Perturbation Parameter Research Articles

A Data-Driven Study of the Drivers of Stratospheric Circulation via Reduced Order Modeling and Data Assimilation

Stratospheric dynamics are strongly affected by the absorption/emission of radiation in the Earth’s atmosphere and Rossby waves that propagate upward from the troposphere, perturbing the zonal flow. Reduced order models of stratospheric wave–zonal interactions, which parameterize these effects, have been used to study interannual variability in stratospheric zonal winds and sudden stratospheric warming (SSW) events. These models are most sensitive to two main parameters: Λ, forcing the mean radiative zonal wind gradient, and h, a perturbation parameter representing the effect of Rossby waves. We take one such reduced order model with 20 years of ECMWF atmospheric reanalysis data and estimate Λ and h using both a particle filter and an ensemble smoother to investigate if the highly-simplified model can accurately reproduce the averaged reanalysis data and which parameter properties may be required to do so. We find that by allowing additional complexity via an unparameterized Λ(t), the model output can closely match the reanalysis data while maintaining behavior consistent with the dynamical properties of the reduced-order model. Furthermore, our analysis shows physical signatures in the parameter estimates around known SSW events. This work provides a data-driven examination of these important parameters representing fundamental stratospheric processes through the lens and tractability of a reduced order model, shown to be physically representative of the relevant atmospheric dynamics.

Current decoupling control of permanent magnet synchronous motor based on improved nonlinear extended state observer

Precise current decoupling is required to achieve good control performance in the vector control of permanent magnet synchronous motor (PMSM), but traditional decoupling methods are unable to solve the problem of poor current decoupling effectiveness when the system inductance parameters are mismatched. Therefore, a decoupling control method of PMSM based on improved nonlinear extended state observer (INESO) is proposed in this paper. Firstly, a smooth, differentiable nonlinear function is used to replace the traditional fal function, which overcomes the problem of discontinuous gain changes. Secondly, a time-varying gain is designed to address the problem of reduced observer performance due to differential peak values in traditional NESO. Finally, the stability of INESO and the current loop closed-loop system is proven, followed by simulation and experimental verification. The simulation and experimental results show the proposed method effectively observes and compensates for system uncertainties, including parameter perturbations, external disturbances, and unmodeled dynamics. This method achieves complete decoupling of d and q-axes currents, while suppressing interference and enhancing the control performance of PMSM. The proposed INESO decoupling method reduces the d-axis current fluctuation about 96% and 90% when the load changes abruptly under motor inductance parameter mismatch, and can reduce q-axis current fluctuation about 88% and 78% when the d-axis current steps, respectively, compared with the conventional Current Feedback Decoupling Control (CFDC) and CDDC decoupling methods.

Investigation of Erying–Powell fluid flow in the elliptical multi‐stenosed artery: Application of perturbation method via polynomial solutions

AbstractIn the current work, we analyzed the non‐Newtonian rheology of blood through a multi‐stenosed artery with a cross‐section of elliptical shape. The blood is regarded as Erying–Powell fluid, and flow is considered to have no slip at the stenotic wall. The mathematical model is processed to a non‐dimensional form, and conditions of mild stenosis are utilized to decrease its nonlinearity. The resulting equations are solved by applying the perturbation technique by considering the fluid characteristic parameter as the perturbation parameter. The solution is completed by using the polynomial of degree four. The solutions of mathematical equations are deeply examined by graphical analysis. The non‐Newtonian impacts are predominant in the surrounding of the stenosed wall along the minor axis of the elliptical artery. The height of stenosis affects the pressure rise and flow resistance. The shear stress at the arterial wall is very high in the stenotic region and has more potent effects in the neighboring boundary point on the minor axis. Progressive stenosis causes a reduction in the blood flow velocity surrounding the arterial wall due to higher resistance to the flow. However, the velocity improves near the center line of the artery. Further, the fluid's velocity is very high in the constricted (stenotic zone) region.

