Application and Non-Homogeneous Index Grey Model NIGM(1,1,k)

2010 ◽  
Vol 34-35 ◽  
pp. 148-152
Author(s):  
Zhe Ming He ◽  
You Xin Luo ◽  
Bin Zeng
Keyword(s):  
Deductive Reasoning ◽  
Least Square Method ◽  
Least Square ◽  
Grey Model ◽  
Dispersion Index ◽  
Index Function ◽  
Proposed Model ◽  
Modeling Accuracy ◽  
Application Fields ◽  
Formula Computing

To improve the modeling accuracy of grey model and broaden its application fields, a non-homogeneous index grey model (termed NIGM(1,1,k)) was built, which is based on the non-homogeneous dispersion index function and the formula computing the parameters of grey model NIGM(1,1,k) was proposed through the least square method. The function of the time response sequence of the proposed grey model was solved by taking differential equations as a deductive reasoning tool. The proposed grey NIGM(1,1,k) model has the characteristic of high precision as well as high adaptability. Examples validate the practicability and reliability of the proposed model.

Prediction of Comprehensive Thermal Error of a Preloaded Ball Screw on a Gantry Milling Machine

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Kuo Liu ◽  
Haibo Liu ◽  
Te Li ◽  
Yongqing Wang ◽  
Mingjia Sun ◽  
...  
Keyword(s):  
Thermal Field ◽  
Thermal Characteristics ◽  
Thermal Error ◽  
Least Square Method ◽  
High Accuracy ◽  
Least Square ◽  
Ball Screw ◽  
Milling Machine ◽  
Thermal Fields ◽  
Proposed Model

The conception of the comprehensive thermal error of servo axes is given. Thermal characteristics of a preloaded ball screw on a gantry milling machine is investigated, and the error and temperature data are obtained. The comprehensive thermal error is divided into two parts: thermal expansion error ((TEE) in the stroke range) and thermal drift error ((TDE) of origin). The thermal mechanism and thermal error variation of preloaded ball screw are expounded. Based on the generation, conduction, and convection theory of heat, the thermal field models of screw caused by friction of screw-nut pairs and bearing blocks are derived. The prediction for TEE is presented based on thermal fields of multiheat sources. Besides, the factors influencing TDE are analyzed, and the model of TDE is established based on the least square method. The predicted thermal field of the screw is analyzed. The simulation and experimental results indicate that high accuracy stability can be obtained using the proposed model. Moreover, high accuracy stability can still be achieved even if the moving state of servo axis changes randomly, the screw is preloaded, and the thermal deformation process is complex. Strong robustness of the model is verified.

scholarly journals Calculation and realization of new method grey residual error correction model

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254154
Author(s):  
Lifang Xiao ◽  
Xiangyang Chen ◽  
Hao Wang
Keyword(s):  
Prediction Model ◽  
Least Square Method ◽  
Residual Error ◽  
Least Square ◽  
Grey Model ◽  
Grey Prediction ◽  
Grey Prediction Model ◽  
True Value ◽  
Prediction Function ◽  
Fitting Method

Aiming at the problem of prediction accuracy of stochastic volatility series, this paper proposes a method to optimize the grey model(GM(1,1)) from the perspective of residual error. In this study, a new fitting method is firstly used, which combines the wavelet function basis and the least square method to fit the residual data of the true value and the predicted value of the grey model(GM(1,1)). The residual prediction function is constructed by using the fitting method. Then, the prediction function of the grey model(GM(1,1)) is modified by the residual prediction function. Finally, an example of the wavelet residual-corrected grey prediction model (WGM) is obtained. The test results show that the fitting accuracy of the wavelet residual-corrected grey prediction model has irreplaceable advantages.

