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System Failure Diagnosis for the Advanced LIGO HAM
Chamber Seismic Isolation System
A THESIS
SUBMITTED TO THE DEPARTMENT OF AERONAUTIC
AND ASTRONAUTIC ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF ENGINEER
Kuo-Feng Tseng
August 2010
http://creativecommons.org/licenses/by-nc/3.0/us/
This dissertation is online at: http://purl.stanford.edu/pv002yn0780
© 2010 by Kuo-Feng Tseng. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.
ii
Approved for the department.
Daniel DeBra, Adviser
Brian Lantz, Adviser
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this thesis in electronicformat. An original signed hard copy of the signature page is on file in University Archives.
iii
iv
Abstract
The Laser Interferometer Gravitational Wave Observatory (LIGO) is a ground-based
observatory which is designed to detect the gravitational waves radiated from
accelerating massive objects in deep space. Currently, we are developing a new system
which upgrades Initial LIGO to Advanced LIGO. However, in Advanced LIGO, the
platforms, which hold the mirrors for the interferometer, contain many sensors and
actuators. Thus, when the system is not running properly, the operator has to spend a lot
of time in order to determine the component which causes the malfunction. Therefore,
developing a method that can easily detect the malfunction of the system and help
operators to determine where the malfunction comes from becomes an important issue.
v
Acknowledgments
I really appreciate my advisor, Daniel B. DeBra, co-advisor, Brain Lantz, and group
members, Graham Allen and Daniel Eugene Clark. They all gave me many helpful
suggestions. Without them, I would not have had any opportunities to be involved in
Advanced LIGO project and this thesis would not exist. Finally, thanks to my family for
their unconditional support.
vi
Table of Contents
1 Introduction……………………………………………………………..1
1.1 LIGO Project Overview………………………………………...…..1
1.2 HAM Chamber System Overview……………………….................2
1.3 Goals…………………………………………………………...…...3
2 HAM Chamber Test Method First Version……………………………...4
2.1 Test Frequency Selection……………………………………...……4
2.2 Generation of Measured system transfer function and Reference
System Transfer Function…………………………………….. 7
2.3 Failure Definition…………………………………………………8
2.3.1 Noise Ratio Definition…………………………………….8
2.3.2 Uncertainty Range of Transfer Function…………………..8
2.3.3 Defining Failure…………………………………………...9
2.4 Applying System Identification………………………………...…..9
2.5 Information from Noise Ratio………………………………..…...11
2.6 Test Result………………………………………………..……….12
2.7 Conclusion……………………………………………………..…22
3 HAM Chamber Test Method Second Version…………………………23
3.1 Difference Between First and Second Version………………...….23
3.2 Applying System Identification with Modification…………...…..23
3.3 Test result……………………………………………………...…..27
3.4 Conclusion……………………………………………………...…34
vii
4 HAM Chamber Test Method by Sending Horizontal and Vertical Test
Signals Simultaneously………………………………………………....35
5 Future Work……………………………………………………….…….38
6 Final Conclusion………………………………………………………..38
Bibliography………………………………………………………………..40
List of Tables
Table 2.1 Transfer Function Matrix for GS-13 Seismometer………………10
Table 2.2 Noise Ratio Matrix for GS-13 Seismometer…………………… 11
viii
List of Figures
Figure 1.1 HAM Chamber System Assembly…………………………………………….3
Figure 2.1 Drive Input Signal of 0.2 and 5 Hz with Gentle Build up and Decay………..5
Figure 2.2 Experimental Displacement Output Frequency Response caused by the Drive
Input Signal in a Properly Functioning Control System………………………6
Figure 2.3 Experimental GS-13 Seismometer Output Frequency Response Caused by
the Drive Input Signal in a Properly Functioning Control System …………..6
Figure 2.4 Drive Input for Measured System Transfer Function………………………….7
Figure 2.5 Uncertainty Range……………………………………………………………..9
Figure 2.6 first version test results for Test 1…………………………………………….13
Figure 2.7 first version test results for Test 2…………………………………………….14
Figure 2.8 first version test results for Test 3…………………………………………….16
Figure 2.9 first version test results for Test 4…………………………………………….18
Figure 2.10 first version test results for Test 5…………………………………………...19
Figure 2.11 first version test results for Test 6…………………………………………...21
Figure 3.1 block diagram of the LIGO HAM chamber system………………………….24
Figure 3.2 second version test results for Test 1…………………………………………28
