Nonlinear Acceleration Research Articles

Data-Based Spacecraft Rendezvous Control by SINDy

In this paper, we demonstrate a new model identification-based control method for spacecraft rendezvous with limited amount of data of data. We use the method of sparse identification for nonlinear dynamics (SINDy) to identify the high-order nonlinear gravitational acceleration in the motion dynamics of spacecraft rendezvous. The control has a feedforward plus feedback structure. The feedforward control uses the nonlinear functions identified by SINDy to compensate the nonlinear high-order acceleration terms, while the feedback control designed by solving a standard linear quadratic regulator (LQR) problem is used to guarantee the stability of the closed-loop system. Numerical results show the effectiveness of the proposed control scheme for spacecraft rendezvous mission. With few state samplings, the dynamics identified based on SINDy achieve better state prediction performance than Clohessy–Wiltshire (CW) equations and the dynamics identified by BP neural networks. Considering the computation and storage burden brought by the data amount in identification, the proposed method is promising in improving the autonomy of spacecraft in missions with complex and uncertain dynamics environment.

Detection of ultrafast electron energization by whistler-mode chorus waves in the magnetosphere of Earth

Electromagnetic whistler-mode chorus waves are a key driver of variations in energetic electron fluxes in the Earth’s magnetosphere through the wave-particle interaction. Traditionally understood as a diffusive process, these interactions account for long-term electron flux variations (> several minutes). However, theories suggest that chorus waves can also cause rapid (< 1 s) electron acceleration and significant flux variations within less than a second through a nonlinear wave-particle interaction. Detecting these rapid accelerations has been a great challenge due to a limited time resolution of conventional particle instruments. Here, we employ an analysis technique to enhance the time resolution of the particle measurements, revealing rapid electron flux variations within less than one second associated with chorus waves. This technique exposes short-lived flux increases significantly larger than those observable with the standard time resolution. Our findings indicate that these transient flux variations result from the nonlinear acceleration of electrons induced by the chorus waves, highlighting the importance of nonlinear wave-particle interactions in creating high energy electrons in the Earth’s magnetosphere. The same acceleration mechanism should operate in the magnetospheres of Jupiter and Saturn where chorus waves are present, and in laboratory plasma environments when chorus-like waves are excited.

A feasibility restoration particle swarm optimizer with chaotic maps for two-stage fixed-charge transportation problems

This paper delves into solving the two-stage non-linear fixed-charge transportation problem (two-stage NFCTP), where each arc is associated with fixed and variable costs that increase proportionally to the square of the units transported. The presence of fixed charges and non-linear components categorizes this problem as NP−hard, leading to computational challenges, inefficiencies, and the risk of local optima. To address these challenges, a feasibility restoration particle swarm optimizer with chaotic maps (CEPSO) is presented. The proposed algorithm introduces (i) non-linear adaptive inertia weight and acceleration coefficients to maintain better exploration and exploitation rates during the search. (ii) Ten chaotic maps are integrated into the acceleration coefficients to enhance optimization capabilities further. (iii) Feasibility restoration mechanisms, including constraint compliance adjustment and ratio adjustment procedures, are incorporated to ensure the feasibility of solutions generated by CEPSO. The algorithm’s performance is evaluated across small and large-scale NFCTPs, ranging from 35 to 1044 dimensions, and compared to existing PSO variants using various evaluation metrics. Experimental analyses demonstrate CEPSO’s superior optimization performance for two-stage NFCTPs, positioning it as an advanced framework in this domain and contributing to the novelty of this study. The related codes can be found using this link: https://github.com/ChauhanDikshit.

