COMPARATIVE STUDY OF THE PRINCIPLES AND APPLICATIONS OF POD AND MSM

为揭示本征正交分解(proper orthogonal decomposition, POD) 与模态叠加法(mode superposi-tion method, MSM) 在基本原理和工程应用中的异同,对POD 和MSM 的数理基础进行了对比性分析;通过风洞试验及动力响应时程分析获得了一座冷却塔的表面脉动风载荷及其脉动响应,以此两个时空随机场为例对POD 和MSM 两种方法的应用进行了对比性阐述. POD 和MSM 均通过引入空间模态和相应的时间坐标,经线性叠加来实现对时空随机场的分解与重建,但两者的应用对象并不一致:前者多用于已知随机载荷场的分析而后者多用于未知结构响应的计算. 两者空间模态和时间坐标的提取方法和数理意义以及各模态对原随机场的贡献等亦不相同. 尽管POD 和MSM 两种方法所得空间模态均有正交性,但时间坐标的正交性仅存在于POD 方法,故POD 各阶模态的本征值之和可以完全反应对原随机场的贡献,而MSM 的模态贡献则存在一定的耦合性.     

Analyzing the fluctuating pressures acting on a circular cylinder using stochastic decomposition

Fluctuating wind pressures acting on bluff bodies are influenced by approaching turbulence and signature (body-induced) turbulence. For a circular cylinder, the signature turbulence is closely related to the formation of Karman vortex shedding. In this paper, proper orthogonal decomposition (POD) and spectral proper transformation techniques (SPT) are applied to the pressure fluctuations acting on a circular cylinder. The physical relationships between the decomposed modes and vortex shedding are discussed to identify the dominant aerodynamic behavior (lift or drag) and to evaluate its contribution to overall behavior. The effect of Reynolds number (Re) is also addressed. It is found that the application of POD and SPT can separate the along-wind and across-wind effects on the cylinder model in both subcritical and supercritical regimes. In contrast to POD, the SPT mode is formulated in the frequency domain, and the dynamic coherent structures can be defined in terms of amplitude and phase angle, which allows detection of the advection features of vortex shedding. In addition, it is observed that the energy contribution of the shedding induced lift force increases with Re and gradually becomes a dominant aerodynamic force at Reynolds numbers in the supercritical regime.     

脉动压力分布同步测量的探讨

动态气动力的研究是实验工作者极为关注的问题。特别对于二元模型动态气动力的测定,必须从脉动的压力分布通过面积加权积分来得到气动力的时间历程,而其先决条件为各测压点压力的时间历程必须是同步的,也就是要测得同一时刻诸多测点的压力。本文介绍了一种比较经济的多点同步测压方法,并对该方法的实施进行了探讨。分别对A/D卡采样的同步性、整套测压系统的同步性以及频响特性进行了测试和验证。经相关性分析,相关系数分别达到0. 9999和 0. 99。最后以圆柱表面脉动压力系数分布的测试为例,给出了单圆柱不同瞬间的压力向量图、按照瞬间压力沿表面积分得到的单个圆柱脉动升力的时间历程,以及升力的脉动频率,表明整套同步测压系统具有很好的实用性,能满足实验的需要。     

Stochastic estimation and proper orthogonal decomposition: Complementary techniques for identifying structure

The Proper Orthogonal Decomposition (POD) as introduced by Lumley and the Linear Stochastic Estimation (LSE) as introduced by Adrian are used to identify structure in the axisymmetric jet shear layer and the 2-D mixing layer. In this paper we will briefly discuss the application of each method, then focus on a novel technique which employs the strengths of each. This complementary technique consists of projecting the estimated velocity field obtained from application of LSE onto the POD eigenfunctions to obtain estimated random coefficients. These estimated random coefficients are then used in conjunction with the POD eigenfunctions to reconstruct the estimated random velocity field. A qualitative comparison between the first POD mode representation of the estimated random velocity field and that obtained utilizing the original measured field indicates that the two are remarkably similar, in both flows. In order to quantitatively assess the technique, the root mean square (RMS) velocities are computed from the estimated and original velocity fields and comparisons made. In both flows the RMS velocities captured using the first POD mode of the estimated field are very close to those obtained from the first POD mode of the unestimated original field. These results show that the complementary technique, which combines LSE and POD, allows one to obtain time dependent information from the POD while greatly reducing the amount of instantaneous data required. Hence, it may not be necessary to measure the instantaneous velocity field at all points in spacesimultaneously to obtain the phase of the structures, but only at a few select spatial positions. Moreover, this type of an approach can possibly be used to verify or check low dimensional dynamical systems models for the POD coefficients (for the first POD mode) which are currently being developed for both of these flows.The authors wish to thank DRET Grant # 90/171, the French Embassy Chateaubriand Fellowship (CIES) program for L. Ukeiley, NASA/Lewis GSRP for D. Cole, NASA/Ames Dryden, NASA/Langley and NSF/CNRS through the international travel grants program for funding various portions of this work.     

