TSCND:Temporal Subsequence-Based Convolutional Network with Difference for Time Series Forecasting

Time series forecasting plays an important role in various fields, such as energy, finance, transport, and weather. Temporal convolutional networks (TCNs) based on dilated causal convolution have been widely used in time series forecasting. However, two problems weaken the performance of TCNs. One is that in dilated casual convolution, causal convolution leads to the receptive fields of outputs being concentrated in the earlier part of the input sequence, whereas the recent input information will be severely lost. The other is that the distribution shift problem in time series has not been adequately solved. To address the first problem, we propose a subsequence-based dilated convolution method (SDC). By using multiple convolutional filters to convolve elements of neighboring subsequences, the method extracts temporal features from a growing receptive field via a growing subsequence rather than a single element. Ultimately, the receptive field of each output element can cover the whole input sequence. To address the second problem, we propose a difference and compensation method (DCM). The method reduces the discrepancies between and within the input sequences by difference operations and then compensates the outputs for the information lost due to difference operations. Based on SDC and DCM, we further construct a temporal subsequence-based convolutional network with difference (TSCND) for time series forecasting. The experimental results show that TSCND can reduce prediction mean squared error by 7.3% and save runtime, compared with state-of-the-art models and vanilla TCN.

Model of Mediating Determinants of Time Differences in INDYCAR

The IndyCar series distinguishes itself by providing the same design and operation of the single-seater to its pilots.The difference in times is then attributable to the skills of the drivers,but considering the data from the races could test this assumption.The objective of this work was to establish a trajectory model to predict race times.A cross-sectional,correlational,and explanatory work was carried out with a sample of 18,474 records in the period from 2020 to 2023 of the IndyCar series.The results show that the time span predicts the time differences.In relation to the studies of acceptance of the technology,the adjustment of this to human capacities to explain the time differences in the series of racing cars is discussed.

Temporal and spatial differences in human activities performed in Urban Green Spaces of Vilnius(Lithuania)

Urban green spaces(UGS)are relevant to city well-being,as recognized by the United Nations’Sustainable Development Goals(SDGs).However,few studies have studied the temporal use of UGS.This work assessed the seasonal,weekly,and daily use of three urban green spaces(Vingis Park,Bernardino Garden,and Jomantas Park)in Vilnius(Lithuania).The study is based on an on-site observation-based survey,which recorded users’characteristics,activities,and weather conditions during summer and winter.The results showed that UGS’s seasonal,weekly,and daily use differed according to park and users’characteristics.Parks with a higher diversity of facilities had a high seasonal difference in the number of observed activities.User numbers were higher in the summer for activities with children,social activities,sports,and water activities than in the winter.Jomantas Park had the lowest variability in user characteristics.Weather variables were linked to changes in users’activities.Higher precipitation and lower temperature were associated with reducing the number of users and the diversity of registered activities.Most of the stationary activities were observed during summer.The diversity of the observed activities was associated with the available facilities rather than the park size.The distribution of stationary activities was spatially correlated with facility/equipment(benches,playgrounds,sports,and fitness equipment)and proximity to water features.The results of this study are relevant for UGS design,planning,and management.

Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic

A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the computation costs,the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations.The effectiveness of the proposed algorithm is verified by the first numerical example.The mass conservation property and stability statement are confirmed by two other numerical examples.

Viscoacoustic prestack reverse time migration based onthe optimal time-space domain high-order finite-difference method

Prestack reverse time migration （RTM） is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference （FD） method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.

A PSO microseismic localization method based on group waves' time difference information

Aiming at the lower microseismic localization accuracy in underground shallow distributed burst point localization based on time difference of arriva（TDOA）,this paper presents a method for microseismic localization based on group waves’ time difference information Firstly, extract the time difference corresponding to direct P wavers dominant frequency by utilizing its propagation characteristics. Secondly, construct TDOA model with non-prediction velocity and identify objective function of particle swarm optimization （PSO）. Afterwards, construct the initial particle swarm by using time difference information Finally, search the localization results in optimal solution space. The results of experimental verification show that the microseismic localization method proposed in this paper effectively enhances the localization accuracy of microseismic explosion source with positioning error less than 50 cm, which can satisfy the localization requirements of shallow burst point and has definite value for engineering application in underground space positioning field.

