The diagnosis of faults in rolling bearings plays a critical role in monitoring the condition and maintaining the performance of rotating machinery, while also preventing major accidents. In this article, a new approach to diagnosing faults in rolling bearings is proposed, using wavelet packet decomposition (WPD) for features extraction and the chaotic sparrow search optimization algorithms (CSSOAs) to optimize the parameters of a deep belief network (DBN). Firstly, the WPD method is used for the decomposition of vibration signals in rolling bearings, which are decomposed into three layers, and reconstruction is performed on the nodes of the last layer based on the decomposition. Furthermore, the energy characteristics of the reconstructed nodes are then utilized as inputs to DBN, and the CSSOA is employed to optimize the hyperparameters of DBN. Ultimately, a fault diagnosis model combining WPD with optimizing parameters is presented. This model is validated on bearing datasets from Case Western Reserve University (CWRU) and Jiangnan University (JNU). Experimental results indicate that the average accuracy achieved when modeling with WPD-CSSOA-DBN on the CWRU dataset is 98.24 % , with a root mean square error of 0.0713. On the JNU bearing dataset, the modeling achieves an average accuracy of 95.15 % with a root mean square error of 0.1018. Compared to other methods, this approach demonstrates stronger feature extraction capabilities and outstanding rolling bearing fault diagnosis abilities.

Compensating for the infinite number of actuator faults considered in nonlinear multi-manipulator systems is a significant, yet a crucial issue for control problems. In view of this, a novel fuzzy adaptive fault-tolerant control algorithm is proposed for nonlinear multi-manipulator systems to eliminate the influence of actuator faults and improve accuracy essentially, as well as achieve the objective of containment. First, a Lyapunov function is constructed by replacing the square term of the error with a series of smooth functions. Moreover, a predefined accuracy function is introduced and a new fuzzy adaptive fault-tolerant containment control scheme is designed. This overcomes the problem that existing methods cannot guarantee the negative-definite property of time derivative of Lyapunov function between two adjacent actuator faults. And it also ensures the boundedness of containment errors. Furthermore, projection-based adaptive parameters and the turning function are fused to compensate the influence of actuator faults. Finally, the effectiveness of the designed control scheme is verified by a simulation example of multiple single-link manipulator systems.

This article investigates global asymptotic stability for neural networks (NNs) with time-varying delay, which is differentiable and uniformly bounded, and the delay derivative exists and is upper-bounded. First, we propose the extended secondary delay partitioning technique to construct the novel Lyapunov-Krasovskii functional, where both single-integral and double-integral state variables are considered, while the single-integral ones are only solved by the traditional secondary delay partitioning. Second, a novel free-weight matrix equality (FWME) is presented to resolve the reciprocal convex combination problem equivalently and directly without Schur complement, which eliminates the need of positive definite matrices, and is less conservative and restrictive compared with various improved reciprocal convex inequalities. Furthermore, by the present extended secondary delay partitioning, equivalent reciprocal convex combination technique, and Bessel-Legendre inequality, two different relaxed sufficient conditions ensuring global asymptotic stability for NNs are obtained, for time-varying delays, respectively, with unknown and known lower bounds of the delay derivative. Finally, two examples are given to illustrate the superiority and effectiveness of the presented method.

This article investigates the command filter-based decentralized prescribed performance adaptive fault-tolerant compensation control strategy for uncertain nonlinear large-scale systems subject to asymmetric time-varying full-state constraints. Via integrating the performance function with command filter-based backstepping technique, the prescribed performance control problem is addressed, under which the complexity of controller design is reduced. Under the prescribed performance control framework, the nonlinear transformed function is constructed so as to ensure that the asymmetric time-varying full-state constraints free from feasibility conditions imposed on virtual control signals are not violated. Besides, the effect of infinite number of time-varying actuator faults is compensated with the aid of projection adaption design. Furthermore, based on the piecewise Lyapunov function analysis, it is rigorously testified that entire involved signals are bounded, desired constraints are not breached and tracking errors within the predefined domains. Finally, the effective performances of the developed control algorithm are confirmed by some simulation results.