Dynamic Differential Equations Research Articles

Machine Learning Algorithms for Identifying Dependencies in OT Protocols

This study illustrates the utility and effectiveness of machine learning algorithms in identifying dependencies in data transmitted in industrial networks. The analysis was performed for two different algorithms. The study was carried out for the XGBoost (Extreme Gradient Boosting) algorithm based on a set of decision tree model classifiers, and the second algorithm tested was the EBM (Explainable Boosting Machines), which belongs to the class of Generalized Additive Models (GAM). Tests were conducted for several test scenarios. Simulated data from static equations were used, as were data from a simulator described by dynamic differential equations, and the final one used data from an actual physical laboratory bench connected via Modbus TCP/IP. Experimental results of both techniques are presented, thus demonstrating the effectiveness of the algorithms. The results show the strength of the algorithms studied, especially against static data. For dynamic data, the results are worse, but still at a level that allows using the researched methods to identify dependencies. The algorithms presented in this paper were used as a passive protection layer of a commercial IDS (Intrusion Detection System).

GDQ computation for thermal vibration of thick FGM plates by using third-order shear deformation theory

The third-order shear deformation theory (TSDT) effects on the thick functionally graded material (FGM) plates under thermal vibration are investigated by using the generalized differential quadrature (GDQ) method. The nonlinear coefficient term of displacement field of TSDT is used to derive the equations of motion for thermal vibration of thick FGM plates. The simpler form stiffness of FGM plates under linear temperature rise is considered in the thermo-elastic stress–strain relations. The dynamic equilibrium differential equations of FGM plates in terms of partial derivatives of displacements and shear rotations subjected to partial derivatives of thermal loads, mechanical loads and inertia terms are derived. Two parametric: environment temperature and FGM power law index effects on the thermal stress and center deflection of FGM thick plates are investigated.

Topology Transformation Analysis on Serial Flexible Variable Topology Mechanism

The flexible variable topology mechanism (FVTM) has become a research focus in the field of the mechanism because of its reconfigurable characteristics, which exhibit excellent adaptability in complicated working environments. In the process of topology transformation, the FVTM often generates impact, which leads to vibration and instability of the flexible elements. It seriously affects the accuracy and reliability of the operation. In view of this, this paper takes the serial-FVTM as an example to analyse its impact characteristics during topology transformation. The impact dynamics model is established by the theorem of impulse. Based on this, the fourth-order Runge-Kutta method is used to solve the dynamics differential equations. Using the control variable method, the influence of different parameters on the impact characteristics of the FVTM is obtained through numerical simulation analysis. Finally, the methods to improve the stability of the FVTM during topology transformation are analysed to expand new ideas for the subsequent research.

Parameter identification of photovoltaic discrete-time equivalent model using the bat algorithm

As the development of photovoltaic (PV) power generation continuously accelerated the total installed capacity of PV, the traditional static load model is difficult to meet the needs of the power grid with the increasing penetration of PV. And the dynamic model of grid-connected PV power generation is complicated and there are plenty parameters need to be identified, so the dynamic model of grid-connected PV power generation are extremely challenging to apply in wide-area power system. In this paper, a discrete-time equivalent model of PV (PDEM) is established based on the third-order dynamic differential equation of the PV power generation system and the parameters of the PDEM are identified using the least squares (LS) and the bat algorithm (BA). Besides, the dynamic characteristics of the PV power generation grid connected system with different permeability and the fitting residuals of the two methods is analyzed in the IEEE14-bus system incorporated into the PV system. The applicability of the PDEM is verified by setting short circuit grounding fault and changing the PV permeability and voltage dip. The simulation results demonstrate that the PDEM has a strong adaptability and good applicability in the case of high PV permeability with a wide application. And the applicability of the BA in identification of PDEM are given in this paper.