Thermal Error Robust Modeling for High-Speed Motorized Spindle

2012 ◽  
Vol 466-467 ◽  
pp. 961-965 ◽  
Author(s):  
Chun Li Lei ◽  
Zhi Yuan Rui ◽  
Jun Liu ◽  
Li Na Ren
Keyword(s):  
High Speed ◽  
Thermal Error ◽  
Least Square Method ◽  
Information Criterion ◽  
Least Square ◽  
Proposed Model ◽  
Nc Machine ◽  
Input Variables ◽  
Thermal Error Model ◽  
Multivariate Autoregressive

To improve the manufacturing accuracy of NC machine tool, the thermal error model based on multivariate autoregressive method for a motorized high speed spindle is developed. The proposed model takes into account influences of the previous temperature rise and thermal deformation (input variables) on the thermal error (output variables). The linear trends of observed series are eliminated by the first difference. The order of multivariate autoregressive (MVAR) model is selected by using Akaike information criterion. The coefficients of the MVAR model are determined by the least square method. The established MVAR model is then used to forecast the thermal error and the experimental results have shown the validity and robustness of this model.

Predicting Model of Container Throughput of Fujian Province Based on Grey Model

2013 ◽  
Vol 401-403 ◽  
pp. 2179-2182
Author(s):  
Fu Xing Li ◽  
Qiao Jing Liu ◽  
Cai Ping Chen
Keyword(s):  
Decision Making ◽  
Development Strategy ◽  
Least Square Method ◽  
Least Square ◽  
Grey Model ◽  
Important Work ◽  
Fujian Province ◽  
Predicting Model ◽  
Port Development

Port container throughput forecast is an important work for wharf project which is an important part of the port development strategy. In this paper, we introduce the optimized grey model and least square method of grey model. Furthermore, we make a forecast for the container throughput by using least square method of grey model and the result can offer the decision-making bases for relevant department.

scholarly journals Forming a Hierarchical Choquet Integral with a GA-Based Heuristic Least Square Method

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1155
Author(s):  
Chen ◽  
Huang
Keyword(s):  
Choquet Integral ◽  
Least Square Method ◽  
Least Square ◽  
Integral Model ◽  
Fuzzy Measures ◽  
Proposed Model ◽  
Choquet Integrals ◽  
The Mean ◽  
Input Variables ◽  
Least Mean Squares Algorithm

: Identifying the fuzzy measures of the Choquet integral model is an important component in resolving complicated multi-criteria decision-making (MCDM) problems. Previous papers solved the above problem by using various mathematical programming models and regression-based methods. However, when considering complicated MCDM problems (e.g., 10 criteria), the presence of too many parameters might result in unavailable or inconsistent solutions. While k-additive or p-symmetric measures are provided to reduce the number of fuzzy measures, they cannot prevent the problem of identifying the fuzzy measures in a high-dimension situation. Therefore, Sugeno and his colleagues proposed a hierarchical Choquet integral model to overcome the problem, but it required the partition information of the criteria, which usually cannot be obtained in practice. In this paper, we proposed a GA-based heuristic least mean-squares algorithm (HLMS) to construct the hierarchical Choquet integral and overcame the above problems. The genetic algorithm (GA) was used here to determine the input variables of the sub-Choquet integrals automatically, according to the objective of the mean square error (MSE), and calculated the fuzzy measures with the HLMS. Then, we summed these sub-Choquet integrals into the final Choquet integral for the purpose of regression or classification. In addition, we tested our method with four datasets and compared these results with the conventional Choquet integral, logit model, and neural network. On the basis of the results, the proposed model was competitive with respect to other models.

Complementary Use of Partial Least-Squares and Artificial Neural Networks for the Annual Electricity Consumption Forecast

2012 ◽  
Vol 512-515 ◽  
pp. 1113-1116 ◽  
Author(s):  
Hui Feng Jiang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Electricity Consumption ◽  
Least Square Method ◽  
Partial Least Square ◽  
Least Square ◽  
Factors Affecting ◽  
The Neural Network ◽  
Proposed Model ◽  
Partial Least Square Method

A model for predicting annual electricity consumption based on the combination of neural network and partial least square method was proposed. The factors affecting the annual electricity consumption are analyzed by means of partial least square method to extract the most important components so that not only the problem of multi-correlation among variables can be solves but also the amount of input dimensions of the neural network can be reduced. Besides, the application of neural network helps to solve the problem of non-linearity of the model. The application example shows that the proposed model has high precision.

scholarly journals A New Information Priority Accumulated Grey Model with Hyperbolic Sinusoidal Term and its Application

