PROGRESS OF GREY SYSTEM MODELS

The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey incidence model, the grey cluster model based on endpoint triangular whitenization functions, the grey cluster model based on center-point triangular whitenization functions, the grey prediction model of the model GM （ 1,1）, and the weighted multi-attribute grey target decision model.

Application of Grey System GM (1,1) model and unary linear regression model in coal consumption of Jilin Province

The data on the coal production and consumption in Jilin Province for the last ten years were collected,and the Grey System GM( 1,1) model and unary linear regression model were applied to predict the coal consumption of Jilin Production in 2014 and 2015. Through calculation,the predictive value on the coal consumption of Jilin Province was attained,namely consumption of 2014 is 114. 84 × 106 t and of 2015 is 117. 98 ×106t,respectively. Analysis of error data indicated that the predicted accuracy of Grey System GM( 1,1) model on the coal consumption in Jilin Province improved 0. 21% in comparison to unary linear regression model.

Study on the Yield Prediction Model of Processing Tomato Based on the Grey System Theory

[Objective] The research aimed to study the yield prediction model of processing tomato based on the grey system theory.[Method] The variation trend of processing tomato yield was studied by using the grey system theory,and GM（1,1）grey model of processing tomato yield prediction was established.The processing tomato yield in Xinjiang during 2001-2009 was as the example to carry out the instance analysis.[Result] The model had the high forecast accuracy and strong generalization ability,and was reliable for the prediction of recent processing tomato yield.[Conclusion] The research provided the reference for the macro-control of tomato industry,the processing and storage of tomato in Xinjiang.

Modeling of the Dyeing Uptake Rate for Direct Dyestuff on Cotton in Batch Dyeing Process Based on Grey System Theory

The grey system theory, with the characteristics of fewer modeling data and higher accuracy, was employed to model the batch dyeing process for the purpose of accurate online control. The GM（1, 1） and GM （0, N） models of the grey system theory were discussed for their feasibilities of modding for batch dyeing process. The combination of direct dyestuff Fast Red F3B on cotton was chosen as a representative of the common dyeing method for describing the modeling process. Firstly, the GM（ 1, 1 ） model and the GM（1, 1） combined with GM（0, N） model were employed to model the equilibrium percentage of dyeing uptake rate. Secondly, an integrated dyeing uptake rate model with three factors （ temperature, salt concentration, and pH） was established based on the adsorption rate equation. Experimental results show that this model has higher accuracy and beetler generalization ability, which can predict the results of batch dyeing process. Due to the application of grey system theory, the model has a lot of advantages, such as being easy to determine the parameter value and small amount of calculation. So it can also be suitable for the same type of combination of dyestuff-fahric by changing the parameters value only.

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.

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.

Using Grey System Theory for Earthquake Forecast

By combining conventional grey correlation analysis, grey clustering method and grey forecasting methods with our multi-goal forecast thoughts and the techniques of grey time series processing, we develop six different grey earthquake forecast models in this paper. Using the record of major earthquakes in Japan from 1872 to 1995, we forecast future earthquakes in Japan. We develop an earthquake forecast model. By using the major earthquakes in Japan from 1872 to 1984, we forecast earthquakes from 1985 to 1995 and check the precision of the grey earthquake models. We find that the grey system theory can be applied to earthquake forecast. We introduce the above analysis methods and give a real example to evaluate and forecast. We also further discuss the problems of how to improve the precision of earthquake forecast and how to strengthen the forecast models in future research.

Prediction of the maximum water inflow in Pingdingshan No.8 mine based on grey system theory

In order to prevent and control the water inflow of mines, this paper built a new initial GM（1, 1） model to torecast the maximum water inflow according to the principle of new information. The effect of the new initial GM（1, 1） model is not ideal by the concrete example. Then according to the principle of making the sum of the squares of the difference between the calculated sequences and the original sequences, an optimized GM（1, I） model was established. The result shows that this method is a new prediction method which can predict the maximum water inflow accurately. It not only conforms to the guide- line of prevention primarily, but also provides reference standards to managers on making prevention measures.

The softening prediction of HSLA steel heat-affected zone based on the grey system

The high-strength low-alloy（ HSLA ） steel heat-affected zone （HAZ）softening was predicted using a grey model. HSLA steel DILLIMAX690E, NK-HITEN61OU2 and BHW35 were taken as examples in the research on ultra-narrow gap automatic welding technology. Test results turned out to be that the errors between the values calculated by the Grey Model （GM） （ 1,1 ） model and their actual value were less than 2%, indicating that the grey prediction method could accurately reflect the actual situation of the high-strength low-alloy steel heat-affected zone softening. This method will play a crucial role in guiding the applications of HSLA steel welded structures in the future.

