Perturbation Parameter Research Articles

A synchronization method based on current orthogonal decomposition considering harmonic components for wireless power transfer system

AbstractIn order to improve the wireless power transfer (WPT) system, an active rectifier is commonly used. Synchronization technology is critical for active rectifier. The traditional synchronization method based on zero‐crossing detection (ZCD) is unstable and not suitable for the case with lots of harmonic component in the resonant current. Here, a new synchronization method with harmonic compensation is proposed for the WPT system without the ZCD of the resonant current. A mathematical model is built to analyse and compensate the impact caused by the harmonic on phase angle. Therefore, the proposed method can be applied to the high‐order resonant network like LCC compensated topology where the harmonic component is rich in the resonant current. For verifying the proposed synchronization method, a laboratory prototype is built. The experimental results prove that the system can operate stably with parameter perturbation and different load. The peak transfer efficiency of the system can achieve the 94.5%.

Effects of rotation and chemical reactions on an electroconvection in Maxwell dielectric nanofluids within anisotropic porous media

ABSTRACT This study explores the complex interactions between rotation, chemical reactions, and electroconvection in Maxwell dielectric nanofluids within anisotropic porous media. The research aims to elucidate how these factors influence the heat transfer efficiency and fluid dynamics under the influence of external alternating current (AC) electric fields. The normal mode method is employed to analyse the stability of the system, allowing for the examination of oscillatory modes and their growth rates. By introducing perturbations in the physical parameters, the study derives a set of ordinary linear differential equations that characterize the system's response to external influences. The coupled differential equations were solved using the Galerkin approach for first approximation while meeting the necessary boundary conditions. Analytical solution of the representative equation for stress-free boundary states yields Rayleigh number formulas for nonoscillatory and oscillatory mode occur. Oscillatory modes are seen for both bottom and top-heavy nanoparticle distributions. The electric Rayleigh number, thermal Prandtl number, and stress relaxation parameter increases, whereas the Brinkman-Darcy number delays the onset of stationary and oscillatory convection. The study finds that positive concentration Rayleigh numbers stabilize the system, while negative ones lead to instability. Additionally, it demonstrates that external alternating current electric fields influence convection behavior and provides formulas for critical Rayleigh numbers, enhancing our understanding of fluid interactions in various engineering and technological applications.

Prescribed Performance Control for PEM Fuel Cell Air Supply System Based on Fully Actuated Approach With Fixed Regulation Time

ABSTRACTThe problem of air feed system control with guaranteed prescribed performance and fixed time control is investigated for proton exchange membrane fuel cell (PEMFC). First of all, the original model of PEMFC air feed system is converted to fully actuated system using higher order fully actuated system (HOFAS) approach. A fixed time extended state observer (ESO) is employed to approximate the cathode pressure. The parameter uncertainty is compensated by an adaptive radial basis function neural network (RBFNN). Then a prescribed performance sliding mode controller is designed with fixed convergence time. The proposed control law could guarantee the prescribed transient response for oxygen excess ratio (OER) error under stack current changing and bounded uncertainty. Lyapunov approach is utilized to proof fixed‐time stability of proposed controller. Simulation results of the study tests illustrate that the presented controller is efficient under constant OER tracking control, constant OER tracking control with parameter perturbation, and variable OER tracking control, respectively.

Uncertainty quantification in the modal analysis of aircraft stiffeners: A Perturbation Technique approach in SFEM

