Identification of Vibrating Structures

512 Pages·1982·22.805 MB·English

by  H. G. Natke (eds.)

INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES
COURSES AND LECTURES - No. 272
IDENTIFICATION
OF
VIBRATING STRUCTURES
EDITED BY
H.G. NATKE
UNIVERSITY OF HANNOVER
SPRINGER-VERLAG WIEN GMBH
This work is subject to copyright.
All rights are reserved,
whether the whole or part of the material is concerned
specifically those of translation, reprinting, re-use of illustrations,
broadcasting, reproduction by photocopying machine
or similar means, and storage in data banks.
© 1982 by Springer-Verlag Wien
Originally published by Springer-Verlag Wien New York in 1982
ISBN 978-3-211-81651-6 ISBN 978-3-7091-2896-1 (eBook)
DOI 10.1007/978-3-7091-2896-1
PREFACE
The dynamic behaviour of novel and complicated structures often needs to be
investigated by system analysis and system identification, since it usually has to meet certain
requirements. A priori knowledge concerning the real system is gained by system analysis
and/or previous tests, and it results in a non-parametric and/or in a parametric mathematical
model. The identification of system parameters, i.e. experimental system analysis, is
performed using measured quantities and taking into account deterministic and stochastic
errors. If results of the identification have to be compared with the results of the system
analysis, and if certain error bounds are exceeded, the model has to be improved. System
identification has to take into account random aspects (errors, test signals), the real dynamic
behaviour (damping coupling, non-linearities) and questions concerning practical handling
(including large systems, economics). A broad understanding of system identification needs
as its basis an extended theory of structural vibrations and estimation (stochastic processes),
and must be coupled with practical aspects including experience and validated software.
The course on Identification of Vibrating Structures, the lecture notes of which are
collected in this volume, deals with the topics mentioned above. First an introduction into
the subject is given, and the theoretical background of vibrating structures and parameter
estimation methods is dealt with. The following lectures deal with several identification
methods including applications. The next papers discuss the indirect identification, that
means the adjustment of theoretical models (results of system analysis) by the results of
vibration tests (estimated values). These parts are supplemented by a presentation of an
example of commercially available hard- and software including applications. For the
practical application of system identification concerning large and complicated structures
synthesizing techniques (substructure techniques) including error analysis are necessary,
which are the subject of the following two papers, followed by identification of non-linear
systems. The closing lectures deal with modern developments, firstly from the point of view
of control theory, and secondly by coming from the theory of stochastic systems. The last
three lectures deal with theoretical aspects, including examples of (simple) systems mainly
with regard to non-deterministic system analysis. This seems to be a flexible and far-reaching
tool worthwhile studying, because several applications with regard to early failure detection
are possible, and it may give impulses towards the identification of linear and non-linear
structures.
I wish to express my thanks to the coauthors, who made a very successful course
possible at Udine, and I hope this volume will be equally well received by the reader.
H.G. Natke
CONTENTS
Page
Identification of vibrating structures: an introduction
by H.G. Natke ................... . 1
Multi-degree-of-freedom systems - a review
by H.G. Natke . . . . . . . . . . . . . . . . ...... 15
Introduction to system identification using parameter estimation methods
by H. Unbehauen .................................... 53
Some identification methods using measured harmonic responses
by R. Fillod ...................................... 121
Identification methods II - concepts and techniques
by E. Breitbach .................. . . . 147
Indirect identification methods I: adjustment of mathematical models by the
results of vibrating tests: using eigensolutions
by G. Lallement . . . . . . . . . . . . .. ...................... 179
Correction of analytical models for damped linear systems using experimentally
obtained forced vibration responses
by H.P. Felgenhauer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. 95
Indirect methods: correction of the results of system analysis by results of
identification - a survey
by H.G. Natke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .... 225