Full-Wave Analysis of Slotline Using Time-Domain Finite-Difference Method

The transmission and dispersive characteristics of slotline are calculated in this paper. The tail of Gaussion pulse is improved because a modified dispersive boundary condition (DBC) is adopted. It leads to a reduction in computer memory requirements and computational time. The computational domain is greatly reduced to enable performance in personal computer. At the same time because edges of a boundary and summits are treated well, the computational results is more accurate and more collector.

Finite difference time domain method forward simulation of complex geoelectricity ground penetrating radar model

The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of curl interface underground or “v” figure complex model, it is difficult to realize. So it is important to forward the complex geoelectricity model. This paper takes two Maxwell’s vorticity equations as departure point, makes use of the principles of Yee’s space grid model theory and the basic principle finite difference time domain method, and deduces a GPR forward system of equation of two dimensional spaces. The Mur super absorbed boundary condition is adopted to solve the super strong reflection on the interceptive boundary when there is the forward simulation. And a self-made program is used to process forward simulation to two typical geoelectricity model.

Integrated method for measuring distance and time difference between small satellites

The advancement of small satellites is promoting the development of distributed satellite systems,and for the latter,it is essential to coordinate the spatial and temporal relations between mutually visible satellites.By now,dual one-way ranging(DOWR)and two-way time transfer(TWTT)are generally integrated in the same software and hardware system to meet the limitations of small satellites in terms of size,weight and power(SWaP)consumption.However,studies show that pseudo-noise regenerative ranging(PNRR)performs better than DOWR if some advanced implementation technologies are employed.Besides,PNRR has no requirement on time synchronization.To apply PNRR to small satellites,and meanwhile,meet the demand for time difference measurement,we propose the round-way time difference measurement,which can be combined with PNRR to form a new integrated system without exceeding the limits of SWaP.The new integrated system can provide distributed small satellite systems with on-orbit high-accuracy and high-precision distance measurement and time difference measurement in real time.Experimental results show that the precision of ranging is about 1.94 cm,and that of time difference measurement is about 78.4 ps,at the signal to noise ratio of 80 dBHz.

Finite Difference Solution of Response Time Delay of Magneto-rhelological Damper

Magneto-rhelological（MR） dampers are devices that employ rheological fluids to modify their mechanical properties. Their mechanical simplicity, high dynamic range, lower power requirements, large force capacity, robustness and safe maimer of operation in cases of failure have made them attractive devices for semi-active real-time control in civil, aerospace and automotive applications. Time response characteristic is one of the most important technical performances of MR dampers, and response time directly affects the control frequency, application range and the actual effect of MR dampers. In this study, one kind of finite difference solution for predicting the response time ofmagneto-rheological dampers from ＂off-state＂ to ＂on-state＂ is put forward. A laminar flow model is used to describe the flow in the MR valve, and a bi-viscous fluid flow model is utilized to describe the relationship of shear stress and shear rate of MR fluid. An explicit difference format is used to diseretize the Novior-Stoks equation, and stability condition of this algorithm is built by Von-Neumann stability criterion. The pressure gradient along the flow duct is solved by a dichotomy algorithm with iteration, and the changing curve of the damping force versus time of MR damper is obtained as well. According to the abovementioned numerical algorithm, the damping forces versus time curves from ＂off-state＂ to ＂on-state＂ of a cylindrical piston type MR damper are computed. Moreover, the MR damper is installed in a material test system（MTS）, the magnetic field in the wire circles of the MR damper is ＂triggered＂ when the MR damper is imposed to do a constant speed motion, and the damping force curves are recorded. The comparison between numerical results and experimental results indicates that this finite difference algorithm can be used to estimate the response time delay of MR dampers.

RETHINKING TO FINITE DIFFERENCE TIME-STEP INTEGRATIONS

The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.

Finite-difference time-domain studies of low-frequency stop band in superconductor-dielectric superlattice

The transmission coefficients of electromagnetic （EM） waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain （SO-FDTD） method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.

Analysis of an Implicit Finite Difference Scheme for Time Fractional Diffusion Equation

Time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∈(0, 1). In this paper, an implicit finite difference scheme for solving the time fractional diffusion equation with source term is presented and analyzed, where the fractional derivative is described in the Caputo sense. Stability and convergence of this scheme are rigorously established by a Fourier analysis. And using numerical experiments illustrates the accuracy and effectiveness of the scheme mentioned in this paper.

