Multivariable empirical modeling of ALS systems using polynomials.

Multivariable polynomial regression (MPR) was used to model plant motion time-series and nutrient recovery data for Advanced Life Support (ALS). MPR has capabilities similar to neural network models in terms of ability to fit multiple-input single-output nonlinear data. It has advantages over neural networks including: reduced overfitting, produces models that are more tractable for optimization, sensitivity analysis, and prediction of confidence intervals. MPR was used to produce nonlinear polynomial time-series models predicting plant projected canopy area versus time and temperature. Temperature was found to not have a statistically significant effect. Models were developed to relate rate and extent of nutrient recovery to treatment parameters, including temperature and use of heat pretreatment or nutrient supplementation. These applications demonstrate MPR's capability to fill "gaps" in an integrated model of ALS. Fundamental models should be used whenever available. However, some components may require empirical modeling. Furthermore, even fundamental models often have empirical constituents. MPR models are proposed to satisfy these needs.