Problem Of Oscillations Research Articles

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.

Hybrid Particle Swarm Optimization for High-Dimensional Latin Hypercube Design Problem

Latin Hypercube Design (LHD) is widely used in computer simulation to solve large-scale, complex, nonlinear problems. The high-dimensional LHD (HLHD) problem is one of the crucial issues and has been a large concern in the long run. This paper proposes an improved Hybrid Particle Swarm Optimization (IHPSO) algorithm to find the near-optimal HLHD by increasing the particle evolution speed and strengthening the local search. In the proposed algorithm, firstly, the diversity of the population is ensured through comprehensive learning. Secondly, the Minimum Point Distance (MPD) method is adopted to solve the oscillation problem of the PSO algorithm. Thirdly, the Ranked Ordered Value (ROV) rule is used to realize the discretization of the PSO algorithm. Finally, local and global searches are executed to find the near-optimal HLHD. The comparisons show the superiority of the proposed method compared with the existing algorithms in obtaining the near-optimal HLHD.

An Improved Perturbation Observation Method with Variable

Aiming at the problems of oscillation and misjudgment in traditional MPPT technology, the influence of voltage disturbance step size on the tracking of the maximum power point is studied. On this basis, an improved method based on the slope and space division of output characteristic curve is proposed. The voltage disturbance is carried out by using a fixed step length outside the set search interval, so that the photovoltaic cells can quickly work near the maximum power point. Reduce the early search time; When the photovoltaic cell is working near the maximum power point, the voltage disturbance is carried out with small steps to avoid the oscillation caused by repeated pulsation of the operating point around the maximum power point. Meanwhile, the search space is further divided to reduce the search interval. Static and dynamic lighting modes were simulated by Simulink.

Optimal design of the forced oscillation frequencies of the minimum surface shell on a circular contour consisting of two inclined ellipses under thermal and power loading

The problem of choosing the optimal design solution is a multi-purpose complex task, the solution of which requires taking into account a wide range of requirements for different stages of implementation. There are several levels of solving optimal design problems. The first level deals with general design models, including the main structural elements, taking into account the physical and geometric features of their behavior. This level can be called the "global" level of optimization. Due to the fact that the automated calculation of structures is impossible without the use of finite element models, and at the next "detailed" level, the parameters that make up this model (coordinates of nodes, physical and geometric properties of individual elements, etc.)
 The choice of a finite element model for optimal design is directly related to the complexity (the possibility of computer implementation) of the optimal design problem. To reduce the computational procedures associated with solving the problem of numerical analysis, an approach based on the approximation of system parameters (displacements, forces, frequencies, waveforms, etc.) can be used.
 The problem of forced oscillations for shells of minimal surfaces is solved by the finite element method using the Lagrange's variational principle. The potential and kinetic deformation energies of the shell of a minimal surface are defined in matrix form as the sum of the potential and kinetic energies of each finite element.
 The optimization algorithm for single-criterion parametric optimization is performed as follows: the objective function is the weight of the shell of the minimum surface on a circular contour consisting of two inclined ellipses, the design variables are the thickness of the shell, and the constraints are represented by the first forced vibration frequency. The results of changing the objective function are a decrease in the weight of the shell by 3050 kg of C240 steel, which is a percentage equivalent of 13.4% without loss of strength and stability of the shell of the minimum surface on a circular contour consisting of two inclined ellipses, which proves the effectiveness of the authors' methodology.

A P&O Based Variable Step Size MPPT Algorithm for Photovoltaic Applications

Maximum power point tracking (MPPT) is an indispensable component of the Photovoltaic (PV) systems to maximize efficiency. Perturb and observe (P&O) is one of the prevalent MPPT methods owing to its easier structure for implementation but it suffers from problems of slow tracking and oscillations around the MPP. In this paper, a modified variable step size MPPT algorithm based on P&O method is proposed to obtain maximum power output from the PV system coupled with a boost DC-DC converter. The proposed method employs the scaled power difference as a control variable to enable variation of step size for each cycle. Results obtained by simulation and experimental work verified that the proposed algorithm is potent mitigating the problems related with classical P&O method.

