Assessment of corrected time-step method for nominal ionospheric gradient calculation: A comparative analysis with spatial approaches

The effect of ionospheric delay on the ground-based augmentation system under normal conditions can be mitigated by determining the value of the nominal ionospheric gradient(σvig).The nominal ionospheric gradient is generally obtained from Continuously Operating Reference Stations data by using the spatial single-difference method(mixed-pair,station-pair,or satellite-pair)or the temporal single-difference method(time-step).The time-step method uses only a single receiver,but it still contains ionospheric temporal variations.We introduce a corrected time-step method using a fixed-ionospheric pierce point from the geostationary equatorial orbit satellite and test it through simulations based on the global ionospheric model.We also investigate the effect of satellite paths on the corrected time-step method in the region of the equator,which tends to be in a more north–south direction and to have less coverage for the east–west ionospheric gradient.This study also addresses the limitations of temporal variation correction coverage and recommends using only the correction from self-observations.All processes are developed under simulations because observational data are still difficult to obtain.Our findings demonstrate that the corrected time-step method yieldsσvig values consistent with other approaches.

An Adaptive Time-Step Backward Differentiation Algorithm to Solve Stiff Ordinary Differential Equations: Application to Solve Activated Sludge Models

A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a high computational cost, slower response, and need for more memory resources. One possible strategy to overcome this problem is to dynamically adjust the time-step with respect to the system’s stiffness. Therefore, small time-steps can be applied when needed, and larger time-steps can be used when allowable. This paper presents a new algorithm for adjusting the dynamic time-step based on a BDF discretization method. The parameters used to dynamically adjust the size of the time-step can be optimally specified to result in a minimum computation time and reasonable accuracy for a particular case of ODEs. The proposed algorithm was applied to solve the system of ODEs obtained from an activated sludge model (ASM) for biological wastewater treatment processes. The algorithm was tested for various solver parameters, and the optimum set of three adjustable parameters that represented minimum computation time was identified. In addition, the accuracy of the algorithm was evaluated for various sets of solver parameters.

A varying time-step explicit numerical inte-gration algorithm for solving motion equa-tion

If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restricted by the stability criterion in computational region. However, the excessively small time-step is usually unnecessary for a large portion of computational region. In this paper, a varying time-step explicit numerical integration algorithm is introduced, and its basic idea is to use different time-step restricted by the stability criterion in different computational region. Finally, the feasibility of the algorithm and its effect on calculating precision are verified by numerical test.

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

On time-step in structural seismic response analysis under ground displacement/acceleration

There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.

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.

Time-stepping finite element analysis on the influence of skewed rotors and different skew angles on the losses of squirrel cage asynchronous motors

To study the influence of skewed rotors and different skew angles on the losses of squirrel cage asynchronous motors,a 5.5-kW motor was taken as an example and the multi-sliced field-circuit coupled time stepping finite element method(T-S FEM)was used to analyze the axially non-uniform fundamental and harmonic field distribution characteristics at typical locations in the stator and rotor cores.The major conclusions are:firstly the skewed rotor exhibits a decrease in the harmonic copper losses caused by slot harmonic currents in the stator winding and rotor bars.Secondly,the skewed rotor shifts the non-uniform distribution of field in the axial direction,which leads to more severe saturation and an increase in iron losses.The heavier the load,the more pronounced the increase in iron losses.Furthermore,the influences of different skew angles on motor losses are studied systematically,with skew angles from 0.5 to 1.5 stator tooth pitch.It is found that the lowest total loss occurs at 0.8 stator tooth pitch,and the slot harmonics can be decreased effectively.

An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation

This paper studies the numerical simulations for the Cahn-Hilliard equation which describes a phase separation phenomenon.The numerical simulation of the Cahn-Hilliardmodel needs very long time to reach the steady state,and therefore large time-stepping methods become useful.The main objective of this work is to construct the unconditionally energy stable finite difference scheme so that the large time steps can be used in the numerical simulations.The equation is discretized by the central difference scheme in space and fully implicit second-order scheme in time.The proposed scheme is proved to be unconditionally energy stable and mass-conservative.An error estimate for the numerical solution is also obtained with second order in both space and time.By using this energy stable scheme,an adaptive time-stepping strategy is proposed,which selects time steps adaptively based on the variation of the free energy against time.The numerical experiments are presented to demonstrate the effectiveness of the adaptive time-stepping approach.

