Improvements in uncertainties in the values of radiant intensity (I) can be accomplished mainly by improvements in the calibration process and in minimizing the difference between the background and engine plume radiance. For engine tests in which the plume is extremely bright, the difference in luminance between the calibration lamp and the engine plume radiance can be so large as to cause relatively large uncertainties in the values of R. This is due to the small aperture necessary on the receiving optics to avoid saturating the instrument. However, this is not a problem with the SSME engine since the liquid oxygen/hydrogen combustion is not as bright as some other fuels. Applying the instrumentation to other type engine tests may require a much brighter calibration lamp

Benzing, Daniel A.

Hopkins, Randall C.

English

NASA Technical Reports Server

_ _ .._ _ '_ / ?, 1997
_ ?/_ NASA / ASEE SUMMER FACULTY FELLOWSHIP PROGRAM
MARSHALL SPACE FLIGHT CENTER
THE UNIVERSITY OF ALABAMA IN HUNTSVILLE
UNCERTAINTY IN CALIBRATION, DETECTION, AND ESTIMATION OF
METAL CONCENTRATIONS IN ENGINE PLUMES USING OPAD
Prepared by:
Academic Rank:
Institution and Department:
NASA / MSFC:
Office:
Division:
MSFC Colleagues:
Randall C. Hopkins / Daniel A. Benzing
Instructor / Graduate Research Assistant
University of Alabama - Tuscaloosa
Dept. of Aerospace Engineering and Mechanics
Instrumentation and Control Branch
Astrionics Laboratory
Anita Cooper
W. T. Powers
William White
XVIII
https://ntrs.nasa.gov/search.jsp?R=19990010019 2020-06-18T00:46:09+00:00Z

