Proper orthogonal decomposition based seismic source wavefield reconstruction for finite element reverse time migration

The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.

Coherency matrix-based proper orthogonal decomposition with application to wind field simulation

Proper Orthogonal Decomposition （POD） provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition （CPOD） is presented as an innovative form of the POD based on cross power spectral density matrices. By introducing a discretizing scheme, the CPOD-based spectral representation method is obtained for use in stochastic simulation. Moreover, some criteria are proposed that allow the truncation order of CPOD to be conveniently determined. A numerical example to illustrate the application of the proposed method for the simulation of a wind velocity field is provided.

Coherent structures over riblets in turbulent boundary layer studied by combining time-resolved particle image velocimetry(TRPIV),proper orthogonal decomposition(POD),and finite-time Lyapunov exponent(FTLE)

Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.

The proper orthogonal decomposition method for the Navier-Stokes equations

The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.

Model reduction for supersonic cavity flow using proper orthogonal decomposition(POD)and Galerkin projection

The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.

Wind Pressures on Structures by Proper Orthogonal Decomposition

Proper orthogonal decomposition （POD） is an effective statistical technique for data reduction and feature extraction of the random field including the wind field. This paper introduces the theory of the POD and illustrates engineering of structures. Using the POD technique, it is shown that wind pressure data can be accurately reconstructed with a limited number of modes using the wind pressure data from wind tunnel test. Comparing the reconstructed values by POD with the original measured values from the wind tunnel test both in the time and frequency domains, it is concluded that the proper orthogonal decomposition（POD） is an efficient and practical technique for deriving the random wind pressure field from limited known data as shown in the pitched roof example in this paper.

An Economical Approach to Flow-Adaptive Moderation of Spurious Ensemble Correlations and Its Application in the Proper Orthogonal Decomposition-Based Ensemble Four Dimensional Variational Assimilation Method

The purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method(PODEn4DVar). Owing to the applications of the sparse processing and EOF decomposition techniques, the computational costs of this proposed sparse flow-adaptive moderation(SFAM) localization scheme are significantly reduced. The effectiveness of PODEn4 DVar with SFAM localization is demonstrated by using the Lorenz-96 model in comparison with the Smoothed ENsemble Correlations Raised to a Power(SENCORP) and static localization schemes, separately. The performance of PODEn4 DVar with SFAM localization shows a moderate improvement over the schemes with SENCORP and static localization, with low computational costs under the imperfect model.

Review of Proper Orthogonal Decomposition Method Applied to Computational Aeroelasticity

Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD） has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.

基于动响应数据特征的桥梁结构损伤识别

介绍了本征正交分解(Proper Orthogonal Decomposition,POD)的基本原理,探讨了POD在桥梁结构损伤识别中的应用。提出了基于动响应数据特征的桥梁结构损伤识别方法,该识别方法基于POD技术对桥梁结构在不同位置、不同时刻收集到的位移快照矩阵(Snapshot Matrix)进行本征正交分解,得到结构的本征正交模态(POMs),进而构造出损伤指标来识别结构的损伤位置及程度,实现了对桥梁结构损伤的多工况识别。并以保定黄花沟桥为例,通过数值模拟试验,验证了该方法的有效性,结果表明POD能够从空心板桥结构的振动响应数据中提取出结构的本质特征,并且提取过程简单、快捷,可为桥梁结构提供一种有效的损伤识别方法。

某SUV气动减阻优化及其流场机制

为了提高整车燃油经济性,本文以某款SUV车型为研究对象,将仿真与试验相结合改善汽车行驶过程中的气动阻力系数。首先通过风洞试验确定对整车气动阻力有重要影响的区域或部件,其次对气动阻力系数贡献值较大的部件或区域进行减阻优化。结果表明,前轮阻风板、尾灯和尾翼对整车气动阻力系数贡献值较大。对前轮阻风板的改型,有效降低正压区面积以及减弱车轮干扰阻力;对尾灯和尾翼的优化设计,改善了尾部负压区,缩短了分离流在后窗上部的再附着的距离。基于本征正交分解方法进行局部流场信息的提取和分析可知,1阶与2阶模态主要构成了该SUV尾流场的关键流态。经试验与仿真验证,相比于初始方案,气动优化组合设计减阻率可达7.5%。本文为新一代SUV改型与升级换代提供了理论基础与技术支持。

