基于正交分解技术的汽车非定常流场分析及重构

为有效开展汽车气动优化设计和主动流动控制技术,采用正交分解(Proper Orthogonal Decomposition,POD)技术分析汽车非定常流场中POD模态的物理意义,并利用重构技术建立汽车外流场瞬态简化模型.大涡模拟(Large Eddy Simulation,LES)仿真结果与实验结果的对比表明该仿真方法有效.POD分析结果表明:低阶模态主要对应分离泡的附着流动,包含流场中较高的能量;其他各个高阶模态含能相对较低,表征小尺度涡的作用.当保留前15阶POD模态时,通过重构技术可获得70%的原流场能量,得到的降阶模型可以较好地捕捉流动的特征.     

基于平衡截断方法的高超声速飞行器模型降阶

本文提出了一种适用于高超声速飞行器数学模型的模型降阶方法.该方法采用基于奇异值分解的投影技术,对高阶的高超声速飞行器数学模型进行平衡变换,进而通过截断获得低阶的微分方程,方便控制器的设计,达到模型降阶的目的.相比于传统的只适用于稳定系统的模型降阶方法,本文提出的模型降阶方法通过右互质分解可以应用于不稳定的系统的模型降阶.为了证明该模型降阶方法的准确性,本文通过平均灰色关联系数的计算,给出基于时域分析的定量验证结果.仿真部分成功应用该方法对美国空军实验室提出的弹性纵向模型实现了降阶,证明了该方法的有效性.     

无人机侧向系统LPV 模型降阶

无人机线性参变(LPV)模型能准确描述其非线性动态特性,但初始建立的LPV模型阶数较高,控制过程计算量较大.为此,提出一种基于平衡截断的LPV模型降阶方法.首先给出LPV系统的适定性、稳定性和平衡实现的定义;然后,提出LPV模型的平衡截断降阶方法.针对无人机侧向系统LTI模型,通过多项式拟合来建立LPV模型,并实现模型降阶.仿真结果表明,降阶模型的阶跃响应满足输出响应的精度要求.     

WANG氏RC互连线模型平衡截断化简的分解算法

平衡截断（Balanced Truncation）是一种有效的模型简化（Model Reduction）方法,它的优点是简化模型有一个误差上限,使简化模型的性能得到保证.该文介绍一种平衡实现的分解算法,并应用Matlab对一4阶的Wang氏RC互连线模型的平衡实现及其模型截断简化进行编程仿真.单位阶跃响应和波特图显示原始模型与平衡模型曲线重合.给出了1阶、2阶、3阶平衡截断简化模型的阶跃响应和波特图,并对简化模型的理论误差上限与模型的实际最大误差进行了对比.方法可用于对IC互连线等模型的简化.     

本征正交分解在数据处理中的应用及展望

本征正交分解(Proper Orthogonal Decomposition,POD)是对高维复杂非线性系统进行降维处理的有效方法之一.本文对POD方法在一系列实际工程领域降维中的研究进行了综述.首先简要介绍POD方法的发展历史,简述POD方法分类,随后详细列举POD方法在粒子图像测速(Particle Image Velocimetry,PIV)技术、计算流体力学(Computational Fluid Dynamics,CFD)数据处理中的应用.对比了POD方法和动态模态分解(Dynamic Mode Decomposition,DMD)方法在实际工程应用中各自的优缺点,结果表明在流场稳定脉动时可采用DMD方法,而其他随时间变化的流场采用POD方法更合适.最后对POD方法的发展尤其是在人工智能领域的应用做出展望.     

汽车主动悬架系统H∞控制器的降阶

基于整车模型设计的主动悬架控制系统,控制器阶数往往较高.在保证主动悬架闭环系统性能的情况下如何尽可能地降低控制器的阶数,是有待解决的问题.本文首先建立汽车7自由度整车悬架模型.针对人体敏感的振动频率范围,设计汽车主动悬架H_∞控制器.在此基础上采用Hankel范数最优降阶法对所设计的高阶控制器进行降阶研究,与模态截取法、均衡截取法进行比较,结果显示Hankel范数最优降阶法能获得更好的降阶效果.对采用降阶和全阶控制器的主动悬架系统进行仿真的结果表明,Hankel范数最优降阶法在较大程度地降低控制器阶数的同时,闭环系统频域和时域特性没有明显降低且汽车乘坐舒适性良好.     