Structural members, such as stiffeners, are crucial in aeronautical structures, providing essential dynamic stiffness. However, variability introduced by manufacturing and assembly processes, as well as material inconsistencies, can lead to uncertainties in structural performance. It is crucial to incorporate these uncertainties into structural analysis to ensure reliable design. This paper utilizes the Stochastic Finite Element Method (SFEM) to address uncertainties in typical structural members used in aeronautics. The Perturbation Technique, based on Taylor series expansions, was employed to model uncertainties in aircraft stiffeners. The study focuses on natural frequencies and modal analysis to evaluate the impact of uncertainties on beams with hat and Z sections, commonly used as stiffeners in aircraft panels. These stiffeners were modeled using the Timoshenko beam theory, and sensitivity analysis was performed to identify key contributors to variability. The perturbation parameter was validated through Monte Carlo simulations. Sensitivity analysis, employing gradient-based methods, identified significant factors affecting variability in natural frequencies. A different perturbation parameter was necessary based on the stiffener's geometry: thickness variations required a perturbation parameter on the order of 10−3, whereas dimensions changes in the flange and height required parameters on the order of 10−2. These results underscore the importance of choosing appropriate perturbation magnitudes to avoid inaccuracies in the deterministic frequency response. Once a perturbation parameter is established, it can be applied to similar regions, ensuring the robustness of the SFEM methodology in analyzing the dynamic response of aeronautical structural reinforcements.

Optical solitons, qualitative analysis, and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation

In this paper, we study the highly dispersive nonlinear perturbation Schrödinger equation, which has arbitrary form of Kudryashov's with sextic‐power law refractive index and generalized nonlocal laws. For the equation has highly dispersive nonlinear terms and higher order derivatives, it cannot be integrated directly, so we build an integrable factor equation for the approximated equation and apply the trial equation method and the complete discrimination system for polynomial method to create new soliton solutions. On the other hand, we use the bifurcation theory to qualitatively analyze the equation and find the model has periodic solutions, bell‐shaped soliton solutions, and solitary wave solutions via phase diagrams. The topological stability of the solutions with respect to the parameters is explored in order to better understand the effect of parameters perturbations on the stability of the model's solutions. Furthermore, we analyze the modulation instability and give the corresponding linear criterion. After accounting for external perturbation terms, we analyze the chaotic behaviors of the equation through the largest Lyapunov exponents and phase diagrams.

General-Kindred physics-informed neural network to the solutions of singularly perturbed differential equations

Physics-informed neural networks (PINNs) have become a promising research direction in the field of solving partial differential equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the field of PINN. The solution of singular perturbation problems often exhibits sharp boundary layers and steep gradients, and traditional PINN cannot achieve approximation of boundary layers. In this manuscript, we propose the General-Kindred physics-informed neural network (GKPINN) for solving singular perturbation differential equations (SPDEs). This approach utilizes asymptotic analysis to acquire prior knowledge of the boundary layer from the equation and establishes a novel network to assist PINN in approximating the boundary layer. It is compared with traditional PINN by solving examples of one-dimensional, two-dimensional, and time-varying SPDE equations. The research findings underscore the exceptional performance of our novel approach, GKPINN, which delivers a remarkable enhancement in reducing the L2 error by two to four orders of magnitude compared to the established PINN methodology. This significant improvement is accompanied by a substantial acceleration in convergence rates, without compromising the high precision that is critical for our applications. Furthermore, GKPINN still performs well in extreme cases with perturbation parameters of 1×10−38, demonstrating its excellent generalization ability.

Statistical Response of ENSO Complexity to Initial Condition and Model Parameter Perturbations

