M.S.

In order to gain a fundamental understanding of actual solid propellant thermal stress problems, the geometry of the solid propellant baa been idealized as a short, circular cylinder with flat ends. It is felt that the consideration of actual curved ends would only unduly have complicated the analysis. The method of solution for the thermal stresses in the finite cylinder, that has been presented in this thesis, utilizes an arbitrarily selected set of cylinder end-conditions. Therefore, different end conditions than the ones employed here might have been considered just as easily. The fundamental difficulties encountered in the thermoelastic analysis of short cylinders are that firstly the problem is at least two-dimensional and secondly, it has mixed boundary conditions since displacements and/or stresses specified along at least four distinct boundaries. It is relatively simple to solve the governing differential equation by the method of separation of variables. The greatest difficulties are encountered in satisfying the various boundary conditions. As a matter of fact the method of solution for the thermal stresses that has been presented in this thesis is applicable only when the temperature distribution throughout the propellant and casing exhibits a particular variation in the axial direction, as shown by Eqs. (39) and (43). With such temperature fields, however the elastic analytic solutions that have been presented are significant since the simultaneous linear algebraic equations, for the arbitrary constants, are easily solved. It is true that, in principle, an infinite number of these arbitrary constants must be determined. From a practical point of view, however, the arbitrary constants can always be reduced to a finite number by truncating the obtained series solutions for the thermal displacements and stresses. / Master of Science

A tetrazole is a 5-membered ring containing 4 nitrogens and 1 carbon. Due to its energetic potential and structural similarity to carboxylic acids, this ring system has a wide number of applications. In this thesis, a new and safe sustainable process to produce tetrazoles was designed that acheived high yields under mild conditions. Also, a technique was developed to form a trityl-protected tetrazole in situ. The rest of this work involved the exploitation of the energetic potential of tetrazoles. This moiety was successfully applied in polymers, ionic liquids, foams, and gels. The overall results from these experiments illustrate the fact that tetrazoles have the potential to serve as a stable alternative to the troublesome azido group common in many energetic materials. Due to these applications, the tetrazole moiety is a very important entity.

This Thesis covers work conducted to understand the mechanisms underpinning the operation of the electrothermal-chemical gun. The initial formation of plasma from electrically exploding wires, through to the development of plasma venting from the capillary and interacting with a densely packed energetic propellant bed is included. The prime purpose of the work has been the development and validation of computer codes designed for the predictive modelling of the elect rothe rmal-ch em ical (ETC) gun. Two main discussions in this Thesis are: a proposed electrically insulating vapour barrier located around condensed exploding conductors and the deposition of metallic vapour resulting in a high energy flux to the surface of propellant, leading to propellant ignition. The vapour barrier hypothesis is important in a number of fields where the passage of current through condensed material or through plasma is significant. The importance may arise from the need to disrupt the fragments by applying strong magnetic fields (as in the disruption of metallic shaped charge jets); in the requirement to generate a metallic vapour efficiently from electrically exploding wires (as per ETC ignition systems); or in the necessity to re-use the condensed material after a discharge (as with lightning divertor strips). The ignition by metallic vapour deposition hypothesis relies on the transfer of latent heat during condensation. It is important for the efficient transfer of energy from an exploded wire (or other such metallic vapour generating device) to the surface of energetic material. This flux is obtained far more efficiently through condensation than from radiative energy transfer, because the energy required to evaporate copper is far less than that required to heat it to temperatures at which significant radiative flux would be emitted

This Thesis covers work conducted to understand the mechanisms underpinning the operation of the electrothermal-chemical gun. The initial formation of plasma from electrically exploding wires, through to the development of plasma venting from the capillary and interacting with a densely packed energetic propellant bed is included. The prime purpose of the work has been the development and validation of computer codes designed for the predictive modelling of the elect rothe rmal-ch em ical (ETC) gun. Two main discussions in this Thesis are: a proposed electrically insulating vapour barrier located around condensed exploding conductors and the deposition of metallic vapour resulting in a high energy flux to the surface of propellant, leading to propellant ignition. The vapour barrier hypothesis is important in a number of fields where the passage of current through condensed material or through plasma is significant. The importance may arise from the need to disrupt the fragments by applying strong magnetic fields (as in the disruption of metallic shaped charge jets); in the requirement to generate a metallic vapour efficiently from electrically exploding wires (as per ETC ignition systems); or in the necessity to re-use the condensed material after a discharge (as with lightning divertor strips). The ignition by metallic vapour deposition hypothesis relies on the transfer of latent heat during condensation. It is important for the efficient transfer of energy from an exploded wire (or other such metallic vapour generating device) to the surface of energetic material. This flux is obtained far more efficiently through condensation than from radiative energy transfer, because the energy required to evaporate copper is far less than that required to heat it to temperatures at which significant radiative flux would be emitted

No description available.

