As reported in the monthly technical progress report for July 1993, a new signal analysis technique called instantaneous frequency correlation (IFC) for time delay estimation was developed which will be incorporated into the ATMS system. In this report, a different technique for time delay estimation called phase difference time derivative estimator (FDTDE) will be discussed. The FDTDE technique does not replace the IFC method since their application conditions are different. The IFC technique can estimate the time delay between two spectral components of two measurement signals when the center frequency of the components is constant, while the FDTDE method can provide accurate time delay estimation when the frequency of the subject component changes linearly such as during engine startup or shut-down

Jong, Jen-Yi

English

NASA Technical Reports Server

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NASA-CR-194785
TECHNICAL PROGRESS REPORT
DECEMBER 1993
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-, DEVELOP ADVANCED NONLINEAR SIGNAL ANALYSIS
" TOPOGRAPHICAL MAPPING SYSTEM
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NASA CONTRACT NO. NAS8-39393
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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
GEORGE C. MARSHALL SPACE FLIGHT CENTER
MARSHALL SPACE FLIGHT CENTER, AL 35812
by
AI SIGNAL RESEARCH, INC.
904 Bob Wallace Ave., Suite 211
Huntsville, AL 35801
AI SIGNAL RESEARCH TECHNICAL REPORT TR-4002-93-12
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AI SIGNAL RESEARCH NASA
Program Manager: J. Jong Contract Monitor: P. Jones
Contracting Officer: L. Van Wagner
https://ntrs.nasa.gov/search.jsp?R=19940020383 2020-06-16T16:33:07+00:00Z
DEVELOP ADVANCED NONLINEAR SIGNAL ANALYSIS
TOPOGRAPHICAL MAPPING SYSTEM
( NASA CONTRACT NO. NAS8-39393 )
The SSME has been undergoing extensive flight certification and developmental testing,
which involves some 250 health monitoring measurements. Under the severe temperature,
pressure, and dynamic environments sustained during operation, numerous major
component failures have occurred, resulting in extensive engine hardware damage and
scheduling losses. To enhance SSME safety and reliability, detailed analysis and
evaluation of the measurements signal are mandatory to assess its dynamic characteristics
and operational condition. Efficient and reliable signal detection techniques will reduce
catastrophic system failure risks and expedite the evaluation of both flight and ground test
data, and thereby reduce launch turn-around time.
The basic objective of this contract are threefold:
(1) Develop and validate a hierarchy of innovative signal analysis techniques for nonlinear
and nonstationary time-frequency analysis. Performance evaluation will be carried
out through detailed analysis of extensive SSME static firing and flight data. These
techniques will be incorporated into a fully automated system.
(2) Develop an advanced nonlinear signal analysis topographical mapping system (ATMS)
to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system
will convert tremendous amount of complex vibration signals from the entire SSME
test history into a bank of succinct image-like patterns while retaining all respective
phase information. High compression ratio can be achieved to allow minimal storage
requirement, while providing fast signature retrieval, pattern comparison, and
identification capabilities.
(3) Integrate the nonlinear correlation techniques into the CSTDB data base with
compatible TOPO input data format. Such integrated ATMS system will provide the
large test archives necessary for quick signature comparison.
This study will provide timely assessment of SSME component operational status, identify
probable causes of malfunction, and indicate feasible engineering solutions. The final
result of this program will yield an ATMS system of nonlinear and nonstationary spectral
analysis software package integrated with the Compressed SSME TOPO Data Base
(CSTDB) on the same platform. This system will allow NASA engineers to retrieve any
unique defect signatures and trends associated with different failure modes and anomalous
phenomena over the entire SSME test history across turbopump families.
REPORTS
In addition to monthly technical progress reports, informal analysis results of SSME test
are prepared and presented at irregular intervals. Software routines and database are
provided for application on MSFC computers. The final report will document all analysis
results, new techniques and computer software generated under this contract.
2
TECHNICAL PROGRESS
This is December !993 monthly technical progress report on the subject contract for the
development of an advanced nonlinear signal analysis topographical mapping system
(ATMS) for SSME diagnostic evaluation. Specific tasks performed in this reporting
period are summarized as follows:
As reported in the monthly technical progress report for July 1993, a new signal analysis
technique called "Instantaneous Frequency Correlation (IFC)" for time delay estimation
was developed which will be incorporated into the ATMS system. In this report, a
different technique for time delay estimation called "Phase Difference Time Derivative
Estimator (FDTDE)" will be discussed. The FDTDE technique does not replace the
IFC method since their application conditions are different. The IFC technique can
