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.

Singular spectrum analysis for the time-variable seasonal signals from GPS in Yunnan Province

Studying the seasonal deformation in GPS time series is important to interpreting geophysical contributors and identifying unmodeled and mismodeled seasonal signals.Traditional seasonal signal extraction used the least squares method,which models seasonal deformation as a constant seasonal amplitude and phase.However,the seasonal variations are not constant from year to year,and the seasonal amplitude and phase are time-variable.In order to obtain the time-variable seasonal signal in the GPS station coordinate time series,singular spectrum analysis(SSA)is conducted in this study.We firstly applied the SSA on simulated seasonal signals with different frequencies 1.00 cycle per year(cpy),1.04 cpy and with time-variable amplitude are superimposed.It was found that SSA can successfully obtain the seasonal variations with different frequencies and with time-variable amplitude superimposed.Then,SSA is carried out on the GPS observations in Yunnan Province.The results show that the time-variable amplitude seasonal signals are ubiquitous in Yunnan Province,and the timevariable amplitude change in 2019 in the region is extracted,which is further explained by the soil moisture mass loading and atmospheric pressure loading.After removing the two loading effects,the SSA obtained modulated seasonal signals which contain the obvious seasonal variations at frequency of 1.046 cpy,it is close with the GPS draconitic year,1.040 cpy.Hence,the time-variable amplitude changes in 2019 and the seasonal GPS draconitic year in the region could be discriminated successfully by SSA in Yunnan Province.

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.

Exponential Decay of Laminated Beam with Nonlinear Time-varying Delay and Microtemperature Effect

This research paper addresses a topic of interest to many researchers and engineers due to its effective applications in various industrial areas.It focuses on the thermoelastic laminated beam model with nonlinear structural damping,nonlinear time-varying delay,and microtemperature effects.Our primary goal is to establish the stability of the solution.To achieve this,and under suitable hypotheses,we demonstrate energy decay and construct a Lyapunov functional that leads to our results.

Time-variant fragility analysis of the bridge system considering time-varying dependence among typical component seismic demands

This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.

Simulation of spatially coupling dynamic response of train-track time-variant system

There exist three problems in the calculation of lateral vibration of the train-track time-variant system athome and abroad and the method to solve them is presented. Spatially coupling vibration analysis model of train-track time-variant system is put forward. Each vehicle is modeled as a multi-body system with 26 degrees of freedomand the action of coupler is also considered. The track structure is modeled as an assembly of track elements with 30degrees of freedom, then the spatially coupling vibration matrix equation of the train-track time-variant system is es-tablished on the basis of the principle of total potential energy with stationary value and the "set-in-right-position"rule. The track vertical geometric irregularity is considered as the excitation source of the vertical vibration of thesystem, and the hunting wave of car bogie frame is taken as the excitation source of lateral vibration of the system.The spatially coupling vibration matrix equation of the system is solved by Wilson-θ direct integration method. Theapproximation of the calculated results to the spot test results demonstrates the feasibility and effectiveness of thepresented analysis method. Finally, some other vibration responses of the system are also obtained.

Time-Variant Reliability-Based Multi-Objective Fuzzy Design Optimization for Anti-Roll Torsion Bar of EMU

Although various types of anti-roll torsion bars have been developed to inhibit excessive roll angle of the electric multiple unit(EMU)car body,it is critical to ensure the reliability of structural design due to the complexity of the problems involving time and uncertainties.To address this issue,amulti-objective fuzzy design optimization model is constructed considering time-variant stiffness and strength reliability constraints for the anti-roll torsion bar.A hybrid optimization strategy combining the design of experiment(DoE)sampling and non-linear programming by quadratic lagrangian(NLPQL)is presented to deal with the design optimization model.To characterize the effect of time on the structural performance of the torsion bar,the continuous-time model combined with Ito lemma is proposed to establish the time-variant stiffness and strength reliability constraints.Fuzzy mathematics is employed to conduct uncertainty quantification for the design parameters of the torsion bar.A physical programming approach is used to improve the designer’s preference and to make the optimization results more consistent with engineering practices.Moreover,the effectiveness of the proposed method has been validated by comparing with current methods in a practical engineering case.

