For the problem of lower precision as well as lower adaptability in non-equidistant GM(1,1) model, applying the new information principle, modeling method of Grey system and accumulated generating operation of reciprocal number, a non-equidistant new information GRM(1,1) model generated by accumulated generating operation of reciprocal number was put forward which was taken the nth component as the initialization. Based on index characteristic of grey model and the definition of integral, the background value in non-equidistant GRM(1,1) was researched and the discrete function with non-homogeneous exponential law was used to fit the accumulated sequence and optimum formula was given. The formula of background value of new information GRM(1,1) model can be used in non-equal interval & equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.

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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.

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.

Monotonically decreasing sequence data for the use of traditional modeling methods to establish the grey model accuracy is not high, grey GM (1,1) model, there is a deviation, the model does not meet the conditions for coordination, generated using the definition of reverse accumulation, full use of system information and unbiased grey GM (1,1) model parameters of the model derived formula, based on reverse incremental build new interest generated by an unbiased model grey GOM (1,1) model for the grey model provides a new method. Data processing examples show that the model's practicality and reliability.