基于POD和Kriging的水滴收集量快速预测方法

数值模拟手段预测翼面处水滴撞击特性通常较为耗时,为快速准确计算结冰条件下的翼面处水滴收集量,提出了基于本征正交分解和代理模型的水滴收集量快速预测方法。首先对FAR 25部附录C中连续最大结冰条件进行优化拉丁超立方采样,通过数值模拟手段获得各采样点在翼面处水滴收集量分布,从而构造样本空间。在此基础上,利用本征正交分解(Proper orthogonal decompostion,POD)方法找到表达和重构水滴收集量的本征模态以及相应的拟合系数。最后,利用Kriging模型建立样本空间中各采样点与拟合系数间的代理模型,实现翼面处水滴收集量分布的快速预测。经多组工况验证表明:该方法可较为准确地预测翼面处水滴收集量分布,其计算成本较数值模拟方法大幅降低,能够为无人机防除冰设计提供有益参考。

基于POD/DMD降阶模型的离心泵蜗壳内非稳态流动分析

为深入研究离心泵蜗壳内非线性耦合流动的本质流动特征,本文以一单级单吸式离心泵蜗壳为研究对象,分别采用本征正交分解和动态模态分解2种降阶模型对蜗壳内非定常流场数据进行模态分析,获取流场主导流动结构,并对原流场进行重构。研究发现:蜗壳内流结构主要由速度正负交错,并且周期性特征与叶频及其倍频相关的成对涡旋组成。本征正交分解和动态模态分解方法均可以捕捉流场主要流动结构,并对原流场进行准确还原,两者重构流场与原流场的均方根误差均在0.4%以内。尽管本征正交分解方法在重构流场时整体均方根误差更小,但无法获取单频率流动结构,而动态模态分解方法可以获得不同频率流动结构对流场的贡献,从而捕捉到复杂流场中的不稳定模态。研究成果可以为增强离心泵全局流动的认知、关键水力部件优化设计及发展主/被动流动控制提供理论参考。

基于Twin Builder的110kV油浸式变压器3维磁场降阶模型及损耗分析

为解决3维变压器磁场有限元仿真计算效率低的问题,提出基于本征正交分解法的磁场降阶模型与基于二次多项式的损耗响应面模型。以1台110 kV变压器为算例,首先建立了考虑绕组涡流损耗的变压器磁场仿真模型,通过仿真分析了其在额定工况下的磁场及损耗分布;其次,通过仿真试验设计获取了多组工况下的磁场与损耗数据,在Twin Builder中训练得到变压器磁场的各降阶模块;最后,搭建面向数字孪生应用的变压器3维磁场降阶模型,实现了变压器磁场损耗的快速计算与云图分布的可视化。与计算单数据相比,仿真结果考虑了涡流效应的绕组损耗在靠近端部时有明显升高,最大值分别出现在高、低压绕组两端,约为绕组中部损耗的1.3~1.65倍。基于该磁场结果建立的降阶模型在计算效率方面较全阶模型有显著提升,将实际仿真时间缩短至0.76s,可满足数字孪生应用场景下的磁场快速计算需求。

