Flutter Boundary Prediction Research Articles

Research on Simulation Technology of Excitation Response of Aircraft Structural Based on Finite Element Model in Flutter Flight Test

To simulate excitation response of the aircraft structural of flutter test aircraft under different excitation methods. A simulation method for excitation response of flutter flight tests based on finite element models has been proposed. This method is based on the finite element model of the aircraft structure. Establish aerodynamic and excitation force models for flutter flight tests. Obtain a simulation model for the excitation response of aircraft flutter flight tests. Solve the model and simulate various excitation methods for flutter flight tests. Firstly, a detailed introduction was given to the excitation modeling method for aircraft flutter flight tests, including two excitation models: external excitation and control surface excitation. Then, the finite element model of the structural dynamics of a single wing with ailerons is taken as the research object. Establish a single wing flutter flight test excitation response model. Implemented simulation of control surface sweep excitation, control surface pulse excitation, and small rocket excitation. The feasibility of this method has been verified. Finally, based on the finite element model of the entire aircraft, a flutter flight test excitation response simulation model was established. We have conducted analysis and research on sensor position optimization, excitation method optimization, excitation response amplitude prediction, and flutter boundary prediction. And the simulation optimization analysis results were compared with the flight test results. Analyzed the promoting effect of flutter flight test excitation response simulation on flight tests.

Flutter Boundary Prediction Based on Structural Frequency Response Functions Acquired from Ground Test

Establishing an accurate, fast, and low-risk flutter boundary prediction method is of great significance for flight vehicle design. In this paper, a ground flutter boundary prediction method (GFBP) based on experimental structural frequency response functions (FRFs) is proposed. A low-order multi-input multi-output (MIMO) aeroelastic system is established by combining the structural FRFs acquired from a ground test and the calculated unsteady aerodynamic FRFs in physical coordinates. The multivariable Nyquist criterion is used to predict the flutter boundary. A fixed-root aluminum plate wing is selected as the research model. A GFBP experiment is carried out for the wing’s normal state, leading-edge clump weight state, and trailing-edge clump weight state. The feasibility and accuracy of the proposed method are verified by comparison with theoretical flutter results, in which the errors of flutter speed and frequency in the test statistics are no more than 1.7%. In a simulation model established by the proposed method, Monte Carlo simulation is used to study the influence of deviations in the mode frequency and damping of the structural FRFs and deviations in the positions of excitation and measurement points in the ground test. The experiment and simulation results show that the proposed method can predict the flutter boundary accurately with accurate positions of excitation and measurement points, and it has good robustness to deviations in the mode frequency and amplitude of the structural FRFs.

Generative model: Impulse response generated from turbulence response in flutter signal

Impulse response facilitates ideal modal parameter estimation in flutter tests. However, impulse excitation is costly, difficult, and risky to execute in flutter engineering tests, so it is difficult to obtain an effective impulse response for modal parameter estimation. Limitations inherent to the physical testing conditions make atmospheric turbulence a common excitation in flutter testing signal processing. Modal analysis of the structural response excited by turbulence from the flutter testing signal is crucial. Existing methods for analyzing structural responses excited by atmospheric turbulence have certain shortcomings. This paper proposes a novel impulse response generative model corresponding turbulence response based on a deep neural network. Frequency and damping ratio calculations become a modal parameter estimation problem for natural excitation relevant to the turbulence response. The turbulence response can be used to calculate the corresponding impulse response through the generative model. The modal parameters of the generated impulse response are estimated by the generative model via Matrix Pencil (MP) method. The results can then be compared with the true model parameters from simulation data. The generative model is shown to accurately generate an impulse response as evidenced by comparison against physical testing data. The impulse response can indeed be generated by the turbulence response based on the generative model. The estimated model parameters of the Stochastic Subspace Identification (SSI) are compared with the generative model via MP in terms of accuracy and computation time, which indicate better on-line monitoring/warning flutter flight test effects. Flutter boundary predictions based on physical testing further validate the engineering applicability of the proposed method.