弹性飞机自动寻优H∞/PID控制器设计

针对弹性飞机高阶性和鲁棒性要求,研究了自动寻优的H∞/PID控制器设计方法.以国外某大型飞机12阶模型作为研究对象,利用平衡截断法进行降阶,得到在较宽频段内近似于全阶模型的6阶模型.基于降阶模型,利用粒子群优化算法得到合适的加权函数及PID控制器参数,用于控制全阶模型.仿真结果证明,在系统同时存在参数不确定性和非参数不确定性的情况下,与H∞混合灵敏度控制器相比,H∞/PID控制器具有更强的鲁棒性,并能取得更好的时域控制效果.     

几种模型降阶方法的仿真对比研究

算法比较研究,比较几种主要模型降阶方法的优缺点,为给工程应用提供方法参考.利用奇异值分解的模型降阶方法具有较好的理论性质,能够保持降阶系统结构特性,但计算成本较高故不适合大规模动态系统的降阶;采用矩匹配的模型降阶方法计算简便,适合大规模系统降阶,但无法保证降阶系统稳定性,也很难求得降阶误差界.最小二乘降阶法同时利用了系统的Gramian矩阵和Krylov子空间理论,结合了二者的优点,使得降阶过程计算简化,保持了降阶系统的结构特性,而且降阶误差进一步减小.仿真算例证明了最小二乘法较前两者具有优越性.     

EEMD与RBF神经网络的太阳黑子月均值预测

太阳黑子月均值是典型的混沌时间序列,具有较强的非线性和非平稳特征,能够反映太阳活动的真实水平。采用一种应用集合经验模态分解（Ensemble Empirical Mode Decomposition,EEMD）与径向基函数（Radial Basis Function,RBF）神经网络组合的预测模型。通过EEMD将原始时间序列分解为若干个不同时间尺度的本征模态函数（Intrinsic Mode Function,IMF）分量,并对这些分量进行建模预测,再将各分量的预测值重构得到原始时间序列的预测值,这样不仅降低了算法的复杂性,而且有利于提高模态分量包含信息的物理意义。仿真结果表明,与经验模态分解（Empirical Mode Decomposition,EMD）结合RBF神经网络的模型相比,该模型具有较高的预测精度。     

基于SVD优化EMD的电梯导靴振动信号故障 特征提取

针对电梯导靴振动信号采用经验模态分解(Empirical Mode Decomposition,EMD)难以直接提取早期微弱故障特征的问题,提出基于奇异值分解(Singular Value Decomposition,SVD)优化经验模态分解的电梯导靴振动信号故障特征提取方法。该方法首先对原始信号进行SVD分解,通过奇异值贡献率原则来确定相空间重组的最佳Hankel矩阵结构,利用曲率谱原则与奇异值贡献率原则相结合来确定有效奇异值的阶次;筛选出包含主要故障信息的奇异值进行信号重构,得到剔除噪声信号与光滑信号的突变信号;然后对突变信号进行EMD分解,得到信号的本征模态函数(Intrinsic Mode Function,IMF)分量。最后,对IMF分量作Hilbert变换,求得其Hilbert边际谱,从而获得电梯导靴故障特征频率信息。仿真结果表明该方法有效改善了EMD难以直接提取早期微弱故障特征的问题,更准确地提取了振动信号的故障特征频率,验证了所述方法的有效性。     

A new approach to model reduction of nonlinear control systems using smooth orthogonal decomposition

A new approach to model order reduction of nonlinear control systems is aimed at developing persistent reduced order models (ROMs) that are robust to the changes in system's energy level. A multivariate analysis method called smooth orthogonal decomposition (SOD) is used to identify the dynamically relevant modal structures of the control system. The identified SOD subspaces are used to develop persistent ROMs. Performance of the resultant SOD‐based ROM is compared with proper orthogonal decomposition (POD)–based ROM by evaluating their robustness to the changes in system's energy level. Results show that SOD‐based ROMs are valid for a relatively wider range of the nonlinear control system's energy when compared with POD‐based models. In addition, the SOD‐based ROMs show considerably faster computations compared to the POD‐based ROMs of same order. For the considered dynamic system, SOD provides more effective reduction in dimension and complexity compared to POD.     

