Journal articles: 'Spectral Proper Orthogonal Decomposition'

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Sieber, Moritz, C. Oliver Paschereit, and Kilian Oberleithner. "Spectral proper orthogonal decomposition." Journal of Fluid Mechanics 792 (March 4, 2016): 798–828. http://dx.doi.org/10.1017/jfm.2016.103.

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The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency-ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods are not suitable when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these ‘rigid’ approaches, we propose a new method termed spectral proper orthogonal decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical systems theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range. The SPOD requires only one additional parameter, which can be estimated from the basic time scales of the flow. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD are only marginally greater than those of the snapshot POD.

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Schmidt, Oliver T., and Tim Colonius. "Guide to Spectral Proper Orthogonal Decomposition." AIAA Journal 58, no. 3 (March 2020): 1023–33. http://dx.doi.org/10.2514/1.j058809.

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He, Xiao, Zhou Fang, Georgios Rigas, and Mehdi Vahdati. "Spectral proper orthogonal decomposition of compressor tip leakage flow." Physics of Fluids 33, no. 10 (October 2021): 105105. http://dx.doi.org/10.1063/5.0065929.

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Baars, Woutijn J., and Charles E. Tinney. "Proper orthogonal decomposition-based spectral higher-order stochastic estimation." Physics of Fluids 26, no. 5 (May 2014): 055112. http://dx.doi.org/10.1063/1.4879255.

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Schmidt, Oliver T., and Aaron Towne. "An efficient streaming algorithm for spectral proper orthogonal decomposition." Computer Physics Communications 237 (April 2019): 98–109. http://dx.doi.org/10.1016/j.cpc.2018.11.009.

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Mendez, M. A., M. Balabane, and J. M. Buchlin. "Multi-scale proper orthogonal decomposition of complex fluid flows." Journal of Fluid Mechanics 870 (May 15, 2019): 988–1036. http://dx.doi.org/10.1017/jfm.2019.212.

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Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.

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Mengaldo, Gianmarco, and Romit Maulik. "PySPOD: A Python package for Spectral Proper Orthogonal Decomposition (SPOD)." Journal of Open Source Software 6, no. 60 (April 16, 2021): 2862. http://dx.doi.org/10.21105/joss.02862.

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Gambassi, Henrique, Paul Ziadé, and Chris Morton. "Sparse sensor-based flow estimation with spectral proper orthogonal decomposition." AIP Advances 12, no. 8 (August 1, 2022): 085208. http://dx.doi.org/10.1063/5.0094874.

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The application of Artificial Neural Networks (ANNs) in developing sensor-based estimators for unsteady flows has become an active area of research over the last decade. One of the challenges in this area is the selection of a low-dimensional subspace that enables the ANN to reconstruct relevant spatiotemporal dynamics in the flow, as both sparsity and interpretability are simultaneously desired. The present study demonstrates the use of a flow-estimation framework based on Long Short-Term Memory (LSTM) neural networks and the time-domain Spectral Proper Orthogonal Decomposition (SPOD) [Sieber et al., “Spectral proper orthogonal decomposition,” J. Fluid Mech. 792, 798–828 (2016)], which was proposed as an extension to the traditional POD. The two-cylinder flow selected for analysis in this study is referred to as the “flip-flop” regime for exhibiting intermittent changes in the phase alignment of the vortices shed by the two cylinders. This flow has dynamics occurring over a wide range of frequencies, and it was selected to demonstrate the usefulness of SPOD in characterizing the wake dynamics of periodic wake flows and to determine if it can provide a better subspace for training and estimation when compared to POD. It was found that a particular SPOD basis obtained with an empirically determined filter length completely separated the frequency centered phenomena present in the spectrum of the most energetic POD modes into different modes. These new SPOD modes were observed to have a direct relationship with the vortex dynamics in the flow, providing direct access to the antiphase and in-phase flow states. The LSTM neural networks estimation capacities were very similar across all the modal spaces investigated, performing well regardless of whether the frequency content of the modal space used for training and estimation was found superimposed in the spectrum of the most energetic modes (POD) or separated into different modes (SPOD). Further investigation is required to determine if this result holds for turbulent flows.

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Cho, Woon, Samir Sahyoun, Seddik M. Djouadi, Andreas Koschan, and Mongi A. Abidi. "Reduced-order spectral data modeling based on local proper orthogonal decomposition." Journal of the Optical Society of America A 32, no. 5 (April 9, 2015): 733. http://dx.doi.org/10.1364/josaa.32.000733.

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Towne, Aaron, Oliver T. Schmidt, and Tim Colonius. "Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis." Journal of Fluid Mechanics 847 (May 29, 2018): 821–67. http://dx.doi.org/10.1017/jfm.2018.283.