A study of a modified design of dumbbell-shaped flux switching tubular linear generator for regular wave energy conversion

Wave energy converters (WEC) use indirect drive hydraulic or turbine-type power take-off (PTO) mechanisms which consist of many moving parts, creating mechanical complexity and increasing the installation and maintenance costs. Linear generator-based direct drive wave energy converters could be a solution to overcome this problem, but the efficiency of the single conventional linear generator is not high enough, and it cannot work satisfactorily in the low-frequency range.In this paper, a novel dumbbell-shaped flux-switching linear generator has been proposed and studied as a power take-off unit for ocean wave energy conversion. The linear generator has a dumbbell-shaped stator, and the design is ameliorated by placing the permanent magnet rings of longitudinally alternating magnetic pole directions in the slots of its stator outer surface and is separated by thin wall steel ring shoulders. The linear generator also has a dumbbell-shaped translator. The stator is hollow where the translator slides inside axially inducing current in the coil. A long permanent magnet is inserted inside the hollow steel dumbbell core of the translator and a copper coil is wound around the outer surface of the moving translator core. The addition of permanent magnets on the outer slots of the stator is found to increase the output power significantly. To facilitate the investigation, the modified generator design has been compared to the conventional linear permanent magnet generator for their performances using the finite element method, as both machines are different in their structures. The results show that the double dumbbell-shaped flux-switching linear generator gives higher power output, magnetic flux density, branch current, and induced voltage. The double dumbbell-shaped flux-switching linear generator is then placed in a cylindrical buoy and investigated in a wave energy converter in the ocean environment. The hydrodynamic response of the cylindrical buoy has been investigated through ANSYS AQWA. The dynamic differential equations of the wave energy converter have been developed and solved for regular waves using Matlab codes. The peak output voltage, power, and the relative displacement of the linear generator translator with respect to the stator fixed with the buoy have been calculated through the Fourier Transform in the frequency domain using a Matlab code and through numerical integrations in the time domain using a Matlab Simulink code. The results in the time and frequency domains are compared and verified with each other. The relative displacement between the translator and stator buoy has been used as motion input of the ANSYS Maxwell simulation model, and the output voltage results of the ANSYS Maxwell simulation model have been compared and verified with those of the Matlab simulation models. The linear generator design in the wave energy converter under the regular wave excitation is further optimized for the maximum ratio of the peak output power to peak cogging force using the central composite design-based response surface method (RSM). The ANOVA analysis is used to validate the response surface model where its R2 coefficient of 99.93% has indicated an excellent fit. The methods and results differ from those presented in previous studies.

Mechanical Analysis and Optimal Design of Wave Energy Device

At present, the global energy problem is serious. Wave energy is the kinetic energy and potential energy of waves on the ocean surface. Because of its high energy density, wide distribution, and long continuous operation of the device, it has become the focus of academic research. The key problem to be solved urgently for the large-scale application of wave energy is how to optimize the energy conversion efficiency of wave energy devices. This paper starts from the Newtonian dynamic equation, analyzes the motion state of the wave energy device in different wave environments, and studies the optimization and control of its power output. This paper first adopts the analysis method of first whole and then isolation, and establishes a one-dimensional coordinate system with the zero point of sea level. Then, the force analysis of the system is carried out, the dynamic differential equation is established, and the initial draft of the system is solved through the initial balance equation. Since the dynamic equation is a second-order linear ordinary differential inhomogeneous linear equation, the fourth-order Runge is used. The Kutta method is used to solve the problem, and the numerical solution for the position and velocity of the float is obtained. Secondly, the movable coordinate system is established with the float as the reference system, and the force analysis of the oscillator is carried out to obtain its relative dynamic equation. Then, the initial relative position of the oscillator is solved through the initial balance equation, and the relative dynamic differential equation is obtained by using the fourth-order Runge-Kutta method to obtain the numerical solution of the relative position and relative velocity of the oscillator with respect to time. Finally, the numerical solution of the absolute position and absolute velocity of the oscillator with respect to time is obtained through coordinate transformation.

Modeling and control analysis of electric driving system considering gear friction based on dual-inertia system

In the electric driving system, the measurement of the motor speed error becomes more and more important, which has an impact on the system vibration suppression. In this paper, based on the single-neuron adaptive PID control method, the dual-inertia system considering gear friction torque is modeled and studied. Firstly, the dual-inertia system with gear friction is established, and dynamic differential equations of it are derived; Then, the comprehensive meshing stiffness and the time-varying friction torque of the gear system are deduced; Next, the Ziegler-Nichlos frequency domain response method is adopted to obtain the parameters of the PID controller. The control methods including the PID, Fuzzy-PID with DOB and single-neuron adaptive PID are utilized to adjust the motor speed of the system; Finally, the effects of gear friction, the moment of inertia of load and control methods on motor speed and system error are analyzed.