A Mixed‐Flux‐Based Nodal Discontinuous Galerkin Method for 3D Dynamic Rupture Modeling

AbstractNumerical simulation of rupture dynamics provides critical insights for understanding earthquake physics, while the complex geometry and heterogeneous material properties of natural faults make numerical method development challenging. The discontinuous Galerkin (DG) method is suitable for handling these complexities. In the DG method, the fault boundary conditions can be conveniently imposed through the upwind flux by solving a Riemann problem based on a velocity‐strain elastodynamic equation. However, the universal adoption of upwind flux can cause spatial oscillations in cases where elements on adjacent sides of the fault surface are not nearly symmetric. Here we propose a nodal DG method with an upwind/central mixed‐flux scheme to solve the spatial oscillation problem and thus reduce the dependence on mesh quality. Our method can achieve high scalability in parallel computing under different orders of accuracy. We verify the new method by comparing simulation results with those from other methods on a series of published benchmark problems with complex fault geometries, heterogeneous materials, off‐fault plasticity, roughness, thermal pressurization, and various versions of fault friction laws. Finally, we demonstrate that our method can be applied to simulate the dynamic rupture process of the 2008 Mw 7.9 Wenchuan earthquake along realistic fault geometry, including branches, step‐overs and a previously neglected sub‐parallel fault segment, offering a high potential to systematically explore the influences of fault zone properties on earthquake rupture dynamics.

Numerical Approximation of Oscillatory Initial Value Problem Using the Homotopy Analysis Algorithm

In this paper, we present numerical approximation for oscillatory initial value problems (IVPs) using the homotopy analysis algorithm. The convergence of the method is discussed and numerical experiments are presented to illustrate the computational effectiveness of the algorithm. The results obtained are in good agreement with the exact solutions and Adomian decomposition method (ADM). These results show that the algorithm introduced here is accurate and easy to apply without linearization.

Robust anti-disturbance control of a high-pressure electro-pneumatic servo valve directly driven by voice coil motor

System uncertainty, external disturbances and complex nonlinearities are the main obstacles for high precision control of HESVs. Due to good anti-disturbance capability and low model dependence, linear active disturbance rejection control (LADRC) is popular in engineering practice. However, when LADRC is applied to HESVs, LADRC has limited anti-disturbance capability for high-pressure gas flow force, slow response speed and small response bandwidth, and quickly causes step oscillations. In this paper, the reasons for the remarkable phenomenon of step oscillations and the limited anti-disturbance capability of LADRC are theoretically analyzed and then proved by simulations and experiments. Subsequently, a new robust anti-disturbance control method (RI-ESO) is proposed for the HESV to solve the problem of step oscillations and further improve the dynamic response and anti-disturbance capability. The RI-ESO combines an extended state observer (ESO) and a robust controller. The partial total disturbance is estimated by ESO and then compensated online. The robust integrated controller (RI) can further compensate the remaining nonlinearities and external disturbances to achieve better control performance. The introduction of ESO can reduce the parameter limitations of the robust controller. Various simulations and experiments demonstrate that the RI-ESO can greatly improve the control performance and anti-disturbance capability of HESVs, and effectively avoid step oscillations.

Stability of Finite Difference Solution of Time-Dependent Schrodinger Equations

In this paper, the stability of finite difference methods for time-dependent Schrodinger equation with Dirichlet boundary conditions on a staggered mesh was considered with explicit and implicit discretization. Using the matrix representation for the numerical algorithm, it is shown that for the explicit finite difference method, the solution is conditionally stable while it becomes unconditionally stable for implicit finite difference methods. A 1D Harmonic Oscillator problem shall be used to illustrate this behaviour.

Harmonic oscillator in the context of the extended uncertainty principle

At large-scale distances where the space-time is curved due to gravity, a nonzero minimal uncertainty in the momentum, [Formula: see text], is being estimated to emerge. The presence of minimal uncertainty in momentum allows a modification to the quantum uncertainty principle, which is known as the extended uncertainty principle (EUP). In this work, we handle the harmonic oscillator problem in the EUP scenario and obtain analytical exact solutions in classical and semi-classical domains. In the classical context, we establish the equations of motion of the oscillator and show that the EUP-corrected frequency is depending on the energy and deformation parameter. In the semi-classical domain, we derive the energy eigenvalue levels and demonstrate that the energy spectrum depends on [Formula: see text], as the feature of hard confinement. Finally, we investigate the impact of the EUP on the harmonic oscillator’s thermodynamic properties by using the EUP-corrected partition functions in the classical limit in the (A)dS backgrounds.

Mechanism Analysis of Multiple Disturbance Factors and Study of Suppression Strategies of DFIG Grid-Side Converters Caused by Sub-Synchronous Oscillation

With the increasing utilization of electronic equipment in the power system, sub-synchronous oscillation (SSO) has occurred many times and caused off-grid accidents because of power oscillation. SSO has become one of the main problems that restrict the development of new energy. In this paper, power oscillation in grid-side converters (GSCs) in doubly-fed induction generators (DFIGs) under SSO is studied. Firstly, the influence mechanism of SSO on GSC multipath disturbance is studied. Secondly, the problem of coupling oscillation caused by PLL output errors after coordinate transformation is studied, and the mathematical model of GSC output power considering SSO multipath disturbance is established. By analyzing the oscillation suppression ability of the quasi-resonant controller under variable SSO states, the key influencing factors of SSO for GSC power oscillation suppression strategies are determined. Furthermore, based on the above theoretical analysis and research, an improved PLL is designed to eliminate the influence of its output errors on the disturbance of GSC. At the same time, a DFIG-GSC power oscillation suppression strategy using an adaptive quasi-resonant controller is designed to eliminate the influence of SSO on the multi-path disturbance of GSC. Finally, the effectiveness of the proposed suppression strategy is verified using simulation and experimental results.

