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.

A new battery modelling method based on simulation error minimization

A new battery modelling method is presented based on the simulation error minimization criterion rather than the conventional prediction error criterion. A new integrated optimization method to optimize the model parameters is proposed. This new method is validated on a set of Li ion battery test data, and the results confirm the advantages of the proposed method in terms of the model generalization performance and long-term prediction accuracy.

Experimental and Modelling Studies of the Thermodynamics and Kinetics of Phase and Structural Transformations in a Gamma TiAl-based Alloy

This work combines microscopy, synchrotron radiation X-ray diffraction, differential scanning calorimetry and thermodynamic calculations in the characterisation of phase transformation behaviour of a Ti–46Al–1.9Cr–3Nb alloy upon continuous heating at constant rates. It has been found that the Ti–46Al–1.9Cr–3Nb alloy after being forged at 1200 °C without further treatment has a duplex microstructure consisting of fine equiaxed and lamellar ? grains with a small amount of a2 plates and particles and about 1 wt.% B2 phase. Differential scanning calorimetry revealed reproducibly several thermal effects upon heating of the as-forged alloy. These thermal effects are related to the equilibration and homogenisation of the sample, change of phase ratios between a2, ? and B2 phases in particular the increase of B2 in respect to a2 and ?, and the following five phase transformations: a2 + ? + B2 a + ? + B2, a + ? + B2 a + ?, ? + a a, a a + ß, a + ß a + ß + L. The observation of these transformations by differential scanning calorimetry is largely in agreement with literature phase diagrams and thermodynamic calculations, though care is needed to consider the different alloy compositions. Kinetics of the ? + a a phase transformation in the Ti–46Al–1.9Cr–3Nb alloy has been quantitatively derived from the calorimetry data, giving phase compositions at any point during the transformation upon continuous heating.

Integrating Aircraft Cost Modelling into Conceptual Design

The article presents cost modeling results from the application of the Genetic-Causal cost modeling principle. Industrial results from redesign are also presented to verify the opportunity for early concept cost optimization by using Genetic-Causal cost drivers to guide the conceptual design process for structural assemblies. The acquisition cost is considered through the modeling of the recurring unit cost and non-recurring design cost. The operational cost is modeled relative to acquisition cost and fuel burn for predominately metal or composites designs. The main contribution of this study is the application of the Genetic-Causal principle to the modeling of cost, helping to understand how conceptual design parameters impact on cost, and linking that to customer requirements and life cycle cost.

Economic modelling of antenatal screening and ultrasound scanning programmes for identification of fetal abnormalities

Objective Within the framework of a health technology assessment and using an economic model, to determine the most clinically and cost effective policy of scanning and screening for fetal abnormalities in early pregnancy. Design A discrete event simulation model of 50,000 singleton pregnancies. Setting Maternity services in Scotland. Population Women during the first 24 weeks of their pregnancy. Methods The mathematical model was populated with data on uptake of screening, prevalence, detection and false positive rates for eight fetal abnormalities and with costs for ultrasound scanning and serum screening. Inclusion of abnormalities was based on the relative prevalence and clinical importance of conditions and the availability of data. Six strategies for the identification of abnormalities prenatally including combinations of first and second trimester ultrasound scanning and first and second trimester screening for chromosomal abnormalities were compared. Main outcome measures The number of abnormalities detected and missed, the number of iatrogenic losses resulting from invasive tests, the total cost of strategies and the cost per abnormality detected were compared between strategies. Results First trimester screening for chromosomal abnormalities costs more than second trimester screening but results in fewer iatrogenic losses. Strategies which include a second trimester ultrasound scan result in more abnormalities being detected and have lower costs per anomaly detected. Conclusions The preferred strategy includes both first and second trimester ultrasound scans and a first trimester screening test for chromosomal abnormalities. It has been recommended that this policy is offered to all women in Scotland.

Modelling of aircraft manufacturing cost at the concept stage

The work presented is concerned with the estimation of manufacturing cost at the concept design stage, when little technical information is readily available. The work focuses on the nose cowl sections of a wide range of engine nacelles built at Bombardier Aerospace Shorts of Belfast. A core methodology is presented that: defines manufacturing cost elements that are prominent; utilises technical parameters that are highly influential in generating those costs; establishes the linkage between these two; and builds the associated cost estimating relations into models. The methodology is readily adapted to deal with both the early and more mature conceptual design phases, which thereby highlights the generic, flexible and fundamental nature of the method. The early concept cost model simplifies cost as a cumulative element that can be estimated using higher level complexity ratings, while the mature concept cost model breaks manufacturing cost down into a number of constituents that are each driven by their own specific drivers. Both methodologies have an average error of less that ten percent when correlated with actual findings, thus achieving an acceptable level of accuracy. By way of validity and application, the research is firmly based on industrial case studies and practice and addresses the integration of design and manufacture through cost. The main contribution of the paper is the cost modelling methodology. The elemental modelling of the cost breakdown structure through materials, part fabrication, assembly and their associated drivers is relevant to the analytical design procedure, as it utilises design definition and complexity that is understood by engineers.

