Unsteady aerodynamics modeling for flight dynamics application

In view of engineering application, it is practicable to decompose the aerodynamics into three components： the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms, while the third is described using a one-order differential equation and a radial-basis-function （RBF） network. For an aircraft configuration, the mathematical models of 6- component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynam- ics, respectively. The results show that： （1） unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; （2） unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and （3） unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected. It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability

Gated Neural Network-Based Unsteady Aerodynamic Modeling for Large Angles of Attack

Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft unsteady aerodynamic design and flight dynamics analysis.In this paper,aiming at the problems of poor generalization of traditional aerodynamic models and intelligent models,an intelligent aerodynamic modeling method based on gated neural units is proposed.The time memory characteristics of the gated neural unit is fully utilized,thus the nonlinear flow field characterization ability of the learning and training process is enhanced,and the generalization ability of the whole prediction model is improved.The prediction and verification of the model are carried out under the maneuvering flight condition of NACA0015 airfoil.The results show that the model has good adaptability.In the interpolation prediction,the maximum prediction error of the lift and drag coefficients and the moment coefficient does not exceed 10%,which can basically represent the variation characteristics of the entire flow field.In the construction of extrapolation models,the training model based on the strong nonlinear data has good accuracy for weak nonlinear prediction.Furthermore,the error is larger,even exceeding 20%,which indicates that the extrapolation and generalization capabilities need to be further optimized by integrating physical models.Compared with the conventional state space equation model,the proposed method can improve the extrapolation accuracy and efficiency by 78%and 60%,respectively,which demonstrates the applied potential of this method in aerodynamic modeling.

IMPROVED AERODYNAMIC APPROXIMATION MODEL WITH CASE-BASED REASONING TECHNIQUE FOR MDO OF AIRCRAFT

To increase the efficiency of the multidisciplinary optimization of aircraft, an aerodynamic approximation model is improved. Based on the study of aerodynamic approximation model constructed by the scaling correction model, case-based reasoning technique is introduced to improve the approximation model for optimization. The aircraft case model is constructed by utilizing the plane parameters related to aerodynamic characteristics as attributes of cases, and the formula of case retrieving is improved. Finally, the aerodynamic approximation model for optimization is improved by reusing the correction factors of the most similar aircraft to the current one. The multidisciplinary optimization of a civil aircraft concept is carried out with the improved aerodynamic approximation model. The results demonstrate that the precision and the efficiency of the optimization can be improved by utilizing the improved aerodynamic approximation model with ease-based reasoning technique.

Comparison and analysis of bare soil evaporation models combined with ASTER data in Heihe River Basin

Based on ASTER （Advanced Spaceborne Thermal Emission and Reflection Radiometer） remote sensing data, bare soil evaporation was estimated with the Penman-Monteith model, the Priestley-Taylor model, and the aerodynamics model. Evaporation estimated by each of the three models was compared with actual evaporation, and error sources of the three models were analyzed. The mean absolute relative error was 9% for the Penman-Monteith model, 14% for the Priestley-Taylor model, and 32% for the aerodynamics model; the Penman-Monteith model was the best of these three models for estimating bare soil evaporation. The error source of the Penman-Monteith model is the neglect of the advection estimation. The error source of the Priestley-Taylor model is the simplification of the component of aerodynamics as 0.72 times the net radiation. The error source of the aerodynamics model is the difference of vapor pressure and neglect of the radiometric component. The spatial distribution of bare soil evaporation is evident, and its main factors are soil water content and elevation.

