An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption

In this paper, we propose an optimal fractional-order accumulative Grey Markov model with variable parameters (FOGMKM (1, 1)) to predict the annual total energy consumption in China and improve the accuracy of energy consumption forecasting. The new model is built upon the traditional Grey model and utilized matrix perturbation theory to study the natural and response characteristics of a system when the structural parameters change slightly. The particle swarm optimization algorithm (PSO) is used to determine the number of optimal fractional order and nonlinear parameters. An experiment is conducted to validate the high prediction accuracy of the FOGMKM (1, 1) model, with mean absolute percentage error (MAPE) and root mean square error (RMSE) values of 0.51% and 1886.6, respectively, and corresponding fitting values of 0.92% and 6108.8. These results demonstrate the superior fitting performance of the FOGMKM (1, 1) model when compared to other six competitive models, including GM (1, 1), ARIMA, Linear, FAONGBM (1, 1), FGM (1, 1) and FOGM (1, 1). Our study provides a scientific basis and technical references for further research in the finance as well as energy fields and can serve well for energy market benchmark research

Hybrid Grey Forecasting Model for Iran's Energy Consumption and Supply

Grey theory deals with systems that are characterized by poor information or for which information is lacking. This study presents an improved grey GM (1, 1) model, using a technique that combines residual modification with Markov Chain model. We use energy consumption and supply of Iran to test the accuracy of proposed model. The results show that the Markov Chain residual modification model achieves reliable and precise results.  Keywords: Grey Forecasting Model; Markov Chain; Energy System JEL Classifications: C15; C53; C6

EV battery state changes & RL considerations

Electric Vehicles are becoming trendy and proved to have no harmful exhaust like traditional fuel-powered vehicles which makes them one of the best solution to reduce greenhouse gas emissions. As the world shifts towards electric vehicle adoption, we will need efficient power sources to provide enough capacity for all these vehicles to function. Lithium-Ion batteries are the driving force behind this new trend. The goal of this research is to analyze the lifespan and long-term ratio composition of Lithium-Ion batteries in electric vehicles by developing two models, an Absorbing Markov Chain model, and a Markov Chain Steady-State Census model. A sensitivity analysis is also conducted to alleviate the scarcity of enough input data. The models show that the lifespan of the new batteries can be extended by 4.5 years, which will have a positive environmental impact and reap economic benefits. Further, the long term composition of batteries in New, remanufactured, repurposed and recycled states can be projected. The increasing demand for EVs globally has created a necessity for more batteries to power them, and these batteries require materials to be made. By considering reverse logistics processes, it is possible to recycle batteries and recover the valuable materials. Not only does this support the environment, but given the rising demand and finite raw material supply, there is an opportunity to capture the economic benefit of recycling. From this research, the recovered materials cobalt, lithium, and nickel are calculated, and this is especially important for the optimal planning of sustainable manufacturing

Developing a hybrid hidden MARKOV model using fusion of ARMA model and artificial neural network for crude oil price forecasting

Crude oil price forecasting is an important component of sustainable development of many countries as crude oil is an unavoidable product that exist on earth. Crude oil price forecasting plays a very vital role in economic development of many countries in the world today. Any fluctuation in crude oil price tremendously affects many economies in terms of budget and expenditure. In view of this, it is of great concern by economists and financial analysts to forecast such a vital commodity. However, Hidden Markov Model, ARMA Model and Artificial Neural Network has many drawbacks in forecasting such as linear limitations of ARMA model which is in contrast to the financial time series which are often nonlinear, ANN is very weak in terms of out-sample forecast and it has very tedious process of implementation, HMM is very weak in an in-sample forecast and has issue of a large number of unstructured parameters. In view of this drawbacks of these three models (ANN, ARMA and HMM), we developed an efficient Hybrid Hidden Markov Model using fusion of ARMA Model and Artificial Neural Network for crude oil price forecasting, MATLAB was employed to develop the four models (Hybrid HMM, HMM, ARMA and ANN). The models were evaluated using three different evaluation techniques which are Mean Absolute Percentage Error (MAPE), Absolute Error (AE) and Root Mean Square Error (RMSE). The findings showed that Hybrid Hidden Markov Model was found to provide more accurate crude oil price forecast than the other three models in which. The results of this study indicate that Hybrid Hidden Markov Model using fusion of ARMA and ANN is a potentially promising model for crude oil price forecasting

Forecasting in Mathematics

Mathematical probability and statistics are an attractive, thriving, and respectable part of mathematics. Some mathematicians and philosophers of science say they are the gateway to mathematics’ deepest mysteries. Moreover, mathematical statistics denotes an accumulation of mathematical discussions connected with efforts to most efficiently collect and use numerical data subject to random or deterministic variations. Currently, the concept of probability and mathematical statistics has become one of the fundamental notions of modern science and the philosophy of nature. This book is an illustration of the use of mathematics to solve specific problems in engineering, statistics, and science in general