Figure 3.3 second version test results for Test 2…………………………………………29
Figure 3.4 second version test results for Test 3…………………………………………31
Figure 3.5 second version test results for Test 4…………………………………………32
Figure 4.1 H1 displacement sensor output comparison….………………………………35
Figure 4.2 V1 displacement sensor output comparison……………………………….…36
Figure 4.3 H1 GS13 seismometer output comparison...…………………………………36
Figure 4.4 V1 GS13 seismometer output comparison...…………………………………37
1
Chapter 1
Introduction
1.1 LIGO Project Overview
The idea of using gravitational waves to observe events such as black holes or compact
binaries is based on Albert Einstein’s general relativity theory. The theory states that a
massive object, which has acceleration, will distort space-time, and radiates gravitational
waves. There are currently several projects such as, LIGO [1], [2], GEO600 [3], VIRGO
[4], and TAMA [5], which use information from gravitational waves to conduct
astronomy research. Several others are under development, such as ACIGA [6], LCGT
[7], and the space-based LISA mission [8].
Laser interferometry can be used to measure gravitational waves by measuring the
differential distance change of two orthogonal laser beams. When no gravitational wave
passes through the interferometer, the two paths of laser beams are the same length. As a
gravitational wave passes through, the path of two laser beams will be distorted and then
produces the periodic change. For further information about gravitational waves and their
detection see Gravitational-wave Detection [9].
Currently, there are two observatories in the LIGO project. One is located in
Livingston Parish, Louisiana, and the other one is located on the Hanford Site in eastern
Washington State. These two observatories are far away from each other so local seismic
events and disturbances are not correlated, but measure the same event occurring in the
universe. Therefore, if the measurements from two observatories have the same periodic
pattern, there is a high possibility that the measurements represent the event occurring in
the deep universe.
2
1.2 HAM Chamber System Overview
In the LIGO project, there are two kinds of chambers, HAM and BSC. The HAM
chamber system is the main focus in this thesis. In the HAM chamber, there is a single
stage active isolation and alignment platform on which some of the interferometer optics
are mounted. The isolation system includes displacement sensors, GS-13 seismometers,
and electromagnetic actuators. The displacement sensors provide alignment and low
frequency information, the GS-13 seismometers provides high frequency information,
and the electromagnetic actuators provide a force in order to reduce the vibration of the
platform at all frequencies. There are three sensors and actuators which measure and
provide forces for vertical motions and another set to measure horizontal motions.
The isolation control system, which reduces the vibration of the platform, includes
isolation loops and damping loops. The isolation loops contain blend filters and isolation
filters, which help combine the information from displacement sensors and GS-13
seismometers. The damping loops are six single-input, single-output (SISO) loops from
the individual GS-13 seismometers to their correspondent actuators.
Figure 1.1 is the assembly of the HAM chamber system. The more detail assembly
of the HAM chamber system and the isolation loops can be found in papers, Enhanced
LIGO HAM ISI Prototype Preliminary Performance Review [10], Low Frequency Active
Vibration Isolation for Advanced LIGO [11], and Performance of LIGO Prototype HAM
ISIs and improvements for the LIGO HAM ISIs [12].
3
Figure 1.1: HAM Chamber System Assembly
1.3 Goals
There will be 5 HAM isolation systems in each Advanced LIGO interferometer and each
HAM chamber system includes 12 sensors measuring the horizontal and vertical motions
of platform and 6 actuators providing horizontal and vertical forces; therefore, during the
weekly-based system inspection, it currently takes too much time and effort to determine
whether any sensors or actuators have failed. In this thesis, a simple test method called a
“watchdog”, which applies system identification on all components, can provide useful
information in order to help operators determine if there is a failed sensor or actuator. The
ultimate goal is to apply the developed method to both HAM and BSC chambers.
