Fractional order Sprott chaos synchronisation‐based real‐time extension power quality detection method

Yau, Her‐Terng; Wang, Cheng‐Chi; Hsieh, Chin-Tsung; Wu, Shang-Yi

doi:10.1049/iet-gtd.2015.0500

Cited by 12 publications

(7 citation statements)

References 32 publications

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“…The chaos theory was proposed by the American meteorologist, Edward Norton Lorenz [27]. Chaos phenomena are characteristic of the nonlinear system theory.…”

Section: The Proposed Methodsmentioning

confidence: 99%

Fault diagnosis of power capacitors using a convolutional neural network combined with the chaotic synchronisation method and the empirical mode decomposition method

Sian

Wang

et al. 2021

IET Science Measure & Tech

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This study combined a Convolutional Neural Network (CNN) with the chaos theory and the Empirical Mode Decomposition (EMD) method for the attenuation fault recognition of power capacitors. First, it built six capacitor analysis models, including normal capacitors, failed capacitors, and normal capacitors attenuated by 20-80%. Then a power testing machine was used for an applied voltage test of the capacitor. The EMD method was combined with the chaos synchronisation detection method to chart the discharge signals of the voltage and current that was captured by a high frequency oscilloscope into a 3D chaotic error scatter plot, as the fault diagnosis feature image. Finally, the CNN algorithm was used for the capacitor fault detection. The advantages of the proposed method are that big data are compressed to extract meaningful feature images, the operating state of the power capacitor can be detected effectively, and faults can be diagnosed according to the electrical signal change of the power capacitor. The actual measurement results showed that the accuracy of the proposed method was as high as 97% and has a high efficiency of noise rejection ability, which indicates that the method could be applied to other power-related fields in the future.

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“…The chaos theory was proposed by the American meteorologist, Edward Norton Lorenz [27]. Chaos phenomena are characteristic of the nonlinear system theory.…”

Section: The Proposed Methodsmentioning

confidence: 99%

Fault diagnosis of power capacitors using a convolutional neural network combined with the chaotic synchronisation method and the empirical mode decomposition method

Sian

Wang

et al. 2021

IET Science Measure & Tech

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“…Fractional order theory was not popular in the past. Most systems were expressed in the form of near-integer order system, as shown in Equations (13) and (14).…”

Section: B Fractional Order Differential Equationsmentioning

confidence: 99%

“…In this paper, the comparison is made between chaotic systems including Lorenz [13], Sprott [14] and Chen-Lee [15], [16] systems. Their corresponding master and slave systems are shown in Equations (3) to (8):…”

Section: Introduction To Related Theories a Chaos Theorymentioning

confidence: 99%

Machine Tool Chatter Identification Based on Dynamic Errors of Different Self-Synchronized Chaotic Systems of Various Fractional Orders

et al. 2019

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Chatter, the vibration between the workpiece and cutting tool, is a common phenomenon during the milling process. Traditionally, the Fourier transform analysis is mainly used to extract the features and determine whether chatter occurs. In this paper, an innovative and practical chatter identification method combining fractional order chaotic system and extension theory is proposed. A lathe spindle with embedded sensors is used in this study. The boundary of chattering state of the lathe spindle is decided by the center of gravity of phase plane of dynamic errors. The boundaries are then fed into extension model and relational function calculation is performed. In this way, chatter identification can be easily achieved based on the position of the chaotic center of gravity. The three chaotic systems, i.e. Lorenz, Chen-Lee, and Sprott, of different fractional orders are used and their results are compared. Compared with the traditional methods, the Fourier transform is time-consuming in terms of mathematical operations and adverse to the establishment of a real-time system. This paper uses the characteristics of the chaotic systems sensitive to input signals in order to more capably detect the boundary state from normal cutting to chattering cutting and more efficiently identify the chatter. The experiment results indicate that the Chen-Lee system (93.5%) exhibits have better chatter diagnosis rate than Lorenz (92.75%) and Sprott (69%) systems. The Chen-Lee system even reaches a diagnosis rate of 100% for orders 0.5 ∼ 0.7. Therefore, the method presented in this paper has a very high diagnosis rate and is thus very effective for chatter identification of machine tools. INDEX TERMS Fraction-order chaotic system, chatter, spindle, machine tool.

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“…A generalization of this theory has led to the rise of the field of fractional differential equations (FDEs) [1], extending the conventional framework of differential equations by incorporating fractional derivatives. This extension has countless applications in various scientific fields, such as quantum mechanics [3,4,5,6,7,8], electrodynamics [9,10,11,12], economics [13,14,15,16], engineering [17,18,19], biology [20,21], and geology [22].…”

Section: Introductionmentioning

confidence: 99%

Caputo fractional standard map: Scaling invariance analyses

Borin

2024

Chaos, Solitons & Fractals

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Fractional order Sprott chaos synchronisation‐based real‐time extension power quality detection method

Cited by 12 publications

References 32 publications

Fault diagnosis of power capacitors using a convolutional neural network combined with the chaotic synchronisation method and the empirical mode decomposition method

Fault diagnosis of power capacitors using a convolutional neural network combined with the chaotic synchronisation method and the empirical mode decomposition method

Machine Tool Chatter Identification Based on Dynamic Errors of Different Self-Synchronized Chaotic Systems of Various Fractional Orders

Caputo fractional standard map: Scaling invariance analyses

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