Long-time behavior of nonclassical diffusion equations with memory on time-dependent spaces

This paper aims to study the long-time behavior of nonclassical diffusion equation with memory and disturbance parameters on time-dependent space. By using the contractive process method on the family of time-dependent spaces and operator decomposition technique, the existence of pullback attractors is first proved. Then the upper semi-continuity of pullback attractors with respect to perturbation parameter ν in M t is obtained. It’s remarkable that the nonlinearity f satisfies the polynomial growth of arbitrary order.

Adaptive neural network H∞$H_\infty$ control for offshore platform with input delay and nonlinearity

AbstractIn this work, an adaptive learning robust controller is proposed to suppress the vibration of offshore platforms, which are subject to waves, winds, varying control delays and parametric perturbations. To realize nonlinear uncertainty approximation under the bounded performance, the controller incorporates both an online adaptive part and an offline fixed part. The adaptive part constructed by neural networks adjusts online, while the fixed part is obtained by regulating the performance. Importantly, adaptive updating strategy does not require accurate values or upper bounds for real‐time control delay or uncertainty. Several comparable experiments demonstrate the feasibility and effectiveness in vibration‐suppression of the designed adaptive controller in shallow/deep water. This scheme significantly reduces system response variations due to structural and hydrodynamic uncertainty, as well as additional random environmental forces caused by winds.

Pattern scaling the parameters of a Markov‐chain gamma‐distribution daily precipitation generator

AbstractGeneral circulation models (GCMs) are the most sophisticated tools at our disposal for studying future climates, but there are limitations to overcome. These include resolutions that may be too coarse for impact assessments, limited or zero availability of some policy‐relevant scenarios, and limited time‐series length for assessing the risk of extreme events. We illustrate how these limitations can be addressed by combining a stochastic precipitation generator (SPG) with pattern scaling (PS) of its key parameters. Computationally inexpensive, SPG parameters can be perturbed to generate time‐series representative of weather under a future climate with high spatial and temporal resolution. If the SPG parameter perturbations are derived directly from GCM simulations projections can only be made for scenarios already simulated by the GCM. Instead, we obtain the parameter perturbations using PS, facilitating emulation of scenarios not necessarily explicitly simulated by the GCM, and where we scale perturbations approximately linearly with global temperature change. PS is commonly applied to estimate perturbations in the mean of climate variables, but rarely to higher‐order parameters as we demonstrate here. We apply PS for the first time, globally, to the parameters of a daily, first‐order Markov‐chain gamma‐distribution SPG using output from the IPSL‐CM6A‐LR GCM to perturb an SPG fitted to observed data from two stations in diverse climates (Santarém, Brazil and Reykjavik, Iceland) to illustrate this novel approach. We produce time series corresponding to a range of GWLs and demonstrate the capability of the combined SPG‐PS approach to study local‐scale, future daily precipitation characteristics, climate and subsequent risk of extreme weather events.

Adaptive active and reactive power control strategy for virtual synchronous generator

SummaryWith the increase in the penetration level of renewables into the grid, the virtual synchronous generator (VSG) concept has emerged as an attractive solution for controlling grid‐tied inverters. The variation in reactive power also affects the real power of the system as well. To address the voltage variations and phase angle variations occurring because of the energy storage elements, the control of the reactive power loop (RPL) is important. Also, it is used to maintain voltage regulation and improve the power factor of the VSG system. This paper focuses on the damping of oscillations occurring because of load variation by proper adjustment of the rotational inertia, damping coefficient, droop coefficient, and regulatory coefficient of reactive power with a proposed adaptive control strategy. Small‐signal analysis of the active and reactive power and point of common coupling (PCC) have been derived, and the detailed dynamic performances are analyzed. The influences of parameters perturbation on PCC voltage and reactive power were investigated. Furthermore, adaptive control includes optimizing dynamic indexes such as rise time, delay time, and response settling time. Finally, the performance and improvement in the results of VSG with and without adaptive control are compared.

