Deformation critical threshold estimation of Xiaowan ultrahigh arch dam with time-varying grey model

The structural behavior of the Xiaowan ultrahigh arch dam is primarily influenced by external loads and time-varying characteristics of dam concrete and foundation rock mass during long-term operation. According to overload testing with a geological model and the measured time series of installed perpendicular lines, the space and time evolution characteristics of the arch dam structure were analyzed, and its mechanical performance was evaluated. Subsequently, the deformation centroid of the deflective curve was suggested to indicate the magnitude and unique distribution rules for a typical dam section using the measured deformation values at multi-monitoring points. The ellipse equations of the critical ellipsoid for the centroid were derived from the historical measured time series. Hydrostatic and seasonal components were extracted from the measured deformation values with a traditional statistical model, and residuals were adopted as a grey component. A time-varying grey model was developed to accurately predict the evolution of the deformation behavior of the ultrahigh arch dam during future operation. In the developed model, constant coefficients were modified so as to be time-dependent functions, and the prediction accuracy was significantly improved through introduction of a forgetting factor. Finally, the critical threshold was estimated, and predicted ellipsoids were derived for the Xiaowan arch dam. The findings of this study can provide technical support for safety evaluation of the actual operation of ultrahigh arch dams and help to provide early warning of abnormal changes.

Combined model based on optimized multi-variable grey model and multiple linear regression

The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to eliminate the random fluctuations or errors of the observational data of all variables, and the combined prediction model together with the multiple linear regression is established in order to improve the simulation and prediction accuracy of the combined model. Finally, a combined model of the MGM（1,2） with optimized background value and the binary linear regression is constructed by an example. The results show that the model has good effects for simulation and prediction.

Dynamic grey model of verification cycle and lifecycle of measuring instrument and its application

Two dynamic grey models DGM (1, 1) for the verification cycle and the lifecycle of measuring instrument based on time sequence and frequency sequence were set up, according to the statistical feature of examination data and weighting method. By a specific case, i.e. vernier caliper, it is proved that the fit precision and forecast precision of the models are much higher, the cycles are obviously different under different working conditions, and the forecast result of the frequency sequence model is better than that of the time sequence model. Combining dynamic grey model and auto-manufacturing case the controlling and information subsystems of verification cycle and the lifecycle based on information integration, multi-sensor controlling and management controlling were given. The models can be used in production process to help enterprise reduce error, cost and flaw.

Mitigating end effects of EMD using non-equidistance grey model

Aiming at mitigating end effects of empirical mode decomposition （EMD）, a new approach motivated by the non- equidistance grey model （NGM） termed as NGM（1,1） is proposed. Other than trapezoid formulas, the cubic Hermite spline is put forward to improve the accuracy of derivative to the accumulated generating operation （AGO） series. Hopefully, it is worth stressing that the proposed NGM（1,1） model is particularly useful for predicting uncertainty data. Qualitative and quantitative comparisons between the proposed approach and other well-known algorithms are carried out through computer simulations on synthetic as well as natural signals. Simulation results demonstrate the proposed method can reduce end effects and improve the decomposition results of EMD.

Lifetime prediction for tantalum capacitors with multiple degradation measures and particle swarm optimization based grey model

A lifetime prediction method for high-reliability tantalum （Ta） capacitors was proposed, based on multiple degradation measures and grey model （GM）. For analyzing performance degradation data, a two-parameter model based on GM was developed. In order to improve the prediction accuracy of the two-parameter model, parameter selection based on particle swarm optimization （PSO） was used. Then, the new PSO-GM（1, 2, co） optimization model was constructed, which was validated experimentally by conducting an accelerated testing on the Ta capacitors. The experiments were conducted at three different stress levels of 85, 120, and 145℃. The results of two experiments were used in estimating the parameters. And the reliability of the Ta capacitors was estimated at the same stress conditions of the third experiment. The results indicate that the proposed method is valid and accurate.

Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus

The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.