Design, modeling, and simulation of a novel transducer for vibration energy recovery system of speed bump

Based on the designed vibration energy recovery system of speed bump, the structure and principle of a novel transducer are introduced in this paper, which is an important part of the system. AMEsim simulation software was used to study the characteristics of the transducer, and the feasibility of the transducer design was verified through modeling and analysis of the dual-cylinder transducer. The coupling model of vehicle speed bump and transducer was analyzed, the dynamic differential equation was listed, and the decoupling operation was carried out. On the basis of the above, Matlab/Simulink was used to establish the model simulation, and the time-domain responses of displacement, velocity, and acceleration of the vibration of the car body, wheel, and transducer in the coupling model system were analyzed. The control variable method was used to further explore the time-domain response of vehicle acceleration in the coupling system only when the vehicle speed changes or the transducer damping changes. Finally, the vibration energy recovery system of the speed bump was built, and the preliminary test proved that the transducer can realize its function.

Existence of solutions for coupled hybrid systems of differential equations for microscopic dynamics and local concentrations

Existence of solutions for coupled hybrid systems of differential equations for microscopic dynamics and local concentrations

Penalty function method for FEM dynamic analysis of trusses with nonlinear multi-node constraints under harmonic load

This work introduces the establishment of the FEM model for investigating the dynamic behavior of trusses, subjected to multi-node constraints, under harmonic excitation based on utilizing the method of Penalty function. The technique for treating the nonlinear relationship of multi-node constraints is developed by using the Penalty function to extremum the Hamiltonian augmented potential energy function and to convert the multi-node constrained relation. The method of Newmark integration is utilized to convert dynamic differential equations of a truss system having multi-node boundary constraints subjected to a time-dependent harmonic force to incremental equations. The incremental-iterative algorithm had been developed based on the Newton-Raphson method, used for solving the dynamic incremental equation of motion for the truss system. Utilizing the constructed algorithm, the Matlab program is written to compute the investigated truss system’s internal force-time response and displacement-time response subjected to harmonic load. The advice for choosing the weight value of the Penalty function is proposed based on analyzing numerical results.

Structural Vibration Suppression Using a Reduced-Order Extended State Observer-Based Nonsingular Terminal Sliding Mode Controller with an Inertial Actuator

In this paper, we mainly aimed to design a reduced-order extended state observer-based active vibration controller for a structural vibration control system with total disturbances, i.e., model uncertainties, higher harmonics, and external excitations. A reduced-order extended state observer (RESO)-based nonsingular terminal sliding mode vibration control (RESO–NTSMVC) method is proposed for the vibration suppression of an all-clamped plate structure with an inertial actuator. First, a second-order state space model of the thin plate, with an inertial actuator, was established by solving the dynamic partial differential equation and analyzing the physical model. Second, the total disturbances, i.e., model uncertainties, higher harmonics, and external excitations, were estimated and compensated for by using a RESO via a feedforward part. Third, a NTSMVC based on an estimated value was designed to obtain a fast-tracking rate and effective vibration suppression performance. In addition, the stability of the closed-loop system was proven by using a Lyapunov stability criterion. Finally, a semi-physical experimental instrument was built based on the MATLAB/Simulink real-time environment and the NI-PCIE6343 acquisition card to verify strong anti-disturbance performance and effective vibration control performance of the designed method. The experimental comparison results showed that the vibration amplitudes of the proposed method could be reduced by 11.7 dB, when the traditional extended state observer-based nonsingular terminal sliding mode vibration control (ESO–NTSMVC) method achieved a control effect of only 6.5 dB. The comparative experimental results showed that the proposed method possessed better vibration suppression performance and anti-disturbance performance.

Affine-periodic solutions for generalized ODEs and other equations

It is known that the concept of affine-periodicity encompasses classic notions of symmetries as the classic periodicity, anti-periodicity and rotating symmetries (in particular, quasi-periodicity). The aim of this paper is to establish the basis of affine-periodic solutions of generalized ODEs. Thus, for a given real number $T> 0$ and an invertible $n\times n$ matrix $Q$, with entries in $\mathbb C$, we establish conditions for the existence of a $(Q,T)$-affine-periodic solution within the framework of nonautonomous generalized ODEs, whose integral form displays the nonabsolute Kurzweil integral, which encompasses many types of integrals, such as the Riemann, the Lebesgue integral, among others. The main tools employed here are the fixed point theorems of Banach and of Krasnosel'skiĭ. We apply our main results to measure differential equations with Henstock-Kurzweil-Stiejtes righthand sides as well as to impulsive differential equations and dynamic equations on time scales which are particular cases of the former.