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We consider the frequency domain form of proper orthogonal decomposition (POD), called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space–time POD problem for statistically stationary flows and leads to modes that each oscillate at a single frequency. This form of POD goes back to the original work of Lumley (Stochastic Tools in Turbulence, Academic Press, 1970), but has been overshadowed by a space-only form of POD since the 1990s. We clarify the relationship between these two forms of POD and show that SPOD modes represent structures that evolve coherently in space and time, while space-only POD modes in general do not. We also establish a relationship between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are in fact optimally averaged DMD modes obtained from an ensemble DMD problem for stationary flows. Accordingly, SPOD modes represent structures that are dynamic in the same sense as DMD modes but also optimally account for the statistical variability of turbulent flows. Finally, we establish a connection between SPOD and resolvent analysis. The key observation is that the resolvent-mode expansion coefficients must be regarded as statistical quantities to ensure convergent approximations of the flow statistics. When the expansion coefficients are uncorrelated, we show that SPOD and resolvent modes are identical. Our theoretical results and the overall utility of SPOD are demonstrated using two example problems: the complex Ginzburg–Landau equation and a turbulent jet.

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Kutkan, Halit, Alberto Amato, Giovanni Campa, and Luis Tay-Wo-Chong. "Modal Decomposition Analysis of Bluff-Body Stabilized Lean Premixed CH4/H2/air Flames Based on LES Data." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 5 (February 1, 2023): 2413–20. http://dx.doi.org/10.3397/in_2022_0343.

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Unsteady flow and flame dynamics of bluff body stabilized CH4/H2/air premixed flames are investigated numerically with LES and modal decomposition techniques. Energy ranked and frequency dependent modes are identified with proper orthogonal (POD), spectral proper orthogonal (SPOD) and dynamic mode decompositions (DMD). Flow and flame coherent structures are extracted based on the axial velocity and heat release rate contours. Two cases, namely 100% CH4/air (V-flame) and 43.4% CH4 + 56.6% H2/air (M-flame), are selected for the analysis. Each case is acoustically excited in large eddy simulation (LES) with harmonic excitation signals at distinct frequencies and with a broadband excitation signal, to produce snapshots for modal decomposition analysis. In POD, the frequencies of the relevant modes are extracted with the discrete Fourier transform (DFT) of time coefficients, while in SPOD and DMD the extracted modes are frequency dependent by nature. Results are compared and commented.

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Noack, Bernd R. "From snapshots to modal expansions – bridging low residuals and pure frequencies." Journal of Fluid Mechanics 802 (August 1, 2016): 1–4. http://dx.doi.org/10.1017/jfm.2016.416.

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Data-driven low-order modelling has been enjoying rapid advances in fluid mechanics. Arguably, Sirovich (Q. Appl. Maths, vol. XLV, 1987, pp. 561–571) started these developments with snapshot proper orthogonal decomposition, a particularly simple method. The resulting reduced-order models provide valuable insights into flow physics, allow inexpensive explorations of dynamics and operating conditions, and enable model-based control design. A winning argument for proper orthogonal decomposition (POD) is the optimality property, i.e. the guarantee of the least residual for a given number of modes. The price is unpleasant frequency mixing in the modes which complicates their physical interpretation. In contrast, temporal Fourier modes and dynamic mode decomposition (DMD) provide pure frequency dynamics but lose the orthonormality and optimality property of POD. Sieber et al. (J. Fluid Mech., vol. 792, 2016, pp. 798–828) bridge the least residual and pure frequency behaviour with an ingenious interpolation, called spectral proper orthogonal decomposition (SPOD). This article puts the achievement of the TU Berlin authors in perspective, illustrating the potential of SPOD and the challenges ahead.

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Hoa, Le Thai, and Nguyen Dong Anh. "Spectral proper transformation and application to gust response prediction of structures." Vietnam Journal of Mechanics 29, no. 1 (March 31, 2007): 25–36. http://dx.doi.org/10.15625/0866-7136/29/1/5588.

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Random turbulent loading on engineering structures which immersed in the atmospheric turbulent flow is often represented as the multi-dimensional and/ or multivariate Gaussian random loading processes. Gust response prediction, however, usually burdens a lot of computational difficulties due to turbulent loading projection on the generalized structural coordinates. In these cases, the decomposition techniques must be required to decouple the multi-variate turbulent loading into the independently generalized turbulent forces, then is associated with the generalized structural modes. This paper will present the proper orthogonal decomposition using the spectral proper transformation in the frequency domain to decouple the multi-variate turbulent loading processes. New approach in the gust response prediction of structures will be formulated with numerical example of cable-stayed bridge.

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Schneider, Nick, Simon Köhler, and Jens von Wolfersdorf. "Experimental Detection of Organised Motion in Complex Flows with Modified Spectral Proper Orthogonal Decomposition." Fluids 8, no. 6 (June 17, 2023): 184. http://dx.doi.org/10.3390/fluids8060184.

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Spectral proper orthogonal decomposition (SPOD) has seen renewed interest in recent years due to its unique ability to decouple organised motion at different timescales from large datasets with limited available information. This paper investigated the unsteady components of the flow field within a simplified turbine centre frame (TCF) model by applying SPOD to experimental, time-resolved flow speed data captured by particle image velocimetry (PIV). It was observed that conventional methods failed to capture the two significant active bands in the power spectrum predicted by preliminary hot wire anemometry measurements. Therefore, a modification to the SPOD procedure, which employs subsampling of the time sequence recorded in the experiment to artificially lower the PIV data acquisition frequency, was developed and successfully deployed to analyse the TCF flow field. The two dynamically active bands were identified in the power spectra, resulting in a closer match to the preceding analyses. Within these bands, SPOD’s ability to capture spatial coherence was leveraged to detect several plausible coherent, fluctuating structures in two perpendicular planes. A partial three-dimensional reconstruction of the flow phenomena suggested that both bands were associated with a distinct mode of organised motion, each contributing a significant percentage of the system’s total fluctuating energy.

