New Numerical Integration Formulations for Ordinary Differential Equations

An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.

Combinative Algorithms for the Multidisciplinary Collaborative Simulation of Complex Mechatronic Products Based on Major Step and Convergent Integration Step

Multidisciplinary collaborative simulation （MCS） is an important area of research in the domain of multidisciplinary design optimization （MDO）.Although previous research for MCS has to some extent addressed some issues like using of multiple tools,integration stability,control of step size,data synchronization,etc,further work is still necessary to study how to achieve improved precision.A theoretical model is formulated to describe and analyze the integration process of MCS.A basic algorithm with equal major steps is proposed based on the model,along with two methods of implementation for the model,namely the serial method and the parallel method.A further algorithm based on convergent integration step is proposed,which has a more flexible strategy for run-time integration.The influence of interpolation techniques on simulation performance is studied as well.Simulations of the performance of various algorithms with different interpolation techniques are performed for both a simple numerical example and a complex mechatronic product.The novel algorithm based on convergent integration step,when used with a high-order interpolation technique,has better performance in terms of precision and efficiency.The innovation of this paper is mainly on the validation of high precision of the proposed convergent integration step algorithm.

Modified precise time step integration method of structural dynamic analysis

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.

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.

APPLICATION OF STEP IN CAD/CAPP INTEGRATION

A brief discussion of the content and methodology of STEP is given, and STEP based strategies for CAD/CAPP information integration is pointed out. A STEP based feature technology in which a three layer feature definition is included is discussed, the content of feature information is analyzed and a stratified CAD feature library is shown. On these bases, a commonly shared part information model is proposed. The architecture of the integrated CAD/CAPP system is presented.

COORDINATION OF THE MOTION PARAMETERS WITHIN STEP-BY-STEP INTEGRATION FOR DYNAMIC EQUATION

A method is presented that coordinates the calculation of the displacement, velocity and acceleration of structures within the time-steps of different types of step-by-step integration. The dynamic equation is solved using an energy equation and the calculating data of the original method. The method presented is better than the original method in terms of calculating postulations and is in better conformity with the system's movement. Take the Wilson-θ method as an example. By using the coordination process, the calculation precision has been greatly im proved (reducing the errors by approximately 90% ), and the greater part of overshooting of the calculation result has been eliminated. The study suggests that the mal-coordination of the motion parameters within the time-step is the major factor that contributes to the result errors of step-by-step integration for the dynamic equation.

ELEMENT－BY－ELEMENT MATRIX DECOMPOSITION ANDSTEP－BY－STEP INTEGRATION METHOD FOR TRANSIENTDYNAMIC PROBLEMS

In this paper a general matrix decomposition scheme as well as an element-by-clement relaxation algorithm combined with step-by -step integration method is presented for transient dynamic problems thus the finite element method can be fromforming global stiffness matrix global mass matrix as well as solyin large scale sparse equations Theory analysis and numerical results show that the presented matrix decomposition scheme is the optimal one The presented algoithm has else physicalmeaning and can be busily applied to finite element codes

Simple Program for Step-by-Step Time Integration in Chemical Kinetics, Applied to Simple Model for Hydrogen Combustion

A simple algorithm is proposed for step-by-step time integration of stiff ODEs in Chemical Kinetics. No predictor-corrector technique is used within each step of the algorithm. It is assumed that species concentrations less than 10-6 mol·L-1 do not activate any chemical reaction. So, within each step, the time steplength Δt of the algorithm is determined from the fastest reaction rate maxR by the formula Δt = 10-6mol·L-1/max R. All the reversible elementary reactions occur simultaneously;however, by a simple book-keeping technique, the updating of species concentrations, within each step of the algorithm, is performed within each elementary reaction separately. The above proposed simple algorithm for Chemical Kinetics is applied to a simple model for hydrogen combustion with only five reversible elementary reactions (Initiation, Propagation, First and Second Branching, Termination by wall destruction) with six species (H2, O2, H, O, HO, H2O). These five reversible reactions are recommended in the literature as the most significant elementary reactions of hydrogen combustion [1] [2]. Based on the proposed here simple algorithm for Chemical Kinetics, applied to the global mechanism of proposed five reversible elementary reactions for hydrogen combustion, a simple and short computer program has been developed with only about 120 Fortran instructions. By this proposed program, the following are obtained: 1) The total species concentration of hydrogen combustion, starting from the sum of initial reactants concentrations [H2] + [O2], gradually diminishes, due to termination reaction by wall destruction, and tends to the final concentration of the product [H2O], that is to the 2/3 of its initial value, in accordance to the established overall stoichiometric reaction of hydrogen combustion 2H2 + O2 → 2H2O. 2) Time-histories for concentrations of main species H2, O2, H, H2O of hydrogen combustion, in explosion and equilibrium regions, obtained by the proposed program, are compared to corresponding ones obtained by accurate computational studies of [3]. 3) In the first step of the algorithm, the only nonzero species concentrations are those of reactants [H2], [O2]. So, the maximum reaction rate is that of the forward initiation reaction max R = Rif = kif[H2] [O2], where the rate constant kif is very slow. Thus, the first time steplength Δt1 = 10-6mol·L-1/max R results long in sec. After the first step, the sequences of all the following Δt’s are very short, in μsec. So, the first time steplength Δt1 can be considered as ignition delay time. 4) It is assumed that explosion corresponds to ignition delay time Δt1 t1 = 10 sec., can be considered as explosion limit curve. This curve is compared to the corresponding one obtained by the accurate computational studies of [2].