Plasma self-driven current in tokamaks with magnetic islands

Abstract Magnetic island perturbations may cause a reduction in plasma self-driven current that is needed for tokamak operation. A novel effect on tokamak self-driven current revealed by global gyrokinetic simulations is due to magnetic-island-induced 3D electric potential structures, which have the same dominant mode numbers as that of the magnetic island, whereas centered at both the inner and outer edge of the island. The non-resonant potential islands are shown to drive a current through an efficient nonlinear parallel acceleration of electrons. In large aspect ratio (large-A) tokamak devices, this new effect can result in a significant global reduction of the electron bootstrap current when the island size is sufficiently large, in addition to the local current loss across the island region due to the pressure profile flattening. It is shown that there exists a critical magnetic island width for large-A tokamaks beyond which the electron bootstrap current loss is global and increases rapidly with the island size. As such, this process may introduce a size limit for tolerable magnetic islands in large-A tokamak devices in the context of steady state operation. On the other hand, the current loss caused by magnetic islands in low-A tokamaks such as spherical tokamak (ST) NSTX/U is minor. The reduction of the axisymmetric current by magnetic islands scales with the square of island width. However, the loss of the current is mainly local to the island region, and the pace of current loss as the island size increases is substantially slower compared to large-A tokamaks. In particular, the bootstrap current reduction in STs is even smaller in the reactor-relevant high-β p regime where neoclassical tearing modes are more likely to develop.

An optimal parameterized Newton-type structure-preserving doubling algorithm for impact angle guidance-based 3D pursuer/target interception engagement

The proposed strategy, finite-time state-dependent Riccati equation (FT-SDRE)-based impact angle guidance, is generally employed to solve the 3D pursuer/target interception model with fixed lateral accelerations. This article expands its application to a general scenario where the lateral acceleration of a target may change. To achieve this, we approximate the accelerations of the azimuth and elevation angles of the target in the inertial frame via second-order finite difference schemes and develop a high-performance FT-SDRE algorithm with structure-preserving doubling algorithms (SDAs). As a result, the update frequency of the controller can be increased, and better guidance of the pursuer can be obtained to address the high maneuverability of the target during the entire interception procedure. At every state of the FT-SDRE, a modified Newton–Lyapunov method is employed to solve the continuous algebraic Riccati equation (CARE), and a new simplified SDA with adaptive optimal parameter selection is proposed for solving the associated Lyapunov equation. Our numerical results demonstrate that the FT-SDRE algorithm accelerated by our proposed methods is approximately three times faster than the FT-SDRE algorithm, in which the MATLAB functions icare and lyap are used to solve the CARE and the Lyapunov equation, respectively, throughout the entire interception procedure. In other words, the control frequency can be increased threefold. In our benchmark cases where the target maneuvers with nonlinear lateral acceleration, the target can be intercepted earlier via the proposed FT-SDRE algorithm.

Crowding accelerates the rotation of a bacterial rotor

Understanding the propulsion of a swimmer in a large group of individuals holds the key to unravelling the intriguing dynamics of active matter collective motion. Here, we develop a two-dimensional (2-D) self-assembled rotor, powered by bacterial flagella. At a water–air interface, the average direction of rotation of a rotor is fixed. When the chiral rotor is put into a 2-D bacterial suspension, we examine the average and fluctuation of the angular velocity of the rotor. Remarkably, the average angular velocity of a rotor is found to increase up to 3 times when the density of surrounding bacterial suspension increases and the increase is nonlinear. In a dense suspension of bacteria, the existence of a rotor disrupts vortices in the surrounding active turbulence, and the acceleration of the rotor is independent of the activity level of the surrounding free bacteria. The nonlinear acceleration thus results from hydrodynamic interaction with surrounding crowdedness that can be quantitatively explained by hydrodynamic simulation. The simultaneity between the acceleration of rotor and free bacteria in active turbulence suggests that crowding-induced acceleration may promote the onset of instability. The result will inspire new active-matter-based microfluidic devices with improved transport properties.

Modified RNN for Solving Comprehensive Sylvester Equation With TDOA Application.

The augmented Sylvester equation, as a comprehensive equation, is of great significance and its special cases (e.g., Lyapunov equation, Sylvester equation, Stein equation) are frequently encountered in various fields. It is worth pointing out that the current research on simultaneously eliminating the lagging error and handling noises in the nonstationary complex-valued field is rather rare. Therefore, this article focuses on solving a nonstationary complex-valued augmented Sylvester equation (NCASE) in real time and proposes two modified recurrent neural network (RNN) models. The first proposed modified RNN model possesses gradient search and velocity compensation, termed as RNN-GV model. The superiority of the proposed RNN-GV model to traditional algorithms including the complex-valued gradient-based RNN (GRNN) model lies in completely eliminating the lagging error when employed in the nonstationary problem. The second model named complex-valued integration enhanced RNN-GV with the nonlinear acceleration (IERNN-GVN) model is proposed to adapt to a noisy environment and accelerate the convergence process. Besides, the convergence and robustness of these two proposed models are proved via theoretical analysis. Simulative results on an illustrative example and an application to the moving source localization coincide with the theoretical analysis and illustrate the excellent performance of the proposed models.

