A Novel Modeling Method of Grey Verhulst Model Based on Optimizing Initial Condition

Abstract

A novel method of optimizing the grey Verhulst model is proposed in this study to improve prediction precision. The weighted average of each component of the first-order accumulative generation operator (1-AGO) sequence on the original sequence is taken as initial value of the initial condition in a time response function. According to the principle of new information priority, this paper takes the respective components of unitization sequence of time ordinal sequence corresponding to the 1-AGO sequence as the weighted coefficients. The time parameter of the initial condition in a time response function is solved by making the average of the absolute values of relative errors minimum between the 1-AGO simulation sequence and 1-AGO sequence. Thereby, the grey Verhulst model based on optimizing the initial condition is built. Finally, the proposed optimal model and two other grey Verhulst models are used to simulate and predict the recycling rate of industrial water. The simulating effect of these three models is examined and the predicting precision is compared and analyzed. The result indicates that all of the three models are qualified residual models and the predicting effect of the optimized model proposed in this study is obviously better than those of the other two models.