Flutter Boundary Prediction in a Global Stochastic Framework

A novel global parametric system identification framework is introduced in this work for aeroelastic modeling under varying flight states. The presented framework is based on the functionally pooled (FP) time-series models that enable explicit analytical inclusion of any admissible flight states into the model parameters and thus the system dynamics. In this paper, the autoregressive (AR) type of the FP model, which is designated as the FP-AR, is employed to interpret the aerodynamics of a wing structure. The data were recorded by accelerometers during a dedicated wind-tunnel flutter test with the airspeed increasing all the way to the flutter boundary. Including the varying flight states defined by the increasing airspeed into the system modeling via the FP technique, the global framework provides a more sophisticated identification results compared with the traditional nonparametric Welch-based spectral estimation. Flutter occurrence is indicated by the stability margin of the aeroelastic system evaluated by the estimated FP-AR parameters based on Jury’s stability criterion. For online application purpose, an iterative state-based FP-AR process is also proposed in this paper. Compared with the standard FP-AR modeling, the iterative realization is a developing process that provides a global approximation of the system dynamics at each flight state. Experimental evaluation demonstrates the feasibility and effectiveness of the proposed global framework in aeroelastic modeling while facilitating an accurate flutter boundary prediction.

Efficient prediction of transonic flutter boundaries for varying Mach number and angle of attack via LSTM network

Transonic aeroelastic analysis can be carried out accurately and efficiently by using the aerodynamic Reduced-Order Modeling (ROM) approach. However, the efficiency and generalization capability of traditional time-dependent ROM should be further enhanced, especially when dealing with the case for varying flight parameters. For such a purpose, a set of flight samples for different Mach numbers and mean angles of attack in transonic regime are selected to cover the concerned parameter space. Subsequently, a typical filtered white Gaussian noise is used as the input signal to excite the dynamical behavior of the aerodynamic system via the direct Computational Fluid Dynamic (CFD) technique, and the corresponding input and output data at all the flight samples are used as the training data set. Afterwards, based on the CFD training data set, the dynamical relationship between aerodynamic output and displacement input for varying Mach number and mean angle of attack can be approximately fitted by using the Long Short Term Memory (LSTM) network, which is a time-series prediction approach of deep learning method. Finally, the transonic flutter boundaries of a NACA 64A010 airfoil are investigated to assess the validity of the proposed approach. The comparison with CFD results shows that, the ROM can predict the unsteady aerodynamic response and aeroelastic characteristics well with low computation cost. In particular, the flutter boundaries of the concerned airfoil at different Mach numbers and mean angles of attack are obtained, due to the absence of time-delay term in surrogate model, the generalization capacity and modeling efficiency of the ROM are improved.

Efficient reduced-order aerodynamic modeling for fast prediction of transonic flutter boundary

In this study, a reduced-order aerodynamic modeling framework by integration of a novel training data interpolation approach and the Eigensystem realization algorithm (ERA) is presented for fast prediction of transonic flutter boundary over a range of flight parameters. First, aerodynamic impulse responses are computed by using the technique of computational fluid dynamics (CFD) at grid points within parameter space, which are selected to cover the transonic regime of concern. Next, the training data interpolation approach by combining the discrete empirical interpolation method with the Kriging technique is used to generate the aerodynamic impulse response at arbitrary flight condition, without performing unsteady CFD simulations. Finally, the interpolated impulse response is used by ERA to extract the linear state-space aerodynamic model, which is coupled with the structural model for flutter characteristics analysis. To illustrate the proposed approach, a NACA 0012 airfoil of two degrees of freedom at zero mean angle of attack is investigated. The transonic flutter boundaries of the airfoil agree well with those obtained by using CFD-based technique.

A New Method of Flutter Boundary Prediction for Progressive Variable Speed Based on EM-KS Algorithm

The flutter test with progression variable speed is actively explored in recent years. This paper proposes an improved Kalman smoothing filter (EM-KS) algorithm based on expectation maximization for the non-stationary characteristics of the signal in this type of experiment, which can effectively improve the estimation accuracy of time-varying parameter modeling. Combining with the flutter time domain criterion, a new method for flutter boundary prediction of flutter test with progression variable speed that can be recursively implemented is given. Finally, the reliability and engineering applicability of this method are validated by numerical simulation and measured data. The results show that the flutter boundary prediction method based on EM-KS does not depend on the assumption of stationary stochastic process, and the accuracy can meet the actual engineering needs.

