An improved GM(1.1) model with background value optimization and Fourier-series residual error correction and its application in cost forecasting of coal mine

• Autorzy: Liu Di , Li Guoqing , Chanda Emmanuel K. , Hu Nailian , Ma Zhaoyang

Identyfikatory

DOI

10.24425/gsm.2019.128528

Warianty tytułu

PL

Ulepszony model GM(1,1) z optymalizacją wartości tła i korekcją błędów resztkowych szeregów Fouriera oraz jego zastosowanie w prognozowaniu kosztów kopalni węgla kamiennego

• Języki publikacji: EN

Abstrakty

EN

This paper researches the application of grey system theory in cost forecasting of the coal mine. The grey model (GM(1.1)) is widely used in forecasting in business and industrial systems with advantages of minimal data, a short time and little fluctuation. Also, the model fits exponentially with increasing data more precisely than other prediction techniques. However, the traditional GM(1.1) model suffers from the poor anti-interference ability. Aimed at the flaws of the conventional GM(1.1) model, this paper proposes a novel dynamic forecasting model with the theory of background value optimization and Fourier-series residual error correction based on the traditional GM(1.1) model. The new model applies the golden segmentation optimization method to optimize the background value and Fourier-series theory to extract periodic information in the grey forecasting model for correcting the residual error. In the proposed dynamic model, the newest data is gradually added while the oldest is removed from the original data sequence. To test the new model’s forecasting performance, it was applied to the prediction of unit costs in coal mining, and the results show that the prediction accuracy is improved compared with other grey forecasting models. The new model gives a MAPE & C value of 0.14% and 0.02, respectively, compared to 1.75% and 0.37 respectively for the traditional GM(1.1) model. Thus, the new GM(1.1) model proposed in this paper, with advantages of practical application and high accuracy, provides a new method for cost forecasting in coal mining, and then help decision makers to make more scientific decisions for the mining operation.

PL

W pracy zbadano zastosowanie teorii szarego systemu w prognozowaniu kosztów kopalni węgla. Szary model (GM(1,1)) jest szeroko wykorzystywany w prognozowaniu w systemach biznesowych i przemysłowych z niewielką ilością danych, krótkim czasem i nieznacznymi wahaniami. Ponadto model dopasowuje wykładniczo dane bardziej dokładnie niż inne techniki prognozowania. Jednak tradycyjny model GM(1,1) ma słabą zdolność przeciwdziałania zakłóceniom. Mając na uwadze wady konwencjonalnego modelu GM(1,1), w artykule zaproponowano – w oparciu o tradycyjny model GM(1,1) – nowy model dynamicznego prognozowania z teorią optymalizacji wartości tła i korektą błędów resztkowych szeregów Fouriera. Nowy model stosuje metodę optymalizacji złotej segmentacji do optymalizacji wartości tła oraz teorię szeregów Fouriera w celu wyodrębnienia okresowych informacji w szarym modelu prognozowania, aby skorygować błąd resztkowy. W proponowanym modelu dynamicznym najnowsze dane są stopniowo dodawane, podczas gdy najstarsze – usuwane z oryginalnej sekwencji danych. Aby przetestować dokładność prognozowania nowego modelu, zastosowano go do prognozowania kosztów jednostkowych pozyskania węgla, a wyniki pokazują, że dokładność prognozowania jest lepsza w porównaniu z innymi szarymi modelami prognozowania. Nowy model daje wartości MAPE & C wynoszące odpowiednio 0,33% i 0,07, w porównaniu z odpowiednio 1,1% i 0,3 dla tradycyjnego modelu GM(1,1). Zatem zaproponowany w artykule, ulepszony model GM(1,1) z zaletami praktycznego zastosowania i wysoką dokładnością, jest nową metodą prognozowania kosztów w górnictwie węgla, która ułatwia decydentom podejmowanie decyzji ugruntowanych naukowo dotyczących operacji pozyskania węgla.

