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
Di Liu 1
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School of Civil and Resource Engineering, University of Science and Technology Beijing
School of Civil, Environmental & Mining Engineering, University of Adelaide,
Submission date: 2019-01-18
Final revision date: 2019-05-28
Acceptance date: 2019-07-14
Publication date: 2019-09-19
Corresponding author
Di Liu   

School of Civil and Resource Engineering, University of Science and Technology Beijing
Gospodarka Surowcami Mineralnymi – Mineral Resources Management 2019;35(3):75-98
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.
prognozowanie kosztów, dynamiczny model szary, optymalizacja wartości tła, korekcja błędów resztkowych z szeregów Fouriera
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.
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