Problem Of Oscillations Research Articles

A novel momentum prototypical neural network to cross-domain fault diagnosis for rotating machinery subject to cold-start

Cross-domain rotating machinery fault diagnosis has achieved great success recently with the development of deep transfer learning. However, conventional deep transfer learning methods encounter a severe decline in prediction accuracy when fault samples are limited. Moreover, conventional deep transfer learning methods require additional parameter tuning rather than cold-start when applied to the target tasks, hampering their implementation in practical fault diagnosis applications. In this paper, a novel method, named momentum prototypical neural network (MoProNet), is proposed for cross-domain few-shot rotating machinery fault diagnosis. The MoProNet progressively updates the support encoder to address the prototype oscillation problem and enable the model to apply limited source domain samples to predict target domain faults with cold-start. The performance of the proposed MoProNet is tested on a bearing dataset and a hardware-in-the-loop high-speed train simulation platform, respectively, with over forty cross-domain few-shot fault diagnosis tasks. The experimental results demonstrate that the proposed MoProNet achieves satisfactory results and outperforms the other comparable methods in the same cross-domain few-shot scenarios with the simple AlexNet backbone.

Synchronous oscillation characteristic and finite-time function projection synchronization control method for microgrids

Due to the nonsynchronization of each microsource node in a microgrid, the physical parameters of each node are not uniform. Therefore, unstable oscillation will occur for the whole microgrid system. To solve the oscillation problem caused by the nonsynchronization of each microsource node in the microgrid, a hierarchical control structure microgrid model is researched in this paper. Based on the theory of chaotic synchronization and finite time, a new microgrid synchronous oscillation characteristic and finite-time function projection synchronization control method is proposed. First, combining complex networks and microgrids, a nonlinear dynamic model of microgrid hierarchical control is established, and the abilities of the small-world network model and the formal network model to adjust for asynchronous oscillations are verified by comparing the two models. Then, aiming at the unsynchronized oscillations caused by external system noise, a new finite-time function projection synchronization control method is proposed. According to the verification results, the method can control external disturbances, avoiding system oscillation.

An alternative way to solve the small oscillations problem

An alternative way to solve the small oscillations problem

A Random Choice Scheme for Transient Mixed Flows

A novel numerical model for describing highly transient mixed flows is presented based on the Preissmann slot approach. To overcome the spurious oscillation problems caused by this approach, a numerical scheme named “random choice method” (RCM), in which flow variables of the next time level are obtained by picking a local Riemann solution state at random, is applied herein. Three numerical tests are performed to verify the ability of the proposed model in simulating from single flows to mixed flows. The results show that the RCM gives sharper shock resolutions as compared with the Godunov-type scheme, which causes the smearing of discontinuities. The proposed model can eliminate the numerical oscillations under flow conditions of switching from free-surface flow to pressurized flow, because of its unconditional stability. On further analysis of the experimental verifications, a hybrid method is presented to improve the performance of RCM in the smooth (nonuniform) parts of the flow.

Polynomial solutions of generalized quartic anharmonic oscillators

This paper deals with the partial solution of the energy eigenvalue problem for generalized symmetric quartic oscillators. Algebraization of the problem is achieved by expressing the Schrödinger operator in terms of the generators of a nilpotent group, which we call the quartic group. Energy eigenvalues are then seen to depend on the values of the two Casimir operators of the group. This dependence exhibits a scaling law which follows from the scaling properties of the group generators. Demanding that the potential gives rise to polynomial solutions in a particular Lie algebra element puts constraints on the four potential parameters, leaving only two of them free. For potentials satisfying such constraints, at least one of the energy eigenvalues and the corresponding eigenfunctions can be obtained in closed analytic form by pure algebraic means. With our approach, we extend the class of quasi-exactly solvable quartic oscillators which have been obtained in the literature by means of the more common textrm{sl}(2,{mathbb {R}}) algebraization. Finally, we show how solutions of the generalized quartic oscillator problem give rise to solutions for a charged particle moving in particular non-constant electromagnetic fields.