A Fractional-Order Creep-Damage Model for Carbonaceous Shale Describing Coupled Damage Caused by Rainfall and Blasting

In order to better understand the shear creep behavior of weak interlayers (carbonaceous shale) under the coupling effect of the rainfall dry–wet cycle and blasting vibration, as well as quantitatively characterize the coupled damage of the rainfall dry–wet cycle and blasting vibration, a series of shear creep tests were carried out. The results show that the combined damage of the rainfall dry–wet cycle and blasting vibration greatly intensifies the creep effect of carbonaceous shale, leading to an increase in deceleration creep time, an increase in steady-state creep rate, and a decrease in long-term strength. The coupling damage of the rainfall dry–wet cycle and blasting vibration in carbonaceous shale was quantitatively characterized. Based on the fractional-order theory, a fractional-order creep-damage constitutive model (DNFVP) was established by introducing the Abel dashpot to describe the coupled damage of the rainfall wet–dry cycle and blasting vibration and the nonlinear creep acceleration characteristics. The three-dimensional creep equation of the model was derived. The effectiveness of the DNFVP model was verified through the inversion of model parameters and fitting of experimental data, providing a basis for in-depth research on the long-term stability of high slopes in mines with weak interlayers.

Individual particle approach to diffusive shock acceleration. Effect of the non-uniform flow velocity downstream of the shock

The momentum distribution of particles accelerated at strong non-relativistic shocks may be influenced by the spatial distribution of the flow speed around the shock. This phenomenon becomes evident in the cosmic-ray-modified shock, where the particle spectrum itself determines the profile of the flow velocity upstream. However, the effects of a non-uniform flow speed downstream are unclear. Hydrodynamics indicates that the spatial variation of flow speed over the length scales involved in the acceleration of particles in supernova remnants (SNRs) could be noticeable. In the present paper, we address this question. We initially followed Bell's approach to particle acceleration and then also solved the kinetic equation. We obtained an analytical solution for the momentum distribution of particles accelerated at the cosmic-ray-modified shock with spatially variable flow speed downstream. We parameterised the downstream speed profile to illustrate its effect on two model cases: the test particle and non-linear acceleration. The resulting particle spectrum is generally softer in Sedov SNRs because the distribution of the flow speed reduces the overall shock compression accessible to particles with higher momenta. On the other hand, the flow structure in young SNRs could lead to harder spectra. The diffusive properties of particles play a crucial role as they determine the distance the particles can return from to the shock, and, as a consequence, the flow speed that they encounter downstream. We discuss a possibility that the plasma velocity gradient could be (at least partially) responsible for the evolution of the radio index and for the high-energy break visible in gamma rays from some SNRs. We expect the effects of the gradient of the flow velocity downstream to be prominent in regions of SNRs with higher diffusion coefficients and lower magnetic field, that is, where acceleration of particles is not very efficient.

A Precision Benchmark Suite for Nuclear Reactor Point Kinetics Equations via Converged Accelerated Taylor Series (CATS)

Extreme benchmarks of 10 or more places for the point kinetics equations for time-dependent nuclear reactor power transients are rare. Therefore, to establish an extreme benchmark, we employ a Taylor series (TS) with continuous analytical continuation to solve the ordinary differential equations of point kinetics including feedback. Nonlinear Wynn-epsilon convergence acceleration confirms the highly precise solutions for neutron and precursor densities. Through adaptive partitioning of time intervals, the proposed Converged Accelerated Taylor Series, or CATS algorithm in double precision, automatically performs successive mesh refinement to obtain high-precision initial conditions for each subinterval, with the intent to reduce propagation error. Confirmation of 10 to 12 places comes from comparison to the BEFD (Backward Euler Finite Difference) algorithm in quadruple precision also developed by the author. We report benchmark results for common cases found in the literature including step, ramp, zigzag, and sinusoidal prescribed reactivity insertions and insertions with nonlinear adiabatic Doppler feedback. We also establish a suite of new prescribed reactivity insertions and insertions with feedback, based on reactivities with Taylor series representations as suggested by the CATS algorithm.

