Simultaneous Model Identification Research Articles

Incremental Model Identification of Bio-processes from Data: Application to Microbial Production of Hyaluronic Acid

The development of reliable kinetic models of bioprocesses from data is a challenging task. In this work, a systematic approach to develop a kinetic model of bioprocess involving single biomass from concentration data is proposed without imposing any kinetic model a priori. The proposed incremental model identification approach decomposes the model-building task into a set of sub-tasks such as determining the yield coefficients and maintenance coefficient, specific growth rate structure identification, and parameter estimation. It is shown that the proposed approach allows identifying the mechanism of product formation. The proposed approach is applied to the microbial production of Hyaluronic acid (HA), an important biopolymer, using a recombinant Lactococcus lactis MKG6. An unstructured kinetic model is developed for the HA production from data. It is shown that HA production is a growth-associated process. Further, the specific growth rate of HA production is identified from a set of rate candidates. It is revealed that the specific growth rate in the HA production follows the non-competitive HA inhibition model. The parameters obtained by the incremental identification are further refined to obtain statistically optimal estimates using the simultaneous model identification. Validation of the identified kinetic model of HA production on new experimental data shows that the proposed approach leads to a reliable kinetic model with the optimal parameter estimates.

Robust Algorithms for Simultaneous Model Identification and Optimization in the Presence of Model-Plant Mismatch

In the presence of model-plant mismatch, the set of parameter estimates obtained using standard model identification procedures cannot accurately predict the gradients of the optimization problem. Hence, a “two-step” approach involving an identification followed by an optimization step, performed repeatedly, often fails to converge to the true process optimum. In our recent work,1 we proposed a new identification procedure that progressively corrects the model for structural error such that the updated set of parameter estimates simultaneously satisfies both identification and optimization objectives with a guaranteed convergence to the true optimum. In this paper, we expanded our previous methodology in two directions: first, a new model correction based on a higher order approximation of model is proposed, and second, the effect of model uncertainties is considered explicitly by formulating a robust optimization problem at each iteration. The resulting improvements are then illustrated using a simulated study of fed-batch penicillin production process.

Simultaneous model identification and optimization in presence of model-plant mismatch

In a standard optimization approach, the underlying process model is first identified at a given set of operating conditions and this updated model is, then, used to calculate the optimal conditions for the process. This “two-step” procedure can be repeated iteratively by conducting new experiments at optimal operating conditions, based on previous iterations, followed by re-identification and re-optimization until convergence is reached. However, when there is a model-plant mismatch, the set of parameter estimates that minimizes the prediction error in the identification problem may not predict the gradients of the optimization objective accurately. As a result, convergence of the “two-step” iterative approach to a process optimum cannot be guaranteed. This paper presents a new methodology where the model outputs are corrected explicitly for the mismatch such that, with the updated parameter estimates the identification and optimization objectives are properly reconciled. With the proposed corrections being progressively integrated over the iterations, the algorithm has guaranteed convergence to the process optimum and also, upon convergence, the final corrected model predicts the process behavior accurately. The proposed methodology is illustrated in a run-to-run optimization framework with a fed-batch bioprocess as a case study.

Online Model Identification for Set-valued State Estimators With Discrete-Time Measurements

AbstractAlthough Kalman Filters provide an optimal solution to the state estimation problem for linear systems, they require knowledge of an accurate description of the model of the system. More robust approaches to Kalman Filtering for systems with uncertain models have been developed, such as set-valued state estimators, which identify the set of possible states that the system may be in, given a description of its uncertainties. The theory behind this class of filters contemplates the possibility of determining if a given system model is feasible with respect to its measurements, but does not explore the possibility of explicitly identifying the system online. This work provides insight into the advantages of performing simultaneous model identification for the class of set-valued estimators, by introducing an Adaptive Set-Valued Estimator, and presenting a practical example of its usage. The results of this robust estimator are then compared to those obtained when using a classical set-valued estimator.

On behavioral model identification

This paper presents theory and algorithms for system identification suitable for the framework of behavioral system theory. An algorithm based on algebraic system theory and realization theory (Ho-Kalman realization) in a subspace model identification framework is presented. The novel approach taken consists of the formulation of input-output data as an impulse response model and the subsequent application of state-space realization. The method provides an approximation framework for simultaneous model identification and signal reconstruction.

On behavioral model identification

This paper presents theory and algorithms for system identification suitable for the framework of behavioral system theory. An algorithm based on algebraic system theory and realization theory (Ho-Kalman realization) in a subspace model identification framework is presented. The novel approach taken consists of the formulation of input–output data as an impulse response model and the subsequent application of state-space realization. The method provides an approximation framework for simultaneous model identification and signal reconstruction.

Mixed graphical models for simultaneous model identification and control applied to glucose–insulin metabolism

In this paper a method for model identification of biological systems described by stochastic linear differential equations using a new computational technique for statistical Bayesian inference, namely mixed graphical models in the sense of Lauritzen and Wermuth, is presented. The model is identified in terms of biological model parameters and noise parameters. This non-linear estimation problem is solved by means of an exact inference algorithm. The parameter estimates are given as a-posteriori distributions which can be interpreted as fuzzy possibility distributions. For model-based simulations of the underlying biological system the model parameters are represented as uncertain parameters with the distributions obtained from the estimation procedure. We apply the presented methods to a model for the glucose–insulin metabolism: the Karlsburg model for type I diabetes.

New approach to constrained predictive control with simultaneous model identification

AbstractA new framework to closed‐loop process identification is proposed. It relies on simultaneous constrained model predictive control (MPC) and identification (MPCI). MPCI obtains sufficient model information on a process under constrained MPC, while minimally disturbing that process. To select a process input at each time step, MPCI solves a constrained optimization problem on‐line with respect to process input values over a finite moving horizon. These process inputs should satisfy all conventional MPC constraints, as well as additional constraints that assure persistent excitation of the process by these inputs. The persistent excitation constraints can be enabled or disabled, according to process identification needs of the closed loop. An iterative scheme is proposed for the numerical solution of the on‐line optimization problem. At each iteration, that iterative scheme finds a suboptimal feasible solution of the on‐line optimization problem by solving a semidefinite programming problem whose global convergence is guaranteed. The effectiveness of the proposed new methodology is illustrated through simulations on a linear time‐varying process.