This thesis contains investigations in the area of polymers herein propellants binders are modified functionally to meet the requirements of future energetic propellants. Chapter 1 contains a broad introduction to the area of recent advances in solid propellants and the numerous applications of ‘Click Chemistry’. Chapters 2 details the materials, characterization tools and the experimental techniques employed for the studies. This is followed by Chapter 3, 4, and 5 which deals with functional modification of various propellants binders, their characterisation and evaluation in propellant formulations. Chapter 6 details with the thermal decomposition of diazides and its reaction with alkenes. The advent of modern rockets has opened a new era in the history of space exploration as well as defence applications. The driving force of the rocket emanates from the propellant – either solid or liquid. Composite solid propellants find an indispensable place, in today’s rockets and launch vehicles because of the inherent advantages such as high reliability, easy manufacturing, high thrust etc. The composite propellant consisting of inorganic oxidiser like ammonium perchlorate, (AP), ammonium nitrate (AN) etc), metallic fuel (aluminium powder, boron etc) and polymeric fuel binder (hydroxyl terminated polybutadiene-HTPB, polybutadiene-acrylic acid-acrylonitrile PBAN, glycidyl azide polymer (GAP), polyteramethylene oxide (PTMO) etc. is used in igniters, boosters, upper stage motors and special purpose motors in large launch vehicles. Large composite solid propellant grains or rocket motors in particular, demand adequate mechanical properties to enable them to withstand the stresses imposed during operation, handling, transportation and motor firing. They should also have a reasonably long ‘potlife’ to provide sufficient window for processing operations such as mixing and casting which makes the selection of binder with appropriate cure chemistry more challenging. In all composite solid propellants currently in use, polymers perform the role of a binder for the oxidiser, metallic fuel and other additives. It performs the dual role of imparting dimensional stability to the composite, provides structural integrity and good mechanical properties to the propellant besides acting as a fuel to impart the required energetics. Conventionally, the terminal hydroxyl groups in the binders like GAP, PTMO and HTPB are reacted with diisocyanates to form a polyurethane network, to impart the necessary mechanical properties to the propellant. A wide range of diisocyantes such as tolylene diisocyanate (TDI) and isophorone diisocyanate (IPDI) are used for curing of these binders. However, the incompatability of isocyanates with energetic oxidisers like ammonium dinitramide (ADN), hydrazinium nitroformate (HNF), short ‘potlife’ of the propellant slurry and undesirable side reactions with moisture are limiting factors which adversely affect the mechanical properties of curing binders through this route. The objective of the present study is to evolve an alternate approach of curing these binders is to make use of the 1,3 dipolar addition reactions between azide and alkyne groups which is a part of ‘Click chemistry’. This can be accomplished by the reaction of azide groups of GAP with triple bonds of alkynes and reactions of functionally modified HTPB/PTMO (azide/alkyne) to yield 1,2,3 -triazole based products. This offers an alternate route for processing of solid propellants wherein, the cured resins that have improved mechanical properties, better thermal stability and improved ballistic properties in view of the higher heat of decomposition resulting from the decomposition of the triazole groups. GAP is an azide containing energetic polymer. The azide groups can undergo reaction with alkynes to yield triazoles. In, Chapter 3 the synthesis and characterisation of various alkynyl compounds including bis propargyl succinate (BPS), bis propargyl adipate (BPA), bis propargyl sebacate (BPSc.) and bis propargyl oxy bisphenol A (BPB) for curing of GAP to yield triazoles networks are studied. The mechanism of the curing reaction of GAP with these alkynyl compounds was elucidated using a model compound viz. 2-azidoethoxyethane (AEE). The reaction mechanism has been analysed using Density Functional Theory (DFT) method. DFT based theoretical calculations implied marginal preference for 1, 5 addition over the 1, 4 addition for the uncatalysed cycloaddition reaction between azide and alkyne group. The detailed characterisation of these systems with respect to the cure kinetics, mechanical properties, dynamic mechanical behaviour and thermal decomposition characteristics were done and correlated to the structure of the network. The glass transition temperature (Tg), tensile strength and modulus of the system increased with crosslink density which in turn is, controlled by the azide to alkyne molar stoichiometry. Thermogravimetic analysis (TGA) showed better thermal stability for the GAP-triazole compared to GAP based urethanes. Though there have been a few reports on curing of GAP with alkynes, it is for the first time that a detailed characterisation of this system with respect to the cure kinetics, mechanical, dynamic mechanical, thermal decomposition mechanism of the polymer is being reported. To extent the concept of curing binders through 1,3 dipolar addition reaction, the binder HTPB as chemically transformed to propargyloxy carbonyl amine terminated polybutadiene (PrTPB) with