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Non-intrusive balancing transformation of highly stiff systems with lightly damped impulse response

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2022年第2229期380卷 20210202-20210202页

作者： Rezaian, Elnaz Huang, Cheng Duraisamy, Karthik Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

Balanced truncation (BT) is a model reduction method that uses a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and lightly damped systems, a non-intrusive data-driven method is developed for balancing discrete-time linear systems via the eigensystem realization algorithm (ERA). The advantage of ERA for balancing transformation makes full-state outputs tractable. Further, ERA enables balancing despite stiffness, by eliminating computation of balancing modes and adjoint simulations. As a demonstrative example, we create balanced reduced-order models (ROMs) for a one-dimensional reactive flow with pressure forcing, where the stiffness introduced by the chemical source term is extreme (condition number 1013), preventing analytical implementation of BT. We investigate the performance of ROMs in prediction of dynamics with unseen forcing inputs and demonstrate stability and accuracy of balanced ROMs in truly predictive scenarios, whereas without ERA, proper orthogonal decomposition-Galerkin and least-squares Petrov-Galerkin projections fail to represent the true dynamics. We show that after the initial transients under unit impulse forcing, the system undergoes lightly damped oscillations, which magnifies the influence of sampling properties on predictive performance of the balanced ROMs. We propose an output domain decomposition approach and couple it with tangential interpolation to resolve sharp gradients at reduced computational costs. This article is part of the theme issue 'Data-driven prediction in dynamical systems'. (C) 2022 The Author(s) Published by the Royal Society. All rights reserved.

关键词： reduced-order modelling balanced truncation eigensystem realization algorithm combustion

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In situ evaluation of dynamic characteristics of prefabricated ballastless track slab using EMA and OMA techniques

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MEASUREMENT 2020年 160卷 107866-107866页

作者： Wang, Liuchong Ping, Wang Zhao, Caiyou Zhen, Junyuan Zhao, Yannan Southwest Jiaotong Univ Key Lab High Speed Railway Engn Minist Educ Chengdu 610031 Peoples R China Southwest Jiaotong Univ Sch Civil Engn Chengdu 610031 Peoples R China

This study focused on the prefabricated ballastless slab tracks first applied in urban rail transit of a city in China. By combining the experimental modal analysis (EMA) and operational modal analysis (OMA) techniques, we evaluated the dynamic characteristics of the tracks using the eigensystem realization algorithm and stochastic subspace identification algorithm to identify modal parameters. This study attempted to determine the characteristics and correlation of the two modal analysis methods to comprehensively reflect the dynamic characteristics of the track slabs. We established a detailed finite element model to analyze the influence of the construction method and structural characteristics of the track slabs on the modal parameters. The results show that the in-situ testing of the track slab modes were subject to the influence of many uncertain factors, resulting in differences between the numerical calculation-based ideal mode shapes and the actual EMA- and OMA-based counterparts. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Prefabricated track slab Experimental modal analysis Operation modal analysis eigensystem realization algorithm Stochastic subspace identification Eigenfrequency

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Data-driven selection of actuators for optimal control of airfoil separation

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THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS 2020年第4期34卷 557-575页

作者： Bhattacharjee, Debraj. Klose, Bjoern Jacobs, Gustaaf B. Hemati, Maziar S. Univ Minnesota Elect & Comp Engn Minneapolis MN 55455 USA San Diego State Univ Aerosp Engn San Diego CA 92182 USA Univ Minnesota Aerosp Engn & Mech Minneapolis MN 55455 USA

We present a systematic approach for determining the optimal actuator location for separation control from input-output response data, gathered from numerical simulations or physical experiments. The eigensystem realization algorithm is used to extract state-space descriptions from the response data associated with a candidate set of actuator locations. These system realizations are then used to determine the actuator location among the set that can drive the system output to an arbitrary value with minimal control effort. The solution of the corresponding minimum energy optimal control problem is evaluated by computing the generalized output controllability Gramian. We use the method to analyze high-fidelity numerical simulation data of the lift and separation angle responses to a pulse of localized body-force actuation from six distinct locations on the upper surface of a NACA 65(1)-412 airfoil. We find that the optimal location for controlling lift is different from the optimal location for controlling separation angle. In order to explain the physical mechanisms underlying these differences, we conduct controllability analyses of the flowfield by leveraging the dynamic mode decomposition with control algorithm. These modal analyses of flowfield response data reveal that excitation of coherent structures in the wake benefits lift control, whereas excitation of coherent structures in the shear layer benefits separation angle control.

