Nonlinearity Characterization for Nonlinear Dynamic System Identification Using an Expert Approach

The identification of nonlinear dynamic systems can be rendered significantly more parsimonious if the nonlinearity present in the system is known. While there are many successful non-parametric nonlinear system identification methods, the resulting models do not describe the nonlinearity in physical terms and are difficult to obtain due to the large number of candidate terms that must be examined. In this paper an expert approach towards the characterization of nonlinearities in a dynamic system is presented. The methodology is based on simulations of dynamic systems with a variety of commonly occurring nonlinear functions. The responses of such systems to various types of excitation are analysed and rules are developed as to what nonlinearity is likely to be present in a system given the dynamic characteristics of measured responses

An Expert System for the Identification of Nonlinear Dynamical Systems

peer reviewedThis paper describes an Expert System that can detect and quantify the nonlinearity present in a given dynamical system and, subsequently, determine and apply the most suitable nonlinear system identification method. The internal workings, algorithms and decision making processes of the Expert System are discussed. For demonstration purposes the Expert System is applied to a nonlinear experimental test-rig. The results show that the Expert System is an automatic tool that will detect nonlinearity, choose the best class of model for the system under investigation and perform optimal parameter estimation, so that the resulting identified models are parsimonious and accurate

Development of An Expert System for the Identification of Nonlinear Vibrating Systems

peer reviewedThe aim of the present work is to attempt to create a logical framework to be used for the identification of nonlinear systems. It is assumed that no single identification method is general enough to work with a significant range of systems. Therefore, this framework is based on the development of an Expert System that will detect and quantify the nonlinearity present in a given dynamical system and, subsequently, determine and apply the most suitable nonlinear system identification method or methods

On the solution of the aeroelastic galloping problem

A global stability analysis of the transverse galloping of a square section beam in a normal steady ow was performed. The analysis was applied to a mathematical model using experimentally measured stationary aerodynamic forces. The system was modelled as an ordinary differential equation with small non-linearity in the velocity term. Three methods are used for the stability analysis: 1. a harmonic balance approach, 2. normal form theory, 3. cell mapping. The resulting stability predictions were compared with each other and with results obtained from numerical integration. It is shown that the hysteretic stability of the non-linear aeroelastic oscillator was captured by all the methods. Additionally, the methods had a varying degree of success in predicting the amplitude of limit cycle oscillations undergone by the aeroelastic oscillator

Limit Cycle Prediction For Subsonic Aeroelastic Systems Using Nonlinear System Identification

peer reviewedThe prediction of aeroelastic instabilities caused by nonlinear unsteady aerodynamic forces acting on aircraft has recently become an important area of research. Emphasis is placed on the capability to predict the occurrence of Limit Cycle Oscillations (LCOs) at both the design and prototype testing stages. In this paper, the prediction of LCOs is attempted for a simulated aeroelastic system subjected to nonlinear subsonic unsteady aerodynamic forces, using system identification. Response data from the simulated system are curve-fitted by means of a series of polynomial basis functions. This approach yields very accurate identified models of the actual system at individual flight conditions. These identified models are extrapolated to a global aeroelastic identified model. Using this model, the flight conditions at which LCOs occur is accurately predicted but the amplitude of the oscillations is underestimated

Stability and Limit Cycle Oscillation Amplitude Prediction for Multi-DOF Aeroelastic Systems with Piecewise Linear Non-Linearities

Discontinuous non-linearities such as freeplay and bilinear stiffness are often encountered in aeroelastic systems, sometimes as a result of wear and tear. It is important to predict the effect of such non-linearities on the dynamic behaviour of a system, so that adequate safety guidelines can be drafted. As a consequence, the prediction of the bifurcation behaviour of a system featuring a discontinuous nonlinearity is crucial. Additionally, the post-bifurcation behaviour of the system is also of interest since it may consist of relatively harmless Limit Cycle Oscillations (LCO) of low amplitude or of unexpected catastrophic high amplitude LCOs. In this paper the bifurcation and post-bifurcation behaviour of a simulated Multi-DOF aeroelastic system with bilinear and freeplay nonlinearities are investigated using the Harmonic Balance method and a novel method for the prediction of the bifurcation conditions and LCO amplitudes. The method is based on the fact that the nonlinearities investigated are piecewise linear. The ratios of the real parts of the system eigenvalues in the various ranges of the bilinear spring are used in order to infer LCO amplitude information. By means of a demonstration on a simulated aeroelastic system with piece-wise linear stiffness, it is shown that the proposed approach is successful in yielding the full bifurcation and post-bifurcation behaviour of the system. Comparison of the amplitude predictions obtained from the Harmonic Balance technique and the Piecewise Linearisation proposed approach show that the latter are more consistent and closer to the true amplitudes throughout the airspeed range. The bifurcation analysis is extended to the special case where the inner stiffness of the bilinear spring is equal to zero, i.e. freeplay stiffness. It is shown that the Piecewise Linear analysis fails to capture the bifurcation behaviour for this case, while the Harmonic Balance method still produces some accurate predictions