A grey model with periodic term for sea-level analysis and its application to the Guangxi coast

A grey model with periodic term for sea-level analysis is presented.The present model keeps some advantages of tea GM (1, 1 )model, which well reflects the trend of sea-level changes and gives out the change rate as well as the acceleration of sea level conveniently.level conveniently.In addition, the present model can reproduce the periodic phenomena of sealevel, hence, it overcomes the shortcomings of the GM(1,1) model that is unsuitable for forecasting monthly mean sealevel with apparent periodicity, and its prediction accuracy is improved.The present model is used to analyse Guangxi coast sea level,the results show that the rise rates of relative sea level at Beihai, Weizhou and Bailongwei are 1 .67,2 .51 and 0.89 mm/a respectively, the relative sea level at Shitoubu has a falling trend with a rate of 0. 5- 1 .0 mm/a, the rise rate of eustatic sea level along the Guangxi coast is 2 .0 mm/a. In comparison with the model with a lineartrend term plus a periodic term, the simulation accuracies of both models are about the same.

Analysis of grey model between seawater environmentalessential factors and phytoplankon dynamics in the Dapeng Bay, the South China Sea

The relation between the dynamics of phytoplankton and essential environmental factors of seawater has been studied. According to the comparison between environmental factors of seawater. and on the basis of mathematical space theory and the four principles of normalization, even symmetry, globality and proximity, smoothing discrete function, the grey derivative and the grey differential equation have been defined, the grey models and relation to the factors (the seawater physical and chemical factors) were estimated. The calculation results indicate that zooplankton,Mn, Fe and dissolved oxygen are the moot important factors.

AXIAL HEAT CONDUCTION MODEL TO PREDICT MAXIMUM HEAT REMOVE OF MINIATURE HEAT PIPE BASED ON GREY MODEL THEORY

Computer chip is always accompanied by the increase of heat dissipation and miniaturization. The miniature heat pipes are widely used in notebook computer to resolve the heat dissipation problems. Maximum heat removed model of miniature heat pipes building by grey model is presented. In order to know the foundation for modeling, the smooth grade of error examination is inquired and the accuracy of grey relational grade is verified. The model can be used to select a suitable heat pipes to solve electric heat problems in the future. Final results show that the grey model only needs four experiment data and its error value is less than 10%, further, it is better than computational fluid dynamics （CFD） model.

Prediction of syphilis incident rate and number in China based on the GM(1,1)grey model

Objective:To explore the feasibility of using grey model GM(1,1)model to predict syphilis,and to provide a theoretical basis for the health sector to develop corresponding strategies.Methods:GM(1,1)model was used to construct and simulate the incident rate and case number of syphilis in China from 2009 to 2018 to predict the change trend.Results:The GM(1,1)prediction model of syphilis incident rate was x^(1)(k+1)=929.367901 e(0.029413k)-906.297901.The GM(1,1)prediction model for the number of syphilis patients was x^(1)(k+1)=1060.278025 e(0.034280k)-1029.639925.For syphilis incidence model,the posterior difference ratio was 0.19819 and the probability of small error was 1.For the syphilis incident number model,the posterior difference ratio was 0.18450 and the probability of small error was 1.The above models have good fitting accuracy with excellent grade level and can be predicted by extrapolation and predicted that the syphilis incidence in 2019-2021 may be 36.15 per 100,000,37.23 per 100,000 and 38.34 per 100,000,respectively.From 2019 to 2021,the number of incident syphilis cases in China may be 503,406,520,962 and 539,130,respectively.Conclusion:The GM(1,1)model can well fit and predict the change trend of syphilis incidence in time series.The prediction model showed that the incidence of syphilis may continue to increase and the number of syphilis cases per year may continue to increase substantially.More effort is needed to strengthen the prevention and treatment of venereal disease,reduce venereal harm to the population and improve the early detection rate of syphilis.

