Techniques for improving the accuracy of the global
approximations used in various Multidisciplinary Design
Optimization (MDO) procedures, while reducing the amount of design
space information required to develop the approximations, were
studied in this research. These improvements can be achieved by incorporating
gradient or sensitivity information into the existing approximation techniques.
An approach to develop response surface approximations based
upon artificial neural networks trained using both state and
sensitivity information is developed. Compared to previous approaches,
this approach does not require weighting the residuals of the targets
and gradients and is able to approximate gradient-consistent response
surfaces with a relatively compact network architecture.
Numerical simulation on selected problems shows that this approach
possesses the capability to develop improved
response surface approximations compared to the non-gradient neural network training approach.
One issue that this approach cannot address properly, however, is to determine
the step size for the design variables in the Taylor Series
expansion that is used to utilize sensitivity-based, approximate
information. It is also a common challenge associated with a particular
gradient-enhanced approach, Database Augmentation. This research develops another gradient-enhanced approach based on Kriging models to solve the problem by including the step size as one of model parameters. This approach can also characterize the uncertainty of approximations, which is another goal of this research. Based on
Database Augmentation, the approach develops Kriging
models by minimizing the Integrated Mean Squared Error (IMSE)
criterion instead of the Maximum Likelihood Estimation (MLE) process often used.
Numerical simulation on selected, small-scale problems
shows that this IMSE-based gradient-enhanced Kriging (IMSE-GEK) approach can improve approximation accuracy by 60~80%
over the non-gradient Kriging approximation.
An analytical approach to compute IMSE was developed to reduce the prohibitive
computing cost associated with applying the IMSE-GEK approach
to high-dimensional problems. Some additional
implementation issues associated with the approach, such as the
database augmenting scheme, the use of variable step sizes and
the inclusion of nugget effects at added points, are also presented.