A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation

In this paper,we will develop a first order and a second order convex splitting,and a first order linear energy stable fully discrete local discontinuous Galerkin(LDG)methods for the modified phase field crystal(MPFC)equation.In which,the first order linear scheme is based on the invariant energy quadratization approach.The MPFC equation is a damped wave equation,and to preserve an energy stability,it is necessary to introduce a pseudo energy,which all increase the difficulty of constructing numerical methods comparing with the phase field crystal(PFC)equation.Due to the severe time step restriction of explicit timemarchingmethods,we introduce the first order and second order semi-implicit schemes,which are proved to be unconditionally energy stable.In order to improve the temporal accuracy,the semi-implicit spectral deferred correction(SDC)method combining with the first order convex splitting scheme is employed.Numerical simulations of the MPFC equation always need long time to reach steady state,and then adaptive time-stepping method is necessary and of paramount importance.The schemes at the implicit time level are linear or nonlinear and we solve them by multigrid solver.Numerical experiments of the accuracy and long time simulations are presented demonstrating the capability and efficiency of the proposed methods,and the effectiveness of the adaptive time-stepping strategy.

逐级加压启动时机对电动硅化法加固软黏土影响

逐级加压法可以有效提高电渗后期处理效果,降低能耗。本实验采用逐级加压的方式对电动硅化法进行优化,以解决电动硅化法中实验后期排水速率低、实验能耗大、电极腐蚀严重等问题。设置4组不同逐级加压启动时间实验研究最佳的逐级加压启动时机,对实验过程中电流、排水量进行监测,分析实验结束后土体的沉降量、含水率、抗剪强度,并计算各实验过程中的能耗系数,深入探究不同加压启动时机对电渗处理效果的影响。结果表明:逐级加压的通电方式可以有效提高电渗处理效果,并且逐级加压存在最佳的加压时机,当电流下降至峰值电流的60%时加压可以有效提高电渗的排水量,增大土体整体抗剪强度,土体均匀性较好,降低实验后期能耗系数。

A Unified FastMemory-Saving Time-SteppingMethod for Fractional Operators and Its Applications

Time-dependent fractional partial differential equations typically require huge amounts of memory and computational time,especially for long-time integration,which taxes computational resources heavily for high-dimensional problems.Here,we first analyze existing numerical methods of sum-of-exponentials for approximating the kernel function in constant-order fractional operators,and identify the current pitfalls of such methods.In order to overcome the pitfalls,an improved sum-of-exponentials is developed and verified.We also present several sumof-exponentials for the approximation of the kernel function in variable-order fractional operators.Subsequently,based on the sum-of-exponentials,we propose a unified framework for fast time-stepping methods for fractional integral and derivative operators of constant and variable orders.We test the fast method based on several benchmark problems,including fractional initial value problems,the time-fractional Allen-Cahn equation in two and three spatial dimensions,and the Schr¨odinger equation with nonreflecting boundary conditions,demonstrating the efficiency and robustness of the proposed method.The results show that the present fast method significantly reduces the storage and computational cost especially for long-time integration problems.

On a Large Time-SteppingMethod for the Swift-Hohenberg Equation

The main purpose of this work is to contrast and analyze a large timestepping numerical method for the Swift-Hohenberg(SH)equation.This model requires very large time simulation to reach steady state,so developing a large time step algorithm becomes necessary to improve the computational efficiency.In this paper,a semi-implicit Euler schemes in time is adopted.An extra artificial term is added to the discretized system in order to preserve the energy stability unconditionally.The stability property is proved rigorously based on an energy approach.Numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches by comparing with the classical scheme.