A STEP-BASED CAD/CAPP INTEGRATION

The information integration of CAD/CAPP is one of the crucial techniques in CIM. Thispaper desicribes an integrated CAD/CAPP system which is implemented by connecting MPIM to BR-CAPP via an interface for data exchange between them. The data exchange between MPIM and BR-CAPP is accomplished through STEP neutral file.

A new simple method of implicit time integration for dynamic problems of engineering structures

This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.

Concurrent Engineering oriented Integrated Product Model Based on STEP

In this paper, the generalized feature concept is put forward according to concurrent engineering. An integrated product model is established based on the generalized feature according to STEP in order to provide enrichment information for product concurrent development process. The integration of the information and function of CAD/CAPP can be realized based on the integrated product model that supports concurrent engineering. IPM has been used successfully in product concurrent development.

DIRECT INTEGRATION METHODS WITH INTEGRAL MODEL FOR DYNAMIC SYSTEMS

A new approach which is a direct integration method with integral model (DIM-IM) to solve dynamic governing equations is presented. The governing equations ore integrated into the integral equations. An algorithm with explicit and predict-correct and self-starting and fourth-order accuracy to integrate the integral equations is given. Theoretical analysis and numerical examples shaw that DIM-IM described in this paper suitable for strong nonlinear and non-conservative system have higher accuracy than central difference, Houbolt, Newmark and Wilson-Theta methods.

A STEP-BY-STEP INTEGRAL METHOD FOR ACTIVELY CONTROLLED STRUCTURES

A new active control method was proposed, in which the analytical control law was deduced by using a step by step integral method to differential equation of motion under the condition of static error being zero. This control law is terse in mathematical expression and convenient for practical use. The simulation results demonstrate that the proposed method can provide much more remarkable peak response reduction of seismically excited structures than the classical LQR method.

基于季节性碳交易机制的园区综合能源系统低碳经济调度

为有效提高碳排放配额分配的合理性,并且避免年度结算时碳排放量超标导致环境污染加剧问题,提出基于奖惩因子的季节性碳交易机制,以园区综合能源系统(park integrated energy system,PIES)为对象进行低碳经济调度。首先,构建包含能量层–碳流层–管理层的综合能源系统(integrated energy system,IES)运行框架,建立电气热多能流供需动态一致性模型;其次,分析系统内“日–季节–年度”碳排放特性,打破传统应用指标法的配额分配方法,采用灰色关联分析法建立碳排放配额分配模型,并基于奖惩阶梯碳价制定季节性碳交易机制;最后,以系统内全寿命周期运行成本及碳交易成本最小为目标,对执行季节性碳交易机制的PIES进行低碳经济调度,分析长时间尺度下季节性储能参与调度的减碳量。搭建IEEE 33节点电网5节点气网7节点热网的PIES,并基于多场景进行算例分析,验证此调度方法能够实现零碳经济运行,保证系统供能可靠性,为建立零碳园区奠定理论基础。

基于信息间隙决策理论的含碳捕集−电转气综合能源系统优化调度

【目的】为科学统筹综合能源系统运行经济性、稳定性和低碳性优化目标,采用何种技术手段以提升能源转化效率,减少系统能源浪费和区域环境污染,是当下综合能源系统合理优化的主要问题。为此,提出一种基于场景生成与信息间隙决策理论的含碳捕集与封存(carbon capture and storage,CCS)—两段式电转气(power to gas,P2G)综合能源系统低碳优化策略。【方法】在技术层面,通过对电P2G两阶段精细化建模,提高氢能利用效率,建立热电联产(combined heating and power,CHP)-CCS-P2G耦合模型;在市场机制层面,引入阶梯型碳交易模型以降低系统中CO_(2)排放量。最终,基于信息间隙决策理论(IGDT)构建不同风险偏好下的优化调度模型。【结果】以典型综合能源系统进行算例分析,仿真结果表明所提模型可提高风光消纳率,实现系统低碳、经济、稳定运行。【结论】该优化策略可有效帮助决策者根据其风险偏好制定风险规避与风险追求策略下的调度方案,实现系统不确定性与经济性的平衡。

