scholarly journals Time-Delayed Polynomial Grey System Model with the Fractional Order Accumulation

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Lin Chen ◽  
Zhibin Liu ◽  
Nannan Ma
Keyword(s):  
System Theory ◽  
Fractional Order ◽  
Grey System Theory ◽  
Small Sample ◽  
System Model ◽  
Grey Prediction ◽  
Grey System ◽  
Forecasting Models ◽  
New Information ◽  
Grey System Model

In this work, a novel time-delayed polynomial grey prediction model with the fractional order accumulation is put forward, which is abbreviated as TDPFOGM(1,1), based on the new grey system theory to predict the small sample in comparison with the existing forecasting models. The new model takes into account the nonhomogeneous term and the priority of new information can be better reflected in the in-sample model. The data in this paper all come from the existing literatures. The results demonstrate that the TDPFOGM(1,1) model outperforms the TDPGM(1,1) and FOGM(1,1) model.

A REPAIRABLE SYSTEM MODELLING: COMBINING GREY SYSTEM THEORY WITH INTERVAL-VALUED FUZZY SET THEORY

2005 ◽  
Vol 12 (03) ◽  
pp. 241-266 ◽  
Author(s):  
R. GUO
Keyword(s):  
System Theory ◽  
Fuzzy Sets ◽  
Underlying Mechanism ◽  
Grey System Theory ◽  
Small Sample ◽  
System Modelling ◽  
Repairable System ◽  
Type I ◽  
Grey System ◽  
Interval Valued

A fundamental but impossible to be addressed problem in repairable system modelling is how to estimate the system repair improvement (or damage) effects because of the large-sample requirements from the standard statistical inference theory. On the other hand, repairable system operating and maintenance data are often imprecise and vague and therefore Type I fuzzy sets defined by point-wise membership functions are often used for the modelling repairable systems. However, it is more logical and natural to argue that Type II fuzzy sets defined by interval-valued membership function, called interval-valued fuzzy sets (IVFS), should be used in characterizing the underlying mechanism of repairable system. In this paper, we explore a small-sample based GM(1,1) modelling approach rooted in the grey system theory to extract the system intrinsic functioning times from the seemly lawless functioning-failure time records and thus to estimate the repair improvement (damage) effects. We further explore the role of interval-valued fuzzy sets theory in the analysis of the system underlying mechanism. We develop a framework of the GM(1,1)-IVFS mixed reliability analysis and illustrate our idea by an industrial example.

Grey system model with the fractional order accumulation

2013 ◽  
Vol 18 (7) ◽  
pp. 1775-1785 ◽  
Author(s):  
Lifeng Wu ◽  
Sifeng Liu ◽  
Ligen Yao ◽  
Shuli Yan ◽  
Dinglin Liu
Keyword(s):  
Fractional Order ◽  
System Model ◽  
Grey System ◽  
Grey System Model

Research on Duration Prediction of the Coupled Task Set Based on the Grey System Theory

2012 ◽  
Vol 220-223 ◽  
pp. 169-173
Author(s):  
Peng Jia ◽  
Qi Gao ◽  
Rong Zhen Xu ◽  
Xiao Chen Zheng ◽  
Gang Liu
Keyword(s):  
System Theory ◽  
Prediction Model ◽  
Grey System Theory ◽  
Small Sample ◽  
Practical Application ◽  
Grey System ◽  
Task Set ◽  
Posterior Variance ◽  
Duration Prediction

In order to solve the problem of duration predicting in the project with poor information, small sample and uncertainty, a method based on grey system theory is put forward to predicting the duration of the coupled task set. A grey duration prediction model GM(1,1) is built, and the accuracy of the model is tested through residual, degree of incidence and posterior variance. Finally, the feasibility of the prediction model is verified by a practical application case.

scholarly journals Prediction Method of Asphalt Pavement Performance and Corrosion Based on Grey System Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Ding-bang Zhang ◽  
Xin Li ◽  
Yi Zhang ◽  
Hang Zhang
Keyword(s):  
System Theory ◽  
Asphalt Pavement ◽  
Prediction Equation ◽  
Grey System Theory ◽  
Small Sample ◽  
Monitoring Data ◽  
Pavement Performance ◽  
Skid Resistance ◽  
Grey System ◽  
Absolute Correlation

The Grey system theory is a new mathematical method to predict data changes in the poor data integrity. As a branch of Grey system theory, the GM (1, 1) model is widely used because only small sample data and simple calculations are needed in prediction of engineering project. It is a critical problem to effectively predict the performance and corrosion of asphalt pavement of highway construction due to the inadequacy of highway performance monitoring data. The smoothness, rut, and pavement skid resistance are three important indexes to evaluate the performance and corrosion of asphalt pavement. This paper has established the prediction model and derived prediction equation of asphalt pavement performance according to the GM (1, 1) model method and then listed the calculation equation of residual and the gray absolute correlation degree. Based on the experience of constructed Dalian-Guangzhou expressway in China, the vectors “a” and “b” in the prediction equation of smoothness, rut, and pavement skid resistance have been calculated by using the original monitoring data. The field monitoring data are compared with the predictive data for residual and the gray absolute correlation. The results reveal that the predicted data of the smoothness, rut, and skid resistance are mostly consistent with the monitoring data, the biggest residual of the above three indexes is smaller than 8.09%, and the gray absolute correlation degrees all exceed 0.9, which means the accuracy of the predicted equation is excellent. The calculation method based on GM (1, 1) model can effectively predict the changing performance index of asphalt pavement.

