Enforcing Model Adequacy in Real-Time Optimization via Dedicated Parameter Adaptation

Iterative real-time optimization schemes that employ modifier adaptation add bias and gradient correction terms to the model that is used for optimization. These affine corrections lead to meeting the first-order necessary conditions of optimality of the plant despite plant-model mismatch. However, since the added terms do not include curvature information, satisfaction of the second-order sufficient conditions of optimality is not guaranteed, and the model might be deemed inadequate for optimization. In the context of modifier adaptation, this paper proposes to include a dedicated parameter-estimation step such that also the second-order optimality conditions are met at the plant optimum. In addition, we propose a procedure to select the best parameters to adapt based on a local sensitivity analysis. A simulation study dealing with product maximization in a fed-batch reactor demonstrates that the proposed scheme can both select the right parameters and determine their values such that modifier adaptation can drive the plant to optimality fast and without oscillations. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Single product, finite horizon, periodic review inventory model with working capital requirements and short-term debt

Margarita Protopappa, Ralf Seifert, Cristopher Ariel Zeballos Avila

In this paper, we build on a single product, finite horizon, periodic review inventory management setting and include key financial aspects such as working capital constraints, payment delays and multiple sources of financing. We numerically solve for the optimal working capital target and the order-up-to level using an embedded Nelder and Mead optimization, and we perform sensitivity analysis on cash flows and short-term debt levels. Our numerical experiments show that when access to short-term debt is granted, the expected cash flows are indeed fairly insensitive to varying short-term debt premiums. However, when short-term debt becomes prohibitive or when downstream payment delays increase, the required working capital target inflates rapidly. (C) 2013 Elsevier Ltd. All rights reserved.

Elsevier2013

Robust multi-objective optimization of gasifier and solid oxide fuel cell plant for electricity production using wood

Ayse Dilan Celebi, François Maréchal, Shivom Sharma

Biomass is an attractive renewable and stored energy that can be converted to transportation fuels, chemicals and electricity using bio-chemical and thermo-chemical conversion routes. Notably, biofuels have relatively lower greenhouse gas emissions compared to the fossil fuels. A biomass gasifier can convert lignocellulosic biomass such as wood into syngas, which can be used in Solid Oxide Fuel Cell (SOFC) to produce heat and electricity. SOFC has very good thermodynamic conversion efficiency for converting methane or hydrogen into electricity, and integration of SOFC with gasifier gives heat integration opportunities that allow one to design systems with electricity production efficiencies as high as 70%. Generally, process design and operational optimization problems have conflicting performance objectives, and Multi-Objective Optimization (MOO) methods are applied to quantify the trade-offs among the objectives and to obtain the optimal values of design and operating parameters. This study optimizes biomass gasifier and SOFC plant for annual profit and annualized capital cost, simultaneously. A Pareto front has been obtained by solving Moo problem, and then net flow method is used to identify some optimal solutions from the Pareto front for the implementation into next phase. The constructed composite curves, which notify maximum amount of possible heat recovery, and first law efficiency also indicate better performance of the integrated plant. Uncertainty of market and operating parameters has been added to the optimization problem, and robust MOO of the integrated plant has been performed, which retains less sensitive Pareto solutions during the optimization. Finally, Pareto solutions obtained via normal and robust MOO approaches are considered for uncertainty analysis, and Pareto solutions obtained via robust MOO found to be less sensitive. (C) 2017 Elsevier Ltd. All rights reserved.

2017

On enforcing the necessary conditions of optimality under plant-model mismatch - What to measure and what to adapt?

Martand Singhal

Industrial processes are run with the aim of maximizing economic profit while simultaneously meeting process-critical constraints. To this end, model-based optimization can be performed to ensure optimal plant operations. Usually, inevitable model inaccuracies are dealt by collecting the plant measurements at the local operating conditions in order to adapt model parameters, followed by numerical re-optimization. This iterative two-step procedure often results in a sub-optimal solution, since the models are typically not designed for optimization. Modifier Adaptation (MA) is a Real-Time Optimization (RTO) technique that directly adds the affine-correction terms to the model. The affine corrections are parametrized in modifiers that are tailored to the optimization needs. This enables modifier adaptation to guarantee, upon convergence, matching the plant and the modified model's optimality conditions. However, computing the modifiers requires estimates of the plant gradients that are obtained via expensive plant experiments. The experimental cost can be reduced by relying more on the model of the considered plant. For example, Directional Modifier Adaptation (DMA) relies on offline-computed local parametric sensitivity analysis performed on the gradient of the Lagrangian function of the model resulting in reduced number of input directions that describe the gradient uncertainty in the model. Thereby, plant gradients are estimated only in a low-dimensional space of privileged input directions considerably reducing the experimental costs. However, local sensitivity analysis is often ineffective when the gradient of the model is considerably nonlinear in parameters. This thesis proposes an online procedure based on global sensitivity analysis for finding the most promising privileged directions that adequately compensates for the model deficiencies in predicting the plant optimality conditions. The discovered privileged directions are such that, upon parametric perturbations, the gradient varies a lot along the privileged directions and varies only a little along the remaining input directions. Consequently, the gradients of the model cost and constraints are corrected only along the privileged directions by adapting modifiers. The resulting methodology is named as Active Directional Modifier Adaptation (ADMA). Several simulation studies conducted show that the proposed approach reaches the near-optimality conditions at a considerably reduced experimental cost. In addition, this thesis attempts to establish a direct relation between the optimality conditions and the parameters of a given model. Model parameters are analyzed to discover mirror parameters that mimic the behavior of modifiers in influencing the optimality conditions. It is proposed to adapt mirror parameters instead of modifiers yielding the benefit of both, modifier adaptation in enforcing optimality conditions and of parameter adaptation in better noise handling and convergence. Moreover, it is investigated how to establish the synergies between privileged input directions with model parameters in order to reduce experimental efforts. The steady-state optimization of a simulated chemical process shows that the privileged directions and the selected parameters work together to reach near-optimal performance. Finally, the study on the power maximization of flying kites leads to the development of trust-region based ADMA method to better control the input step size.