azidoethoxy carbonyl amine terminated polybutadiene (AzTPB) and propargyloxy polybutadiene (PTPB). Similarly, PTMO was convnerted to propargyloxy polytetramethylene oxide (PTMP). Triazole-triazoline networks were derived by the reaction of the binders with alkyne/azide containing curing agents. The cure characteristics of these polymers (PrTPB with AzTPB, PTPB with GAP and PTMP with GAP) were studied by DSC. The detailed characterisations of the cured polymers for were done with respect to the, mechanical, dynamic mechanical behaviour and thermal decomposition characteristics were done. Propellant level studies were done using the triazoles derived from GAP, PrTPB-AzTPB, PTPB and PTMP as binder, in combination with ammonium perchlorate as oxidiser. The propellants were characterised with respect to rheological, mechanical, safety, as well as ballistic properties. From the studies, propellant formulations with improved energetics, safety characteristics, processability and mechanical properties as well defect free propellants could be developed using novel triazole crosslinked based binders. Chapter 6, is aimed at understanding the mechanism of thermal decomposition of diazido compounds in the first section. For this, synthesis and characterisation of a diazido ester 1,6 –bis (azidoacetoyloxy) hexane (HDBAA) was done. There have been no reports on the thermal decomposition mechanism of diazido compounds, where one azide group may influence the decomposition of the other. The thermal decomposition mechanism of the diazido ester were theoretically predicted by DFT method and corroborated by pyrolysis-GC-MS studies. In the second section of this chapter, the cure reaction of the diazido ester with the double bonds of HTPB has been investigated. The chapter 6B reports the mechanism of Cu (I) catalysed azide-alkene reaction validated using density functional theory (DFT) calculations in isomers of hexene (cis-3-hexene, trans-3-hexene and 2-methy pentene: model compound of HTPB) using HDBAA. This the first report on an isocyanate free curing of HTPB using an azide. Chapter 7 of the thesis summarizes the work carried out, the highlights and important findings of this work. The scope for future work such as development of high performance eco-friendly propellants based on triazoles in conjunction with chlorine-free oxidizer like ADN, synthesis of compatible plasticisers and suitable crosslinkers have been described. This work has given rise to one patent, three international publications and four papers in international conferences in the domain.

Thesis (MScIng)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: It was shown in an earlier study that it is possible to predict the spectral radiance of rocket combustion plumes directly from the propellant composition and motor parameters. Little is published in the open literature on this subject, but the current trend is to use determinative methods like computational fluid dynamics and statistical techniques to simulate wide band radiance based on blackbody temperature assumptions. A limitation of these methods is the fact that they are computationally expensive and rather complex to implement. An alternative modeling approach was used which did not rely on solving all the nonlinearities and complex relationships applicable to a fundamental model. A multilayer perceptron based Neural Network was used to develop a parametric functional mapping between the propellant chemical composition and the motor design and the resulting spectral irradiance measured in a section of the plume. This functional mapping effectively models the relationship between the rocket design and the plume spectral radiance. Two datasets were available for use in this study: Emission spectra from solid propellant rockets and flare emission spectra. In the case of the solid rocket propellants, the input to the network consisted of the chemical composition of the fuels and four motor parameters, with the output of the network consisting of 146 scaled emission spectra points in the waveband from 2-5 microns. The four motor parameters were derived from equations describing the mass flow characteristics of rocket motors. The mass flow through the rocket motor does have an effect on the shape of the plume of combustion gases, which in turn has an effect on the infrared signature of the plume. The characteristics of the mass flow through the nozzle of the rocket motor determine the thermodynamic properties of the combustion process. This then influences the kind of chemical species found in the plume and also at what temperature these species are radiating energy.The resultant function describing the plume signature is: Plume signature f {p T A fuel composition} t , , , , 1 1 = ε It was demonstrated that this approach yielded very useful results. Using only 18 basic variables, the spectra were predicted properly for variations in all these parameters. The model also predicted spectra that agree with the underlying physical situation when changing the composition as a whole. By decreasing the Potassium content for example, the model demonstrated the effect of a flame suppressant on the radiance in this wavelength band by increasing the predicted output. Lowering the temperature, which drives the process of molecular vibration and translation, resulted in the expected lower output across the spectral band. In general, it was shown that only a small section of the large space of 2 propellant classes had to be measured in order to