LEGENDRE SERIES SOLUTIONS FOR TIME-VARIATION DYNAMICS

In this topic, a new. approach to the analysis of time-variation dynamics is proposed by use of Legendre series expansion and Legendre integral operator matrix. The theoretical basis for effective solution of time-variation dynamics is therefore established, which is beneficial to further research of time-variation science.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Time-variation of the near 5-month period of sunspot numbers

The variation of the near 5-month period of sunspot numbers is discussed on the basis of the wavelet transform of the daily sunspot number series in the 14th-22nd solar cycles. The result shows that the period exists in every cycle and its energy density (amplitude) is comparatively large in the peak section of the cycle. In the distinct cycle, the length and intensity of the period is different, which means that the period varies with time. The near 25-day period is also analyzed and it is found to be time-variable and even not very stable in the peak section of the cycle. The variations of the two periods show that the near 5-month period should not be simply regarded as the multiples of the near 25-day period.

GRACE time-variable gravity and its application to geoscience:Quantitative analysis of relevant literature

The Gravity Recovery and Climate Experiment(GRACE)is the most important gravity satellite to date in human history.Since its launch in 2002,GRACE time-varying gravity has had an unprecedented impact on earth science and has generated revolutionary changes.Because of natural phenomena such as climate warming,glacial melting,sea level rise,and earthquakes,earth science research has become an increasingly popular discipline in recent years.This article summarizes the importance of GRACE time-varying gravity,its application to geoscience,and its development.We analyzed the historical development and current status of GRACE time-varying gravity as well as research hotspots by searching the literature in the core collection databases of the China National Knowledge Infrastructure and the Web of Science over the past 20 years.The CiteSpace and VOSviewer software packages were applied with reference to the principle of literature metrology.Our investigation and analysis of characteristic indexes,such as the numbers of publications,co-occurrence of keywords,and co-citation of documents,uncovered the wide application and promotion of gravity satellites,especially GRACE time-varying gravity,in earth science.The results showed that the number of publications addressing GRACE data and time-varying gravity theory is increasing annually and that the USA,China,and Germany are the main producers.The Chinese Academy of Sciences,the National Aeronautics and Space Administration of the United States,and the Helmholtz Association of German Research Centres rank among the top three institutions in the world in terms of producing the most publications on this topic.We found that GRACE time-varying gravity plays unique roles in measuring changes in terrestrial water storage changes,ice and snow melting and sea level changes,and(co)seismic gravity changes,as well as in promoting other disciplines.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

Epidemic threshold influenced by non-pharmaceutical interventions in residential university environments

The control of highly contagious disease spreading in campuses is a critical challenge.In residential universities,students attend classes according to a curriculum schedule,and mainly pack into classrooms,dining halls and dorms.They move from one place to another.To simulate such environments,we propose an agent-based susceptible–infected–recovered model with time-varying heterogeneous contact networks.In close environments,maintaining physical distancing is the most widely recommended and encouraged non-pharmaceutical intervention.It can be easily realized by using larger classrooms,adopting staggered dining hours,decreasing the number of students per dorm and so on.Their real-world influence remains uncertain.With numerical simulations,we obtain epidemic thresholds.The effect of such countermeasures on reducing the number of disease cases is also quantitatively evaluated.

Nuclear magnetic resonance experiments on the time-varying law of oil viscosity and wettability in high-multiple waterflooding sandstone cores