Ritz-POD法的原理及应用

提出一种在频域内分析大跨度屋盖结构的风振响应的Ritz-POD法。该方法用本征正交分解法(POD法)分解脉动风压场,得到占优的前几阶本征模态作为荷载的空间分布形式;根据此荷载空间分布形式生成Ritz向量,用Ritz向量直接叠加法分析结构风振响应,以解决大跨度屋盖结构多振型参与振动且高阶振型对结构响应贡献可能较大这一问题。运用该方法分析一单层球面网壳的风振响应,并与振型分解法对比,结果表明Ritz-POD法仅用少量的Ritz向量进行结构风振响应分析便可达到较高精度。     

多自由度柔性结构非线性随机振动响应分析方法

随机等效线性化方法是多自由度结构非线性随机振动分析的有效方法,然而柔性结构隐式的系统方程限制了该方法的应用.本文首先提出了把多自由度柔性结构隐式系统方程显式化的等效非线性系统建立方法,该方法结合模态分析,将系统几何非线性作用等效为模态坐标的高次多项式组合,把多自由度物理系统转化为容易求解的模态系统;在此基础上运用随机等效线性化技术建立柔性结构非线性随机振动响应分析方法.该方法通过引入虚拟激励原理,大幅提高了计算效率,使对多自由柔性结构的非线性随机振动响应分析成为可能.通过算例分析,本文分析结果和精确解与数值模拟解的比较结果表明,本文方法具有较好的计算精度和较高的计算效率,能够应用于实际柔性工程结构的随机振动响应分析.     

Reduced order borehole induction modelling

This article presents a new reduced order model based on proper orthogonal decomposition (POD) for solving the electromagnetic equation for borehole modelling applications. The method aims to accurately and efficiently predict the electromagnetic fields generated by an array induction tool – an instrument that transmits and receives electrical signals along different positions within a borehole. The motivation for this approach is in the generation of an efficient ‘forward model’ (which provides solutions to the electromagnetic equation) for the purpose of improving the efficiency of inversion calculations (which typically require a large number of forward solutions) that are used to determine surrounding material properties. This article develops a reduced order model for this purpose as it can be significantly more efficient to compute than standard models, for example, those based on finite elements. It is shown here how the POD basis functions are generated from the snapshot solutions of a high resolution model, and how the discretised equations can be generated efficiently. The novelty is that this is the first time such a POD model reduction approach has been developed for this application, it is also unique in its use of separate POD basis functions for the real and complex solution fields. A numerical example for predicting the electromagnetic field is used to demonstrate the accuracy of the POD method for use as a forward model. It is shown that the method retains accuracy whilst reducing the costs of the computation by several orders of magnitude in comparison to an established method.     

建筑结构基于巴斯金风速谱的系列风振响应的简明封闭解

针对巴斯金风速谱激励下的建筑结构顺风向振动响应表达式复杂的问题,提出了一种简明封闭解法.巴斯金随机谱广泛应用于描述脉动风、随机地震动和路面不平顺等各种随机激励,本文基于留数定理给出巴斯金风速功率谱的二次正交式.综合运用复模态法和虚拟激励法获得了建筑结构系列响应(位移、层间位移及其变化率)功率谱的统一形式的二次正交式,并根据谱矩的定义获得了建筑结构系列响应的方差和谱矩及绝对加速度方差的简明封闭解.运用本文方法对一8层建筑结构进行分析,并与传统虚拟激励法进行对比研究,表明本文所得封闭解正确,并可用于验证虚拟激励法在谱矩和方差分析时的精度和效率.由于本文方法含有复模态法,故可用于各类线性结构基于巴斯金谱的随机响应分析和基于动力可靠度及舒适度的动力优化分析.     

