A fault diagnosis solution is proposed in this article for the uncertainty and external disturbance problems in the main drive system of a rolling mill based on analytical redundancy. Considering the nonlinear friction damping, a system is mathematically modeled, and a bank of nonlinear Luenberger observers is designed. The generalized residual set theory is used to isolate two typical fault types of the system. To optimize the anti-disturbance ability of the observer, the disturbance attenuation factor is introduced. The influence of external disturbance on fault estimation is reduced by adjusting the disturbance attenuation factor. Using Lyapunov stability theory, the convergence analysis of the observer dynamic error equation is provided. The observer gain is obtained through resolving the optimality issue under the linear matrix inequality constraint. Numerical simulations of a 2030-mm tandem cold rolling mill were conducted to demonstrate the practicability of the approach. This fault diagnosis scheme is important to improve the stability of system operation.

By calibrating the inter-system bias (ISB), an inter-system model can be achieved to improve the performance of multi-global navigation satellite system (GNSS) positioning. A number of studies were carried out to compose inter-system models among code division multiple access (CDMA) systems. However, due to the frequency division multiple access (FDMA) technique, GLONASS phase and code observations suffer from inter-frequency phase bias (IFPB) and inter-frequency code bias (IFCB) respectively, which make it difficult to obtain the ISB among GLONASS and CDMA systems. In addition, most of the current inter-system models are unable to handle mixed frequencies. A new single difference-based uniform inter-system model suitable for all of the CDMA and FDMA frequency combinations is proposed in this study. We first utilize a particle filter approach to extract the IFPB rate. Afterwards, the multi-ISB parameters can be estimated by the proposed model simultaneously. Four short baselines containing the signals of GLONASS, GPS, BDS3, BDS2, Galileo, and QZSS are selected to validate the model. The quantitative results indicate that the IFPB rate can be extracted precisely by a particle filter within ten epochs. The inter-system phase bias valuations are sufficiently stable on a daily scale and have standard deviation near 0.01 cycles. After de-weighting the GLONASS code observations to reduce the influence of IFCB, the inter-system code bias is also stable. Furthermore, imposing the stable ISB on the multi-GNSS inter-system model can effectively improve the single-frequency real-time kinematic positioning accuracy and reliability for severely obstructed situations with only a small number of satellites observed.

Considering the occurrence of actuator faults in the wind turbine generator main drive system, a fault model of the wind turbine generator main drive system is established. First, an adaptive sliding mode observer is designed to estimate the actuator faults, which is able to identify and reconstruct the faults quickly and provides the necessary information for the implementation of fault-tolerant control. In order to improve the design process of the observer, the gain matrix solution problem is transformed into an optimization problem subject to linear matrix inequality constraints. Secondly, considering the existence of unmodeled dynamics and external noise disturbances in the main drive system, an adaptive feedback fault-tolerant controller is designed using the fault reconstruction information after an actuator failure occurs in the system to compensate for the system errors caused by actuator failures, unmodeled dynamics, and external noise disturbances, which ensures a stable operation of the system. Finally, a simulation study of a 5 MW wind turbine system shows that at an average wind speed of 7.5 m/s and a turbulence intensity of class A, the system is restored to a normal state after the addition of the fault-tolerant controller, and the generator electromagnetic torque error is only 1.89%, which verifies the validity of the proposed method.

In order to address the problem that the main drive system of rolling mill is easily affected by the impact of biting steel, and considering the nonlinear friction damping and the external perturbations of the main drive system of rolling mill during the rolling process, a fault model of the main drive system of rolling mill is established, and a fault diagnosis and fault tolerance control method of the main drive system of rolling mill based on the nonlinear sliding-mode observer is proposed. In order to suppress the influence of external perturbations on fault diagnosis, a nonlinear sliding-mode observer is constructed for fault diagnosis and fault reconfiguration of the system, and the robustness of the observer to fault reconfiguration is improved by using the sliding-mode control rate [ ], and the stability of the designed nonlinear sliding-mode observer is proved using Lyapunov’s stability theorem. In order to ensure that the system can operate normally even after a fault occurs, a reference model is designed, and a new controller is redesigned for fault-tolerant control of the system by adding a fault compensation term to the original control scheme using fault estimation information. Through the simulation study of the main drive system of stand F4 of 2030 mm cold rolling mill, it is verified that the observer can accurately track the system state with an angular velocity error of 2.45% and detect and estimate the main drive system failure of rolling mill with an estimation error of no more than 0.04% after a fault occurs; the fault-tolerant control of the main drive system of rolling mill is carried out by using the fault information to restore the system to its normal state, and the angular velocity error is 1.89%.

Aiming at the shortcomings of the Golden Jackal optimization algorithm, such as low convergence accuracy and easy falling into the optimal local solution, an improved Golden Jackal optimization algorithm was proposed. First, sine and piecewise linear (SPM) chaotic mapping was introduced to increase the population number to achieve the purpose of initial population diversity. The self-adaptive weight and sine–cosine algorithm improved the position update formula of the Golden Jackal optimization algorithm, so the global search ability of the golden jackal algorithm is improved, and avoid the algorithm that fell into local optimality. Second, simulation experiments with eight standard test functions are performed to prove that the algorithm has excellent optimization ability. The improved Golden Jackal optimization algorithm was applied to optimize the kernel parameters of hybrid kernel principal component analysis. A fault diagnosis model is proposed to improve the golden jackal algorithm to optimize the kernel principal component analysis. Finally, the proposed method is used to fault diagnosis in the hot strip mill process. According to the study of simulation results, the faulty data can be identified effectively by this method, the accuracy is up to 100%, and the fault false alarm rate is greatly reduced.

In this article, the problem of multiple fault detection, isolation and reconfiguration of the rolling mill main drive system containing external disturbances is investigated. Considering the nonlinear frictional damping between the rolls and the rolled parts, a nonlinear mathematical model of the main drive system of the mill is established. A comprehensive fault diagnosis scheme based on observer is addressed for this system subjected to unknown external interference. The proposed scheme is divided into two parts. In the first stage, a set of sliding mode observers is designed for system fault detection, and a fault isolation criterion is proposed based on observer redundancy and generalised residual set theory to reveal the fault source. In the second stage, combined with the iterative learning algorithm, an iterative learning-unknown input observer is constructed to realise the accurate estimation of the fault signal. Unlike the existing fault estimation methods, the iterative learning-unknown input observer designed in this article uses the state estimation error of the previous iteration to estimate the fault signal in the current iteration period. Using H ∞ synthesis to design observers for the system will guarantee fault diagnosis robustness. The Lyapunov theory and linear matrix inequality are introduced to prove the convergence of the proposed observer. The simulation study of a 1780-mm hot strip mill evaluates the proposed scheme. Simulation results demonstrate that the sliding mode observer approach can detect faults in the main drive system and isolate faults accurately. In contrast, the iterative learning-unknown input observer method has the lowest fault reconfiguration error (99.87% smaller than the extended state observer, 99.77% smaller than the unknown input observer) and achieves accurate fault signal tracking.