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Abbaszadeh, Mostafa, and Mehdi Dehghan. "The proper orthogonal decomposition modal spectral element method for two-dimensional viscoelastic equation." Thin-Walled Structures 161 (April 2021): 107429. http://dx.doi.org/10.1016/j.tws.2020.107429.

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Zheng, Zhongquan C., Meihua Zhang, and Zhijian Wang. "Spectral proper orthogonal decomposition analysis of flowfield for supersonic nozzle jet noise reduction." Journal of the Acoustical Society of America 150, no. 4 (October 2021): A131. http://dx.doi.org/10.1121/10.0007870.

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Li, Xiao-Bai, Guang Chen, Xi-Feng Liang, Dong-Run Liu, and Xiao-Hui Xiong. "Research on spectral estimation parameters for application of spectral proper orthogonal decomposition in train wake flows." Physics of Fluids 33, no. 12 (December 2021): 125103. http://dx.doi.org/10.1063/5.0070092.

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Hu, Jiawei, Yangang Wang, Hanru Liu, Weixiong Chen, and Yong Xu. "Comparative Study on Modal Decomposition Methods of Unsteady Separated Flow in Compressor Cascade." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 38, no. 1 (February 2020): 121–29. http://dx.doi.org/10.1051/jnwpu/20203810121.

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The present work investigated the vortex structure and fluctuation frequency characteristics generated by boundary layer separation of a high-load compressor cascade using modal decomposition methods. The dominant modes and dynamic behaviors of unsteady flow in the cascade were obtained, and the differences of three modal decomposition methods (Proper Orthogonal Decomposition, Dynamic Mode Decomposition and Spectral Proper Orthogonal Decomposition) in feature recognition of cascade flow were discussed. The results show that:(1) The POD method can accurately extract the dominant spatial structure of the flow field, but the modal coefficients are multi-frequency coupled, which makes the dominant modal characteristics of cascade flow unclear. (2) The standard DMD method can obtain the spatial-temporal single frequency mode of cascade flow, as well as their growth rates and frequencies. However, this method is likely to capture the suboptimal mode of large amplitude with large attenuation rate, and fails to obtain the high-frequency coherent structure, which makes it impossible to obtain the dominant feature with limited mode number. (3) The SPOD method, based on spectral characteristics, can obtain spatial and temporal single frequency modes, and there is no modal screening problem. The use of spectral estimation method (SPOD) reduces the sensitivity to numerical noise. This method can obtain the low-rank behavior of cascade flow, which is helpful to understand cascade flow mechanisms. Therefore, SPOD method is more advantageous for the modal analysis of unsteady separated flow in high-load compressor cascade.

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Milani, Pedro M., David S. Ching, Andrew J. Banko, and John K. Eaton. "Shear layer of inclined jets in crossflow studied with spectral proper orthogonal decomposition and spectral transfer entropy." International Journal of Heat and Mass Transfer 147 (February 2020): 118972. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2019.118972.

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Heidt, Liam, Tim Colonius, Akhil Nekkanti, Oliver T. Schmidt, Igor A. Maia, and Peter Jordan. "Application of spectral proper orthogonal decomposition and resolvent analysis to periodically forced supersonic jets." Journal of the Acoustical Society of America 150, no. 4 (October 2021): A176. http://dx.doi.org/10.1121/10.0008036.

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Feng, Xiangzhou, Jianqin Suo, Qiandong Li, and Longxi Zheng. "Modal Decomposition Study of the Non-Reactive Flow Field in a Dual-Swirl Combustor." Energies 16, no. 17 (August 25, 2023): 6182. http://dx.doi.org/10.3390/en16176182.

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The modal decomposition study of the non-reactive flow field in a dual-swirl combustor is investigated through the large eddy simulation. The formation mechanism and function of various recirculation zones are elaborated by analyzing the time-averaged and instantaneous velocity contours of the center section. The precessing vortex core (PVC) is first visualized by the pressure iso-surface, and the evolution process is presented. Different dimensionality reduction methods are adopted to identify the coherent structures from the flow field. The most energetic spatial structure corresponding to the PVC and its second-order harmonic structure is extracted by the classical proper orthogonal decomposition (POD). The coherent structures with high frequency have relatively low energy content. In addition, a spectral proper orthogonal decomposition (SPOD) method, which can implement spatial-temporal decomposition simultaneously, is introduced to obtain the energy-based spatial structures at all characteristic frequencies. A triple-helix with azimuth wave number m = 3 and a quadruple-helix with azimuth wave number m = 4 are discovered as the third-order and the fourth-order harmonics of single-helix, respectively.

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HENNINGSON, DAN S. "Description of complex flow behaviour using global dynamic modes." Journal of Fluid Mechanics 656 (July 20, 2010): 1–4. http://dx.doi.org/10.1017/s0022112010002776.