Introduction
The idea of extracting chemical data from the analysis of the electromagnetic
(EM) spectrum is not new. Holding a copper wire in a sufficiently hot flame
produces a characteristic green region in the flame. The copper atoms are exited to
such a high energy state that they emit electromagnetic radiation at several
wavelengths, with green light being dominant. The atomic structure determines
the wavelengths of EM emitted, and since all elements are unique, no two elements
will emit EM at exactly the same wavelengths. Thus each element has its own
unique spectral signature. For example, in the same flame, the element nickel will
emit EM at wavelengths different than copper.
wavelength is the electromagnetic spectrum
of mckel, as shown in Fig. 1. Since this
spectrum is unique, a spectrometric detector
some distance from the flame would allow a
user to determine the presence of nickel,
copper, or both, in the flame.
Individual spectra for other elements
vary in complexity, some having few atomic
transitions (peaks), others having many.
Three germane points of importance to this
paper result from Fig. 1 and the associated
radiation physics: 1) every element has it's
own "spectral signature," 2) the emission will
contain atomic transitions at wavelengths
which may not be part of the visible spectrum,
and 3) the intensity of the emission is a
function of the quantity of emitting matter
present in addition to the system temperature
and other quantum variables.
A plot of radiant intensity versus
2.0E-3
SPECTRA OUTPUT FOR NICKEL
i r [ r =
1 6E-3 --
1.2E-3 --
8 0E-4 --
4 0E-4 --
0.0E+0 i
3300 3450 3600 3750
t
_:[ I :,: I , I L i ii
3900 4050 4200 4350
Wavelength
Fig. 1. Example Emission Spectra for
Nickel.
Rocket plumes are emissive events subject to the same physics (with more
complications of course) as burning nickel or copper over an open flame. The
Optical Plume Anomaly Detection (or OPAD) program (Cooper, et al, 1997) was
initiated by researchers at MSFC as an effort to take advantage of the wealth of
information contained in the exhaust plume of a rocket engine. The initial idea was
to identify anomalous spectral events which were consistent with known
mechanical failures and then use them as templates in the health monitoring of
future engine tests (ground or in-flight). This could then be coupled with the
anomalous events found in the vibrational and other sensor data to determine the
overall state, or health, of the engine.
The "template idea," however, was soon replaced by even more ambitious
goals as a result of some initial findings in the TTB experimental program
(Benzing, et al, 1997). The spectral data from one test in particular revealed a
major occurrence of a metallic species which was indigenous to the SSME
XVIII - 1
preburner faceplate. An even closer evaluation of the amount of metallic species
present versus time showed an initial erosive event of the metal followed by
numerous other anomalous emissions, all leading up to an engine-threatening
erosion of the faceplate. This meant that anomalous events could be predicted.
As a result of these findings, the
( I !
Fault Detection
*Are thee my
anomali_?
•What's_hcse_env/
o_the_r.l_
•C_n B_e an_ml_s
mc¢ be i_l_td7
Fig. 2. Monitoring the SSME Exhaust
Plume using the OPAD System.
focus of the researchers turned to not only
anomaly detection but also metal
quantification. In other words, health
monitoring now involved the simultaneous
tasks of anomaly detection and
determination of the severity of the
anomaly, as illustrated in Fig. 2. This
meant that the free atom densities of all
the metals of interest within the engine
would have to be predicted for every
temporal scan taken by the instruments.
The metal quantification process would
essentially give metal concentration versus
time. Spikes in this time trace would then
be indicative of a metal erosion.
The neural network extracts radiant intensity data from the electromagnetic
spectrum of the exhaust plume and uses these values to predict concentrations, as
well as temperature and broadening parameter, of metals in the flame (Whitaker,
et al, 1997). Fig. 3 illustrates the network's
operation. As the intensities of the
electromagnetic radiation are extracted
from the spectrum, the uncertainties in
those values are propagated through the
network and result in uncertainties in the
predictions of number density, broadening
parameter, and temperature.
Calculation of the uncertainties
begins with an examination of the
procedure used to calibrate the
instruments used in the OPAD system.
_ Terap©rltm'e
• l[ _ Nidc©t I mwll"f_liP.rmt.cl_,-
Fig. 3. Basic Operation of the Neural
Network.
Uncertainties in Instrument Calibration
The purpose of instrument calibration is :o determine the response of each
photodetector, or the ratio of incoming radiation to outgoing voltage. During an
engine test, the radiant intensity, I, at each photodetector is
I =(It -IB)" R (units are W/(str cm 2 ang)) (1)
XVIII - 2
where I7 is the radiant intensity during engine firing and IB is the radiant intensity
of the background, or ambient light. These two values are measured in "counts"
since the analog-to-digital
Receiving Optics TOP VIEW
_Screen
Fig. 4. Calibration Procedure for the OMA, One of
Several OPAD Instruments.
converter installed in the
computer converts the voltages
released by each photodetector
into an integer. In order to
calculate the radiant intensity, I,
during the test, the value of R
must be determined from
calibration.
Fig. 4 shows a typical
calibration for the OMA, one of
several spectrometers that can be
used as part of the OPAD system.
Using a calibrated irradiance lamp of known intensifies across a segment of the
electromagnetic spectrum allows the values of R in the above equation to be
determined. During calibration, lamp radiation is reflected off of a screen of known
reflectance properties at a certain distance from the receiving optics. Therefore, the
only unknown in Equation 1 is R. Thus,
linterp°lated )2
-
(2)
where IL is the lamp intensity (in counts) at the photodetector, and IB is the
background. Any uncertainty in R will be propagated though Equation 1 during an
engine test.
Some of the sources of uncertainty in R include instrument noise,
uncertainties in the lamp irradiance, uncertainties in the screen reflectance, the
distance between the lamp and reflectance screen, the distance between the screen
and the receiving optics, background fluctuations (such as sun and shade, time of
day, changing surroundings, etc.), and others.
Due to time constraints, the uncertainty in R was determined using
statistical methods. Several hundred sample calibration scans were taken at
different times and the environmental factors (sun, temperature, humidity, etc.)
noted. Then values of R were calculated for each photodetector for these scans.
Values of R were determined by the mean of the data points and the uncertainties
were reported as one standard deviation, as in Equations 3 and 4, respectively.