Airship aerodynamic model estimation using unscented Kalman filter

An airship model is made-up of aerostatic,aerodynamic,dynamic,and propulsive forces and torques.Besides others,the computation of aerodynamic forces and torques is difficult.Usually,wind tunnel experimentation and potential flow theory are used for their calculations.However,the limitations of these methods pose difficulties in their accurate calculation.In this work,an online estimation scheme based on unscented Kalman filter(UKF)is proposed for their calculation.The proposed method introduces six auxiliary states for the complete aerodynamic model.UKF uses an extended model and provides an estimate of a complete state vector along with auxiliary states.The proposed method uses the minimum auxiliary state variables for the approximation of the complete aerodynamic model that makes it computationally less intensive.UKF estimation performance is evaluated by developing a nonlinear simulation environment for University of Engineering and Technology,Taxila(UETT)airship.Estimator performance is validated by performing the error analysis based on estimation error and 2-σ uncertainty bound.For the same problem,the extended Kalman filter(EKF)is also implemented and its results are compared with UKF.The simulation results show that UKF successfully estimates the forces and torques due to the aerodynamic model with small estimation error and the comparative analysis with EKF shows that UKF improves the estimation results and also it is more suitable for the under-consideration problem.

Adaptive WNN aerodynamic modeling based on subset KPCA feature extraction

In order to accurately describe the dynamic characteristics of flight vehicles through aerodynamic modeling, an adaptive wavelet neural network (AWNN) aerodynamic modeling method is proposed, based on subset kernel principal components analysis (SKPCA) feature extraction. Firstly, by fuzzy C-means clustering, some samples are selected from the training sample set to constitute a sample subset. Then, the obtained samples subset is used to execute SKPCA for extracting basic features of the training samples. Finally, using the extracted basic features, the AWNN aerodynamic model is established. The experimental results show that, in 50 times repetitive modeling, the modeling ability of the method proposed is better than that of other six methods. It only needs about half the modeling time of KPCA-AWNN under a close prediction accuracy, and can easily determine the model parameters. This enables it to be effective and feasible to construct the aerodynamic modeling for flight vehicles.

Wavelet neural network aerodynamic modeling from flight data based on pso algorithm with information sharing and velocity disturbance

For the accurate description of aerodynamic characteristics for aircraft,a wavelet neural network (WNN) aerodynamic modeling method from flight data,based on improved particle swarm optimization (PSO) algorithm with information sharing strategy and velocity disturbance operator,is proposed.In improved PSO algorithm,an information sharing strategy is used to avoid the premature convergence as much as possible;the velocity disturbance operator is adopted to jump out of this position once falling into the premature convergence.Simulations on lateral and longitudinal aerodynamic modeling for ATTAS (advanced technologies testing aircraft system) indicate that the proposed method can achieve the accuracy improvement of an order of magnitude compared with SPSO-WNN,and can converge to a satisfactory precision by only 60 120 iterations in contrast to SPSO-WNN with 6 times precocities in 200 times repetitive experiments using Morlet and Mexican hat wavelet functions.Furthermore,it is proved that the proposed method is feasible and effective for aerodynamic modeling from flight data.

Added Mass Effect and an Extended Unsteady Blade Element Model of Insect Hovering

During the insect flight, the force peak at the start of each stroke contributes a lot to the total aerodynamic force. Yet how this force is generated is still controversial. Two current explanations to this are wake capture and Added Mass Effect （AME） mechanisms. To study the AME, we present an extended unsteady blade element model which takes both the added mass of fluid and rotational effect of the wing into account. Simulation results show a high force peak at the start of each stroke and are quite similar to the measured forces on the physical wing model. We found that although the Added Mass Force （AMF） of the medium contributes a lot to this force peak, the wake capture effect further augments this force and may play a more important role in delayed mode. Furthermore, we also found that there might be an unknown mechanism which may augment the AME during acceleration period at the start of each stroke, and diminish the AME during deceleration at the end of each stroke.

Flight dynamics modeling and analysis for a Mars helicopter

Flight dynamics modeling for the Mars helicopter faces great challenges.Aerodynamic modeling of coaxial rotor with high confidence and high computational efficiency is a major difficulty for the field.This paper builds an aerodynamic model of coaxial rotor in the extremely thin Martian atmosphere using the viscous vortex particle method.The aerodynamic forces and flow characteristics of rigid coaxial rotor are computed and analyzed.Meanwhile,a high fidelity aerodynamic surrogate model is built to improve the computational efficiency of the flight dynamics model.Results in this paper reveal that rigid coaxial rotor can bring the Mars helicopter sufficient controllability but result in obvious instability and control couplings in forward flight.This highlights the great differences in flight dynamics characteristics compared with conventional helicopters on Earth.