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A novel method for performing spectral analysis of a fluid flow solely based on snapshot sequences from numerical simulations or experimental data is presented by Schmid (J. Fluid Mech., 2010, this issue, vol. 656, pp. 5–28). Dominant frequencies and wavenumbers are extracted together with dynamic modes which represent the associated flow structures. The mathematics underlying this decomposition is related to the Koopman operator which provides a linear representation of a nonlinear dynamical system. The procedure to calculate the spectra and dynamic modes is based on Krylov subspace methods; the dynamic modes reduce to global linear eigenmodes for linearized problems or to Fourier modes for (nonlinear) periodic problems. Schmid (2010) also generalizes the analysis to the propagation of flow variables in space which produces spatial growth rates with associated dynamic modes, and an application of the decomposition to subdomains of the flow region allows the extraction of localized stability information. For finite-amplitude flows this spectral analysis identifies relevant frequencies more effectively than global eigenvalue analysis and decouples frequency information more clearly than proper orthogonal decomposition.

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Zhang, Bingchao, Hong Hu, Hideki Kikumoto, and Ryozo Ooka. "Turbulence-induced ventilation of an isolated building: Ventilation route identification using spectral proper orthogonal decomposition." Building and Environment 223 (September 2022): 109471. http://dx.doi.org/10.1016/j.buildenv.2022.109471.

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Chen, Lizhong, and Chris W. Letchford. "Simulation of Multivariate Stationary Gaussian Stochastic Processes: Hybrid Spectral Representation and Proper Orthogonal Decomposition Approach." Journal of Engineering Mechanics 131, no. 8 (August 2005): 801–8. http://dx.doi.org/10.1061/(asce)0733-9399(2005)131:8(801).

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Le, Thai Hoa, Yukio Tamura, and Masaru Matsumoto. "Spanwise pressure coherence on prisms using wavelet transform and spectral proper orthogonal decomposition based tools." Journal of Wind Engineering and Industrial Aerodynamics 99, no. 4 (April 2011): 499–508. http://dx.doi.org/10.1016/j.jweia.2011.01.008.

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Zhang, Bingchao, Ryozo Ooka, and Hideki Kikumoto. "Analysis of turbulent structures around a rectangular prism building model using spectral proper orthogonal decomposition." Journal of Wind Engineering and Industrial Aerodynamics 206 (November 2020): 104213. http://dx.doi.org/10.1016/j.jweia.2020.104213.

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DELVILLE, J., L. UKEILEY, L. CORDIER, J. P. BONNET, and M. GLAUSER. "Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition." Journal of Fluid Mechanics 391 (July 25, 1999): 91–122. http://dx.doi.org/10.1017/s0022112099005200.

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Large-scale structures in a plane turbulent mixing layer are studied through the use of the proper orthogonal decomposition (POD). Extensive experimental measurements are obtained in a turbulent plane mixing layer by means of two cross-wire rakes aligned normal to the direction of the mean shear and perpendicular to the mean flow direction. The measurements are acquired well into the asymptotic region. From the measured velocities the two-point spectral tensor is calculated as a function of separation in the cross-stream direction and spanwise and streamwise wavenumbers. The continuity equation is then used for the calculation of the non-measured components of the tensor. The POD is applied using the cross-spectral tensor as its kernel. This decomposition yields an optimal basis set in the mean square sense. The energy contained in the POD modes converges rapidly with the first mode being dominant (49% of the turbulent kinetic energy). Examination of these modes shows that the first mode contains evidence of both known flow organizations in the mixing layer, i.e. quasi-two-dimensional spanwise structures and streamwise aligned vortices. Using the shot-noise theory the dominant mode of the POD is transformed back into physical space. This structure is also indicative of the known flow organizations.

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ROWLEY, CLARENCE W., IGOR MEZIĆ, SHERVIN BAGHERI, PHILIPP SCHLATTER, and DAN S. HENNINGSON. "Spectral analysis of nonlinear flows." Journal of Fluid Mechanics 641 (November 18, 2009): 115–27. http://dx.doi.org/10.1017/s0022112009992059.

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We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.

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Raju, Martin, S. L. N. Desikan, and Aravind Vaidyanathan. "Transient characteristics of a typical vacuum ejector—An experimental study." Physics of Fluids 34, no. 9 (September 2022): 096108. http://dx.doi.org/10.1063/5.0100810.

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Using simultaneous measurements of unsteady pressures in conjunction with time-resolved Schlieren images and oil flow visualization, we investigate the characteristics of a typical vacuum ejector's starting transient, steady-state, and shut-down transient. With varying primary jet chamber pressure, the pressure evolution in the secondary chamber shows smooth, perturbed, rapid, and steady evacuation stages, as well as hysteresis and rapid filling stages. It is noticed that the evacuation in the secondary chamber is improved during stopping transient just before the unstart event. By using oil flow images, we illustrate the separation bubble characteristics during each stage of the vacuum ejector operation and their influence on the pressure evolution. Through cross correlation, it has been determined that the primary jet flapping during the starting transient causes the jet to attach to one of the diffuser walls. We also demonstrate that the primary jet undergoes both longitudinal and lateral oscillations in the starting transient, the former having a major effect on unsteadiness in the secondary chamber using proper orthogonal decomposition and spectral proper orthogonal decomposition algorithms and power spectral density (PSD). Simultaneous acquisition of unsteady pressures and high-speed Schlieren images allow us to correlate the frequency peaks (PSD spectra) in the flow. Using magnitude-squared coherence and cross correlation analyses, we confirm communication of unsteadiness and its direction of propagation between the secondary chamber and the diffuser. In this study, we demonstrate that a high ramping rate of primary jet chamber pressure reduces the unsteadiness in the secondary chamber during the transient starting phase.

