Tilman Barz

Model-based identifiable parameter determination applied to a simultaneous saccharification and fermentation process model for bio-ethanol production

In this work, a methodology for the model‐based identifiable parameter determination (MBIPD) is presented. This systematic approach is proposed to be used for structure and parameter identification of nonlinear models of biological reaction networks. Usually, this kind of problems are over‐parameterized with large correlations between parameters. Hence, the related inverse problems for parameter determination and analysis are mathematically ill‐posed and numerically difficult to solve. The proposed MBIPD methodology comprises several tasks: (i) model selection, (ii) tracking of an adequate initial guess, and (iii) an iterative parameter estimation step which includes an identifiable parameter subset selection (SsS) algorithm and accuracy analysis of the estimated parameters. The SsS algorithm is based on the analysis of the sensitivity matrix by rank revealing factorization methods. Using this, a reduction of the parameter search space to a reasonable subset, which can be reliably and efficiently estimated from available measurements, is achieved. The simultaneous saccharification and fermentation (SSF) process for bio‐ethanol production from cellulosic material is used as case study for testing the methodology. The successful application of MBIPD to the SSF process demonstrates a relatively large reduction in the identified parameter space. It is shown by a cross‐validation that using the identified parameters (even though the reduction of the search space), the model is still able to predict the experimental data properly. Moreover, it is shown that the model is easily and efficiently adapted to new process conditions by solving reduced and well conditioned problems.

Close-Loop Stochastic Dynamic Optimization Under Probabilistic Output-Constraints

In this work, two methods based on a nonlinear MPC scheme are proposed to solve close-loop stochastic dynamic optimization problems assuring both robustness and feasibility with respect to output constraints. The main concept lies in the consideration of unknown and unexpected disturbances in advance. The first one is a novel deterministic approach based on the wait-and-see strategy. The key idea is here to anticipate violation of output hard-constraints, which are strongly affected by instantaneous disturbances, by backing off of their bounds along the moving horizon. The second method is a new stochastic approach to solving nonlinear chance-constrained dynamic optimization problems under uncertainties. The key aspect is the explicit consideration of the stochastic properties of both exogenous and endogenous uncertainties in the problem formulation (here-and-now strategy). The approach considers a nonlinear relation between the uncertain input and the constrained output variables.

Performance Analysis of Shooting Algorithms in Chance-Constrained Optimization

Abstract An important aspect for model-based design and development as well as for process monitoring and control is the consideration of uncertain process parameters. One approach for the explicit consideration of such uncertainties is the formulation of Chance-Constrained optimization problems. Within the last years, several different methods for the efficient solution of these problems have been presented. In this work, chance constraints are evaluated following the idea of the variable mapping approach. Because the efficiency of the original approach deteriorates with an increasing number of uncertain parameters, the probability integration has been extended recently to the exploitation of sparse grids. In this work, additional techniques for improving the efficiency of the variable mapping approach are presented. Firstly, the solution of a subproblem, the so called shooting task is analyzed in detail and enhanced through an idea called here result recycling. Secondly, possible extensions are presented which make use of second order derivative information. The new methods are verified by application to an industrially validated process model of a vacuum distillation column for the separation of multicomponent fatty acids.

PROCESS OPTIMIZATION AND CONTROL UNDER UNCERTAINTY: A CHANCE CONSTRAINED PROGRAMMING APPROACH

Abstract A novel chance constrained programming approach for process optimization of large-scale nonlinear dynamic systems and control under uncertainty is proposed. The stochastic property of the uncertainties is explicitly considered in the problem formulation in which some input and state constraints are to be complied with predefined probability levels. This incorporates the issue of feasibility and the contemplation of trade-off between profitability and reliability. The approach considers a nonlinear relation between the uncertain input and the constrained variables. It also involves novel efficient algorithms both to consider time-dependent uncertainties and to compute the probabilities and, simultaneously, their gradients. To demonstrate the performance of the proposed method, a chance constrained NMPC scheme for the online optimization of a batch reactor under safety restrictions, and the optimal operation and control of a coupled two-pressure column system are discussed to show the efficiency and potential for optimization and control under uncertainty.

A new approach to chance constrained process optimization and control under time-dependent uncertainties

Abstract In this work, a novel approach to solving nonlinear chance-constrained dynamic optimization problems under time-dependent uncertainties is proposed. The approach considers a nonlinear relation between the uncertain input and the constrained output variables. In fact, the approach is relevant to all cases when uncertainty can be described by any kind of joint correlated multivariate distribution function. The essential challenge lies in the efficient computation of the probabilities of holding the constraints, as well as their gradients. However, the main novelties of this approach are that nonlinear chance constrained dynamic optimization can now also be realized efficiently even for those cases where no monotonic relation between uncertain input and constrained output exists. This is necessary, particularly, for those process systems where the decision variables are critical to the question of whether there is monotony or not. Furthermore, novel efficient algorithms are proposed to consider dynamic random variables. Thus, the solution of the problem has the feature of prediction, robustness and being closed-loop The performance of the proposed approach will be demonstrated through application to the optimal operation and control of a high pressure column embedded in a heat integrated column system. In addition, a novel chance constrained nonlinear MPC scheme is introduced to show the efficiency and potential of the chance constrained approach for online optimization and control under uncertainty.

Implementation of Optimal Decisions in the Presence of Uncertainty

Abstract In this work, the implementation of optimal and robust decisions in the presence of various uncertainties comprising the model parameters, external conditions and the closed loop behavior of basic controllers is presented. In order to compute optimal and reliable decisions, a chance constrained optimization problem is formulated. The efficient solution approach is based on the relaxation of the original stochastic problem formulation to a standard NLP problem. By this means, nominal optimal solutions are relocated in order to guarantee both feasibility and process operation as close to the true optimum as possible. The solution implicates the minimization of additional costs which result from conservative strategies so as to compensate for uncertainty. The experimental verification of the developed approach is carried out on a distillation pilot plant for the separation of an azeotropic mixture.

Efficient Computation of First- and Second-Order Sensitivities Using an Internal Forward Differentiation Scheme

Abstract In this work, an approach for the forward integration of first and second order sensitivities for dynamic simulation and optimization problems is presented. The implementation is done following the idea of internal numeric differentiation. The integration of the dynamic system is done by an implicit Runge-Kutta discretization of the state equations, namely Orthogonal Collocation on Finite Elements. Based on the discrete solution of each integration step, sensitivities are generated using the chain rule and the implicit function theorem. In doing so, parts of the information produced in the integration step can be reused, and thus, the cost for the generation of sensitivities is minimized. The presented approach is applied to the solution of a dynamic moel-based optimal experimental design problem for the parameter determination in a gas desulfurizing process.