Discontinuity waves in temperature and diffusion models

We analyse shock wave behaviour in a hyperbolic diffusion system with a general forcing term which is qualitatively not dissimilar to a logistic growth term. The amplitude behaviour is interesting and depends critically on a parameter in the forcing term. We also develop a fully nonlinear acceleration wave analysis for a hyperbolic theory of diffusion coupled to temperature evolution. We consider a rigid body and we show that for three-dimensional waves there is a fast wave and a slow wave. The amplitude equation is derived exactly for a one-dimensional (plane) wave and the amplitude is found for a wave moving into a region of constant temperature and solute concentration. This analysis is generalized to allow for forcing terms of Selkov–Schnakenberg, or Al Ghoul-Eu cubic reaction type. We briefly consider a nonlinear acceleration wave in a heat conduction theory with two solutes present, resulting in a model with equations for temperature and each of two solute concentrations. Here it is shown that three waves may propagate.

Theoretical Development and Numerical Validation of an Asymmetric Linear Bilateral Control Model- Case Study for an Automated Truck Platoon

In this paper, we theoretically develop and numerically validate an asymmetric linear bilateral control model (LBCM) , in which the motion information (e.g., position and speed) from the immediate leading vehicle and the immediate following vehicle of a subject vehicle in an automated vehicle platoon are weighted differently to determine the control inputs to the subject vehicle. The novelty of the asymmetric LBCM is that using this model all the follower vehicles in a platoon can adjust their acceleration and deceleration to closely follow a constant desired time gap to improve platoon operational efficiency while maintaining local and string stability. We theoretically analyze the local stability of the asymmetric LBCM using the condition for asymptotic stability of a linear time-invariant system and prove the string stability of the asymmetric LBCM using a space gap error attenuation approach. Then, we evaluate the efficacy of the asymmetric LBCM by simulating a closely coupled cooperative adaptive cruise control (CACC) platoon of fully automated trucks in various non-linear acceleration and deceleration states. We choose automated truck platooning as a case study since heavy-duty trucks experience higher delays and lags in the powertrain system, and limited acceleration and deceleration capabilities than passenger cars. To evaluate the platoon operational efficiency of the asymmetric LBCM, we compare the performance of the asymmetric LBCM to a baseline model, i.e., the symmetric LBCM, for different powertrain delays and lags. Our analyses showed that the asymmetric LBCM can handle any combined powertrain delays and lags up to 0.6 sec while maintaining a constant desired time gap during a stable platoon operation, whereas the symmetric LBCM fails to ensure stable platoon operation as well as maintain a constant desired time gap for any combined powertrain delays and lags over 0.2 sec. These findings demonstrate the potential of the asymmetric LBCM in improving platoon operational efficiency and stability of an automated truck platoon.

Early warning signals of grassland ecosystem degradation: A case study from the northeast Qinghai-Tibetan Plateau

As a typical vulnerable ecosystem, alpine steppes can be subject to nonlinear accelerations in degradation, once tipping points are reached or exceeded, and thus far more effort and investment will be needed, to reverse the degraded status of such ecosystems, if effective preventive measures or interventions are not adopted sufficiently early. Thus, detecting early warning signals of tipping events is extremely important for ecosystem protection and recovery, but remains highly challenging. For alpine steppes, coverage or biomass loss and species invasion are both key transitions. Using multi-source data, including ground surveys and remote sensing images with different resolutions, we tried to screen and identify potential early-warning signals for alpine grassland degradation events and analyze their efficacy. The results showed that the degradation levels derived from spatial heterogeneity information combined with a vegetation index were reliable, as was verified by ground surveys, and could illustrate the degradation process of a grassland ecosystem. Six common early-warning signals (variance, skewness, and autocorrelation, from both the spatial and temporal domains) were tested according to degradation degree, and spatial autocorrelation and temporal autocorrelation had the best performances, as they could indicate different degradation levels, and the change trends of temporal autocorrelation could provide early-warning functions. A waved change of spatial variance could reflect a vegetation growth dynamic that might indicate species invasion. In this study, the threshold values of spatial and temporal autocorrelation were 0.7 and 0.2, respectively, and from these, the thresholds of vegetation coverage and biomass were then obtained. However, these signals and thresholds had some limitations during application. These findings provide insights into better understanding of the alpine grassland degradation process, and contribute to a better management approach for vulnerable ecosystems using early-warning methods.