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Kume, Kenji, and Naoko Nose-Togawa. "An Adaptive Orthogonal SSA Decomposition Algorithm for a Time Series." Advances in Data Science and Adaptive Analysis 10, no. 01 (January 2018): 1850002. http://dx.doi.org/10.1142/s2424922x1850002x.

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Singular spectrum analysis (SSA) is a nonparametric spectral decomposition of a time series into arbitrary number of interpretable components. It involves a single parameter, window length [Formula: see text], which can be adjusted for the specific purpose of the analysis. After the decomposition of a time series, similar series are grouped to obtain the interpretable components by consulting with the [Formula: see text]-correlation matrix. To accomplish better resolution of the frequency spectrum, a larger window length [Formula: see text] is preferable and, in this case, the proper grouping is crucial for making the SSA decomposition. When the [Formula: see text]-correlation matrix does not have block-diagonal form, however, it is hard to adequately carry out the grouping. To avoid this, we propose a novel algorithm for the adaptive orthogonal decomposition of the time series based on the SSA scheme. The SSA decomposition sequences of the time series are recombined and the linear coefficients are determined so as to maximizing its squared norm. This results in an eigenvalue problem of the Gram matrix and we can obtain the orthonormal basis vectors for the [Formula: see text]-dimensional subspace. By the orthogonal projection of the original time series on these basis vectors, we can obtain adaptive orthogonal decomposition of the time series without the redundancy of the original SSA decomposition.

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Zhang, Yang, and Maarten Vanierschot. "Determination of single and double helical structures in a swirling jet by spectral proper orthogonal decomposition." Physics of Fluids 33, no. 1 (January 1, 2021): 015115. http://dx.doi.org/10.1063/5.0032985.

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Greig, David, Kamran Siddiqui, Panagiota Karava, and Ahmed Elatar. "Investigation of fundamental flow mechanisms over a corrugated waveform using proper orthogonal decomposition and spectral analyses." International Journal of Thermal Sciences 96 (October 2015): 160–72. http://dx.doi.org/10.1016/j.ijthermalsci.2015.05.003.

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Zhang, Qun, Peng Zhang, Shun-li Sun, Ya-heng Song, Yi-fei Li, Xin Wang, and Han Hai. "Large eddy simulation study of flow field characteristics of a combustor with two coaxial swirlers." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 234, no. 5 (August 27, 2019): 625–42. http://dx.doi.org/10.1177/0957650919870420.

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The cold and reaction flow fields of a combustor with two coaxial swirlers are investigated by means of large eddy simulation. Effective data processing methods such as proper orthogonal decomposition and fast Fourier transform are employed for analysis. The complex flow phenomena such as swirling jet, shear layer, recirculation zone, and precession vortex core are observed and their characteristics are analyzed. The dynamics of the flame and its interactions with the complex swirling flows and large-scale eddies are characterized. The precession vortex core structures and its influences on the combustion process are emphatically explored. It is found that the outer shear layer produces spiral precession vortex core cantilever structures and the change of structural characteristics of the PVC determines the pressure pulsation frequency of the combustor. The results also indicate precession vortex core accelerates the mixing of unburned and burned mixture, leading to the ignition. The principal structures are studied by determining the highest energy modes via proper orthogonal decomposition. The modes are classified according to energy size. By means of proper orthogonal decomposition four-decomposition method, the vortexes of different energy and scales in swirling flow field are classified and analyzed in detail, the flow field is reconstructed, and the large-scale coherent structures and small energy flow structures are obtained. A spectral map of the turbulent kinetic energy density exhibits the −5/3 slope given by the Kolmogorov–Obukhov law. Based on the analysis of the vortex structures and their evolution, and the analysis of the transports and distributions of flow field characteristic parameters, a novel unsteady swirling flow combustion organization mechanism is proposed. It is found that combustion mainly occurs in low-energy small-scale vortexes, releasing a large amount of heat. High-temperature gas enters the recirculation zone and continues to provide energy for the precession vortex cores.

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Saranyasoontorn, Korn, and Lance Manuel. "Low-Dimensional Representations of Inflow Turbulence and Wind Turbine Response Using Proper Orthogonal Decomposition." Journal of Solar Energy Engineering 127, no. 4 (July 7, 2005): 553–62. http://dx.doi.org/10.1115/1.2037108.

