Fractional Cumulative Residual Mean Relative Entropy and Its Application in an Aeroengine Gas Path System

Abstract

Mean relative entropy has a wide range of applications in measuring information differences. However, relative entropy is difficult to approximate from empirical distribution entropy. Therefore, we replace the probability density function in the mean relative entropy with the residual distribution function and add the form of fractional-order calculation, named fractional-order cumulative residual mean relative entropy. The fractional cumulative residual average relative entropy can be approximated by the empirical entropy of the sample data, and the fractional calculation form is beneficial to revealing the details and information of the underlying system. Some statistical properties of the new entropy are given. Empirical fractional cumulative residual mean relative entropy is shown to converge to the theoretical value. Finally, fractional cumulative residual mean relative entropy is used to analyze aeroengine gas path data.