S. Feyo de Azevedo

A simulated annealing approach to the solution of minlp problems

An algorithm (M-SIMPSA) suitable for the optimization of mixed integer non-linear programming (MINLP) problems is presented. A recently proposed continuous non-linear solver (SIMPSA) is used to update the continuous parameters, and the Metropolis algorithm is used to update the complete solution vector of decision variables. The M-SIMPSA algorithm, which does not require feasible initial points or any problem decomposition, was tested with several functions published in the literature, and results were compared with those obtained with a robust adaptive random search method. For ill-conditioned problems, the proposed approach is shown to be more reliable and more efficient as regards the overcoming of difficulties associated with local optima and in the ability to reach feasibility. The results obtained reveal its adequacy for the optimization of MINLP problems encountered in chemical engineering practice.

Tuning of observer-based estimators: theory and application to the on-line estimation of kinetic parameters

This paper deals with the tuning of observer-based estimators. Initially, these algorithms were designed for estimating on-line kinetic parameters, like specific growth rates, in bioprocesses, and have proved to be very successful in practical applications. Here a systematic tuning approach that allows a decoupled estimation of each parameter and the assignment of the estimator dynamics independently of the process dynamics is proposed. The presented approach is illustrated on an animal cell culture example in numerical simulation and with real-life data

Optimization of reactive distillation processes with simulated annealing

A simulated annealing-based algorithm (MSIMPSA) suitable for the optimization of mixed integer non-linear programming (MINLP) problems was applied to the synthesis of a non-equilibrium reactive distillation column. A simulation model based on an extension of conventional distillation is proposed for the simulation step of the optimization problem. In the case of ideal vapor}liquid equilibrium, the simulation results are similar to those obtained by Ciric and Gu (1994, AIChE Journal, 40(9), 1479) using the GAMS environment and to those obtained with the AspenPlus modular simulator. The optimization results are also similar to those previously reported and similar to those using an adaptive random search algorithm (MSGA). The optimizations were also performed with non-ideal vapor}liquid equilibrium, considering either distributed feed and reaction trays or single feed and reaction tray. The results show that the optimized objective function values are very similar, and mostly independent of the number of trays and of the reaction distribution. It is shown that the proposed simulation/optimization equation-oriented environments are capable of providing optimized solutions which are close to the global optimum, and reveal its adequacy for the optimization of reactive distillation problems encountered in chemical engineering practice. ( 2000 Elsevier Science Ltd. All rights reserved.

Hybrid modelling of biochemical processes: A comparison with the conventional approach

Abstract This paper addresses attitudes and forms of process modelling in biochemical engineering. Bakers yeast production in a fed-batch fermenter, at laboratory scale, is employed as case-study. Three modelling approaches are described and compared, viz. — the conventional mechanistic approach, formulations based on different artificial neural network (ANN) topologies and a hybrid mechanistic-ANN structure. A standard 2-step procedure of model development, estimation (training) and validation with two independent sets of experiments, has been carried out. The mechanistic model, using reaction kinetic schemes from the literature, fine tuned by classical non-linear regression, gave smooth predictions for the validation data runs, but showed limited ability in predicting the test data. The ANN were able to describe experiments at the training stage, but failed the validation (i.e. extrapolation) procedure, giving oscillatory predictions of the process state. Additionally, this approach suffers from a strong influence of the net parameters, which must be chosen by trial and error. The hybrid model predictions are good with the training and very satisfactory with the experimental test data. The indication is that the latter is a powerful tool for process modelling in biochemical engineering, particularly when limited theoretical knowledge of the process is available.

Quantification of the morphology of sucrose crystals by image analysis

Automated image analysis procedures combined with discriminant factorial analysis (DFA) have been developed to classify agglomerated sucrose crystals according to their shape. The crystals are observed by optical microscopy. Agreement between manual and automated classifications is 90% in average. Each crystal is characterised by its own degree of agglomeration, calculated from the output of the classification. Mono-crystals are further classified into two types according to the habit of their projected silhouette. The use of these techniques is illustrated on commercial sucrose and batch-crystallised particles obtained in a lab-scale reactor in presence of impurities (dextran, raffinose, glucose, sodium carbonate) known to modify the sucrose crystal habit.