Abstract Studying the response of a climate system to perturbations has practical significance. Standard methods in computing the trajectory-wise deviation caused by perturbations may suffer from the chaotic nature that makes the model error dominate the true response after a short lead time. Statistical response, which computes the return described by the statistics, provides a systematic way of reaching robust outcomes with an appropriate quantification of the uncertainty and extreme events. In this paper, information theory is applied to compute the statistical response and find the most sensitive perturbation direction of different El Niño–Southern Oscillation (ENSO) events to initial value and model parameter perturbations. Depending on the initial phase and the time horizon, different state variables contribute to the most sensitive perturbation direction. While initial perturbations in sea surface temperature (SST) and thermocline depth usually lead to the most significant response of SST at short and long ranges, respectively, initial adjustment of the zonal advection can be crucial to trigger strong statistical responses at medium range around 5–7 months, especially at the transient phases between El Niño and La Niña. It is also shown that the response in the variance triggered by external random forcing perturbations, such as the wind bursts, often dominates the mean response, making the resulting most sensitive direction very different from the trajectory-wise methods. Finally, despite the strong non-Gaussian climatology distributions, using Gaussian approximations in the information theory is efficient and accurate for computing the statistical response, allowing the method to be applied to sophisticated operational systems. Significance Statement The purpose of this work is to better understand how El Niño–Southern Oscillation (ENSO) responds to changes in its initial state and internal dynamics or external forcings. A statistical quantification of this response allows for the comprehension of the triggering conditions and the effect of climate change on the occurrence frequency and strength of each type of ENSO event. Such a study also allows to detect the most sensitive perturbation directions, which has practical significance in guiding anthropogenic activities. The approach used to study the response in this work is through the framework of information theory, which allows for an unbiased and robust assessment of the statistical response that is not affected by the turbulent dynamics of the system.

Numerical Treatment for the Caputo-Fabrizio Fractional Smoking Model using an Efficient Numerical Technique

Smoking is a prevalent social behavior widely practiced worldwide, especially in settings such as schools and some significant gatherings. Based on the World Health Organization (WHO), smoking is the third leading source of human mortality and the primary preventable cause of disease. This study introduces a highly efficient simulation technique to analyze and solve the Caputo-Fabrizio (CF) fractional smoking model. We numerically solve the fractional integral equations (FIEs) with Simpson’s 1/3 rule, an effective numerical integration technique. We concentrate on clarifying the stability/convergence of the proposed strategy. We juxtapose the outcomes derived using the Runge-Kutta method (RK4) with those obtained through the implemented methodology. The findings indicate that the used technique provides a simple and efficient instrument for simulating the solution of these models. The principal advantage of the proposed method is its dependence on a limited number of straightforward steps, devoid of long-term consequences or reliance on a perturbation parameter.

Evaluation of Wellbore Stability by Small Parameter Perturbation Nonlinear Elastoplastic Model

Abstract Wellbore instability is a frequent occurrence during drilling and a popular research topic among petroleum workers. Most of the previous studies simplified the hardening stage and ignored or classified it into the elastic stage. Engineering practice shows that the total stress–strain process of rock can more truly reflect the bearing and deformation characteristics of rock. This study establishes a total stress–strain constitutive model by combining the perturbation index equation with the linear elastic equation. Additionally, the physical model of rock around the well is presented using the total deformation theory for the plastic zone. The stress field of the rock surrounding the well is analyzed based on the physical model of the rock surrounding the well, taking into account the influence of rock strength and geostress state. The relationship between rock strength, geostress state, drilling fluid density, and plastic radius is given. The calculation method of drilling fluid density limit is also given. The practical application demonstrates that the stability of a borehole wall can be evaluated by analyzing the size and direction of the plastic radius, as well as the distribution of radial, tangential, and shear stress for various combinations of stress states and rock strengths. The maximum shear stress is always found in the softening zone, which is also the region where wellbore instability is most likely to happen. Therefore, the area within the softening radius is regarded as an unstable area, and the softening radius can be used to determine the range of wellbore instability.

Ecological success of extreme halophiles subjected to recurrent osmotic disturbances is primarily driven by congeneric species replacement.

