H∞范数的上界和收敛性

研究了线性系统传递函数矩阵的H∞范数上界问题，对特征值对应的若当块的最大阶数为2的系统给出了其H∞范数的一个显式上界，利用相关结果构造了H∞范数的收敛序列。     

基于遗传算法的不确定压电柔性结构H_2/H_∞混合振动控制

无穷范数和2-范数是优化控制理论的两个重要系统性能指标。前者考虑可能发生振动的最坏情况,过于保守;后者考虑系统的综合性能,未考虑共振情况;将两种指标结合起来将会同时兼顾鲁棒稳定性和系统时域性能。该文考虑不确定压电柔性结构模态参数的不确定性及模型误差,建立了结构模态空间的线性分式模型,给出了一种基于遗传算法的结构混合动态输出反馈振动控制器设计方法。首先通过线性矩阵不等式得到了多个无穷范数性能指标下的控制器,然后通过遗传算法对所得到的控制器进行了系统2-范数性能优化,设计了兼顾鲁棒性和系统时域性能要求的混合动态输出反馈控制器。     

有阻尼结构线性振动系统的模态综合

研究了线性阻尼结构振动系统的模态综合技术．在线性阻尼结构振动系统实变换进行方程解耦的还原变换的基础上，构造了线性阻尼结构振动系统的固定界面模态综合方法。这一方法克服了以往的模态综合法中无法同时给出子结构刚度、阻尼和质量矩阵，以及只能给出复系数时域方程等不足，可直接给出子结构经模态降阶后的刚度、阻尼和质量矩阵。综合得到的整体方程仍是时域中的实系数二阶振动方程。数值算例表明了本文方法的正确和可行。     

空间范数在压电柔性结构振动控制中的应用研究

在空间范数定义的基础上,推导出了结构模态空间范数的计算公式。考虑压电柔性结构振动控制中作动器分布对结构建模与控制性能的影响,利用模态空间范数度量各个模态对结构动力响应的贡献,并对结构进行了模态选择与模型降阶。利用所建立的降阶模型,设计了一个对受外部干扰结构进行振动抑制的动态输出反馈]]>;     

基于状态空间法的圆弧曲梁面内动力学分析

该文采用状态空间法研究了圆弧曲梁面内动力学特性。通过选择合适的状态变量，建立了相应的状态空间列式，并给出了固有频率和振动模态的求解过程。进一步通过引入辛内积的概念，建立了三种工程常见边界条件(简支、固支和自由)下圆弧曲梁面内振动模态关于质量和旋转惯量的正交关系式。在此基础上，运用模态叠加法给出了非齐次状态方程的解析解，并得到了圆弧曲梁在竖向移动集中荷载作用下的瞬态响应。数值算例结果表明该文方法是十分精确和可靠的。     

挠性结构系统的变量与模态耦合测度

本文研究了具有非对称性质的线性二阶矩阵系统Mq+Cq+Kq=f的耦合测度问题.利用复模态分析理论,导出系统状态变量、控制变量和观测变量与模态的耦合测度矩阵,以定量地描述系统的耦合特性,同时讨论了它们在挠性结构系统模态控制中的应用.最后给出一个实际算例.     

基于复模态的结构有限元动态模型修正理论

本文首先基于对阻尼的理解以及振动系统为实模态的一组充分必要条件，提出了用于复模态结构修正的恰当的阻尼模型和阻尼误差模型，进而结合复振型正交条件给出了修正模型及计算方法，并总结了这一方法的优点。     

分布式TMD对双密频结构的减振研究

针对密集频率结构的减振问题,以典型的2自由度对称结构为例,研究基于H2性能的梯度优化法对密集模态振动减振的分布式TMD(tuned mass dampers)的参数优化和减振效果。建立适合闭环静力反馈控制的组合系统模型,将基于H2性能的梯度优化法扩展至分布式TMD的参数优化;定义针对密集模态振动的控制输出和无量纲评价指标,分析了控制输出的模态控制权重对优化参数和评价指标的影响,指出能使评价指标峰值相等的模态控制最优权重,进一步给出优化参数和评价指标随模态密集度的变化规律;与经典方法对TMD的设计相对比,分析和验证了基于H2性能优化的分布式TMD的良好减振效果,并确认在TMD个数增多时基于H2性能的梯度优化法将具有更佳的优化效果。     

基于模态价值分析的结构动力学模型降阶

针对小阻尼和无阻尼结构，提出了一种模态价值分析方法，用于在模态坐标下的动力学模型降阶问题。在得到系统动力学方程的基础上，首先进行模态分析，然后由模态参数和系统的输入输出矩阵计算各模态的价值，最后选择若干价值最大的模态向量形成变换矩阵对系统进行降阶。通过两个算例说明本文方法是对通常选择低频模态的降阶方法的改进，提高了低阶模型的精度。     

