Abstract
During the design and development of mechanical systems, mathematical models
are a common tool to analyze, predict and characterize the behavior
of a structure. For a model to accurately describe the
physical behavior of a system, the model type and structure must be suitable
for the analysis type. In structural dynamics, simulations employing finite
element models of lightweight structures are used to assess the vibration
response due to internal and external loads. With appropriately chosen
approximations for the model, the simulation results depend on the values of
model parameters. The identification of such parameters, the
determination of their role and quantitative contribution towards the behavior
of a model, is an important task during the process of modeling. Measurement
data from experiments are used as reference values to tune and validate the
results from model analyses.
Complex structures with a significant number of sub-components tend to require
complex models in order to reflect their physical behavior accurately. This
increases the number of parameters, which poses difficulties during the
identification process due to overlaps in parameter effects. Furthermore the
size of associated optimization problems increases prohibitively.
This thesis presents a multi-stage approach for identifying model parameters of
complex lightweight structures. Instead of identifying model parameters for a
fully integrated structure at once, sub-assemblies and individual parts are
analyzed separately. Model parameters identified in sub-assembly stages are
then incorporated into an assembled model. As measurement data and identified
parameters are associated with uncertainty distributions, errors in the
identification of parameters of upstream stages propagate into higher assembly
models. Accordingly, such propagating errors should be minimized in early
stages. Additionally, this effect has to be taken into account during the
refinement of existing parameter in later stages and for the assessment
of model accuracy at higher assembly levels.
The staged identification has been applied to two distinct structures: First,
in order to validate the principles of staged identification,
a cantilevered truss-like space frame beam structure has been modeled and
measured in an laboratory setup. Data from previous studies pertaining the
structure as well as new measurements from experimental modal analysis have been
used to identify a finite element model. The structure was divided into a cell
and a short beam configuration in order to simulate sub-assemblies for the staged
approach.
A second, more complex, structure which motivated the work on this thesis is
the SOFIA Telescope Assembly. A legacy finite element model, constructed
during the design and integration phase of the telescope, exists but was
modeled with a focus on the qualification regarding flight-worthiness
and the fulfillment of specifications using conservative
parameter values. The model has been updated
through staged parameter identification in order to be suitable for simulations
under the environment of operational conditions with a focus on
dynamic characteristics affecting the optical path. A multitude of data sources
from the project documentation archive as well as new measurements with
test benches and flight hardware have been used to update single parts
and major assemblies, such as the Primary Mirror Assembly and
Secondary Mirror Mechanism of the telescope. Comparisons of modal analyses
using the updated integrated Telescope Assembly model with ground-based
and in-flight modal surveys show the improvement of accuracy of the model.
Together with the reorganization of model structure and handling through
program scripts, the new model is suitable for further analyses in support
of improving the performance of the observatory through enhanced control systems
and the reduction of image jitter.
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