An Adaptive Lasso Grey Model for Regional FDI Statistics Prediction

To overcome the deficiency of traditional mathematical statistics methods,an adaptive Lasso grey model algorithm for regional FDI(foreign direct investment)prediction is proposed in this paper,and its validity is analyzed.Firstly,the characteristics of the FDI data in six provinces of Central China are generalized,and the mixture model’s constituent variables of the Lasso grey problem as well as the grey model are defined.Next,based on the influencing factors of regional FDI statistics(mean values of regional FDI and median values of regional FDI),an adaptive Lasso grey model algorithm for regional FDI was established.Then,an application test in Central China is taken as a case study to illustrate the feasibility of the adaptive Lasso grey model algorithm in regional FDI prediction.We also select RMSE(root mean square error)and MAE(mean absolute error)to demonstrate the convergence and the validity of the algorithm.Finally,we train this proposedal gorithm according to the regional FDI statistical data in six provinces in Central China from 2006 to 2018.We then use it to predict the regional FDI statistical data from 2019 to 2023 and show its changing tendency.The extended work for the adaptive Lasso grey model algorithm and its procedure to other regional economic fields is also discussed.

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.

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.

Hybrid grey model to forecast monitoring series with seasonality

The grey forecasting model has been successfully applied to many fields. However, the precision of GM(1,1) model is not high. In order to remove the seasonal fluctuations in monitoring series before building GM(1,1) model, the forecasting series of GM(1,1) was built, and an inverse process was used to resume the seasonal fluctuations. Two deseasonalization methods were presented , i.e., seasonal index-based deseasonalization and standard normal distribution-based deseasonalization. They were combined with the GM(1,1) model to form hybrid grey models. A simple but practical method to further improve the forecasting results was also suggested. For comparison, a conventional periodic function model was investigated. The concept and algorithms were tested with four years monthly monitoring data. The results show that on the whole the seasonal index-GM(1,1) model outperform the conventional periodic function model and the conventional periodic function model outperform the SND-GM(1,1) model. The mean Absolute error and mean square error of seasonal index-GM(1,1) are 30.69% and 54.53% smaller than that of conventional periodic function model, respectively. The high accuracy, straightforward and easy implementation natures of the proposed hybrid seasonal index-grey model make it a powerful analysis technique for seasonal monitoring series.

Fractional derivative multivariable grey model for nonstationary sequence and its application

Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.

Comparison of Two Grey Models’ Applicability to the Prediction of Passenger Flow in Sanya Airport

The city airport serves as a fundamental infrastructure for air trans-portation,with its development planning largely contingent upon the prognosti-cation of future airport activities’busyness.Given the multifarious factors that influence passengerflow,such as population size,economic structure,industrial policy,geographical location,and comprehensive transportation,grey system has the characteristic of incomplete information,and the passenger traffic at the airport conforms to this feature.In this article,the GM(1,1)grey prediction model and the GM(2,1)grey prediction model are respectively applied to predict the passengerflow of Sanya Airport,and the suitability of each model is compared.The out-comes show that the GM(2,1)grey model outperforms the GM(1,1)grey model in relation to the average relative error rate,the single point maximum error,the mean square error of relative error,and the average relative accuracy.

Prediction of Total Output Value of Construction Industry in Jiangxi Province Based on Grey Prediction Model

In order to realize the accurate prediction of the total output value of construction industry in the future,the grey prediction model is used to compare the measured value with the predicted value from 2012 to 2021,and based on the existing data,the total output value of construction industry in Jiangxi Province in the next five years is predicted.The results show that the grey prediction model has a good prediction effect,and the error between the predicted value and the measured value is within 14%,which provides a basis for policy adjustment and resource optimization.

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.

Fault Prediction Based on Dynamic Model and Grey Time Series Model in Chemical Processes

This paper combines grey model with time series model and then dynamic model for rapid and in-depth fault prediction in chemical processes. Two combination methods are proposed. In one method, historical data is introduced into the grey time series model to predict future trend of measurement values in chemical process. These predicted measurements are then used in the dynamic model to retrieve the change of fault parameters by model based diagnosis algorithm. In another method, historical data is introduced directly into the dynamic model to retrieve historical fault parameters by model based diagnosis algorithm. These parameters are then predicted by the grey time series model. The two methods are applied to a gravity tank example. The case study demonstrates that the first method is more accurate for fault prediction.