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.

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).

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.

An improved interval model updating method via adaptive Kriging models

Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction method.This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods.Therefore,an improved IMU method via the adaptive Kriging models is proposed.This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers.These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is accomplished.During the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity information.Local sampling is then performed in key subspaces based on the maximum mean square error(MMSE)criterion.The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements.The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell.The results show that the updated results of the interval model are in good agreement with the experimental results.

Classification and Visualization of Surrounding Rock Mass Stability Based on Multi-Dimensional Cloud Model

The classification of the stability of surrounding rock is an uncertain system with multiple indices.The Multidimensional Cloud Model provides an advanced solution through the use of an improved model of One-dimensional Cloud Model.Setting each index as a one-dimensional attribute,the Multi-dimensional Cloud Model can set the digital characteristics of each index according to the cloud theory.The Multi-dimensional cloud generator can calculate the certainty of each grade,and then determine the stability levels of the surrounding rock according to the principle of maximum certainty.Using this model to 5 coal mine roadway surrounding rock examples and comparing the results with those of One-dimensional and Two-dimensional Cloud Models,we find that the Multi-dimensional Cloud Model can provide a more accurate solution.Since the classification results of the Multidimensional Cloud Model are difficult to be presented intuitively and visually,we reduce the Multi-dimensional Cloud Model to One-dimensional and Two-dimensional Cloud Models in order to visualize the results achieved by the Multi-dimensional Cloud Model.This approach provides a more accurate and intuitive method for the classification of the surrounding rock stability,and it can also be applied to other types of classification problems.

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.

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.

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.

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.

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.

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.

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.

Improved grey prediction model based on exponential grey action quantity

With the passage of time, it has become important to investigate new methods for updating data to better fit the trends of the grey prediction model. The traditional GM（1,1） usually sets the grey action quantity as a constant. Therefore, it cannot effectively fit the dynamic characteristics of the sequence, which results in the grey model having a low precision. The linear grey action quantity model cannot represent the index change law. This paper presents a grey action quantity model, the exponential optimization grey model（EOGM（1,1））, based on the exponential type of grey action quantity; it is constructed based on the exponential characteristics of the grey prediction model. The model can fully reflect the exponential characteristics of the simulation series with time. The exponential sequence has a higher fitting accuracy. The optimized result is verified using a numerical example for the fluctuating sequence and a case study for the index of the tertiary industry＇s GDP. The results show that the model improves the precision of the grey forecasting model and reduces the prediction error.

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.

A New Modified GM (1,1) Model: Grey Optimization Model

Based on the optimization method, a new modified GM (1,1) model is presented, which is characterized by more accuracy prediction for the grey modeling.

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.

Grey Markov chain and its application in drift prediction model of FOGs

A novel grey Markov chain predictive model is discussed to reduce drift influence on the output of fiber optical gyroscopes (FOGs) and to improve FOGs' measurement precision. The proposed method possesses advantages of grey model and Markov chain. It makes good use of dynamic modeling idea of the grey model to predict general trend of original data. Then according to the trend, states are divided so that it can overcome the disadvantage of high computational cost of state transition probability matrix in Markov chain. Moreover, the presented approach expands the applied scope of the grey model and makes it be fit for prediction of random data with bigger fluctuation. The numerical results of real drift data from a certain type FOG verify the effectiveness of the proposed grey Markov chain model powerfully. The Markov chain is also investigated to provide a comparison with the grey Markov chain model. It is shown that the hybrid grey Markov chain prediction model has higher modeling precision than Markov chain itself, which prove this proposed method is very applicable and effective.

Prediction Model Based on the Grey Theory for Tackling Wax Deposition in Oil Pipelines

Problems involving wax deposition threaten seriously crude pipelines both economically and operationally. Wax deposition in oil pipelines is a complicated problem having a number of uncertainties and indeterminations. The Grey System Theory is a suitable theory for coping with systems in which some information is clear and some is not, so it is an adequate model for studying the process of wax deposition. In order to predict accurately wax deposition along a pipeline, the Grey Model was applied to fit the data of wax deposition rate and the thickness of the deposited wax layer on the pipe-wall, and to give accurate forecast on wax deposition in oil pipelines. The results showed that the average residential error of the Grey Prediction Model is smaller than 2%. They further showed that this model exhibited high prediction accuracy. Our investigation proved that the Grey Model is a viable means for forecasting wax deposition. These findings offer valuable references for the oil industry and for firms dealing with wax cleaning in oil pipelines.

Improved unequal interval grey model and its applications

A new method to improve prediction precision of GM（1,1） model with unequal time interval is presented.The grey derivative is multiplied by a parameter to guarantee the time response function satisfying approximately exponential function distribution.To simplify the process of parametric estimation,an approximate value is taken for the multiplied parameter.Then the estimators of coefficient of development and grey action quantity can be derived.At the same time,the principle of the new information priority is also considered.We take the last item of the first-order accumulated generation operator（1-AGO） on raw data sequence as the initial condition in the time response function.Then the new information can be taken full advantage of through the improved initial condition.Some properties of this new model are also discussed.The presented method is actually a combination of improvement of grey derivative and improvement of the initial condition.The results of an example indicate that the proposed method can improve prediction precision prominently.

A new grey forecasting model based on BP neural network and Markov chain

A new grey forecasting model based on BP neural network and Markov chain was proposed. In order to combine the grey forecasting model with neural network, an important theorem that the grey differential equation is equivalent to the time response model, was proved by analyzing the features of grey forecasting model（GM（1,1））. Based on this, the differential equation parameters were included in the network when the BP neural network was constructed, and the neural network was trained by extracting samples from grey system＇s known data. When BP network was converged, the whitened grey differential equation parameters were extracted and then the grey neural network forecasting model （GNNM（1,1）） was built. In order to reduce stochastic phenomenon in GNNM（1,1）, the state transition probability between two states was defined and the Markov transition matrix was established by building the residual sequences between grey forecasting and actual value. Thus, the new grey forecasting model（MNNGM（1,1）） was proposed by combining Markov chain with GNNM（1,1）. Based on the above discussion, three different approaches were put forward for forecasting China electricity demands. By comparing GM（1, 1） and GNNM（1,1） with the proposed model, the results indicate that the absolute mean error of MNNGM（1,1） is about 0.4 times of GNNM（1,1） and 0.2 times of GM（I, 1）, and the mean square error of MNNGM（1,1） is about 0.25 times of GNNM（1,1） and 0.1 times of GM（1,1）.