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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/16334 |
| Date | 04 1900 |
| Creators | Hamp, Niko |
| Contributors | Knoetze, J. H., Aldrich, C., University of Stellenbosch. Faculty of Engineering. Dept. of Process Engineering. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | xxx, 301 leaves : ill. |
| Rights | University of Stellenbosch |
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