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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/16254 |
| Date | 04 1900 |
| Creators | Barnard, Paul Werner |
| Contributors | Knoetze, J. H., Roodt, J.H.S., 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 | xxii, 234 leaves : ill. |
| Rights | University of Stellenbosch |
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