A simulated oil viscosity prediction model is established according to the relationship between simulated oil viscosity and geometric mean value of T2spectrum,and the time-varying law of simulated oil viscosity in porous media is quantitatively characterized by nuclear magnetic resonance(NMR)experiments of high multiple waterflooding.A new NMR wettability index formula is derived based on NMR relaxation theory to quantitatively characterize the time-varying law of rock wettability during waterflooding combined with high-multiple waterflooding experiment in sandstone cores.The remaining oil viscosity in the core is positively correlated with the displacing water multiple.The remaining oil viscosity increases rapidly when the displacing water multiple is low,and increases slowly when the displacing water multiple is high.The variation of remaining oil viscosity is related to the reservoir heterogeneity.The stronger the reservoir homogeneity,the higher the content of heavy components in the remaining oil and the higher the viscosity.The reservoir wettability changes after water injection:the oil-wet reservoir changes into water-wet reservoir,while the water-wet reservoir becomes more hydrophilic;the degree of change enhances with the increase of displacing water multiple.There is a high correlation between the time-varying oil viscosity and the time-varying wettability,and the change of oil viscosity cannot be ignored.The NMR wettability index calculated by considering the change of oil viscosity is more consistent with the tested Amott(spontaneous imbibition)wettability index,which agrees more with the time-varying law of reservoir wettability.

Adaptive Event-Triggered Time-Varying Output Group Formation Containment Control of Heterogeneous Multiagent Systems

In this paper,a class of time-varying output group formation containment control problem of general linear hetero-geneous multiagent systems(MASs)is investigated under directed topology.The MAS is composed of a number of tracking leaders,formation leaders and followers,where two different types of leaders are used to provide reference trajectories for movement and to achieve certain formations,respectively.Firstly,compen-sators are designed whose states are estimations of tracking lead-ers,based on which,a controller is developed for each formation leader to accomplish the expected formation.Secondly,two event-triggered compensators are proposed for each follower to evalu-ate the state and formation information of the formation leaders in the same group,respectively.Subsequently,a control protocol is designed for each follower,utilizing the output information,to guide the output towards the convex hull generated by the forma-tion leaders within the group.Next,the triggering sequence in this paper is decomposed into two sequences,and the inter-event intervals of these two triggering conditions are provided to rule out the Zeno behavior.Finally,a numerical simulation is intro-duced to confirm the validity of the proposed results.

Efficient simulation of spatially correlated non-stationary ground motions by wavelet-packet algorithm and spectral representation method

Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.

Complementary-Label Adversarial Domain Adaptation Fault Diagnosis Network under Time-Varying Rotational Speed and Weakly-Supervised Conditions

Recent research in cross-domain intelligence fault diagnosis of machinery still has some problems,such as relatively ideal speed conditions and sample conditions.In engineering practice,the rotational speed of the machine is often transient and time-varying,which makes the sample annotation increasingly expensive.Meanwhile,the number of samples collected from different health states is often unbalanced.To deal with the above challenges,a complementary-label(CL)adversarial domain adaptation fault diagnosis network(CLADAN)is proposed under time-varying rotational speed and weakly-supervised conditions.In the weakly supervised learning condition,machine prior information is used for sample annotation via cost-friendly complementary label learning.A diagnosticmodel learning strategywith discretized category probabilities is designed to avoidmulti-peak distribution of prediction results.In adversarial training process,we developed virtual adversarial regularization(VAR)strategy,which further enhances the robustness of the model by adding adversarial perturbations in the target domain.Comparative experiments on two case studies validated the superior performance of the proposed method.

Research on Anti-Fluctuation Control of Winding Tension System Based on Feedforward Compensation

In the fiber winding process,strong disturbance,uncertainty,strong coupling,and fiber friction complicate the winding constant tension control.In order to effectively reduce the influence of these problems on the tension output,this paper proposed a tension fluctuation rejection strategy based on feedforward compensation.In addition to the bias harmonic curve of the unknown state,the tension fluctuation also contains the influence of bounded noise.A tension fluctuation observer(TFO)is designed to cancel the uncertain periodic signal,in which the frequency generator is used to estimate the critical parameter information.Then,the fluctuation signal is reconstructed by a third-order auxiliary filter.The estimated signal feedforward compensates for the actual tension fluctuation.Furthermore,a time-varying parameters fractional-order PID controller(TPFOPID)is realized to attenuate the bounded noise in the fluctuation.Finally,TPFOPID is enhanced by TFO and applied to control a tension control system considering multi-source disturbances.The stability of the method is analyzed by using the Lyapunov theorem.Finally,numerical simulations verify that the proposed scheme improves the tracking ability and robustness of the system in response to tension fluctuations.