Grey System Judgment on Reliability of Mechanical Equipment

he Grey system theory -was applied in reliability analysis of mechanical equip-ment. It is a new theory and method in reliability engineering of mechanical engineering of mechanical equipment. Through the Grey forecast of reliability parameters and the reliability forecast of parts and systems, decisions were made in the real operative state of e-quipment in real time. It replaced the old method that required mathematics and physical statistics in a large base of test data to obtain a pre-check , and it was used in a practical problem. Because of applying the data of practical operation state in real time, it could much more approach the real condition of equipment; it-was applied to guide the procedure and had rather considerable economic and social benefits.

A dynamic influence model of social network hotspot based on grey system

The outbreak of hotspot in social network may contain complex dynamic genesis. Using user behavior data from hotspots in social network, we study how different user groups play different roles for a hotspot topic. Firstly, by analyzing users' behavior records, we mine group situation that promotes the hotspot.Several major attributions in a hotspot outbreak, such as individual, peer and group triggers, are defined formally according to the view-point of social identity, social interaction, retweet depth and opinion leader. Secondly,for the problem of the uneven and sparse data in each stage of hotspot topic's life cycle, we propose a dynamic influence model based on grey system to formalize the effect of different groups. Then the process of hotspot evolution driven by distinct crowd is showed dynamically. The experimental result confirms that the model is able not only to qualify users' influence on a hotspot topic but also to predict effectively an upcoming change in a hotspot topic.

GREY DISPLACEMENT INPUT－OUTPUT MODELS OF MINERAL PROCESSING－METALLURGY SYSTEM

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Design of adaptive backoff algorithm for satellite network using grey system

In contention-based satellite communication system, collisions between data packets may occur due to the randomly sending of the packets. A proper delay before each＇ transmission can reduce the data collision rate. As classical random multiple access protocol, the slotted ALOHA （S-ALOHA） reduces the data collision rate through time slot allocation and synchronous measures. In order to improve the stability and throughput of satellite network, a backoff algorithm based on S-ALOHA will be effective. A new adaptive backoff algorithm based on S-ALOHA using grey system was proposed, which calculates the backofftime adaptively according to the network condition. And the network condition is estimated by each user terminal according to the prediction of the channel access success ratio using the model GM （1,1） in grey system. The proposed algorithm is compared to other known schemes such as the binary exponential backoff （BEB） and the multiple increase multiple decrease （MIMD） backoff. The performance of the proposed algorithm is simulated and analyzed. It is shown that throughput of the system based on the proposed algorithm is better than of system based on BEB and MIMD backoff. And there are also some improvements of the delay performance compared to using BEB. The proposed algorithm is especially effective for large number of user terminals in the satellite networks.

Multi-Objective Optimization of Fused Deposition Modeling for Mechanical Properties of Biopolymer Parts Using the Grey-Taguchi Method

The urgent need to develop customized functional products only possible by 3D printing had realized when faced with the unavailability of medical devices like surgical instruments during the coronavirus-19 disease and the ondemand necessity to perform surgery during space missions.Biopolymers have recently been the most appropriate option for fabricating surgical instruments via 3D printing in terms of cheaper and faster processing.Among all 3D printing techniques,fused deposition modelling(FDM)is a low-cost and more rapid printing technique.This article proposes the fabrication of surgical instruments,namely,forceps and hemostat using the fused deposition modeling(FDM)process.Excellent mechanical properties are the only indicator to judge the quality of the functional parts.The mechanical properties of FDM-processed parts depend on various process parameters.These parameters are layer height,infill pattern,top/bottom pattern,number of top/bottom layers,infill density,flow,number of shells,printing temperature,build plate temperature,printing speed,and fan speed.Tensile strength and modulus of elasticity are chosen as evaluation indexes to ascertain the mechanical properties of polylactic acid(PLA)parts printed by FDM.The experiments have performed through Taguchi’s L27orthogonal array(OA).Variance analysis(ANOVA)ascertains the significance of the process parameters and their percent contributions to the evaluation indexes.Finally,as a multiobjective optimization technique,grey relational analysis(GRA)obtains an optimal set of FDM process parameters to fabricate the best parts with comprehensive mechanical properties.Scanning electron microscopy(SEM)examines the types of defects and strong bonding between rasters.The proposed research ensures the successful fabrication of functional surgical tools with substantial ultimate tensile strength(42.6 MPa)and modulus of elasticity(3274 MPa).

HIERARCHIC GREY QUASI-PREFERRED ANALYSIS MODEL AND ITS APPLICATION

The grey quasi-preferred analysis (GQPA) is one of important methods for realizing system analysis to conquer the limitations of the existing GQPA model, without any considerations to the difference of the different behavioral factor′s importance. It could not be used to analyze the complex system with multi-hierarchy correlation factors, the weighted synthetic method for calculating abstract incidence degrees between the system beha-vioral characteristics and correlative factors in different hierarchies is given out,and the hierarchic grey quasi-preferred analysis (HGQPA) model is established. The effectiveness of the HGQPA model is tested by the scientific-technical system of Jiangsu Province. The depth and the range of the application of GQPA are developed, and the HGQPA model is regarded as a new approach to systemically analyze the complex systems with multi-hierarchy correlation factors.