estimate the time delay between two spectral components of two measurement signals
when the center frequency of the component are constant. While the FDTDE method
can provide accurate time delay estimation when the frequency of the subject
component changes linearly such as during engine startup or shut-down. The major
advantage of the IFC technique is that it can estimate time delay from the newly
generated Instantaneous Frequency Variation (IFV) signal without being subjected to
the ambiguity limitation due to the 2_ phase wrapped around effect. However, the
condition for the IFC technique to be applicable is quite restrictive. This is due to the
frequency of the newly generated IFV signal for correlation analysis is greatly reduced
from the original waveform. As a result, high signal to noise ratio and large number of
ensemble average is required in order to reduce the statistical variation of the
correlation function estimation. In addition, long period of stationary signal is required
in order to generated a accurate estimation of Instantaneous Frequency Variation (IFV)
signal. On the other hand, by taking advantage of a special property of signal when its
frequency changes linearly, time delay information can be identified directly from the
signal's FFT phase slope by the FDTDE method. As a result, the signal condition
requirement would not be as restrictive as the IFC method.
Time delay estimation is an important task in machinery diagnostics. When an
anomalous frequency component is observed at various measurement locations, it is
always highly desirable to be able to identify the source of the anomaly by determining
the wave propagation path from the time lead/lag information of these measurement
signal. The conventional approach for time delay estimation of a stationary discrete
spectral component is by using either the cross-correlation function of the band-passed
signal in the time domain or the phase difference of the transfer function in the
frequency domain. However, a critical limitation exists for these conventional
techniques. The time delays estimated from these two methods are subjected to a 2_
phasewrapped around effect, which introduces ambiguities in the delay estimation.
Therefore, these techniques are only valid when the time lag/lead involved is small and
is within the 2x window.
As well known, the phase difference between two spectral components is directly
related to their time delay within an unknown integer multiple of 2x. However, if the
frequency of the subject spectral component changes linearly, such phase wrapping
ambiguity can be avoided from the time derivative (or slope) of phase difference
information. To demonstrate this, let's consider the following FM signal:
x(t) = cos[ 2x (0.5 f t2 + fo t) + Px ] (1)
The instantaneous frequency fit) of x(t) is:
fit) = f t + fo (2)
let y(t) be a time delayed version of x(t):
y(t) = x(t-x)
= cos[ 2x (0.5 f (t-x) 2 + fo (t-x)) + Px ]
= cos[ 2rr (0.5 f (t-x) 2 + fo (t-x)) + Px +
2x (0.5 f "c2- fo x - fxt) ]
= cos[ 2x (0.5 f (t-x) 2 + fo (t-z)) + Py ]
(3)
The phase difference between x(t) and y(t) becomes:
Pxy = Py-Px = 2x (0.5 f x2 - fo x - fxt) (4)
Phase difference Pxy can be directly estimated from the FFT of the signal, and the time
delay x can be obtained from equation (4). However, this estimation is subjected to a
2x ambiguity due to the phase wrapping. Notice that, the time derivative of the phase
difference P'xy (or the phase slope) still retains the desired time delay information since:
P'xy = d(Pxy)/dt = - 2x fx (5)
Equation (5) states that, there exists a unique relationship between the phase slope P'xy
and the time delay x when the frequency of signal changes linearly. (such relationship
no longer exists if the signal's frequency stays constant since its frequency slope f
would become zero). The major advantage provided by such relationship is that the
phase slope P'xy is no longer subjected to the phase wrapping effect. As a result, the
2x phase ambiguity in the resulting time delay estimation will be removed.
A computersimulation is performed in order to demonstrate this technique. An FM
signal with linearly varying frequency is generated as below:
x(t) = cos[ 2r_ (0.5 f t 2 + fo t) ]
The initial frequency fo is 2000 Hz with frequency slope f being 4.54545 Hz/sec. The
sampling frequency used is 10,240 Hz. Figure 1 shows the PSD isoplot of the
simulation signal. Notice that, the required linearly varying frequency is apparent.
Three time delay versions are artificially generated by delaying the reference signal by
5, 20, and 100 samples respectively. Figure 2 shows the time histories of the reference
signal along with these three time delayed signals. Figure 3 shows their corresponding
PSDs at S+I second. Figure 4 shows (a) the frequency tracking of the spectral
component, (b) the RMS amplitude of the component of the reference signal, (c) the
RMS amplitude of the component of the 5-point delay signal, and (d) the FFT phase
difference time data between the reference and the 5-point delay signal. The two
required parameters fo and f' can also be calculated directly from the frequency tracking
plot in figure 4-a. Figure 5 and 6 show the same information between the reference and
the 20-point, the 100-point delay signals respectively.
Notice that, the phase difference time data indeed shows an apparent linear trend which
is directly related to the time delay x. This phase slope P'xy can be obtained from this