Set-Membership Filtering Approach to Dynamic Event-Triggered Fault Estimation for a Class of Nonlinear Time-Varying Complex Networks

The present study addresses the problem of fault estimation for a specific class of nonlinear time-varying complex networks,utilizing an unknown-input-observer approach within the framework of dynamic event-triggered mechanism(DETM).In order to optimize communication resource utilization,the DETM is employed to determine whether the current measurement data should be transmitted to the estimator or not.To guarantee a satisfactory estimation performance for the fault signal,an unknown-input-observer-based estimator is constructed to decouple the estimation error dynamics from the influence of fault signals.The aim of this paper is to find the suitable estimator parameters under the effects of DETM such that both the state estimates and fault estimates are confined within two sets of closed ellipsoid domains.The techniques of recursive matrix inequality are applied to derive sufficient conditions for the existence of the desired estimator,ensuring that the specified performance requirements are met under certain conditions.Then,the estimator gains are derived by minimizing the ellipsoid domain in the sense of trace and a recursive estimator parameter design algorithm is then provided.Finally,a numerical example is conducted to demonstrate the effectiveness of the designed estimator.

Command filtered integrated estimation guidance and control for strapdown missiles with circular field of view

In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated estimation guidance and control nonlinear model with limited actuator deflection angle is established considering the seeker's FOV constraint.The boundary time-varying integral barrier Lyapunov function(IBLF)is employed in backstepping design to constrain the body line-of-sight(BLOS)in IEGC system to fit a circular FOV.Then,the nonlinear adaptive controller is designed to estimate the changing aerodynamic parameters.The generalized extended state observer(GESO)is designed to estimate the acceleration of the maneuvering targets and the unmatched time-varying disturbances for improving tracking accuracy.Furthermore,the command filters are used to solve the"differential expansion"problem during the backstepping design.The Lyapunov theory is used to prove the stability of the overall closed-loop IEGC system.Finally,the simulation results validate the integrated system's effectiveness,achieving high accuracy strikes against maneuvering targets.

Numerical Simulation of Slurry Diffusion in Fractured Rocks Considering a Time-Varying Viscosity

To analyze the effects of a time-varying viscosity on the penetration length of grouting,in this study cement slur-ries with varying water-cement ratios have been investigated using the Bingham’sfluidflow equation and a dis-crete element method.Afluid-solid coupling numerical model has been introduced accordingly,and its accuracy has been validated through comparison of theoretical and numerical solutions.For different fracture forms(a single fracture,a branch fracture,and a fracture network),the influence of the time-varying viscosity on the slurry length range has been investigated,considering the change in the fracture aperture.The results show that under different fracture forms and the same grouting process conditions,the influence of the time-varying viscosity on the seepage length is 0.350 m.

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

Time-varying parameters estimation with adaptive neural network EKF for missile-dual control system

In this paper, a filtering method is presented to estimate time-varying parameters of a missile dual control system with tail fins and reaction jets as control variables. In this method, the long-short-term memory(LSTM) neural network is nested into the extended Kalman filter(EKF) to modify the Kalman gain such that the filtering performance is improved in the presence of large model uncertainties. To avoid the unstable network output caused by the abrupt changes of system states,an adaptive correction factor is introduced to correct the network output online. In the process of training the network, a multi-gradient descent learning mode is proposed to better fit the internal state of the system, and a rolling training is used to implement an online prediction logic. Based on the Lyapunov second method, we discuss the stability of the system, the result shows that when the training error of neural network is sufficiently small, the system is asymptotically stable. With its application to the estimation of time-varying parameters of a missile dual control system, the LSTM-EKF shows better filtering performance than the EKF and adaptive EKF(AEKF) when there exist large uncertainties in the system model.

