Technical Assessment:

This summer I worked on two projects: further determining the
variability of a set of manufactured parts and an exploration of the
literature on statistical inference and uncertainty quantification.

I was provided with contour inspection data for 100 spherical marine
floats.  After correcting the data for differences in coordinate
systems and units, I found probability distributions for the mean
radius of the spheres using a maximum likelihood estimate.  I then
looked at variation in the radius of curvature along the meridian.
The pattern that emerged for radius of curvature was indicative of the
manufacturing process used to create the spheres.  The distribution is
being used in probabilistic finite element code to link the variation
in geometry with variation in crushing load.

In order to begin developing an idea for a master's thesis I spent
some time doing a literature search on different methods of
uncertainty quantification and developing a procedure by which one can
ask a deterministic question (How will a particular manufactured part
perform?) of a probabilistic model (Built from the distribution of all
parts produced.) and quantify the uncertainty in the resulting
inference.  In the description below we are using a 'model' to
describe a 'part' in terms of several 'key parameters' and gauging its
'performance'.

The procedure is as follows:

1) Develop a nominal model for your process 
   
   a) This can by either analytical or numerical
   
   b) Determine which model components are deterministic and which are
   probabilistic

   c) Find the key parameters of the model and ensure that they are
   all observable


2) Develop a statistical model

   a) Find distributions for your key parameters by sampling from your
   population; also find the covariance matrix for the key parameters

   b) Given the above distributions for your key parameters find the
   distribution(s) for your performance metrics

   c) Organize the interrelationship between your parameters and
   performance into an influence diagram

   d) Define an 'Average' part for the population by finding the mean
   key parameter vector


3) Infer performance of a particular member of the population
   
   a) Measure the key parameter vector for the part of interest

   b) Feed this information into the influence diagram you developed
   above to find a new estimate for the performance now conditioned on
   the above measurement.


4) Find confidence
   
   a) Calculate the Mahalanobis distance, r, between the part of interest
   and the population mean part.

   b) The smaller r the closer your part of interest is to other parts
   which you used in developing the statistical from which you made
   your inference and therefore you can be more confident in that
   inference.




Evaluation of my involvement in the EIP:

This summer I had much more independence than last summer.  I was told
to continue my work from last, but also to spend a significant portion
of my time exploring various fields that interest me.  I looked as
using wavelets to identify feature is the contour data above that were
more visible in the frequency domain.  I learned about different
method of accounting for uncertainty in engineering systems, focusing
on Bayesian techniques where one uses experiment to reduce
uncertainty.  Eventually I developed a plan for the thesis project
outlined above.  My mentor and I are trying to publish at least two
conference publications before I begin the bulk of the thesis and two
after.  These four papers will allow me to structure the background
that led me to the thesis topic and the actual work itself, thereby
making the thesis much easier to prepare.  I believe that at this
time, my involvement in the EIP has been quite successful and has
prepared to enter the graduate phase.