New Non-Equidistant Optimum GM(1,1) of Line-Drawing Data Processing in Computer Aided Design

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.

Novel non-equidistant GM(1,1) model with modified x(t<inf>n</inf>) taken as the initial value for line-drawing data processing

“…[4], their corresponding mean relative error are 2.30607% and 2.31258%. If we build grey GM (1,N) model of line-drawing data processing [9] , the corresponding mean relative error is 0.2629%, but the calculating is very complex.…”

“…[7] and [8] is not high, and then, it is generally used for the qualitative analysis and unsuitable for fitting or prediction. Based on the requirement of GM(1,N) with many variables and high accuracy in the engineering, the optimum GM(1,N) model was built by optimizing the grey derivative background value [9] , and improving distinguished method of parameter. It overcomes the shortcoming of present GM (1, N) model, and expands the use scope of GM (1,N) model, resulting in higher precision and simplification.…”

The new non-equidistant optimum GM(1,1) of line-drawing data processing in computer aided design

“…(3) To calculate the total related degree of the model , the precision of the model is "bad" [9] .. Mean relative error is 0.92314 %.…”

“…Based on the requirement of GM(1,N) with many variables and high accuracy in the engineering, in Ref . [9], the optimum GM(1,N) model was built by optimizing the grey derivative background value, and improving distinguished method of parameter. It overcomes the shortcoming of present GM (1, N) model, and expands the use scope of GM (1,N) model, resulting in higher precision and simplification.…”

The Non-equidistant Optimum GM(1,1) with Modified nth Component be Taken as Initial Value and Its Application to Metal Cutting

“…Based on the requirement of GM(1,N) with many variables and high accuracy in the engineering, in Ref. [10], the optimum GM(1,N) model was built by optimizing the grey derivative background value, and improving distinguished method of parameter. It overcomes the shortcoming of present GM (1,N) model, and expands the use scope of GM (1,N) model, resulting in higher precision and simplification.…”