Summary This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

Small-scale wind energy harvesting, which can replace batteries to power small electronic devices and realize self-powered systems, has been extensively studied. To improve the working wind-speed range and output power of small-scale wind energy generation systems, we propose a synergetic hybrid piezoelectric and triboelectric mechanism for galloping wind energy harvesting. In this mechanism, a piezoelectric energy harvester (PEH) works in the vibration area and starts working at low wind speeds, while triboelectric nanogenerators work at the vibration boundaries and cooperate with the PEH at high wind speeds. The triboelectric nanogenerator boundaries can (1) constrain the maximum deformation of the beam at high wind speeds to avoid damage to the PEH, (2) increase the vibration frequency to enhance the electromechanical conversion efficiency, and (3) allow the PEH to have a low equivalent stiffness to work effectively at low wind speeds. A dynamic model is presented to characterize the synergetic hybrid piezoelectric–triboelectric wind energy harvester (SHPTWEH) and this is verified by experiments. The results show that the triboelectric nanogenerator boundaries greatly expand the effective working wind-speed range, and the total average power output by the prototype SHPTWEH was 0.24 mW at a wind speed of 14 m/s, which was 2.3 times that of the PEH alone.

The vibration signal of an early rolling bearing is nonstationary and nonlinear, and the fault signal is weak and difficult to extract. To address this problem, this paper proposes a genetic mutation particle swarm optimization variational mode decomposition (GMPSO-VMD) algorithm and applies it to rolling bearing vibration signal fault feature extraction. Firstly, the minimum envelope entropy is used as the objective function of the GMPSO to find the optimal parameter combination of the VMD algorithm. Then, the optimized VMD algorithm is used to decompose the vibration signal of the rolling bearing and several intrinsic mode functions (IMFs) are obtained. The envelope spectrum analysis of GMPSO-VMD decomposed rolling bearing fault signal IMF1 was carried out. Moreover, the feature frequency of the four fault states of the rolling bearing are extracted accurately. Finally, the GMPSO-VMD algorithm is utilized to analyze the simulation signal and rolling bearing fault vibration signal. The effectiveness of the GMPSO-VMD algorithm is verified by comparing it with the fixed parameter VMD (FP-VMD) algorithm, complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) algorithm and empirical mode decomposition (EMD) algorithm.

A gear fault diagnosis method based on kurtosis criterion variational mode decomposition (VMD) and self-organizing map (SOM) neural network is proposed. Firstly, the VMD algorithm is used to decompose the gear vibration signal, and the instantaneous frequency mean is calculated as the evaluation index, and the characteristic curve is drawn to screen out the most relevant intrinsic mode functions (IMFs) of the original vibration signal. Then, the number of VMD decompositions is determined, and the kurtosis value of IMFs are extracted to form the feature vectors. Then, the kurtosis value feature vectors of IMFs are normalized to form the kurtosis value normalized vectors. Finally, the normalized vectors of kurtosis value are input into SOM neural network to realize gear fault diagnosis. When the number of training times of SOM neural network is 100, the gear fault category is accurately classified by SOM neural network. The results show that when the training times of SOM neural network is 100 times, the gear fault diagnosis method, based on the kurtosis criterion VMD and SOM neural network is 100%, which indicates that the new method has a good effect on gear fault diagnosis. Appl. Sci. 2019, 9, 5424 2 of 25 the decomposed mode is fixed. It is better to use different wavelet bases for the analysis of different signals to achieve the best processing effect. EMD and LMD are prone to endpoint effect and mode mixing during the decomposition process. Therefore, Dragomiretskiy [9] proposed a variational mode decomposition to solve the problems caused by EMD and LMD in the decomposition process. Wang [10] used variational mode decomposition (VMD) to extract various fault features of the gearbox under strong noise environment, and compared with the ensemble empirical mode decomposition (EEMD) decomposition results, it shows that the algorithm can effectively improve the signal-to-noise ratio of the signal. Li [11] proposed a fault diagnosis method based on VMD and generalized composite multi-scale dynamic entropy (GCMSDE) to identify different health conditions of planetary gearboxes. Feng [12] uses VMD to decompose the planetary gearbox vibration signal into several intrinsic mode functions (IMFs), and performs Fourier transform on the amplitude envelope and instantaneous frequency of the sensitive IMFs to obtain the amplitude and frequency demodulation spectrum. The planetary gearbox faults have been detected based on demodulation and have been successfully identified on all three gears (sun gear, planetary gear, and ring gear). Wang [13] used the improved VMD algorithm to diagnose the gearbox and compared it with EEMD to verify the effectiveness of the proposed method. Si [14] proposes an improved VMD linked wavelet denoising method, which can suppress high frequency narrowband noise and normal noise in electromagnetic acoustic transducer (EMAT) signal, and this method can retain defect information.In recent years, researchers have studied a large number of fault classification algorithms. Among them, the gear fault...

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