Application of Evolutionary Algorithms in Guaranteed Parameter Estimation

Model-based optimization and control is becoming more and more important in the process industries and in general. Modelling almost always involves the estimation of parameters from available data. The parameter estimation problem is usually posed as the minimization of the prediction error or the maximization of the likelihood function. If the uncertainty of the measurements taken from a real process is assumed to be an interval around the measured values, a set of parameter vectors exists that is able to describe the behavior of the systems within these uncertainties. Guaranteed parameter estimation deals with the problem of determining all parameter vectors that are compatible with uncertain observations. The solution of guaranteed parameter estimation problems for nonlinear dynamic models is computationally very demanding. In this contribution we present a memetic algorithm that determines the sets of feasible model parameters efficiently. It is applied to the estimation of kinetic parameters of a model that describes a copolymerization reaction. In the memetic algorithm, the fitness evaluation is based on the distance of the feasible solutions to each other, thus the presented approach is not restricted to a specific type of models

Condition-based operational optimization of industrial combined heat and power plants under time-sensitive electricity prices

This paper presents an approach to the inclusion of the degradation of the equipment due to ramp-up and shut-down in the optimization of the response of chemical and power plants to the variation of the prices on the market for electric power. The state-of-the-art approach neglects the influence of the operating strategy on the degradation of the plant equipment and leads to aggressive responses to the price levels. The proposed Mixed Integer Linear Programming formulation maximizes the profit of a combined heat and power plant taking into account the reduction of the lifetime of the equipment that results from the operating strategy. A case study demonstrates the benefit of the proposed approach

Iterative process design with surrogate-assisted global flowsheet optimization

Flowsheet optimization is an important part of process design where commercial process simulators are widely used, due to their extensive library of models and ease of use. However, the application of a framework for global flowsheet optimization upon them is computationally expensive. Based on machine learning methods, we added mechanisms for rejection and generation of candidates to a framework for global flowsheet optimization. These extensions halve the amount of time needed for optimization such that the integration of the framework in a workflow for iterative process design becomes applicable

Comparison of dual based optimization methods for distributed trajectory optimization of coupled semi-batch processes

The physical and virtual connectivity of systems via flows of energy, material, information, etc., steadily increases. This paper deals with systems of sub-systems that are connected by networks of shared resources that have to be balanced. For the optimal operation of the overall system, the couplings between the sub-systems must be taken into account, and the overall optimum will usually deviate from the local optima of the sub-systems. However, for reasons, such as problem size, confidentiality, resilience to breakdowns, or generally when dealing with autonomous systems, monolithic optimization is often infeasible. In this contribution, iterative distributed optimization methods based on dual decomposition where the values of the objective functions of the different sub-systems do not have to be shared are investigated. We consider connected dynamic systems that share resources. This situation arises for continuous processes in transient conditions between different steady states and in inherently discontinuous processes, such as batch production processes. This problem is challenging since small changes during the iterations towards the satisfaction of the overarching constraints can lead to significant changes in the arc structures of the optimal solutions for the sub-systems. Moreover, meeting endpoint constraints at free final times complicates the problem. We propose a solution strategy for coupled semi-batch processes and compare different numerical approaches, the sub-gradient method, ADMM, and ALADIN, and show that convexification of the sub-systems around feasible points increases the speed of convergence while using second-order information does not necessarily do so. Since sharing of resources has an influence on whether trajectory dependent terminal constraints can be satisfied, we propose a heuristic for the computation of free final times of the sub-systems that allows the dynamic sub-processes to meet the constraints. For the example of several semi-batch reactors which are coupled via a bound on the total feed flow rate, we demonstrate that the distributed methods converge to (local) optima and highlight the strengths and the weaknesses of the different distributed optimization methods

Analysis of a memetic algorithm for global optimization in chemical process synthesis

Engineering optimization often deals with very large search spaces which are highly constrained by nonlinear equations that couple the continuous variables. In this contribution the development of a memetic algorithm (MA) for global optimization in the solution of a problem in the chemical process engineering domain is described. The combination of an evolutionary strategy and a local solver based on the general reduced gradient method enables the exploitation of a significant reduction in the search space and of the ability of local mathematical programming solvers to efficiently handle large continuous problems containing equality constraints. The global performance of the MA is improved by the exclusion of regions that are defined by approximations of the basins of attraction of the local optima. The MA is compared to the combination of a scatter search based multi-start heuristic using OQNLP and the local solver CONOPT

Surrogate modeling of thermodynamic equilibria: applications, sampling and optimization