Global vs Blow-Up Solutions and Optimal Threshold for Hyperbolic ODEs with Possibly Singular Nonlinearities

We consider a hyperbolic ordinary differential equation perturbed by a nonlinearity which can be singular at a point and in particular this includes MEMS type equations. We first study qualitative properties of the solution to the stationary problem. Then, for small value of the perturbation parameter as well as initial value, we establish the existence of a global solution by means of the Lyapunov function and we show that the omega limit set consists of a solution to the stationary problem. For strong perturbations or large initial values, we show that the solution blows up. Finally, we discuss the relationship between upper bounds of the perturbation parameter for the existence of time-dependent and stationary solutions, for which we establish an optimal threshold.

Tension spline approach to singularly perturbed delay differential equations involving large delay

To solve the singlularly perturbed delay differential equations of convection type, spline in tension technique is used. Taylor series approximation is used to tackle the first order derivative term involved in the problem and finally a tridiagonal scheme is obtained, which is then solved by Thomas algorithm. An example is illustrated to show the method's applicability and it is solved numerically for different values of perturbation parameter. The maximum absolute errors and rate of convergence are given in tables and it is seen that our method is of first order convergent.

A generalized isogeometric boundary element method for the uncertain analysis of infinite domain two-dimensional acoustic problems

The key aim of this paper is to provide a new nth generalized order perturbed isogeometric fast multistage technique of boundary elements to compute the propagation of time harmonics in an infinite region. Structural geometry and boundary integral equations are constructed by using non-uniform rational B-splines. The source of system uncertainty is believed to be the incident plane wave number’s unpredictability. The actual field, depending on the input random variables, is simulated using the extended nth-order perturbation method. The field and kernel values for boundary integral formulas are generated via the nth-order generalized series of Taylor expansions using perturbation parameters. The fast multipole method (FMM) is utilized to speed up the process. The effectiveness and correctness of the proposed algorithm are verified by Monte Carlo simulations (MCs) with numerical examples.

Dynamic analysis and optimal control of a stochastic investor sentiment contagion model considering sentiments isolation with random parametric perturbations

Investor sentiment contagion has a profound influence on economic and social development. This paper explores the diverse influences of various investor sentiments in modern society on the economy and society. It also investigates the interference of various uncertain factors on investor sentiments in the modern economy and society. On this basis, the dual-system stochastic SPA2G2R model was constructed, incorporating positive and negative sentiments, as well as a supervision and isolation mechanism. The global existence of positive solutions was established, and sufficient conditions for the disappearance and steady distribution of investor sentiment were calculated. An optimal control strategy for the stochastic model was put forward, with numerical simulation supporting the theoretical analysis results. A comparison with parameter changes in the deterministic model was also conducted. The research reveals a competitive relationship between different investor sentiments. Enhancing societal guidance mechanisms promotes positive investor sentiment contagion. Timely control by the supervisory department effectively curbs the spread of investor sentiment. Additionally, white noise promotes investor sentiment contagion, suggesting effective regulation through control of noise intensity and disturbance parameters.

Revisiting coupled CDM-massive neutrino perturbations in diverse cosmological backgrounds

Massive neutrinos are well-known to cause a characteristic suppression in the growth of structures at scales below the neutrino free-streaming length. A detailed understanding of this suppression is essential in the era of precision cosmology we are entering into, enabling us to better constrain the total neutrino mass and possibly probe (beyond)-ΛCDM cosmological model(s). Instead of the usual N-body simulation or Boltzmann solver, in this article we consider a two-fluid framework at the linear scales, where the neutrino fluid perturbations are coupled to the CDM (+ baryon) fluid via gravity at redshifts of interest. Treating the neutrino mass fraction f ν as a perturbative parameter, we find solutions to the system with redshift-dependent neutrino free-streaming length in ΛCDM background via two separate approaches. The perturbative scale-dependent solution is shown to be in excellent agreement with numerical solution of the two-fluid equations valid to all orders in f ν, and also agrees with results from CLASS to a good accuracy. We further generalize the framework to incorporate different evolving dark energy backgrounds and found sub-percent level differences in the suppression, all of which lie within the observational uncertainty of BOSS-like surveys. We also present a brief discussion on the prospects of the current analysis in the context of upcoming missions.