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A demonstration of the use of Proper Orthogonal Decomposition (POD) is presented for the identification of energetic modes that characterize the spatial random field describing the inflow turbulence experienced by a wind turbine. POD techniques are efficient because a limited number of such modes can often describe the preferred turbulence spatial patterns and they can be empirically developed using data from spatial arrays of sensed input/excitation. In this study, for demonstration purposes, rather than use field data, POD modes are derived by employing the covariance matrix estimated from simulations of the spatial inflow turbulence field based on standard spectral models. The efficiency of the method in deriving reduced-order representations of the along-wind turbulence field is investigated by studying the rate of convergence (to total energy in the turbulence field) that results from the use of different numbers of POD modes, and by comparing the frequency content of reconstructed fields derived from the modes. The National Wind Technology Center’s Advanced Research Turbine (ART) is employed in the examples presented, where both inflow turbulence and turbine response are studied with low-order representations based on a limited number of inflow POD modes. Results suggest that a small number of energetic modes can recover the low-frequency energy in the inflow turbulence field as well as in the turbine response measures studied. At higher frequencies, a larger number of modes are required to accurately describe the inflow turbulence. Blade turbine response variance and extremes, however, can be approximated by a comparably smaller number of modes due to diminished influence of higher frequencies.

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35

Windemuth, Christian, Martin Lange, and Ronald Mailach. "Analysis of the Unsteady Flow Field in a Steam Turbine Control Valve using Spectral Proper Orthogonal Decomposition." International Journal of Turbomachinery, Propulsion and Power 6, no. 2 (May 21, 2021): 11. http://dx.doi.org/10.3390/ijtpp6020011.

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A significant share of the conversion of thermal into electrical energy is realized by steam turbines. Formerly designed for continuous operation, today’s requirements include extended part load operation that can be accompanied by highly unstable flow conditions and vibrations within the control valve of the turbine. The prediction of the flow at part load conditions requires large computational efforts with advanced turbulence modeling in order to compute the flow at a reasonable accuracy. Due to the unsteadiness of the flow, the evaluation of the numerical results itself is a major challenge. The turbulent structures require statistical approaches, of which the use of Spectral Proper Orthogonal Decomposition (SPOD) has proven itself as a powerful method. Within this paper, the application of the method on a critical operating point with a temporal excitation of pressure oscillations observed in the experiments with dry air is presented. Using SPOD, the dominating flow phenomena were isolated and flow structures visualized.

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Zhang, Bingchao, Ryozo Ooka, and Hideki Kikumoto. "Identification of three-dimensional flow features around a square-section building model via spectral proper orthogonal decomposition." Physics of Fluids 33, no. 3 (March 2021): 035151. http://dx.doi.org/10.1063/5.0041395.

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Chu, Shijun, Chao Xia, Hanfeng Wang, Yajun Fan, and Zhigang Yang. "Three-dimensional spectral proper orthogonal decomposition analyses of the turbulent flow around a seal-vibrissa-shaped cylinder." Physics of Fluids 33, no. 2 (February 1, 2021): 025106. http://dx.doi.org/10.1063/5.0035789.

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Karami, Shahram, and Julio Soria. "Analysis of Coherent Structures in an Under-Expanded Supersonic Impinging Jet Using Spectral Proper Orthogonal Decomposition (SPOD)." Aerospace 5, no. 3 (July 6, 2018): 73. http://dx.doi.org/10.3390/aerospace5030073.

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Kadu, Pravin Ananta, Yasuhiko Sakai, Yasumasa Ito, Koji Iwano, Masatoshi Sugino, Takahiro Katagiri, Toshiyuki Hayase, and Koji Nagata. "Application of spectral proper orthogonal decomposition to velocity and passive scalar fields in a swirling coaxial jet." Physics of Fluids 32, no. 1 (January 1, 2020): 015106. http://dx.doi.org/10.1063/1.5131627.

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Wang, Tianyuan, Qingqing Yang, Yeting Tang, Hongda Shi, Qin Zhang, Mengfei Wang, Andrey Epikhin, and Andrey Britov. "Spectral Analysis of Flow around Single and Two Crossing Circular Cylinders Arranged at 60 and 90 Degrees." Journal of Marine Science and Engineering 10, no. 6 (June 14, 2022): 811. http://dx.doi.org/10.3390/jmse10060811.

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Two modal decomposition techniques, including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), were used to identify the wake patterns past single and two crossing cylinders in 60° and 90° arrangements with gap ratio G = 4. The flow was simulated using direct numerical simulations (DNS) for Reynolds numbers Re = 100. From modal analysis, the flow’s spatial scale decreased with increasing modal frequency. Two main modes were identified in the wake of the cylinders, namely spatially antisymmetric and symmetric modes. Antisymmetric and symmetric modes were related to the cylinders’ vortex shedding and shedding vortices’ shift motion, respectively, whose frequencies were odd and even multiples of the cylinders’ lift force frequency. In addition, a low-frequency mode concerning the shadowing effect of the downstream cylinder (DC) in 90° arrangement was found in the wake of the DC centre.

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Avanzi, Filippo, Francesco De Vanna, Yin Ruan, and Ernesto Benini. "Design-Assisted of Pitching Aerofoils through Enhanced Identification of Coherent Flow Structures." Designs 5, no. 1 (February 14, 2021): 11. http://dx.doi.org/10.3390/designs5010011.

