Working group 3- Identification of non-linear systems

in Mechanical Systems & Signal Processing (2003), 17(1), 177-178

Researchers in structural dynamics have long recognised the importance of diagnosing and modelling non-linearity. The last 20 years have witnessed a shift in emphasis from single degree-of-freedom (sdof ... [more ▼]

Researchers in structural dynamics have long recognised the importance of diagnosing and modelling non-linearity. The last 20 years have witnessed a shift in emphasis from single degree-of-freedom (sdof) to multi-degree-of-freedom (mdof) non-linear structural dynamics. The main feature of the program of COST F3 Working Group 3 was to identify the behaviour of a structure which exhibits a localised non-linear component. Inside this working group, two benchmarks were defined and studied intensively, thereby allowing to evaluate different identification methods and compare their efficiency and specificity. For this purpose, a large amount of data (time and frequency measurements) was collected and proposed to COST F3 participants. The two benchmarks that are described in the following are: * The VTT benchmark proposed by M. Juntunen from the VTT Technical Research of Finland; * The ECL benchmark proposed by F. Thouverez from the Ecole Centrale de Lyon (France). The VTT benchmark is essentially one-dimensional but with a type of non-linearity that is not known a priori. This is different from the ECL benchmark designed to implement a cubic stiffness hardening but which address mdof systems. The ECL benchmark was challenging in the sense that the considered structure is continuous and that several modes participate in the response. *Supported by a grant from the Belgian National Fund for Scientific Research. # 2003 Elsevier Science Ltd. All rights reserved. [less ▲]

On the exploitation of chaos to build reduced-order models

in Computer Methods in Applied Mechanics & Engineering (2003), 192(13-14), 1785-1795

The present study focuses on the model reduction of non-linear systems. The proper orthogonal decomposition is exploited to compute eigenmodes from time series of displacement. These eigenmodes, called ... [more ▼]

The present study focuses on the model reduction of non-linear systems. The proper orthogonal decomposition is exploited to compute eigenmodes from time series of displacement. These eigenmodes, called the proper orthogonal modes, are optimal with respect to energy content and are used to build a low-dimensional model of the non-linear system. For this purpose, the proper orthogonal modes obtained from a chaotic orbit are considered. Indeed, such an orbit is assumed to cover a portion of the phase space of higher dimension, and hence of greater measure. This higher dimensional data is further assumed to contain more information about the system dynamics than data of a lower-dimensional periodic orbit. In an example, it is shown that the modes for this particular behaviour are more representative of the system dynamics than any other set of modes extracted from a non-chaotic response. This is applied to a buckled beam with two permanent magnets and the reduced-order model is validated using both qualitative and quantitative comparisons. (C) 2003 Elsevier Science B.V. All rights reserved. [less ▲]

Auto-associative neural networks, Part II: Feacture extraction for non-linear model updating

in 8th Internationale Conference on Recent Advances in Structural Dynamics, Southampton, 2003 (2003)

Auto-associantive neural networks, Part I: Replacement of missing sensor values,

in 8th Internationale Conference on Recent Advances in Structural Dynamics, Southampton, 2003 (2003)

"European Cost action F3 on structural dynamics. WG3: identification of non-linear systems.Activities and Results"

in International Conference on Noise and Vibration Engineering, Leuven, 2002 (2002, September)

Non-linear generalization of principal component analysis: From a global to a local approach

in Journal of Sound & Vibration (2002), 254(5), 867-876

Principal component analysis (PCA), also known as proper orthogonal decomposition or Karhunen-Loeve transform, is commonly used to reduce the dimensionality of a data set with a large number of ... [more ▼]

Principal component analysis (PCA), also known as proper orthogonal decomposition or Karhunen-Loeve transform, is commonly used to reduce the dimensionality of a data set with a large number of interdependent variables. PCA is the optimal linear transformation with respect to minimizing the mean square reconstruction error but it only considers second-order statistics. If the data have non-linear dependencies, an important issue is to develop a technique which takes higher order statistics into account and which can eliminate dependencies not removed by PCA. Recognizing the shortcomings of PCA, researchers in the field of statistics and neural networks have developed non-linear extensions of PCA. The purpose of this paper is to present a non-linear generalization of PCA, called VQPCA. This algorithm builds local linear models by combining PCA with clustering of the input space. This paper concludes by observing from two illustrative examples that VQPCA is potentially a more effective tool than conventional PCA. (C) 2002 Elsevier Science Ltd. All rights reserved. [less ▲]