An improved dynamic model and numerical simulation of yarn in the ring spinning system

The nonlinear dynamic behavior of ballooning yarn in the ring spinning system is investigated. An improved dynamic model of ballooning yarn with axial conveying speed is established. Based on Hamilton’s law of variation principle, the three-dimensional dynamic differential equations are derived. Then, the shooting method is employed to solve the two-point boundary value problem of ordinary differential equations. The numerical results of balloon profiles and distribution tension curves of ballooning yarns are discussed. The numerical results imply that with the increase of Ω, the yarn conveying speed increases, the minimum tension at the guide eye increases, and the helical loops of the balloon profile decrease. It is also found that as Ω increases, the spatial area of the guide eye tension [Formula: see text] that forms the dynamic balloon decreases. When the yarn conveying speed is medium or high, under different tensions at the guide eye, the yarn tensions along the height direction of the balloon change in the same trend, and the tensions of the ballooning yarn at the same height are very close. In addition, with the increase of Ω, the distribution tension of the ballooning yarn changes significantly under the same guide eye tension.

RENORMALIZATION GROUP METHOD FOR A CLASS OF LAGRANGE MECHANICAL SYSTEMS

Considering the important role of small parameter perturbation term in mechanical systems, the perturbed dynamic differential equations of Lagrange systems are established. The basic idea and method of solving ordinary differential equations by normal renormalization group method are transplanted into a kind of Lagrange mechanical systems, the renormalization group equations of Euler-Lagrange equations are obtained, and the first-order uniformly valid asymptotic approximate solution of Lagrange systems with a single-degree-of-freedom is given. Two examples are used to show the calculation steps of renormalization group method in detail as well as to verify the correctness of the method. The innovative finding of this paper is that for integrable Lagrange systems, its renormalization group equations are also integrable and satisfy the Hamilton system's structure.

Attitude Error and Contact Influencing Characteristic Analysis for a Composite Docking Test Platform

The design and analysis of a new type of three-jaw docking mechanism capable of space rendezvous and docking are presented. In addition, a composite docking test platform capable of both vertical and horizontal docking is created. On the basis of kinematics theory, a global coordinate system is built, and the attitude error is assessed based on the error angle. On the basis of dynamic theory, the multi-body dynamic differential equation of the composite docking platform is derived, and the impact-induced interaction state of the locking pawls is studied. The simulation software is then used to jointly simulate the test platform and the docking mechanism under the two conditions of frontal and oblique docking, and to analyze the attitude law caused by the change of docking impact force. This provides a solid foundation for future research into the application of space rendezvous theory to small spacecraft.

On the Use of Half-Implicit Numerical Integration in Multibody Dynamics

Abstract This work highlights the use of half-implicit numerical integration in the context of the index three differential algebraic equations (DAEs) of multibody dynamics. Although half-implicit numerical integration is well established for ordinary differential equations problems, to the best of our knowledge, no formal discussion covers its use in the context of index three DAEs of multibody dynamics. We wish to address this since when compared to fully implicit methods, half-implicit integration has two attractive features: (i) the solution method does not require the computation of the Jacobian associated with the constraint, friction, contact, or user-defined applied forces; and (ii) the solution is simpler to implement. Moreover, for nonstiff problems, half-implicit numerical integration yields a faster solution. Herein, we outline the numerical method and demonstrate it in conjunction with three mechanisms. We report on convergence order behavior and solution speed. The Python software developed to generate the results reported is available as open in a public repository for reproducibility studies.

Modelling and dynamical analysis of rotating variable-stiffness composite laminated revolving shell with elastic constraints using complete-gradient ANCF

In the model of rotating variable-stiffness composite laminated revolving shell (RVSCLRS), the element must be able to accurately describe the meridional direction and easily eliminate the initial stress in the initial bending configuration. To meet the requirements, a new type of complete-gradient ANCF space curved trapezoid element is proposed, and the fitting technology of bicubic Bézier revolving surface is used to initialize it. By using this element and artificial spring groups, the nonlinear dynamic differential equation of RVSCLRS with different boundary condition is established. Based on the linearization of this equation, the eigenvalue equation at the equilibrium position is derived. Compared with the numerical results of the degradation model, the validity of the proposed model is verified. By exploring the influence of boundary conditions, material structure, load and angular speed on RVSCLRS, it shows even if the material structure and boundary conditions are the same, the change of meridian has a significant impact on the stress distribution and vibration characteristics of the RVSCLRS.