scholarly journals Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System Theory

Materials ◽  
2019 ◽  
Vol 12 (14) ◽  
pp. 2237 ◽  
Author(s):  
Qihong Zhou ◽  
Liqun Lin ◽  
Ge Chen ◽  
Zhaoqun Du
Keyword(s):  
System Theory ◽  
Prediction Error ◽  
Fiber Diameter ◽  
Grey System Theory ◽  
Grey Prediction ◽  
Grey System ◽  
Average Prediction Error ◽  
Background Value ◽  
High Prediction ◽  
Fitting Error

This paper provides a new method for predicting the diameter of electrospun nanofibers. Based on the grey system theory, the effects of polyacrylonitrile mass fraction, voltage, flow rate, and receiving distance on fiber diameter were studied. The GM(1,1) (grey model) model and DNGM(1,1) (The DNGM (1,1) model is based on the whitening differential equation using parameters to Directly estimate the approximate Non-homogeneous sequence Grey prediction Model) model were established to predict fiber diameter by a single-factor change, and the results showed high prediction accuracy. The multi-variable grey model MGM(1,n) (MGM(1,n) is a Multivariate Grey prediction Model) was used for prediction of fiber diameter when multiple factors change simultaneously. The results showed that the average modeling fitting error is 8.62%. The background value coefficients of the MGM(1,n) model were optimized, the average modeling fitting error was reduced to 1.01%, and the average prediction error was reduced to 1.33%. Combining the fractional optimization with the background-value coefficient optimization, the optimal background-value coefficient α and the order r were selected. The results showed that the average modeling fitting error is 0.85%, and the average prediction error is 0.38%. The results demonstrate that the grey system theory can effectively predict the diameter of polyacrylonitrile electrospinning fibers with high prediction accuracy. This theory can increase the control of nanofiber diameters in production.

Research of Accidents due to Human Factor in Coal Mine Based on GM Model

2015 ◽  
Vol 1092-1093 ◽  
pp. 692-695 ◽  
Author(s):  
Shang Quan Ma ◽  
Jing Fu
Keyword(s):  
System Theory ◽  
Incomplete Information ◽  
Coal Mine ◽  
Human Factor ◽  
Grey System Theory ◽  
Forecasting Model ◽  
Grey System ◽  
Forecasting Models ◽  
Grey Forecasting ◽  
Development Tendency

Grey forecast can master the developing law of system through dealing with incomplete information of system at present. On the basis of actual data of Feng Feng Coal Mine, the grey forecasting model for coal mine accidents due to human factor in Feng Feng by using the grey system theory in this paper, it is shown that models which are built have good precisions. Safety and production of Feng Feng Coal Mine are forecasted by using grey forecasting models which are built. The results show that the forecasting models will help coal mines to forecast accidents due to human factor next year and generally tally with development tendency of Feng Feng Coal Mine.

scholarly journals Explanation of terms of grey forecasting models

2017 ◽  
Vol 7 (1) ◽  
pp. 123-128 ◽  
Author(s):  
Sifeng Liu ◽  
Yingjie Yang
Keyword(s):  
System Theory ◽  
Design Methodology ◽  
Grey System Theory ◽  
Grey System ◽  
Content Type ◽  
Forecasting Models ◽  
Grey Forecasting ◽  
Key Terms ◽  
Practical Implications

Purpose The purpose of this paper is to present the terms of grey forecasting models and techniques. Design/methodology/approach The definitions of basic terms about grey forecasting models and techniques are presented one by one. Findings The reader could know the basic explanation about the important terms about various grey forecasting models and techniques from this paper. Practical implications Many of the authors’ colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors. Originality/value It is a fundamental work to standardise all the definitions of terms for a new discipline. It is also propitious to spread and universal of grey system theory.

Prediction of Technical Reserves Based on Grey Model — GM(1,1): Evidence from Non-life Egyptian Insurance Market

2019 ◽  
Vol 10 (9) ◽  
pp. 852-860
Author(s):  
Mahmoud Elsayed ◽  
◽  
Amr Soliman ◽  
Keyword(s):  
System Theory ◽  
Grey System Theory ◽  
Insurance Market ◽  
Grey Model ◽  
Loss Ratio ◽  
Grey System ◽  
Mathematical Technique ◽  
Supervisory Authority ◽  
Error Ratio ◽  
Using Data

Grey system theory is a mathematical technique used to predict data with known and unknown characteristics. The aim of our research is to forecast the future amount of technical reserves (outstanding claims reserve, loss ratio fluctuations reserve and unearned premiums reserve) up to 2029/2030. This study applies the Grey Model GM(1,1) using data obtained from the Egyptian Financial Supervisory Authority (EFSA) over the period from 2005/2006 to 2015/2016 for non-life Egyptian insurance market. We found that the predicted amounts of outstanding claims reserve and loss ratio fluctuations reserve are highly significant than the unearned premiums reserve according to the value of Posterior Error Ratio (PER).

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