Small-signal modeling and wide-band oscillation analysis with the high proportion of renewable energy integrated through LCC-HVDC

With the high proportion of renewable energy through high-voltage direct current (HVDC) transmission into the grid and the application of high proportion of power electronic equipment, in the modern power system, the traditional electromagnetic conversion equipment represented by synchronous generators is gradually replaced by power electronic equipment, which in a high level has been affecting the dynamic behavior of the power system. In recent years, the wide-band oscillation problem of unknown mechanism continues to appear in power systems, which poses a major threat to the security, stability, and operation of power systems. Therefore, based on the typical oscillation event, this paper constructs a typical small-signal model of the new power system which is composed of synchronous generator, HVDC transmission equipment, and renewable energy generation equipment. The model is suitable for the analysis of wide-band oscillation problem of the new power system with renewable energy as the main body. The comparison of time-domain response with the detailed time-domain model shows that the proposed small-signal model can well reflect the dynamic behavior of the detailed time-domain model. Based on the model, the influence of access distance, access proportion, and operation and control modes of renewable energy integrated through LCC-HVDC on the wide-band oscillation characteristics of the system is analyzed, and the correctness of the analysis is verified by the detailed time-domain model.

Interval estimation on hyper-order of meromorphic solutions of complex linear differential equations with uncertain coefficients

The authors address the complex oscillation problems of all solutions of homogenous linear differential equations with meromorphic coefficients. Sufficient conditions for estimating the growth of meromorphic solution with infinite order have been proposed based on Nevanlinna value distribution theory. Compared with the existing results, the proposed hyper-order of all meromorphic solutions with infinite order can be estimated in terms of a bounded interval which includes information of order of growth of meromorphic functions and meromorphic polynomial coefficients.

A Grey Wolf Optimizer algorithm based fuzzy logic power system stabilizer for single machine infinite bus system

Low-frequency power oscillations in power systems have always been a serious risk for a stable power system. A fuzzy logic power system stabilizer (FLPSS) is proposed to mitigate system oscillation problems. Aimed at parameter configuration and rule setting of FLPSS, Grey Wolf Optimizer (GWO) based FLPSS is utilized to achieve quicker settling time and improve the damping oscillation effectiveness. Comparative studies between the proposed GWO-based FLPSS and conventional stabilizers are performed on a single-machine infinite bus system(SMIBS). The simulation results demonstrate the GWO-based FLPSS can better dampen out low-frequency oscillations and maintain the electricity network stability.

Exact solution to the problem of slow oscillations in coronal loops and its diagnostic applications

Magnetoacoustic oscillations are nowadays routinely observed in various regions of the solar corona. This allows them to be used as means of diagnosing plasma parameters and processes occurring in it. Plasma diagnostics, in turn, requires a sufficiently reliable MHD model to describe the wave evolution. In our paper, we focus on obtaining the exact analytical solution to the problem of the linear evolution of standing slow magnetoacoustic (MA) waves in coronal loops. Our consideration of the properties of slow waves is conducted using the infinite magnetic field assumption. The main contribution to the wave dynamics in this assumption comes from such processes as thermal conduction, unspecified coronal heating, and optically thin radiation cooling. In our consideration, the wave periods are assumed to be short enough so that the thermal misbalance has a weak effect on them. Thus, the main non-adiabatic process affecting the wave dynamics remains thermal conduction. The exact solution of the evolutionary equation is obtained using the Fourier method. This means that it is possible to trace the evolution of any harmonic of the initial perturbation, regardless of whether it belongs to entropy or slow mode. We show that the fraction of energy between entropy and slow mode is defined by the thermal conduction and coronal loop parameters. It is shown for which parameters of coronal loops it is reasonable to associate the full solution with a slow wave, and when it is necessary to take into account the entropy wave. Furthermore, we obtain the relationships for the phase shifts of various plasma parameters applicable to any values of harmonic number and thermal condition coefficient. In particular, it is shown that the phase shifts between density and temperature perturbations for the second harmonic of the slow wave vary between π/2 to 0, but are larger than for the fundamental harmonic. The obtained exact analytical solution could be further applied to the interpretation of observations and results of numerical modelling of slow MA waves in the corona.