Time-variant reliability analysis of three-dimensional slopes based on Support Vector Machine method

In the reliability analysis of slope, the performance functions derived from the most available stability analysis procedures of slopes are usually implicit and cannot be solved by first-order second-moment approach. A new reliability analysis approach was presented based on three-dimensional Morgenstem-Price method to investigate three-dimensional effect of landslide in stability analyses. To obtain the reliability index, Support Vector Machine （SVM） was applied to approximate the performance function. The time-consuming of this approach is only 0.028% of that using Monte-Carlo method at the same computation accuracy. Also, the influence of time effect of shearing strength parameters of slope soils on the long-term reliability of three-dimensional slopes was investigated by this new approach. It is found that the reliability index of the slope would decrease by 52.54% and the failure probability would increase from 0.000 705% to 1.966%. In the end, the impact of variation coefficients of c andfon reliability index of slopes was taken into discussion and the changing trend was observed.

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.

Spatial distribution characteristics and mechanism of nonhydrological time-variable gravity in China's Mainland

The purpose of this study is to explore nonhydrological mass transfer in China's Mainland.For this purpose,gravity recovery and climate experiment(GRACE)data were obtained to study the spatial distribution of time variant gravity signals in China's Mainland.Then,from auxiliary hydrological data processed according to the current hydrological model,a new more comprehensive hydrological model of China's Mainland was constructed.Finally,the time variant signals of this new hydrological model were removed from the time variant gravity field computed from GRACE data,thus obtaining a description of the nonhydrological mass transfer of China's Mainland.The physical sources and mechanisms of the resulting mass transfer are then discussed.The improved,more realistic,hydrological model used here was created by selecting the hydrological components with the best correlations in existing hydrological models,by use of correlation calculation,analysis,and comparison.This improved model includes water in soils and deeper strata,in the vegetation canopy,in lakes,snow,and glaciers,and in other water components(mainly reservoir storage,swamps,and rivers).The spatial distribution of the transfer signals due to nonhydrological mass in China's Mainland was obtained by subtracting the combined hydrological model from the GRACE time-variable gravity field.The results show that the nonhydrological signals in China's Mainland collected in GRACE data were mainly positive signals,and were distributed in the Bohai Rim and the northern and eastern parts of the Tibetan Plateau.The above nonhydrological mass transfer signals have been studied further and are discussed.The results show that the nonhydrological mass migration signals in the Bohai Rim region originate primarily from sea level change and marine sediment accumulation.The mass accumulation from Indian plate collision in the Tibetan Plateau appears to be the main reason for the increase in the residual gravity field in that region.

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.

Time-Variant Reliability Analysis of FPSO Hull Girder Considering Corrosion Based on Statistics

FPSO is a kind of important exploitation platform used in ocean oil and gas industry, which has the unique character of mooring at outsea for a long time. Since it can not be inspected and maintained thoronghly at dock like other kinds of ships, the reliability of FPSO hull girder during the whole service should be focused. Based on latest corrosion database and rational corrosion model, the ultimate strength of one FPSO is calculated under the conditions of slight, moderate and severe corrosion. The results not only provide the reliabihty under different corrosion conditions, but also do well for further inspection and maintenance research. The results provide necessary foundation for deciding inspection intervals and maintenance measure, which has practical sense to improve the general safety level of ocean engineering.

Seismologic applications of GRACE time-variable gravity measurements

The Gravity Recovery and Climate Experiment（GRACE） has been measuring temporal and spatial variations of mass redistribution within the Earth system since2002. As large earthquakes cause significant mass changes on and under the Earth＇s surface,GRACE provides a new means from space to observe mass redistribution due to earthquake deformations. GRACE serves as a good complement to other earthquake measurements because of its extensive spatial coverage and being free from terrestrial restriction. During its over 10 years mission,GRACE has successfully detected seismic gravitational changes of several giant earthquakes,which include the 2004 Sumatra–Andaman earthquake,2010 Maule（Chile） earthquake,and 2011 Tohoku-Oki（Japan） earthquake. In this review,we describe by examples how to process GRACE timevariable gravity data to retrieve seismic signals,and summarize the results of recent studies that apply GRACE observations to detect co- and post-seismic signals and constrain fault slip models and viscous lithospheric structures. We also discuss major problems and give an outlook in this field of GRACE application.