successfully generate a model that could predict emission spectra for other designs in those classes. The same principal was then applied to predicting the infrared spectral emission of a burning flare. The brick type flare considered in this study will ignite and the solid fuel will burn on all surfaces. Since there are no physical parameters influencing the plume as in the case of the rocket nozzles it was required to search for parameters that could influence the flare plume. It was possible to calculate thermodynamic properties for the flare combustion process. These parameters were then reduced to 4 parameters, namely: the oxidant-fuel ratio, equilibrium temperature, the molar mass and the maximum combustion temperature. The input variables for the flares thus consisted of the chemical composition and 4 thermodynamic parameters described above. The network proposed previously was improved and optimised for a minimum number of variables in the system. The optimised network marginally improved on the pevious results (with the same data), but the training time involved was cut substantially. The same approach to the optimization of the network was again followed to determine the optimal network structure for predicting the flare emission spectra. The optimisation involved starting out with the simplest possible network construction and continuouslyincreasing the variables in the system until the solution predicted by the network was satisfactory. Once the structure of the network was determined it was possible to optimise the training algorithms to further improve the solution. In the case of the solid rocket propellant emission data it was felt that it would be important to be able to predict the chemical composition of the fuel and the motor parameters using the infrared emission spectra as input. This was done by simply reversing the optimised network and exchanging the inputs with the outputs. The results obtained from the reversed network accurately predicted the chemical composition and motor parameters on two different test sets. The predicted spectra of some of the solid propellant rocket test sets and flare test sets did not compare well with the expected values. This was due to the fact that these test sets were in a sparsely populated area of the variable space. These outliers are normally removed from training data, but in this case there wasn’t enough data to remove outliers. To obtain an indication of the strength of the correlation between the predicted and measured line spectra two parameters were used to test the correlation between two line spectra. The first parameter is the Pearson product moment of coefficient of correlation and gives an indication of how good the predicted line spectra followed the trend of the measured spectral lines. The second parameter measures the relative distance between a target and predicted spectral point. For both the solid propellants and the flares the correlation values was very close to 1, indicating a very good solution. Values for the two correlation parameters of a test set of the flares were 0.998 and 0.992. In order to verify the model it was necessary to prove that the solution yielded by the model is better than the average of the variable space. Three statistical tests were done consisting of the mean-squared-error test, T-test and Wilcoxon ranksum test. In all three cases the average of the variable space (static model) and the predicted values (Neural Network model) were compared to the measured values. For both the T-test and the Wilcoxon ranksum test the null hypothesis is rejected when t < -tα = 1.645 and then thealternative hypothesis is accepted, which states that the error of the NN model will be smaller than that of the static model. The mean squared error for the static model was 0.102 compared to the 0.0167 of the neural net, for a solid propellant rocket test set. A ttest was done on the same test set, yielding a value of –2.71, which is smaller than – 1.645, indicating that the NN model outperforms the static model. The Z value for this test set is Z = -11.9886, which is a much smaller than –1.645. The results from these statistical tests confirm that neural network is a valid conceptual model and the solutions yielded are unique. / AFRIKAANSE OPSOMMING: In ‘n vroeër studie is bewys hoe dit moontlik is om die spektrale irradiansie van ‘n vuurpyl se verbrandingspluim te voorspel vanaf slegs die dryfmiddelsamestelling en vuurpylmotoreienskappe. In die literatuur is daar min gepubliseer oor hierdie onderwerp. Dit wil voorkom asof meer deterministiese metodes gebruik word om die probleem op te los. Metodes soos CFD simulasies en statistiese analises word tans verkies om wyeband radiansie te voorspel gebaseer op perfekte swart ligaam teorie. ‘n Groot beperking van hierdie metodes is die feit dat die berekeninge kompleks is en baie lank neem om te voltooi. ‘n Alternatiewe benadering is gebruik, wat nie poog om al die nie-liniêre en komplekse verbande uit eerste beginsels op te los nie. ‘n Neurale netwerk is gebruik om ‘n funksionele verband te skep tussen die chemiese samestelling van die dryfmiddel, vuurpylmotor ontwerp en die spektrale irradiansie van die vuurpyl se pluim. Die funksionele verband kan nou effektief die afhanklikheid van die dryfmiddelsamestelling, vuurpylmotor ontwerp en die spektrale uitset modelleer. Twee datastelle was beskikbaar vir analise: Emissie spektra van vaste dryfmiddel vuurpyle en ook van vaste dryfmiddel fakkels. Die invoer tot die