Advances in Mathematical Physics

The informatization construction of the power grid is becoming increasingly popular, business application systems are constantly emerging, and power-related data is rapidly expanding. These discrete power data are scattered in various application systems, and it is not easy to directly provide advanced enterprise applications. The establishment of intelligent power statistical model is an urgent need for constructing power grid informatization. This paper proposes a model of an electric energy metering system based on intelligent sensor data and introduces the existing digital metering system. This model is the integration and promotion of business integration based on the digital metering system. It is the first time to apply new metering equipment, such as measurement and control devices with integrated metering functions, and new metering technologies, such as IEC 61850 electricity meter reading applications. It is hoped that this paper can lay a foundation for further research.

In this paper, the effect of a fractional constitutive model on the rheological properties of fluids and its application in numerical simulation are investigated, which is important to characterize the rheological properties of fluids and physical characteristics of materials more accurately. Based on this consideration, numerical simulation and analytical study of unsteady fractional Oldroyd-B viscoelastic flow are carried out. In order to improve the degree of accuracy, the mixed partial derivative including the fractional derivative in the differential equation is converted effectively by integrating by parts instead of by direct discretization. Then, the stability, convergence, and unique solvability of the difference scheme are verified. The validity of the finite difference method is tested by making comparisons with analytical solutions for two kinds of fractional Oldroyd-B viscoelastic flow. Numerical results obtained using the finite difference method are in good agreement with analytical solutions obtained via the variable separation method. Viscoelastic characteristics of the unsteady Poiseuille flow are similar to the second-order fluid or integer-order Oldroyd-B fluid when the parameter is close to 0 or to 1. Oscillation characteristics of fractional viscoelastic oscillatory flow are similar to those of the classical viscoelastic fluid under the same condition. Compared with the previous research, the present work studies the rheological properties of fluids with the finite difference method, and the application of fractional constitutive models in describing the rheological properties of fluids is developed. Meanwhile, more cases reflecting the fractional-order characteristics are given. The present method can accurately capture the flow characteristics of unsteady fractional Oldroyd-B viscoelastic fluid and is applicable for the generalized fractional fluid.

In this study, the exact solutions of the Biswas-Arshed equation with the beta time derivative, which has an important role and physically means that it represents the pulse propagation in an optical fiber, nuclear, and particle physics, are obtained using the modified exponential function method. Exact solutions consisting of hyperbolic, trigonometric, rational trigonometric, and rational function solutions demonstrate the competence and relevance of the proposed method. In addition, the physical properties of the obtained exact solutions are shown by making graphical representations according to different parameter values. It is seen that the method used is an effective technique, since these solution functions obtained with all these cases have periodic function properties.

This paper studies the stability criterion of integral time-varying recurrent neural networks (RNNs) with zero lower bound and finite-time synchronization based on improved sliding mode control (SMC). Firstly, a sufficient criterion for universal asymptotic stability of RNNs with integral time-varying delays is obtained by estimating a tight upper bound of augmented Lyapunov-Krasovskii functional (LKF) derivative with inequality scaling technique and mutually convex combined inequality. Secondly, in order to eliminate the time that error system state trajectory slides along sliding mode flow pattern until convergence at the origin, based on drive response and SMC theory, a suitable sliding mode controller is designed by considering that sliding mode flow pattern is equal to synchronization error. Finally, maximum allowable upper bound of delay under different delay derivatives are obtained by considering trajectory change of input function under different initial value. Synchronization trajectory of drive and response systems with mismatched parameters and activation functions under the influence of controller are studied, and synchronization time which is required for error system to reach stability is obtained. Simulation results show that the introduction of integral delay can be more comprehensive from both difference and area, so that drive system state is eventually steady at equilibrium point and synchronized with response system. Stability criterion of this paper not only has less conservative and computation complexity but also has shorter synchronization control time.

The correlation filtering algorithm of infrared spectral data for dim and small target tracking is studied to improve the tracking accuracy of small and weak targets and to track small and weak targets in real time. After the image noise reduction processing by the mean shift filtering algorithm, the infrared small and weak target image data model is constructed by using the denoised infrared small and weak target image. And the brightness value and position of unknown small and weak targets are obtained. The tracking and measurement model of small and weak targets is built. The joint probabilistic data association algorithm is used to calculate the probability that each measurement is associated with its possible source targets, and the particle filter is used to update the tracking status of small and weak targets to achieve real-time tracking of small and weak targets. The experimental results show that the algorithm can enhance the edge contour information of small and weak images, so as to accurately track small and weak targets moving in any track, and has good real-time tracking and accuracy. There is a small deviation between the tracking track of weak and small targets tracked by the algorithm and the actual track, and the root mean square difference of tracking weak and small targets is within 2 pixels. In addition, the detection probability of detecting weak and small targets is less affected by SNR environmental factors.

In this article, the dynamics of the fuzzy fractional order enzyme Michaelis Menten model are investigated. To study problems with uncertainty, fuzzy fractional technique is applied. Using fuzzy theory, the sequential iterations of the model are calculated by applying fractional calculus theory and the homotopy perturbation method. A comparison is given for fractional and fuzzy results, and the numerical findings validate the fuzzy fractional case. Using MATLAB software, the results are simulated for various fractional orders, corresponding to the provided data. The simulations demonstrate the model’s appropriateness.