Stability and LCO Amplitude Prediction for Aeroelastic Systems with Aerodynamic and Structural Nonlinearities Using Numerical Continuation

This paper deals with the prediction of stability boundaries and Limit Cycle Oscillation amplitudes for aeroelastic systems with nonlinear unsteady aerodynamic loads and/or nonlinearity in the structure. The Numerical Continuation method is used to accurately predict bifurcation conditions and LCO amplitudes for aeroelastic systems with various types of nonlinearity without the need for extensive CFD calculations. It is shown that it is possible to completely characterise the stability of systems undergoing subcritical and supercritical bifurcations. The method is applied to a pitch-plunge airfoil subjected to transonic aerodynamics and freeplay structural nonlinearity. The results from this analysis are compared to those obtained from full numerical simulation to ensure their accuracy

Improved Implementation of the Harmonic Balance Method

Harmonic Balance (HB) methods have been applied to non-linear aeroelastic problems since the 1980s. As the computational power available to researchers has increased, so has the order of calculated HB solutions. However, the computational cost of a HB solution increases with the square of the order. Additionally, the traditional Newton-Raphson, Broyden, Toeplitz Jacobian and other techniques used for the solution of the non-linear algebraic problem at the heart of the HB methodology rely on a good initial guess for the unknown coefficients. If there are many such coefficients the probability that a good guess will be available is very low and the HB scheme may well fail. In this paper a search procedure using Genetic Algorithms (GA) is introduced to evaluate the coefficients of a harmonic balance solution. It is shown that the GA can provide high quality initial guesses for the HB coefficients. The method is applied to an aeroelastic galloping-type problem

Stability and Limit Cycle Oscillation Amplitude Prediction for Simple Nonlinear Aeroelastic Systems

The prediction of the bifurcation and post-bifurcation behaviour of nonlinear aeroelastic systems is becoming a major area of research in the aeroelastic community due to the need for improved transonic aeroelastic prediction, the use of non-linear control systems, and new construction techniques that reduce the amount of inherent damping. In this paper, a novel application of the Centre Manifold Theorem is used to accurately predict bifurcation conditions and Limit Cycle Oscillation amplitudes for simple aeroelastic systems with various types of nonlinearity. A simple aeroelastic system with hardening cubic stiffness nonlinearity is considered and is demonstrated to display a wide variety of bifurcation phenomena. These make it dif cult for some of the standard existing methods, such as Normal Form, Cell Mapping and Tangential Linearisation, to quantify the Limit Cycle Oscillation amplitudes through the entire speed range of the system. Then, the proposed approach is introduced and applied to the same system. It is shown that it can accurately predict the limit cycle amplitudes of the system undergoing all types of bifurcation. Finally, the new technique is applied to the same system but with softening cubic stiffness nonlinearity. It is shown that the method can accurately predict both the static and dynamic divergence boundaries and that it can be used to draw a worst-case stability boundary, inside which the solution is always stable

Bifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem

A global stability and bifurcation analysis of the transverse galloping of a square section beam in a normal steady flow has been implemented. The model is an ordinary differential equation with polynomial damping nonlinearity. Six methods are used to predict bifurcation, the amplitudes and periods of the ensuing Limit Cycle Oscillations: (i) Cell mapping, {ii} Harmonic Balance, (iii) Higher Order Harmonic Balance,(iv) Centre Manifold linearization, (v) Normal Form and (vi) Numerical Continuation. The resulting stability predictions are compared with each other and with results obtained from numerical integration. The advantages and disadvantages of each technique are discussed. It is shown that, despite the simplicity of the system, only two of the methods succeed in predicting its full response spectrum. These are Higher Order Harmonic Balance and Numerical Continuation