Passive Localization Using Time Difference of Arrival and Frequency Difference of ArrivalWC

In order to improve the accuracy and engineering feasibility of four-Satellite localization system, the frequency difference measurement is introduced to the four-Satellite TDOA (Time Difference of Arrival) localization algorithm. The TDOA/FDOA (Frequency Difference of Arrival) localization algorithm is used to optimize the GDOP (geometric dilution of precision) of four-Satellite localization. The simulation results show that the absolute position measurement accuracy has little influence on TDOA/FDOA localization accuracy as compared with TDOA localization. Under the same conditions, TDOA/FDOA localization has better accuracy and its GDOP shows more uniform distribution in diamond configuration case. The localization accuracy of four-Satellite TDOA/FDOA is better than the localization accuracy of four-Satellite TDOA.

A Time-Domain Numerical Simulation for Free Motion Responses of Two Ships Advancing in Head Waves

The constant panel method within the framework of potential flow theory in the time domain is developed for solving the hydrodynamic interactions between two parallel ships with forward speed.When solving problems within a time domain framework,the free water surface needs to simultaneously satisfy both the kinematic and dynamic boundary conditions of the free water surface.This provides conditions for adding artificial damping layers.Using the Runge−Kutta method to solve equations related to time.An upwind differential scheme is used in the present method to deal with the convection terms on the free surface to prevent waves upstream.Through the comparison with the available experimental data and other numerical methods,the present method is proved to have good mesh convergence,and satisfactory results can be obtained.The constant panel method is applied to calculate the hydrodynamic interaction responses of two parallel ships advancing in head waves.Numerical simulations are conducted on the effects of forward speed,different longitudinal and lateral distances on the motion response of two modified Wigley ships in head waves.Then further investigations are conducted on the effects of different ship types on the motion response.

Structure-dependent difference equations for time integration

A structure-dependent explicit method with enhanced stability properties is proposed in this study. In general, the method offers unconditional stability for structural systems except those with a particular instantaneous stiffness hardening behavior. In addition, it is second-order accurate and displays no overshooting in high frequency responses. Numerical experiments reveal that the proposed method saves a substantial amount of computational effort in solving inertial problems where only the low frequency responses are of interest, when compared to a general second-order accurate integration method.

Adaptive Modeling and Forecasting of Time Series by Combining the Methods of Temporal Differences with Neural Networks

This paper discusses the modeling method of time series with neural network. In order to improve the adaptability of direct multi-step prediction models, this paper proposes a method of combining the temporal differences methods with back-propagation algorithm for updating the parameters continuously on the basis of recent data. This method can make the neural network model fit the recent characteristic of the time series as close as possible, therefore improves the prediction accuracy. We built models and made predictions for the sunspot series. The prediction results of adaptive modeling method are better than that of non-adaptive modeling methods.

The Real-Time,High Precision Phase Difference Measurement of Electron Density in HL-2A Tokamak

This paper introduces a real-time high precision measurement of phase difference based on Field Programmable Gate Array（FPGA） technology,which has been successfully applied to laser grating interference measurement and real-time feedback of plasma electron density in HL-2A tokamak.It can track the changes of electron density while setting the starting point of the density curve to zero.In a laboratory test,the measuring accuracy of phase difference is less than 0.1°,the time resolution is 80 ns,and the feedback delay is 180 μs.

A Novel Absorbing Boundary Condition for the Frequency-Dependent Finite-Difference Time-Domain Method

A new absorbing boundary condition (ABC) for frequency dependent finite difference time domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (FD) 2TD method. On the basis of digital filter designing and vector algebra, the absorbing boundary condition under arbitrary angle of incidence are derived. The transient electromagnetic problems in two dimensions and three dimensions are calculated and the validity of the ABC is verified.

A Finite-Difference Approach to the Time-Dependent Mild-Slope Equation

A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity. The Enler predietor-corrector method and the three-point finite-difference method with varying spatial steps are adopted to discretize the time derivatives and the two-dimensional horizontal ones, respectively, thus leading both the time and spatial derivatives to the second-order accuracy. The boundary conditions for the present model are treated on the basis of the general conditions for open and fixed boundaries with an arbitrary reflection coefficient and phase shift. Both the linear and nonlinear versions of the numerical model are applied to the wave propagation and transformation over an elliptic shoal on a sloping beach, respectively, and the linear version is applied to the simulation of wave propagation in a fully open rectangular harbor. From comparison of numerical results with theoretical or experimental ones, it is found that they are in reasonable agreement.