Polynomial Nonlinear State Space Identification of an Aero-Engine Structure

Most nonlinear identification problems often require prior knowledge or an initial assumption of the mathematical law (model structure) and data processing to estimate the nonlinear parameters present in a system, i.e. they require the functional form or depend on a proposition that the measured data obey a certain nonlinear function. However, obtaining prior knowledge or performing nonlinear characterisation can be difficult or impossible for certain identification problems due to the individualistic nature of practical nonlinearities. For example, joints between substructures of large aerospace design frequently feature complex physics at local regions of the structure, making a physically motivated identification in terms of nonlinear stiffness and damping impossible. As a result, black-box models which use no prior knowledge can be regarded as an effective method. This paper explores the pragmatism of a black-box approach based on Polynomial Nonlinear State Space (PNLSS) models to identify the nonlinear dynamics observed in a large aerospace component. As a first step, the Best Linear Approximation (BLA), noise and nonlinear distortion levels are estimated over different amplitudes of excitation using the Local Polynomial Method (LPM). Next, a linear state space model is estimated on the non-parametric BLA using the frequency domain subspace identification method. Nonlinear model terms are then constructed in the form of multivariate polynomials in the state variables while the parameters are estimated through a nonlinear optimisation routine. Further analyses were also conducted to determine the most suitable monomial degree and type required for the nonlinear identification procedure. Practical application is carried out on an Aero-Engine casing assembly with multiple joints, while model estimation and validation is achieved using measured sine-sweep and broadband data obtained from the experimental campaign

Impact hammer-based analysis of nonlinear effects in bolted lap joint

This work presents an experimental investigation into the dynamic behavior of a bolted joint beam configuration. The impact hammer is chosen as an alternative to classical harmonic excitation methods. The structural responses are explored for a range of the joint tightening toques and various levels of impulse hammer excitations. A symmetric beam assembly made of two nominally identical steel beams is studied. Symmetric modes are found to be sensitive to the test parameters. For given torque, impact-based varying joint loading conditions are used to induce the nonlinear joint effects. A linear data processing strategy is used to observe the nonlinear behavior indirectly. The dynamic joint behavior is described in the form of the modal frequency-damping ratio performance maps represented by the two-parametric approximating quadratic response surface models. This model maps the joint conditions on the corresponding dynamic characteristics of interest and it will serve as a basis for the parametric linear joint model developmen

Parameter subset selection based damage detection of aluminium frame structure

Abstract: A three storey aluminium frame structure was tested in multiple damage cases. All damage scenarios, simulated by the localized stiffness changes, were associated with joint areas of the structure. Further, between damage tests the structure was returned to its healthy reference conditions and was again measured. In this paper, a parameter subset selection methodology is applied to an updated finite element model of the structure, together with a previously demonstrated approach employing concepts of model sensitivity subspace angles, first order model representation and mixed response residuals for damage detection. The objective of this paper is the evaluation of these methods on a real experimental structure with significant complexity, represented by an imprecise reference mathematical model and in the environment with uncertain reference structural state. The questions of symmetry, mixed response residuals and semi-localized parameterization are also addressed in this work. Introduction Vibration-based damage detection has potential to form a part of integrated health monitoring subsystems in spatially extended mechanical systems. A useful feature of this approach is its global nature to detect changes in the composition and distribution of three basic structural properties; mass, damping and stiffness; and the effect of their changes on measurable and identifiable dynamic properties such as modal properties. Changes in the modal properties are attributable to the changes in basic structural properties, such as stiffness, or specific damage event in the mechanical system. The two major problems associated with this approach are: (i) limited quality, quantity, autonomy (e.g. unknown system inputs) and relevancy (e.g. sensitivity of the observed modal information) of the measured data, and (ii) linearity assumptions inherent in this method. Recent developments in measurement and identification techniques address many experimental aspects of these problems. Questions of relevancy are still being studied and are partially addressed in this paper. Ultimately, structural damage is mostly associated with nonlinear modes of operation, such as cracks, friction, etc. However, the use of "small vibrations" allows the use of the above-mentioned methodology even in these situations. In the current study the choices are made such that potential nonlinearities may affect detection and intermediate results. The concept of parameter subset selection was originally applied in the context of model updating in [2] used subset selection for damage detection and location. Titurus et al. The objective of this paper is to evaluate parameter subset selection ideas in vibration-based damage detection in the realistic context of medium complexity. The structure of choice is a

Novel frame model for mistuning analysis of bladed disc systems

The work investigates the application of a novel frame model to reduce the computational cost of the mistuning analysis of bladed disc systems. A full-scale finite element (FE) model of the bladed disc is considered as benchmark. The single blade frame configuration is identified via an optimization process. The individual blades are then assembled by 3D springs, whose parameters are determined via calibration process. The dynamics of the novel beam frame assembly is also compared to those obtained from three state-of-the-art FE-based reduced order models (ROMs): a lumped parameter approach; a Timoshenko beam assembly, and component mode synthesis (CMS) based techniques with free and fixed interfaces. The development of these classical ROMs to represent the bladed disc is also addressed in detail. A methodology to perform the mistuning analysis is then proposed and implemented. A comparison of the modal properties and forced response dynamics between the aforementioned ROMs and the full-scale FE model is presented. The case study demonstrates that the beam frame assembly can predict the variations of the blade amplitude factors with results being in agreement with the full-scale FE model. The CMS based ROMs underestimate the maximum amplitude factor, while the results obtained from beam frame assembly are generally conservative. The beam frame assembly is 4 times more computationally efficient than the CMS fixed-interface approach. This study proves that the beam frame assembly can efficiently predict the mistuning behavior of bladed discs when low order modes are of interest