桅杆风致破坏机理研究

桅杆风致破坏的情况屡见不鲜。桅杆的非线性是相当复杂的,它是由拉索的几何非线性和拉索的张力产生的,拉索的张力又依赖于拉索的几何位置。研究指出由于在经常性风荷载作用下,桅杆产生空间混沌振动,并由此产生疲劳破坏的结果,但这些研究仅限于确定性情况。本文中将研究扩展到随机问题,数值计算结果表明该系统存在随机混沌现象,其响应平均值与平均应力指出混沌性质。为了进一步研究桅杆破坏机理,因此在本文中,既考虑突发性故障问题,又考虑随机疲劳寿命问题,并给出时间与应力极值概率。     

大跨度桥梁空间脉动风场的计算机模拟

针对现有Deodatis方法模拟大跨度桥梁空间脉动风场中存在的计算量问题,通过对谱分解矩阵引入插值近似,减少谱分解的次数,从而提高该谐波合成法的计算效率,并节省内存花费,实现了对三维空间脉动风场的有效模拟。改进方法模拟的脉动风速样本仍保持各态历经性,且逐渐收敛到目标功率谱。用改进的Deodatis方法模拟了润扬长江悬索桥桥面主梁上作用的纵向脉动风速。结果表明,该改进措施对Deodatis方法的应用效果非常明显,改进的Deodatis方法模拟脉动风速样本的相关函数与目标相关函数均吻合良好。尽管改进后的Deo-datis方法对谱分解矩阵采用了插值近似,但模拟的随机风速样本仍具有很好的精度。     

随机风-浪一体化降维建模及风机结构可靠度研究

基于随机脉动风场和随机波浪力场的谱表示降维模拟方法,采用脉动风速Davenport谱与波浪P-M谱对风、浪谱参数进行一体化构造,并应用相同的基本随机变量来保障风、浪模拟的概率信息一致,实现了随机风-浪一体化降维建模。进一步,基于ANSYS有限元软件建立了近海风机塔架数值计算模型,并以顶点位移为指标,进行了三种工况下结构的动力可靠度分析。数值算例验证了随机风-浪一体化降维建模方法的有效性。结构动力分析结果表明,风荷载对风机塔架顶点位移响应的影响占主导地位,同时波浪荷载的作用亦不可忽略。此外,随机风-浪一体化降维方法生成的代表性样本概率信息完备,可与概率密度演化理论结合实现海工结构在风浪共同作用下的精细化动力响应及可靠度分析。     

Extended Proper Orthogonal Decomposition: Application to Jet/Vortex Interaction

The Proper Orthogonal Decomposition (POD) is used in the present work to study the interactions between different regions of a flow. The standard analysis would select structures that are best correlated with the entire fluctuating velocity field. It is therefore not helpful if one flow region S of interest contains only a small percentage of the total kinetic energy. Using POD modes computed in the sub-domain S only, extended modes are introduced using the method of snapshots. We demonstrate that they provide a decomposition of the velocity field in the whole domain and that the extended mode number p provides the only local contribution to the velocity field correlated with the projection of the velocity field on POD mode p in S. This method is general and can be applied to either experimental or numerical velocity fields. As an example, it is applied to the analysis of an internal turbulent flow in a model engine cylinder with tumble. Data are obtained at a given phase with Particle Image Velocimetry. We focus our analysis on the middle of the intake stroke when the energy containing intake jet rolls up to feed a large vortex structure. Preferred directions of the jet/vortex interaction are clearly identified. This revised version was published online in July 2006 with corrections to the Cover Date.     

Applications of biorthogonal decompositions in fluid–structure interactions

This paper is dedicated to the study of the orthogonal decomposition of spatially and temporally distributed signals in fluid–structure interaction problems. First application is concerned with the analysis of wall-pressure distributions over bluff bodies. The need for such a tool is increasing due to the progress in data-acquisition systems and in computational fluid dynamics. The classical proper orthogonal decomposition (POD) method is discussed, and it is shown that heterogeneity of the mean pressure over the structure induces difficulties in the physical interpretation. It is then proposed to use the biorthogonal decomposition (BOD) technique instead; although it appears similar to POD, it is more general and fundamentally different since this tool is deterministic rather than statistical. The BOD method is described and adapted to wall-pressure distribution, with emphasis on aerodynamic load decomposition. The second application is devoted to the generation of a spatially correlated wind velocity field which can be used for the temporal calculation of the aeroelastic behaviour of structures such as bridges. In this application, the space–time symmetry of the BOD method is absolutely necessary. Examples are provided in order to illustrate and show the satisfactory performance and the interest of the method. Extensions to other fluid–structure problems are suggested.     

