Distribution Entropy Of Time Series And Its Application

Distribution entropy is an effective index to describe the dynamic complexity of time series.The algorithm is less dependent on parameters,has high stability and strong operability,and can effectively capture the small changes of time series.In order to further study the dynamic state change of time series,three new algorithms are proposed based on the classical distribution entropy(Dist En),and the effectiveness of three algorithms in chaotic state recognition of time series and the influence of parameters are systematically analyzed.The distribution entropy is further applied to the complexity analysis of ore-forming element grade sequence,which provides a novel idea for exploring the relationship between the complexity of ore-forming element grade sequence and mineralization grade.The main research conclusions are as follows:(1)By combining Dist En with the moving window technique,the moving distribution entropy(M-Dist En),moving cut data-distribution entropy(MC-Dist En)and moving weighted distribution entropy(MW-Dist En)are proposed.The validity of the three new algorithms for chaotic state change recognition is verified by using the chaotic sequence generated by Logistic map and Henon map.(2)The influence of the main parameters of M-Dist En,MC-Dist En and MW-Dist En algorithms on the calculation results is systematically analyzed.The results show that the moving step size has little influence on the results of the three algorithms,and the variation trend of the results of different moving step sizes is almost the same.For different moving window lengths,both M-Dist En and MW-Dist En algorithms have little effect on the results,and the stability of the results is better with the increase of the moving window length.Under different window lengths of moving removal window lengths,the results of MC-Dist En algorithm fluctuate to a certain extent,and the increase of the moving removal window length will make the results fluctuate less.(3)The chaotic state recognition effects of various algorithms are compared and analyzed.The results show that neither the moving t-test algorithm nor the Mann-Kendall algorithm can accurately identify the chaotic state of the sequence and its position of state change,and the recognition effect of chaotic state is not ideal.In the case of a fixed embedding dimension,M-Dist En algorithm has the best state recognition effect on chaotic sequences with small difference,and the recognition effectiveness and stability are better than M-Samp En and M-PE algorithms.Then,MC-Dist En and MW-Dist En algorithms are better for chaotic state recognition with high intensity.(4)The distribution entropy algorithm is used to analyze the complexity characteristics of the distribution structure of Cu grade series in Jiama porphyry copper deposit in Tibet.It is found that the Dist En values of Cu grade series in different drilling holes are different from the mean values of M-Dist En,MW-Dist En and MW-Dist En algorithm,and the distribution entropy decreases with the decrease of mineralization grade.The results show that the complexity of ore-forming element grade is related to the development of ore body,that is,the distribution entropy value can be used as a new effective index for the identification of different mineralization grades,which provides a reference for further quantitative characterization and analysis of the complexity of ore deposits.