Determinism Measurement in Time Series by Chaotic Approach and Its Applications

Abstract

Frequently irregular-looking time series may have a deterministic cause, which is why it is called deterministic chaos. Even if a time series has a little noise, it is not always easy to recognize noise by looking at data. Fast Fourier transform (FFT) is used to extract characteristic frequencies. A chaotic time series consists of an infinite number of frequency elements, producing a broad continuous power spectrum but has few distinguishable characteristics. We propose a way, called trajectory parallel measurement (TPM), based on the chaotic approach to distinguish determinism and randomness in a time series, and apply this to a chaotic time series with random noise, summarizing the results of practical application in diagnosing automatic transmission.