To understand how extreme halophiles respond to recurrent disturbances, we challenged the communities thriving in salt-saturated (~36% salts) ~230L brine mesocosms to repeated dilutions down to 13% (D13 mesocosm) or 20% (D20 mesocosm) salts each time mesocosms reached salt saturation due to evaporation (for 10 and 17cycles, respectively) over 813days. Depending on the magnitude of dilution, the most prevalent species, Haloquadratum walsbyi and Salinibacter ruber, either increased in dominance by replacing less competitive populations (for D20, moderate stress conditions), or severely decreased in abundance and were eventually replaced by other congeneric species better adapted to the higher osmotic stress (for D13, strong stress conditions). Congeneric species replacement was commonly observed within additional abundant genera in response to changes in environmental or biological conditions (e.g. phage predation) within the same system and under a controlled perturbation of a relevant environmental parameter. Therefore, a genus is an ecologically important level of diversity organization, not just a taxonomic rank, that persists in the environment based on congeneric species replacement due to relatively high functional overlap (gene sharing), with important consequences for the success of the lineage, and similar to the success of a species via strain-replacement. Further, our results showed that successful species were typically accompanied by the emergence of their own viral cohorts, whose intra-cohort diversity appeared to strongly covary with, and likely drive, the intra-host diversity. Collectively, our results show that brine communities are ecologically resilient and continuously adapting to changing environments by transitioning to alternative stable states.

A Novel Method for Analyzing Global Bifurcation and Global Hysteresis of FGM Truncated Conical Shell Structure

In the dynamic bifurcation and dynamic hysteresis of a system, our first consideration is the tiny changes in time that can lead to variations in the vector field, potentially causing the occurrence of system dynamic bifurcation and dynamic hysteresis. This paper presents a novel method for analyzing the global bifurcation and hysteresis of Functionally Graded Material (FGM) truncated conical shell structure under aerodynamics and in-plane force along meridian near internal resonances. This method involves introducing the ratio of vector fields as a periodic perturbation parameter in the system’s nonlinear second-order ordinary differential governing equations. This allows for the analysis of the nonlinear ordinary differential equations as algebraic equations, yielding algebraic expressions that only involve parameters and do not contain state variables. Subsequently, the global bifurcation set and global hysteresis set of FGM truncated conical shell structure are obtained, providing the parameters interval ranges for the stability and instability of FGM truncated conical shell structure. By utilizing MAPLE software for numerical simulation, the images of the global bifurcation set and global hysteresis set about the amplitude of in-plane load are first simulated numerically. Subsequently, the amplitude graphs of the equilibrium points are numerically simulated for validation. The results demonstrate a perfect alignment between the images of the global bifurcation set and global hysteresis set and the data from the amplitude graphs of the equilibrium point. Due to the periodicity of the periodic perturbation parameter, it shuttles between different persistent regions as other parameters change, leading to the generation of chaotic solutions in the governing equations. The validity of the obtained results is confirmed through comparisons with existing literature.

Compensation Function Observer-Based Backstepping Sliding-Mode Control of Uncertain Electro-Hydraulic Servo System

Observer-based control is the most commonly used method in the control of electro-hydraulic servo system (EHSS) with uncertainties, but it suffers from the drawback of low accuracy under the influence of large external load forces and disturbances. To address this problem, this paper proposes a novel compensation function observer-based backstepping sliding-mode control (BSMC) approach to achieve high-accuracy tracking control. In particular, the model uncertainties, including nonlinearities, parameter perturbations and external disturbances are analyzed and treated together as a lumped disturbance. Then, a fourth-order compensation function observer (CFO) is constructed, which fully utilizes the system state information to accurately estimate the lumped disturbance. On this basis, the estimate of the lumped disturbance is incorporated into the design of a backstepping sliding-mode controller, allowing the control system to compensate for the disturbance effect. The stability of the closed-loop control system under the CFO and BSMC is rigorously proven through the use of the Lyapunov theory, which guarantees that all the tracking error signals converge exponentially to the origin. Comparative simulations are carried out to show the effectiveness and efficiency of the proposed approach, i.e., compared with PID and ESO-based BSMC methods, the tracking accuracy is respectively improved by 94.86% and 88.19% under the influence of large external load forces and disturbances.