油浸式变压器绕组瞬态温升降阶快速计算方法

油浸式电力变压器绕组温升监测是保证其安全稳定运行的重要手段。为了改善采用有限元方法计算油浸式电力变压器绕组瞬态温升时存在效率不高的问题,提出一种结构保留的本征正交分解(SPOD)与离散经验插值方法(DEIM)相结合的计算策略。首先,该文采用最小二乘有限元法(LSFEM)与迎风有限元法(UFEM)构建变压器绕组瞬态温升计算控制方程;其次,针对控制方程的特点,引入SPOD方法,通过将采样时间内的计算结果构成快照矩阵,建立降阶模型,降低有限元刚度矩阵的计算阶数,提高求解有限元方程的效率;然后,为了改善本征正交分解方法对于非线性问题效率提升不高的缺陷,结合DEIM算法,对有限元方程中的非线性项进行插值处理,从而减少每一时步形成总体刚度矩阵的时间,进一步提高总体计算效率。为了验证文章所提算法的精确性及高效性,根据油浸式电力变压器绕组的基本特点,建立了单分区分匝绕组传热模型,对其瞬态传热过程进行计算,结果表明:基于SPOD-DEIM的有限元降阶计算能够在保证精度的前提下有效提高计算效率,与全阶计算结果相比,流场与温度场的计算误差均不超过1.5%,且计算效率提升5.1倍。同时,为了充分说明SPOD-DEIM算法在工程应用中的价值,该文基于110 kV变压器绕组搭建了温升实验平台,建立了八分区分匝绕组数值计算模型,对算法的精度、效率及工程应用价值进行了验证及讨论,计算及实验结果表明:精度方面,降阶计算较全阶计算的瞬态全过程计算误差小于2.5%,且与实验结果相比,误差不超过5.41K;效率方面,降阶计算的全过程计算时间为54.28 h,与全阶计算相比,计算效率提升至10.57倍,与商业仿真软件Fluent相比,效率提升至6.37倍,充分说明所提算法的高效性及工程应用价值,为大型电力设备快速仿真提供新思路。

面向数字孪生模型应用的油浸式变压器绕组温度POD-RBFLP降阶计算方法

了解油浸式电力变压器绕组的温度情况是保证其运行稳定性的关键,也是当前针对油浸式变压器数字孪生分析的必然需求。为了快速地获得变压器绕组的稳态温度,该文提出一种基于本征正交分解(proper orthogonal decomposition,POD)和包含线性多项式的径向基函数响应面法(radial basis function response surface method including linear polynomial,RBFLP)的降阶计算模型。首先,讨论POD方法的降阶特性,并设计一种基于留一法交叉验证的自适应获得快照矩阵方法,以提高计算精度及效率;其次,采用响应面方法建立POD模态系数与绕组工况的相关关系,旨在实现通过绕组工况快速获得POD模态系数,从而跳过对降阶模型的复杂非线性计算,进而高效重构绕组温度场。相关算例表明,该方法具有较好的计算精度和效率,在50组测试工况下,与全阶计算相比,误差不超过2.5 K,且总计算时间仅为1.45 s;最后,基于110 kV变压器绕组搭建温升试验平台,试验结果表明,降阶计算结果相较于试验结果,平均计算误差不超过2 K,且单步计算时间仅为0.03 s,相较于同等规模的全阶计算,计算效率有较大幅度地提升。

基于POD-αATS的油浸变压器瞬态温升降阶自适应变步长计算方法

针对油浸式电力变压器瞬态温升计算效率过低的问题,该文提出本征正交分解-αATS(proper orthogonal decomposition-adaptive time stepping based onαfactor,POD-αATS)降阶自适应变步长瞬态计算方法。首先,推导变压器绕组瞬态温升计算的有限元离散方程;其次,采用POD降阶算法改善传统瞬态计算中存在的条件数过大及方程阶数过高的问题;同时对于瞬态计算中的时间步长选择问题,提出适用于非线性问题的αATS变步长策略;然后,为验证方法的有效性,基于110 kV油浸式电力变压器绕组的基本结构建立二维八分区数值计算模型,同时将计算结果与基于110 kV绕组的温升实验结果进行对比。数值计算及实验结果表明,所提算法与全阶定步长算法在流场和温度场中的精度几乎相同,且流场计算效率提升约45倍,温度场计算效率提升约38倍,计算速度得到显著提高。这一点在温升实验中同样得到验证,说明该文所提算法的准确性、高效性及一定的工程实用性。

