Model correlation and damage location for large space truss structures: Secant method development and evaluation

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated

Use of system identification techniques for improving airframe finite element models using test data

A method for using system identification techniques to improve airframe finite element models using test data was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory

Theoretical and Software Considerations for General Dynamic Analysis Using Multilevel Substructured Models

An approach is presented for the dynamic analysis of complex structure sy~t'=!!!S using the finite element method and multilevel substructured models. The fixedinterface method is selected for substructure reduction because of its efficiency, accurac and adaptability to restart and reanalysis. This method is extended to reduction of substructures which are themselves composed of reduced substructures. Emphasis is placed on the implementation and performance of the method in a general purpose software system. Solution algorithms consistent with the chosen data structures are presented in detail. This study demonstrates that successful finite element software requires the use of software executives to supplement the algorithmic language. As modeling and analysis techniques become more complex, proportionally more implementation effort is spent on data and computer resource management. Executive systems are essential tools for these tasks. The complexity of the implementation of restart and reanalysis porcedures also illustrate the need for executive systems to support the non computational aspects of the software. The example problems show that significant computational efficiencies can be achieved through proper use of substructuring and reduction techniques without sacrificing solution accuracy. The unique restart and reanalysis capabilities developed in this study and the flexible procedures for multilevel substructured modeling allow analysts to achieve economical yet accurate analyses of complex structural systems

Model updating of modal parameters from experimental data and applications in aerospace

The research in this thesis is associated with different aspects of experimental analyses of structural dynamic systems and the correction of the corresponding mathematical models using the results of experimental investigations as a reference. A comprehensive finite-element model updating software technology is assembled and various novel features are implemented. The software technology is integrated into an experimental test facility for structural dynamic identification and used in a number of real life aerospace applications which illustrate the advantages of the new features. To improve the quality of the experimental reference data a novel non-iterative method for the computation of optimised multi-point excitation force vectors for Phase Resonance Testing is introduced. The method is unique in that it is based entirely on experimental data, allows to determine both the locations and force components resulting in the highest phase purity, and enable to predict the corresponding mode indicator. A minimisation criterion for the real-part response of the test structure with respect to the total response is utilised and, unlike with the application of other methods, no further information such as a mass matrix from a finite-element model or assumptions on the structure's damping characteristics is required. Performance in comparison to existing methods is assessed in a numerical study using an analytical eleven-degrees-of-freedom model. Successful applications to a simple laboratory satellite structure and under realistic test conditions during the Ground Vibration Test on the European Space Agency's Polar Platform are described. Considerable improvements are achieved with respect to the phase purity of the identified mode shapes as compared to other methods or manual tuning strategies as well as the time and effort involved in the application during Ground Vibration Testing. Various aspects regarding the application of iterative model updating methods to aerospace-related test structures and live experimental data are discussed. A new iterative correction parameter selection technique enabling to create a physically correct updated analytical model and a novel approach for the correction of structural components with viscous material properties are proposed. A finite-element model of the GARTEUR SM-AG19 laboratory test structure is updated using experimental modal data from a Ground Vibration Test. In order to assess the accuracy and physical consistency of the updated model a novel approach is applied where only a fraction of the mode shapes and natural frequencies from the experimental data base is used in the model correction process and analytical and experimental modal data beyond the range utilised for updating are correlated. To evaluate the influence of experimental errors on the accuracy of finite-element model corrections a numerical simulation procedure is developed. The effects of measurement uncertainties on the substructure correction factors, natural frequency deviations, and mode shape correlation are investigated using simulated experimental modal data. Various numerical models are generated to study the effects of modelling error magnitudes and locations. As a result, the correction parameter uncertainty increases with the magnitude of the experimental errors and decreases with the number of modes involved in the updating process. Frequency errors, however, since they are not averaged during updating, must be measured with an adequately high precision. Next, the updating procedure is applied to an authentic industrial aerospace structure. The finite-element model of the EC 135 helicopter is utilised and a novel technique for the parameterisation of substructures with non-isotropic material properties is suggested. Experimental modal parameters are extracted from frequency responses recorded during a Shake Test on the EC 135-S01 prototype. In this test case, the correction process involves the handling of a high degree of modal and spatial incompleteness in the experimental reference data. Accordingly, new effective strategies for the selection of updating parameters are developed which are both physically significant and likewise have a sufficient sensitivity with respect to the analytical modal parameters. Finally, possible advantages of model updating in association with a model-based method for the identification and localisation of structural damage are investigated. A new technique for identifying and locating delamination damages in carbon fibre reinforced polymers is introduced. The method is based on a correlation of damage-induced modal damping variations from an elasto-mechanic structure to the corresponding data from a numerical model in order to derive information on the damage location. Using a numerical model enables the location of damages in a three-dimensional structure from experimental data obtained with only a single response sensor. To acquire sufficiently accurate experimental data a novel criterion for the determination of most appropriate actuator and sensor positions and a polynomial curve fitting technique are suggested. It will be shown that in order to achieve a good location precision the numerical model must retain a high degree of accuracy and physical consistency

