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The Multi-scale Entropy Feature of the Chaotic Leader in the Cloud-ground Lightning
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摘要: 针对不规则脉冲簇难以判别问题，将多尺度熵应用于不规则先导分析中，探讨闪电信号不规则脉冲分析应用中多尺度熵关键参量的选择方法。在此基础上，将不规则先导与直窜先导及梯级先导闪电信号的多尺度熵进行比较。统计分析表明：不规则先导和直窜先导熵值随尺度先增加后趋于平稳，但熵值有很大差异；梯级先导熵值随尺度变化不明显，整体呈增长趋势，与不规则先导的熵值在大于3的尺度上也有所差异，因此当尺度大于3时可将熵值大于1.5的先导归类为不规则先导，熵值小于1.5的先导归类为梯级先导或直窜先导。不规则先导的特征熵平均值为2.0~2.1，最大值范围为2.6~2.8，最小值范围为1.51~1.59。Abstract: The chaotic leader is different from stepped leader and dart leader with distinctive features. It has many narrow pulses, causing strong high-frequency radiation. The pulse occurs right at the position of preceding stepped leader and dart leader, but its structure, width and interval all show significant irregularities. The chaotic leader is a new and special one with no exact definition of its pulse characterization so far.Multi-scale entropy is applied to the analysis of chaotic leader, and some key parameters applying in the lightning irregular pulse signal analysis are given after detailed analysis. Dart leader signal, stepped leader signal and the chaotic leader signal are analyzed with the given method and the results are compared, and case studies of the three-leader multi-scale entropy features prove the feasibility of this method. It's found out through statistical analysis that 3 leaders are different in entropy value especially when the scale is greater than 3, and thus they can be clearly distinguished by entropy values. Entropy value greater than 1.5 may indicate chaotic leader, and entropy value less than 1.5 is classified as stepped leader or dart leader. Furthermore chaotic leader and dart leader entropy value both increase with scales first and then stabilize but stepped leader entropy value doesn't change much. Characteristic entropy values for the chaotic leader are given: The average is about 2.0—2.1, the maximum is 2.6—2.8, and the minimum is 1.51—1.59. Based on the analysis of multi-scale entropy characteristics of 3 leaders, the physical meaning of the irregularity is also discussed. The irregularity degree of chaotic electric field pulse can be reflected by the entropy value: The greater the entropy value is, the greater the degree of irregularity. The characteristics of the electric field pulse in the waveform is directly related with the development of the discharge process. For the dart leader or stepped leader, the smaller entropy value illustrates that its discharge is regular. The chaotic leader in small scale with larger entropy directly demonstrates that in this range scale its discharge, polarity and intensity are irregular. It shows the electric discontinuity somewhere in the leader development channel during a certain period before the occurrence of subsequent stroke.
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Key words:
- sample entropy;
- multi-scale entropy;
- dart leader;
- stepped leader;
- chaotic leader
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图 2 不同尺度随机信号和正弦信号的熵
Fig. 2 The entropy of random signal and sinusoidal signal with different scales
图 3 直窜先导 (a)、梯级先导 (b) 和不规则先导 (c) 快电场变化波形
Fig. 3 The fast electric field change waveforms of dart leader (a), stepped leader (b) and chaotic leader (c)
图 4 梯级先导与不规则先导多尺度熵比较
Fig. 4 Multi-scale entropy comparison between stepped leader and the chaotic leader
图 5 直窜先导与梯级先导及不规则先导的多尺度熵
Fig. 5 Multi-scale entropy statistical analysis and comparison between dart leader, stepped leader and the chaotic leader
表 1 不规则先导的ESP(m，0.15DS，N)
Table 1 ESP(m, 0.15DS, N) of the chaotic leader
m 样本1 样本2 样本3 N=500 N=3000 N=5000 变化率/% N=500 N=3000 N=5000 变化率/% N=500 N=3000 N=5000 变化率/% 1 0.99 0.99 0.90 8 1.18 1.40 1.23 4 0.77 0.70 0.69 10 2 0.82 0.82 0.77 5 0.89 1.06 0.90 1 0.61 0.59 0.58 6 3 0.81 0.80 0.73 9 0.82 0.98 0.80 2 0.60 0.53 0.52 14 4 0.75 0.77 0.70 7 0.85 0.91 0.74 13 0.52 0.50 0.48 7 注：变化率指N=5000时相对于N=500时的样本熵的变化。下同。 
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表 2 不规则先导的ESP(2，r，N)
Table 2 ESP(2, r, N) of the chaotic leader
r 样本1 样本2 样本3 N=500 N=3000 N=5000 变化率/% N=500 N=3000 N=5000 变化率/% N=500 N=3000 N=5000 变化率/% 0.1DS 1.06 1.12 1.07 2 1.17 1.36 1.17 0.1 0.74 0.74 0.74 0.4 0.15DS 0.82 0.83 0.78 5 0.89 1.06 0.91 1 0.62 0.59 0.58 6 0.2DS 0.67 0.66 0.60 10 0.72 0.88 0.75 4 0.53 0.49 0.47 11 0.25DS 0.55 0.55 0.49 12 0.62 0.76 0.64 5 0.46 0.41 0.40 13
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表 3 直窜先导、梯级先导与不规则先导的样本熵特征
Table 3 Entropy features of dart leader stepped leader and the chaotic leader
尺度 直窜先导 梯级先导 不规则先导 平均值 最大值 最小值 平均值 最大值 最小值 平均值 最大值 最小值 1 0.1202 0.5203 0.0072 0.7060 1.2214 0.4309 1.2021 2.3356 0.7126 2 0.1985 0.7521 0.0128 0.7498 1.2929 0.3849 1.7055 2.3379 1.1297 3 0.2599 0.7803 0.0172 0.7616 1.2814 0.3734 1.9150 2.4108 1.3624 4 0.3145 0.8307 0.0221 0.7875 1.2425 0.4075 2.0139 2.6005 1.5211 5 0.3557 0.8551 0.0268 0.8111 1.2231 0.4215 2.0532 2.5217 1.5161 6 0.4122 0.8711 0.0311 0.8549 1.3519 0.4513 2.0956 2.8274 1.5393 7 0.4440 0.8821 0.0354 0.8822 1.3135 0.4853 2.0894 2.5642 1.5600 8 0.4732 0.8930 0.0394 0.9156 1.4629 0.4929 2.0826 2.6472 1.5700 9 0.5027 0.9218 0.0432 0.9645 1.4789 0.5245 2.0175 2.6232 1.5284 10 0.5138 0.9852 0.0463 0.9620 1.4390 0.5381 2.0728 2.8824 1.5192
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