基于子循环自适应串行交错时间匹配算法的油浸式变压器绕组瞬态温升计算

针对传统算法存在的步长调整及耦合点选择问题,该文提出基于子循环自适应串行交错(SCAS)的时间匹配算法。首先,在步长调整方面,通过加入自适应(ATS)-启发式(HTS)混合变步长算法,解决步长无法实时调整的问题;然后,针对耦合点选择问题,该文在传统常规串行交错(CSS)时间匹配算法及现有改进方案子循环常规串行交错(SCSS)的基础上,提出SCAS时间匹配算法,采用自适应方案确定计算时间窗及预定耦合点,并引入指数平滑法对其精度进行保证;最后,该文基于110 kV油浸式电力变压器建立二维瞬态单分区分匝绕组模型,并将所提算法与其他传统方法进行对比分析。结果表明:在精度方面,与传统CSS算法相比SCAS算法的流场及温度场最大平均相对误差均不超过0.45%,在可接受误差范围内;在效率方面,SCAS算法总体计算效率较CSS算法提高了近20倍。同时,为了说明所提算法的工程价值,该文搭建基于110 kV变压器绕组模型的温升实验平台,将SCAS时间匹配算法应用于该模型中,实验结果表明:在精度方面,SCAS算法与实验达到稳态时最大绝对误差为2.7 K;在计算效率上,本文所提算法的计算效率较传统算法提升约46倍,计算步数约为传统的1/47,减少了计算冗余。

基于定子电流法的绕线转子无刷双馈发电机偏心故障研究

绕线转子无刷双馈电机在船舶轴带发电以及风力发电等领域中具有良好的应用前景。转子偏心是一种常见的机械故障,威胁着现代化工业体系的稳定运转,因此实现其状态检测和故障诊断非常关键。由于无刷双馈电机具有特殊的定、转子绕组结构以及复杂的气隙磁场,因此传统的故障检测方法无法直接用于该类电机。该文通过定子电流法提取了功率绕组电流的特征频率分量作为故障指标,实现对静偏心、动偏心以及混合偏心的无创诊断。建立故障电机的时步有限元模型,并通过详细的故障机理分析,得出不同类型的偏心故障可能导致的特征频率信号。最后,以一台2/4对极无刷双馈电机为例,并通过有限元仿真、样机试验验证解析法的结论,为绕线转子无刷双馈电机偏心故障的精准检测提供了理论依据。

向后微分公式在六角形几何物理-热工耦合上的应用

针对六角形几何物理-热工耦合求解问题,提出了一种二阶变步长向后微分公式,物理和热工采用相同的步长和时间离散格式,并利用变步长技巧,提高计算效率。物理-热工采用模块化方式耦合,物理模块采用基于六角形几何的节块法,热工采用子通道程序,2个模块之间的数据传递通过共享内存的方式实现,开发了基于向后微分公式的HEXCOB-BDF程序。利用两个VVER堆芯弹棒事故验证该方法在物理-热工耦合上的准确性和计算效率。计算结果表明,HEXCOB-BDF程序与KIKO3D,DYN3D,PARCS计算结果相符,同时计算时间约为隐式Euler法计算时间的1/4。表明本文算法具有较好的准确性和较高的计算效率,可为六角形几何物理-热工耦合求解提供参考。

双延迟深度确定性策略的AUV路径规划控制

为了在复杂未知环境中提升水下机器人的实时控制精度,提出一种基于双延迟深度确定性策略的水下机器人路径规划控制方法。在没有环境先验知识的情况下,通过在线测量使用双延迟深度确定性策略算法计算水下无人机的连续控制输入。考虑洋流随机高斯模型,引入一种综合奖励函数,并且提出一种基于阶跃强化学习的六自由度动力学水下无人机自适应运动规划和避障技术。仿真结果表明提出方法能够有效实现位置环境下的高精度实时控制,并且具有一定的泛化能力。