AN IMPROVED RANDOM-SEARCH ALGORITHM FOR NON-LINEAR OPTIMIZATION

Abstract An adaptive random search optimization algorithm is presented, which is found to be very efficient in dealing with non-linear constrained and unconstrained problems. The major differences relatively to previously reported algorithms are that variable, parameter dependent compression vectors are employed in the contraction of the search regions and that shifting strategies incorporating “wrong-way” moves are enforced. The algorithm was tested with 24 severe functions published in the literature. Results were compared with those obtained employing another random search method and with published work. The proposed algorithm is shown to be more robust and more efficient in what concerns the overcoming of difficulties associated with local optima, the sensitivity to search intervals and associated compression factors, the starting solution vector and the dependency upon the random number sequence. The results obtained reveal the adequacy of the algorithm for the optimization of a broad range of problems encountered in chemical engineering practice.

Stability, dynamics of convergence and tuning of observer-based kinetics estimators

This work discusses issues concerning stability, tuning and dynamics of convergence of observer-based kinetics estimators. The analysis focuses on both continuous and discrete time formulations of the estimation algorithms. Concerning the former, it is shown that, with proper tuning, stability can be guaranteed, while simultaneously imposing a desired quasi-time invariant second order time response for the convergence of estimates to true values. Concerning the latter, an algorithm is presented, based on a forward Euler discretisation, whose error system is shown to be linear time-invariant. Furthermore, stability conditions were derived, which define the stable domain for the discretisation period as function of the tuning parameters. The theory is illustrated with a case-study of Baker’s yeast fermentation. Results clearly confirm the theoretical developments. In particular, results concerning the stability domain for the Euler-based discrete formulation of the estimator are shown to have relevant practical implications. # 2002 Elsevier Science Ltd. All rights reserved.

On-line monitoring of a sugar crystallization process

The present paper reports a comparative evaluation of four multivariate statistical process control (SPC) techniques for the on-line monitoring of an industrial sugar crystallization process. The process itself is challenging since it is carried out in multiple phases and there exists strong non-linear and dynamic effects between the variables. The methods investigated include classical on-line univariate statistical process control, batch dynamic principal component analysis (BDPCA), moving window principal component analysis (MWPCA), batch observation level analysis (BOL) and time-varying state space modelling (TVSS). The study is focused on issues of on-line detection of changes in crystallization process operation, the early warning of process malfunctions and potential production failures; problems that have not been directly addressed by existing statistical monitoring schemes. The results obtained demonstrate the superior performance of the TVSS approach to successfully detect abnormal events and periods of bad operation early enough to allow bad batches and related losses in amounts of recycled sucrose to be significantly reduced.

How to increase the performance of models for process optimization and control

Some key aspects of obtaining hybrid process models which perform well and that can be used in process supervision, optimization and control are discussed from the point of view of the benefit/cost-ratio. The importance of starting with a clear definition of the problem and a corresponding quantitative objective function is shown. In order to enhance the benefit/cost-ratio above the threshold of acceptance, a series of procedures is proposed: in the beginning an exploratory process data analysis is suggested to classify the process variables according to their importance and to facilitate the development of black- and grey-box models. Efficient validation of the model is shown to be indispensable. Hybrid model approaches proved to have to significant advantages, since they allow the activation of a larger portion of the available a-priori knowledge. Applications of hybrid models with respect to process optimization require new techniques, since the classical approaches are too difficult to use and are restricted to well-performing models. Finally, powerful software tools are required to implement the different algorithms at the production plants and to allow the efficient conversion of the ideas to real benefits.

A study on the convergence of observer-based kinetics estimators in stirred tank bioreactors

Abstract This paper is devoted to the tuning problem of an observer-based algorithm for the on-line estimation of reaction rates in stirred tank bioreactors. The relation between the dynamics of convergence and the tuning procedure is explored. The method proposed imposes a variable second-order dynamics on the convergence of the estimator. This approach is shown to compare favourably with a pole placement based technique, in an application to a bakers yeast fed-batch fermentation.