Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session H10: Nonlinear Dynamics: Model Reduction I |
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Chair: Oliver Schmidt, University of California - San Diego Room: 3A |
Monday, November 25, 2019 8:00AM - 8:13AM |
H10.00001: Linear Reduced-order Model based on Particle-image-velocimetry Data of Flow Field around Airfoil Controlled by Plasma Actuator Koki Nankai, Kento Suzuki, Atsushi Komuro, Taku Nonomura, Keisuke Asai A linear reduced-order model of flow fields around an airfoil controlled by a dielectric-barrier-discharge plasma actuator (DBDPA) is constructed based on particle image velocimetry (PIV) data. Velocity field data around a NACA0015 airfoil with random input by the DBDPA at the chord Reynolds number of 64,000 were acquired using PIV in a wind tunnel test. Subsequently, lower-dimensional description of the data was obtained by proper orthogonal decomposition (POD). The coefficient matrix of the linear model was computed using the least-squares approximation with the POD-mode coefficients and control input data, similar to dynamic mode decomposition with control. The effects of the control input corresponding to the voltage amplitude of DBDPA on the low-dimensional velocity fields reconstructed by the first ten POD modes were investigated from the input matrix. It is demonstrated that the velocity fields are more sensitive to the input change than the average value of the input. This result implies that the present model can show the well-known flow control characteristic that DBDPA with intermittent actuation such as the burst mode or nanosecond-pulse-driven mode is more effective for the separation control of flow fields than continuous actuation. [Preview Abstract] |
Monday, November 25, 2019 8:13AM - 8:26AM |
H10.00002: Reduced-order Modeling and Estimation for Buoyancy-driven Flow Control Sanjana Vijayshankar, Piyush Grover, Saleh Nabi We consider the problem of data-driven reduced-order modeling and state estimation of buoyancy-driven turbulent flows in the built environment. First, we investigate the efficacy of data-driven techniques such as Eigensystem Realization Algorithm (ERA) and Dynamic Mode Decomposition (DMD) for systems described by Boussinesq equations. The resulting reduced-order models are suitable for real-time control applications. We employ these reduced-order models to construct reduced-order observers for systems operating in forced and mixed convection regimes. Exhaustive numerical simulations (both DNS and RANS) in the context of energy efficient buildings and internal flows are provided to validate the accuracy and computational benefits of this approach. [Preview Abstract] |
Monday, November 25, 2019 8:26AM - 8:39AM |
H10.00003: Machine learning of sequential data for non-intrusive reduced-order models Romit Maulik, Arvind Mohan, Sandeep Madireddy, Bethany Lusch, Prasanna Balaprakash, Daniel Livescu We study implementations of machine learning strategies for time-series data for non-intrusive reduced-order models of non-linear partial differential equations. Our reduced space is obtained with an $L_2$-optimal proper orthogonal decomposition (POD) with subsequent truncation. We then study the performance of these techniques for systems that require closure due to insufficient resolution of all of the energy in the system. Accurate non-linear dynamics in POD space are learned through recurrent neural networks and neural ordinary differential equations which utilize history, analogous to the Mori-Zwanzig formalism, to retain the effects of the unresolved modes. We also detail the use of attention to maintain the precision of learning for long-term prediction horizons and conclude by discussing distributed hyperparameter search strategies using asynchronous model-based Bayesian optimization. [Preview Abstract] |
Monday, November 25, 2019 8:39AM - 8:52AM |
H10.00004: A Simple POD-Galerkin Model Based on Computational or Experimental Data of Flows with Moving Boundaries Mingjun Wei, Bolun Xu, Haotian Gao, John Hrynuk POD-Galerkin projection has been popular as a systematical approach for model order reduction of a complex dynamic system such as a fluid flow described by Navier-Stokes equations. However, the classical POD-Galerkin projection is derived only in a fixed domain, which limits its application on many fluid-structure interaction problems featuring moving boundaries or morphing domains. We have developed a simple modification to allow an easy implementation accounting for structural effects to extend the application of POD-Galerkin projection to a broad range of flows with moving boundaries. Recently, the modified approach was further improved to achieve better accuracy near the moving solid boundaries. The improved approach has been applied not only to direct numerical simulation data but also to experimental data. The experimental data includes the PIV measurement of the flow field for a rotating ellipse with incoming flow in a closed-loop wind tunnel. [Preview Abstract] |
Monday, November 25, 2019 8:52AM - 9:05AM |
