Y. Govers
H. Haddad Khodaparast
M. Link
J.E. Mottershead

Abstract The problem of stochastic model updating is addressed by means of the application of two methods (covariance and interval model updating) to the DLR AIRMOD structure which is repeatedly disassembled and reassembled to provide a database of modal variability due to uncertainty in joint and support stiffnesses and masses of cables and screws. The covariance method is based on an assumption of small uncertainty and implemented at each step of an iterative approach by forward propagation of uncertain parameters using a multivariate normal distribution. The interval approach is based on a Kriging meta-model, thereby providing a very efficient surrogate to replace the expensive full finite element model. This allows a mapping from multiple output measurements to define a hypercube bounded by intervals of parameter uncertainty. It is shown that the measured data is fully enclosed by the hyper-ellipses and hypercubes of the covariance and interval methods respectively. As expected, the interval method is found to be more conservative than the covariance approach but still provides useful estimates without restriction by any assumption of probability distribution. Highlights • The problem of stochastic model updating is addressed. • Results are compared from two methods (covariance and interval model updating). • Real test data is taken from the AIRMOD structure a replica of GARTEUR SM-AG19. • Similar parameter bounds could be identified from both methods.

The application of a stochastic model updating technique using Monte-Carlo inverse propagation and multivariate multiple regression to converge a set of analytical models with randomised updating parameters upon a set of nominally identical physical structures is considered. The structure in question is a short beam manufactured from two components, one of folded steel and the other flat. The two are connected by two rows of spot-welds. The main uncertainty in the model is concerned with the spot-weld but there is also considerable manufacturing variability, principally in the radii of the folds. [All rights reserved Elsevier]

A method for the separation of close modes by the sequential application of fictitious modifications is applied to cyclically symmetric and axisymmetric structures. The theoretical approach, based on the manipulation of measured receptances from linear systems, is applied to two physical problems; a slotted retaining nut and the turbine casing from an aero-engine. Synthesised receptances from a multiple-input multiple-output curve-fitting routine are used in order to reduce the effect of measurement noise. However, it is revealed that certain of the receptances obtained by adding a fictitious mass (or grounded spring) are very sensitive to measurement inaccuracies at the natural frequencies of the unmodified structure. Fortunately, not all of the modified receptances are sensitive in this way, and the insensitive ones are sufficient to allow an accurate estimation of the natural frequencies and mode shapes of a system modified by a point mass

Complex and defective zeros can occur in cross receptance measurements. The complex zeros always occur in sets of two pairs of complex conjugates so that they are not detectable by a phase change. When complex zeros are present, the vibration is not completely eliminated at the frequency of those zeros. Repeated defective zeros may appear in cross receptances without cancellation by a pole. The number of uncancelled repeated zeros will not exceed by more than one the difference between the algebraic and geometric multiplicity of the repeated eigenvalues

The conditions for the creation of nodes of normal modes of vibration from the cancellation of poles and zeros are established when either the poles or the zeros (or both) appear as repeated eigenvalues. The analysis is illustrated by numerical examples including the case of a pole-zero cancellation at every co-ordinate at the same frequency which is shown to occur whenever there are repeated poles. If there are repeated poles and repeated zeros at the same frequency then the number of poles must be either one more, one less or equal to the number of zeros

This paper addresses the problem of determining unknown physical connectivities for inclusion in a finite element model by using standard frequency response measurements. In general, neither the topology nor the stiffness of such connectivities are known. A method is presented based on two systems of equations from finite elements and vibration measurements. When the equations are constrained so that an assumed connection is undeformed, then the eigenvalues and vectors of the two systems will be identical if the remainder of the structure is accurately modelled. A numerical example, in the form of a finite element truss structure, is used to illustrate the application of the method. It is demonstrated that the approach is tolerant of parameter errors elsewhere in the model

The main focus of this paper is on pole-zero cancellation in structures by unit-rank modifications. The modifications may be achieved by passive stiffnesses or by active control techniques. A review of the classical theory on unit-rank modification is included and new results are obtained to explain the existence of coincident zeros in point and cross receptances. The necessary and sufficient conditions are established for the production of a vibration node by pole-zero cancellation. The classical theory is used to bring about the cancellation of poles and zeros, and numerical examples are used to illustrate the application of the technique

It is well known that finite element predictions are often called into question when they are in conflict with test results. The area known as model updating is concerned with the correction of finite element models by processing records of dynamic response from test structures. Model updating is a rapidly developing technology, and it is intended that this paper will provide an accurate review of the state of the art at the time of going to press. It is the authors' hope that this work will prove to be of value, especially to those who are getting acquainted with the research base and aim to participate in the application of model updating in industry, where a pressing need exists

Demonstrates how the two damping parameters associated with the non-linear nth-power velocity model can be identified from the time series records of the displacement and velocity responses to sinusoidal excitation. No restriction is imposed on the level of damping present and estimates are acquired by minimizing the square of the error between observed responses and those predicted by a linearized model. The problems of noise contamination and uncertain initial conditions are treated by using simulated data and converged estimates are presented with computation times measured in CPU seconds on a VAX 11/780 computer

A sequential, least squares, frequency domain filter is presented for the identification of structural vibration parameters from measured responses and known excitations. The validity of the approach is demonstrated by using simulated data for two multi-degree of freedom systems. Parameter estimates are given as they converge, together with computation times measured in CPU seconds on an IBM 3083 computer

The past fifteen years have seen an explosion in the use of numerical methods, such as finite elements and turnkey CAD systems, in engineering design centres. Rapid development is currently taking place in second generation CAD systems utilising geometric modellers and sculptured surface packages which can be linked to finite element models and other previously separate areas of computer application such a N.C. machining. The strategy of this paper is to discuss some such systems which are just emerging from the development phase at Lucas Research Centre and to show some typical applications.