Stochastic optimization of a mass-in-mass cell with piecewise hybrid nonlinear–linear restoring force

This article investigates the optimization under uncertainty of a mass-in-mass meta-cell for its potential use within a metamaterial. The specificity of the proposed mass-in-mass system stems from the hybrid nonlinear–linear stiffness at the inner level. It is well known that these systems are highly sensitivity to small perturbations in loading conditions or design parameters. In fact, the sensitivity is such that the system can exhibit discontinuous behaviors. Therefore the proposed optimization approach not only accounts for sources of uncertainties but also can handle discontinuous responses. The objective of the stochastic optimization is to find the stiffness properties of the mass-in-mass system which minimize the expected value of a specific efficiency metric. In order to better understand the system’s dynamic behavior and the origins of the discontinuities, slow invariant manifolds and frequency response curves are provided. The efficiency of the optimized system with hybrid stiffness is compared with that of a similar optimized system featuring pure cubic nonlinearity.

Robust Fault Estimation and Fault‐Tolerant Control for a Class of Fuzzy Singularly Perturbed Systems With State Time Delay Based on Learning Observer

ABSTRACTThis article studies the problem of fault estimation (FE) and dynamic output fault‐tolerant control (DOFTC) for a class of Takagi–Sugeno (T–S) fuzzy singularly perturbed systems (SPSs) which subject to time delay, external disturbance and actuator fault. A new fault estimation and fault‐tolerant control scheme was proposed and designed for the influence of the change of perturbation parameter on the singularly perturbed system. This scheme adopts the Takagi–Sugeno (T–S) fuzzy model, learning observer and dynamic output feedback fault‐tolerant mechanism, so that the system has multi‐time‐scale dynamic stability. The results show that this method has more accurate estimation effect, faster convergence speed, and very fast steady‐state response of fault‐tolerant control when faults occur. Furthermore, when constructing the Lyapunov function, the improved matrix was selected to ensure that the closed‐loop system is stable for all , and at the same time, the conservativeness of the results was reduced. Finally, the feasibility and correctness of the proposed design method were illustrated through two numerical examples.

Topologically Protected Plasmonic Bound States in the Continuum.

Experimental realizations of bound states in the continuum (BICs) with strong robustness and advanced maneuverability in optical loss systems remain a long-standing challenge in nanophotonics. Here, we propose and fabricate a paradigm of diatomic metagratings incorporating the Su-Schrieffer-Heeger model into the design of plasmonic nanocavities to demonstrate optical resonators with a continuous "quasi-BICs (qBICs)-BICs-qBICs" transition. These resonators feature a topological band inversion, making high-quality (Q) resonances immune to the perturbation of incident angles and geometrical parameters. Furthermore, we strive to establish theoretical models to verify the topological nature of BICs-inspired resonances and introduce nonlinear optical probes to quantify strongly enhanced local fields at high-Q resonances. Our findings may provide a simple yet feasible design strategy for facilitating the dissipationless manipulation of surface/interface-enhanced light-matter interactions at the nanoscale, substantially broadening the functional scope of metaphotonics.

A PNP ion channel deep learning solver with local neural network and finite element input data

Abstract This paper presents a deep learning method for solving an improved one-dimensional Poisson–Nernst–Planck ion channel (PNPic) model, called the PNPic deep learning solver. The solver combines a novel local neural network, adapted from the neural network with local converging inputs, with an efficient PNPic finite element solver, developed in this work. In particular, the local neural network is extended to handle the complexities of the PNPic model—a system of nonlinear convection–diffusion and elliptic equations with multiple subdomains connected by interface conditions. The PNPic finite element solver efficiently generates input and reference datasets for fast training the local neural network, as well as input datasets for quickly predicting PNPic solutions with high accuracy for a family of PNPic models. Initial numerical tests, involving perturbations of model parameters and interface locations, demonstrate that the PNPic deep learning solver can generate highly accurate numerical solutions.