4
Chapter 2
HAM Chamber Test Method First Version
To inspect the health of the LIGO HAM chamber system, one compares the measured
system transfer function with the reference system transfer function at test frequencies. If
the difference between the measured system transfer function and the reference system
transfer function exceeds a certain value, the system has failed its inspection. In this
chapter, we include Test Frequencies Selection, Generation of the measured system
transfer function and the Reference System Transfer Function, Failure Definition,
Applying System Identification, and Noise Ratio. Test results and conclusions are at the
end of this chapter.
2.1 Test Frequency Selection
To select test frequencies, there are several factors that need to be considered. First, it is
unlikely to have a sensor or an actuator that acts properly at one frequency but fails at
other frequencies. Therefore, it is unnecessary to inspect the system at all frequencies.
When a failure is detected, we will follow-up with more detailed tests, but those
component level tests are not in the scope of this work. Second, the lower edge of the
detection band for the observatory is 10 Hz. Thus, in order to possibly run the inspection
without interrupting the observatory, the selected frequency should be lower than 10 Hz.
Third, when carrying out the inspection, the actuators contain both drive input and signals
from the damping loops. Therefore, to reduce the effect caused by the actuators which
don’t contain the drive input, the selected test frequency shouldn’t be the frequency at
which the damping loops have maximum loop gain. Currently the maximum gain of the
damping loops is at 1 Hz. Fourth, the displacement sensors are more sensitive to the
signals below 1 Hz and the GS-13 seismometers are more sensitive to the signals above 1
Hz. Thus, the drive input needs to contain frequency signals below and above 1 Hz in
order to inspect both displacement sensors and GS-13 seismometers.
5
Based on the four factors above and the descriptions of the different drive signal
properties from the book System Identification [13], the drive input signal used in the
current HAM chamber test method includes 0.2 Hz and 5 Hz sine waves. In order to
avoid abrupt changes, the first and last 20 seconds of the drive input signal, which are not
used to calculate transfer functions, are designed to increase gradually. Furthermore, the
drive input signal contains an integer number of periods that can mitigate the effect of
FFT leakage [13]. Figure 2.1 is the drive input signal for generating a reference system
transfer function. The response of the displacement sensor and GS-13 seismometers is
shown in Figure 2.2 and 2.3.
0 10 20 30 40 50 60 70-8000
-6000
-4000
-2000
0
2000
4000
6000
8000total drive series
Time (seconds)
Drive I
nput
(counts
)
Figure 2.1: Drive Input Signal of 0.2 and 5 Hz with Gentle Build up and Decay
Total Drive Series
Time (Seconds)
Dri
ve In
pu
t(co
un
ts)
6
Figure 2.2: Experimental Displacement Output Frequency Response caused by the Drive
Input Signal in a Properly Functioning Control System
Figure 2.3: Experimental GS-13 Seismometer Output Frequency Response Caused by
the Drive Input Signal in a Properly Functioning Control System
7
2.2 Generation of Measured System Transfer Function and
Reference System Transfer Function
Because the disturbances of the HAM Chamber system are not correlated at different test
time segments, averaging measurements of the system transfer function will improve the
signal to noise ratio of the system transfer function that should be equal to the reference
system transfer function. Figure 2.3 is also the drive signal for generating the reference
system transfer function. The difference between the reference system transfer function
and the measured system transfer function is that for the measured system transfer
functions, only one experiment is carried out in order to shorten the health inspection
time; therefore, to achieve a better signal to noise ratio of measured system transfer
function, the duration of the drive input has to be increased. Figure 2.4 is the drive input
for generating the measured system transfer function.