关键词： Flow control Flow separation eigensystem realization algorithm Dynamic mode decomposition Lagrangian coherent structures

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Modal Identification of Aerodynamic Models for Spanwise Lift Distribution Control

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JOURNAL OF AIRCRAFT 2020年第4期57卷 664-677页

作者： Dias, Joaquim N. Hubbard, James E., Jr. Univ Maryland Dept Aerosp Engn College Pk MD 20742 USA Brazilian Air Force Brasilia DF Brazil Texas A&M Univ Texas A&M Engn Expt Stn College Stn TX 77843 USA Texas A&M Univ Dept Mech Engn College Stn TX 77843 USA

This work presents modal identification results for the unsteady three-dimensional flow around a wing featuring multiple trailing edge flaps. The unsteady spanwise lift distribution is modeled using the unsteady vortex lattice method, which yields a linear, time-invariant, high-order state-space model. The eigensystem realization algorithm is applied for model order reduction and modal identification, providing aerodynamic mode shapes and associated eigenvalues. The wing is considered rigid, so that the dynamic mode shapes associated with the spanwise lift distribution are purely aerodynamic. It is observed that the spatial-temporal discretization of the numerical model and flap dimensions inherently limit the number of modes that can be properly identified. Open-loop simulation results demonstrate the modal behavior of the aerodynamic system. Finally, aerodynamic mode shapes for different wing planforms are also presented for comparison. By expanding the system output (lift distribution) as a truncated superposition of aerodynamic mode shapes, a low-order multiple-input and multiple-output modal representation can be obtained, suitable for controller synthesis. Ultimately, this novel approach will be applied to gust alleviation, in order to keep a desired lift distribution profile using shape control techniques.

关键词： Aerodynamic Configurations Model Order Reduction eigensystem realization algorithm State Space Representation Aspect Ratio Analysis of Fluid Flow Trailing Edge Flap Horseshoe Vortex Lift Coefficient Compressible Flow

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Vertical vibration modeling for 2:1-roping traction elevator

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JOURNAL OF VIBROENGINEERING 2022年第2期24卷 290-304页

作者： Shi, Jipeng Zhang, Weimin Wu, Chengjun Xi An Jiao Tong Univ Sch Mech Engn Xian 710049 Shaanxi Peoples R China

This paper presents a vertical vibration model for 2:1-roping traction elevator system. In this model, masses of suspension ropes are considered and their kinetic energy is calculated by applying Rayleigh method. Equations of motion for free vibration are derived. To verify the improvement of the model, an output dependent only modal test scheme using eigenvalue realization algorithm is conducted to obtain natural frequencies from a real elevator installation. The comparison of experimental results and numerical results of proposed model and previous similar models is presented on calculation of natural frequencies. The results show that proposed model is able to reflect the 5th natural frequencies more exactly under 0 % and 100 % load conditions.

关键词： traction elevator vertical vibration model natural frequency eigensystem realization algorithm

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Dynamic Mode Decomposition for Compressive System Identification

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AIAA JOURNAL 2020年第2期58卷 561-574页

作者： Bai, Zhe Kaiser, Eurika Proctor, Joshua L. Kutz, J. Nathan Brunton, Steven L. Univ Washington Dept Mech Engn Seattle WA 98195 USA Inst Dis Modeling Bellevue WA 98004 USA Univ Washington Dept Appl Math Seattle WA 98195 USA

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, two recent innovations that extend dynamic mode decomposition to systems with actuation and systems with heavily subsampled measurements are integrated and unified. When combined, these methods yield a novel framework for compressive system identification. It is possible to identify a low-order model from limited input-output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data are available, it is possible to dramatically accelerate downstream computations by first compressing the data. This unified framework is demonstrated on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, this architecture is explored on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data.

