The symbolic regression problem is to find a function, in symbolic form, that fits a given data set. Symbolic regression provides a means for function identification. This research describes an adaptive hybrid system for symbolic function identification of thermo-physical model that combines the genetic programming and a modified Marquardt nonlinear regression algorithm. Genetic Programming (GP) system can extract knowledge from the data in the form of symbolic expressions, i.e. a tree structure, that are used to model and derive equation of state, mixing rules and phase behavior from the experimental data (properties estimation). During the automatic evolution process of GP, the function structure of generated individual module could be highly complicated. To ensure the convergence of the regression, a modified Marquardt regression algorithm is used. Two stop criteria are attached to the traditional Marquardt algorithm to enforce the algorithm repeat the regression process before it stops. Statistic analysis is applied to the fitted model. Residual plot is used to test the goodness of fit. The χ2-test is used to test the model's adequacy. Ten experiments are run with different form of input variables, number of data points, standard errors added to data set, and fitness functions. The results show that the system is able to find models and optimize for its parameters successfully.

Local thermodynamic models are practical alternatives to computationally expensive rigorous models that involve implicit computational procedures and often complement them to accelerate computation for real-time optimization and control. Human-centered strategies for development of these models are based on approximation of theoretical models. Genetic Programming (GP) system can extract knowledge from the given data in the form of symbolic expressions. This research describes a fully data driven automatic self-evolving algorithm that builds appropriate approximating formulae for local models using genetic programming. No a-priori information on the type of mixture (ideal/non ideal etc.) or assumptions are necessary. The approach involves synthesis of models for a given set of variables and mathematical operators that may relate them. The selection of variables is automated through principal component analysis and heuristics. For each candidate model, the model parameters are optimized in the inner integrated nested loop. The trade-off between accuracy and model complexity is addressed through incorporation of the Minimum Description Length (MDL) into the fitness (objective) function. Statistical tools including residual analysis are used to evaluate performance of models. Adjusted R-square is used to test model's accuracy, and F-test is used to test if the terms in the model are necessary. The analysis of the performance of the models generated with the data driven approach depicts theoretically expected range of compositional dependence of partition coefficients and limits of ideal gas as well as ideal solution behavior. Finally, the model built by GP integrated into a steady state and dynamic flow sheet simulator to show the benefits of using such models in simulation. The test systems were propane-propylene for ideal solutions and acetone-water for non-ideal. The result shows that, the generated models are accurate for the whole range of data and the performance is tunable. The generated local models can indeed be used as empirical models go beyond elimination of the local model updating procedures to further enhance the utility of the approach for deployment of real-time applications.

The thesis deals with nonlocal model simulations of the three-point-bening test series. The model is applied to set of beams of variable size and notch depth. The intention is to identify such parameters that would provide the response of the nonlocal model similar to experimental data from the comprehensive fracture tests performed at the Northwestern University. Size and shape of the process zone are estimated from the discrete model results and according to that the parameters of weight function and material for the nonlocal model are identified. Results obtained with the model are compared to the experimental data.