The Optimization of Grey Derivative and Parameters Based on Unbiased Verhulst Model

For the error analysis of grey Verhulst model, the concept of optimizing the grey derivative and the parameters at the same time is proposed to develop a new prediction model. Firstly, let k be a continuous value directly and take the derivative of the first order accumulated function. After that the original sequence of grey differential equation must be replaced by the derivative function obtained in the previous step, thus the optimal grey differential equation which matches with whitenization differential equation and the parameter α can be got. Then we can find the parsing expressions of parameter α and β through the least square method used in target function to archive the dual optimization of the parameters and the translational constant. Combine with the above two steps, a new grey Verhulst model can be obtained. The result shows that the model is simulated and predicted with complete coincidence to meet Logistic function curve. Finally, experiments show the validity and rationality of this method, they also illustrate the correctness of the conclusion.

並列關鍵字

Grey Verhulst model ； Grey derivative ； Solving parameters ； Least square method ； Logistic function

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