Virtual Synchronous Generator (VSG) Control Strategy Based on Improved Damping and Angular Frequency Deviation Feedforward

The output active power of a grid-connected inverter controlled by a traditional virtual synchronous generator (VSG) has the problems of oscillation and steady-state errors. A VSG control strategy based on improved damping and angular frequency deviation feedforward is proposed. This strategy reduces the steady-state error of active power by adding a transient damping link to a traditional VSG damping feedback channel. At the same time, the angular frequency deviation feedforward compensation is used to improve the response speed of the VSG to the active power instruction and reduce the active power overshoot in the dynamic process. First, the VSG active power closed-loop small-signal model is established. The effects of inertia and damping on the dynamic and steady-state performance of the VSG are analyzed by the root locus method. The effect of the proposed control strategy on the system is analyzed by using a closed-loop zero-pole diagram. This strategy improves the precision of active power control the dynamic performance of the system effectively. Finally, the effectiveness and superiority of the proposed control strategy are verified by Matlab/Simulink simulation and semi-physical simulation platform RT-LAB.

Real-Time Nonlinear Control Allocation Framework for Vehicles with Highly Nonlinear Effectors Subject to Saturation

Hybrid Unmanned Aerial Vehicles UAV are vehicles capable of take-off and landing vertically like helicopters while maintaining the long-range efficiency of fixed-wing aircraft. Unfortunately, due to their wing area, these vehicles are sensitive to wind gusts when hovering. One way to increase the hovering wind-rejection capabilities of hybrid UAV is through the addition of extra actuators capable of directing the thrust of the rotors. Nevertheless, the ability to control UAVs with many actuators is strictly related to how well the Control Allocation problem is solved. Generally, to reduce the problem complexity, conventional (CA) methods make use of linearized control effectiveness in order to optimize the inputs that achieve a certain control objective. We show that this simplification can lead to oscillations if it is applied to thrust vectoring vehicles, with pronounced non-linear actuator effectiveness. When large control objectives are requested or actuators saturate, the linearized effectiveness based CA methods tend to compute a solution far away from the initial actuator state, invalidating the linearization. A potential solution could be to impose limits on the solution domain of the linearized CA algorithm. However, this solution only reduces the oscillations at the expense of a lag in the vehicle acceleration response. To overcome this limitation, we present a fully nonlinear CA method, which uses an Sequential Quadratic Programming (SQP) algorithm to solve the CA problem. The method is tested and implemented on a single board computer that computes the actuator solution in real time onboard a dual axis tilting rotor quad-plane. Flight test experiments confirm the problem of severe oscillations in the linearized effectiveness CA algorithms and show how the only algorithm able to optimally solve the CA problem is the presented Nonlinear method.

A comprehensive modelling and experimental approach for damped oscillations in U-tubes via Easy JavaScript Simulations

In recent years, science simulations have become popular among educators due to their educational usefulness, availability, and potential for increasing the students’ knowledge on scientific topics. In this paper, we introduce the implementation of a user-friendly simulation based on Easy Java/JavaScript Simulations (EJS) to study the problem of damped oscillations in U-tubes EJS. Furthermore, we illustrate various advantages associated with the capabilities of EJS in terms of design and usability in order to encourage teachers to use it as an educational supplement to physics laboratories.

A New Hybrid Block Method via Combined Hermite Polynomials and Exponential Functions as Basis Function

This paper presents the derivation and implementation of a hybrid block method for solving stiff and oscillatory first-order initial value problems of ordinary differential equations (ODEs). The hybrid block method was derived by continuous collocation and interpolation using combined Hermite polynomials and exponential functions as the basis function to produce a continuous implicit Linear Multistep Method (LMM) of order nine and implement in block form. The basic properties of the derived method were studied, and the hybrid block integrator was demonstrated to be zero-stable, convergent, consistent, and to have an A-stable region of absolute stability, which made it suitable for stiff and oscillatory ordinary differential equations. The use of a combined basis in the generation of LMMs is worthy of universal acceptance. The technique indicates that, utilizing an interpolation and collocation approach, continuous LMMs can be derived from combinations of any polynomials and exponential functions. On two sampled stiff and oscillatory problems, the new integrator was tested. The numerical results indicate that our new hybrid block integrator is computationally efficient and outperforms existing methods in terms of accuracy