Aerodynamic Damping Prediction for Turbomachinery Based on Fluid-Structure Interaction with Modal Excitation

Aerodynamic damping predictions are critical when analyzing aeroelastic stability. A novel method has been developed to predict aerodynamic damping by employing two single time-domain simulations, specifically, one with the blade impulsed naturally in a vacuum and one with the blade impulsed in flow. The focus is on the aerodynamic damping prediction using modal excitation and the logarithmic decrement theory. The method is demonstrated by considering the first two bending modes with an inter-blade phase angle (IBPA) of 0° on a transonic compressor. The results show that the flutter boundary prediction is basically consistent with the experiment. The aerodynamic damping prediction with an IBPA of 180° is also performed, demonstrating that the method is suitable for different traveling wave mode representations. Furthermore, the influence of the amplitude of modal excitation and mechanical damping using the Rayleigh damping model for aerodynamic damping was also investigated by employing fluid-structure coupled simulations.

Wing Flutter Prediction by a Small-Disturbance Euler Method on Body-Fitted Curvilinear Grids

Time-accurate coupled fluid and structure solutions for the unsteady Euler equations are too expensive for routine aeroelastic computation. The small-disturbance Euler (SD-Euler) method is shown to be an efficient and accurate method for computation of the frequency-domain generalized aerodynamics forces, even in the transonic region. The SD-Euler method reduces the unsteady problem to a steady flow solution for the perturbation so that the generalized aerodynamics forces can be evaluated directly, enabling substantial reduction of computational time. A SD-Euler solver on body-fitted curvilinear grids has been developed and validated using two-dimensional airfoil and three-dimensional wing rigid-body pitching test cases. Frequency-domain flutter analyses of the Isogai wing model and the AGARD 445.6 weakened wing are performed using this new solver. Flutter boundary predictions by the SD-Euler method agree well with the results by a coupled fluid–structure method. The flutter mode shift phenomenon for the Isogai wing model and the AGARD 445.6 weakened wing is also demonstrated by using the frequency-domain method.

Online EMD-Wavelet Method for Flutter Test Excited by Atmospheric Turbulence

Empirical Mode Decomposition (EMD) and Wavelet method have been widely used in the vibration signal analysis, mainly because of the powerful ability of blind modal separation. In the flutter test, modal identification and modal trajectories tracking online can help to ensure the test safety. However, traditional EMD method is only suitable for offline data batching, which limits its applications to the real-time or near real-time signal analysis. For this reason, according to the online processing requirements of flutter test under the turbulent excitation conditions, combining with wavelet spectrum analysis, an online EMD method based on a sliding window for structural modal identification and flutter boundary prediction (FBP) is proposed in this paper. The corresponding mathematical principles and implementation algorithms are given as well, which decompose the measured signal into the Intrinsic Mode Function (IMF) firstly, and then estimate the modal parameters by using the wavelet power spectrum method. The FBP result is typically obtained online during the test process by using curve fitting and extrapolation of the modal damping. The numerical simulations and test data from a low-speed wind tunnel flutter test are used to verify the effectiveness and engineering feasibility of the proposed method.

Development and Testing of Hypersonic Flutter Test Capability

To investigate the hypersonic flutter behavior of wings and all-movable control surfaces, a hypersonic wind tunnel flutter test capability has been developed by the China Academy of Aerospace Aerodynamics. This Paper outlines the design of the hypersonic flutter test rig; demonstrates the utility of the rig and the flutter test technique for hypersonic flutter research; and assesses the repeatability of the hypersonic flutter test, the application of subcritical flutter boundary identification methods, the effect of the rate of increase of dynamic pressure on flutter, and the aerodynamic heating effect. Descriptions of the data acquisition system and the experimental procedure are presented. Four models with the same design were tested for flutter at Mach numbers of 4.95 and 5.95. A wavelet time–frequency domain analysis method was employed to evaluate the trend of structural frequency coupling. The results showed good repeatability of the test. Both the flutter margin method and the damping ratio extrapolation method had high prediction accuracy in flutter boundary prediction. The rate of increase of dynamic pressure did not have any significant effect on the flutter boundary. However, a high rate of increase of dynamic pressure resulted in unsuccessful flutter prediction for the damping ratio extrapolation method. The leading edge and the windward side of the model were the parts subject to severe aerodynamic heating, but their temperatures were lower than the stagnation temperature of the airflow.