Adaptive data fusion framework for modeling of non-uniform aerodynamic data

Multi-fidelity Data Fusion(MDF)frameworks have emerged as a prominent approach to producing economical but accurate surrogate models for aerodynamic data modeling by integrating data with different fidelity levels.However,most existing MDF frameworks assume a uniform data structure between sampling data sources;thus,producing an accurate solution at the required level,for cases of non-uniform data structures is challenging.To address this challenge,an Adaptive Multi-fidelity Data Fusion(AMDF)framework is proposed to produce a composite surrogate model which can efficiently model multi-fidelity data featuring non-uniform structures.Firstly,the design space of the input data with non-uniform data structures is decomposed into subdomains containing simplified structures.Secondly,different MDF frameworks and a rule-based selection process are adopted to construct multiple local models for the subdomain data.On the other hand,the Enhanced Local Fidelity Modeling(ELFM)method is proposed to combine the generated local models into a unique and continuous global model.Finally,the resulting model inherits the features of local models and approximates a complete database for the whole design space.The validation of the proposed framework is performed to demonstrate its approximation capabilities in(A)four multi-dimensional analytical problems and(B)a practical engineering case study of constructing an F16C fighter aircraft’s aerodynamic database.Accuracy comparisons of the generated models using the proposed AMDF framework and conventional MDF approaches using a single global modeling algorithm are performed to reveal the adaptability of the proposed approach for fusing multi-fidelity data featuring non-uniform structures.Indeed,the results indicated that the proposed framework outperforms the state-of-the-art MDF approach in the cases of non-uniform data.

Downwash modelling for three-lifting-surface aircraft configuration design

This paper introduces a semi-empirical model to predict the downwash gradient at the horizontal tail of a three-lifting-surface aircraft.The superposition principle applied to well established formulations valid for two lifting surfaces is not a reasonable approach to calculate the downwash of a canard-wing-tail layout,and this paper demonstrates that such a basic technique leads to incorrect results.Therefore,an ad hoc prediction model is proposed that considers the combined nonlinear effects of canard and main wing inductions on tail downwash,being based on a full factorial design sweep of CFD simulations obtained by varying the main geometrical parameters of the three lifting surfaces.A suitable analytical formula for the downwash gradient is established through a process of data analysis and factor extraction.The presented model extends the validity of the available models for traditional two-lifting-surface designs by means of a correction factor.The engineering estimation method introduced here exhibits an acceptable accuracy,as well as relatively small prediction errors,and it is suitable for conceptual and preliminary studies of threesurface layouts.The value of this methodology is confirmed by the validation with the results of numerical and experimental investigations on a case study aircraft.

Unstable unsteady aerodynamic modeling based on least squares support vector machines with general excitation

Common,unsteady aerodynamic modeling methods usually use wind tunnel test data from forced vibration tests to predict stable hysteresis loop.However,these methods ignore the initial unstable process of entering the hysteresis loop that exists in the actual maneuvering process of the aircraft.Here,an excitation input suitable for nonlinear system identification is introduced to model unsteady aerodynamic forces with any motion in the amplitude and frequency ranges based on the Least Squares Support Vector Machines(LS-SVMs).In the selection of the input form,avoiding the use of reduced frequency as a parameter makes the model more universal.After model training is completed,the method is applied to predict the lift coefficient,drag coefficient and pitching moment coefficient of the RAE2822 airfoil,in sine and sweep motions under the conditions of plunging and pitching at Mach number 0.8.The predicted results of the initial unstable process and the final stable process are in close agreement with the Computational Fluid Dynamics(CFD)data,demonstrating the feasibility of the model for nonlinear unsteady aerodynamics modeling and the effectiveness of the input design approach.

