Abstract: Traditional information entropy has certain limitations in analyzing the complexity of time series, as it does nottake into account the sequential relationship among successive elements. To address this issue, this paper pro-poses an improved entropy. First, order entropy is defined to measure the uncertainty of the sequence of succes-sive elements, and joint order entropy and average order entropy are further introduced to study the complex de-pendency between two time series. Then, these entropy -based measurement methods are applied to random se-quences following different distributions and to performance parameter sequences of aircraft engines to verify theeffectiveness of the improved method. The results show that the improved entropy can effectively measure the un-certainty in time series, and the influence of time delay on order entropy and average order entropy is relativelysmall.

Key words: order entropy, complexity analysis, time series, time delay, aircraft engine