Dual Event-Triggered Control for Asynchronous Scheduling Parameter Varying Networked Switched Systems Under DoS Attacks

Networked switched quasi-linear parameter varying (LPV) systems can effectively describe the parameter degradation or perturbation of actual systems. For a quasi-LPV networked control system, it may be threatened by various attacks, and the communication barriers caused by attacks, delays, and triggers further make the scheduling between the controller and the system asynchronous. In this article, the event-triggered control for switched quasi-LPV system subject to denial-of-service attacks and scheduling asynchronization is concerned. Two event-triggering mechanisms are utilized to reasonably adjust the communication frequency of state and scheduling variables, which can reduce their transmission risk of being attacked. Under the influence of periodic and aperiodic DoS attacks, complete event-triggered control schemes for networked switched quasi-LPV system are given. Especially, a set of sufficient conditions for analysis and synthesis is presented, which solves the tricky problem of scheduling asynchronization. Finally, a numerical simulation and a switched <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> system example are given to verify the effectiveness of the proposed method.

A stable numerical method for singularly perturbed Fredholm integro differential equation using exponentially fitted difference method

This paper implemented a stable numerical scheme for solving singularly perturbed linear second-order Fredholm integro-differential equation. A parameter-uniform numerical method was constructed using an exponentially fitted finite difference method to approximate the differential part and the composite Simpson 1/3 rule for the integral part of the equation. The scheme’s stability and convergence analysis has been carried out. The maximum absolute errors and the rate of convergence are tabulated for different values of the perturbation parameter ɛ and mesh sizes using different numerical test examples.

Improved dynamic event-triggered [formula omitted] control for networked fuzzy singularly perturbed systems with hidden Markov fading channels

In this paper, the dynamic event-triggered H∞ control problem is explored for networked fuzzy slow sampling singularly perturbed systems (S3PSs) subject to hidden Markov fading channels. To alleviate the communication burden more effectively, an improved dynamic event-triggered scheme (DETS) is constructed for networked fuzzy S3PSs, under which two auxiliary internal dynamic variables are considered into event-triggered condition. The fading channel phenomena with randomly time-varying amplitudes are characterized by the finite state Markov process. Meanwhile, considering the actual network mode may be unmeasurable, a hidden Markov mode detector is exploited to estimate the actual network mode, by which the control signal can be adjusted appropriately. By constructing the singular perturbation parameter (SPP)-dependent Lyapunov functional, sufficient conditions are obtained to guarantee the mean square stability of networked fuzzy S3PSs. Besides, the numerical ill-conditioned problem of networked fuzzy S3PSs can be avoided. Finally, a tunnel diode circuit example is proposed to illustrate the effectiveness of the main results.

Optimization Strategy for Output Voltage of CCM Flyback Converter Based on Linear Active Disturbance Rejection Control

To solve the problem of system output voltage fluctuation caused by interferences such as load fluctuation and internal inductor parameter perturbation in a flyback converter, a second-order linear active disturbance rejection control (LADRC) strategy based on output voltage is proposed in this paper. A small-signal model of a CCM flyback converter is established, and the equivalent transfer function of voltage control based on second-order LADRC is derived. A second-order LADRC is constructed, and a parameter design method for the controller is proposed. The response characteristics of the output voltage of the converter under five internal and external disturbances of different control strategies are compared and studied using MATLAB R2022b/Simulink simulation software, and a CCM flyback converter experimental platform based on dSPACE is built to verify the corresponding comparative experiments. The simulation and experimental results jointly verify the superiority of the control strategy for the anti-interference and robustness of the output voltage of the CCM flyback converter.

