(340h) Multi-Rate Data-Driven Models for Lactic Acid Fermentation - Parameter Identification and Prediction

Recursive time series, multi-input single output (MISO) models are developed for two bacterial cultures producing lactic acid with lactose as the limiting substrate, with concentrations of biomass (X), lactose (S), and lactic acid (P), considered as outputs, being measured at different sampling frequencies. Biomass concentration, X, is measured much less frequently than are lactose and lactic acid concentrations. A composite of an autoregressive (AR) model and a dual rate-autoregressive with exogenous input (ARX) model is used. For S and P, a single rate-AR model is used, while for the less frequently measured X, a dual rate-ARX model is used. Appropriate parameter constraints are imposed in parameter estimation algorithms and stability of the algorithms is examined and ensured, enabling reliable output prediction. The modified constrained least squares (MCLS) algorithm-based hybrid models for X - dual rate for parameter identification and single rate for output prediction, permitting inter-sample output estimation - allow for output prediction at the frequency of faster sampled inputs. The more frequent output prediction vis-à-vis output sampling will have substantial utility in process optimization and model predictive control. The data required for parameter estimation are generated from simulated batch experiments using a well-tested first principles model (FPM) for each bacterial strain considering random variations in kinetic parameters in a FPM, dynamic disturbances, and measurement error for an output. The predictions of the single rate-AR and dual rate-ARX models for S, P, and X track very well the data for these for both bacterial strains. The prediction accuracy can be increased using data from prior experiments. The MCLS algorithm enables more accurate parameter identification with better convergence rate and results in better prediction vis-à-vis predictions of conventional dual rate algorithms, which are unstable. While, as anticipated, the predictions of the MISO models become less precise with an increase in the prediction horizon (tp), the error for higher tp’s is within reasonable limits. Use of data from prior experiments with dynamic similarities will help in assigning the model parameters in the initial portion of an experiment and will lead to more accurate output prediction. The simpler and much less rigid structure of the data-driven models facilitates frequent updating of parameters and prediction of process trajectories, increasing their utility in representation, monitoring and control of these processes. The framework developed here is easily extended to fed-batch and continuous cultures with additional inputs being the composition and flow rate of the feed medium. The framework is not specific to the experimental database or the FPMs used to generate simulated experimental data and can be easily extended to other experimental databases obtained via actual experiments or simulated experiments using an appropriate FPM. Extension of the data-driven models to the case of infrequent sampling of certain outputs is also discussed.