In this article, an adaptive output feedback prescribed performance controller is proposed for a hydraulic system with matched and mismatched uncertainties (including parametric uncertainties and uncertain nonlinearities), which always exist in physical hydraulic systems, and degrade the internal state stability and tracking response performance. By integrating the adaptive control and disturbance observer into the extended state observer, the matched and mismatched uncertainties can be feedforward compensated in the output feedback control. Then, based on the fusion of prescribed performance function and barrier Lyapunov function, the proposed practical method is designed via backstepping method for hydraulic systems, all states are maintained within a preset range by constraining the upper bound of the control errors and the output tracking error is kept within a predetermined boundary that decreases with time. Moreover, the stability of closed-loop system is analyzed by Lyapunov theory. Finally, comparative experimental results are obtained to verify the control performance of the proposed control strategy.

Multi-scale permutation entropy (MPE) is an effective nonlinear dynamic approach for complexity measurement of time series and it has been widely applied to fault feature representation of rolling bearing. However, the coarse-grained time series in MPE becomes shorter and shorter with the increase of the scale factor, which causes an imprecise estimation of permutation entropy. In addition, the different amplitudes of the same patterns are not considered by the permutation entropy used in MPE. To solve these issues, the time-shift multi-scale weighted permutation entropy (TSMWPE) approach is proposed in this paper. The inadequate process of coarse-grained time series in MPE was optimized by using a time shift time series and the process of probability calculation that cannot fully consider the symbol mode is solved by introducing a weighting operation. The parameter selections of TSMWPE were studied by analyzing two different noise signals. The stability and robustness were also studied by comparing TSMWPE with TSMPE and MPE. Based on the advantages of TSMWPE, an intelligent fault diagnosis method for rolling bearing is proposed by combining it with gray wolf optimized support vector machine for fault classification. The proposed fault diagnostic method was applied to two cases of experimental data analysis of rolling bearing and the results show that it can diagnose the fault category and severity of rolling bearing accurately and the corresponding recognition rate is higher than the rate provided by the existing comparison methods.

The vibration signals of rolling bearings are often nonlinear and non-stationary. Multiscale entropy (MSE) has been widely applied to measure the complexity of nonlinear mechanical vibration signals, however, at present only the single channel vibration signals are used for fault diagnosis by many scholars. In this paper multiscale entropy in multivariate framework, i.e., multivariate multiscale entropy (MMSE) is introduced to machinery fault diagnosis to improve the efficiency of fault identification as much as possible through using multi-channel vibration information. MMSE evaluates the multivariate complexity of synchronous multi-channel data and is an effective method for measuring complexity and mutual nonlinear dynamic relationship, but its statistical stability is poor. Refined composite multivariate multiscale fuzzy entropy (RCMMFE) was developed to overcome the problems existing in MMSE and was compared with MSE, multiscale fuzzy entropy, MMSE and multivariate multiscale fuzzy entropy by analyzing simulation data. Finally, a new fault diagnosis method for rolling bearing was proposed based on RCMMFE for fault feature extraction, Laplacian score and particle swarm optimization support vector machine (PSO-SVM) for automatic fault mode identification. The proposed method was compared with the existing methods by analyzing experimental data analysis and the results indicate its effectiveness and superiority.

As a powerful tool for measuring complexity and randomness, multivariate multi-scale permutation entropy (MMPE) has been widely applied to the feature representation and extraction of multi-channel signals. However, MMPE still has some intrinsic shortcomings that exist in the coarse-grained procedure, and it lacks the precise estimation of entropy value. To address these issues, in this paper a novel non-linear dynamic method named composite multivariate multi-scale permutation entropy (CMMPE) is proposed, for optimizing insufficient coarse-grained process in MMPE, and thus to avoid the loss of information. The simulated signals are used to verify the validity of CMMPE by comparing it with the often-used MMPE method. An intelligent fault diagnosis method is then put forward on the basis of CMMPE, Laplacian score (LS), and bat optimization algorithm-based support vector machine (BA-SVM). Finally, the proposed fault diagnosis method is utilized to analyze the test data of rolling bearings and is then compared with the MMPE, multivariate multi-scale multiscale entropy (MMFE), and multi-scale permutation entropy (MPE) based fault diagnosis methods. The results indicate that the proposed fault diagnosis method of rolling bearing can achieve effective identification of fault categories and is superior to comparative methods.

Empirical wavelet transform (EWT) is a recently developed non-stationary signal decomposition approach. However, the number of spectrum divisions needs to be preset first, and the performance of spectrum division is inferior for a strong noisy or non-stationary signal caused by the mode mixing problem. To address this issue, a novel non-stationary signal decomposition method termed zero-phase filter-based adaptive Fourier decomposition (ZPF-AFD) is proposed in this paper. In the ZPF-AFD method, the number of spectrum divisions is adaptively determined first using the envelope entropy (EE) metric. Next, the spectral envelope processing (SEP) is applied to achieve an adaptive spectrum division. Last, the zero-phase filter (ZPF) is utilized to filter the frequency domain signal to obtain the components. The ZPF can effectively eliminate the mode mixing problem of EWT because of its no transition phase. The proposed ZPF-AFD approach is contrasted with the existing EMD, VMD, and EWT approaches through analyzing the simulated and measured signals in rolling bearing with local failures. The experimental results demonstrate that the proposed ZPF-AFD method has the best anti-noise and diagnosis accuracy, and its diagnosis performance is superior to the compared methods.

Rotation speed and propulsive force are the two critical parameters in the work of the air-borne bolting rig. To address the problem that unreasonable rotation speed and propulsive force will induce the breakage of the drill pipe and the inability of the drill bit to cut coal adequately this paper proposes an adaptive control strategy for the air-borne bolting rig based on genetic algorithm optimization. Firstly, we obtain the corresponding coal hardness by the real-time acquisition of the working torque of the drill pipe. Then we calculate the reasonable rotation speed of the hydraulic motor and the propulsive force of the hydraulic cylinder on the coal of different hardness. Secondly, the genetic algorithm is applied to optimize the parameters of the PID (proportion integration differentiation) controller so that the system may attain the target value fast and reliably and achieve adaptive control. Finally, a simulation model of the slewing system and the propulsion system of the air-borne bolting rig are established in the AMESim hydraulic software, and the simulation tests were carried out under two distinct working conditions: single coal hardness and coal hardness of sudden change. The results indicate that the PID control strategy based on genetic algorithm optimization has a shorter response time, a smaller overshoot, and a lower steady-state error than the traditional PID control strategy.