neurale netwerk van die vuurpyle het bestaan uit die chemiese samestelling van die dryfmiddel en 4 vuurpylmotor eienskappe. Die uitvoer van die netwerk het weer bestaan uit 146 spektrale irradiansie waardes in die golflengte band van 2-5μm. Die 4 vuurpylmotor eienskappe is afgelei uit massavloei teorie vir vuurpyl motors, aangesien die uitvloei van die produkgasse ‘n invloed op die pluim van die motor sal hê. Die massavloei het weer ‘n effek op die spektrale handtekening van die pluim. Die eienskappe van die massavloei deur die mondstuk van die vuurpylmotor bepaal die termodinamiese eienskappe van die verbrandingsproses. Die invloed op die verbrandingsproses bepaal weer watter tipe produkte gevorm word en by watter temperatuur hulle energie uitstraal. Die gevolg is dat ‘n funksie gedefinieer kan word wat die pluim beskryf.Pluim handtekening = f{, temperatuur, mondstuk keël grootte, vernouings verhouding van mondstuk, dryfmiddelsamestelling} Deur net 18 invoer nodes te gebruik kon die netwerk die irradiansie suksesvol voorspel met ‘n variansie in al die invoer waardes. Deur byvoorbeeld die Kalium inhoud van die dryfmiddel samestelling te verminder het die model die vermindering van ‘n vlam onderdrukker suksesvol nageboots deurdat die irradiansie ‘n hoër uitset gehad het. Die sensitiwiteit van die model is verder getoets deur die temperatuur in die verbrandingskamer te verlaag, met ‘n korrekte laer irradiansie uitset, as gevolg van die feit dat die temperatuur die molekulêre vibrasie en translasie beweging beheer. Dieselfde benadering is gebruik om die model te bou vir die voorspelling van die fakkels se infrarooi irradiansie. Anders as die vuurpylmotors vind die verbranding in die geval van die fakkels in die atmosfeer plaas. Dit was dus ook nodig om na die termodinamiese eienskappe van die fakkel verbranding te kyk. Verskeie parameters is bereken, maar 4 parameters, naamlik die brandstof-suurstof verhouding, temperatuur, molêre massa en die maksimum verbrandingstemperatuur, tesame met die dryfmiddel samestelling kon die irradiansie van die fakkels suskesvol voorspel. Die bestaande netwerk struktuur vir die vuurpylmotors is verbeter en geoptimiseer vir ‘n minimum hoeveelheid veranderlikes in die stelsel. Die geoptimiseerde netwerk het ‘n klein verbetering in die voorspellings getoon, maar die oplei het drasties afgeneem. Dieselfde benadering is gebruik om die optimale netwerk vir die fakkels te bepaal. Optimisering van die netwerk struktuur is bereik deur met die eenvoudigste struktuur te begin en die hoeveelheid veranderlikes te vermeerder totdat ‘n bevredigende oplossing gevind is. Na die struktuur van die netwerk bevestig is, kon die oordragfunksies op die nodes verder geoptimiseer word om die model verder te verbeter. Dit het verder geblyk dat dit moonlik is om die netwerk vir die vuurpylmotors om te draai sodat die irradiansie gebruik word om die dryfmiddel samestelling en motor eienskappe te voorspel. Die netwerk is eenvoudig omgedraai en die insette het die uitsette geword.Die resultate van die omgekeerde netwerk het bevestig dat dit wel moontlik is om die dryfmiddel samestelling en motor eienskappe te voorspel vanaf die irradiansie. Die voorspelde spektra van beide die vuurpylmotors en die fakkels het nie altyd goed gekorreleer met die gemete data nie. Van die spektra kom voor in ‘n lae digtheidsdeel van die veranderlike ruimte. Dit het tot gevolg gehad dat daar nie genoeg data vir opleiding van die netwerk in die omgewing van die toetsdata was nie. Hierdie data is eintlik uitlopers en moet verwyder word van die opleidingsdata, maar daar is alreeds nie genoeg data beskikbaar om die uitlopers te verwyder nie. Dit is nodig om te bepaal hoe goed die voorspelde data vergelyk met die gemete data. Twee parameters is gebruik om te bepaal hoe goed die data korreleer. Die eerste is die “Pearson product moment of coefficient of correlation”, wat ‘n goeie aanduiding gee van hoe goed die voorspelde waardes die gemete waardes se profiel volg. Die tweede parameter meet die relatiewe afstand tussen die teiken en die voorspelde waardes. Vir beide die vuurpylmotors en die fakkels het die toetsstelle ‘n korrelasiewaarde van baie na aan 1 gegee, wat ‘n goeie korrelasie is. Die waardes van die twee parameters vir een van die fakkel toetstelle was onderskeidelik 0.998 en 0.992. Die model is geverifieer deur te bepaal of die model ‘n beter oplossing bied as die gemiddeld van die veranderlike ruimte. Drie statistiese toetse is gedoen: “Mean-squarederror” toets, T-toets en ‘n “Wilcoxon ranksum” toets. In al drie gevalle word die gemiddelde van die veranderlike ruimte (statiese model) en die voorspelde waardes (Neurale netwerk model) teen die gemete waardes getoets. Vir beide die T-toets en die “Wilcoxon ranksum” toets word die nul hipotese verwerp indien t < ta = 1.645 en dan word die alternatiewe hipotese aanvaar, wat bepaal dat die fout van die neurale netwerk model kleiner is as die van die statiese model. Die “mean-squared-error” van die statiese model was 0.102, in vergelyking met 0.0167 van die neurale netwerk model vir ‘n vuurpylmotor toetsstel. ‘n T-toets is gedoen vir dieselfde toetsstel, met ‘n resultaat van-2.71, wat kleiner is as –1.645 en aandui dat die neurale netwerk model weereens beter presteer as die statiese model. Die Z waarde uit die “Wilcoxon ranksum” toets is Z=- 11.9886, wat baie kleiner is as –1.645. Die resultate van die statitiese toetse toon dat die neurale netwerk ‘n geldige model is en die oplossings van die model ook uniek is.

