Methods in Model Order Reduction(MOR) field

Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industry requirements,analytically tractable and computationally cheap models must be designed.This is the essence task of Model Order Reduction(MOR).This article describes the basics of MOR optimization,various way of designing MOR,and gives the conclusion about existing methods.In addition,it proposed some heuristic footpath.

A Real-time Cutting Model Based on Finite Element and Order Reduction

Telemedicine plays an important role in Corona Virus Disease 2019(COVID-19).The virtual surgery simulation system,as a key component in telemedicine,requires to compute in real-time.Therefore,this paper proposes a realtime cutting model based on finite element and order reduction method,which improves the computational speed and ensure the real-time performance.The proposed model uses the finite element model to construct a deformation model of the virtual lung.Meanwhile,a model order reduction method combining proper orthogonal decomposition and Galerkin projection is employed to reduce the amount of deformation computation.In addition,the cutting path is formed according to the collision intersection position of the surgical instrument and the lesion area of the virtual lung.Then,the Bezier curve is adopted to draw the incision outline after the virtual lung has been cut.Finally,the simulation system is set up on the PHANTOM OMNI force haptic feedback device to realize the cutting simulation of the virtual lung.Experimental results show that the proposed model can enhance the real-time performance of telemedicine,reduce the complexity of the cutting simulation and make the incision smoother and more natural.

An Adaptive Substructure-Based Model Order Reduction Method for Nonlinear Seismic Analysis in OpenSees

Structural components may enter an initial-elastic state,a plastic-hardening state and a residual-elastic state during strong seismic excitations.In the residual-elastic state,structural components keep in an unloading/reloading stage that is dominated by a tangent stiffness,thus structural components remain residual deformations but behave in an elastic manner.It has a great potential to make model order reduction for such structural components using the tangent-stiffness-based vibration modes as a reduced order basis.In this paper,an adaptive substructure-based model order reduction method is developed to perform nonlinear seismic analysis for structures that have a priori unknown damage distribution.This method is able to generate time-varying substructures and make nonlinear model order reduction for substructures in the residual-elastic phase.The finite element program OpenSees has been extended to provide the adaptive substructure-based nonlinear seismic analysis.At the low level of OpenSees framework,a new abstract layer is created to represent the time-varying substructures and implement the modeling process of substructures.At the high level of OpenSees framework,a new transient analysis class is created to implement the solving process of substructure-based governing equations.Compared with the conventional time step integration method,the adaptive substructure-based model order reduction method can yield comparative results with a higher computational efficiency.

Advances of Model Order Reduction Research in Large-scale System Simulation

Model Order Reduction (MOR) plays more and more imp or tant role in complex system simulation, design and control recently. For example , for the large-size space structures, VLSI and MEMS (Micro-ElectroMechanical Systems) etc., in order to shorten the development cost, increase the system co ntrolling accuracy and reduce the complexity of controllers, the reduced order model must be constructed. Even in Virtual Reality (VR), the simulation and d isplay must be in real-time, the model order must be reduced too. The recent advances of MOR research are overviewed in the article. The MOR theor y and methods may be classified as Singular Value decomposition (SVD) based, the Krylov subspace based and others. The merits and demerits of the different meth ods are analyzed, and the existed problems are pointed out. Moreover, the applic ation’s fields are overviewed, and the potential applications are forecaste d. After the existed problems analyzed, the future work is described. There are som e problems in the traditional methods such as SVD and Krylov subspace, they are that it’s difficult to (1)guarantee the stability of the original system, (2) b e adaptive to nonlinear system, and (3) control the modeling accuracy. The f uture works may be solving the above problems on the foundation of the tradition al methods, and applying other methods such as wavelet or signal compression.