Meandering jets in shallow rectangular reservoirs: POD analysis and identification of coherent structures

The effect of the shallowness on meandering jets in a shallow rectangular reservoir is investigated. Four meandering flows were investigated in an experimental shallow rectangular reservoir. Their boundary conditions were chosen to cover a large range of friction numbers (defined with the sudden expansion width). Due to the unsteady characteristics of the flows, a proper orthogonal decomposition (POD) of the fluctuating part of the surface velocity fields measured using Large-Scale Particle Image Velocity was used for discriminating the flow structures responsible for the meandering of the jet. Less than 1 % of the calculated POD modes significantly contribute to the meandering of the jet, and two types of instability are in competition in such a flow configuration. The sinuous mode is the dominant mode in the flow, and it induces the meandering of the flow, while the varicose mode is a source of local mixing and weakly participates to the flow. The fluctuating velocity fields were then reconstructed using the POD modes corresponding to 80 % of the total mean fluctuating kinetic energy, and the coherent structures were identified using the residual vorticity, their centres being localised using a topology algorithm. The trajectories of the structures centres emphasise that at high friction number the coherent structures are small and laterally paired in the near, middle and far fields of the jet, while with decreasing friction number, the structures merge into large horizontal vortices in the far field of the jet, their trajectories showing more variability in space and time. The analysis of the stability regime finally reveals that the sinuous mode is convectively unstable and may become absolutely unstable at the end of the reservoir when the friction number is small.     

Wind tunnel and full-scale study of wind effects on a super-tall building

This paper presents the analyzed results from a combined wind tunnel and full-scale study of the wind effects on a super-tall building with a height of 420 m in Hong Kong. In wind tunnel tests, mean and fluctuating forces and pressures on the building models for the cases of an isolated building and the building with the existing surrounding condition are measured by the high-frequency force balance technique and synchronous multi-pressure sensing system under two typical boundary layer wind flow fields. Global and local wind force coefficients and structural responses are presented and discussed. A detailed study is conducted to investigate the influences of incident wind direction, upstream terrain conditions and interferences from the surroundings on the wind loads and responses of the high-rise structure. On the other hand, full-scale measurements of the wind effects on the super-tall building have been performed under typhoon conditions. The field data, such as wind speed, wind direction, structural acceleration and displacement responses have been simultaneously and continuously recorded during the passage of 12 typhoons since 2008. Analysis of the field measured data is carried out to investigate the typhoon effects on the super-tall building. Finally, the model test results are compared with the full-scale measurements for verification of the wind tunnel test techniques. The comparative study shows that the wind tunnel testing can provide reasonable predictions of the structural resonant responses. The resonant displacement responses are comparable to the background displacement responses so that the contribution of the background responses to the total displacement responses should not be underestimated. The outcome of the combined wind tunnel and full-scale study is expected to be useful to engineers and researchers involved in the wind-resistant design of super-tall buildings.     

随机风作用下高速列车非定常气动载荷的计算方法

基于Cooper理论和谐波叠加法计算随车移动点的脉动风速,分析不同风向角下脉动风速的功率谱密度特性.在横风下高速列车非定常气动载荷计算方法的基础上,建立了侧风下高速列车非定常气动载荷的计算方法,并用此方法分析了侧向随机风作用下非定常气动载荷的统计特性,给出了各气动载荷的峰值因子.研究表明,当风向角接近90°时,无量纲功率谱会往高频移动,风向角对脉动风速的影响较小;在各个风向角下,气动载荷的标准差与平均值的比值仅依赖于侧偏角,侧力与侧滚力矩的峰值因子相同,摇头力矩与点头力矩的峰值因子相同.     

随机风速下高速列车的运行安全可靠性

基于可靠性理论提出了随机风速作用下高速列车风致安全分析的新方法, 这种方法可以对随机风速作用下高速列车的运行安全可靠性进行有效评估.首先基于Cooper理论和谐波叠加法计算随车移动点的脉动风速, 建立随机风速作用下高速列车非定常气动载荷的计算方法, 并通过数值仿真得到气动载荷系数的标准差随侧偏角的变化规律. 然后建立高速列车车辆系统动力学模型, 并对计算模型的正确性进行验证.最后以随机风速、侧力系数、升力系数、侧滚力矩系数、摇头力矩系数和点头力矩系数为基本随机变量, 研究随机风速作用下高速列车的运行安全可靠性和可靠性灵敏度, 给出随机风速作用下高速列车的概率特征风速曲线.研究结果表明:随着车速和风速的增大, 系统的失效概率增大;通过可靠性灵敏度分析发现侧力系数和侧滚力矩系数对高速列车的运行安全影响最大, 应该特别注意这两个参数的变化对高速列车运行安全性的影响;传统确定性方法得到的高速列车的安全域曲线偏于保守, 基于可靠性的方法可得到更合理的安全域曲线.     

脉动风压测压管路系统的动态特性分析

利用基于高精度的流体管道耗散模型所建立起来的传递矩阵方法分析了小管径测压管路的动态特性并做了试验对比 ,得到了非常满意的结果 ,同时用编写的程序对脉动风压测试中所采用的一些常用的加管路阻尼器的方法作了模拟计算分析 ,得到一些比较有用的结论 ,应用本文的方法可以精确分析测压管路的动态特性并可以将结果用于风洞试验多路脉动风压测试中信号畸变的修正