. LTC, Rio de Janeiro.
Nunes, L.N.; Kluck, M.M.; Fachel, J.M.G. 2009. Uso da imputação múltipla de dados faltantes: uma simulação utilizando dados epidemiológicos. Cad. Saúde Pública, vol. 25, n.2, pp.268-278.https://doi.org/10.1590/S0102-311X2009000200005. DOI: https://doi.org/10.1590/S0102-311X2009000200005
Oliveira, L.F.C.; Fioreze, A.P.; Medeiros, A.M.M.; Silva. M.A.S. 2010. Comparação de metodologias de preenchimento de falhas de séries históricas de precipitação anual. Revista Brasileira de Engenharia Agrícola e Ambiental, v.14, n.11, p.1186-1192. DOI: https://doi.org/10.1590/S141543662010001100008. DOI: https://doi.org/10.1590/S1415-43662010001100008
Ooba, M.; Hirano, T.; Mogami, J.; Hirata, R. 2006. Comparisons of Gap-Filling Methods for Carbon Flux Dataset: A Combination of a Genetic Algorithm and an Artificial Neural Network. Ecological Modelling, vol.198, n.3-4, pp.473-486. 10.1016/j.ecolmodel.2006.06.006. DOI: https://doi.org/10.1016/j.ecolmodel.2006.06.006
Ramli, M.N.N.; Yahaya, A.S.; Ramli, N.A.; Yusof, N.F.F.M.; Abdullah, M.M.Ab. 2013. Roles of Imputation Methods for Filling the Missing Values: A Review. Advances in Environmental Biology, v.7, n.12, p.3861-3869.
Rubin D.B. 1996. Multiple Imputation after 18+ years. Journal of the American Statistical Association, v.91, p.473-489. DOI: https://doi.org/10.2307/2291635. DOI: https://doi.org/10.1080/01621459.1996.10476908
Ruezzene, C.B., Miranda, R.B., Tech, A.R.B., Mauad, F.F. 2021. Preenchimento de Falhas em Dados de Precipitação através de Métodos Tradionais e por Inteligência Artificial. Revista Brasileira de Climatologia, 29, 177–204. https://ojs.ufgd.edu.br/rbclima/article/view/1518.
Sciscenko, I., Arques, A., Micó, P., Mora, M., García-Ballesteros, S. 2022. Emerging applications of EEM-PARAFAC for water treatment: a concise review, Chemical Engineering Journal Advances, vol. 10, 100286. ISSN 2666-8211. https://doi.org/10.1016/j.ceja.2022.100286. DOI: https://doi.org/10.1016/j.ceja.2022.100286
Silva Junior, A. A., Gomes, R.S.R., Musis, C.R., Novais, J.W.Z., Maionchi, D., Figueiredo, J.M. 2024. Preenchimento de falhas em séries temporais da temperatura do ar: uma comparação entre modelos de Machine Learning. Revista Brasileira de Climatologia, 35(20), 362–377. https://doi.org/10.55761/abclima.v35i20.17649. DOI: https://doi.org/10.55761/abclima.v35i20.17649
Tavares, P.S., Pilotto, I.L., Chou, S.C., Souza, S.A., Fonseca, L.M.G. Chagas, J. D. 2024. A Dataset of High-Resolution Climate Change Projections Over South America with Bias Correction. Derbyana, ISSN 2764-1465, 45: e821, 2024. DOI: 10.69469/derb.v45.821. DOI: https://doi.org/10.69469/derb.v45.821
Tomasi, G.; Bro, R. 2005. Parafac and missing values. Sicence Direct, Chemometrics and Intelligent Laboratory Systems, v.75, n.2, p.163-180. 10.1016/j.chemolab.2004.07.003. DOI: https://doi.org/10.1016/j.chemolab.2004.07.003
Turova, P., Styles, I., Timashev, V., Kravets, K., Grechnikov, A., Lyskov, D., Samigullin, T., Podolskiy, I., Shpigun, O., Stavrianidi, A.
(2021). Unsupervised methods in LC-MS data treatment: Application for potential chemotaxonomic markers search, Journal of Pharmaceutical and Biomedical Analysis, vol. 206, 114382. ISSN 0731-7085, https://doi.org/10.1016/j.jpba.2021.114382. DOI: https://doi.org/10.1016/j.jpba.2021.114382
Weerakody, P.B., Wong, K.W., Wang, G., Ela, W. 2021. A review of irregular time series data handling with gated recurrent neural networks, Neurocomputing, 441 (161-178). https://doi.org/10.1016/j.neucom.2021.02.046. DOI: https://doi.org/10.1016/j.neucom.2021.02.046
Zhang, P. 2003. Multiple imputation: Theory and method. International Statistical Review, v.71(3), 581-592. https://www.jstor.org/stable /1403830. DOI: https://doi.org/10.1111/j.1751-5823.2003.tb00213.x
Zhang, Y., Thorburn, P.J. 2021. A dual-head attention model for time series data imputation, Computers and Electronics in Agriculture, vol.189, 106377. ISSN 0168-1699. https://doi.org/10.1016/j.compag.2021.106377. DOI: https://doi.org/10.1016/j.compag.2021.106377
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