Enhanced POD projection basis with application to shape optimization of car engine intake port

In this paper we present a rigorous method for the construction of enhanced Proper Orthogonal Decomposition (POD) projection bases for the development of efficient Reduced Order Models (ROM). The resulting ROMs are seen to exactly interpolate global quantities by design, such as the objective function(s) and nonlinear constraints involved in the optimization problem, thus narrowing the search space by limiting the number of constraints that need to be explicitly included in the statement of the optimization problem. We decompose the basis into two subsets of orthogonal vectors, one for the representation of constraints and the other one, in a complementary space, for the minimization of the projection errors. An explicit algorithm is presented for the case of linear objective functions. The proposed method is then implemented within a bi-level ROM and is illustrated with an application to the multi-objective shape optimization of a car engine intake port for two competing objectives: CO₂ emissions and engine power. We show that optimization using the proposed method produces Pareto dominant and realistic solutions for the flow fields within the combustion chamber, providing further insight into the flow properties.     

A multi-point reduced-order modeling approach of transient structural dynamics with application to robust design optimization

Predicting the transient response of structures by high-fidelity simulation models within design optimization and uncertainty quantification often leads to unacceptable computational cost. This paper presents a reduced-order modeling (ROM) framework for approximating the transient response of linear elastic structures over a range of design and random parameters. The full-order response is projected onto a lower-dimensional basis spanned by modes computed from a proper orthogonal decomposition (POD) of full-order model simulation results at multiple calibration points. The basis is further enriched by gradients of the POD modes with respect to the design/random parameters. A truncation strategy is proposed to compensate for the increase in basis vectors due to the proposed enrichment strategies. The accuracy, efficiency and robustness of the proposed framework are studied with a two-dimensional model problem. The numerical results suggest that the proposed ROM approach is well suited for large parameter changes and that the number of basis vectors needs to be increased only linearly with the number of design and random parameters to maintain a particular ROM performance. The application of the proposed ROM approach to robust shape optimization demonstrates significant savings in computational cost over using full-order models. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.     

Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction

We present a framework to solve a finite-time optimal control problem for parabolic partial differential equations (PDEs) with diffusivity-interior actuators, which is motivated by the control of the current density profile in tokamak plasmas. The proposed approach is based on reduced order modeling (ROM) and successive optimal control computation. First we either simulate the parabolic PDE system or carry out experiments to generate data ensembles, from which we then extract the most energetic modes to obtain a reduced order model based on the proper orthogonal decomposition (POD) method and Galerkin projection. The obtained reduced order model corresponds to a bilinear control system. Based on quasi-linearization of the optimality conditions derived from Pontryagin’s maximum principle, and stated as a two boundary value problem, we propose an iterative scheme for suboptimal closed-loop control. We take advantage of linear synthesis methods in each iteration step to construct a sequence of controllers. The convergence of the controller sequence is proved in appropriate functional spaces. When compared with previous iterative schemes for optimal control of bilinear systems, the proposed scheme avoids repeated numerical computation of the Riccati equation and therefore reduces significantly the number of ODEs that must be solved at each iteration step. A numerical simulation study shows the effectiveness of this approach.     

Model reduction in model predictive control of combined water quantity and quality in open channels

Model predictive control (MPC) is an advanced real-time control technique that uses an internal model to predict the future system behavior and generates optimal control actions by solving an optimization problem. MPC has been more and more applied for controlling open water systems, especially open water channels. Most of the research however focuses on water quantity (water level) control. Since water quality management is recently attracting more attention, extending MPC on combined water quantity and quality management is a logical next step.In this paper, we study the application of complex models in MPC to control both water quantity and quality. However, because of the online optimization of MPC, the computational time becomes an issue. In order to reduce the computational time, a model reduction technique, Proper Orthogonal Decomposition (POD), is applied to reduce the model order. The method is tested on a Polder flushing case. The results show that POD can significantly reduce the model order for both water quantity and quality with high accuracy. The MPC using the reduced model performs well in controlling combined water quantity and quality in open water channels.     