0 10 20 30 40 50 60 70 80 90-8000
-6000
-4000
-2000
0
2000
4000
6000
8000Total Drive Series
Time (Seconds)
Dri
ve in
pu
t (c
ou
nts
)
Figure 2.4 Drive Input for Measured System Transfer Function
8
2.3 Failure Definition
In this chapter, we start from the Noise Ratio Definition and Uncertainty Range of
the transfer function, and then the Noise Ratio Definition and Uncertainty Range are used
to define the failure condition.
2.3.1 Noise Ratio Definition
Before defining failure conditions, we first have to define the noise ratio (NR) and
uncertainty range for measured system transfer function and reference system transfer
function. Equation (2-1) below is the definition of noise ratio.
(2-1)
In equation (2-1), is the magnitude of the
output at test frequency and for the measured system transfer function, there is no
for only one test. Therefore, the
is estimated by
,
where A1 through A6 are the magnitudes at the frequencies close to the test frequency.
2.3.2 Uncertainty Range of Transfer Function
The radius of uncertainty range for reference system transfer function is calculated from
the standard deviation of several tests. For measured system transfer function, there is no
standard deviation for only one test; however, the major part of the noise is caused by
ground motion. Therefore, the numerator of the noise ratio (NR) can be seen as the
magnitude estimation of noise at test frequencies. Thus, the noise of the system transfer
function can be defined as , where Gn(w) is the noise of the system
9
transfer function and G(w) is the system transfer function. The magnitude of Gn(w) is
defined as the radius of the uncertainty range.
Figure 2.5: Uncertainty Range
2.3.3 Defining Failure Condition
There are two different failure definitions that need to be defined. The first failure
definition is for transfer functions. When the measured system transfer function is not
enclosed by the uncertainty range of the reference system transfer function, the system is
considered to have a malfunction. To be more conservative, the radius of the uncertainty
range of reference system transfer function is tripled. The second failure definition is
defined for a given noise ratio. When the noise ratio of the measured system transfer
function is larger than the noise ratio of the reference system transfer function, the system
is considered to have a malfunction or the test is considered to be too noisy. The details of
the noise ratio are covered in section 2.4.
2.4 Applying System Identification
System Identification is a well-developed technique which can identify the transfer
function of a system from its input signal and its output signal. For a linear system such
as LIGO HAM chamber, the Fourier transform of output Y(w) equals the transfer
function of system G(w) times Fourier transform of the drive input U(w). Therefore, with
Re
Im
R
Vector R: measured system transfer function
Length r : radius of uncertainty range
r = magnitude of Gn(w)
r
Uncertainty
Range Vector R: reference system transfer function
Length r : radius of uncertainty range
r = standard deviation
10
known drive inputs and the monitored output from sensors, the transfer function G(w) at
test frequencies from each actuator to each sensor can be derived by . To further
identify the parts of the system that are not performing at their nominal level, the transfer
function of each horizontal sensor and actuator pair is put into a matrix form shown in
Table 2.1 below,
Table 2.1: Transfer Function Matrix for GS-13 Seismometer
In Table 2.1, GHnm are transfer functions for each horizontal actuator to each horizontal
GS-13 seismometer and GVnm are transfer functions for each vertical actuator to each
vertical GS-13 seismometer. The effect of drive inputs from the horizontal actuators to
vertical GS-13 seismometers and the vertical actuators to horizontal GS-13 seismometers
are small and require larger drive inputs to get good signal to noise ratios, so the
upper-right and lower-left blocks are close to zero. The diagonal entries in Table 2.1
above are the main indicators that show the conditions of the system. To identify the
failed parts, the first step is to compare the value of the diagonal entries in Table 2.1 with
the reference system transfer function and then assign a -1 score to the transfer functions
which satisfy the failure condition. Next, if no diagonal entries get -1, the system is
considered healthy. However, if any diagonal entries show incorrect values, the system is
considered to have a malfunction. Then, we attempt to distinguish between sensor and
actuator failures. The summation of the scores of the row that includes the failure
diagonal entry is the score of the sensor related to that failure diagonal entry, and the
summation of the scores of column is the score of the actuator related to that failure
ACTH1 ACTH2 ACTH3 ACTV1 ACTV2 ACTV3
GS-13H1 GH11 GH12 GH13 ~0 ~0 ~0
GS-13H2 GH21 GH22 GH23 ~0 ~0 ~0
GS-13H3 GH31 GH32 GH33 ~0 ~0 ~0
GS-13V1 ~0 ~0 ~0 GV11 GV12 GV13
GS-13V2 ~0 ~0 ~0 GV21 GV22 GV23
GS-13V3 ~0 ~0 ~0 GV31 GV32 GV33
11
diagonal entry. Finally, from the score, the most probable sensor or actuator that may
have failed can be identified.