结构动力问题的高阶精确时步群积分方法

高阶精确时间积分方法可为与时间相关的高频复杂动力行为提供高精度的预测结果,但既有高阶精确时间积分方法普遍存在计算工作量偏大的问题,难以满足实际结构线性和非线性动力分析日益增长的计算需求。该文提出了一种基于时步群的高阶精确时间积分方法,将p(p≥2)个相邻的未知时步组成待求解的时步群,以结构动力方程积分解为基础构建逐时步群求解结构动态响应的时间积分方案。在对每个时步群进行积分的过程中,无需联立求解方程,仅通过矩阵乘法运算即可一次性地计算得到时步群内全部p个时步的动态响应。数值特性分析以及线性与非线性算例试验均表明,该文算法精度高、稳定性好、数值耗散可控,在选择较大的时间步距情形下依然能够稳定地获得高精度的计算结果。相较传统二阶精度时间积分方法,该文算法的计算效率亦有较大幅度地提高。

基于COMGRU的AUV航路轨迹预测方法

针对采用神经网络预测自主水下机器人航迹存在滞后性的问题,本文提出一种基于信息压缩的改进门控循环神经网络,用于水下自主机器人航路多步轨迹预测。该算法将水下自主机器人航行轨迹附近的障碍物位置信息、海流信息以及时空轨迹信息共同构成的地理位置信息进行数据压缩处理,作为本文预测网络的输入,以提高网络训练效率。实验验证该算法减少了水下自主机器人航迹多步预测的滞后性且具有较高的准确率。

考虑记忆时间的LSTM模型在赣江流域径流预报中的应用

在气候变化条件下,准确的径流预测对水资源的规划与管理十分重要。本文基于长短时记忆神经网络(LSTM)模型,采用赣江流域外洲、峡江以及栋背水文站的逐日流量以及CN05.1日降水数据构建3个不同面积流域的径流预测模型,并通过设置不同情景分析:模型的有效预见期与不同流域平均产汇流时间之间的关系,有效预见期内LSTM径流预测模型精度与记忆时间之间的关系,不同长度的预见期与模型最佳记忆时间之间的关系,同时探讨LSTM径流预测所需的记忆时间与流域面积的关系。结果表明:(1)综合考虑降水和前期径流情景下的径流预测效果最好,当预见期为1 d时,外洲、峡江、栋背站的纳什效率系数(NSE)分别可达0.98、0.96以及0.90;且其有效预见期与仅考虑降水信息的有效预见期相同,均与流域平均产汇流时间相近。(2)随着预见期的延长,不同情景下的预测精度均有不同程度的下降,其中仅考虑前期径流情景的下降率最大,说明降水信息较前期径流对径流预测效果的提升更重要。同时,随着流域面积的增加,相同预见期内径流预测精度均有所提升。(3)当预见期相同时,随记忆时间的延长,不同径流预测模型的预测精度均先上升至最高,接着具有下降趋势,最后逐渐趋于稳定。且在有效预见期内,随着预见期的延长,最佳记忆时间均有增大趋势,当达到最长的有效预见期时,对应的最佳记忆时间均为14 d。此外,在赣江流域的模拟结果表明,随着流域面积的增大,LSTM的最佳记忆时间减小。研究结果可为赣江流域的径流预报提供参考,同时有助于推求其他流域采用机器学习进行径流预测所需的最佳记忆时间。

基于改进深度强化学习的SCR脱硝系统复合控制研究

针对选择性催化还原(Selective catalytic reduction,SCR)脱硝系统延迟大、扰动多等特点,提出了一种基于改进双延迟深度确定性策略梯度(Twin delayed deep deterministic policy gradient,TD3)的SCR脱硝系统复合控制策略。首先,提出了一种融合多步时序差分(Muti-step temporal-difference,MSTD)和优先经验回放(Prioritized experience replay,PER)的改进TD3算法。该算法在策略更新时使用MSTD计算回报,同时利用PER选择重要的经验进行学习,以此提高TD3算法的策略学习能力并加速算法的学习过程。其次,通过设计多维状态观测,综合考虑SCR脱硝系统的前馈信号和验证反馈信号来实现SCR脱硝系统的复合控制,进而维持出口NOx浓度的稳定性。最后,进行仿真实验验证,结果表明基于MSTD-PER-TD3算法的复合控制策略能更有效地克服入口NOx浓度波动对出口NOx浓度的影响,并具有优秀的抗干扰能力和鲁棒性。