2021 ◽  
Vol 1 (2) ◽  
pp. 5-19
Author(s):  
Xue Tian ◽  
Wenqing Wu ◽  
Xin Ma ◽  
Peng Zhang
Keyword(s):  
Natural Gas ◽  
Fossil Fuels ◽  
Optimal Parameter ◽  
Estimation Method ◽  
Least Square ◽  
Grey Model ◽  
Grey Forecasting ◽  
New Information ◽  
Proposed Model ◽  
Whale Optimization

Compared to fossil fuels, natural gas is cleaner energy, which has developed rapidly in recent years. Studying the urban supply of natural gas has implications for the development of natural gas. In this paper, the new information priority accumulation method is integrated into the grey forecasting model with the hyperbolic sinusoidal driving term, and then the new grey model is used to predict the urban natural gas supply. The system's linear parameters are calculated by the least square estimation method, and the optimal parameter of the new information accumulated priority is determined by the Whale Optimization Algorithm. Finally, the supply of urban gas is forecasted using the proposed model, and comparative analyses with the four other forecasting models are presented.  

scholarly journals Influence of Operating Parameters on Running-in Wear of EN-31 Steel

2016 ◽  
Vol 13 (1) ◽  
pp. 1-2
Author(s):  
M. Hanief ◽  
M. F. Wani
Keyword(s):  
Surface Roughness ◽  
Wear Rate ◽  
Least Square Method ◽  
Least Square ◽  
Coefficient Of Determination ◽  
Percentage Error ◽  
Model Parameters ◽  
Operating Parameters ◽  
Proposed Model ◽  
En 31

Abstract In this paper, effect of operating parameters (temperature, surface roughness and load) was investigated to determine the influence of each parameter on the wear rate. A mathematical model was developed to establish a functional relationship between the running-in wear rate and the operating parameters. The proposed model being non-linear, it was linearized by logarithmic transformation and the optimal values of model parameters were obtained by least square method. It was found that the surface roughness has significant effect on wear rate followed by load and temperature. The adequacy of the model was estimated by statistical methods (coefficient of determination (R2) and mean absolute percentage error (MAPE)) .

A Study of Power Spectral Density Models of Earthquake Ground Motion

2011 ◽  
Vol 90-93 ◽  
pp. 1503-1510
Author(s):  
Fu Jun Liu ◽  
Yu Hua Zhu ◽  
Xiao Hui Ma
Keyword(s):  
Random Process ◽  
Ground Motion ◽  
Process Model ◽  
Least Square Method ◽  
Least Square ◽  
Process Models ◽  
Earthquake Ground Motion ◽  
Power Spectral ◽  
Proposed Model ◽  
Power Spectral Densities

In this paper, a modified random process model of earthquake ground motion based on the model proposed by JinPing Ou is presented. The parameters in the model except the factor S0 are determined by using the least square method and the power spectral densities of 361 earthquake records. Then the method for determining the parameter S0 is proposed. The good performance of the proposed model in this paper in modeling the earthquake ground motion on firm ground is demonstrated by comparing it with other random process models.

Automatic Identification and Optimization Algorithm of Existing Railway Planar Feature Points

2013 ◽  
Vol 779-780 ◽  
pp. 894-898
Author(s):  
Wei Liu ◽  
Hao Pu ◽  
Wei Li ◽  
Hai Feng Zhao
Keyword(s):  
Optimization Algorithm ◽  
Least Square Method ◽  
Least Square ◽  
Automatic Identification ◽  
Engineering Practice ◽  
Feature Points ◽  
Proposed Model ◽  
Acceleration Method ◽  
Planar Feature ◽  
Identification Model

In order to achieve the reconstruction of existing horizontal railway alignments, automatic identification model and optimization algorithm for existing railway planar feature points are proposed. Firstly total least square method of constraint adjustment quantity is proposed, based on which, automatic identification model is built. Then an evaluation function with the radius of circular curve and the lengths of two transition curves as parameters is presented. Based on the direction acceleration method, a reconstruction optimization algorithm is proposed to optimize this ternary implicit function. The proposed model and algorithm can realize the automatic fitting of measuring points and the optimal localization of planar feature points. Example shows that the reconstruction result is considerably superior to the traditional method and is feasible for the engineering practice.

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