Predicting changes in Bitcoin price using grey system theory

Bitcoin is currently the leading global provider of cryptocurrency.Cryptocurrency allows users to safely and anonymously use the Internet to perform digital currency transfers and storage.In recent years,the Bitcoin network has attracted investors,businesses,and corporations while facilitating services and product deals.Moreover,Bitcoin has made itself the dominant source of decentralized cryptocurrency.While considerable research has been done concerning Bitcoin network analysis,limited research has been conducted on predicting the Bitcoin price.The purpose of this study is to predict the price of Bitcoin and changes therein using the grey system theory.The first order grey model(GM(1,1))is used for this purpose.It uses a firstorder differential equation to model the trend of time series.The results show that the GM(1,1)model predicts Bitcoin’s price accurately and that one can earn a maximum profit confidence level of approximately 98%by choosing the appropriate time frame and by managing investment assets.

Optimization approach hydroforming car beam billets based grey system theory

Perfect combination of structural size parameters of the hydroforming billets is essential to obtain even wall thicknesses of the car beam. Finite element （ FE ） analysis on hydroforming car beam was carried out, and the results were optimized according to multiple quality objectives by the grey system theory. With bending angle, bending radius and hight difference along the axis direction as variables, orthogonal FE analyses were conducted and the minimum and maximum wall thicknes ses of the billets with different sizes were obtained. Taking the minimum and maximum wall thick nesses as two references, the correlation coefficient between the data for reference and those for comparison by the grey system theory reduced multi objectives to a single quality objective, and the average correlation level of every billet facilitated the optimization of size parameters for hydroform ing car beam. The trial production showed that the optimization approach satisfied the need of hy droforming car beams.

Probability estimation based on grey system theory for simulation evaluation

In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed.On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore,the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.

Application of Grey System Theory in Design For Cost (DFC)

Design For Cost (DFC) is a branch of Design For X (DFX). In this paper, wedefined DFC as a design method that analyzed and evaluated the product's life cycle cost (LCC), thenmodified the design to reduce the LCC. Nowadays it is a very difficult thing to obtain LCC data inChina or in developing countries. Statistical methods can not be used because available LCC data arefew. In order to solve this problem, we used grey system theory. Then relations of cost factorswere analyzed in LCC using grey relevant methods, and a GM(1,1) model between design parameters andLCC was established. Using this model, we can estimate and control LCC by changing design parametersat the beginning of the design stage.

Map Building for a Mobile Robot Based on Grey System Theory

In this paper, a new method for mobile robot map building based on grey system theory is presented, by which interpretation and integration of sonar readings can be solved robustly and efficiently. The conception of 'grey number is introduced to model and handle the uncertainty of sonar reading. A new data fusion approach based on grey system theory is proposed to construct environment model. Map building experiments are performed both on a platform of simulation and a real mobile robot. Experimental results show that our method is robust and accurate.

Analysis of aerobic granular sludge formation based on grey system theory

Based on grey entropy analysis, the relational grade of operational parameters with aerobic granular sludge＇s granulation indicators was studied. The former consisted of settling time （ST）, aeration time （AT）, superficial gas velocity （SGV）, height/diameter （H/D） ratio and organic loading rates （OLR）, the latter included sludge volume index （SVI） and set-up time. The calculated result showed that for SVI and set-up time, the influence orders and the corresponding grey entropy relational grades （GERG） were： SGV （0.9935） 〉 AT （0.9921） 〉 OLR （0.9894） 〉 ST （0.9876） 〉 H/D （0.9857） and SGV （0.9928） 〉 H/D （0.9914） 〉 AT （0.9909） 〉 OLR （0.9897） 〉 ST （0.9878）. The chosen parameters were all key impact factors as each GERG was larger than 0.98. SGV played an important role in improving SVI transformation and facilitating the set-up process. The influence of ST on SVI and set-up time was relatively low due to its dual functions. SVI transformation and rapid set-up demanded different optimal I-I/D ratio scopes （10-20 and 16-20）. Meanwhile, different functions could be obtained through adjusting certain factors＇ scope.

