Grey Spline Absolute Correlation Model With Noisy Data

The grey incidence model is a quantitative tool for measuring the relationship among system factors.Traditionally,the grey incidence model is directly established on the observed values,neglecting the disturbance of the noise data,hence the derived grey incidence rank may not correctly reflect the actual relationship among system factors.In fact,the observed data consists of both the true value and some noise that can not be avoided in the data collection process.With aim of attenuating the noise data's influence on the model,we put forward an absolute degree of grey incidence model based on smoothing noisy data with cubic spline.In the paper,firstly,the image method is used to demonstrate that the polygonal line and natural cubic spline interpolating noise perturbation sequence will increase the concavity and convexity of the sequence locus.Thus,it can be shown that the noise will be transferred to the absolute of grey incidence model and affect the correlation rank derived from the model.Secondly,we construct the truncation basis of cubic spline functions which can weaken the noise,then we derive the spline function to approximate the system's locus,and then we follow the classic method to construct the new model.Some properties are demonstrated.Finally,data with white noise of different levels demonstrates how the model works well with better robustness than the traditional grey incidence model.