Model Order Reduction for Coupled Dynamic Characterization of Torsional Micromirrors

Numerical solutions could not perform rapid system-level simulation of the behavior of micro-electro-mechanical systems（MEMS） and analytic solutions for the describing partial differential equations are only available for simple geometries.Model order reduction（MOR） can extract approximate low-order model from the original large scale system.Conventional model order reduction algorithm is based on first-order system model,however,most structure mechanical MEMS systems are naturally second-order in time.For the purpose of solving the above problem,a direct second-order system model order reduction approach based on Krylov subspace projection for the coupled dynamic study of electrostatic torsional micromirrors is presented.The block Arnoldi process is applied to create the orthonormal vectors to construct the projection matrix,which enables the extraction of the low order model from the discretized system assembled through finite element analysis.The transfer functions of the reduced order model and the original model are expanded to demonstrate the moment-matching property of the second-order model reduction algorithm.The torsion and bending effect are included in the finite element model,and the squeeze film damping effect is considered as well.An empirical method considering relative error convergence is adopted to obtain the optimal choice of the order for the reduced model.A comparison research between the full model and the reduced model is carried out.The modeling accuracy and computation efficiency of the presented second-order model reduction method are confirmed by the comparison research results.The research provides references for MOR of MEMS.

Sliding Mode Control Design via Reduced Order Model Approach

This paper presents a design of continuous-time sliding mode control for the higher order systems via reduced order model. It is shown that a continuous-time sliding mode control designed for the reduced order model gives similar performance for thc higher order system. The method is illustrated by numerical examples. The paper also introduces a technique for design of a sliding surface such that the system satisfies a cost-optimality condition when on the sliding surface.

Performance of cumulant-based rank reduction estimator in presence of unexpected modeling errors

Compared with the rank reduction estimator(RARE) based on second-order statistics(called SOS-RARE), the RARE based on fourth-order cumulants(referred to as FOC-RARE) can handle more sources and restrain the negative impacts of the Gaussian colored noise. However, the unexpected modeling errors appearing in practice are known to significantly degrade the performance of the RARE. Therefore, the direction-of-arrival(DOA) estimation performance of the FOC-RARE is quantitatively derived. The explicit expression for direction-finding(DF) error is derived via the first-order perturbation analysis, and then the theoretical formula for the mean square error(MSE) is given. Simulation results demonstrate the validation of the theoretical analysis and reveal that the FOC-RARE is more robust to the unexpected modeling errors than the SOS-RARE.

Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors

Compared to the rank reduction estimator(RARE)based on second-order statistics(called SOS-RARE),the RARE employing fourth-order cumulants(referred to as FOC-RARE)is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise.However,in the presence of unexpected modeling errors,the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE,even for a known array covariance matrix.For this reason,the angle resolution capability of the FOC-RARE was theoretically analyzed.Firstly,the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method.Then,with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution,the theoretical formulas for the angle resolution probability of the FOC-RARE were presented.Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling errors than that of the SOS-RARE from the resolution point of view.

轴向流作用下均布非线性弹簧支承二维壁板的复杂响应

考虑刚性导流段和尾流段对流场的影响,建立轴向流作用下二维板的非线性流固耦合运动控制方程,用有限差分法对控制方程进行离散。为了克服差分网格较多时带来的计算规模较大的问题,对控制方程用主模态缩减法缩减自由度,然后对离散方程进行数值积分,得到系统的复杂响应,分析其分岔和混沌特性。计算结果表明,以来流流速幅值和阻尼参数为可变参数时,系统具有极其复杂的动态响应,通过分岔图、相图和庞加莱截面图等方法判断了系统多种形式的周期、拟周期和混沌运动,在以来流流速幅值为可变参数时,系统一开始经由周期倍化分岔的方式进入混沌;在以阻尼系数为可变参数时,经由倒周期倍化分岔的方式从混沌运动退回到周期振动。