结构振动模态截断的能量判据

通过在结构状态响应向量空间中定义一个函数，并证明该函数数学实质为范数、物理意义为结构能量；建立了模态截断的能量判据，从理论上证明了该判据的收敛性；以高拱坝结构在地震荷载作用下的模态截断为例，计算结果表明：(1)由于能量判据为标量，因此计算收敛性易于实现；(2)由能量判据作出的模态截断能够提高结构振动分析的精度；(3)对于高拱坝，由于其频率密集，应取10阶以上乃至更多模态进行分析。     

基于区域极点配置的汽车主动悬架H2/H 控制

利用混合H2/H 控制方法设计了某重载车辆悬架控制器。以此种方法设计出的控制器,通过H 控制指标保证被控对象约束输出传递函数的无穷范数低于适当γ值的同时,最小化一个给定的H2性能指标函数,较好的解决了悬架系统性能和系统鲁棒性之间的折衷优化控制问题,同时,通过将闭环极点配置在指定位置,保证了系统的动态性能,结果显示,通过将单一范数（H2或H ）控制方法改进为混合范数H2/H 控制方法,强化了每种范数各自的优势,系统综合性能品质得到了保证。     

非线性RLW方程的经济型差分-流线扩散法

本文对非线性正则长波(RLW)方程的周期初边值问题提出了一种基于线性有限元空间的经济型差分-流线扩散(EFDSD)法,利用能量估计方法证明了该方法的稳定性和收敛性,得到了L2模拟丰满误差估计和H1模丰满误差估计。与以前的方法相比,该方法具有稳定性能好,便于实际编程计算等优点。     

A mathematical model to optimize decisions to impact multi-attribute rankings

We formulate the problem of how to climb in multi-attribute rankings with known weights using mathematical optimization. A model is derived based on familiar practices used in rankings in higher education where several attributes are combined using known weights to obtain a score. The method applies in any situation where multiple attributes are used to rank entities. We invoke several assumptions such as independence among attributes and that administrators can affect the values of some of the attributes and know the cost of doing so. Our results suggest that a strategy to advance in the rankings is to focus on modifying the value of fewer rather than more attributes. The model is generalized to allow for synergies and antagonisms among the attributes.     

弹性飞机的混合 最优PID控制器参数优化

基于弹性飞机的降阶模型设计控制器时需要考虑模型降阶带来的降阶误差,这就需要设计的控制器具有较强的鲁棒性。为此,以某弹性飞机12阶模型为例,研究了基于弹性飞机降阶模型的混合 最优PID控制器的参数优化。首先基于平衡截断法得到了6阶降阶模型。然后,根据全阶模型和降阶模型的频域降阶误差选取了合适的鲁棒加权函数。之后,给出了闭环系统跟踪误差 范数的一种简化计算方法用于 优化指标的计算。最后基于差分进化算法进行了混合 最优PID控制器的参数寻化。仿真结果表明,与 混合灵敏度控制器相比,优化得到的混合 最优PID控制器具有更强的鲁棒性,能同时镇定参数和非参数两种不确定性。对弹性形变模态也有较好的抑制作用,刚性模态也取得了很好的响应效果。     

基于子结构的参数化模型降阶方法

针对参数化模型降阶方法在多维参数维度的情况下面临采样点过多、离线构建降阶模型数据库时间长等问题,提出了一种基于子结构的参数化模型降阶方法。在固定界面模态综合法的基础上,设置标准模态矩阵,利用不同参数主模态矩阵之间的Frobenius范数最小准则确定了转换矩阵,推导了子结构降阶矩阵各元素的变换公式,对其进行坐标转换;对参数空间上的采样点重复整个计算过程生成了坐标兼容的离线数据库。并以电磁振动台动圈为例,采用该方法对均布采样样本点展开了仿真研究。结果表明,此方法能大幅减少采样点的个数及模型生成与计算时间,提高降阶模型离线训练效率;所构建的参数化降阶模型具备很高的在线计算效率及计算准确度。     

Fast dynamic performance optimization of complicated beam-type structures based on two new reduced physical models

In this article, two new model reduction methods for fast dynamic performance optimization of complicated beam-type structures are presented. In the new model reduction methods the projection of structural nodal degrees of freedom is carried out using the localized base vectors, which are obtained by physical hypothesis. The first new model reduction method constructs the base vectors based on the assumption of block-wise rigid body motion modified by minimizing the displacement error measured in strain energy. The second new model reduction method is based on the plane cross-section assumption, and the cross-sectional warp deformation is also taken into consideration. Then, two reduced optimization models based on each method and design variable decomposition are formulated and solved. Both reduced optimization models are compared with the response surface method-based structural optimization approach. Some examples are presented to demonstrate the feasibility and effectiveness of the proposed methods.     