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This study discusses a general framework to identify the unsteady features of a flow past an oscillating aerofoil in deep dynamic stall conditions. In particular, the work aims at demonstrating the advantages for the design process of the Spectral Proper Orthogonal Decomposition in accurately producing reliable reduced models of CFD systems and comparing this technique with standard snapshot-based models. Reynolds-Averaged Navier-Stokes system of equations, coupled with k−ω SST turbulence model, is used to produce the dataset, the latter consisting of a two-dimensional NACA 0012 aerofoil in the pitching motion. Modal analysis is performed on both velocity and pressure fields showing that, for vectored values, a proper tuning of the filtering process allows for better results compared to snapshot formulations and extract highly correlated coherent flow structures otherwise undetected. Wider filters, in particular, produce enhanced coherence without affecting the typical frequency response of the coupled modes. Conversely, the pressure field decomposition is drastically affected by the windowing properties. In conclusion, the low-order spectral reconstruction of the pressure field allows for an excellent prediction of aerodynamic loads. Moreover, the analysis shows that snapshot-based models better perform on the CFD values during the pitching cycle, while spectral-based methods better fit the loads’ fluctuations.

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Elistratov, S. A. "POD-based Hydrodynamical Structures Visualization in Flows with an Internal Wave Attractor." Scientific Visualization 15, no. 2 (June 2023): 125–33. http://dx.doi.org/10.26583/sv.15.2.11.

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Hydrodynamical structure attending a flow can be hid and hardly to reveal. One of the methods to find them is to use mode decomposition (such as Proper orthogonal decomposition, POD). The method represents the field given as a series of spatial modes multiplied by corresponding temporal coefficients. In the article the method is discussed applyingly to a complex flow with a wave attractor structure. Attractor modes present structured vortex-like figure which cannot be claimed to be aleatory. As it turns out POD modes are not just a formal decomposition but have a physical origin: they are connected with instability cascade minor frequencies, as spectral investigation shows. Another consequence of that is that one of the collateral structure maximum can be visible. This proposition is proven as the structure is found to be visible in the flow itself.

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Murakami, Tomoyuki, Yuichiro Nishida, and Tetsuro Taniguchi. "Study on Phase Characteristics of Wind Pressure Fields around a Prism Using Complex Proper Orthogonal Decomposition." Wind 3, no. 1 (February 8, 2023): 35–63. http://dx.doi.org/10.3390/wind3010004.

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Wind loads for the design of wind-resistant high-rise buildings are generally evaluated based on spectral modal analysis or time-history response analysis using wind pressure data obtained from wind tunnel experiments with rigid models. The characteristics of the fluctuating wind pressures around vibrating buildings must be evaluated for relevant wind-resistant designs because the wind pressures around buildings are affected by their vibrations. One of the methods to investigate fluctuating fields is complex proper orthogonal decomposition (CPOD), which can express complicated pressure fields, including advection phenomena, as coherent structures. This paper presents the phase characteristics of fluctuating wind pressures around rigid and elastic models of a square-sectioned prism evaluated via CPOD analysis using the results of wind tunnel experiments. The evaluation procedure for the symmetricity of the fluctuating wind pressure modes obtained via CPOD is presented. The similarity of fluctuating wind pressure fields is evaluated as the congruency of the planes formed by the 1st- and 2nd-eigenmodes. With symmetricity and similarity, the fluctuating wind pressure fields are classified into three types: resonant and non-resonant states in smooth flow, and in gradient flow. The characteristics of the three types of wind pressure fields are shown, respectively, in the symmetric and anti-symmetric modes.

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Luo, Zhendong, and Shiju Jin. "A REDUCED-ORDER EXTRAPOLATION SPECTRAL-FINITE DIFFERENCE SCHEME BASED ON THE POD METHOD FOR 2D SECOND-ORDER HYPERBOLIC EQUATIONS." Mathematical Modelling and Analysis 22, no. 5 (September 21, 2017): 569–86. http://dx.doi.org/10.3846/13926292.2017.1334714.

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In this study, a reduced-order extrapolation spectral-finite difference (ROESFD) scheme based on the proper orthogonal decomposition (POD) method is set up for the two-dimensional (2D) second-order hyperbolic equations. First, the classical spectral-finite difference (CSFD) method for the 2D second-order hyperbolic equations and its stability, convergence, and flaw are introduced. Then, a new ROESFD scheme that has very few degrees of freedom but holds sufficiently high accuracy is set up by the POD method and its implementation is offered. Finally, three numerical examples are offered to explain the validity of the theoretical conclusion. This implies that the ROESFD scheme is viable and efficient for searching the numerical solutions of the 2D second-order hyperbolic equations.

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Lui, Hugo F. S., and William R. Wolf. "Construction of reduced-order models for fluid flows using deep feedforward neural networks." Journal of Fluid Mechanics 872 (June 14, 2019): 963–94. http://dx.doi.org/10.1017/jfm.2019.358.

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We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

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Deng, Zhi, Zifeng Yang, and Wen-Li Chen. "Experimental investigation of the flow control over an airfoil with owl-inspired trailing-edge modification: On the material, length, and spacing sensitivity." Physics of Fluids 35, no. 2 (February 2023): 025135. http://dx.doi.org/10.1063/5.0136758.