Convex Relaxations for Graph and Inverse Eigenvalue Problems

This thesis is concerned with presenting convex optimization based tractable solutions for three fundamental problems: 1. Planted subgraph problem: Given two graphs, identifying the subset of vertices of the larger graph corresponding to the smaller one. 2. Graph edit distance problem: Given two graphs, calculating the number of edge/vertex additions and deletions required to transform one graph into the other. 3. Affine inverse eigenvalue problem: Given a subspace ε ⊂ &#x1D54A;ⁿ and a vector of eigenvalues λ ∈ ℝⁿ, finding a symmetric matrix with spectrum λ contained in ε. These combinatorial and algebraic problems frequently arise in various application domains such as social networks, computational biology, chemoinformatics, and control theory. Nevertheless, exactly solving them in practice is only possible for very small instances due to their complexity. For each of these problems, we introduce convex relaxations which succeed in providing exact or approximate solutions in a computationally tractable manner. Our relaxations for the two graph problems are based on convex graph invariants, which are functions of graphs that do not depend on a particular labeling. One of these convex relaxations, coined the Schur-Horn orbitope, corresponds to the convex hull of all matrices with a given spectrum, and plays a prominent role in this thesis. Specifically, we utilize relaxations based on the Schur-Horn orbitope in the context of the planted subgraph problem and the graph edit distance problem. For both of these problems, we identify conditions under which the Schur-Horn orbitope based relaxations exactly solve the corresponding problem with overwhelming probability. Specifically, we demonstrate that these relaxations turn out to be particularly effective when the underlying graph has a spectrum comprised of few distinct eigenvalues with high multiplicities. In addition to relaxations based on the Schur-Horn orbitope, we also consider outer-approximations based on other convex graph invariants such as the stability number and the maximum-cut value for the graph edit distance problem. On the other hand, for the inverse eigenvalue problem, we investigate two relaxations arising from a sum of squares hierarchy. These relaxations have different approximation qualities, and accordingly induce different computational costs. We utilize our framework to generate solutions for, or certify unsolvability of the underlying inverse eigenvalue problem. We particularly emphasize the computational aspect of our relaxations throughout this thesis. We corroborate the utility of our methods with various numerical experiments.</p

Dynamics, identification and control of multibody systems

2010 - 2011The central goal of this work is to put in an unified framework Dynamics, Identification and Control of multibody systems. A multibody system is a mechanical system constituted of interconnected rigid and deformable components which can undergo large translational and rotational displacements. The description of the motion of multibody systems is the leitmotif of Multibody Dynamics. On the other hand, System Identification is the art of determining a mathematical model of a physical system by combining information obtained from experimental data with that derived from an a priori knowledge. In addition, the System Identification methods can be successfully employed to refine a multibody model obtained from fundamental principles of Dynamics by using experimental data. In particular, applied System Identification methods allows to get modal parameters of a dynamical system using force and vibration measurements. On the other hand, the raison d’etre of Control Theory is to study how to design a control system which can influence the dynamic of a mechanical system in order to make it behave in a desirable manner. Consequently, it is intuitive to understand that these three seemingly unconnected subjects (Multibody Dynamics, System Identification, Control Theory) are actually strongly linked together. Therefore, the study of one of these subjects cannot be separated from the study of the other two. The structure of this works represents an attempt to encompass the essence of Multibody Dynamics, System Identification and Control Theory. [edited by author]X n.s

Identification of structural parameters and hydrodynamic effects for forced and free vibration

Statistically-based estimation techniques are presented in this study. These techniques incorporate structural test data to improve finite element models used for dynamic analysis. Methods are developed to identify optimum values of the parameters of finite element models describing structures. The parameters which may be identified are : element area, mass density, and moment of inertia; lumped mass and stiffness; and the Rayleigh damping coefficients. A technique is described for incorporating hydrodynamic effects on small bodies by identifying equivalent structure mass, stiffness, and damping properties. Procedures are presented for both the free vibration problem and for forced response in the time domain. The equations for parameter identification are formulated in terms of measured response, calculated response, the prior estimate of the parameters, and a weighting matrix. The form of the weighting matrix is presented for three identification schemes : Least Squares, Weighted Least Squares, and Bayesian. The weighting matrix is shown to be a function of a sensitivity matrix relating structural response to the parameters of the finite element model. Sensitivities for the forced vibration problem are derived from the Wilson Theta equations, and are presented for the free vibration problem. The algorithm used for parameter identification is presented, and its implementation in a computer program is described. Numerical examples are included to demonstrate the solution technique and the validity and capability of the identification method. All three estimation schemes are found to provide efficient and reliable parameter identification for many modeling situations