linear trend of the phase difference time data as shown in figure 4-d, 5-d and 6-d.
These parameters of P'xy are: 0.0139, 0.055676, and 0.2788 rad/sec for the three
delayed signals. From this information, the time delays x can then be estimated based
on the relationship of equation (5).
The values of f, P'xy, the estimated time delay x, and the estimated time delay D in
samples for the three cases in figure 4, 5, and 6 are shown below:
ref/5-point ref/20-point ref/100-point Unit
f -4.5454 -4.5454 -4.5454 Hz/sec
P'xy 0.0139 0.055676 0.2788 rad/sec
"_ 0.4882 1.952 9.766 msec
D 5 20 100 sample
The estimated time delay in sample (D) of 5, 20, and 100 indeed correctly recover their
corresponding true time delays for these three cases.
This simulation study indicates that the FDTDE technique can correctly estimate time
delay from the phase slope of signal with linearly varying frequency without being
subjected to the ambiguity limitation due to the 2n phase wrapping effect. In addition,
5
the condition for this technique to be applicable is not as restrictive as the IFC method.
Asshown above, this process only requires the standard FFT operation and the phase
difference tracking. Unlike the IFC method which requires "instantaneous" information
(i.e. IFV) estimation, the signal to noise ratio requirement is less strict for the FDTDE
method since the FFT phase information is processed in "block" operation.
Figure 7 shows an example in a laboratory environment suitable for application of the
FDTDE time delay estimation. The data is taken from a test of a series of air flow tests
at the MSFC air flow facility (AFF). As shown in the isoplot in figure 7-a, an
anomalous frequency component was observed whose frequency changes linearly from
4400 Hz to 4260 Hz from S÷10 to S+50 second. Figure 7-b show the PSDs at two
measurement locations. The purpose of these tests is to characterize the facility
generated noise. In order to identify the source of this anomaly, the wave propagation
direction of this anomaly along the air flow pipe must first be determined.
Figure 8 shows (a) the frequency tracking of the anomaly, (b) the RMS amplitude of
the anomaly at measurement XB03, (c) the RMS amplitude of the anomaly at a down
stream measurement FH03, and (d) the FFT phase difference time data between these
two measurements. Notice that, the phase difference time data indeed shows an
apparent linear trend (phase slope) which is directly related to their time delay. The two
required parameters fo and f can be calculated from the frequency tracking plot in
figure 8-a. This phase slope P'xy is obtained from the phase difference time data in
figure 8-d. From this information, the time delay is then estimated based on the
relationship of equation (5). The resulting time delay estimated is 1.7 msee. This time
delay corresponds to a distance of 2 feet based on an average acoustic speed of 1180
ft./see. This distance is close to the actual physical length between these two
measurement locations. In addition, the positive phase slope shown in figure 8-d
clearly indicates that the anomaly in XB03 is leading the FH03. This lead/lag
information is critical in determining the source of anomaly. More detailed analysis and
application by using the FDTDE technique for the AFF test will be continued in the
next reporting period.
Prepared and approved by
Jen Jong
Program Manager
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1. AGENCY US'E ONLY (Leave blank) 2. REPORT OATE ;1. REP T T P O A C V
December 31, 1993 N_ni_lty _p_g_eg_r 1993
4. TITLE AND SUBTITLE S. FUNOING NUMBERS
Develop Advanced Nonlinear Signal
Analysis Topographical Mapping System NAS8-39393
_. AUTHOR(S)
Jen-Yi, Jong
m == =,,,,,,
7. PERFORMING ORGANIZATION NAME{S) AND AOORESS(ES)
AI SIGNAL RESEARCH, INC.
904 Bob Wallace Ave., Suite 211
Huntsville, AL 35801
9. SPONSORING/MONI.TORINGAGENCYNAME(S)ANDADORESS(ES)
Procurement Office, AP29-I
George C. Marshall Space Flight Center
NASA
Marshall Space Flight Center, AL 35812
;8. PERFORMING ORGANIZATION
REPORT NUMBER
TR-4002-93-12
10. SPONSORING / MONITORING
AGENCY REPORT NUMBER
11. SUPPLEMENTARY NOTES
12a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 woras)
As reported in the monthly technical progress report for July 1993, a new signal analysis
technique called "Instantaneous Frequency Correlation (IFC)" for time delay estimation
was developed which will be incorporated into the ATMS system. In this report, a
different technique for time delay estimation called "Phase Difference Time Derivative
Estimator (FDTDE)" will be discussed. The FDTDE technique does not replace the
IFC method since their application conditions are different. The IFC technique can
estimate the time delay between two spectral components of two measurement signals
when the center frequency of the component are constant. While the FDTDE method
can provide accurate time delay estimation when the frequency of the subject
component changes linearly such as during engine startup or shut-down.
14. SUBJECT TERMS
17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION
OF REPORT OF THIS PAGE
19. SECURITY CLASSIFICATION
OF ABSTRACT
15. NUMBER OF PAGES
]4
16. PRICE CODE
20. LIMITATION OF ABSTRACT
NSN 7540-01-280-55OO Stanc_a;cl ;orm 298 (Rev 2.89)


Develop advanced nonlinear signal analysis topographical mapping system

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