l _j-'x, (3)]2=--
n J=l
XVIII - 3
or: x,-_) (4)
Uncertainties in the distances between the screen and lamp and the screen and the
receiving optics were determined but not propagated through the calibration
procedure due to time constraints; they will be included in future studies. Once
these uncertainties were determined, then the uncertainties in the radiant
intensity during an engine test could be determined.
Uncertainties in the Measured Photodetector Radiant Intensity
The uncertainty in I in Equation 1 can be determined mathematically using well
known statistics. For each photodetector (there may be over 2000) in the
instrument, the absolute uncertainty in/, expressed UI, is
(5)
where U1,T and UI, e are the uncertainties in the measured exhaust plume and
background (pre-test) radiance, and UR is the uncertainty in the photodetector
response. Evaluating the partial derivatives results in a simple expression:
(U1) 2 =(U_.TR) 2 +(UI,BR) 2 +(UR(Ir --IB)) 2 (6)
Use of Equation 6 allows one to not only evaluate the overall uncertainty, but also
determine the major contributors. This shows the experimenter what areas of the
experiment should be improved.
To evaluate these equations by hand would be extremely time consuming for
experiments of several hundred scans using instruments of over 2000
photodetectors. Therefore, five ANSI standard C programs were written to convert
raw data from the instruments a standard format, analyze the data for entire scans
or for individual photodetectors, create histograms and temporal charts, and
compute the mean, standard deviation, and absol.ute and relative uncertainties in
any measurement, whether it be counts (such as I_) or values of R. These programs
can average several background scans, or ran=iomly mix background (IB) and
calibration (IL) or engine test (IT) scans. The results of these programs are then
substituted into Equation 6.
Analysis of each term for photodetector number 099 of the OMA instrument
is shown in Table 1.
XVIII - 4
(Uz) =7501E -08 W
str .cm z •ang
(UI,rR_ =1.198E -16
(U_,BR) 2 =7.862E -18
(U R(It -I B))2 = 1.170E -15
Table 1. Contributions
to the Uncertainty for
Photodetector #99 in the
OMA Instrument.
The data used in the analysis in Table 1 are
from an SSME test. The results clearly show that
the uncertainty (expressed as lv) in background
measurements contribute the least to the overall
uncertainty. However, for photodetector number 99,
UR is 3.641E-10 (4.802%), and in the third term UR
is multiplied by a large number (IT - IB = 1030
counts on average). Thus if the exhaust plume is
extremely bright, then this error term dominates,
and the errors during the calibration process become
very important.
Propagation Through the Neural Network
The neural network takes the intensity
values from Equation 1 and predicts temperature,
number density, and broadening parameter for the flow. What can be said of the
uncertainties in these estimates? Generally speaking there are three main sources
of uncertainty in the radial basis function neural network (RBFNN) estimation: 1)
error due to the inability of the neural model to completely map the underlying
physical relationship, 2) uncertainty in the training data as a result of the
Spectra6* models' inability to completely describe the physical nature of the flow
emission, and 3) uncertainties introduced during the calibration/response function
creation processes.
Typically, the statement of uncertainties in a neural network prediction
involve only error estimates that are based on the neural model's inability to fit the
training data. No consideration is given to the error component introduced through
the acquisition of the actual testing or training data sets. The terse technical note
described herein serves to highlight this error component and provide a means by
which its effects can be quantified.
The general architecture of the RBFNN is given in Fig. 5 below. It is
assumed that prior knowledge of the uncertainties in the inputs has been
established. The figure shows a fully connected RBF network with radial kernels
and associated weighting factors. The kernel function can be any radially
symmetric function; that is, a function which has a "local" behavior such as the
Gaussian, Cauchy, or Multiquadric. The output quantities (yk) are then given by
the basis function expansion of Equation 7.
rtl
yk=Xw,,(g,.) (7)
]=1
The Spectra6 model is a computer program that produces the training data for the RBFNN
Inputs into the program are quantum variables; outputs are an electromagnetic spectrum and
associated temperature, number density, and broadening parameter. (Cooper, et al, 1997)
XVIII - 5
11+ fi/l
_W11
.v_
Fig. 5. RBFNN General Architecture.
Note, the bias term in Equation 7 is not included because it drops out in the partial
derivative expansion. For the sake of analysis, assume the kernel function is a
Gaussian (Equation 8) and that the network coefficients (wii, pa) have already been
established. Further assume that any uncertainties associated with the network
inputs are independent and random. With these conditions, the uncertainty in an
output variable can be obtained via Equation 9 below.
(,-am,)
gm = exp = --
R _ (8)
(9)
Through a trivial (just kidding)
evaluated as,
partial expansion, the partial derivatives can be
As an example, the paritial expansion has been worked out for the Gaussian kernel
below,
" ))v3'__.,_k= _ wjkg J ,, _ I. - la j. (11)
O_n J=l
XVIII - 6
Conclusions
Improvements in uncertainties in the values of radiant intensity (!) can be
accomplished mainly by improvements in the calibration process and in minimizing
the difference between the background and engine plume radiance. For engine
tests in which the plume is extremely bright, the difference in luminance between
the calibration lamp and the engine plume radiance can be so large as to cause
relatively large uncertainties in the values of R. This is due to the small aperture
necessary on the receiving optics to avoid saturating the instrument. However, this
is not a problem with the SSME engine since the liquid oxygen / hydrogen
combustion is not as bright as some other fuels. Applying the instrumentation to
other type engine tests may require a much brighter calibration lamp.
References
Cooper, A.E., Powers, W.T., Wallace, T.L., Buntine, W., "Recent Results in the
Analysis of Large Rocket Engine anomalies Utilizing State-of-the-Art Spectral
Modeling Algorithms," 1997 JANNAF.
Benzing, Daniel A., Hopkins, Randall C., Whitaker, Kevin W., "OPAD: An
Innovative Rocket Engine Health Monitoring System," Proceedings of the 16th
Annual Digital Avionics System Conference, 1997.
Whitaker, K L., Moore, D., Benzing, D.A., "A Neural Network Approach to Anomaly
Detection in Spectra," 35th Aerospace Sciences Meeting & Exhibit, AIAA-97-0223,
Reno, NV, 1997
XVIII - 7
V


Uncertainty in Calibration, Detection and Estimation of Metal Concentrations in Engine Plumes Using OPAD

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