Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in computational and experimental aeroelasticity are reviewed. Computational results include the development of computationally efficient reduced-order models (ROMs) using an Euler/Navier–Stokes flow solver and the analytical derivation of Volterra kernels for a nonlinear aeroelastic system. Experimental results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the active aeroelastic wing (AAW) aircraft.

[1]  David J. Piatak,et al.  A New Forced Oscillation Capability for the Transonic Dynamics Tunnel , 2002 .

[2]  J. G. Leishman,et al.  A state-space model of unsteady aerodynamics in a compressible flow for flutter analyses , 1989 .

[3]  Muhammad R. Hajj,et al.  Fundamental–subharmonic interaction: effect of phase relation , 1993, Journal of Fluid Mechanics.

[4]  Liviu Librescu,et al.  VOLTERRA SERIES APPROACH FOR NONLINEAR AEROELASTIC RESPONSE OF 2-D LIFTING SURFACES , 2001 .

[5]  Raymond E. Gordnier,et al.  Transonic flutter simulations using an implicit aeroelastic solver , 2000 .

[6]  E. Baeyens,et al.  Identification of multivariable Hammerstein systems using rational orthonormal bases , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[7]  J. Bendat.  New techniques for nonlinear system analysis and identification from random data , 1990 .

[8]  Julius S. Bendat,et al.  Nonlinear System Techniques And Applications , 1990 .

[9]  Carlos E. S. Cesnik,et al.  Aerodynamic impulse response of a panel method , 2001 .

[10]  Andrew Arena,et al.  Acceleration CFD-based aeroelastic predictions using system identification , 1998 .

[11]  Andrew J. Kurdila,et al.  Multiresolution methods for reduced order models for dynamical systems , 1999 .

[12]  Donald F. Keller,et al.  Measurement of Unsteady Pressure Data on a Large HSCT Semispan Wing and Comparison with Analysis , 2002 .

[13]  Earl H. Dowell,et al.  Eigenmode Analysis in Unsteady Aerodynamics: Reduced Order Models , 1997 .

[14]  Louis N. Cattafesta,et al.  Adaptive Identification of Fluid-Dynamic Systems , 2001 .

[15]  Liviu Librescu,et al.  Aeroelastic Response of Swept Aircraft Wings in a Compressible Flow Field , 2001 .

[16]  Earl H. Dowell,et al.  Flutter Analysis Using Nonlinear Aerodynamic Forces , 1984 .

[17]  David E. Parekh,et al.  AVIA: Adaptive Virtual Aerosurface , 2000 .

[18]  Michael F. Shlesinger,et al.  Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers , 1993 .

[19]  Mark Sheplak,et al.  Reduced order modeling for low Reynolds number flow control , 1999, Smart Structures.

[20]  Michael Amitay,et al.  Virtual Aerodynamic Shape Modification at Low Angles of Attack using Synthetic Jet Actuators , 2001 .

[21]  Martin Goland,et al.  Principles of aeroelasticity , 1975 .

[22]  R. H. Ricketts,et al.  Some recent applications of XTRAN3S , 1983 .

[23]  David J. Lucia,et al.  Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory , 2003 .

[24]  Dimitri N. Mavris,et al.  Reduced-Order Models Based on CFD Impulse and Step Responses , 2001 .

[25]  Andrew Arena,et al.  Development of a discrete-time aerodynamic model for CFD-based aeroelastic analysis , 1999 .

[26]  E. Powers,et al.  Digital Bispectral Analysis and Its Applications to Nonlinear Wave Interactions , 1979, IEEE Transactions on Plasma Science.

[27]  O. Nelles.  Nonlinear System Identification , 2001 .

[28]  Lawrence N. Virgin,et al.  Introduction to Experimental Nonlinear Dynamics , 2000 .

[29]  Keith Worden,et al.  Nonlinearity in Structural Dynamics , 2019 .

[30]  Robert C. Scott,et al.  Identification of Computational and Experimental Reduced-Order Models , 2003 .