Non‐Newtonian laminar pulsating heat and fluid flow in plane duct

AbstractIn the present study, laminar pulsating power‐law momentum and heat transfer in a uniformly heated plane duct is studied analytically. Assuming that fully developed conditions exist both hydrodynamically and thermally, a perturbation series method is utilized to derive analytical solutions for the momentum and energy balance equations, and the amplitude is prescribed as the perturbation parameter. For varying values of the power‐law index (), representing pseudoplastic, Newtonian, and dilatant fluids, effects of dimensionless amplitude () and frequency () on periodic and period‐averaged friction factor and Nusselt number are obtained. The results obtained for Newtonian fluid are shown to be in good harmony with the corresponding findings in the open literature.

Traveling waves in a quintic BBM equation under both distributed delay and weak backward diffusion

In this paper, we focus on the existence of periodic and solitary waves for a quintic Benjamin–Bona–Mahony (BBM) equation with distributed delay and diffused perturbation. The corresponding traveling wave equation is transformed into a three-dimensional dynamical system, which is regarded as a singularly perturbed system for small perturbation parameter. By geometric singular perturbation theory, the three-dimensional dynamical system can be reduced to a near-Hamiltonian planar system and a locally invariant manifold diffeomorphic to the critical manifold with normally hyperbolicity can be constructed. Further, the existence of periodic wave and solitary wave are established by proving the persistence of periodic and homoclinic orbits of the near-Hamiltonian planar system for sufficiently small perturbation, and their existence conditions for the delayed quintic BBM equation have also been obtained. The uniqueness of periodic wave is established by analyzing the monotonicity of ratios of Abelian integrals form a Chebyshev set. Moreover, the monotonicity of wave speed is proved, and the supremum and infimum of wave speed are gotten. Numerical simulations are in complete agreement with the theoretical predictions.

Numerical study of flame inclination instability in a packed bed with extra lean methane/air intake by an adaptive multi-scale model

The common numerical method to simulate the evolution of flame instability during filtration combustion mainly includes volume average method and pore scale simulation. However, they are not satisfying in computation accuracy and cost respectively. In this paper, a self-developed adaptive multi-scale model is built to study the inclination instability of the flame front in a packed bed with honeycomb ceramics. The perturbations on the distribution of the intake parameters and physical properties of fillings in the packed bed lead to the flame inclination. The influences of the amplitude and range of the perturbations on the flame inclination development are investigated. The development mechanism of flame inclination is analyzed by method of flow competition (MFC) theory. The results show that the increase of the flame inclination angle will enhance the transversal heat transfer. Subsequently, the radiation and conduction fluxes restrain the increase of the flame inclination. Under the same level of perturbation amplitude, the result shows that the influence sequences of the four factors for the flame inclination are as follows: fillings porosity, feed flow rate, fillings heat capacity, and feed concentration. In addition, larger amplitude of perturbation leads to higher maximum flame inclination angle. However, the perturbation range has little influence on the development of flame inclination angle. Finally, the flame inclination is restrained successfully through adding new perturbation of intake parameters or elimination of initial perturbation. The above.studies are quite meaningful to the stable operation and wide application of porous media combustion technology in the utilization of low calorific value gas energy.

Model-free adaptive chaos control for the boost converter

In order to solve the dynamic analysis and chaotic motion control problems of the current-mode-controlled Boost converter system, a state equation model in the continuous current mode is established. The evolutionary path of the periodic motion of the system through the doubling bifurcation to the chaotic motion is analyzed by the bifurcation diagram, Poincaré sections and phase portraits. Then, according to the fundamental principle of the resonant parametric perturbation (RPP) method, a controller is designed based on the model-free adaptive control (MFAC) method to output the perturbation amplitude, and the disturbance quantity is calculated according to the perturbation amplitude. By adding a small amplitude disturbance to the controllable parameter of the controlled system, the chaotic motion of the system is guided to expected periodic orbit. The advantage of this method is that no precise mathematical model (PMM) of the system is required. At the same time, the design of the controller is simple and easy to implement.