К вопросу об устойчивости различных стационарных точек в задаче о малых колебаниях аэродинамического маятника в потоке среды

Построена математическая модель движения аэродинамического маятника в потоке среды. На основании теории квазистационарного обтекания пластинки средой получена система дифференциальных уравнений движения тела, в которую входят экспериментальные аэродинамические функции. Проведен переход к новым безразмерным переменным. Показано нарушение единственности решений уравнений движения. Проведен геометрический анализ областей неоднозначности в подпространстве фазовых переменных. Решены уравнения равновесия и найдены различные стационарные точки. Методом Раусса – Гурвица построены области устойчивости на плоскости различных безразмерных параметров. The analysis of the teleological concept of goal has shown that this concept has a dual nature: idealistic and materialistic. The article considers the principle of dualism as the key one. Therefore, from the point of view of cybernetics, the idealistic aspect of the goal is proposed to be interpreted as an idealized result, which is described by one or more mathematical logics of ML. The ML device serves as a tool for selecting the targeted behavior of a complex object or system S in accordance with the expert evaluation of EE. The materialistic aspect of the goal is understood as obtaining a real result RR through an object or system S. If by S we mean a team of robots configured to fulfill one or more goals, then a qualitative analysis of the behavior of such a system can be carried out using agent-based modeling. The robot collective model is a set of interconnected classes of intelligent agents. Any class of agents is characterized by an 11-digit set, which describes the ability of a class of agents to achieve their goals by adapting through training without finding the most effective actions. Agent-based modeling allows you to judge the degree of achievement of the goal.

Regularization Strategy Aided Robust Unsupervised Learning for Wireless Resource Allocation

Unsupervised learning (UL) is widely used in the wireless resource allocation problems due to its lower computational complexity and better performance compared with traditional optimization algorithms. Since wireless resource allocation problems usually have several constraints, primal-dual learning based UL framework are widely adopted. However, the primal-dual learning approach has the problem of oscillation around the constraint threshold while training and there may be serious constraint violations when deployment. In addition, although the output of the neural network can also be restricted to the feasible region by the penalty function method, the optimality of such training methods cannot be guaranteed. In this paper, we combine the primal dual learning method with the penalty function method and propose a regularized unsupervised learning (RUL) framework to enhance the robustness of the primal-dual learning based UL framework. In the proposed RUL framework, we use regularization techniques to improve the robustness of primal-dual learning by reducing the risk of constraint violations while training. A quadratic penalty term is introduced into the Lagrangian function of the wireless optimization problem where the constraints can be equivalent to equality constraints to form its augmented Lagrangian function. In the simulation, we give a simple point to point power optimization problem as an example to show that the proposed RUL can improve the robustness of constraint convergence, and can also accelerate training speed.

Generalized Multiphase-Shift Transient Modulation for Dual-Active-Bridge Series-Resonant Converter

Given the wide-range applications of bidirectional dual-active-bridge series-resonant converter (DABSRC), its complex nonlinear dynamic behavior is an interesting phenomenon that deserves attention of power electronics engineers. It is observed that if the control variables (i.e., phase-shift angles) are directly updated through conventional transient modulation, large-amplitude transient oscillations and dc offsets will be induced in the high-frequency-link voltages and currents during transient stage, which can ultimately degrade the converter's waveform quality significantly. The relatively few prior works in studying the transient oscillatory behavior of DABSRC have only focused on single-phase-shift modulation. In this article, a new transient modulation method referred to as generalized trajectory-switching modulation (GTSM) is first proposed for enhancing the transient performance of multi-phase-shift modulated DABSRC. GTSM can simultaneously mitigate the problems of transient oscillations and dc offsets regardless of operation modes and power-flow directions, thus always ensuring safe transient operation. It also enables the resonant voltages and currents as well as magnetizing current to seamlessly reach the desired new steady-state values swiftly. Finally, the said theoretical claims are verified experimentally under both open loop and closed loop with model predictive control, and the influence of deviations from nominal resonant tank's parameters on GTSM is also considered.

