Novel Non-Equidistant Optimum GM(1,1) and its Application to 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 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.