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.

Orbital instability and prediction of a Bunsen flame tip motion with burner rotation

“…TPM, based on the algorithm proposed by Fujimoto and Iokibe [23], is used in a way similar to its use in Refs. [24,25], as follows:…”

“…4. As was the case in previous studies in which Γ was determined [23], the asymptotic value of the slope as shown in Fig. 3 is used to determine Γ .…”

Estado del arte en detección de fugas y propuesta de máquina de soporte vectorial para el análisis de estanqueidad en envases

“…Con base en estudios anteriores (Takens, 1981) se puede asumir que el ruido de fondo está conformado por elementos no determinísticos, mientras que las señales producidas por la fuga del gas a alta presión contienen componentes determinísticas. Con el fin de discriminar entre los dos tipos de señales adquiridas, se usa el método TPM (por las siglas de trajectory parallel measure) (Fujimoto & Lokibe, 1999), con el cual se puede determinar la presencia de fuga comparando con un valor umbral fijado.…”