A novel approach to dynamic modelling of polymer extrusion for improved process control

Polymer extrusion is a complex process and the availability of good dynamic models is key for improved system operation. Previous modelling attempts have failed adequately to capture the non-linearities of the process or prove too complex for control applications. This work presents a novel approach to the problem by the modelling of extrusion viscosity and pressure, adopting a grey box modelling technique that combines mechanistic knowledge with empirical data using a genetic algorithm approach. The models are shown to outperform those of a much higher order generated by a conventional black box technique while providing insight into the underlying processes at work within the extruder.

Single-ionization of helium at Ti:sapphire wavelengths: rates and scaling laws

We present a numerical and theoretical study of intense-field single-electron ionization of helium at 390 nm and 780 nm. Accurate ionization rates (over an intensity range of (0.175-34) X10^14 W/ cm^2 at 390 nm, and (0.275 - 14.4) X 10^14 W /cm^2 at 780 nm) are obtained from full-dimensionality integrations of the time-dependent helium-laser Schroedinger equation. We show that the power law of lowest order perturbation theory, modified with a ponderomotive-shifted ionization potential, is capable of modelling the ionization rates over an intensity range that extends up to two orders of magnitude higher than that applicable to perturbation theory alone. Writing the modified perturbation theory in terms of scaled wavelength and intensity variables, we obtain to first approximation a single ionization law for both the 390 nm and 780 nm cases. To model the data in the high intensity limit as well as in the low, a new function is introduced for the rate. This function has, in part, a resemblance to that derived from tunnelling theory but, importantly, retains the correct frequency-dependence and scaling behaviour derived from the perturbative-like models at lower intensities. Comparison with the predictions of classical ADK tunnelling theory confirms that ADK performs poorly in the frequency and intensity domain treated here.

Unlinked vital events in census-based longitudinal studies can bias subsequent analysis

Objective: To examine the potential biases arising from the nonlinkage of census records and vital events in longitudinal studies.
Study Design and Setting: A total of 56,396 deaths of residents of Northern Ireland in the 4 years after the 2001 Census were linked to the 2001 Census records. The characteristics of matched and nonmatched death records were compared using multivariate logistic regression. Subject attributes were as recorded on the death certificate.
Results: In total, 3,392 (6.0%) deaths could not be linked to a census record. Linkage rates were lowest in young adults, males, the unmarried, people living in communal establishments, or living in areas that were more deprived or had recorded low census enumeration. For those aged less than 65 years at census, this linkage would exclude from analysis 20.2% of suicides and 19.7% of deaths by external causes.
Conclusion: The nonlinkage of census and death records is a combination of nonenumeration at census and deficient information about the deceased recorded at the time of death. Unmatched individuals may have been more disadvantaged or socially isolated, and analysis based on the linked data set may therefore show some bias and perhaps understate true social gradients.

Genetic algorithms for local controller network construction

Local Controller Networks (LCNs) provide nonlinear control by interpolating between a set of locally valid, subcontrollers covering the operating range of the plant. Constructing such networks typically requires knowledge of valid local models. This paper describes a new genetic learning approach to the construction of LCNs directly from the dynamic equations of the plant, or from modelling data. The advantage is that a priori knowledge about valid local models is not needed. In addition to allowing simultaneous optimisation of both the controller and validation function parameters, the approach aids transparency by ensuring that each local controller acts independently of the rest at its operating point. It thus is valuable for simultaneous design of the LCNs and identification of the operating regimes of an unknown plant. Application results from a highly nonlinear pH neutralisation process and its associated neural network representation are utilised to illustrate these issues.

Neural modelling, control and optimisation of an industrial grinding process

This paper describes the development of neural model-based control strategies for the optimisation of an industrial aluminium substrate disk grinding process. The grindstone removal rate varies considerably over a stone life and is a highly nonlinear function of process variables. Using historical grindstone performance data, a NARX-based neural network model is developed. This model is then used to implement a direct inverse controller and an internal model controller based on the process settings and previous removal rates. Preliminary plant investigations show that thickness defects can be reduced by 50% or more, compared to other schemes employed. (c) 2004 Elsevier Ltd. All rights reserved.