关键词： System Identification Compression Ratio Fluid Flow Sensors Freestream Velocity Pitching Airfoil Singular Value Decomposition eigensystem realization algorithm Vorticity Particle Image Velocimetry

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Data-Guided Aerial Tracking

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2020年第8期43卷 1540-1549页

作者： Vasisht, Soumya Mesbahi, Mehran Univ Washington William E Boeing Dept Aeronaut & Astronaut Seattle WA 98195 USA

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Identification of nonlinear aerodynamic systems with application to transonic aeroelasticity of aircraft structures

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NONLINEAR DYNAMICS 2020年第2期100卷 1037-1056页

作者： Liu, Haojie Gao, Xiumin Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing Peoples R China Nanjing Tech Univ Sch Phys & Math Sci Nanjing 210016 Peoples R China

In this study, identification of nonlinear aerodynamic systems based on an improved nonlinear state-space modeling approach is presented to predict transonic aeroelastic behaviors of aircraft structures. It starts with identifying a linear state-space aerodynamic model by using the eigensystem realization algorithm and observer/Kalman filter identification methods. Subsequently, the remaining parameters of the nonlinear state-space aerodynamic model are determined through an output error-minimization procedure, based on a new training data generation methodology. To illustrate the approach, two- and three-dimensional transonic aeroelastic configurations are studied. The transonic aeroelastic behaviors predicted via the proposed approach agree well with those obtained via computational fluid dynamics technique in the interested range of dynamic pressure.

关键词： Nonlinear aerodynamic systems Transonic aeroelastic behaviors Computational fluid dynamics Nonlinear state-space aerodynamic model eigensystem realization algorithm

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Calculating Impulse and Frequency Response of Large Power System Models for realization Identification

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IEEE TRANSACTIONS ON POWER SYSTEMS 2020年第5期35卷 3825-3834页

作者： Rimorov, Dmitry Rergis, C. M. Kamwa, Innocent Moeini, Ali Huang, Jinan Darvishi, Atena Fardanesh, Bruce Hydro Quebec Res Inst Varennes PQ J3X 1S1 Canada CINVESTAV Dept Elect Engn Guadalajara 45019 Mexico Ctr Ensenanza Tecn Ind CETI Colomos Guadalajara 44635 Mexico New York Power Author White Plains NY 10601 USA

The article proposes a computationally efficient and robust method for estimating impulse or frequency response in the context of black-box multiple-input-multiple-output linear model identification of large power systems from simulations. The proposed approach is validated in conjunction with two realization algorithms - ERA method that is based on the established Ho-Kalman procedure for minimal realization, and the relatively new Loewner matrix based method. Practical aspects of identification in presence of numerical noise and nonlinearities are discussed. Study cases presented in the article include a linear model equivalent of a large-scale power system and the full-scale nonlinear transient model of the Eastern Interconnection.

关键词： Power system stability Computational modeling Numerical models Frequency response MIMO communication Analytical models Power system dynamics eigensystem realization algorithm frequency response impulse response Loewner matrix power system electromechanical models small-signal stability system identification

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Reduced-order Modeling and Acoustic Optimization of the Noise Generated by Boundary Layer Instabilities Convecting Over an Elastic Trailing-Edge

Reduced-order Modeling and Acoustic Optimization of the Nois...

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AIAA Aviation Forum

作者： Nardini, Massimiliano Sandberg, Richard D. Univ Melbourne Dept Mech Engn Parkville Vic 3010 Australia

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

A novel reduced-order fluid-structure interaction acoustic model for the noise generated by the unsteady deflection of an elastic trailing-edge (TE) subjected to an incident pressure field is presented. The model is obtained from Direct Numerical Simulation (DNS) using system identification and model reduction techniques. The mathematical formulation of the model and its validation against DNS are presented. The developed model is adopted to investigate the noise reduction potential of an elastic TE in the presence of aerodynamic fluctuations caused by boundary layer instabilities. For that purpose, a gradient-based optimization framework is introduced to find the combination of structural parameters that offers the largest noise reduction over a rigid TE. The acoustic and structural response of this optimal elastic TE are validated and discussed. Finally, the optimal solution is tested in off-design conditions, showing low sensitivity to variations of the structural parameters and of the amplitude of the incident fluctuations.

关键词： Turbulent Boundary Layer Trailing Edges Direct Numerical Simulation Fluid Structure Interaction Euler Bernoulli Beams System Identification Free Stream Velocity eigensystem realization algorithm Power Spectral Density Young's Modulus

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