Unsteady aerodynamic modeling at high angles of attack using support vector machines

Abstract Accurate aerodynamic models are the basis of flight simulation and control law design. Mathematically modeling unsteady aerodynamics at high angles of attack bears great difficulties in model structure determination and parameter estimation due to little understanding of the flow mechanism. Support vector machines （SVMs） based on statistical learning theory provide a novel tool for nonlinear system modeling. The work presented here examines the feasibility of applying SVMs to high angle.-of-attack unsteady aerodynamic modeling field. Mainly, after a review of SVMs, several issues associated with unsteady aerodynamic modeling by use of SVMs are discussed in detail, such as sele, ction of input variables, selection of output variables and determination of SVM parameters. The least squares SVM （LS-SVM） models are set up from certain dynamic wind tunnel test data of a delta wing and an aircraft configuration, and then used to predict the aerodynamic responses in other tests. The predictions are in good agreement with the test data, which indicates the satisfving learning and generalization performance of LS-SVMs.

Aerodynamic Modeling and Parameter Estimation from QAR Data of an Airplane Approaching a High-altitude Airport

Aerodynamic modeling and parameter estimation from quick accesses recorder （QAR） data is an important technical way to analyze the effects of highland weather conditions upon aerodynamic characteristics of airplane. It is also an essential content of flight accident analysis. The related techniques are developed in the present paper, including the geometric method for angle of attack and sideslip angle estimation, the extended Kalman filter associated with modified Bryson-Frazier smoother （EKF-MBF） method for aerodynamic coefficient identification, the radial basis function （RBF） neural network method for aerodynamic mod- eling, and the Delta method for stability/control derivative estimation. As an application example, the QAR data of a civil air- plane approaching a high-altitude airport are processed and the aerodynamic coefficient and derivative estimates are obtained. The estimation results are reasonable, which shows that the developed techniques are feasible. The causes for the distribution of aerodynamic derivative estimates are analyzed. Accordingly, several measures to improve estimation accuracy are put forward.

High-speed wind tunnel test of the CAE aerodynamic validation model

For the purpose of establishing and validating aerodynamic performance predictions at transonic Mach numbers, a wind tunnel test was conducted in the High-Speed Tunnel（HST） of the German-Dutch Wind Tunnels. The test article is the aerodynamic validation model from the Chinese Aeronautical Establishment, which is a full-span scale model representation of a business jet aircraft. The wind tunnel test comprised of parallel deployments of balance, pressures, infrared thermography, and model marker measurement techniques. Dedicated investigations with a dummy support were conducted as well, in order to derive and correct for the interference that the support system imposed on the overall model loads. This enabled the establishment of a comprehensive dataset in which the steady overall model loads, the wing load distribution, the state of the wing boundary layer, and the aeroelastic wing shape were quantified for conditions up to and beyond the cruise Mach number of 0.85.

Aerodynamicmodeling using an end-to-end learning attitude dynamics network for flight control

A novel identification method of aerodynamicmodels using a physics neural network,named the attitude dynamics network,which incorporates the attitude dynamics of an aircraft without any prior aerodynamic knowledge,is proposed.Then a learning controller,which combines feedback linearization with sliding mode control,is developed by introducing the learned aerodynamicmodels.The merit of the identification method is that the aerodynamicmodels can be learned end-to-end by the physics network directly from the flight data.Consequently,the paper uses an offline scheme and an online scheme to combine the identification process and the control process.In the offline scheme,learning the aerodynamic models and controlling the aircraft compose a cascade system,whereas the online scheme,similar to Learn-to-Fly,is a parallel system.Specifically,in the offline scheme,the physics neural network is trained by sufficient offline flight data,and then the trained network is substituted into the controller.The online scheme refers to the controller making the aircraft fly to generate flight data and sending these data to the deep network at the time of training,while the deep network provides the trained aerodynamic models to the controller at other times.Simulation results show that both under nominal and disturbance aerodynamic conditions,the network trained offline with a large amount of nominal data approximate the aerodynamicmodels well.Thus,the performance of the controller reaches a good level;for the online scheme,the predictive capability of the network increases and the performance of the controller improves with more training data.

