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.

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.

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.

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.

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.

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.

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。

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。

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%。

风力机翼型S809绕流流动特性的POD和DMD对比分析

失速时的流动分离现象对风力机叶片的气动性能有重要影响,S809作为典型水平轴风力机翼型,在临界失速攻角下气动性能会大幅降低。基于流动特征提取的非定常流场降阶模型(reduced-order model,ROM)是进一步深入了解非定常流动的重要手段。本文通过计算流体力学方法得到轻、深失速攻角下翼型的流动特征,对时变速度场进行本征正交分解(proper orthogonal decomposition,POD)和动态模态分解(dynamic mode decomposition,DMD)分析,得到轻、深失速下翼型的非定常流场信息(能量占比、模态频率等)。通过两种方法的对比,结果表明,POD和DMD方法能够准确捕捉流动过程中的非定常结构和升力主频相同的典型模态,但是POD方法由于基于能量特征,在捕捉模态时会忽略与升力主频相近但能量较小的流动结构,而基于频率特征的DMD方法能够准确获得场的演化信息(增长率、频率等)。本文研究有利于针对主频结构发展相应的流动控制方法,从而改善翼型流场情况,提高气动性能。

基于Q-POD的脉动背压下压气机流场特性

针对一台自由活塞发动机(FPEG)匹配的电动压气机,研究了脉动背压条件下压气机的瞬态特性,并将脉动背压和稳定背压工况进行对比,揭示了压气机内部不同形成机理的非定常特征.采用四重本征正交模态分解(Q-POD)法,对压气机非定常流场进行了降阶重构.基于局部熵产率,对分解后的四重流场结构逐一分析,量化并定位了压气机非定常流动中的不可逆损失.结果表明:有/无脉动背压的熵产差异在叶轮中接近17%,在压壳中仅为1%.叶轮中的大尺度结构扰动耗散熵产占主导,扩压器中直接湍流耗散熵产占比超过92%.脉动背压通过改变压气机中大尺度相干结构进而影响瞬时流场结构.大尺度涡结构在环形通道内周向发展是造成扩压器中不可逆损失的主要因素.

基于POD-ANNS的架空输电线路舞动响应预测

针对塔线体系下覆冰八分裂导线的舞动特性,通常采用有限元法(FEM)获取舞动响应,但是FEM往往会花费大量时间,获取舞动响应的时间成本巨大,有限模型搭建难度大、类型繁多,同时也必须考虑动力学求解中计算不收敛等棘手问题。因此,获得不同参数、工况下的舞动响应比较困难。该文提出了一种混合代理模型,该模型能基于本征正交分解(POD)和人工神经网络(ANNS)实现舞动响应的快速预测。将FEM得到的舞动响应组合成快照矩阵,然后基于POD方法得到快照矩阵的POD模态基系数和POD模态;使用3种代理模型(BPNN、RBFNN、CNN)预测POD模态基系数,线性组合预测的POD模态基系数和POD模态,实现舞动响应的快速预测;还对比了3种混合模型下(POD-BPNN、POD-RBFNN、POD-CNN)的预测误差,预测时间。结果表明:3种混合模型均能快速、准确地得到目标响应,并且POD-RBFNN混合模型的误差更小;快照数量达到60个,基本可表征出全部样本的特征。

POD算法在飞机RAT舱温度预测中的应用研究

冲压空气涡轮(RAT)系统是飞机的应急发电系统,在飞机失去主交流电源后为飞机供电,RAT平时回收在非气密区的RAT舱内,在应急工况下释放到气流中。RAT舱温度很大程度上决定了RAT的释放时间,进而影响飞机在应急工况下的安全性,RAT舱的温度预测对于应急供电下的安全性具有重要意义。通过本征正交分解(POD)将RAT舱温度与高度、大气静温、飞行速度、RAT舱周围舱温度作为模型整体进行统一分析,并通过RAT舱温度简化模型及简化模型与完整模型的映射关系,选取试验数据作为样本数据,利用POD算法进行RAT舱温度预测。结果表明:1阶模态占据所有模态的比重超过99%,归一化处理后预测结果的平均绝对误差最小可达到0.063,均方根误差最小达到0.07;POD算法可以在样本数据基础上,通过模态重构有效预测RAT舱的温度信息。

Numerical investigation of the effect of wedge-type cavitating-bubble generator on attached unsteady cavitating flows using proper orthogonal decomposition method

The objective of this work is to reveal the effect of a passive control method called wedge-type cavitating-bubble generator(WCG)on the cloud cavitation dynamics of National Advisory Committee for Aeronautics(NACA)66 hydrofoil.The simulations are performed using the Partially-averaged Navier-Stokes(PANS)method coupled with the Zwart cavitation model.The proper orthogonal decomposition(POD)method is applied to extract the dominant flow structures.The results show that the WCG can induce the attached cavity to occur just behind the WCG instead of the hydrofoil leading edge.During the periodical time-evolution process of the unsteady cavity,it is found that the attached cavity with a larger scale around the hydrofoil with WCG has a rougher surface,accompanied with more shedding behaviors of small cavities.This is further illustrated by the POD modes,that is,the mode 1 and modes 2–4 present the large and small cavity vortex structures respectively.Meanwhile,the dominant frequencies of 50 Hz,47.5 Hz are given by the POD method respectively for the hydrofoils without and with WCG,which is in good agreement with that of FFT analysis.In addition,the correlation distribution of POD modal coefficients shows that the WCG can strengthen the vortex energy as well as the turbulence intensity.