Thesis (MScIng)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: The emission spectrum measured in the middle infrared (IR) band from the plume of a rocket can be used to identify rockets and track inbound missiles. It is useful to test the stealth properties of the IR fingerprint of a rocket during its design phase without needing to spend excessive amounts of money on field trials. The modelled predictions of the IR spectra from selected rocket motor design parameters therefore bear significant benefits in reducing the development costs. In a recent doctorate study it was found that a fundamental approach including quantum-mechanical and computational fluid dynamics (CFD) models was not feasible. This is first of all due to the complexity of the systems and secondly due to the inadequate calculation speeds of even the most sophisticated modern computers. A solution was subsequently investigated by use of the ‘black-box’ model of a multi-layer perceptron feed-forward neural network with a single hidden layer consisting of 146 nodes. The input layer of the neural network consists of 18 rocket motor design parameters and the output layer consists of 146 IR absorbance variables in the range from 2 to 5 μm wavelengths. The results appeared promising for future investigations. The available data consist of only 18 different types of rocket motors due to the high costs of generating the data. The 18 rocket motor types fall into two different design classes, the double base (DB) and composite (C) propellant types. The sparseness of the data is a constraint in building adequate models of such a multivariate nature. The IR irradiance spectra data set consists of numerous repeat measurements made per rocket motor type. The repeat measurements form the pure error component of the data, which adds stability to training and provides lack-of-fit ANOVA capabilities. The emphasis in this dissertation is on comparing the feed-forward neural network model to the linear and neural network partial least squares (PLS) modelling techniques. The objective is to find a possibly more intuitive and more accurate model that effectively generalises the input-output relationships of the data. PLS models are known to be robust due to the exclusion of redundant information from projections made to primary latent variables, similarly to principal components (PCA) regression. The neural network PLS techniques include feed-forward sigmoidal neural network PLS (NNPLS) and radial-basis functions PLS (RBFPLS). The NNPLS and RBFPLS algorithms make use of neural networks to find non-linear functional relationships for the inner PLS models of the NIPALS algorithm. Error-based neural network PLS (EBNNPLS) and radial-basis function network PLS (EBRBFPLS) are also briefly investigated, as these techniques make use of non-linear projections to latent variables. A modification to the orthogonal least squares (OLS) training algorithm of radial-basis functions is developed and applied. The adaptive spread OLS algorithm (ASOLS) allows for the iterative adaptation of the Gaussian spread parameters found in the radial-basis transfer functions. Over-fitting from over-parameterisation is controlled by making use of leaveone- out cross-validation and the calculation of pseudo-degrees of freedom. After cross-validation the overall model is built by training on the entire data set. This is done by making use of the optimum parameterisation obtained from cross-validation. Cross-validation also gives an indication of how well a model can predict data unseen during training. The reverse problem of modelling the rocket propellant chemical compositions and the rocket physical design parameters from the IR irradiance spectra is also investigated. This problem bears familiarity to the field of spectral multivariate calibration. The applications in this field readily make use of PLS and neural network modelling. The reverse problem is investigated with the same modelling techniques applied to the forward modelling problem. The forward modelling results (IR spectrum predictions) show that the feedforward neural network complexity can be reduced to two hidden nodes in a single hidden layer. The NNPLS model with eleven latent dimensions outperforms all the other models with a maximum average R2-value of 0.75 across all output variables for unseen data from cross-validation. The explained variance for the output data of the overall model is 94.34%. The corresponding explained variance of the input data is 99.8%. The RBFPLS models built using the ASOLS training algorithm for the training of the radialbasis function inner models outperforms those using K-means and OLS training algorithms. The lack-of-fit ANOVA tests show that there is reason to doubt the adequacy of the NNPLS model. The modelling results however show promise for future development on larger, more representative data sets. The reverse modelling results show that the feed-forward neural network model, NNPLS and RBFPLS models produce similar results superior to the linear PLS model. The RBFPLS model with ASOLS inner model training and 5 