H10.00005: Flow Field Reconstruction and Filtering Using Spectral Proper Orthogonal Decomposition Akhil Nekkanti, Oliver Schmidt The spectral variant of proper orthogonal decomposition (SPOD) decomposes a flow field into orthogonal modes that evolve coherently in both space and time, and that are optimally ranked by their energy. Just like in the case of standard proper orthogonal decomposition (POD), SPOD permits the reconstruction of the data from the modes and their expansion coefficients, and benefits from the optimality of the expansion. In this contribution, we show how the fact that SPOD is conducted in the frequency domain can be leveraged to achieve a number of goals. In particular, we use truncated series reconstructions and frequency-dependent scaling to facilitate low-rank approximations, band-pass filtering, pre-whitening and de-noising of experimental data. It is demonstrated, for example, that even a rank-1 SPOD approximation, which retains only one mode per frequency, is capable of capturing the significant dynamics of a fully turbulent flow field. Finally, we show how an iterative procedure can be employed for gappy data reconstruction. Two test cases are considered: large eddy simulation data of a turbulent jet and particle image velocimetry fields of the turbulent wake behind a flat plate at high angle of attack. [Preview Abstract] |
Monday, November 25, 2019 9:05AM - 9:18AM |
H10.00006: Towards reduced-order SPOD-Galerkin models for turbulent flows Tianyi Chu, Oliver T. Schmidt We explore the use of spectral proper orthogonal decomposition (SPOD) to construct reduced-order Galerkin models of turbulent flows under a linear time-invariant approximation. The motivation behind this particular modeling approach is the theoretical correspondence between the empirical SPOD technique and operator-based resolvent analysis, which considers optimal responses to a stochastically forced linear system. For the example of a Mach $0.9$ turbulent jet, a recent study found a surprising agreement between SPOD modes computed from large-eddy simulation data and mean flow-based resolvent analysis. The same data is used in this work. Since the SPOD modes are orthogonal in a space-time inner product, the time-domain Galerkin model requires an oblique projection of the data onto the non-orthogonal modal basis. The resulting reduced-order model for the expansion coefficients is advanced in time by the linearized Navier-Stokes operator, and closed-loop control techniques, such as minimal-energy feedback control, are employed to calibrate the reduced-order model. To offset the difference between the linear approximation and the true, non-linear solution, we further incorporate the forcing statistics, inferred from applying the discrete linear operator to the data, into the model. [Preview Abstract] |
Monday, November 25, 2019 9:18AM - 9:31AM |
H10.00007: Fast Greedy Optimization of Sensor Selection in Measurement with Correlated Noise Keigo Yamada, Yuji Saito, Taku Nonomura, Keisuke Asai, Tomohiro Okudera In the present study, a novel determinant-based greedy method under the correction from a covariance matrix of sensor noise intensity is proposed. This method selects noise-tolerant sensors to minimize the reconstruction error of the weighted least square problem considering sensor noise covariance. Especially, the presented algorithm prevents us from selecting similar points which have similar sensor noise, resulting in the reliable estimated state. We apply the method to the climate datasets of the National Oceanic and Atmospheric Administration (NOAA) and compare the results to those of the conventional method. This comparison shows that the proposed method creates accurate reconstruction system even with the correlated sensor noises. [Preview Abstract] |
Monday, November 25, 2019 9:31AM - 9:44AM |
H10.00008: Integrating sensor data into reduced-order models with deep learning Nirmal Jayaprasad Nair, Andres Goza Efficiently leveraging limited sensor data in reduced-order models (ROMs) is key to enabling real-time control of a range of fluid flows. Two primary challenges to achieving this goal are: i) while the ROM evolves on a low-dimensional space, sensor data is typically related to the ROM via an intermediate step that involves the high-dimensional fluid state, ii) although a physical interpretation of the ROM state space may be derived, it is rarely obvious how to directly relate physical measurements to this low-dimensional representation. To address both challenges, we propose a flow-field estimation methodology where the sensor data is directly mapped to the ROM state space without involving the high-dimensional flow state. The flow-field can be efficiently recovered via the ROM approximation, if desired. We employ a neural-network architecture that learns the nonlinear mapping between the sensors and state space. We emphasize that the proposed estimation framework is agnostic to the ROM employed, and can therefore be incorporated into ROMs derived by Galerkin projection, regression, etc. Our methodology is demonstrated on problems involving parametric 1D diffusion and 2D flow over an airfoil. [Preview Abstract] |
