Chaos Edge Recognition And Application Based On Permutation Entropy

Permutation entropy is an effective index which can be used to describe the dynamic complexity of a time series,and it can effectively enlarge the small changes of a sequence.In this paper,a new chaotic edge recognition method named moving cut data-permutation entropy(MC-PE)is proposed,and the effectiveness of this method and the other three permutation entropy methods is analyzed and compared.Then the influence factors of MC-PE method are discussed.Finally,the weighted permutation entropy is applied to the data of metallogenic element content sequence to provide a new idea to discuss the relationship between the complexity of metallogenic element content sequence and mineralization grade.The main research contents are as follows:(1)The ideal time series generated by Logistic equation is used to test the effectiveness of four sequence edge recognition methods base on permutation entropy,which are compared with the traditional dynamic state recognition methods.M-PE,M-WPE and MC-PE can effectively identify two edge points of the ideal time series.MC-WPE cannot recognize the edge points of the sequence.The two traditional dynamic state recognition methods,sliding t test and Mann-Kendall,only recognize one edge point.The first three methods base on permutation entropy are superior to the sliding t test and Mann-Kendall in edge recognition of sequences.(2)Through comparative analysis of the effectiveness results,it is found that the rising range of PE(m)value obtained by M-WPE method is steeper than that obtained by M-PE method,which conforms to the process of sliding data and has a better discrimination.However,the M-PE method does not reach the maximum value within the rising range,and the M-WPE method is superior to the M-PE method.On the other hand,M-PE depends on the size of the sliding window method,the result has an ascending mutation interval similar in size to the sliding window,so the edge point of the M-PE method point position error is larger.The position of edge points obtained by MC-PE method can be accurate within the W range of the sliding removal window,and this method is almost does not depend on the sliding removal window,which is obviously superior to the M-PE method.(3)The chaotic time series generated by Lorenz equation and random numbers are constructed,and the influence of data sample size and noise on MC-PE method is analyzed.The results show that MC-PE method is less dependent on the sample size of time series and has stronger anti-interference ability against peak noise and white Gaussian noise.(4)By using weighted permutation entropy algorithm,the complexity characteristics of Au element grade sequences in the gold mine of Dayingezhuang and Cu element grade sequences in the copper mine of Jiama are analyzed,and the WPE values obtained are correlated with different mineralization grades.The entropy values are as follows: middle mineralization >strong mineralization > weak mineralization > null mineralization,which shows that weighted permutation entropy is an effective tabulation to identify the mineralization intensity.