Papers by Keyword: Background Value

Paper TitlePage

Authors: Zhong Hu Yuan, Feng Guo, Xiao Xuan Qi
Abstract: After analyzing background value error of the traditional MGM(l,m) model, the paper used the functions with non-homogeneous exponential law to fit the accumulated sequences for every variable, and get the optimal formula of background value of MGM(l,m) model, which was used for establishing the model. And the optimization effect is verified by examples. The result shows that the proposed method can significantly improve the prediction accuracy of the traditional MGM(l,m) model, and the effectiveness of the proposed method is shown.
1513
Authors: Yao Chen
Abstract: On the base of the basic differential equation, a new GM (1,1) model applying to non-homogenous index series was established by optimizing the background of original differential equation. Meanwhile, solution algorithm and efficiency of the optimization model was presented and verified in the paper respectively. The results showed that this nonlinear discrete gray prediction model significantly improves the simulation accuracy and is suitable for the non-homogeneous high-growth series. Therefore, our research has certain theory significance and the practical application value for simulation of grey model.
2543
Authors: De Gang Liao, You Xin Luo
Abstract: The accuracy of the traditional grey model is not high for the monotonic decreasing data. The paper uses the opposite-direction accumulated method and makes full use of new information combined with optimization of the background values. It induces the formula of the parameters in the model and establishes the grey new information GOM(1,1) model in which it is based on the opposite-direction accumulated operation and optimization of the background values. It is a new method of the grey model. The examples show it is with higher accuracy than that of non-new information model.
33
Authors: Yue Hua Cai, Wei Yue Xiao, Bin Zeng
Abstract: As the monotonic decreasing data the traditional grey model is characteristic with low accuracy, using reciprocal generating operation, making full use of the new information, optimizing the background values, the formula of the parameters was induced and the grey new information GRM(1,1) model was established based on reciprocal accumulating and background value optimization. It provides a new way for the grey model. The examples show the new information model has high accuracy than the non-new information model.
188
Authors: Yue Hua Cai, Wu Jun Zeng
Abstract: Considering the problems in determining the initial value of the non-equidistant new information GM(1,1) model, the author analyzed its modeling mechanism to find out the causes of the problem. A new method for initiating value for the model is proposed to minimize the quadratic sum of the fitting error, and a initiating formula is deduced. The model with the proposed formula enjoys a high precision and adaptability, and its practicability and reliability have been validated by examples.
833
Authors: You Xin Luo
Abstract: Based on the exponential trait of grey model and the definition of integral, the reconstruction method of GM(1,1) model’s background value of non-equal distance sequence was put forward and a kind of non-equidistant optimum grey model GM(1,1) to line-drawing data processing in computer aided design was proposed. The mean relative error is taken as the optimum objective function. The power mutation particle swarm optimization program PMPSO1.0 was compiled with Matlab 7.6 software to make optimization. Two examples were given, their results were compared with the results based other Grey models, respectively. The method can be used for model establishing on equal interval, as well as on non-interval. Moreover, GM(1,1) model’s fitting precision and prediction is advanced and the scope of application is enlarged. The model is simple and practical, and has a generalizing value in the field of CAD.
1561
Authors: You Xin Luo, Wei Yue Xiao
Abstract: The non-equal-interval direct optimum Verhulst GM(1,1) model was built which extended equal interval to non-equal-interval and suited for general data modeling and estimating parameters of direct Verhulst GM(1,1)by optimizing the background value and modified x(n) be taken as initial value. The new model need not pre-process the primitive data, accumulated generating operation (AGO) and inverse accumulated generating operation (IAGO). It was not only suited for equal interval data modeling, but also for non-equal interval data modeling. The new model chooses the modified nth component of X(0) as the starting conditions of the grey differential model. As the new information is fully used, the accuracy of fitting is higher. The example showed that the new model was simple and practical. The new model was worth expanding and applying in test data processing or test on-line monitoring and social science and engineering science.
1555
Authors: You Xin Luo, Bin Zeng
Abstract: Based on grey system, a new kind of new information non-equidistant optimum grey model GM(1,1) to line-drawing data processing in computer aided design was proposed in which the response function is based on new information x(tn) . The objective function is built to make the fitting mean relative error least and the program was compiled with bacterial foraging algorithm (BFA) combined with particle swarm optimization (PSO) algorithm to optimize the background value and modify the initial value x(tn) of response function. The method of precision inspection was introduced. The programming was authorized with MATLAB7.6 language. Two examples were given, their results were compared with the results based other Grey models, respectively. The method can be used for model establishing on equal interval, as well as on non-interval. Moreover, GM(1,1) model’s fitting precision and prediction is advanced and the scope of application is enlarged. The model is simple and practical, and has a generalizing value in the field of CAD.
349
Authors: You Xin Luo, De Gang Liao
Abstract: Based on the exponential trait of grey model and the definition of integral, the reconstruction method of GM(1,1) model’s background value function of non-equal distance sequence was put forward and a kind of non-equidistant optimum grey model GM(1,1) to line-drawing data processing in computer aided design was proposed. The new model chooses the modified first component of X(0) obtained by optimizing as the starting conditions of the grey differential model and the parameter of the background value function also obtained by optimizing with chaos immune particle swarm optimization algorithm (CIPSO) to make the fitting mean relative error least. The method of precision inspection was introduced. Then, the programming was authorized with MATLAB7.6 language. An example was given, the results were compared with the results based other Grey models, respectively. The method can be used for model establishing on equal interval, as well as on non-interval. Moreover, GM(1,1) model’s fitting precision and prediction is advanced and the scope of application is enlarged. The model is simple and practical, and has a generalizing value in the field of CAD.
355
Authors: You Xin Luo
Abstract: Based on grey system theory, a novel kind of non-equidistant optimum grey model GM(1,1) with optimizing modified the nth component taken as initial value of response function of grey differential equation and reconstructing the background value function to obtain the approximately expressions of parameters of the background value function was proposed, the method of precision inspection was introduced. The example was given. The method can be used for model establishing on equal interval, as well as on non-interval. Moreover, GM(1,1) model’s fitting precision and prediction is advanced and the scope of application is enlarged. The model is simple and practical, and has a generalizing value in metal cutting data process.
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