Time-Series Chaos Quantification via Subdivision Entropy
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Solution Overview
Problem
Conventional methods for quantifying chaos in time-series data, such as the Lyapunov exponent, are inefficient for real-time processing and require large amounts of data, making them impractical for high accuracy and speed.
Innovation Solution
A time-series data evaluation device that calculates a high-precision chaotic scale function by dividing intervals into sub-divisions, using both outer and inner measure entropies, and correcting entropies with actual data existence rates to achieve faster and more accurate chaos quantification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Lyapunov exponent method is used to quantify chaos in time-series data, then measurement precision is improved, but productivity deteriorates due to requiring large amounts of data and complicated procedures
Solution Approach 1:
The patent segments the calculation process into distinct components: probability calculation unit computes p(i) values, division entropy calculation unit computes entropy for each divided interval, and summation calculation unit aggregates results. This segmentation allows each unit to operate independently and efficiently, improving processing speed while maintaining accuracy.
Solution Approach 2:
The patent performs preliminary actions by pre-defining the divided intervals Ai and their boundaries before processing the time-series data. The probability calculation unit pre-computes p(i) values for each interval, which are then reused in the entropy calculation. This preliminary preparation reduces computational complexity during real-time processing.
2Measurement precision
If the number of divisions M is increased to improve accuracy of chaos measurement, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent divides the interval I into M equal parts Ai, and each Ai is further divided into Q equal parts Bi. This hierarchical segmentation allows the system to manage complexity by breaking down the overall calculation into smaller, more manageable sub-calculations that can be performed independently and then aggregated.
Solution Approach 2:
The patent introduces the parameter Q (number of subdivisions per divided interval) as an additional degree of freedom. By adjusting Q independently of M, the system can optimize the balance between accuracy and computational complexity. The probability calculation and entropy calculation are performed with respect to these parameters, allowing flexible control over measurement precision versus device complexity.
Data Source
AI summary
To achieve high accuracy and high processing speed, a time series data evaluation device is equipped with a probability calculation unit 201 that calculates the probability p(i) that ξt∈Ai; a division entropy calculation unit 202 that calculates division entropy using the measure in the subdivision interval by setting a subdivision section Bi (i=1, 2, . . . , M×Q) by further dividing the divided section Ai (i=1, 2, . . . , M) into Q equal parts; and a summation calculation unit 203 that performs a summation calculation of the divided interval range regarding the multiplication of the probability p(i) and the division entropy.