Słowa kluczowe

EN

cost forecasting; dynamic grey model; background value optimization; Fourier series; residual error correction

PL

prognozowanie kosztów; model szary dynamiczny; optymalizacja wartości tła; korekcja błędów resztkowych; szeregi Fouriera

• Wydawca: Instytut Gospodarki Surowcami Mineralnymi i Energią PAN ; Komitet Zrównoważonej Gospodarki Surowcami Mineralnymi PAN
• Czasopismo: Gospodarka Surowcami Mineralnymi
• Rocznik: 2019
• Tom: T. 35, z. 3
• Strony: 75--98
• Opis fizyczny: Bibliogr. 28 poz., rys., tab., wykr.

Twórcy

autor

Liu Di

• School of Civil and Resource Engineering, University of Science and Technology Beijing, China; ORCID iD: 0000-0001-6868-5198

autor

Li Guoqing

• School of Civil and Resource Engineering, University of Science and Technology Beijing, China; ORCID iD: 0000-0001-7079-3665

autor

Chanda Emmanuel K.

• School of Civil, Environmental & Mining Engineering, University of Adelaide, Australia; ORCID iD: 0000-0003-3089-8782

autor

Hu Nailian

• School of Civil and Resource Engineering, University of Science and Technology Beijing, China; ORCID iD: 0000-0003-3807-8316

autor

Ma Zhaoyang

• School of Civil and Resource Engineering, University of Science and Technology Beijing, China; ORCID iD: 0000-0002-8292-4447

