Optimisation of Kinetic Parameters for an After-treatment Catalyst

Mathematical modelling has become an essential tool in the design of modern catalytic systems. Emissions legislation is becoming increasingly stringent, and so mathematical models of aftertreatment systems must become more accurate in order to provide confidence that a catalyst will convert pollutants over the required range of conditions. 
Automotive catalytic converter models contain several sub-models that represent processes such as mass and heat transfer, and the rates at which the reactions proceed on the surface of the precious metal. Of these sub-models, the prediction of the surface reaction rates is by far the most challenging due to the complexity of the reaction system and the large number of gas species involved. The reaction rate sub-model uses global reaction kinetics to describe the surface reaction rate of the gas species and is based on the Langmuir Hinshelwood equation further developed by Voltz et al. [1] The reactions can be modelled using the pre-exponential and activation energies of the Arrhenius equations and the inhibition terms. 
The reaction kinetic parameters of aftertreatment models are found from experimental data, where a measured light-off curve is compared against a predicted curve produced by a mathematical model. The kinetic parameters are usually manually tuned to minimize the error between the measured and predicted data. This process is most commonly long, laborious and prone to misinterpretation due to the large number of parameters and the risk of multiple sets of parameters giving acceptable fits. Moreover, the number of coefficients increases greatly with the number of reactions. Therefore, with the growing number of reactions, the task of manually tuning the coefficients is becoming increasingly challenging. 
In the presented work, the authors have developed and implemented a multi-objective genetic algorithm to automatically optimize reaction parameters in AxiSuite®, [2] a commercial aftertreatment model. The genetic algorithm was developed and expanded from the code presented by Michalewicz et al. [3] and was linked to AxiSuite using the Simulink add-on for Matlab. 
The default kinetic values stored within the AxiSuite model were used to generate a series of light-off curves under rich conditions for a number of gas species, including CO, NO, C_{3H8 and C3H6. These light-off curves were used to generate an objective function.} 
This objective function was used to generate a measure of fit for the kinetic parameters. The multi-objective genetic algorithm was subsequently used to search between specified limits to attempt to match the objective function. In total the pre-exponential factors and activation energies of ten reactions were simultaneously optimized. 
The results reported here demonstrate that, given accurate experimental data, the optimization algorithm is successful and robust in defining the correct kinetic parameters of a global kinetic model describing aftertreatment processes.

Linking Parametric CAD with Adjoint Surface Sensitivities

The goal of this work is to present an efficient CAD-based adjoint process chain for calculating parametric sensitivities (derivatives of the objective function with respect to the CAD parameters) in timescales acceptable for industrial design processes. The idea is based on linking parametric design velocities (geometric sensitivities computed from the CAD model) with adjoint surface sensitivities. A CAD-based design velocity computation method has been implemented based on distances between discrete representations of perturbed geometries. This approach differs from other methods due to the fact that it works with existing commercial CAD packages (unlike most analytical approaches) and it can cope with the changes in CAD model topology and face labeling. Use of the proposed method allows computation of parametric sensitivities using adjoint data at a computational cost which scales with the number of objective functions being considered, while it is essentially independent of the number of design variables. The gradient computation is demonstrated on test cases for a Nozzle Guide Vane (NGV) model and a Turbine Rotor Blade model. The results are validated against finite difference values and good agreement is shown. This gradient information can be passed to an optimization algorithm, which will use it to update the CAD model parameters.

Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

Scheduling and Platforming Trains at Busy Complex Stations

We consider the problem of train planning or scheduling for large, busy, complex train stations, which are common in Europe and elsewhere, though not in North America. We develop the constraints and objectives for this problem, but these are too computationally complex to solve by standard combinatorial search or integer programming methods. Also, the problem is somewhat political in nature, that is, it does not have a clear objective function because it involves multiple train operators with conflicting interests. We therefore develop scheduling heuristics analogous to those successfully adopted by train planners using ''manual'' methods. We tested the model and algorithms by applying to a typical large station that exhibits most of the complexities found in practice. The results compare well with those found by traditional methods, and take account of cost and preference trade-offs not handled by those methods. With successive refinements, the algorithm eventually took only a few seconds to run, the time depending on the version of the algorithm and the scheduling problem. The scheduling models and algorithms developed and tested here can be used on their own, or as key components for a more general system for train scheduling for a rail line or network.Train scheduling for a busy station includes ensuring that there are no conflicts between several hundred trains per day going in and out of the station on intersecting paths from multiple in-lines and out-lines to multiple platforms, while ensuring that each train is allowed at least its minimum required headways, dwell time, turnaround time and trip time. This has to be done while minimizing (costs of) deviations from desired times, platforms or lines, allowing for conflicts due to through-platforms, dead-end platforms, multiple sub-platforms, and possible constraints due to infrastructure, safety or business policy.

Distribution-based adaptive bounding genetic algorithm for continuous optimisation problems

A new search-space-updating technique for genetic algorithms is proposed for continuous optimisation problems. Other than gradually reducing the search space during the evolution process with a fixed reduction rate set ‘a priori’, the upper and the lower boundaries for each variable in the objective function are dynamically adjusted based on its distribution statistics. To test the effectiveness, the technique is applied to a number of benchmark optimisation problems in comparison with three other techniques, namely the genetic algorithms with parameter space size adjustment (GAPSSA) technique [A.B. Djurišic, Elite genetic algorithms with adaptive mutations for solving continuous optimization problems – application to modeling of the optical constants of solids, Optics Communications 151 (1998) 147–159], successive zooming genetic algorithm (SZGA) [Y. Kwon, S. Kwon, S. Jin, J. Kim, Convergence enhanced genetic algorithm with successive zooming method for solving continuous optimization problems, Computers and Structures 81 (2003) 1715–1725] and a simple GA. The tests show that for well-posed problems, existing search space updating techniques perform well in terms of convergence speed and solution precision however, for some ill-posed problems these techniques are statistically inferior to a simple GA. All the tests show that the proposed new search space update technique is statistically superior to its counterparts.

Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D < n(2/3). The local search procedure employs the stopping criterion (In/delta)(D/gamma) where m is an estimation of the average number of neighbouring conformations, gamma relates to the mean of non-zero differences of the objective function for neighbouring conformations, and 1-delta is the confidence that a minimum conformation has been found. The bound complies with the results obtained for the ten benchmark problems. (c) 2008 Elsevier Ltd. All rights reserved.

Population pharmacokinetic and pharmacogenetic analysis of 6-mercaptopurine in paediatric patients with acute lymphoblastic leukaemia

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT center dot The cytotoxic effects of 6-mercaptopurine (6-MP) were found to be due to drug-derived intracellular metabolites (mainly 6-thioguanine nucleotides and to some extent 6-methylmercaptopurine nucleotides) rather than the drug itself. center dot Current empirical dosing methods for oral 6-MP result in highly variable drug and metabolite concentrations and hence variability in treatment outcome. WHAT THIS STUDY ADDS center dot The first population pharmacokinetic model has been developed for 6-MP active metabolites in paediatric patients with acute lymphoblastic leukaemia and the potential demographic and genetically controlled factors that could lead to interpatient pharmacokinetic variability among this population have been assessed. center dot The model shows a large reduction in interindividual variability of pharmacokinetic parameters when body surface area and thiopurine methyltransferase polymorphism are incorporated into the model as covariates. center dot The developed model offers a more rational dosing approach for 6-MP than the traditional empirical method (based on body surface area) through combining it with pharmacogenetically guided dosing based on thiopurine methyltransferase genotype. To investigate the population pharmacokinetics of 6-mercaptopurine (6-MP) active metabolites in paediatric patients with acute lymphoblastic leukaemia (ALL) and examine the effects of various genetic polymorphisms on the disposition of these metabolites. Data were collected prospectively from 19 paediatric patients with ALL (n = 75 samples, 150 concentrations) who received 6-MP maintenance chemotherapy (titrated to a target dose of 75 mg m(-2) day(-1)). All patients were genotyped for polymorphisms in three enzymes involved in 6-MP metabolism. Population pharmacokinetic analysis was performed with the nonlinear mixed effects modelling program (nonmem) to determine the population mean parameter estimate of clearance for the active metabolites. The developed model revealed considerable interindividual variability (IIV) in the clearance of 6-MP active metabolites [6-thioguanine nucleotides (6-TGNs) and 6-methylmercaptopurine nucleotides (6-mMPNs)]. Body surface area explained a significant part of 6-TGNs clearance IIV when incorporated in the model (IIV reduced from 69.9 to 29.3%). The most influential covariate examined, however, was thiopurine methyltransferase (TPMT) genotype, which resulted in the greatest reduction in the model's objective function (P