Powder reduction kinetics of dicalcium ferrite,calcium ferrite,and hematite: Measurement and modeling

Shrinking core model is widely applied to describe the reduction of iron ore pellets, but limited to the illustration on powder sample. The reduction of powder materials is commonly observed in blast furnace production but has been rarely investigated. In this study, thermal kinetics analysis was conducted to describe the powder reduction of dicalcium ferrite (2CaO?Fe₂O₃, C₂F), calcium ferrite (CaO?Fe₂O₃, CF), and hematite (Fe₂O₃, H), with particle sizes below 70 µm. Isothermal reduction experiments were performed through thermogravimetry analysis under CO atmosphere. The reduction degrees and reaction rate constants increased in the order of C₂F, CF, and H at 1123, 1173, and 1223 K. The reduction rate analysis illustrated that the reduction of C₂F, CF, and H appeared as one-, two-, and three-stage reactions, respectively. Moreover, the reduction of C₂F and CF proceeded as the 2D reaction mechanism described by Avrami–Erofeev (A-E) equation. The reduction of H was initially controlled by 2D, followed by the 3D A-E kinetics equation. Phase with superior reducibility could be reduced by CO in more dimensions of sample layers. The reduction degrees and rate change expressed by A-E equations were verified to be in accordance with the experimental data. A new kinetics model was proposed to elucidate the reduction of C₂F, CF, and H in ultrafine powder compared with that in pellets. The reduction process in the powdered samples comprised independent reduction stages caused by uniform CO diffusion in powdered particles.     

基于l_(2,p)-范数的ECT图像重建算法

针对电容层析成像系统图像重建过程中Tiknonov正则化解过度光滑引起的重建图像细节信息丢失问题,引入l_(2,p)(0p≤1)的混合范数作为正则化算法的数据项和正则化项。混合范数l_(2,p)利用了欧氏范数l_2的光滑性和分数范数l_p(0p≤1)的稀疏性,不仅比范数L_(2,1)具有更好的联合稀疏性,对噪声的抗干扰性也更强,进而针对l_(2,p)矩阵范数的非凸、非Lipschitz连续问题提出一种新的电容层析成像图像重建模型。实验结果表明,基于矩阵混合范数l_(2,p)极小化优化模型的正则化算法相比牛顿迭代、奇异值分解、共轭梯度算法具有更强的适应性,更高的图像分辨率及更好的成像质量。     

Interdigitated array electrode as an alternative to the rotated ring-disk electrode for determination of the reaction products of dioxygen reduction

Electrochemical reduction of dioxygen in aqueous media can proceed to water, hydrogen peroxide, or a mixture of the two. The production of hydrogen peroxide, classically established with the rotated ring-disk electrode, can also be quantitatively assessed at interdigitated array (IDA) electrodes, where dioxygen is reduced at the set of microband generator electrodes and any H(2)O(2) produced is detected by its oxidation (back to O(2)) at the interdigitated set of microband collector electrodes. The sensitivity of the IDA for H(2)O(2) detection is higher owing to its more complete collection, and to the ensuing regeneration of O(2), which leads to an amplification of the generator currents. The production of H(2)O(2) is thus reflected both in the ratio of collector and generator electrode currents [the collection efficiency, coll(τ)] and in the ratio of the generator current with the collector potential on to that with it off [amplification factor, ampl(τ)]. The necessary theory for interpretation of the fraction ε of H(2)O(2) produced per dioxygen reduced is presented, based on conformal mapping techniques. Explicit equations are derived for ε at long times that are independent of the IDA dimensions and that can be used with any two-product electrochemical reaction analogous to the dioxygen reduction. Experimental data are presented for dioxygen reduction in acidic and basic media to illustrate application of the theory.     

Accelerated mesh sampling for the hyper reduction of nonlinear computational models

In nonlinear model order reduction, hyper reduction designates the process of approximating a projection‐based reduced‐order operator on a reduced mesh, using a numerical algorithm whose computational complexity scales with the small size of the projection‐based reduced‐order model. Usually, the reduced mesh is constructed by sampling the large‐scale mesh associated with the high‐dimensional model underlying the projection‐based reduced‐order model. The sampling process itself is governed by the minimization of the size of the reduced mesh for which the hyper reduction method of interest delivers the desired accuracy for a chosen set of training reduced‐order quantities. Because such a construction procedure is combinatorially hard, its key objective function is conveniently substituted with a convex approximation. Nevertheless, for large‐scale meshes, the resulting mesh sampling procedure remains computationally intensive. In this paper, three different convex approximations that promote sparsity in the solution are considered for constructing reduced meshes that are suitable for hyper reduction and paired with appropriate active set algorithms for solving the resulting minimization problems. These algorithms are equipped with carefully designed parallel computational kernels in order to accelerate the overall process of mesh sampling for hyper reduction, and therefore achieve practicality for realistic, large‐scale, nonlinear structural dynamics problems. Conclusions are also offered as to what algorithm is most suitable for constructing a reduced mesh for the purpose of hyper reduction. Copyright © 2016 John Wiley & Sons, Ltd.