Dynamic Models of Heating and Cooling Coils with One-Dimensional Air Distribution

This paper presents the simulation models of the plate-fin, air-to-water (or water vapour) heat exchangers used as air-heating or air-cooling and dehumidifying coils in the HVAC (Heating, Ventilation and Air-Conditioning) systems. The thermal models are used to calculate the heat exchange between distributing air and coil pipes and outlet temperatures of air and heat or chilled fluid. The aerodynamic models are used to account for the pressure drop of the air crossing the coil tubes. They can also be used to optimize the structures of such coils. The models are based on principal laws of heat and mass conservation and fluid mechanics. They are transparent and easy to use. In our work, a coil is considered as an assembly of numbers of basic elements in which all the state variables are unique. Therefore we can conveniently simulate the coils with different structures and different geometric parameters. Two modular programs TRNSYS (Transient System Simulation) and ESACAP are utilized as supporting softwares which make the programming and simulation greatly simplified. The coil elements and a real coil were simulated. The results were compared with the data offered by the manufacturer (company SOFICA) and also with those obtained using critical methods such as NTU method, etc. and good agreement is attained.

High-dimensional aerodynamic data modeling using a machine learning method based on a convolutional neural network

Modeling high-dimensional aerodynamic data presents a significant challenge in aero-loads prediction, aerodynamic shape optimization, flight control, and simulation. This article develops a machine learning approach based on a convolutional neural network (CNN) to address this problem. A CNN can implicitly distill features underlying the data. The number of parameters to be trained can be significantly reduced because of its local connectivity and parameter-sharing properties, which is favorable for solving high-dimensional problems in which the training cost can be prohibitive. A hypersonic wing similar to the Sanger aerospace plane carrier wing is employed as the test case to demonstrate the CNN-based modeling method. First, the wing is parameterized by the free-form deformation method, and 109 variables incorporating flight status and aerodynamic shape variables are defined as model input. Second, more than 7000 sample points generated by the Latin hypercube sampling method are evaluated by performing computational fluid dynamics simulations using a Reynolds-averaged Navier-Stokes flow solver to obtain an aerodynamic database, and a CNN model is built based on the observed data. Finally, the well-trained CNN model considering both flight status and shape variables is applied to aerodynamic shape optimization to demonstrate its capability to achieve fast optimization at multiple flight statuses.

Self-contained eigenvector algorithm applied to the identification of aerodynamic derivatives of bridge model

On one hand, when the bridge stays in a windy environment, the aerodynamic power would reduce it to act as a non-classic system. Consequently, the transposition of the system’s right eigenmatrix will not equal its left eigenmatrix any longer. On the other hand, eigenmatrix plays an important role in model identification, which is the basis of the identification of aerodynamic derivatives. In this study, we follow Scanlan’s simple bridge model and utilize the information provided by the left and right eigenmatrixes to structure a self-contained eigenvector algorithm in the frequency domain. For the purpose of fitting more accurate transfer function, the study adopts the combined sine-wave stimulation method in the numerical simulation. And from the simulation results, we can conclude that the derivatives identified by the self-contained eigenvector algorithm are more dependable.

Numerical Method for Evaluating Aircraft's Stability Parameters through an Aerodynamic Model

A numerical method is developed to evaluate the dynamic stability parameters of aircraft. This method is based on the aerodynamic model proposed by Etkin. His model is analyzed and generalized. After giving the specific forms of the aerodynamic model, the dynamic stability parameters are determined by the unsteady flow field computation and a parameter identification technique. Numerical experiments show that this method is accurate in predicting the dynamic stability characteristics of blunt cones in hypersonic flight.