Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series

Zhou, Shuang; Wang, Xingyuan; Zhou, Wenjie; Zhang, Chuan

doi:10.1016/j.physa.2021.126563

Cited by 15 publications

(4 citation statements)

References 50 publications

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“…Then, for the determination of the model order, in order to avoid the single limitation of calculation, reduce the complexity and increase the adaptability of the optimization sequence length change, considering that the l-order nonlinear autoregressive model can be equivalent to the phase space reconstruction [19], with the delay time of 1 and the embedding dimension of l + 1, a joint calculation strategy of the model order based on the organic combination of G-P correlation dimension [20] and Akaike information criterion (AIC) is proposed, as shown in Equation (5).…”

Section: Methodsmentioning

confidence: 99%

n-Dimensional Chaotic Time Series Prediction Method

et al. 2022

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Chaotic time series have been involved in many fields of production and life, so their prediction has a very important practical value. However, due to the characteristics of chaotic time series, such as internal randomness, nonlinearity, and long-term unpredictability, most prediction methods cannot achieve high-precision intermediate or long-term predictions. Thus, an intermediate and long-term prediction (ILTP) method for n-dimensional chaotic time series is proposed to solve this problem. Initially, the order of the model is determined by optimizing the preprocessing and constructing the joint calculation strategy, so that the observation sequence can be decomposed and reorganized accurately. Furthermore, the RBF neural network is introduced to construct a multi-step prediction model of future sequences, with a feedback recursion mechanism. Compared with the existing prediction methods, the error of the ILTP method can be reduced by 1–6 orders of magnitude, and the prediction step can be increased by 10–20 steps. The ILTP method can provide reference technology for the application of time series prediction with chaotic characteristics.

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Section: Methodsmentioning

confidence: 99%

n-Dimensional Chaotic Time Series Prediction Method

et al. 2022

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“…This method is simpler and more efficient than the nonlinearity index stated above in terms of computational complexity and costs. Moreover, fractal analysis has been proven to be effective in discovering the complexity of nonlinear dynamical systems in many applications. , …”

Section: Diagnosis Techniquesmentioning

confidence: 99%

“…Moreover, fractal analysis has been proven to be effective in discovering the complexity of nonlinear dynamical systems in many applications. 163,164 The authors later proposed to use the biamplitude ratio analysis as a nonlinearity measure in refs 165 and 166. The biamplitude ratio computed from the bispectrum can indicate the harmonic content relative to the fundamental frequency.…”

Section: Diagnosis Techniquesmentioning

confidence: 99%

Controller Performance Monitoring: A Survey of Problems and a Review of Approaches from a Data-Driven Perspective with a Focus on Oscillations Detection and Diagnosis

Bounoua

Aftab

Omlin

2022

Ind. Eng. Chem. Res.

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Optimal operations of industrial control systems require rigorous monitoring to ensure safety, increase profitability, and minimize plant maintenance downtime. Thus, controller performance monitoring has been actively pursued by the research community, resulting in increased research publications over the past two decades. The availability of large data sets, the so-called big data era, has led impetus to the data-driven domain of controller performance monitoring. In this paper, a comprehensive review of the data-driven research in the CPM domain is presented. To illustrate the rationale behind the research efforts, a succinct explanation of the faults observed in control loops and their influence on overall controller performance is also presented. The paper then provides the publicly available data repositories adopted by most researchers to assess and compare their performance monitoring techniques realistically. Moreover, a review of the most eminent techniques proposed so far concerning both detection and diagnosis phases is presented.

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“…Through the analysis of time series data, it is possible to reveal the underlying patterns and laws in the data, discover the correlation and periodicity between events, and then deeply understand the nature and mechanism of the event itself, providing strong support for research in related disciplines. Specifically, a deep understanding of time trends [ 14 ], periodicity [ 15 , 16 ], correlation [ 17 , 18 ], etc., can be gained and valuable information can be further extracted, such as anomaly detection [ 19 , 20 , 21 ], classification [ 22 , 23 , 24 ], clustering [ 25 , 26 ], etc. These studies require a large amount of time series data for experiments to test the effectiveness and practicality of different algorithms and techniques, optimize the parameters and structure of algorithms, evaluate the performance and accuracy of different techniques, and train machine learning models.…”

Section: Introductionmentioning

confidence: 99%

Survey of Time Series Data Generation in IoT

Hu,

Sun,

et al. 2023

Sensors

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Nowadays, with the rapid growth of the internet of things (IoT), massive amounts of time series data are being generated. Time series data play an important role in scientific and technological research for conducting experiments and studies to obtain solid and convincing results. However, due to privacy restrictions, limited access to time series data is always an obstacle. Moreover, the limited available open source data are often not suitable because of a small quantity and insufficient dimensionality and complexity. Therefore, time series data generation has become an imperative and promising solution. In this paper, we provide an overview of classical and state-of-the-art time series data generation methods in IoT. We classify the time series data generation methods into four major categories: rule-based methods, simulation-model-based methods, traditional machine-learning-based methods, and deep-learning-based methods. For each category, we first illustrate its characteristics and then describe the principles and mechanisms of the methods. Finally, we summarize the challenges and future directions of time series data generation in IoT. The systematic classification and evaluation will be a valuable reference for researchers in the time series data generation field.

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Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series

Cited by 15 publications

References 50 publications

n-Dimensional Chaotic Time Series Prediction Method

n-Dimensional Chaotic Time Series Prediction Method

Controller Performance Monitoring: A Survey of Problems and a Review of Approaches from a Data-Driven Perspective with a Focus on Oscillations Detection and Diagnosis

Survey of Time Series Data Generation in IoT

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