Population-based local search for protein folding simulation in the MJ energy model and cubic lattices

We present experimental results on benchmark problems in 3D cubic lattice structures with the Miyazawa-Jernigan energy function for two local search procedures that utilise the pull-move set: (i) population-based local search (PLS) that traverses the energy landscape with greedy steps towards (potential) local minima followed by upward steps up to a certain level of the objective function; (ii) simulated annealing with a logarithmic cooling schedule (LSA). The parameter settings for PLS are derived from short LSA-runs executed in pre-processing and the procedure utilises tabu lists generated for each member of the population. In terms of the total number of energy function evaluations both methods perform equally well, however. PLS has the potential of being parallelised with an expected speed-up in the region of the population size. Furthermore, both methods require a significant smaller number of function evaluations when compared to Monte Carlo simulations with kink-jump moves. (C) 2009 Elsevier Ltd. All rights reserved.

A Hybrid Evolutionary Approach to the Nurse Rostering Problem

Nurse rostering is a difficult search problem with many constraints. In the literature, a number of approaches have been investigated including penalty function methods to tackle these constraints within genetic algorithm frameworks. In this paper, we investigate an extension of a previously proposed stochastic ranking method, which has demonstrated superior performance to other constraint handling techniques when tested against a set of constrained optimisation benchmark problems. An initial experiment on nurse rostering problems demonstrates that the stochastic ranking method is better in finding feasible solutions but fails to obtain good results with regard to the objective function. To improve the performance of the algorithm, we hybridise it with a recently proposed simulated annealing hyper-heuristic within a local search and genetic algorithm framework. The hybrid algorithm shows significant improvement over both the genetic algorithm with stochastic ranking and the simulated annealing hyper-heuristic alone. The hybrid algorithm also considerably outperforms the methods in the literature which have the previously best known results.

An Analytical Study of Surplus Value using a Value Driven Design Methodology

People are now becoming more environmentally aware and as a consequence of this, industries such as the aviation industry are striving to design more environmentally friendly products. To achieve this, the current design methodologies must be modified to ensure these issues are considered from product conception through to disposal. This paper discusses the environmental problems in relation to the aviation industry and highlights some logic for making the change from the traditional Systems Engineering approach to the recent design paradigm known as Value Driven Design. Preliminary studies have been undertaken to aid in the understanding of this methodology and the existing surplus value objective function. The main results from the work demonstrate that surplus value works well bringing disparate issues such as manufacture and green taxes together to aid decision making. Further, to date studies on surplus value have used simple sensitivity analysis, but deeper consideration shows non-linear interactions between some of the variables and further work will be needed to fully account for complex issues such as environmental impact and taxes.