Models based on first principles are an effective way to model chemical processes. The quality of these depends critically on the accurate description of thermodynamic equilibria. This is provided by modern thermodynamic models, e.g., PC-SAFT, but they come with a high computational cost, which makes process optimization challenging. This can be addressed by using surrogate models to approximate the equilibrium calculations. A high accuracy of the surrogate model can be achieved by carefully choosing the points at which the original function is evaluated to create data for the training of the surrogate models, called sampling. Using a case study, different approaches to sampling are discussed and evaluated with a focus on new approaches to adaptive sampling

Price-based coordination of interconnected systems with access to external markets

Many industrial processes are coupled via multiple networks of energy and materials to achieve a resource and energy efficient production. In many cases however, setting up an integrated optimization problem for all units or plants that are directly connected to the networks is not possible, especially when not all information can be shared. In such cases, dual decomposition or price-based coordination can be used, where optimal transfer prices are iteratively determined at which the networks are balanced and the resources are allocated optimally between the participants. In this contribution, price-based coordination is extended to include the situation where limited resources can be bought or sold at predefined prices from external markets (e.g. via pipelines) and the resulting algorithms are demonstrated for a realistic example

Modeling and energy efficiency analysis of the steelmaking process in an electric arc furnace

This paper presents a comprehensive model of an industrial electric arc furnace (EAF) that is based upon several rigorous first-principles submodels of the heat exchange in the EAF and practical experience from an industrial melt shop. The model is suited for process simulation, optimization, and control applications. It assumes that the energy demand of the process is satisfied by six sources, the electric arc, the oxy-fuel burners, the oxygen lances, the combustion of coal, and the oxidation of metal in the liquid and in the solid phase. The energy exchange between the liquid and the solid phase due to liquid metal splashing is also considered. The different mechanisms of heat exchange are represented in the model as follows: (a) the radiative heat exchange from the arc to the other phases is computed using the DC circuit analogy, where the view factors are calculated using exact formulae and Monte-Carlo algorithms. (b) The energy input from the oxy-fuel burner is modeled using simplified geometries for which heat transfer relationships are known. (c) The amount of heat released by the oxidation of solid metal is described by the quadratic corrosion formula. (d) The energy exchange from the bath to the solid phase due to splashing is modeled using relationships and experimental data that are available in the literature. The model contains the melting rates and the efficiency of the oxygen lancing as free parameters; their values were computed by a least squares fit to process data of an industrial Ultra-High-Power EAF. In comparison with existing EAF models, the model presented here describes the dynamic behavior of the melting process more realistically. Based on the model, time-dependent energy efficiency curves for the various contributions and for the overall process are computed and discussed

Virtual splitting of shared resource networks for pricebased coordination with portfolio tariffs

In the process industries the optimal allocation of shared resources among physically coupled subsystems is key to an efficient operation of the overall system, e. g., an integrated production site. If the subsystems have a certain level of autonomy or it is desired to grant confidentiality to the constituent subsystems, price-based coordination can be employed, where an independent system operator (ISO) iteratively adjusts transfer prices for the shared resources until the demand and the supply match, i. e., the shared resource networks are balanced. In this contribution, a modified subgradient price update scheme is presented, which can be used for systems that are connected to external resources, such as pipelines, through which certain amounts of the resources can be exchanged at prices that are fixed in portfolio tariffs. The approach virtually splits the shared resource networks to account for the different price regimes in the available tariff. The principle is illustrated in a simulation study of a production site with three productions plants that are connected to an external distribution grid

Numerical estimation of the geometry and temperature of an alternating current steelmaking electric arc

A channel arc model (CAM) that predicts the temperature and the geometry of an electric arc from its voltage and impedance set-points is presented. The core of the model is a nonlinear programming (NLP) formulation that minimizes the entropy production of a plasma column, the physical and electrical properties of which satisfy the Elenbaas–Heller equation and Ohm's law. The radiative properties of the plasma are approximated utilizing the net emission coefficient (NEC), and the NLP is solved using a global numerical solver. The effects of the voltage and impedance set-points on the length of the electric arc are studied, and a linear formula that estimates the length of the arc in terms of its electrical set-points is deducted. The length of various electric arcs is measured in a fully operative electric arc furnace (EAF), and the results are used to validate the proposed models. The errors in the predictions of the models are 0.5 and 0.4 cm. In comparison, the existing empirical and Bowman formulae estimate the length of the experimental arcs with errors of 2.1 and 2.6 cm. A simplified formula to estimate the temperature of an electric arc in terms of its electrical set-points is also presented