Grey Prediction Fuzzy Control of the Target Tracking System in a Robot Weapon

Grey modeling can be used to predict the behavioral development of a system and find out the lead control values of the system. By using fuzzy inference, PID parameters can be adjusted on line by the fuzzy controller with PID parameters self-tuning. According to the characteristics of target tracking system in a robot weapon, grey prediction theory and fuzzy PID control ideas are combined. A grey prediction mathematical model is constructed and a fuzzy PID controller with grey prediction was developed. Simulation result shows fuzzy PID control algorithm with grey prediction is an efficient method that can improve the control equality and robustness of traditional PID control and fuzzy PID control, and has much better performance for target tracking.

TIME SERIES AND GREY MODEL DIAGNOSIS METHOD USED TO CRACK PROBLEMS

In this paper,the vibration signals in the fatigue crack growth process in a chinese steel used in a mining machinery were analyzed by the frequency spectrum, the time series and grey system model,and the critical criterion for crack initiation was proposed.

Modeling Arctic Boundary Layer Cloud Streets at Grey-zone Resolutions

To better understand how model resolution affects the formation of Arctic boundary layer clouds,we investigated the influence of grid spacing on simulating cloud streets that occurred near Utqiaġvik(formerly Barrow),Alaska,on 2 May 2013 and were observed by MODIS(the Moderate Resolution Imaging Spectroradiometer).The Weather Research and Forecasting model was used to simulate the clouds using nested domains with increasingly fine resolution ranging from a horizontal grid spacing of 27 km in the boundary-layer-parameterized mesoscale domain to a grid spacing of 0.111 km in the large-eddy-permitting domain.We investigated the model-simulated mesoscale environment,horizontal and vertical cloud structures,boundary layer stability,and cloud properties,all of which were subsequently used to interpret the observed roll-cloud case.Increasing model resolution led to a transition from a more buoyant boundary layer to a more shear-driven turbulent boundary layer.The clouds were stratiform-like in the mesoscale domain,but as the model resolution increased,roll-like structures,aligned along the wind field,appeared with ever smaller wavelengths.A stronger vertical water vapor gradient occurred above the cloud layers with decreasing grid spacing.With fixed model grid spacing at 0.333 km,changing the model configuration from a boundary layer parameterization to a large-eddy-permitting scheme produced a more shear-driven and less unstable environment,a stronger vertical water vapor gradient below the cloud layers,and the wavelengths of the rolls decreased slightly.In this study,only the large-eddy-permitting simulation with gird spacing of 0.111 km was sufficient to model the observed roll clouds.

Grey relationship analysis and grey forecasting modeling on thermal stability of synthetic single diamond

Through analyzing 7 Ib-type samples of synthetic single diamonds by their DTA and TG in air, we ascertained the extrapolated onset temperature on the curves of DTA as the characteristic temperature of their thermal stabilities. Based on the grey system theory, we analyzed 4 factors influential in the thermal stability by the grey relationship analysis, a quantitative method, and derived the grey relationship sequence, that is, the rank of the influence extent of 4 factors on the thermal stability. Furthermore, we established the grey forecasting model, namely GM(1,5), for predicting the thermal stability of single diamonds with their intrinsic properties, which was then examined by a deviation-probability examination. The results illustrate that it is reasonable to take the Extrapolated Onset Temperature in DTA as the characteristic temperature for thermal stability (TS) of Ib-type synthetic single diamonds. The nitrogen content and grain shape regularity of diamonds are dominating factors. Likewise, grain size and compressive strength are minor factors. In addition, GM(1,5) can be used to predict the thermal stability of Ib-type synthetic single diamonds available. The precision rank of GM(1,5) is ‘GOOD’.

Equivalency and unbiasedness of grey prediction models

In order to deeply research the structure discrepancy and modeling mechanism among different grey prediction models, the equivalence and unbiasedness of grey prediction models are analyzed and verified. The results show that all the grey prediction models that are strictly derived from x^（0）（k） ＋az^（1）（k） = b have the identical model structure and simulation precision. Moreover, the unbiased simulation for the homogeneous exponential sequence can be accomplished. However, the models derived from dx^（1）/dt ＋ ax^（1）= b are only close to those derived from x^（0）（k） ＋ az^（1）（k） = b provided that ｜a｜ has to satisfy｜a｜ 0.1; neither could the unbiased simulation for the homogeneous exponential sequence be achieved. The above conclusions are proved and verified through some theorems and examples.