不确定转子系统动力学降阶模型构建与模型散度参数辨识

在航空、航天、船舶等领域的实际工程转子系统中,广泛存在高维复杂的非线性系统。在航空发动机转子系统、燃气轮机转子系统等重点研究领域,通常还难以对高维复杂非线性系统进行直接的数据处理和分析统计。针对不确定性转子系统的模型维度较高等问题,提出了一种模型不确定性动力学降阶计算模型构建和模型散度参数辨识方法。首先,根据确定性动力学模型和静态矩阵降阶方法,完善了确定性动力学降阶模型;然后,基于随机矩阵理论和非参数动力学建模方法,提出了不确定性动力学降阶模型;最后,利用系统确定性模型的一阶临界转速、振型和实验数据,对不确定性动力学模型的散度参数进行了辨识;为了验证散度参数辨识方法的有效性,笔者又在转子实验平台上进行了实验验证。研究结果表明:实验结果与降阶之后振动响应均值的差异性较小,且与不确定性动力学模型相差不超过10%,表明所采用的理论模型在描述转子系统行为方面具备了较高的准确性和可靠性,该模型可以为深入研究模型不确定性转子系统提供参考。

基于“全局-局部”搜索的核反应堆运行孪生反问题求解

反应堆运行孪生在反应堆运行过程中为反应堆提供实时的参数和物理场估计,为后续相关安全参数计算提供输入。反问题求解是反应堆运行孪生的核心模块,是确保运行孪生参数和物理场估计的实时性和准确性的关键。当前的运行孪生反问题求解方法依赖于初始参数的估计,其估计精度直接决定数字孪生的精度。为了提高运行孪生反问题求解精度和计算效率,本文提出了“全局-局部”搜索(GLS)的反问题求解方法。对基于华龙一号构建的反应堆运行孪生进行了测试,考察了观测量无噪声和有噪声时反问题求解的精度和计算效率。结果表明,此方法可为反应堆运行孪生提供实时准确的参数和物理场估计,为工程实践打下了基础。

基于数据驱动的主燃油计量装置故障诊断

为建立主燃油计量装置的故障诊断方法,提出一种基于快速存取记录器(QAR)数据的燃油计量参数估计模型建模方法,并结合液压机械控制装置工作原理,给出了基于燃油计量参数残差设计的主燃油计量装置故障诊断方案。设计基于系统辨识的燃油计量活门位置(FMVP)估计模型,采取降阶处理策略以提高模型的估计精度和动态响应速度,在此基础上给出基于多项式拟合的燃油流量(FF)估计模型。结果表明:所建立的FMVP模型估计残差不超过±2%,FF估计模型残差不超过±5%;该方案能够有效地诊断出燃油计量活门故障、线性可变差动位移传感器故障和热式流量计故障。该方案结构简单,不需要大量的调试技术,提高了故障检测精度,具有工程应用前景。

基于Krylov子空间降阶的温控算法研究

针对当前常用的散热前馈获取方法存在耗时长、能耗大、步骤繁杂等缺点,文中提出引入模型降阶方法获取散热前馈。通过3组实验获取控制对象响应特性;对在ANSYS Workbench仿真平台建立的控制对象模型进行校正,使仿真模型特性与实际控制对象特性尽可能相同;使用Krylov子空间法对仿真模型进行降阶,降阶后的模型可以通过Matlab计算得出散热前馈;以差示扫描量热仪炉体为控制对象验证散热前馈-PID控制策略的效果。实验结果表明,在环境温度至300℃范围内,扫描模式温控误差小于±5%,恒温模式温控误差小于±0.2℃。

导弹伺服系统多物理场建模设计

导弹伺服系统是包含机械、电气、电磁、控制等多物理场的复杂机电系统。针对传统理想线性仿真技术存在的模型颗粒度不够、仿真精度不高的问题,开展细颗粒度多物理场仿真技术研究。对伺服系统的伺服电机、电路、控制算法、传动机构进行精确物理场建模,然后采用基于VHDL-AMS的统一语言建模技术、模型降阶技术和联合仿真技术相结合,实现伺服系统集成化多物理场仿真。仿真结果和样机试验结果对比表明:模型颗粒度高,仿真精度可达到87%。通过该方法可对系统进行高精度、高保真度的虚拟验证,降低研制风险。