Internal Resonance of the Coupling Electromechanical Systems Based on Josephson Junction Effects.

The internal resonances of the coupling vibration among electro-dynamic modes of an NEMS are studied for the coupling resonators connected on a Josephson junction. The methodology adopted involves coupling a resonator connected on a Josephson junction. The mathematical model of the coupled system is then obtained by considering the regulatory nonlinear effect of the phase difference of that Josephson junction. The resulting dynamic differential equation is deduced by considering the nonlinear terms of the Josephson junction and the nanobeam. The multi-scale method is then used to obtain the 1:1:1 resonant amplitude-frequency response equation of the coupled electromechanical system. The influence of the phase difference of the Josephson junction, magnetic field, external excitation and other factors are analyzed based on the internal resonant amplitude of the coupled system. The simulation results illustrate that the changes in the values of the magnetic field, excitation amplitude and divided resistances can lead to a remarkable change in the values of the nanobeam frequency and amplitude. The internal resonance principle is used to generate a mutual conversion and amplification among electrical signals and mechanical signals. This research provides a theoretical framework and a numerical approach for improving the sensitivity of magnetic quality detection.

Eavesdropping and Anti-Eavesdropping Game in UAV Wiretap System: A Differential Game Approach

Despite its advantages of flexility and low-cost networking, unmanned aerial vehicle (UAV) communications face various attacks such as eavesdropping. Existing studies on secure UAV communications assume fixed-location eavesdroppers and rarely consider interactions between legitimate nodes and eavesdroppers. In this paper, we investigate eavesdropping and anti-eavesdropping interaction between a UAV-enabled eavesdropper (UAV-E) and a UAV-enabled base station (UAV-BS) in a downlink wiretap system. The UAV-E aims to wiretap downlink signals by adaptively adjusting its trajectory while the UAV-BS aims to maximize secrecy-sum-rate with minimum power consumption by jointly optimizing user scheduling, power control, and trajectory. Dynamic differential equations are formulated to characterize motions of UAVs, following which a zero-sum differential game is formulated to model the “pursuit-evasion” interaction between the UAV-BS and the UAV-E. Definition and existence of Nash equilibrium (NE) are provided. To obtain the NE, Pontryagins minimum principle is leveraged to solve the trajectory design problem. Further, Gauss-Seidel-like implicit finite-difference method is leveraged to obtain saddle-point strategies at NE. Finally, numerical results are provided to verify the effectiveness of the proposed game model. It is revealed that the differential game can well-characterize the strategy interactions between UAVs. Moreover, results show that the initial positions and weights of UAVs, the energy consumption factor, and the user scheduling have key impacts on motion interactions between the UAV-BS and the UAV-E and further on UAV-BS’s power control.

Mathematical and information models of decision support systems for explosion protection

This paper is dedicated to the issue of mathematical and information modeling of the combustion-to-explosion transition that makes it possible to create an adequate mathematical and information support for decision support systems (DSS) for automatedcontrol of explosive objects.A simple mathematical model for the transition of combustion to explosion is constructed. This model is based on solving mathematical problems of the hydrodynamic stability of flames and detonation waves. These problems are reduced to solving eigenvalue problems for linearized differential equations of gas dynamics. Mathematical model is universal enough. It provides opportunities for making simple analytical estimates for the explosive induction distance and the time of the shock wave formation. The possibilities of the transition of slow combustion to both a deflagration explosion and a detonation wave are considered. Theoretical estimates of the explosive induction distance and the time of the combustion-to-explosion transition are obtained. These estimates are expressed by algebraic a formula, the use of which save computer resources and does not require significant computer time. The application of fuzzy logic makes it possible to use the proposed mathematical model of the combustion-to-explosion transition for real potentially explosive objects in industry and transport.Mathematical models of potentially explosive objects are based on combination of the fuzzy logic and classical mathematical methods. These models give possibilities for creating corresponding information models. Thus mathematical and information support of DSS for automated control systems of explosive objects is developed. The main advantage of these DSS is that it makes it possible for decision makers to do without experts. In particular, developed mathematical and information models create the base forsoftware of DSS for explosion safety of grain elevators. Appropriate software is developed and some calculations are performed. These calculations are useful not only from the point of view of testing the proposed method of mathematical modeling of a grain elevator as a potentially explosive object or testing the software itself, but also from the point of view of the grain elevator designing.