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We experimentally investigate the effect of material, length, and spacing of trailing-edge extensions on controlling the flow over an airfoil based on our recent experimental work. Force measurements and flow field quantifications were carried out to investigate the aerodynamic performance and flow structures in the wake of an airfoil and, thus, to reveal differences in control effectiveness and mechanisms. Moreover, multi-scale proper orthogonal decomposition and spectral proper orthogonal decomposition are employed to extract coherent flow structures in the flow field. The results indicate that the owl feather can improve the aerodynamic performance, while artificial materials lead to decreased lift-to-drag ratio. However, nylon has optimal adaptability and robustness in controlling turbulent fluctuations, including Reynolds stress and turbulent kinetic energy at different angles of attack (AOAs). The length sensitivity is highly associated with the AOA, i.e., the optimal length increases with the increase in AOA. In addition, the spacing sensitivity correlates with the Reynolds number (Re), i.e., the optimal spacing decreases with higher Re at high AOA. These differences root in the competition effect between the increasing adverse pressure gradient and the interference on regular vortex shedding. It is concluded that nylon with mediate length (L = 0.2D) and relatively large spacing (S = 0.5B) is recommended for wake control and noise attenuation of the S833 airfoil.

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Zhao, Ning, Zhilong Xu, Liuliu Peng, Xiaolong Li, Xiaowei Chen, and Xuewei Wang. "Simulation of Nonseparable Nonstationary Spatially Varying Ground Motions with an Enhanced Interpolation Approximation Approach." Applied Sciences 12, no. 13 (July 4, 2022): 6757. http://dx.doi.org/10.3390/app12136757.

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An enhanced interpolation approach is developed for simulating nonseparable nonstationary ground motions on the basis of the spectral representation method, which mainly contains two steps of interpolations and an optimization. Firstly, the interpolation technique is utilized to reduce the Cholesky decomposition time of the lagged coherence matrix. The square root of the evolutionary power spectral density is then decoupled into several time and frequency discrete functions using the proper orthogonal decomposition (POD) interpolation technique, which results in the availability of the fast Fourier transform (FFT) technique in the simulation. Compared with existing decoupling schemes, the POD interpolation achieves a significant efficiency improvement with a slight accuracy reduction. Finally, the simulation formula is further optimized to reduce the number of FFT operations. The accuracy and efficiency of this method are verified with the numerical examples of nonstationary ground motions simulation. Results show that the error introduced by two-step interpolations is fairly small and the simulation agrees with the targets very well. Furthermore, the efficiency generating sample function is significantly enhanced.

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Nilsson, Stefan, Hua-Dong Yao, Anders Karlsson, and Sebastian Arvidson. "Effects of Aeroelastic Walls on the Aeroacoustics in Transonic Cavity Flow." Aerospace 9, no. 11 (November 14, 2022): 716. http://dx.doi.org/10.3390/aerospace9110716.

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The effects of elastic cavity walls on noise generation at transonic speed are investigated for the generic M219 cavity. The flow is simulated with the Spalart–Allmaras (SA) improved delayed detached-eddy simulation (IDDES) turbulence model in combination with a wall function. The structural analysis software uses a modal formulation. The first 50 structural normal mode shapes are included in the simulation, spanning frequencies of 468–2280 Hz. Results are compared with those from a reference simulation with rigid cavity walls. A spectral analysis of pressure fluctuations from a microphone array above the cavity evinces a distinct tone at 816 Hz, which is absent in the reference simulation. Furthermore, the power of the 4th Rossiter mode at 852 Hz is depleted, implying a significant energy transfer from the fluid to the structure. Spectral proper orthogonal decomposition (SPOD) is employed for analyses of cavity wall pressure fluctuations and wall displacements. The SPOD mode energy spectra show results consistent with the spectra of the microphone array with respect to the tone at 816 Hz and the depletion of the energy at the 4th Rossiter mode. Furthermore, the SPOD mode energy spectra show energy spikes at additional frequencies, which coincide with structural eigenfrequencies.

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Zhang, Bingchao, Lei Zhou, Tim K. T. Tse, Liangzhu Wang, Jianlei Niu, and Cheuk Ming Mak. "Extended spectral proper orthogonal decomposition for analysis of correlated surrounding flow structures and wind load components of a building." Journal of Wind Engineering and Industrial Aerodynamics 240 (September 2023): 105512. http://dx.doi.org/10.1016/j.jweia.2023.105512.

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Meng, Yu, Wenming Sun, Hongbin Gu, Fang Chen, and Ruixu Zhou. "Supersonic Combustion Mode Analysis of a Cavity Based Scramjet." Aerospace 9, no. 12 (December 15, 2022): 826. http://dx.doi.org/10.3390/aerospace9120826.

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Since flame stability is the key to the performance of scramjets, scramjet combustion mode and instability characteristics were investigated by using the POD method based on a cavity-stabilized scramjet. Experiments were developed on a directly connected scramjet model that had an inlet flow of Mach 2.5 with a cavity stabilizer. CH* chemiluminescence, schlieren, and a wall static pressure sensor were employed to observe flow and combustion behavior. Three typical combustion modes were classified by distinguishing averaged CH* chemiluminescence images of three ethylene fuel jet equivalence ratios. The formation reason was explained using schlieren images and pressure characteristics. POD modes (PDMs) were determined using the proper orthogonal decomposition (POD) of sequential flame CH* chemiluminescence images. The PSD (power spectral density) of the PDM spectra showed large peaks in a frequency range of 100–600 Hz for three typical stabilized combustion modes. The results provide oscillation characteristics of three scramjet combustion modes.

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Journal articles on the topic 'Spectral Proper Orthogonal Decomposition'

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