latent dimensions stands out slightly as the best model. It is found that it is feasible to separately find the optimum model complexity (number of latent dimensions) for each output variable. The average R2-value across all output variables for unseen data is 0.43. The average R2-value for the overall model is 0.68. There are output variables with R2-values of over 0.8. The forward and reverse modelling results further show that dimensional reduction in the case of PLS does produce the best models. It is found that the input-output relationships are not highly non-linear. The non-linearities are largely responsible for the compensation of both the DB- and C-class rocket motor designs predictions within the overall model predictions. For this reason it is suggested that future models can be developed by making use of a simpler, more linear model for each rocket class after a class identification step. This approach however requires additional data that must be acquired. / AFRIKAANSE OPSOMMING: Die emissiespektra van die uitlaatpluime van vuurpyle in die middel-infrarooi (IR) band kan gebruik word om die vuurpyle te herken en om inkomende vuurpyle op te spoor. Dit is nuttig om die uitstralingseienskappe van ‘n vuurpyl se IR afdruk te toets, sonder om groot bedrae geld op veldtoetse te spandeer. Die gemodelleerde IR spektrale voorspellings vir ‘n bepaalde stel vuurpylmotor ontwerpsparameters kan dus grootliks bydra om motorontwikkelingskostes te bemoei. In ‘n onlangse doktorale studie is gevind dat ‘n fundamentele benadering van kwantum-meganiese en vloeidinamika-modelle nie lewensvatbaar is nie. Dit is hoofsaaklik as gevolg van die onvoldoende vermoë van selfs die mees gesofistikeerde moderne rekenaars. ‘n Moontlike oplossing tot die probleem is ondersoek deur gebruik te maak van ‘n multilaag perseptron voorwaartse neurale netwerk met 146 nodes in ‘n enkele versteekte laag. Die laag van invoer veranderlikes bestaan uit agtien vuurpylmotor ontwerpsparameters en die uitvoerlaag bestaan uit 146 IR-absorbansie veranderlikes in die reeks golflengtes vanaf 2 tot 5 μm. Dit het voorgekom dat die resultate belowend lyk vir toekomstige ondersoeke. Weens die hoë kostes om die data te genereer bestaan die beskikbare data uit slegs agtien verskillende tipes vuurpylmotors. Die agtien vuurpyl tipes val verder binne twee ontwerpsklasse, naamlik die dubbelbasis (DB) en saamgestelde (C) dryfmiddeltipes. Die yl data bemoeilik die bou van doeltreffende multiveranderlike modelle. Die datastel van IR uitstralingspektra bestaan uit herhaalde metings per vuurpyltipe. Die herhaalde metings vorm die suiwer fout komponent van die data. Dit verskaf stabilitieit tot die opleiding op die data en verder die vermoë om ‘n analise van variansie (ANOVA) op die data uit te voer. In hierdie tesis lê die klem op die vergelyking tussen die voorwaartse neurale netwerk en die lineêre en neurale netwerk parsiële kleinste kwadrate (PLS) modelleringstegnieke. Die doel is om ‘n moontlik meer insiggewende en akkurate model te vind wat effektief die in- en uitvoer verhoudings kan veralgemeen. Dit is bekend dat PLS modelle meer robuus kan wees weens die weglating van oortollige inligting deur projeksies op hoof latente veranderlikes. Dit is analoog aan hoofkomponente (PCA) regressie. Die neurale netwerk PLS-tegnieke sluit in voorwaartse sigmoïdale neurale netwerk PLS (NNPLS) en radiale-basis funksies PLS (RBFPLS). Die NNPLS en RBFPLS algoritmes maak gebruik van die neurale netwerke om nie-lineêre funksionele verbande te kry vir die binne PLS-modelle van die nie-lineêre iteratiewe parsiële kleinste kwadrate (NIPALS) algoritme. Die fout-gebaseerde neurale netwerk PLS (EBNNPLS) en radiale-basis funksies PLS (EBRBFPLS) is ook weens hulle nie-lineêre projeksies na latente veranderlikes kortiliks ondersoek. ‘n Aanpassing tot die ortogonale kleinste kwadrate (OLS) opleidingsalgoritme vir radiale-basis funksies is ontwikkel en toegepas. Die aangepaste algoritme (ASOLS) behels die iteratiewe aanpassing van die verspreidingsparameters binne die Gauss-funksies van die radiale-basis transformasie funksies. Die oormatige parameterisering van ‘n model word beheer deur kruisvalidering met enkele weglatings en die berekening van pseudo-vryheidsgrade. Na kruisvalidering word die algehele model gebou deur opleiding op die volledige datastel. Dit word gedoen deur van die optimale parameterisering gebruik te maak wat deur kruisvalidering bepaal is. Kruisvalidering gee ook ‘n goeie aanduiding van hoe goed ‘n model ongesiende data kan voorspel. Die modellering van die vuurpyle se chemiese en fisiese ontwerpsparameters (omgekeerde probleem) is ook ondersoek. Hierdie probleem is verwant aan die veld van spektrale multiveranderlike kalibrasie. Die toepassings in die veld maak gebruik van PLS en neurale netwerk modelle. Die omgekeerde probleem word dus ondersoek met dieselfde modelleringstegnieke wat gebruik is vir die voorwaartse probleem. Die voorwaartse modelleringsresultate (IR voorspellings) toon dat die kompleksiteit van die voorwaartse neurale netwerk tot twee versteekte nodes in ‘n enkele versteekte laag