Demand forecasting for aircraft engine aftermarket

Thesis (M.B.A.)--Massachusetts Institute of Technology, Sloan School of Management; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering; in conjunction with the Leaders for Manufacturing Program at MIT, 2008.Includes bibliographical references.In 2006, Pratt and Whitney launched the Global Material Solutions business model aiming to supply spare parts to non-OEM engines with minimum 95% on-time delivery and fill-rate. Lacking essential technical knowledge of the target engines, predictability and associated confidence of the parts demands are very limited. This thesis focuses on exploring alternative and innovative approaches to providing more accurate demand forecasts based on limited information. Approaches including application of fundamental sampling theorems, random walk simulations based on Markov Chain simplification, and sensitivity analysis on incremental scrap rates were introduced. A software tool, based on the sensitivity analysis was introduced for all gas path parts. The methodology could potentially be applicable to industries other than Aerospace.by Kien K. Ho.S.M.M.B.A

Pronóstico de la demanda de gasolina en Colombia empleando modelos estocásticos

Metodología de estimación para la demanda de gasolina en Colombia, basada en modelos estocásticos, con el fin de obtener pronósticos precisos que brinden mayores beneficios económicos a las empresas del sector petrolero.Demand Forecasting methodology for oil y gas in Colombia based on stochastic models in order to obtain accurate forecasts that provides greater economic benefits to Oil y Gas companies.Administrador (a) de EmpresasPregrad

Future Electricity Demand of the Emerging European Countries and the CIS Countries

Nowadays, one of the leading factors used in the evaluation of a country’s economic development is energy consumption. Because of economic growth, demand for energy is also increasing. In this study, the emerging European countries’ (the Czech Republic, Poland, Romania, Turkey) and the CIS countries’ (Kazakhstan, Russia, Ukraine, Uzbekistan)  electricity consumption has been forecasted for five years period (2015-2019). In the study, GM(1,1) Rolling Model, which is developed in the framework of Grey System Theory is used as a mathematical model for real-time forecasting. The results of the study show that there will not be a significant change in electricity demand in this two area during the 2015-2109 period.&nbsp

Enhancing statistical wind speed forecasting models : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering at Massey University, Manawatū Campus, New Zealand

In recent years, wind speed forecasting models have seen significant development and growth. In particular, hybrid models have been emerging since the last decade. Hybrid models combine two or more techniques from several categories, with each model utilizing its distinct strengths. Mainly, data-driven models that include statistical and Artificial Intelligence/Machine Learning (AI/ML) models are deployed in hybrid models for shorter forecasting time horizons (< 6hrs). Literature studies show that machine learning models have gained enormous potential owing to their accuracy and robustness. On the other hand, only a handful of studies are available on the performance enhancement of statistical models, despite the fact that hybrid models are incomplete without statistical models. To address the knowledge gap, this thesis identified the shortcomings of traditional statistical models while enhancing prediction accuracy. Three statistical models are considered for analyses: Grey Model [GM(1,1)], Markov Chain, and Holt’s Double Exponential Smoothing models. Initially, the problems that limit the forecasting models' applicability are highlighted. Such issues include negative wind speed predictions, failure of predetermined accuracy levels, non-optimal estimates, and additional computational cost with limited performance. To address these concerns, improved forecasting models are proposed considering wind speed data of Palmerston North, New Zealand. Several methodologies have been developed to improve the model performance and fulfill the necessary and sufficient conditions. These approaches include adjusting dynamic moving window, self-adaptive state categorization algorithm, a similar approach to the leave-one-out method, and mixed initialization method. Keeping in view the application of the hybrid methods, novel MODWT-ARIMA-Markov and AGO-HDES models are further proposed as secondary objectives. Also, a comprehensive analysis is presented by comparing sixteen models from three categories, each for four case studies, three rolling windows, and three forecasting horizons. Overall, the improved models showed higher accuracy than their counter traditional models. Finally, the future directions are highlighted that need subsequent research to improve forecasting performance further

New Progress of Grey System Theory in The New Millennium

Purpose – The purpose of this paper is to summarize the progress in grey system research during 2000- 2015, so as to present some important new concepts, models, methods and a new framework of grey system theory. Design/methodology/approach –The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “Kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of GM(1,1), such as Even Grey Model(EGM), Original Difference Grey Model(ODGM), Even Difference Grey Model(EDGM), Discrete Grey Model(DGM) and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well. Findings –The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper. Practical implications – A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science, and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate. Originality/value –The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section. Keywords Grey systems theory, Operations of grey numbers, Buffer operators, Grey forecasting models, Grey incidence analysis models, Grey cluster evaluation models, Grey decision models, Combined grey models, Grey contro