2.5 Information From Noise Ratio
The noise ratio also contains information about the system health. If the noise ratio of the
measured system transfer function is significantly larger than the noise ratio of the
reference system transfer function, the noise ratio shows either a failure of the system or
an unusual strong ground vibration caused by the environment. To identify failed parts
from noise ratio, the noise ratio of each sensor and actuator pair is also put into a matrix
form shown in the Table 2.2, similar to Table 2.1 in chapter 2.3. Next, the noise ratio of
the measured system transfer function is compared with the noise ratio of the reference
system transfer function. A -1 score is assigned to the sensor and actuator pairs if their
noise ratio is larger than the noise ratio of the reference system transfer function. Finally,
the score of each sensor and each actuator is calculated by applying the same method
used in chapter 2.3. To further identify whether the high noise ratio is caused by ground
motion, several tests are performed. If all tests give the same result, the high noise ratio is
unlikely to be caused by ground motion and more likely to be caused by a system failure.
Table 2.2: Noise Ratio Matrix for GS-13 Seismometer
ACTH1 ACTH2 ACTH3 ACTV1 ACTV2 ACTV3
GS-13H1 RH11 RH12 RH13
GS-13H2 RH21 RH22 RH23
GS-13H3 RH31 RH32 RH33
GS-13V1 RV11 RV12 RV13
GS-13V2 RV21 RV22 RV23
GS-13V3 RV31 RV32 RV33
12
2.6 Test Result
Test Result Explantion:
For each vibration isolation stage, there are sensors and actuators. Our design is
principally a single input single output relationship between sensors and actuators. The
model for our design is never perfectly realized but adequate performance is achieved if
they are close enough. When we measure the transfer function, there are uncertainties as
well as allowable tolerances in what we have learned by experiment in how closely they
agree. In the following results, we present the results of facts in which
X: Measured System Transfer Function
O: Reference System Transfer Function
Circle about X: Uncertainty Range for Measured System Transfer Function
Circle about O: Uncertainty Range for Reference System Transfer Function
When no actuators or sensors are disconnected (under normal conditions), we should
expect the Circle for O will either completely enclose the Circle for X or has the
overlapped region with the Circle for X. However, due to the cross coupling caused by
the damping loops which will be introduced in the next chapter, some test results have the
Circle for O close to the Circle for X, but don’t have the overlapped region. On the other
hand, when the corresponding actuators or sensors are disconnected, the X and the Circle
for X will be no longer close to the Circle for O, and the magnitude of the X will be close
to zero.