阶梯式提升:设计人才应用实践能力培养探索与实践

在新世纪,新一轮科技革命和产业革命正在蓬勃兴起,工业化经济正转向知识经济,专业化的设计教育也正面临着新的挑战。为了探索一种地方高校设计类专业学生设计应用能力有效提升路径,重点关注设计教育过程中如何通过校企产教融合推动人才培养提质增效:整合技能、知识、素养,优化知行合一的培养模式;培养、输出、协同聚力,丰富设计课程实践体系;对接内容、情境、师资,推动设计教育资源共享;转变教学场所、元素、方式,优化设计教学形式。淮阴工学院教学实践表明,相关群体的积极参与,教学内容、教学形式的改革,优质教学平台的支撑,能够有效提升学生设计应用能力。

中外合作办学人才培养新模式研究——以“混凝土结构”课程为例

随着国家对中外合作办学的支持,越来越多的高校致力于对中外合作办学模式的探讨。青岛理工大学土木工程学院以“混凝土结构”课程为例,针对中美合作办学培养新模式构建了经济全球化背景下源源不断培养国际人才的教学体系:中外教师先后对同一门课程进行线下课堂与远程授课紧密结合的“三位一体”教学,实行“分步走一体化”的流程,保证学生能够立足于国内外的混凝土建筑案例,夯实专业基础,充分拓宽国际视野。与传统中外合作办学模式相比,新型模式避免了赴外求学可能面临的种种风险,提高了学生对外文专业知识的了解程度。最终达到培养着眼于国际视野的高素质技术人才的目标,保证各种突发情况下国际化人才教育培养不停摆。

一种适用于复杂电网下的高精度锁相环

针对现有并网逆变器在电网电压谐波复杂的情况下难以精确锁定电压频率和相位的问题,结合传统锁相环结构与自适应算法的理论提出一种高精度的锁相方法。依据对传统锁相环在复杂电网下的弊端分析,确定了锁相环采用传统低通滤波器、带通滤波器时的滤波效果与延时的矛盾关系。根据最小均方算法的高自适应特性与快速跟踪特点,结合锁相环中坐标变换公式,确定算法的输入输出以及权重矩阵,构建基于派克变换的最小均方算法矩阵模型。通过将所需的电压正序分量设置为不断更新的权重矩阵来进行高精度的滤波,同时通过引入均方瞬时误差和自相关估计均值来进行变步长控制,提高滤波更新速度,以适用于复杂程度不确定的电网电压进行自适应滤波锁相。对仿真和样机实验的结果表明:采用基于派克变换的最小均方算法的改进型双二阶广义积分锁相方法,可以在不降低动态响应速度的前提下,提高锁相环的滤波效果,进而提高并网逆变器在电网畸变严重场景下锁定电压频率和相位的跟踪精度。

城轨列车自动驾驶积分反步线性自抗扰控制

针对列车在外部干扰和不确定动态下的速度控制问题,设计了融合积分反步法和线性自抗扰的复合控制方案.首先,考虑列车具有强耦合性,为了更加符合列车真实的纵向动力学特性和受力情况,建立了具有时变系数的多质点模型.其次,为了降低参数调节的难度,跟踪微分器和扩张状态观测器均采用线性形式.跟踪微分器用于求取微分信号,同时具有滤波作用.利用跟踪微分器对虚拟控制量进行求导,正好可解决反步法中存在的“微分爆炸”问题.扩张状态观测器用于实时估计总和扰动.此外,利用积分反步法改进了误差反馈控制律,设计了一种积分反步线性自抗扰控制(IBS-LADRC)算法.最后,证明了观测误差的收敛性及闭环系统稳定性.结合杭州地铁6号线AH型动车组参数和实际线路数据进行仿真,并将IBSLADRC与反步法、线性自抗扰算法、PID控制进行对比,结果表明:IBS-LADRC方法下各动力单元速度误差均处在±0.04 km/h以内,加速度处在±1 m/s2以内,加速度和速度误差均变化较平稳;车钩力相对其他3类方法最小,变化也最平缓,最大车钩力仅为2 320 N;本文控制策略对列车期望速度具有较高的跟踪精度,有利于保证车钩安全,防止车钩断裂,并提高列车运行的安全性、平稳性及乘客舒适度.

计及P2G及碳捕集的风光氢储综合能源系统低碳经济调度

在“双碳”目标下,为提高风光能源利用效率、优化资源配置、促进综合能源系统降碳减排,提出了一种风光氢储综合能源系统低碳经济调度模型。首先,考虑氢能作为新型储能能源所具有的低碳特性和调度优势,引入两阶段运行的电转气(power-to-gas,P2G)技术模型,以氢能为连接纽带,实现了系统内电、热、气能之间的耦合传递。其次,引入碳捕集设备及阶梯式碳交易机制,以进一步降低系统的碳排放。然后,构建以购能成本、碳交易成本、运行成本和弃风弃光成本最小为目标的低碳经济调度模型,并运用CPLEX求解器进行求解。最后,通过对多个运行情景的优化结果对比分析,验证了模型在消纳风光出力、促进系统深度脱碳、推动多能源互补和增加系统经济效益方面的有效性。