Frequency domain approaches for the identification of an experimental beam with a local nonlinearity

in 20th International Modal Analysis Conference, Los Angeles, 2002 (2002, February)

Two approaches for the identification of multi-degree-of-freedom non-linear systems in the frequency domain have recently been introduced, i.e., the conditioned reverse path (CRP) method and the non ... [more ▼]

Two approaches for the identification of multi-degree-of-freedom non-linear systems in the frequency domain have recently been introduced, i.e., the conditioned reverse path (CRP) method and the non-linear identification through feedback of the outputs (NIFO) method. The key idea of these methods is to eliminate the distortions caused by the presence of non-linearities in frequency response functions. In this paper, the theoretical background of the CRP and NIFO methods is briefly recalled. Then, the ability of these techniques to identify the behaviour of an experimental cantilever beam with a local geometrical non-linearity is tested. The results obtained with both methods are compared and discussed. [less ▲]

A frequency domain versus a time domain identification technique for nonlinear parameters applied to wire rope isolators

in Journal of Dynamic Systems Measurement and Control-Transactions of the Asme (2001), 123(4), 645-650

The present paper aims to compare two techniques for identification of nonlinear dynamical systems. The Conditioned Reverse Path method, which is a frequency domain technique, is considered together with ... [more ▼]

The present paper aims to compare two techniques for identification of nonlinear dynamical systems. The Conditioned Reverse Path method, which is a frequency domain technique, is considered together with the Restoring Force Surface method, a time domain technique. Both methods are applied for experimental identification of wire rope isolators and the results are compared. Finally, drawbacks and advantages of each technique are underlined. [less ▲]

Proper orthogonal decomposition for model updating of non-linear mechanical systems

in Mechanical Systems & Signal Processing (2001), 15(1)

Proper orthogonal decomposition (POD), also known as Karhunen}Loeve (K}L) decomposition, is emerging as a useful experimental tool in dynamics and vibrations. The POD is a means of extracting spatial ... [more ▼]

Proper orthogonal decomposition (POD), also known as Karhunen}Loeve (K}L) decomposition, is emerging as a useful experimental tool in dynamics and vibrations. The POD is a means of extracting spatial information from a set of time-series data available on a domain. The use of (K}L) transform is of great help in non-linear settings where traditional linear techniques such as modal-testing and power-spectrum analyses cannot be applied. These decomposition can be used as an orthogonal basis for e$cient representation of the ensemble. The POM have been interpreted mainly as empirical system modes and the application of POD to measured displacements of a discrete structure with a known mass matrix leads to an estimation of the normal modes. We investigate the use of the proper orthogonal modes of displacements for the identi"cation of parameters of non-linear dynamical structures with an optimisation procedure based on the di!erence between the experimental and simulated POM. A numerical example of a beam with a local non-linear component will illustrate the method. (C) 2001 Academic Press [less ▲]

Identification of wire rope isolators using the restoring force surface method

in International Conference on Structural Systems Identification, Kassel, 2001 (2001)

The restoring force surface method offers an efficient and reliable identification of non-linear single-degree-of-freedom systems. The method may be extended to multidegree-of-freedom systems but by ... [more ▼]

The restoring force surface method offers an efficient and reliable identification of non-linear single-degree-of-freedom systems. The method may be extended to multidegree-of-freedom systems but by loosing the key advantage of the method which lies in the two-dimensional representation for single-degree-of-freedom systems. An experimental application of the restoring force surface method is considered in the present paper. The structure investigated consists of wire rope isolators mounted between a load mass and a base mass. These helical isolators were found to be characterised by a non-linear behaviour. The results obtained are discussed in details and the advantages and drawbacks of the method are underlined. [less ▲]