A Comparative Study of Two Common Pump-Controlled Hydraulic Circuits for Single-Rod Actuators

Pump-controlled hydraulic circuits are proven to be more efficient than conventional valve-controlled circuits. Pump-controlled hydraulic circuits for double rod cylinders are well developed and are in use in many practical applications. Existing pump-controlled circuits for single-rod actuators experience oscillation issues under specific operating conditions; that is identified as a critical operating zone on the load-velocity plane. The challenge in these circuits is to find out the proper way to compensate for the differential flow at both sides of the cylinder in all operating conditions. The two main types of valves commonly used by researchers, to compensate for differential flow in single-rod cylinder circuits, are: pilot-operated check valves, and shuttle valves. In this research, a performance comparison between circuits equipped with either valves, in terms of the size of the critical zone and the oscillations’ characteristics, was accomplished. Simulation studies showed that the circuits that utilize pilot-operated check valves possesses smaller oscillatory zones and less severe oscillations, when compared to circuits with shuttle valves. Experimental work verified the simulation results and proved the accuracy of the mathematical models. Hence, pump-controlled circuits with pilot-operated check valves are recommended to be the basic platform for further efforts to solve the oscillation problem in pump-controlled circuits.

Rusanov’s Third-Order Accurate Scheme for Modeling Plasma Oscillations

A modification of the well-known Rusanov third-order accurate scheme is proposed for modeling nonrelativistic oscillations of a cold plasma. Only first- and second-order accurate schemes were used earlier for similar computations in Eulerian variables. In the case of a test problem with a smooth solution, the errors of the constructed scheme are investigated and compared with the errors of the MacCormack scheme. For the problem of free plasma oscillations induced by a short intense laser pulse, numerical results are presented concerning the conservation of energy and an additional function for both schemes and the accuracy of the electron density in the center of the domain. It is concluded that the Rusanov scheme is superior theoretically, although the MacCormack scheme is more suitable for applications, primarily, for computations of long-lived processes and cold plasma oscillations similar to actual ones. A theoretical analysis of approximation and stability, together with experimental observations of quantitative characteristics of the error for the most sensitive quantities, significantly improves the reliability of the computations.

NUMERICAL APPROXIMATION OF OSCILLATORY INITIAL VALUE PROBLEMS USING THE HOMOTOPY ANALYSIS ALGORITHM

In this paper, we present numerical approximation for oscillatory initial value problems (IVPs) using the homotopy analysis algorithm. The convergence of the method is discussed and numerical experiments are presented to illustrate the computational effectiveness of the algorithm. The results obtained are in good agreement with the exact solutions and Adomian decomposition method (ADM). These results show that the algorithm introduced here is easy to apply without linearization.

Intelligent Control of a Space Manipulator Ground Unfold Experiment System with Lagging Compensation

In ground testing of space manipulators, gravity compensation is a critical testing requirement. The objective of this paper was to design a space manipulator gravity compensation test platform for ground tests and solve the problems of force control oscillation and precision degradation caused by the execution lag encountered in the development process. An intelligent PID controller was designed for this active-suspension gravity compensation experimental mechanism of a space manipulator on the ground, and a specially designed second-order method was used to solve the problem of the execution lag in this mechanism. The intelligent controller was developed based on adaptive dynamic programming and redesigned to improve its transient performance. The simulation was carried out, and its results were compared with the results on a real machine to demonstrate the effectiveness of this set of experimental controllers. This paper compares in detail the results of the designed method on system input and output and shows the effectiveness of this method in dealing with the execution lag of the mechanism. In conclusion, in this work, we successfully designed and implemented an intelligent PID controller for an active-suspension gravity compensation experimental mechanism of a space manipulator on the ground, and the experimental results demonstrate the effectiveness of the proposed method.

Subsynchronous oscillation analysis method based on broad learning system

This paper presents a method to analyze the Sub Synchronous Oscillation (SSO) problem based on broad learning system (BLS), which can quickly analyze the risk of SSO in a system and take measures. The simulation system is constructed by the eigenvalue analysis method to obtain training data, that solves the problem which is difficult to obtain actual data in SSO problem and makes the model more accurate and the conclusion more convincing. Subsequently, BLS is applied for feature extraction and the prediction model is constructed, the model can show the deep relationship between the oscillation source and topology of the system as well as various operating data, which is difficult to be expressed by formula. The system was tested and validated in the 41-bus system. The feature importance analysis method which comes from eXtreme Gradient Boosting (XGboost) algorithm is proposed and combined with the BLS prediction model, which can analyze the influence of each variable on the prediction results in different series compensation levels, and is validated in the 41-bus system, that makes the results of prediction more interpretable. Finally, the results of simulation show that the model can predict data with high accuracy and give adjustment plans for effective control of the system to avoid the risk of SSO.