[31]  A Silva Walter,et al.  Reduced-Order Modeling: Cooperative Research and Development at the NASA Langley Research Center , 2001 .

[32]  W. Rugh.  Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .

[33]  R. Temam.  Navier-Stokes Equations and Nonlinear Functional Analysis , 1987 .

[34]  Eduardo Alves Rodrigues.  Linear and nonlinear discrete-time state-space modeling of dynamic systems for control applications , 1993 .

[35]  Patrick Reisenthel,et al.  Development of a nonlinear indicial model for maneuvering fighter aircraft , 1996 .

[36]  Walter A. Silva,et al.  Development of Reduced-Order Models for Aeroelastic Analysis and Flutter Prediction Using the CFL3Dv6.0 Code , 2002 .

[37]  John T. Batina,et al.  Wing flutter computations using an aerodynamic model based on the Navier-Stokes equations , 1996 .

[38]  D. J. Johns.  Book Reviews : A Modern Course in Aeroelasticity: E.H. Dowell, editor and author H.C. Curtiss, Jr., R.H. Scanlan, F. Sisto, co-authors Sijthoff and Noordhoff; The Netherlands, 1978 , 1980 .

[39]  P. Beran,et al.  Reduced-order modeling: new approaches for computational physics , 2004 .

[40]  Roger Temam,et al.  Navier–Stokes Equations and Nonlinear Functional Analysis: Second Edition , 1995 .

[41]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[42]  Walter A. Silva,et al.  Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses , 1993 .

[43]  F. Marques,et al.  IDENTIFICATION AND PREDICTION OF UNSTEADY TRANSONIC AERODYNAMIC LOADS BY MULTI-LAYER FUNCTIONALS , 2001 .

[44]  Robert C. Scott,et al.  Experimental steady and unsteady aerodynamic and flutter results for HSCT semispan models , 2000 .

[45]  G. Govind,et al.  Multi-layered neural networks and Volterra series: The missing link , 1990, 1990 IEEE International Conference on Systems Engineering.

[46]  R. D'Andrea,et al.  Nonlinear System Identification of Multi-Degree-of-Freedom Systems , 2003 .

[47]  Julian F. Scott,et al.  An Introduction to Turbulent Flow , 2000 .

[48]  B. Dickinson.  Modeling of nonlinear systems from input-output data , 1983, The 22nd IEEE Conference on Decision and Control.

[49]  Liviu Librescu,et al.  Nonlinear Stability and Response of Lifting Surfaces Via Volterra Series , 2001 .

[50]  Vito Volterra,et al.  Theory of Functionals and of Integral and Integro-Differential Equations , 2005 .

[51]  M. Schetzen.  Measurement of the Kernels of a Non-linear System of Finite Order† , 1965 .

[52]  Daniella E. Raveh,et al.  Aircraft aeroelastic analysis and design using CFD-based unsteady loads , 2000 .

[53]  Klein Vladislav,et al.  Estimation of Aircraft Unsteady Aerodynamic Parameters From Dynamic Wind Tunnel Testing , 2001 .

[54]  Vimal Singh,et al.  Perturbation methods , 1991 .

[55]  David Nixon.  Unsteady transonic aerodynamics , 1989 .

[56]  William T. Baumann,et al.  Accurate Modeling of Nonlinear Systems using Volterra Series Submodels , 1987, 1987 American Control Conference.

[57]  G. Tomlinson,et al.  Nonlinearity in Structural Dynamics: Detection, Identification and Modelling , 2000 .

[58]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[59]  Ioannis Pitas,et al.  Nonlinear Digital Filters - Principles and Applications , 1990, The Springer International Series in Engineering and Computer Science.

[60]  J. T. Bialasiewicz,et al.  Neural network modeling of nonlinear systems based on volterra series extension of a linear model , 1992, Proceedings of the 1992 IEEE International Symposium on Intelligent Control.

[61]  M. Phan,et al.  Identification of observer/Kalman filter Markov parameters: Theory and experiments , 1993 .

