Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

to bring the two into agreement. In this sense, the models are simply used to verify
reality. However, recent trends in complex structures require models to serve as
predictors of future behavior. Since models, by definition, are only approximations to
reality, there is considerable risk and uncertainty involved in the prediction process.
The field of uncertainty and stochastic modeling is growing rapidly. Researchers
are working to understand the sources of model uncertainty, develop models of it
and propagate the effects of this uncertainty to provide bounds, or statistics, on the
performance predictions.
There are many sources of possible model uncertainty, including global modeling,
or model structure errors, parametric errors, discretization errors and environmental
discrepancies [23, 27, 12, 93]. However, of these, parametric uncertainty is treated
most often in the literature as it is the easiest to model and the most difficult to reduce
due to lack of sufficient experimental data. There are several forms of uncertainty
models with probabilistic models being the most popular. Simonian has compiled
a database of measured damping data from twenty-three satellites [106]. He applies
statistical models built from this data to an electro-optic jitter problem to obtain the
probability density function of the performance, optical pointing error. Hasselman has
also been a contributer in this area. He uses a generic modeling database derived from
prior analysis and testing to generate uncertainty models for modal mass, damping
and stiffness parameters [53, 52]. He compares the use of linear covariance, interval
prediction and Monte Carlo propagation of the uncertainties through the analysis to
obtain statistical bounds on frequency response functions.
A short-coming of statistical models is that often the data used to build the un-
certainty model is insufficient. Furthermore, the data that does exist originates from
diverse structural systems making the application to a particular system, such as an
interferometer, suspect. In this sense, the uncertainty model itself is uncertain. Ben-
Haim and Elisakoff present an alternative to probabilistic models in their monograph
on convex uncertainty modeling [15, 41]. The authors suggest that the performance
predictions obtained through statistical analysis are quite sensitive to the distribution
chosen for the uncertainty model. Therefore, convex, or bounded, models present an
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