13
Test 1: Under Normal
Conditions
-0.018 -0.017 -0.016 -0.0150.089
0.09
0.091
0.092
Sensor DispH1
ActH1
-0.015 -0.014 -0.0130.0855
0.086
0.0865
0.087
0.0875
0.088
Sensor DispH2
ActH2
-0.016 -0.015 -0.0140.087
0.088
0.089
0.09
Sensor DispH3
ActH3
0.011 0.0115 0.012 0.0125-0.0664
-0.0662
-0.066
-0.0658
-0.0656
Sensor DispV1
ActV1
0.011 0.0115 0.012 0.0125-0.067
-0.0665
-0.066
-0.0655
Sensor DispV2
ActV2
0.0105 0.011 0.0115 0.012-0.0655
-0.065
-0.0645
-0.064
-0.0635
Sensor DispV3
ActV3
0.011 0.0115 0.012 0.01250.072
0.0725
0.073
0.0735
0.074
Sensor GEOH1
ActH1
0.011 0.0115 0.012 0.01250.075
0.0755
0.076
0.0765
0.077
Sensor GEOH2
ActH2
0.01 0.012 0.0140.0745
0.075
0.0755
0.076
0.0765
0.077
Sensor GEOH3
ActH3
0.04 0.045 0.05 0.0550.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV1
ActV1
0.046 0.048 0.05 0.0520.206
0.208
0.21
0.212
0.214
Sensor GEOV2
ActV2
0.04 0.045 0.05 0.0550.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV3
ActV3
Figure 2.6: first version test results for Test 1
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score: GS-13 test Actuator Score
14
0 0 0 0 0 0 0 0 0 0 0 0
Displacement Sensor Score:
0 0 0 0 0 0
GS-13- Seismometer Score:
0 0 0 0 0 0
The test is conducted under normal conditions in which no actuators and sensors had
been intentionally disconnected.
Test 2: Disconnect ACTUATORH1
-0.02 -0.01 0 0.01-0.05
0
0.05
0.1
Sensor DispH1
ActH1
-0.015 -0.014 -0.0130.085
0.086
0.087
0.088
Sensor DispH2
ActH2
-0.016 -0.015 -0.0140.087
0.088
0.089
0.09
Sensor DispH3
ActH3
0.011 0.0115 0.012 0.0125-0.0664
-0.0662
-0.066
-0.0658
-0.0656
Sensor DispV1
ActH1
0.011 0.0115 0.012 0.0125-0.067
-0.0665
-0.066
-0.0655
Sensor DispV2
ActH2
0.0105 0.011 0.0115 0.012-0.0655
-0.065
-0.0645
-0.064
-0.0635
Sensor DispV3
ActH3
15
-0.01 0 0.01 0.02-0.02
0
0.02
0.04
0.06
0.08
Sensor GEOH1
ActH1
0.01 0.012 0.014 0.0160.075
0.0755
0.076
0.0765
0.077
Sensor GEOH2
ActH2
0.01 0.012 0.014 0.0160.0745
0.075
0.0755
0.076
0.0765
0.077
Sensor GEOH3
ActH3
0.04 0.045 0.05 0.0550.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV1
ActH1
0.046 0.048 0.05 0.0520.206
0.208
0.21
0.212
0.214
Sensor GEOV2
ActH2
0.04 0.045 0.05 0.0550.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV3
ActH3
Figure 2.7: first version test results for Test 2
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score:
-3 -3 0 0 0 0
GS-13 test Actuator Score
-3 -3 -3 0 0 0
Displacement Sensor Score:
-3 -3 0 0 0 0
GS-13- Seismometer Score:
-3 -3 -3 0 0 0
Disptest Actuator Score from NR:
-3 0 0 0 0 0
GS-13 test Actuator Score from NR
-3 0 0 0 0 0
Displacement Sensor Score from NR:
-1 0 0 0 0 0
GS-13- Seismometer Score from NR:
-1 0 0 0 0 0
Overall Disptest Actuator Score:
-6 -3 0 0 0 0
Overall GS-13 test Actuator Score:
-6 -3 -3 0 0 0
Overall Displacement Sensor Score:
-4 -3 0 0 0 0
Overall GS-13 Sensor Score:
-4 -3 -3 0 0 0
Test result: ACTH1 has the lowest score.
This test is conducted when the ACTH1 is intentionally disconnected. We can see the
measured system transfer function in the plots related to ACTH1 is far away from the
16
reference system transfer function. However, some of the plots which are not related to
the ACTH1 also have been affected. These effects leave the ambiguity for which we can’t
conclude that the only failure is ACTH1. The ambiguity also occurred in the following test
results. In Chapter 3 the cause for the ambiguity will be discussed and a method which
can solve this problem is presented.