A Hybrid Sobolev Gradient Method for Learning NODEs

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in ordinary differential equations is considered, with the typical application of finding weights of a neural ordinary differential equation (NODE) for a residual network with time continuous layers. The differential equation is treated as an abstract and isolated entity, termed a standalone NODE (sNODE), to facilitate for a wide range of applications. The proposed parameter reconstruction is performed by minimizing a cost functional covering a variety of loss functions and penalty terms. Regularization via penalty terms is incorporated to enhance ethical and trustworthy AI formulations. A nonlinear conjugate gradient mini-batch optimization scheme (NCG) is derived for the training having the benefit of including a sensitivity problem. The model (differential equation)-based approach is thus combined with a data-driven learning procedure. Mathematical properties are stated for the differential equation and the cost functional. The adjoint problem needed is derived together with the sensitivity problem. The sensitivity problem itself can estimate changes in the output under perturbation of the trained parameters. To preserve smoothness during the iterations, the Sobolev gradient is calculated and incorporated. Numerical results are included to validate the procedure for a NODE and synthetic datasets and compared with standard gradient approaches. For stability, using the sensitivity problem, a strategy for adversarial attacks is constructed, and it is shown that the given method with Sobolev gradients is more robust than standard approaches for parameter identification.

Piezo-viscous micropolar fluid flow between two parallel annular disks

A theoretical analysis of the piezo-viscous dependence of micropolar fluid flow between parallel annular disks has been conducted. It is assumed that viscosity changes exponentially with pressure. Pressure is analytically approximated using a small perturbation method with the viscosity coefficient as the perturbation parameter. Squeeze film time, pressure, and load carrying capacity are calculated and graphically demonstrated across various viscosity–pressure characteristics. The study examines how an increase in cross-viscosity correlates with notable growth in pressure, response time, and bearing load. According to the results, micropolar fluid offers an increase in the load-bearing capacity and therefore lengthens the response time to prevent the contact of parallel annular disks. These observations are useful for bearings, seals, and lubrication systems, where controlling viscosity and pressure is crucial for smooth operation and productivity. As the limiting case of micro-polar fluid when the coupling number tends to zero or the couple stress parameter approaches infinity, without the annular ring, the present derivation agrees well with the Newtonian viscous case of parallel planar squeezing disks described by Bird et al. [Transport Phenomena (John Wiley & Sons, 2006)].

Location of the collinear equilibrium points in the elliptic restricted three-body problem with various perturbation effects

Abstract This study aims to examine the elliptic restricted three-body problem (ERTBP) by modifying the classical case and applying various perturbation sources to the three-body system. In this study, the locations of the Lagrange collinear equilibrium points of ERTBP were examined. We consider that the first primary body emits radiation and has an oblate shape. In contrast, the second primary body was considered to be elongated and approximated as a finite straight-segment. In addition, the perturbations from the disk-like structure around the three-body system were also included. The equations of motion of the infinitesimal body are presented in a dimensionless pulsating coordinate system. Three collinear equilibrium points were identified. The locations of the collinear equilibrium points were calculated numerically for several cases of perturbation values and also presented versus eccentricity over its range. We observed that the position of the collinear equilibrium points (L 1, L 2, and L 3) shifted when perturbing parameters were included, as opposed to where they were in the classical ERTBP.

Value-Positivity for Matrix Games

Matrix games are the most basic model in game theory, and yet robustness with respect to small perturbations of the matrix entries is not fully understood. In this paper, we introduce value positivity and uniform value positivity, two properties that refine the notion of optimality in the context of polynomially perturbed matrix games. The first concept captures how the value depends on the perturbation parameter, and the second consists of the existence of a fixed strategy that guarantees the value of the unperturbed matrix game for every sufficiently small positive parameter. We provide polynomial-time algorithms to check whether a polynomially perturbed matrix game satisfies these properties. We further provide the functional form for a parameterized optimal strategy and the value function. Finally, we translate our results to linear programming and stochastic games, where value positivity is related to the existence of robust solutions. Funding: This research was supported by Fondation CFM pour la Recherche, the H2020 European Research Council [Grant ERC-CoG-863818 (ForM-SMArt)], the Austrian Science Fund [Grant 10.55776/COE12], ANID Chile [Grant ACT210005], and Agence Nationale de la Recherche [Grant ANR-21-CE40-0020].