Temporal extension of Laplacian Eigenmaps for unsupervised dimensionality reduction of time series

A novel non-linear dimensionality reduction method, called Temporal Laplacian Eigenmaps, is introduced to process efficiently time series data. In this embedded-based approach, temporal information is intrinsic to the objective function, which produces description of low dimensional spaces with time coherence between data points. Since the proposed scheme also includes bidirectional mapping between data and embedded spaces and automatic tuning of key parameters, it offers the same benefits as mapping-based approaches. Experiments on a couple of computer vision applications demonstrate the superiority of the new approach to other dimensionality reduction method in term of accuracy. Moreover, its lower computational cost and generalisation abilities suggest it is scalable to larger datasets. © 2010 IEEE.

Prophylactic ranitidine treatment in critically ill children - a population pharmacokinetic study

Aims: To characterize the population pharmacokinetics of ranitidine in critically ill children and to determine the influence of various clinical and demographic factors on its disposition. Methods: Data were collected prospectively from 78 paediatric patients (n = 248 plasma samples) who received oral or intravenous ranitidine for prophylaxis against stress ulcers, gastrointestinal bleeding or the treatment of gastro-oesophageal reflux. Plasma samples were analysed using high-performance liquid chromatography, and the data were subjected to population pharmacokinetic analysis using nonlinear mixed-effects modelling. Results: A one-compartment model best described the plasma concentration profile, with an exponential structure for interindividual errors and a proportional structure for intra-individual error. After backward stepwise elimination, the final model showed a significant decrease in objective function value (-12.618; P <0.001) compared with the weight-corrected base model. Final parameter estimates for the population were 32.1lh for total clearance and 285l for volume of distribution, both allometrically modelled for a 70kg adult. Final estimates for absorption rate constant and bioavailability were 1.31h and 27.5%, respectively. No significant relationship was found between age and weight-corrected ranitidine pharmacokinetic parameters in the final model, with the covariate for cardiac failure or surgery being shown to reduce clearance significantly by a factor of 0.46. Conclusions: Currently, ranitidine dose recommendations are based on children's weights. However, our findings suggest that a dosing scheme that takes into consideration both weight and cardiac failure/surgery would be more appropriate in order to avoid administration of higher or more frequent doses than necessary.

A Novel Method to Enable Trade-offs Across the Whole Product Life of an Aircraft Using Value Driven Design

The increasing need to understand complex products and systems with long life spans, presents a significant challenge to designers who increasingly require a broader understanding of the operational aspects of the system. This demands an evolution in current design practice, as designers are often constrained to provide a subsystem solution without full knowledge of the global system operation. Recently there has been a push to consider value centric approaches which should facilitate better or more rapid convergence to design solutions with predictable completion schedules. Value Driven Design is one such approach, in which value is used as the system top level objective function. This provides a broader view of the system and enables all sub-systems and components to be designed with a view to the effect on project value. It also has the capacity to include value expressions for more qualitative aspects, such as environmental impact. However, application of the method to date has been restricted to comparing value in a programme where the lifespan is fixed and known a priori. This paper takes a novel view of value driven design through the surplus value objective function, and shows how it can be used to identify key sensitivities to guide designers in design trade-off decisions. By considering a new time based approach it can be used to identify optimum programme life-span and hence allow trade-offs over the whole product life.

Surrogate-based analysis and optimization for the design of heat sinks with jet impingement

Heat sinks are widely used for cooling electronic devices and systems. Their thermal performance is usually determined by the material, shape, and size of the heat sink. With the assistance of computational fluid dynamics (CFD) and surrogate-based optimization, heat sinks can be designed and optimized to achieve a high level of performance. In this paper, the design and optimization of a plate-fin-type heat sink cooled by impingement jet is presented. The flow and thermal fields are simulated using the CFD simulation; the thermal resistance of the heat sink is then estimated. A Kriging surrogate model is developed to approximate the objective function (thermal resistance) as a function of design variables. Surrogate-based optimization is implemented by adaptively adding infill points based on an integrated strategy of the minimum value, the maximum mean square error approach, and the expected improvement approaches. The results show the influence of design variables on the thermal resistance and give the optimal heat sink with lowest thermal resistance for given jet impingement conditions.