A Novel Rolling and Fractional-ordered Grey System Model and Its Application for Predicting Industrial Electricity Consumption

Accurate and reasonable prediction of industrial electricity consumption is of great significance for promoting regional green transformation and optimizing the energy structure.However,the regional power system is complicated and uncertain,affected by multiple factors including climate,population and economy.This paper incorporates structure expansion,parameter optimization and rolling mechanism into a system forecasting framework,and designs a novel rolling and fractional-ordered grey system model to forecast the industrial electricity consumption,improving the accuracy of the traditional grey models.The optimal fractional order is obtained by using the particle swarm optimization algorithm,which enhances the model adaptability.Then,the proposed model is employed to forecast and analyze the changing trend of industrial electricity consumption in Fujian province.Experimental results show that industrial electricity consumption in Fujian will maintain an upward growth and it is expected to 186.312 billion kWh in 2026.Compared with other seven benchmark prediction models,the proposed grey system model performs best in terms of both simulation and prediction performance metrics,providing scientific reference for regional energy planning and electricity market operation.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

Expansion modelling of discrete grey model based on multi-factor information aggregation

This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.

Prediction model of interval grey number based on DGM(1,1)

In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.

Fundamental definitions and calculation rules of grey mathematics: a review work

Grey mathematics is the mathematical foundation of the grey system theory. Recently, some important results have been achieved. In order to accelerate the development of grey mathematics, the results are summarized and redefined. This paper includes the fundamental definitions and calculation rules of the grey hazy set, grey number, grey matrix and grey function. Grey mathematics includes four types of operation, i.e. the grey operation, the whitened operation, the covered operation and the only potential true operation. According to its intrinsic quality, the covered operation, which differs from the interval one, is called as the whole-proximate calculation that means the proximate calculation spreads through the whole range of the covered set of every grey number, and we confirm that it may be a new branch of computational or applied mathematics. The overview should develop the grey system theory and grey mathematics.

Grey-based approach for estimating software reliability under nonhomogeneous Poisson process

Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most used one.However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.

Optimization approach of background value and initial item for improving prediction precision of GM(1,1) model

A combination method of optimization of the back-ground value and optimization of the initial item is proposed. The sequences of the unbiased exponential distribution are simulated and predicted through the optimization of the background value in grey differential equations. The principle of the new information priority in the grey system theory and the rationality of the initial item in the original GM（1,1） model are ful y expressed through the improvement of the initial item in the proposed time response function. A numerical example is employed to il ustrate that the proposed method is able to simulate and predict sequences of raw data with the unbiased exponential distribution and has better simulation performance and prediction precision than the original GM（1,1） model relatively.

Improvement and application of GM(1,1) model based on multivariable dynamic optimization

For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the background value as a variable related to k.At the same time,the initial value is set as a variable,and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error(MRE).Combined with the domestic natural gas annual consumption data,the classical model and the improved GM(1,1)model are applied to the calculation and error comparison respectively.It proves that the improved model is better than any other models.

Big Data-Based Transformer Substation Fault Prediction Method

Transformer substations play a major role in power systems.The fault of a transformer substation will jeopardize the safety and effective operation of the power system.The fault signal of a transformer substation includes the fault status and fault occurrence time.In this paper,we propose a transformer substation fault prediction method based on big data analysis.Thus,a new transformer substation fault prediction method is developed by combining the advantages of decision tree algorithms and grey system theory to predict the fault status and occurrence time with high accuracy.As a case study,the transformer substation fault signals obtained from a region in the southwest of China are analyzed using the proposed method based on big data.The experimental results confirm that the proposed method achieves high-accuracy fault prediction.

A New Method for Forecasting the Life Test Data of Mechanical Products

The model for forecasting the test data on mechanical products is established in the application of the grey system theories. A new formula of the background value is introduced into the model. The result of an example shows the method can reduce test expense and enhance the precision of forecasting.

The Application of Grey Prediction toCommunication Network Planning

The first and foremost task of communication network planning is macro forecasting to theservice volume ,and the quality of planning ultimately depends upon the accuracy of forecasting. Theconventional methods usually as forecasting model are increase rate method, time sequence extensionmethod, regression correlation analysis method. However, nowadays in market economy drvelopingstage ,to meet the vigorous demand, communication servtice business, particularly the telecommunicationservice is drveloping rapidly such that forcasting by the conventional method fails achieve the goalfavourably. Thus we should emancipate our mind thinking deeply into the communication conoiationand the method of forecasting. To this end ,the author exploited the laiter ,introducing GM(1, 1) modelas forcastzng means. Comparint with the forecasting results from several other niodels the GM(1.1)has better reliability. Is has been put into practice in many urban telecomrnunication network planning. Allresults obtatned are desirable.