Complex Modal Analysis for the Time-Variant Dynamical Problem of Rotating Pipe Conveying Fluid

A semi-analytical form of complex modal analysis is proposed for the time-variant dynamical problem of rotating pipe conveying fluid system.The complex mode superposition method is introduced for the dynamic analysis in the time and frequency domains,in which appropriate orthogonality conditions are constructed to decouple the time-variant equation of motion.Consequently,complex frequencies and modes of vibration are analytically formulated and the variations of frequencies and damping of the system are evaluated.Numerical time-variant example of rotating pipe conveying fluid illustrates the effectiveness and accuracy of this method.Furthermore,the proposed solution scheme is also applicable to other similar time-variant dynamical problems.

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.

Semi-supervised learning based hybrid beamforming under time-varying propagation environments

Hybrid precoding is considered as a promising low-cost technique for millimeter wave(mm-wave)massive Multi-Input Multi-Output(MIMO)systems.In this work,referring to the time-varying propagation circumstances,with semi-supervised Incremental Learning(IL),we propose an online hybrid beamforming scheme.Firstly,given the constraint of constant modulus on analog beamformer and combiner,we propose a new broadnetwork-based structure for the design model of hybrid beamforming.Compared with the existing network structure,the proposed network structure can achieve better transmission performance and lower complexity.Moreover,to enhance the efficiency of IL further,by combining the semi-supervised graph with IL,we propose a hybrid beamforming scheme based on chunk-by-chunk semi-supervised learning,where only few transmissions are required to calculate the label and all other unlabelled transmissions would also be put into a training data chunk.Unlike the existing single-by-single approach where transmissions during the model update are not taken into the consideration of model update,all transmissions,even the ones during the model update,would make contributions to model update in the proposed method.During the model update,the amount of unlabelled transmissions is very large and they also carry some information,the prediction performance can be enhanced to some extent by these unlabelled channel data.Simulation results demonstrate the spectral efficiency of the proposed method outperforms that of the existing single-by-single approach.Besides,we prove the general complexity of the proposed method is lower than that of the existing approach and give the condition under which its absolute complexity outperforms that of the existing approach.

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.

Distribution rules of remaining oil by bottom water flooding and potential exploitation strategy in fault-controlled fractured-vuggy reservoirs

Based on the tectonic genesis and seismic data of fault-controlled fractured-vuggy reservoirs,the typical fractured-vuggy structure features were analyzed.A 3D large-scale visual physical model of“tree-like”fractured-vuggy structure was designed and made.The experiments of bottom-water flooding and multi-media synergistic oil displacement after bottom-water flooding were conducted with different production rates and different well-reservoir configuration relationships.The formation mechanisms and distribution rules of residual oil during bottom-water flooding under such fractured-vuggy structure were revealed.The producing characteristics of residual oil under different production methods after bottom-water flooding were discovered.The results show that the remaining oil in"tree-like"fractured-vuggy structure after bottom-water flooding mainly include the remaining oil of non-well controlled fault zones and the attic remaining oil at the top of well controlled fault zones.There exists obvious water channeling of bottom-water along the fault at high production rate,but intermittent drainage can effectively weaken the interference effect between fault zones to inhibit water channeling.Compared with the vertical well,horizontal well can reduce the difference in flow conductivity between fault zones and show better resistance to water channeling.The closer the horizontal well locates to the upper part of the“canopy”,the higher the oil recovery is at the bottom-water flooding stage.However,comprehensive consideration of the bottom-water flooding and subsequent gas injection development,the total recovery is higher when the horizontal well locates in the middle part of the“canopy”and drills through a large number of fault zones.After bottom water flooding,the effect of gas huff and puff is better than that of gas flooding,and the effect of gas huff and puff with large slug is better than that of small slug.Because such development method can effectively develop the remaining oil of non-well controlled fault zones and the attic remaining oil at the top of well controlled fault zones transversely connected with oil wells,thus greatly improving the oil recovery.

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.