[62]  Kajal Gupta,et al.  CFD-based aeroelastic analysis of the X-43 hypersonic flight vehicle , 2001 .

[63]  Jerry Jenkins,et al.  Relationships among nonlinear aerodynamic indicial response models, oscillatory motion data, and stability derivatives , 1989 .

[64]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[65]  Taehyoun Kim,et al.  Evaluation of CFL3D for Unsteady Pressure and Flutter Predictions , 2003 .

[66]  Richard J. Prazenica,et al.  Multiresolution methods for representation of Volterra series and dynamical systems , 2000 .

[67]  B. Epureanu.  Time-filtered limit cycle computation for aeroelastic systems , 2001 .

[68]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[69]  Flutter Characterization of the Flexible HSCT Semispan Model , 2003 .

[70]  Robert C. Scott,et al.  Identification of Experimental Unsteady Aerodynamic Impulse Responses , 2005 .

[71]  J. Juang.  Applied system identification , 1994 .

[72]  Taehyoun Kim,et al.  An efficient response-based modal analysis for dynamic systems with multiple inputs , 2001 .

[73]  Walter A. Silva,et al.  Application of nonlinear systems theory to transonic unsteady aerodynamic responses , 1993 .

[74]  C. Evans,et al.  Nonlinear system modelling: how to estimate the highest significant order , 2002, IMTC/2002. Proceedings of the 19th IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.00CH37276).

[75]  M. Amitay,et al.  Virtual aero-shaping of a Clark-Y airfoil using synthetic jet actuators , 2001 .

[76]  Philip S. Beran,et al.  Reduced-order modeling - New approaches for computational physics , 2001 .

[77]  Jer-Nan Juang,et al.  An eigensystem realization algorithm for modal parameter identification and model reduction. [control systems design for large space structures] , 1985 .

[78]  RobertF Brown,et al.  A topological introduction to nonlinear analysis , 1993 .

[79]  W. Rugh,et al.  A note on the identification of discrete-time polynomial systems , 1979 .

[80]  Jerry Jenkins,et al.  A Volterra kernel identification scheme applied to aerodynamic reactions , 1990 .

[81]  Robert C. Scott,et al.  Experimental Identification of Unsteady Aerodynamic Impulse Responses , 2003 .

[82]  Yuan-Cheng Fung,et al.  An introduction to the theory of aeroelasticity , 1955 .

[83]  H. Saunders,et al.  A Modern Course in Aeroelasticity , 1981, Solid Mechanics and its Applications.

[84]  Walter A. Silva,et al.  Reduced-Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses , 1999 .

[85]  Earl H. Dowell,et al.  Modeling of Fluid-Structure Interaction , 2001 .

[86]  Muhammad R. Hajj,et al.  Nonlinear Flutter Aspects of the Flexible HSCT Semispan Model , 2003 .

[87]  Leon O. Chua,et al.  Measuring Volterra kernels , 1983 .

[88]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[89]  Earl H. Dowell,et al.  Reduced order system identification of nonlinear aeroelastic systems , 2001 .

[90]  W. Silva,et al.  Discrete-time linear and nonlinear aerodynamic impulse responses for efficient cfd analyses , 1997 .

[91]  Mordechay Karpel,et al.  Time-domain aeroservoelastic modeling using weighted unsteady aerodynamic forces , 1990 .

[92]  J. P. Giesing,et al.  Subsonic Unsteady Aerodynamics for General Configurations. Part 1. Volume I. Direct Application of the Nonplanar Doublet-Lattice Method , 1971 .

[93]  Muhammad R. Hajj,et al.  Perspective: Measurements and Analyses of Nonlinear Wave Interactions With Higher-Order Spectral Moments , 1997 .

[94]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[95]  C. M. Place,et al.  An Introduction to Dynamical Systems , 1990 .

[96]  Richard J. Prazenica,et al.  Volterra Kernel Identification and Extrapolation for the F/A-18 Active Aeroelastic Wing , 2004 .