包含快照选择策略的POD-QDEIM油浸式变压器绕组瞬态温升降阶算法研究及其实验验证

为了提高采用有限元方法对油浸式电力变压器绕组瞬态温升进行仿真的计算速度,该文提出一种包含快照选择策略的本征正交分解(proper orthogonal decomposition,POD)-基于列主元QR分解的离散经验插值(QR factorization-discrete empirical interpolation method,Q-DEIM)(POD-QDEIM)算法。首先,文章基于最小二乘有限元法与迎风有限元法推导绕组流热耦合计算方程;其次,通过引入POD方法,降低有限元方程阶数提高求解效率;同时提出POD自适应快照选择策略,在保证降阶模型精度的前提下,减小快照矩阵规模;随后,为了改善POD方法求解非线性问题时效率不高的劣势,文章结合基于Q-DEIM方法,通过插值的方法形成方程中的非线性项,从而提高每一时步非线性项的形成效率;最后,基于110 kV油浸式电力变压器绕组基本结构,建立了八分区分匝绕组传热模型以及绕组温升试验装置对所提算法进行验证,仿真及实验结果表明POD-QDEIM降阶算法的计算精度在工程上属于可接受范围,其计算效率较全阶计算提升了近11.72倍,说明该算法在油浸式电力变压器绕组瞬态温升快速仿真领域的工程应用价值。

基于测点聚类的POD-BPNN风压重构方法

文章提出本征正交分解(POD)与聚类分析结合的结构表面风压测点分类与关键测点布置方法,基于少量测点的风压数据,通过POD与误差反向传播神经网络(BPNN)方法实现方柱结构表面风压时程的重构。机器学习数据集为多风向角均匀来流下单方柱测压风洞试验得到的测点风压时程。将44个测点的风压时程数据POD降维,并采用K-means++聚类分析得到方柱周向轮廓系数分布,并基于轮廓系数的多风向角平均值,得到12、16、20和24个关键测点的轴对称布置方案。以关键测点的风压时程数据为训练集,采用POD-BPNN方法重构方柱表面其余测点所在位置的风压时程,并将风压时程及其统计值同试验结果对比。从12~20测点方案,风压重构精度逐步提升;20测点和24测点方案的重构风压差异较小,二者都能较好地重构方柱表面风压分布,仅在0°风向角方柱脉动风压误差偏大。

利用长短期记忆神经网络的改进POD-Galerkin降阶模型及其在流场预测中的应用

针对标准POD-Galerkin降阶模型在流场快速预测中存在误差而导致精度不高的问题,提出了一种利用长短期记忆神经网络的改进POD-Galerkin降阶模型。使用本征正交分解对流场进行降维,投影得到低维降阶模型,引入两个长短期记忆神经网络,建立从POD-Galerkin降阶模型到实际POD模态时间系数之间的修正映射、低阶模态时间系数与高阶模态时间系数之间的扩展映射,分别用于消除标准POD-Galerkin降阶模型的误差累积和扩展降阶模型的阶数,从而实现物理驱动与数据驱动混合的流动降阶模型的构建。将改进POD-Galerkin降阶模型应用于二维圆柱绕流的流场预测,通过与原始标准POD-Galerkin降阶模型的对比,分析了所提模型的精度和计算速度。结果表明:添加神经网络修正项后的降阶模型相较于标准POD-Galerkin降阶模型,有效提升了降阶模型的精度,预测各阶模态时间系数的均方根误差能够减小1~2个数量级,预测的流场更接近原始流场;在预测相同阶数的情况下,计算时间显著减小,基于4阶和6阶扩展的8阶改进降阶模型相较于原始8阶POD-Galerkin降阶模型预测速度分别提高了约56%和25%。