The Origin of Cosmic Structures Part 6: CMB Anisotropy

In a recent series of papers, we introduced a new model of nucleosynthesis in which the matter content of the universe came into existence at a time of about 4 × 10-5 s. At that time, a small percentage of the vacuum energy was converted into neutron/antineutron pairs with a very small excess of neutrons. This process was regulated by an imprint that was established in the vacuum during an initial Plank-era inflation. Immediately after their inception, annihilation and charge exchange reactions proceeded at a very high rate and ran to completion after an interval of about 10-11 s. By then, all the antibaryons had disappeared thereby establishing the matter/antimatter asymmetry of the universe. What remained were very high densities of mesons and leptons, somewhat lower densities of protons and neutrons, and finally, the very high density of photons that eventually became the CMB. The density of matter so created varied from one location to another in such a manner as to account for all cosmic structures and because the energy density of the photons varied in proportion to that of the matter, the CMB-to-be came into existence with an anisotropic spectrum already in place. For structures, the size of galaxy clusters, the initial anisotropy magnitudes were on the order of 25%. In this paper, we will follow the subsequent evolution of the photons and show that this model predicts with accuracy the temperature of the warmest anisotropies in the observed CMB spectrum. .

Robust Parameter Identification Method of Adhesion Model for Heavy Haul Trains

A robust parameter identification method based on Kiencke model was proposed to solve the problem of the parameter identification accuracy being affected by the rail environment change and noise interference for heavy-duty trains. Firstly, a Kiencke stick-creep identification model was constructed, and the parameter identification task was transformed into a quadratic programming problem. Secondly, an iterative algorithm was constructed to solve the problem, into which a time-varying forgetting factor was added to track the change of the rail environment, and to solve the uncertainty problem of the wheel-rail environment. The Granger causality test was adopted to detect the interference, and then the weights of the current data were redistributed to solve the problem of noise interference in parameter identification. Finally, simulations were carried out and the results showed that the proposed method could track the change of the track environment in time, reduce the noise interference in the identification process, and effectively identify the adhesion performance parameters.

Tensor Decomposition-Based Channel Estimation and Sensing for Millimeter Wave MIMO-OFDM V2I Systems

An integrated sensing and communication(ISAC)scheme for a millimeter wave(mmWave)multiple-input multiple-output orthogonal frequency division multiplexing(MIMO-OFDM)Vehicle-to-Infrastructure(V2I)system is presented,in which both the access point(AP)and the vehicle are equipped with large antenna arrays and employ hybrid analog and digital beamforming structures to compensate the path loss,meanwhile compromise between hardware complexity and system performance.Based on the sparse scattering nature of the mmWave channel,the received signal at the AP is organized to a four-order tensor by the introduced novel frame structure.A CANDECOMP/PARAFAC(CP)decomposition-based method is proposed for time-varying channel parameter extraction,including angles of departure/arrival(AoDs/AoAs),Doppler shift,time delay and path gain.Then leveraging the estimates of channel parameters,a nonlinear weighted least-square problem is proposed to recover the location accurately,heading and velocity of vehicles.Simulation results show that the proposed methods are effective and efficient in time-varying channel estimation and vehicle sensing in mmWave MIMOOFDM V2I systems.

The Reality of Baryonic Acoustic Oscillations

The initial idea for baryonic acoustic oscillations (BAO) came about during early efforts to understand the origin of galaxies by studying perturbed versions of the Friedmann-Robertson-Walker (FRW) model. In more recent times, the emphasis has shifted to the idea that 2-point galaxy correlations embedded in the distribution of matter by the BAO could be used as a standard ruler to fix the parameters of cosmological models. In this paper, we first consider the actual business of extracting the correlation length from large data sets of measured galaxy locations. To facilitate this process, we introduce a much-improved method for extracting the correlation peak from the data set. Fundamental to this process in any model is the use of a fiducial cosmological model to transition from redshift space to comoving coordinate space where the correlations actually exist. The belief is that the correlation length so determined can then be reverted to redshift space to fix the parameters of cosmological models. We show, however, that this process is circular and hence of no value whatsoever for fixing model parameters. All one obtains are the parameters of the model used to transition to comoving space in the first place. Finally, we present simple arguments that show that the idea of BAO being responsible for the structure of the universe, i.e. the cosmic web, is unworkable.