Abstract
When the chaotic characteristics of manufacturing quality level are studied, it is not practical to use chaotic methods because of the low speed of calculating the correlation integral. The original algorithm used to calculate the correlation integral is studied after a computer hardware upgrade. The result is that calculation of the correlation integral can be sped up only by improving the algorithm. This is accomplished by changing the original algorithm in which a single distance threshold-related correlation integral is obtained from one traversal of all distances between different vectors to a high-efficiency algorithm in which all of the distance threshold-related correlation integrals are obtained from one traversal of all of the distances between different vectors. For a time series with 3000 data points, this high-efficiency algorithm offers a 3.7-fold increase in speed over the original algorithm. Further study of the high-efficiency algorithm leads to the development of a super-high-efficiency algorithm, which is accomplished by changing the original and high-efficiency algorithms, in which the add-one operation of the Heaviside function is executed n times, such that the execution of the add-one operation occurs only once. The super-high-efficiency algorithm results in increases in the calculation speed by up to 109 times compared with the high-efficiency algorithm and by approximately 404 times compared with the original algorithm. The calculation speed of the super-high-efficiency algorithm is suitable for practical use with the chaotic method.
Highlights
The chaotic characteristics of manufacturing quality level using data containing 588 daily product defect frac-How to cite this paper: Gong, Z.P. (2015) A Super-High-Efficiency Algorithm for the Calculation of the Correlation Integral
The original, high-efficiency, and super-high-efficiency algorithms served as the working algorithms with the time series data coming from the Logistic, Hénon, Lorenz, and HZ systems
Due to restrictions imposed by the 2 Gb of memory, the calculation experiment could only be performed for 1 to 13 dimensional embedded time series constructed from the 3000 data points of the Logistic, Hénon, and Lorenz systems
Summary
The chaotic characteristics of manufacturing quality level using data containing 588 daily product defect frac-How to cite this paper: Gong, Z.P. (2015) A Super-High-Efficiency Algorithm for the Calculation of the Correlation Integral. The manufacturing quality level was proven to be chaotic if the correlation dimension was fractional in a study that used the G-P algorithm [4] in the calculation of the correlation dimension. The manufacturing quality level time series was first reconstructed as a multi-dimensional phase space, and the distances between vectors in the reconstructed phase space were calculated under a certain embedded dimension. The correlation dimension was determined by log-log coordinates between the correlation integral and the distance threshold value. The problem with this process was the amount of time wasted in calculating the correlation integral, which was a huge obstacle if research results were to be useful in actual practice. The process for calculating the correlation integral must be improved
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