gereduseer kan word. Die NNPLS model met elf latente dimensies vaar die beste van alle modelle, met ‘n maksimum R2-waarde van 0.75 oor alle uitvoer veranderlikes vir die ongesiende data (kruisvalidering). Die verklaarde variansie vir die uitvoer data vanaf die algehele model is 94.34%. Die verklaarde variansie van die ooreenstemmende invoer data is 99.8%. Die RBFPLS modelle wat gebou is deur van die ASOLS algoritme gebruik te maak om die PLS binne modelle op te lei, vaar beter in vergelyking met die K-gemiddeldes en OLS opleidingsalgoritmes. Die toetse wat ‘n ‘tekort-aan-passing’ ANOVA behels, toon dat daar rede is om die geskiktheid van die NNPLS model te wantrou. Die modelleringsresultate lyk egter belowend vir die toekomstige ontwikkeling van modelle op groter, meer verteenwoordigde datastelle. Die omgekeerde modellering toon dat die voorwaartse neurale netwerk, NNPLS en RBFPLS modelle soortgelyke resultate produseer wat die lineêre PLS model s’n oortref. Die RBFPLS model met ASOLS opleiding van die PLS binne modelle word beskou as die beste model. Dit is lewensvatbaar om die optimale modelkompleksiteite van elke uitvoerveranderlike individueel te bepaal. Die gemiddelde R2-waarde oor alle uitvoerveranderlikes vir ongesiende data is 0.43. Die gemiddelde R2-waarde vir die algehele model is 0.68. Daar is van die uitvoer veranderlikes wat R2-waardes van 0.8 oortref. Die voor- en terugwaartse modelleringsresultate toon verder dat dimensionele reduksie in die geval van PLS die beste modelle lewer. Daar is ook gevind dat die nie-lineêriteite grootliks vergoed vir die voorspellings van beide DB- en Ctipe vuurpylmotors binne die algehele model. Om die rede word voorgestel dat toekomstige modelle ontwikkel kan word deur gebruik te maak van eenvoudiger, meer lineêre modelle vir elke vuurpylklas nadat ‘n klasidentifikasiestap uitgevoer is. Die benadering benodig egter addisionele praktiese data wat verkry moet word.

O objetivo desta pesquisa foi comparar as alterações cefalométricas de pacientes com má oclusão de Classe II divisão 1, tratados com os aparelhos Jasper Jumper e Twin Force Bite Corrector, associados ao aparelho ortodôntico fixo. A amostra foi composta por 120 telerradiografias em norma lateral de 60 pacientes, os quais foram divididos em 3 grupos: Grupo Experimental 1, constituído por 20 pacientes com idade inicial média de 12,39 anos, tratados por meio do aparelho Jasper Jumper associado ao aparelho fixo, por um período médio de 2,42 anos; Grupo Experimental 2, contendo 20 pacientes com idade inicial média de 11,83 anos, tratados com o aparelho Twin Force associado ao aparelho fixo, com tempo médio de tratamento de 2,59 anos; Grupo Controle, composto por 20 jovens, com idade inicial média de 12,13 anos e observados por um período médio de 2,21 anos. As alterações foram comparadas entre os grupos, por meio da Análise de Variância e do teste de Tukey. Observou-se que ambos os tratamentos apresentaram um efeito restritivo na maxila, houve melhora significante da relação maxilomandibular nos dois protocolos de tratamento avaliados e promoveram rotação horária do plano oclusal. O grupo Jasper Jumper, promoveu uma significante limitação do desenvolvimento vertical dos molares superiores em relação aos outros grupos. Os incisivos inferiores exibiram maior protrusão e uma extrusão dos molares inferiores nos grupos 1 e 2. Ambos os aparelhos melhoraram significantemente a relação maxilomandibular, os trespasses horizontal, vertical e a relação molar. Os protocolos de tratamento promoveram retrusão dos lábios superiores. / The aim of this study was to compare the cephalometric changes in patients with Class II Division 1 malocclusion, treated with the Jasper Jumper and Twin Force Bite Corrector, associated with fixed orthodontic appliances. The sample consisted of 120 lateral cephalometric radiographs of 60 patients, divided into 3 groups: Experimental Group 1 comprised 20 patients with initial mean age of 12.39 years, treated with the Jasper Jumper appliance associated with device fixed for an average period of 2.42 years; Experimental group 2 with 20 patients with initial mean age of 11.83 years, treated with Twin Force unit associated with braces, with an average treatment time of 2.59 years; Control Group, composed of 20 individuals, average initial age of 12.13 years and observed for an average period of 2.21 years. The changes were compared between groups by ANOVA followed by Tukey test. It was observed that both treatments presented a restrictive effect on the maxilla; there was significant improvement in the maxillomandibular relationship in the two treatment protocols groups evaluated and clockwise rotation of the occlusal plane. The Jasper Jumper group, provided a significant limitation of the vertical development of the maxillary molars in relation to other groups. The lower incisors showed greater protrusion and extrusion of mandibular molars in groups 1 and 2. Both appliances provided significant improvement of maxillomandibular relationship, overjet, overbite and molar relationship. Groups 1 and 2 presented retrusion of the upper lip.