基于GEP算法的高阶常微分方程预测模型

针对动态系统预测建模中建模效率低,无显式模型的缺陷。提出一种基于基因表达式编程（GEP）的高阶常微分方程预测模型（GEP-HODE）。将一维数据的变化特性使用高阶微分进行表示,通过GEP对高阶微分数据进行建模,得到显式模型。对高阶常微分方程模型进行降阶处理,使用数值方法进行求解,得到预测值。该方法利用了GEP算法“基因型-表现型”的编码特性,实现了模型建立与参数优化的同步,大幅度提升建模效率。以太阳黑子年平均数作为实验数据建模预测,结果表明,该方法相比GP混合建模方法有更高的效率,相比混合BP神经网络模型等方法有更好的精度。     

Bi-level model reduction for coupled problems

In this work a methodology is proposed for the optimization of coupled problems, and applied to a 3D flexible wing. First, a computational fluid dynamics code coupled with a structural model is run to obtain the pressures and displacements for different wing geometries controlled by the design variables. Secondly, the data are reduced by Proper Orthogonal Decomposition (POD), allowing to expand any field as a linear combination of specific modes; finally, a surrogate model based on Moving Least Squares (MLS) is built to express the POD coefficients directly as functions of the design variables. After the validation of this bi-level model reduction strategy, the approximate models are used for the multidisciplinary optimization of the wing. The proposed method leads to a reduction of the weight by 6.6%, and the verification of the solution with the accurate numerical solvers confirms that the solution is feasible.     

Reduced order modeling based on POD of a parabolized Navier–Stokes equations model II: Trust region POD 4D VAR data assimilation

A reduced order model based on Proper Orthogonal Decomposition (POD) 4D VAR (Four-dimensional Variational) data assimilation for the parabolized Navier–Stokes (PNS) equations is derived. Various approaches of POD implementation of the reduced order inverse problem are studied and compared including an ad-hoc POD adaptivity along with a trust region POD adaptivity. The numerical results obtained show that the trust region POD 4D VAR provides the best results amongst all the POD adaptive methods tested in all error metrics for the reduced order inverse problem of the PNS equations.     

最小p范数准则α谱估计及载波频率检测

针对共变系数矩阵和分数低阶协方差矩阵估计ARSαS信号α谱精度不高的情况,提出了一种最小p范数准则的α谱估计方法。该方法对传统的奇异值分解（SVD）方法估计ARSαS信号模型最小阶数进行改进,得到一种分数低阶的奇异值分解方法（FLO-SVD）,然后利用最小p范数准则和IRLS算法求出信号模型参数,用于作α谱估计。应用于脉冲噪声环境下的QPSK信号的仿真表明,改进后的方法对α谱有更好的估计,对载波频率有更准确的检测性能。     

An advanced order acceptance model for hybrid production strategy

Competitors stand out through commitment to providing excellent customer service. Many organizations strive to promote their order promising system to generate more reliable quotes with quantity and due date constraints. This paper develops a Capable-to-Promise (CTP) based Order Acceptance Model (OAM) for a Hybrid Production Strategy (HPS) based on the positioning of the Customer Order Decoupling Points. The proposed model allocates the uncommitted availability and planned production receipts to current and anticipation of future needs. A Mixed-Integer Linear Programming (MILP) is developed to determine the optimal order quantities based on the resource availability. The proposed model efficiently mitigates the risk of not being reliable in the commitments due to discrepancies between the real and unused quantities. The CTP based OAM is compatible with a HPS with both make-to-order (MTO) and make-to-stock (MTS). The presented model encompasses four steps. First, demands for MTO products are collected in batches on daily basis and a forecasting model is applied to predict orders for MTS products. Secondly, the quantity-based Revenue Management approach is used to prioritize orders. Afterwards, the optimization model assesses the availability of resources in order to produce collected orders. The final step is to accept valuable orders based on the resource availability. In order to illustrate the applications of the modeling approach, two case studies are provided.