A flutter prediction method with low cost and low risk from test data

The most common approach to flight flutter testing is to track estimated modal damping ratios of an aircraft over a number of fight conditions. However, the risk is inevitable when this method is utilized since the aircraft must fly near the flutter boundary. In this paper, a method with low cost and low risk for flutter boundary prediction is proposed. Based on structural modal parameters from the ground vibration test (GVT) and the structural response at the sub-critical speed, the generalized aerodynamic force coefficient vector can be solved. The generalized displacement vector is designed as the input and the generalized aerodynamic force coefficient vector as the output. System identification is used to construct the reduced-order aerodynamic model. The aeroelastic model based on experimental results can be constructed by coupling the structural motion equation and the aerodynamic equation in state space. Analyzing the characteristics of the fluid–structure coupling system changing with the dynamic pressure, the flutter onset behaviors can be solved by the eigenvalue method. Wind tunnel tests confirm that this method only needs one wind-on test at the sub-critical speed to predict the flutter onset with a certain precision even the reference dynamic pressure is far from the flutter critical point.

Novel Nonstationarity Assessment Method for Hypersonic Flutter Flight Tests

Hypersonic aircraft have been rapidly developed in recent years both theoretically and experimentally. Aerothermoelastic simulation is very challenging due to its inherent complexity, but physical tests are a workable approach. Flutter tests with variable speed are a popular alternative to hypersonic tests which provide nonstationary structural response data. This paper proposes a nonstationarity assessment method based on energy distribution in the time-frequency domain. The proposed method reveals the nonstationarity level corresponding to the appropriate modal identification algorithm or flutter boundary prediction (FBP) method. Several classic flutter criteria are utilized to build a hypersonic aircraft FBP framework. Numerical simulation and experimental applications demonstrate the effectiveness and feasibility of the proposed method, which facilitates accurate flutter predictions for the subcritical turbulence response during hypersonic flutter flight.

Flutter Test Data Processing Based on Improved Hilbert-Huang Transform

Flutter tests are conducted primarily for the purpose of modal parameter estimation and flutter boundary prediction, the accuracy of which is severely affected by the acquired data quality, structural modal density, and nonstationary conditions. An improved Hilbert-Huang Transform (HHT) algorithm is presented in this paper which mitigates the typical mode mixing effect via modulation. The algorithm is validated by theory, by numerical simulation, and per actual flight flutter test data. The results show that the proposed method could extract the flutter model parameters and predict the flutter speed more accurately, which is feasible for the current flutter test data processing.

Prediction of Flutter Boundary Using Flutter Margin for The Discrete-Time System

Flutter testing in a wind tunnel is generally conducted at subcritical speeds to avoid damages. Hence, The flutter speed has to be predicted from the behavior some of its stability criteria estimated against the dynamic pressure or flight speed. Therefore, it is quite important for a reliable flutter prediction method to estimates flutter boundary. This paper summarizes the flutter testing of a wing cantilever model in a wind tunnel. The model has two degree of freedom; they are bending and torsion modes. The flutter test was conducted in a subsonic wind tunnel. The dynamic data responses was measured by two accelerometers that were mounted on leading edge and center of wing tip. The measurement was repeated while the wind speed increased. The dynamic responses were used to determine the parameter flutter margin for the discrete-time system. The flutter boundary of the model was estimated using extrapolation of the parameter flutter margin against the dynamic pressure. The parameter flutter margin for the discrete-time system has a better performance for flutter prediction than the modal parameters. A model with two degree freedom and experiencing classical flutter, the parameter flutter margin for the discrete-time system gives a satisfying result in prediction of flutter boundary on subsonic wind tunnel test.

Flutter Boundary Prediction of a Two Dimensional Airfoil in Transonic Flight Regime with the Preset Angles of Attack

Angle of attack has impact on transonic flow filed and aerodynamic force, but most of current researches on flutter use zero angle hypothesis, which has no consideration about angle of attack. Therefore, we use unsteady Reynold Averaged Navier-Stokes (RANS) equation and structural dynamic equation to establish the time domain aeroelastic analysis method. The solution in time domain is the fourth-order implicit Adams linear multi-step method which is based on prediction-correction method. The numerical simulations were used to analyze the transonic flutter boundary of Isogai Case A Model which was based on zero angle condition and nonzero angle respectively. The simulation results show that the reduced flutter speed decreases as the preset angle of attack decreases between 0.73 and 0.76, which shows a 12.5% decrease of the flutter speed at the farthest. Nonzero angle makes the transonic dip weaker and wider than fully turbulent flow. Changing in angle of attack of 6°, the flutter speed in the deepest position of transonic dip has increased by 124% compared to the flutter speed of 0°. Therefore, when flutter characters of airfoil is analyzed, the effects of the initial angle of attack must be taken into account in order to analyze flutter boundary correctly. In other words, increasing the angle of attack offers a way to control the system in terms of delaying flutter.