Bibliografia

• [1] Aydoğdu, G. and Yildiz, O. 2017. Forecasting the annual electricity consumption of Turkey using a hybrid model [In:] 2017 25th Signal Processing and Communications Applications Conference (SIU), IEEE, pp. 1–4.
• [2] Bahrami et al. 2014 – Bahrami, S., Hooshmand, R.A. and Parastegari, M. 2014. Short term electric load forecasting by wavelet transform and grey model improved by PSO (particle swarm optimization) algorithm. Energy 72, pp. 434–442.
• [3] Chang et al. 2015 – Chang, C.J., Li, D.C., Huang, Y.H. and Chen, C.C. 2015. A novel gray forecasting model based on the box plot for small manufacturing data sets. Applied Mathematics and Computation 265, pp. 400–408.
• [4] Chen, P.Y. and Yu, H.M. 2014. Foundation settlement prediction based on a novel NGM model. Mathematical Problems in Engineering 2014, pp. 1–8.
• [5] Dang et al. 2007 – Dang, Y.G., Liu, S.F. and Mi, C.M. 2007. Study on characteristics of the strengthening buffer operators. Control and Decision 22, pp. 730.
• [6] Deb et al. 2017 – Deb, C., Zhang, F., Yang, J., Lee, S.E. and Shah, K.W. 2017. A review on time series forecasting techniques for building energy consumption. Renewable and Sustainable Energy Reviews 74, pp. 902–924.
• [7] Deng, J.L. 1982. Control problems of grey systems. Sys. & Contr. Lett. 1, pp. 288–294.
• [8] Chysels, E. and Ozkan, N. 2015. Real-time forecasting of the US federal government budget: A simple mixed frequency data regression approach. International Journal of Forecasting 31, pp. 1009–1020.
• [9] Li et al. 2009 – Li, D.W., Xu, H.J., Liu, D.L. and Xue, Y. 2009. Improved Grey Markov Model and Its Application in Prediction of Flight Accident Rate. China Safety Science Journal (CSSJ) 19(9), pp. 53–57.
• [10] Hou et al. 2013 – Hou, Y.B., Wang, J.M., Zhang, X., Shi, S.S. and Li, Z.D. 2013. The application of improved grey model on coal cost forecasting. China Mining Magazine 22(5), pp. 49–52.
• [11] Jandoc et al. 2015 – Jandoc, R., Burden, A.M., Mamdani, M., Lévesque, L.E. and Cadarette, S.M. 2015. Interrupted time series analysis in drug utilization research is increasing: systematic review and recommendations. Journal of Clinical Epidemiology 68(8), pp. 950–956.
• [12] Lee et al. 2016 – Lee, S., Cho, C., Hong, E.K. and Yoon, B. 2016. Forecasting mobile broadband traffic: Application of scenario analysis and Delphi method. Expert Systems with Applications 44, pp. 126–137.
• [13] Lin et al. 2016 – Lin, C.C., Deng, D.J., Kang, J.R., Chang, S.C. and Chueh, C.H. 2016. Forecasting rare faults of critical components in LED epitaxy plants using a hybrid grey forecasting and harmony search approach. IEEE Transactions on Industrial Informatics 12(6), pp. 2228–2235.
• [14] Liu, S. 1997. The trap in the prediction of a shock disturbed system and the buffer operator. Journal-Huazhong University of Science and Technology Chinese Edition 25, pp. 25–27.
• [15] Liu et al. 2016 – Liu, X., Moreno, B. and García, A.S. 2016. A grey neural network and input-output combined forecasting model. Primary energy consumption forecasts in Spanish economic sectors. Energy 115, pp. 1042–1054.
• [16] Lu, S.L. 2019. Integrating heuristic time series with modified grey forecasting for renewable energy in Taiwan. Renewable Energy 133, pp. 1436–1444.
• [17] Özdemir, A. and Özdagoglu, G. 2017. Predicting product demand from small-sized data: grey models. Grey Systems: Theory and Application 7(1), pp. 80–96.
• [18] Patra et al. 2016 – Patra, A.K., Gautam, S., Majumdar, S. and Kumar, P. 2016. Prediction of particulate matter concentration profile in an opencast copper mine in India using an artificial neural network model. Air Quality, Atmosphere & Health 9(6), pp. 697–711.
• [19] Sun et al. 2016 – Sun, X., Sun, W., Wang, J., Zhang, Y. and Gao, Y. 2016. Using a Grey–Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China. Tourism Management 52, pp. 369–379.
• [20] Tan, C. and Chang, S. 1996. Residual correction method of Fourier series to GM (1, 1) model [In:] Proceedings of the first national conference on grey theory and applications, Kauhsiung, Taiwan, pp. 93–101.
• [21] Tsai, S.B. 2016. Using grey models for forecasting China’s growth trends in renewable energy consumption. Clean Technologies and Environmental Policy 18(2), pp. 563–571.
• [22] Wang, Z.X. 2013. An optimized Nash nonlinear grey Bernoulli model for forecasting the main economic indices of high technology enterprises in China. Computers & Industrial Engineering 64(3), pp. 780–787.
• [23] Xia, M. and Wong, W.K. 2014. A seasonal discrete grey forecasting model for fashion retailing. Knowledge-Based Systems 57, pp. 119–126.
• [24] Xie et al. 2015 – Xie, N.M., Yuan, C.Q. and Yang, Y.J. 2015. Forecasting China’s energy demand and self-sufficiency rate by grey forecasting model and Markov model. International Journal of Electrical Power & Energy Systems 66, pp. 1–8.
• [25] Yang, M.H. and Guo, D.Y. 2012. The application of grey forecasting model in the cost forecast of coal mine. Value Engineering 31, pp. 128–129.
• [26] Yu et al. 2016 – Yu, T., Xiang, L. and Wu, D. 2016. Grey system and BP neural network model for industrial economic forecasting. Recent Patents on Computer Science 9(1), pp. 40–45.
• [27] Zhang, C. and Anadon, L.D. 2014. A multi-regional input–output analysis of domestic virtual water trade and provincial water footprint in China. Ecological Economics 100, pp. 159–172.
• [28] Zhao et al. 2012 – Zhao, Z., Wang, J., Zhao, J. and Su, Z. 2012. Using a grey model optimized by differential evolution algorithm to forecast the per capita annual net income of rural households in China. Omega 40(5), pp. 525–532.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).