Application of system identification with commercially available hardware and
software
by P. Catchpole .................................... 257
Modal synthesis - modal correction - modal coupling
by E. Breitbach ................ . . . . . . . . . . . . . . . . 321
Linearized error analysis in synthesis techniques
by H.G. Natke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
Identification of nonlinear systems
by E. Breitbach ......... . ... 373
Some modern developments in system identification using parameter estimation
methods
by H. Unbehauen ... 405
Modern methods of covariance analysis and applications
by W. Wedig ...................... . ....... 445
Integration of nonlinear stochastic systems and applications to the crack
identification
by W. Wedig ...................................... 473
Stochastic systems with distributed parameters
by W. Wedig ...................................... 493
IDENTIFICATION OF VIBRATING STRUCTURES:
AN INTRODUCTION
H.G. Natke
Curt-Risch-Institut
Universitat Hannover
The dynamic behaviour of novel and complicated structu-
res has to be investigated by system analysis based on
drawings (Fig. 1). Starting from a physical model, neglec-
ting all physical effects which are not relevant to the pro-
blem to be investigated, one has to build up the mathemati-
cal model as a structured equation (parametric model). In
certain cases it has to be simplified compared to the phy-
sical model. The parameter values of the model have to be
calculated using the drawings. Taking into account the
loadings (-assumptions) the dynamic system response can be
predicted. System analysis results therefore in a parametric
computational model. Its accuracy depends on the influence
2 H.G. Natke
ANALYSIS IDENTIFICATION
( COMPUTATIONAL (TEST MODEll
MODEL)
MEASUREMENT -,
~---t SYSTEM SYSTEM(MODI-
FlED SYSTEM) I
I
I
I
I
-----,---- I
-4
I
I
I
I I
IL __ _ I
I
I
I
-,
I
PREDICTION INDIRECTI DIRECT
OBSERVATION
IDENTIFICA TlON
PARAME NON-PARA
TRICAL METRICAL
I
____________ ..JI
Fig. 1 Principal proceeding in system
analysis and identification
Introduction 3
of the introduced simplifications and assumptions. If the
structure to be investigated is novel and experiences of
comparable structures are not available the errors of the
predicted results are unknown, the results may be useful
for investigations but cannot prove the qualification of
the structure.
Because of the unknown uncertainties of the computa
tional model in the case mentioned above, tests have to be
carried out additionally. These tests may concern the
loading configurations (static, dynamic), but only a few
loading configurations can be realized by testing for eco
nomic and testing limits e.g. Other more interesting tests
concern the dynamic behaviour of the system itself: System
identification (Fig. 1). The system under test is modified
by the measuring and excitation equipment, it is called the
measurement system (Fig. 1). The physical model of the
measurement system and the a priori knowledge resulting from
system analysis and/or previous tests (e.g. of subsystems)
lead to a mathematical model which may be structured (para
metric)or unstructured (non-parametric). The direct or in
direct observed quantities enable an estimation of the model
characteristics for describing the dynamic behaviour of the
system under test. If the model is structured, it results in
estimated parameter values. Because of the stochastic
disturbances within the measured signals - besides a possible
4 H.G. Natke
stochastic excitation - estimation methods have to be
applied.
With the above briefly described identification process
one yields the test model which can be compared with the
computational model. The comparison may be done with the
values of the system parameters or with the predicted or
estimated results of the computational or the test model.
In general the comparison is unsatisfactory regarding error
bounds depending on the given problem, so that an improve
ment of the computational model is necessary. Sometimes the
comparison results in an iterative procedure concerning an
improved physical model of identification concerning e.g.
the test equipment or environment. If the structured mathe
matical models of system analysis and identification are
equal, the improvement of the computational model reduces
in a parameter adjustment.
For better understanding Fig. 2 gives a classification
of the identification problem to the structural problem. The
direct problem is the known task of system analysis. The
inverse problem is partitioned into the design, input, and
identification problem as described briefly in Fig. 2.
The definition of identification by Zadek (1962) is:
The determination on the basis of input and output (Fig. 3)
of a system within a specified class of systems,to which
the system under test is equivalent.