Control Method of Seamless Transfer from Grid-Connected Mode to Isolated Mode for Microgrid Demonstration

It’s easy to cause transient oscillation problems when the microgrid transfers from the grid-connected mode to the isolated mode, so a control method of seamless transfers from the grid-connected mode to the isolated mode for microgrid demonstration is proposed. The switching control strategy of the outer loop controller for the master unit(s) makes the reference value of the current inner-loop controller the same when the microgrid transfers to isolated mode. While the switching control strategy of phase locked loop (PLL) uses an ample-hold assign the output angle of grid-connected PLL to the oscillator adopted by the microgrid in isolated mode at the switching moment. Finally, the sub-regional control strategy uses different control strategies to reserve more spinning capacity for the master unit(s) which divides the power balance into 3 regions. At last, the simulation is verified that the proposed control method not only realizes the seamless transfer from grid-connected operation to islanded operation for the microgrid but also improves the anti-disturbance ability of the microgrid in isolated mode.

Boundary value problems of integrodifferential equations under boundary conditions taking into account physical nonlinearity

When solving integrodifferential equations under boundary conditions, taking into account physical nonlinearity, a broad class of boundary-value problems of oscillations arises associated with various boundary conditions at the edges of a flat element. When taking into account non-stationary external influences, the main parameters is the frequency of natural vibrations of a flat component, taking into account temperature, prestressing, and other factors. The study of such problems, taking into account complicating factors, reduces to solving rather complex problems. The difficulty of solving these problems is due to both the type of equations and the variety. We analyze the results of previous works on the boundary problems of vibrations of plane elements. Possible boundary conditions at the edges of a flat element and the necessary initial conditions for solving particular problems of self-oscillation and forced vibrations, and other problems are considered. The set of equations, boundaries, and initial conditions make it possible to formulate and solve various boundary value problems of vibrations for a flat element. The oscillation equations for a flat element in the form of a plate given in this paper contain viscoelastic operators that describe the viscous behavior of the materials of a flat component. In studying oscillations and wave processes, it is advisable to take the kernels of viscoelastic operators regularly, since only such operators describe instantaneous elasticity and then viscous flow.

Low cost inertial sensor attitude fixation algorithm and accuracy analysis

Aiming at the problems of angle oscillation, slow convergence speed, and low accuracy of traditional algorithms in low cost inertial element attitude determination, this study proposes an improved attitude algorithm based on geomagnetic correction robust model assisted adaptive step gradient descent. Firstly, a robust ellipsoid fitting algorithm is proposed to correct the geomagnetic anomaly data. Then, an adaptive step size model is established based on the momentum gradient descent method, and the iterative optimization parameters are automatically adjusted according to the error function. At the same time, the dynamic limiting mean filter is used to constrain the attitude angle, to calculate the optimal attitude information of the sensor. Finally, the algorithm is verified by static and dynamic experimental data. The results show that the improved algorithm can effectively suppress the angle oscillation, optimize the attitude convergence effect, and improve the accuracy of low cost inertial sensor attitude calculation.

Stabilized low-order finite-element formulation for static and dynamic simulation of saturated soils based on a hybrid integration scheme

This paper presents a stabilized linear finite-element formulation for three-dimensional (3D) elastoplastic static and dynamic coupled analyses of the soil skeleton and pore fluid. The proposed hybrid integration scheme can improve the speed and accuracy of the simulation while ensuring stability. The one-point reduced integration with hourglass stabilization and anti-locking strategy was used for the stress–strain calculation, while the full integration was adopted for analyzing other parts, such as the fluid phase. A robust pore-pressure stabilization method was derived to solve the oscillation problem for equal-order linear interpolation in the incompressible-undrained limit. In the field of large-scale 3D elastoplastic coupled solid–fluid simulations, academia has been committed to finding a method that considers the speed, stability, and accuracy of the simulation. The proposed finite-element formulation provides an effective solution for this purpose.

