Solving Nonlinear Systems Using Qualitative Reasoning

Principal Investigators:

Janet Rogers and Abbie O'Gallagher, ITL/MCSD

Current Collaborator:

Elizabeth Bradley, University of Colorado, Boulder

Customers:

Human-Machine Interface Technologies
A.I. Researchers
Image Recognition Technologies

Project Description and Expected Products:

Research methods and test procedures to automate the determination of the underlying functional relationships describing processes with spatial or time dimensions. Provide tools that bypass the need for operator intervention in the determination of starting values for the nonlinear least squares procedures used to fit the data generated by such processes, and provide techniques for assessing the adequacy of the fitted results. Make automated optimizing procedures and assessment tools available through the World Wide Web.

Benefits:

By applying the automation tools developed in this project, scientists will gain improved understanding of complex and poorly specified systems, and will be freed to devote their time and creative thought to more demanding tasks.

Motivation:

As shown by the Statistical Reference Data project, it is often the case that general optimization procedures are not robust when applied to difficult problems. The optimization package ODRPACK, developed by MCSD staff, however, has been shown to be highly reliable for a wide variety of models. Because the PIs have intimate knowledge of ODRPACK, this project provides a unique opportunity to integrate important new capabilities into this software package, thereby making a significant improvement to general purpose nonlinear least squares modeling tools available to researchers. Also, because starting values are critically important for all nonlinear least squares procedures, any tools developed for automatically determining starting values will be invaluable to any researcher applying this optimization technique.

Note that the aim of this project is emphatically not to build a tool that is tuned for one particular application domain, but rather to provide methods for solving problems of interest to a wide variety of industries. It is therefore especially appropriate for ITL/MCSD to be involved in this effort because of the broad impact that this research is expected to have.

FY96 Milestones:

[January 1996]

Developed and tested prototype procedure for establishing starting values.

[June 1996]

Expanded test base of data and models to examine.

[July 1996]

Improved procedure for selecting starting values and initial conditions by employing filtering techniques on the data, thereby enabling automated fitting of 3 of the 5 models currently being examined with no operator intervention.

[July 1996]

Developed prototype test for determining adequacy of fitted results.

[July 1996]

Added simple bounding procedure for model parameters.

[August 1996]

Improve procedures for selecting starting values, and examine the adequacy of the techniques developed for assessing the adequacy of the fit.

[September 1996]

Test and verify tools developed on a corpus of harder models in a variety of domains.

FY97 and FY98 Milestones:

• Explore improved filtering techniques through developement and incorporation of wavelet transform procedures.
• Continue testing and verification of procedures and assessment tools.
• Draft working paper describing results, and submit proposal to present research at A.I. conference to be held in Italy in late FY97.
• Expand test base to include problems specifically from the area of image processing.
• Translate ODRPACK to Fortran 90, and add bounds capability to facilitate further development of automated procedures and assessment techniques.