A New RBF Neural Network-Based Fault-Tolerant Active Control for Fractional Time-Delayed Systems

Heuristic computing with active set method for the nonlinear Rabinovich-Fabrikant model

The current study shows a reliable stochastic computing heuristic approach for solving the nonlinear Rabinovich-Fabrikant model. This nonlinear model contains three ordinary differential equations. The process of stochastic computing artificial neural networks (ANNs) has been applied along with the competences of global heuristic genetic algorithm (GA) and local search active set (AS) methodologies, i.e., ANNs-GAAS. The construction of merit function is performed through the differential Rabinovich-Fabrikant model. The results obtained through this scheme are simple, reliable, and accurate, which have been calculated to optimize the merit function by using the GAAS method. The comparison of the obtained results through this scheme and the conventional reference solutions strengthens the correctness of the proposed method. Ten numbers of neurons along with the log-sigmoid transfer function in the neural network structure have been used to solve the model. The values of the absolute error are performed around 10-07 and 10-08 for each class of the Rabinovich-Fabrikant model. Moreover, the reliability of the ANNs-GAAS approach is observed by using different statistical approaches for solving the Rabinovich-Fabrikant model.

Research on Fractional-Order Global Fast Terminal Sliding Mode Control of MDF Continuous Hot-Pressing Position Servo System Based on Adaptive RBF Neural Network

In this paper, a novel fractional-order global fast terminal sliding mode control (FGFTSMC) strategy based on an adaptive radial basis function (RBF) neural network is proposed to improve the performance of a medium density fiberboard (MDF) continuous hot-pressing position servo system with parameter perturbation and external load disturbance. Primarily, the mathematical model of the MDF continuous hot-pressing position servo system is constructed based on the dynamic equation of the hydraulic system. Then, a FGFTSMC is designed to speed up the convergence rate of the system, in which an adaptive law is used to estimate the upper bound of the unknown parameters to overcome the existing parameter perturbation of the system. In addition, an RBF neural network is introduced to approximate the external load disturbance of the system. The stability of MDF continuous hot-pressing position servo system based on the control scheme developed in this paper is proven using the Lyapunov theory. Finally, the simulation results show that the presented control scheme can effectively ensure the tracking accuracy of the system and enhance the robustness of the system.

Dynamical Investigation, Electronic Circuit Realization and Emulation of a Fractional-Order Chaotic Three-Echelon Supply Chain System

This study is concerned with dynamical investigation, electrical circuit realization, and emulation of a fractional three-echelon supply chain system. In the financial realm, long-term memory effects play important roles. On the other hand, most financial systems are uncertain with unknown nonlinear dynamics. However, most studies on nonlinear supply chains neither consider the fractional calculus nor take advantage of state-of-the-art emulation methods. These issues motivated the current study. A fractional-order chaotic three-echelon supply chain system is studied. At first, the system’s dynamic is studied through Lyapunov exponent and bifurcation diagrams. It is shown that a slight deferent in some parameters of the system can dramatically change the behavior of the system. Then, a real-time analog circuit is designed and implemented to investigate the system’s chaotic behavior. This way, the system’s chaotic attractors are empirically demonstrated. Finally, emulation and interpolation of the fractional-order chaotic system using the Gaussian process have been studied, and its luminous results have been presented.

Optimal Reinforcement Learning-Based Control Algorithm for a Class of Nonlinear Macroeconomic Systems

Due to the vital role of financial systems in today’s sophisticated world, applying intelligent controllers through management strategies is of crucial importance. We propose to formulate the control problem of the macroeconomic system as an optimization problem and find optimal actions using a reinforcement learning algorithm. Using the Q-learning algorithm, the best optimal action for the system is obtained, and the behavior of the system is controlled. We illustrate that it is possible to control the nonlinear dynamics of the macroeconomic systems using restricted actuation. The highly effective performance of the proposed controller for uncertain systems is demonstrated. The simulation results evidently confirm that the proposed controller satisfies the expected performance. In addition, the numerical simulations clearly confirm that even when we confined the control actions, the proposed controller effectively finds optimal actions for the nonlinear macroeconomic system.

Fault Critical Point Prediction Method of Nuclear Gate Valve with Small Samples Based on Characteristic Analysis of Operation

The number of fault samples for the new nuclear valve is commonly rare; thus, the machine learning algorithm is not suitable for the fault prediction of this kind of equipment. In order to overcome this difficulty, this paper proposes a novel method for the fault critical point prediction of the gate valve based on the characteristic analysis of the operation process variables. The operation process of gate valve switch often contains various fault characteristics and information, and this method first adopts the Shannon entropy to describe the power spectrum of vibration signal relevant to the operation process of gate valve switch, and then employs the mean value of the power spectrum entropy as an indirect process variable and further investigates the differences between the indirect process variable under the healthy state and the fault state with a different fault degree. In addition, the power signal of the gate valve is also employed as the direct process variable and the features of the direct process variable under the healthy state and the fault state with different fault degrees are also investigated. Based on the previous indirect process variable and direct process variable, the prediction approach for the critical point of the gate valve fault is established by analyzing the change in the indirect process variable and direct process variable before and after faults. Finally, the data of a nuclear gate valve experiment are employed to demonstrate the feasibility of the proposed method and the results show that the proposed method can effectively predict the fault critical point of the mentioned nuclear gate valve. If the diagnostic threshold is set properly, the critical point prediction of a nuclear gate valve fault can be realized as 100% or close to 100%. Furthermore, the proposed method can be directly applied to the nuclear gate valve in a nuclear power plant to improve the operation reliability of the valve. At the same time, the method can be applied to the fault diagnosis and prediction of valves in other fields, such as the chemical industry.

Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

A mathematical model for SARS-CoV-2 in variable-order fractional derivative

A new coronavirus mathematical with hospitalization is considered with the consideration of the real cases from March 06, 2021 till the end of April 30, 2021. The essential mathematical results for the model are presented. We show the model stability when R 0 < 1 in the absence of infection. We show that the system is stable locally asymptotically when R 0 < 1 at infection free state. We also show that the system is globally asymptotically stable in the disease absence when R 0 < 1 . Data have been used to fit accurately to the model and found the estimated basic reproduction number to be R 0 = 1.2036 . Some graphical results for the effective parameters are drawn for the disease elimination. In addition, a variable-order model is introduced, and so as to handle the outbreak effectively and efficiently, a genetic algorithm is used to produce high-quality control. Numerical simulations clearly show that decision-makers may develop helpful and practical strategies to manage future waves by implementing optimum policies.

A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models

The present work is to solve the nonlinear singular models using the framework of the stochastic computing approaches. The purpose of these investigations is not only focused to solve the singular models, but the solution of these models will be presented to the extended form of the delayed, prediction and pantograph differential models. The Gudermannian function is designed using the neural networks optimized through the global scheme "genetic algorithms (GA)", local method "sequential quadratic programming (SQP)" and the hybridization of GA-SQP. The comparison of the singular equations will be presented with the exact solutions along with the extended form of delayed, prediction and pantograph based on these singular models. Moreover, the neuron analysis will be provided to authenticate the efficiency and complexity of the designed approach. For the correctness and effectiveness of the proposed approach, the plots of absolute error will be drawn for the singular delayed, prediction and pantograph differential models. For the reliability and stability of the proposed method, the statistical performances "Theil inequality coefficient", "variance account for" and "mean absolute deviation'' are observed for multiple executions to solve singular delayed, prediction and pantograph differential models.

Computational fluid dynamic simulations to improve heat transfer in shell tube heat exchangers

Improving the thermal efficiency of shell-tube heat exchangers is essential in industries related to these heat exchangers. Installing heat transfer boosters on the side of the converter tube is one of the most appropriate ways to enhance heat transfer and increase the efficiency of this equipment. In this article, spring turbulence is studied using the computational fluid dynamics tool. The displacement heat transfer coefficient and the friction coefficient were selected as the primary target parameters, and the effect of using spring tabulators on them was investigated. The ratio of torsion step length to turbulence pipe length, wire diameter to pipe diameter ratio, and flow regime was studied as the main simulation variables, and the simulation results were compared with a simple pipe. The effect of water-acting fluid, R22, and copper Nanofluid on tubes containing turbidity was compared and investigated. This study showed that due to the pressure drop, the pipe with a torsional pitch to pipe length ratio of 0.17, a turbulent diameter to pipe diameter ratio of 0.15, and a Reynolds number of 50,000 with fluid R22 has the best performance for heat transfer.

Synchronization of the Glycolysis Reaction-Diffusion Model via Linear Control Law

The Selkov system, which is typically employed to model glycolysis phenomena, unveils some rich dynamics and some other complex formations in biochemical reactions. In the present work, the synchronization problem of the glycolysis reaction-diffusion model is handled and examined. In addition, a novel convenient control law is designed in a linear form and, on the other hand, the stability of the associated error system is demonstrated through utilizing a suitable Lyapunov function. To illustrate the applicability of the proposed schemes, several numerical simulations are performed in one- and two-spatial dimensions.

Research on the investment efficiency based on grey correlation-DEA model

Small and medium-sized enterprises (SMEs) are an important part of stimulating market vitality. In the post-pandemic era, the ability of SMEs to absorb employment plays an important role in stabilizing society and promoting economic growth. This paper selects 226 sample data from 2014 to 2017 measures the investment efficiency of small and medium-sized enterprises and makes a further analysis its influencing factors. Because there is a lag between investment and output. In this paper, the grey correlation analysis is used. Measuring the investment efficiency of SMEs by using BBC-DEA method. The study found that the overall investment efficiency of SMEs is low. Considering from the inside of the enterprise, this paper uses the Tobit model to make an empirical analysis. It is found that the influence of board structure and agency cost on investment efficiency are significantly negative. Growth, ownership concentration, equity incentive, salary incentive, profitability of SMEs have a significant positive effect on the investment efficiency of enterprises.