Monday, November 25, 2019 9:44AM - 9:57AM |
H10.00009: Determinant based Fast Greedy Optimization on Sparse Sensor Selection Yuji Saito, Keigo Yamada, Taku Nonomura, Keisuke Asai, Daisuke Tsubakino, Yasuo Sasaki The problem of optimally placing sensors to reduce calculation cost and reconstruction error arises naturally in scientific experiments. It is especially difficult to speedily select optimal sensors when the number of sensors is larger than POD modes. In this study, the authors have developed and proposed an extended determinant-based greedy algorithm based on a QR discrete empirical interpolation method (QDEIM) for the optimal sensor placement problem. The key point of this idea is that optimal sensors are obtained by the QDEIM method until the number of sensors is equal to POD modes. After that, new sensors are calculated by applying both of the determinant formula and matrix inversion lemma. We demonstrate the effectiveness of this algorithm on datasets related to climate science, and compare all calculation results; random sensors, convex approximation and a previously proposed QR algorithm in addition to the determinant-based greedy algorithm. We show that the calculation time of the proposed extended determinant-based greedy algorithm is faster than that of other methods with almost the same level of reconstruction error. [Preview Abstract] |
Monday, November 25, 2019 9:57AM - 10:10AM |
H10.00010: Network-based identification of influential structures to modify turbulent flows Muralikrishnan Gopalakrishnan Meena, Kunihiko Taira The nonlinear interactions among vortical structures in turbulence make their characterization and control a challenge. We use network theory to formulate and characterize the web of interactions among vortical elements in two- and three-dimensional decaying isotropic turbulence. The nodes of these networks correspond to vortical elements in the flow field and the connections among them are weighted by the induced velocity. Network-based community detection algorithm is used to identify network connector (inter-community) and peripheral (intra-community) structures that resemble shear-layer and vortex-core type structures, respectively. We assess the influence of these structures to the neighboring vortical structures by performing DNS with added impulse perturbations to the identified network-based structures. We compare our findings with those from traditional forms of structure identification and observe enhanced turbulent mixing with the present approach. We discuss the implications of the present network-based technique for active flow control. [Preview Abstract] |
Monday, November 25, 2019 10:10AM - 10:23AM |
H10.00011: Physics-informed Echo State Networks for the prediction of chaotic systems Luca Magri, Francisco Huhn, Nguyen Anh Khoa Doan We suggest Echo State Networks (ESN), a data science technique, to predict the evolution of chaotic dynamical systems, namely those of high-fidelity fluid dynamics simulations, LES and DNS. Data generated from high-fidelity simulations carry high computational cost and thus only small amounts are available. While this usually poses a limitation to data science techniques -- unlike the traditional big data, this problem lives in the world of "small data" --, this can be balanced by leveraging physical knowledge of the system in study, that is, while ESNs can be trained purely on past observations, their performance can be improved, for example, by including a loss term that represents the system's physics and penalizes non-physical predictions in the training phase. We explore the characteristics and performance of physics-informed ESN models, from a nonlinear dynamics point-of-view, in reproducing chaotic dynamical systems. Finally, we look into potential applications to fluid dynamics problems, such as prediction of extreme events or sensitivities of time-averaged cost functionals. [Preview Abstract] |
Monday, November 25, 2019 10:23AM - 10:36AM |
H10.00012: Dimensionality Reduction and Reduced Order Modeling for Traveling Wave Physics Ariana Mendible, Aleksander Aravkin, Wes Lowrie, Steven Brunton, J. Nathan Kutz Large scale spatiotemporal data are ubiquitous across many fields of science and engineering, especially in fluids. Standard dimensionality reduction techniques based on the singular value decomposition (SVD) often fail to provide a compact representation of traveling waves because the SVD is inherently a space-time separation of variables. This necessitates a data-driven method to decompose and reduce spatiotemporal systems with multiple traveling waves. In this work, we investigate alternative approaches to dimensionality reduction that are designed specifically to separate and represent interpretable traveling wave structures in a low-dimensional form Using a shifted SVD, we formulate an unsupervised, optimization-based framework for identifying parsimonious wave speed models from many candidate models. We demonstrate our method on example systems which pose challenges of non-periodicity, nonlinearity, and changing wave speed. [Preview Abstract] |
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