Nonlinear Regression Modeling for Engineering Applications: Modeling, Model Validation, and Enabling Design of Experiments
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Typically, on a generic regression application such as y = a + bx + cx2 there are no constraints on the optimization. The coefficients a, b, and c could have either positive or negative values. However, in phenomenological models coefficients represent phenomena and their values are constrained. For example, a delay and a time constant must both have non-negative values. Further, in regression of a model to fit an engineering application there are many other variables to consider. One application could be to fit a distillation column tray-to-tray model to data by adjusting coefficients representing tray efficiency and ambient heat losses. Here, there are many other constraint considerations than just those on the decision variables (DVs), such as whether tray efficiency should be non-negative. Constraints would include internal model variables that relate to physical limits (order, equilibrium, composition) and asymptotic limits (equilibrium, steady-state values, idealization limit). Constraints could be single limits (non-negative), bounds (0–100%), combinations (reflux must be less than boil-up), or discretization (integer values for a delay counter).