In this study we used a non-autonomous Chua’s circuit, and the fractional Lorenz chaos system. This was combined with the Extension theory detection method to analyze the voltage signals. The bearing vibration signals, measured using an acceleration sensor, were introduced into the master and slave systems through a Chua’s circuit. In a chaotic system, minor differences can cause significant changes that generate dynamic errors. The matter-element model extension can be used to determine the bearing condition. Extension theory can be used to establish classical and sectional domains using the dynamic errors of the fault conditions. The results obtained were compared with those from discrete Fourier transform analysis, wavelet analysis and an integer order chaos system. The diagnostic rate of the fractional-order master and slave chaotic system could reach 100% if the fractional-order parameter adjustment was used. This study presents a very efficient and inexpensive method for monitoring the state of ball bearings.

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.

This study proposed the concept of sparse and low-rank matrix decomposition to address the need for aviator’s night vision goggles (NVG) automated inspection processes when inspecting equipment availability. First, the automation requirements include machinery and motor-driven focus knob of NVGs and image capture using cameras to achieve autofocus. Traditionally, passive autofocus involves first computing of sharpness of each frame and then use of a search algorithm to quickly find the sharpest focus. In this study, the concept of sparse and low-rank matrix decomposition was adopted to achieve autofocus calculation and image fusion. Image fusion can solve the multifocus problem caused by mechanism errors. Experimental results showed that the sharpest image frame and its nearby frame can be image-fused to resolve minor errors possibly arising from the image-capture mechanism. In this study, seven samples and 12 image-fusing indicators were employed to verify the image fusion based on variance calculated in a discrete cosine transform domain without consistency verification, with consistency verification, structure-aware image fusion, and the proposed image fusion method. Experimental results showed that the proposed method was superior to other methods and compared the autofocus put forth in this paper and the normalized gray-level variance sharpness results in the documents to verify accuracy.

Tool wear and damage are unavoidable in machines which operate for long periods. The main objective of this study was the prediction and understanding of tool wear ahead of time. To achieve this a real-time monitoring system was needed which incidentally also improves product yield and efficiency. Traditionally, tool wear and working life have been estimated by past experience. To monitor the state of the tool, we used a method employing fractional-order chaotic self-synchronization system matched with extension theory to analyze, extract, and measure tool vibration signals. The fractional-order Chen–Lee chaotic system was used to detect differences in micro vibrations, resulting from different degrees of tool wear, and these were introduced into the master and slave systems. The extreme changes produced by micro differences in the chaotic system, and matter element module design based on the extension theory, were used to accurately determine tool status. Chaos theory, wavelet packet analysis, and Fast Fourier transform were then used to compare the results. This method can reduce the number of sensors and the time required for real-time monitoring of expected life compared to previous determination methods where temperature and current diagnostics must be included.