核反应堆物理计算数据同化研究进展

为了更全面深刻地认识用于核反应堆物理计算中的数据同化理论,介绍了数据同化在反应堆物理领域的两大应用方向,即最佳参数估计和物理场重构。详细分析了基于模型降阶的数据同化理论,包括模型降阶理论基础和基于本征正交分解的模型降阶;分别介绍了广义经验插值法和稳定格式本征正交分解,并给出了部分数值结果。讨论了反应堆物理领域中开展不确定度分析和量化的相关工作进展。此外,为了进一步确保数据同化结果的精度和可靠性,强调了不确定度分析的重要性并对其进行介绍。分析表明:基于模型降阶的数据同化方法具有计算效率高、精度高的优点,是核工程领域数据同化的新兴发展方向。

计及内环控制小信号稳定性的构网型变流器模型降维方法

随着电力系统电力电子化程度加深,具有电压源特性的构网型变流器将成为未来电力系统的常规装备之一。为了准确高效地分析含构网型装备的电力系统控制运行与安全稳定特性,需对具有强非线性特性的构网型变流器进行降阶。传统的基于电流环、电压环简化的降阶方法构建的简化模型由于忽略了内环控制与线路耦合阻抗对装备同步稳定性的潜在影响,在部分场景下难以保证稳定性分析的准确性。基于此,在现有降阶方法的基础上,充分考虑内环控制的小信号特性与线路耦合阻抗的影响,提出了一系列改进的简化模型,并就各简化模型对频域、特征值、时域分析的适应性进行了分析。分析得出在各类场景下没有能始终保持高精度的简化模型,需要根据场景更换模型简化方法,并根据分析结果总结了变流器简化模型选择与控制参数整定的相关依据。

面向互联系统的一类保结构模型降阶方法

互联系统作为一类特殊的复杂系统,其物理性质与系统的拓扑结构密切相关.因此在降阶过程中同时保持原始系统的耦合结构具有重要的现实意义.基于此,本文针对互联系统研究了一类保结构的模型降阶方法.首先,利用移位Legendre多项式正交分析技术,从归一化角度提出了计算互联系统可控与可观Gram矩阵的低秩分解算法.其次,结合平衡截断与主子空间投影方法,提出了一类保结构的降阶方法,并证明了降阶模型的保稳定性.最后,通过数值实验验证了所提方法的可行性与有效性.

基于分布式新能源与配网网络重构的降损技术

考虑分布式新能源出力随机性对调控策略执行效果的影响,研究了基于电压风险评估和主动重构的日前调度技术。基于光伏出力预测和负荷预测,以电压安全概率风险最小为目标,以开合联络开关为控制变量,应用二阶锥松弛过的Distflow潮流模型进行求解,获取电压安全概率风险最小的配网重构方案。通过对IEEE 33节点配网进行算例分析,仿真结果验证了所提基于电压风险评估与主动重构的日前降损策略的可行性。

Weighted Self-Adaptive Threshold Wavelets for Interpolation Point Selection Used in Interconnect MOR

As process technology development,model order reduction( MOR) has been regarded as a useful tool in analysis of on-chip interconnects. We propose a weighted self-adaptive threshold wavelet interpolation MOR method on account of Krylov subspace techniques. The interpolation points are selected by Haar wavelet using weighted self-adaptive threshold methods dynamically. Through the analyses of different types of circuits in very large scale integration( VLSI),the results show that the method proposed in this paper can be more accurate and efficient than Krylov subspace method of multi-shift expansion point using Haar wavelet that are no weighted self-adaptive threshold application in interest frequency range,and more accurate than Krylov subspace method of multi-shift expansion point based on the uniform interpolation point.