The Frequency Spectrum Analysis of Wideband Oscillations of Grid-Connected Voltage Source Converter

With the widespread application of voltage source converters (VSCs) in power systems with high renewable resource penetration, the problem of wideband oscillations caused by interactions between power converters and the power grid has drawn great attention. This paper presents a new methodology for simplifying the mathematical derivations of the impedance model of a VSC. Using the new simplified model, the stability and spectrum characteristics of the performance of the VSC can be clearly analyzed. The proposed second-order d-q impedance model of a grid-connected VSC in the presence of a PLL not only mathematically demonstrates that wideband oscillatory modes always occur in conjugate pairs, but also delivers a clear vision of the physical essence of these wideband oscillations. A classic modal analysis is executed in this paper to demonstrate the stability and frequency spectral characteristics of wideband oscillations in a VSC integrated system. The impact of the control parameters of the VSC on wideband oscillatory stability is thoroughly analyzed by modal analysis using ‘DIgSILENT PowerFactory’ as well as hardware-in-the-loop experiments. This methodology can be considered a powerful tool for the control design of VSCs in the modern power system.

An accurate power control strategy for electromagnetic rotary power controllers

AbstractWith the rapid development of active distribution networks, the “petal”‐type distribution network has become the mainstream power supply structure. Power control methods for active distribution networks should be further studied to ensure the safe and reliable power supply of a distribution system. An electromagnetic rotary power flow controller (RPFC) is a feasible solution for controlling power in active distribution networks. However, when testing the effectiveness of the PQ decoupled control method for RPFC based on instantaneous reactive power theory, difficulties were encountered with the synchronous control of the rotor position angle of two rotating‐phase transformers, and the accuracy of power control was unsatisfactory. Given this condition, PQ control is improved in three ways. First, the system's periodic oscillation problem is solved via variable speed control. Second, the servo motor‐rotary phase‐shifting transformer synchronous rotation scheme, which reduces power control error and improves stability, is designed. Third, the overshoot phenomenon in power control is improved using the variable‐domain fuzzy proportional‐integral adaptive method. Experimental results show that the proposed advanced control scheme exhibits good dynamic and static performance in power control scenarios and achieves effective improvement in RPFC.

Finite time adaptive synchronous control for fractional‐order chaotic power systems

AbstractAs a complex non‐linear system, the chaotic oscillation of power system seriously threatens the safe and stable operation of power grids. In this paper, a finite time adaptive synchronization control method is proposed to mitigate the problem of chaotic oscillation in the power system. The proposed method can realize chaos control and parameter identification by completely synchronizing the fractional‐order chaotic power system with the stable fractional‐order power system to identify parameters within a finite time. The fractional Lyapunov stability theory is used for numerical simulation. Theoretical and simulation results show that this method can effectively stabilize the system in a finite time. It is proved that compared with the adaptive synchronous control method, the control method is simpler in design, shorter in action time, and more meaningful in engineering practice.

Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation

We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by nonstationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed to accurately detect all oscillatory frequencies. A further phase-adjusted local change point detection algorithm is applied in the frequency domain to detect the locations at which the oscillatory pattern changes. Our method is shown to be able to detect all oscillatory frequencies and the corresponding change points within an accurate range with a prescribed probability asymptotically. A Gaussian approximation scheme and an overlapping-block multiplier bootstrap methodology for sums of complex-valued high dimensional nonstationary time series without variance lower bounds are established, which could be of independent interest. This study is motivated by oscillatory frequency estimation and change point detection problems encountered in physiological time series analysis. An application to spindle detection and estimation in electroencephalogram recorded during sleep is used to illustrate the usefulness of the proposed methodology. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.