Assessment of Advanced Flutter Flight-Test Techniques and Flutter Boundary Prediction Methods

The paper presents an experimental study, conducted by the Israel Air Force, aimed at the assessment of several advanced flutter flight-test techniques that are designed to improve the efficiency and accuracy of flutter tests. These include the autoregressive moving-average and operational modal analysis system identification methods, the use of various system stability parameters, and the use of atmospheric turbulence versus prescribed flaperon motion as the source of structural response excitation. The methods are evaluated based on data from a dedicated transonic flight test of the F-16 platform. All of the tested methods are able to accurately predict the instability onset. The operational modal analysis method has the advantage that it does not require a priori knowledge of the instability mechanism, whereas the autoregressive moving-average method is easier to implement and straightforward to use in real time. Excitation by atmospheric turbulence is found to be adequate in the current test case, in which the modes are lightly damped and highly suitable for system identification methods that rely on stochastic inputs. The use of autoregressive moving-average and operational modal analysis methods based on responses to atmospheric turbulence appears to offer an accurate and cost-effective flutter testing methodology.

An efficient iterative model reduction method for aeroviscoelastic panel flutter analysis in the supersonic regime

Abstract The flutter boundary prediction of complex aeroelastic systems is not an easy task. In some cases, these analyses may become prohibitive due to the high computational cost and time associated with the large number of degrees of freedom of the aeroelastic models, particularly when the aeroelastic model incorporates a control strategy with the aim of suppressing the flutter phenomenon, such as the use of viscoelastic treatments. In this situation, the use of a model reduction method is essential. However, the construction of a modal reduction basis for aeroviscoelastic systems is still a challenge, owing to the inherent frequency- and temperature-dependent behavior of the viscoelastic materials. Thus, the main contribution intended for the present study is to propose an efficient and accurate iterative enriched Ritz basis to deal with aeroviscoelastic systems. The main features and capabilities of the proposed model reduction method are illustrated in the prediction of flutter boundary for a thin three-layer sandwich flat panel and a typical aeronautical stiffened panel, both under supersonic flow.

Uncertain reduced-order modeling for unsteady aerodynamics with interval parameters and its application on robust flutter boundary prediction

Computational fluid dynamics based unsteady aerodynamic reduced-order models can significantly improve the efficiency of transonic aeroelastic analysis. In this paper, the concept of the conventional model reduction method based on the system identification theory is extended to aerodynamic subsystems with the consideration of computational fluid dynamics-induced interval uncertainties in simulation to get the aerodynamic reduced-order model as uncertain as the original aerodynamic subsystem. The interval estimation of identified coefficients involved in the uncertain reduced-order model is obtained by utilizing the first-order interval perturbation method. The stability problem of the interval aeroelastic state-space model formulated based on the constructed uncertain aerodynamic reduced-order model is equivalently transformed into a standard interval eigenvalue problem associated with a real non-symmetric interval matrix in which the interval bounds of eigenvalues are evaluated by virtue of the first-order interval matrix perturbation algorithm. A new stability criterion for the interval aeroelastic state matrix is defined to predict the robust flutter boundary of the concerned uncertain aeroelastic system. Two numerical examples with respect to the uncertain aerodynamic ROM constructions and robust flutter boundary predictions of the two-dimensional Isogai wing and the three-dimensional AGARD 445.6 wing in transonic regime are implemented to assess the validity and accuracy of the presented approach. The obtained results are also compared with Monte Carlo simulation solutions as well as numerical and experimental results in the literatures indicating that the proposed method can provide a more robust and conservative prediction on the flutter boundary of an aeroelastic system compared with conventional deterministic aeroelastic analysis approaches.

Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions

In this paper, porosity-dependent aero-hygro-thermal instability of functionally graded (FG) panels is investigated by developing a higher-order refined shear deformable theory for the first time. Porosities are randomly distributed around the cross section of FG panel. Hygro-thermo-elastic material properties of porous FG panel are described using a modified power-law function accounting for even and uneven porosity distributions. Based on the presented refined shear deformation theory, it is possible to examine instability regions of thicker FG panels without using a shear correction factor. Employing extended Hamilton’s principle, the governing equations of FG panel under supersonic airflow simulated via first-order piston theory are obtained. It is concluded that porosity volume fraction, type of porosities, hygro-thermal environment, material gradation and slenderness ratio have major roles on the prediction of divergence and flutter boundaries of porous FG panels.