GNN-LSTM-based fusion model for structural dynamic responses prediction

With the rapid growth of deep learning technology, the potential for its use in structural engineering has substantially increased in recent years. This study proposes an innovative deep-learning fusion network architecture based on the graph neural network (GNN) and long short-term memory (LSTM) network. The proposed fusion model can accurately predict nonlinear floor acceleration, velocity, and displacement responses of typical steel moment-resisting frames (SMRF) with 4 through 7 stories subjected to strong ground motions. The fusion model framework overcomes a major drawback in existing deep learning models as it can predict the dynamic responses of various structures. This has widened the range of potential applications of structural surrogate models generated through deep learning technology on the design and analysis of building structures with different geometries. Additionally, this paper presents two LSTM-optimized learning strategies, namely packing padded sequences and sequences compression strategies. These strategies improve the model’s performance significantly without modifying its architecture. Finally, this study reveals that the model’s internal graph embedding is highly correlated with certain critical structural parameters, such as the first natural period and the height of a building. This shows that the proposed fusion model is interpretable and has the ability to extract vital information that influences structural dynamic responses.

NlTGCR: A Class of Nonlinear Acceleration Procedures Based on Conjugate Residuals

nlTGCR: A Class of Nonlinear Acceleration Procedures Based on Conjugate Residuals

A Variant of the Second-Moment Method for k-Eigenvalue Calculations

The second-moment (SM) method is a linear variant of the quasi-diffusion (QD) method for accelerating the iterative convergence of Sn source calculations. It has several significant advantages relative to the QD method, diffusion synthetic acceleration, and nonlinear diffusion acceleration. Here, we define a variant of this method for k-eigenvalue calculations that retains the advantages of the original method, and we computationally demonstrate the efficacy of the method for simple example calculations. In particular, this method has two important properties. First, it is a linear acceleration scheme requiring only the solution of a pure k-eigenvalue diffusion equation with a corrective source term as opposed to a k-eigenvalue drift-diffusion equation. Second, unconditional stability is achieved even when the diffusion equation is not discretized in a manner consistent with the Sn spatial discretization. We are unaware of any other scheme that has these properties. We also show a connection between our method and the k-eigenvalue acceleration technique of Barbu and Adams, which motivated us to develop our SM method.

Upstream motion of chorus wave generation: comparisons with observations

An understanding of the development of strong very low frequency chorus elements is important in the study of the rapid MeV electron acceleration observed during radiation belt recovery events. During such events, chorus elements with long-duration (20–40 ms), strong (|Bw| 0.5–2.0 nT) subpackets with smoothly varying frequency and phase capable of producing nonlinear energy gain of 1%–2% for multi-MeV seed electrons. For such strong chorus elements, we examine the consequences of an upstream motion of the chorus wave generation region using Van Allen Probes observations and nonlinear theory. For a given upstream velocity, vs, resonant electron energy (50–350 keV) and pitch angle (105–115 deg) are uniquely determined for each wave frequency. We examine the effect of an upstream vs on the inhomogeneity factor that controls wave growth. For steadily increasing upstream motion as the chorus element evolves, vs/c ranging over [-0.001, −0.065], nonlinear wave growth takes place at ≥ 50% of the theoretical maximal value during the development of the observed strong subpackets. For the cases examined, resonant electron energies and pitch angles closely match those of the observed injected electron flux enhancements responsible for chorus development and the nonlinear acceleration of MeV radiation belt electrons.

