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This paper describes the fault diagnosis in the operation of industrial ball bearings. In order to cluster the very small differential signals of the four classic fault types of the ball bearing system, the chaos synchronization (CS) concept is used in this study as the chaos system is very sensitive to a system's variation such as initial conditions or system parameters. In this study, the Chen-Lee chaotic system was used to load the normal and fault signals of the bearings into the chaos synchronization error dynamics system. The fractal theory was applied to determine the fractal dimension and lacunarity from the CS error dynamics. Extenics theory was then applied to distinguish the state of the bearing faults. This study also compared the proposed method with discrete Fourier transform and wavelet packet analysis. According to the results, it is shown that the proposed chaos synchronization method combined with extenics theory can separate the characteristics (fractal dimension vs. lacunarity) completely. Therefore, it has a better fault diagnosis rate than the two traditional signal processing methods, i.e., Fourier transform and wavelet packet analysis combined with extenics theory. OPEN ACCESSEntropy 2014, 16 5359

Many different methods have been proposed for determining islanding and most of them have drawbacks. The main issue is the difficulty of detecting islanding when the current and voltage values are of the same phase or the frequency remains within the normal range of the grid when islanding occurs. In this study, a non-autonomous Chua's circuit was used to preprocess the grid signal after which a method based on the fractional Lorenz chaotic system and extension theory was used to analyze the preprocessed voltage signal. The capability of a chaotic system to amplify an extremely small signal was effectively utilized for the diagnosis of grid islanding. Simulation results showed that the diagnostic accuracy of the proposed method could be 100% and no other diagnostic method has offered such accuracy. Furthermore, the method proposed in this study is simple, easy to implement, and could be used as a portable system for the real-time monitoring and diagnosis of islanding in a conventional home grid system. detection based on new active disturbance [7] and one for active movement frequency anti-islanding detection [8]. Even though these methods can reduce the time taken to detect islanding, they can also affect the stability of the system or even lead to overall harmonic distortion. Furthermore, if the operating area (for islanding detection) includes other relatively stable power sources connected in parallel such as cogeneration systems. These methods will fail. New algorithms such as the Neural Network Algorithm (NNA) [9] have also been used in detecting islanding. Even though the neural network learns fast, it has a free mode and error tolerance and allows the use of reverse transmission direction to modify the weight and make corrections after repetition. It has a complicated training process that takes a long time. Accurate determinations cannot be made with other algorithms such as Fuzzy Theory [10] or the Genetic Algorithm (GA) [11] when the voltage, frequency, and phase differences are small. The Goertzel Algorithm [12], which is a Discrete Fourier Transformation (DFT) [13], has been recommended in some studies, but the conversion time is long and the width of the Fourier conversion window is fixed. This means that, when the time domain requires high resolution, the harmonic resolution will drop and the method is less than optimal. In 2015, a new, very accurate method has been proposed by Wang et al., which uses the Lorenz integer order [14] to detect islanding. However, many nonlinear systems exhibit fractional-order behavior. Therefore, if the fractional-order concept is considered in the diagnosis system, more accuracy can be obtained with a real physical system. In this study, the use of a non-autonomous Chua's circuit [14] for preliminary processing of the grid signal is described. This is followed by fractional Lorenz chaotic synchronization [15] and the product element model characteristics of the self-synchronization dynamic error are then analyzed. Afterward, the extension method is used to detect th...

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At present, vibration signals are processed and analyzed mostly in the frequency domain. The spectrum clearly shows the signal structure and the specific characteristic frequency band is analyzed, but the number of calculations required is huge, resulting in delays. Therefore, this study uses the characteristics of a nonlinear system to load the complete vibration signal to the unified chaotic system, applying the dynamic error to analyze the wind turbine vibration signal, and adopting extenics theory for artificial intelligent fault diagnosis of the analysis signal. Hence, a fault diagnostor has been developed for wind turbine rotating blades. This study simulates three wind turbine blade states, namely stress rupture, screw loosening and blade loss, and validates the methods. The experimental results prove that the unified chaotic system used in this paper has a significant effect on vibration signal analysis. Thus, the operating conditions of wind turbines can be quickly known from this fault diagnostic system, and the maintenance schedule can be arranged before the faults worsen, making the management and implementation of wind turbines smoother, so as to reduce many unnecessary costs.