Investigation and Development of Globally Convergent Methods for Solving Multiple Non-Linear Functions
Aurel Systems Inc. offers a commercial dynamic process simulation program called CADSIM Plus™ (www.aurelsystems.com). At several places in the program sets of nonlinear equations must be solved or nonlinear functions must be minimized (for example, solving pressure flow networks, solving for independent variables given sets of user defined dependent variables, solving for both temperatures on a heat exchanger with condensation or flash). The intern’s research project involved investigating various mathematical algorithms and developing a suite of general optimization routines which had to be integrated with the CADSIM Plus™ simulator. The over-arching goal of the project was to improve the robustness, run-time speed and accuracy of CADSIM Plus™. During the internship, the research team implemented many different types of optimization techniques in CADSIM Plus™ to test for suitability. The research resulted in a deepened understanding of the challenges faced by the company in terms of the types of mathematical optimization techniques that will need to be investigated. Further research will be conducted into optimization methods that can accommodate a moving target and physical limits including multi-variable process control.