Nonlinear ground acceleration tracking mechanism for seismic control of high-rise buildings considering soil-structure interaction

In this paper, a novel two-step nonlinear ground acceleration feedback mechanism is proposed for vibration mitigation of building structures considering soil-structure interaction. Hence, an observer based receding horizon control (RHC) scheme is presented for active control of the structures. Afterward, a nonlinear two-step auto-regressive framework is appended to the RHC formulations to consider the adaptive seismic term in the resulted control law. Soil-structure interaction (SSI) is also considered in the controller structure regarding soft, medium, and dense soil conditions. A data-driven approach is then introduced for lessening the complexity of the proposed framework for practical applications. A forty-story building equipped with active mass damper (AMD) subjected to earthquake excitations is selected as the numerical study. The superiority of the proposed method is evaluated compared to other control strategies including conventional RHC, ideal RHC, and linear version of the proposed controllers. The outcomes indicate the remarkable accuracy of the proposed method against mentioned control approaches.

An optimal membership function based Fuzzy-[formula omitted] stabilizer design to suppress low frequency oscillation in synchronous generator

An optimal membership function-based fractional order fuzzy proportional integral (Fuzzy-PIλ) power system stabilizer (PSS) is designed to suppress low frequency oscillation (LFO) in a synchronous generator connected to an infinite bus power system. Speed deviation and the change in speed deviation of synchronous generator due to LFO are taken as inputs of the fuzzy controller, and the parameters of a fractional-order PI controller (proportional gain, integral gain, and the fractional term in integral control action) are taken as fuzzy output variables. The range, scaling, and shape of the membership functions of the fuzzy controller are optimized such that it can tune the fractional order proportional integral (PIλ) stabilizer under any disturbance or parametric uncertainty in the synchronous generator. The advantage of the proposed stabilizer is that it can handle a wide range of disturbances and adjust the gains of the control parameters for the system. A nonlinear dynamic acceleration coefficient-based class-topper optimization is applied to optimize the fuzzy settings. The robustness and sensitivity of the proposed optimal Fuzzy-PIλ stabilizer are verified under different scenarios for the synchronous generator and compared with available results.

The Influence of Midlevel Shear and Horizontal Rotors on Supercell Updraft Dynamics

Abstract Large midlevel (3–6 km AGL) shear is commonly observed in supercell environments. However, any possible influence of midlevel shear on an updraft has been relatively unexplored until now. To investigate, we ran 10 simulations of supercells in a range of environments with varying midlevel shear magnitudes. In most cases, larger midlevel shear results in a storm motion that is faster relative to the low-level hodograph, meaning that larger midlevel shear leads to stronger low-level storm-relative flow. Because they are physically connected, we present an analysis of the effects of both midlevel shear and low-level storm-relative flow on supercell updraft dynamics. Larger midlevel shear does not lead to an increase in cohesive updraft rotation. The tilting of midlevel environmental vorticity does lead to localized areas of larger vertical vorticity on the southern edge of the updraft, but any dynamical influence of this is overshadowed by that of much larger horizontal vorticity in the same area associated with rotor-like circulations. This storm-generated horizontal vorticity is the primary driver behind lower nonlinear dynamic pressure on the southern flank of the midlevel updraft when midlevel shear and low-level storm-relative flow are larger, which leads to a larger nonlinear dynamic pressure acceleration in those cases. Storm-generated horizontal vorticity is responsible for the lowest nonlinear dynamic pressure anywhere in the midlevel updraft, unless the mesocyclone becomes particularly intense. These results clarify the influence of midlevel shear on a supercell thunderstorm, and provide additional insight on the role of low-level storm-relative flow on updraft dynamics. Significance Statement Persistent rotation in supercell thunderstorms results from the tilting of horizontal spin into the vertical direction. This initially horizontal spin is the result of shear, which is a change in wind speed and/or direction with height. More shear in the layer 0–3 km above ground level is well understood to lead to stronger rotation within the storm, but the influence of shear in the 3–6-km layer is unclear and is investigated here. We find that horizontal spin originating in the 3–6-km layer has little impact on vertically oriented thunderstorm rotation. Instead, intense regions of horizontal spin that are generated by the storm itself (rather than having originated from the background environment) dominate storm dynamics at midlevels.