Test 3: Disconnect ACTUATORH1 and ACTUATORH2
-0.02 -0.01 0 0.01-0.05
0
0.05
0.1
Sensor DispH1
ActH1
-0.02 -0.01 0 0.01-0.05
0
0.05
0.1
Sensor DispH2
ActH2
-0.016 -0.015 -0.0140.086
0.087
0.088
0.089
0.09
0.091
Sensor DispH3
ActH3
0.011 0.0115 0.012 0.0125-0.0664
-0.0662
-0.066
-0.0658
-0.0656
Sensor DispV1
ActV1
0.011 0.0115 0.012 0.0125-0.067
-0.0665
-0.066
-0.0655
Sensor DispV2
ActV2
0.0105 0.011 0.0115 0.012-0.0655
-0.065
-0.0645
-0.064
-0.0635
Sensor DispV3
ActV3
-0.01 0 0.01 0.02-0.02
0
0.02
0.04
0.06
0.08
Sensor GEOH1
ActH1
-0.01 0 0.01 0.02-0.02
0
0.02
0.04
0.06
0.08
Sensor GEOH2
ActH2
0.01 0.015 0.020.074
0.075
0.076
0.077
Sensor GEOH3
ActH3
0.04 0.045 0.05 0.0550.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV1
ActV1
0.046 0.048 0.05 0.0520.206
0.208
0.21
0.212
0.214
Sensor GEOV2
ActV2
0.04 0.045 0.05 0.0550.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV3
ActV3
Figure 2.8: first version test results for Test 3
17
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score:
-3 -3 -3 0 0 0
GS-13 test Actuator Score
-3 -3 -3 0 0 0
Displacement Sensor Score:
-3 -3 -3 0 0 0
GS-13- Seismometer Score:
-3 -3 -3 0 0 0
Disptest Actuator Score from NR:
-3 -3 0 0 0 0
GS-13 test Actuator Score from NR
-3 -3 0 0 0 0
Displacement Sensor Score from NR:
-2 -2 0 0 0 0
GS-13- Seismometer Score from NR:
-2 -2 0 0 0 0
Overall Disptest Actuator Score:
-6 -6 -3 0 0 0
Overall GS-13 test Actuator Score:
-6 -6 -3 0 0 0
Overall Displacement Sensor Score:
-5 -5 -3 0 0 0
Overall GS-13 Sensor Score:
-5 -5 -3 0 0 0
Test result: ACTH1 and ACTH2 both have the lowest score.
Test 4: Disconnect ACTUATORV1
-0.018 -0.017 -0.016 -0.0150.0895
0.09
0.0905
0.091
0.0915
0.092
0.0925
Sensor DispH1
ActH1
-0.015 -0.0145 -0.014 -0.0135 -0.0130.0855
0.086
0.0865
0.087
0.0875
0.088
Sensor DispH2
ActH2
-0.016 -0.0155 -0.015 -0.0145 -0.0140.087
0.0875
0.088
0.0885
0.089
0.0895
0.09
Sensor DispH3
ActH3
-5 0 5 10 15
x 10-3
-0.08
-0.06
-0.04
-0.02
0
0.02
Sensor DispV1
ActV1
0.011 0.0115 0.012 0.0125-0.0668
-0.0666
-0.0664
-0.0662
-0.066
-0.0658
-0.0656
Sensor DispV2
ActV2
0.0105 0.011 0.0115 0.012-0.0655
-0.065
-0.0645
-0.064
-0.0635
Sensor DispV3
ActV3
18
0.011 0.0115 0.012 0.01250.072
0.0725
0.073
0.0735
Sensor GEOH1
ActH1
0.011 0.0115 0.012 0.01250.075
0.0755
0.076
0.0765
Sensor GEOH2
ActH2
0.01 0.011 0.012 0.013 0.0140.0745
0.075
0.0755
0.076
0.0765
0.077
Sensor GEOH3
ActH3
0 0.02 0.04 0.06-0.1
0
0.1
0.2
0.3
Sensor GEOV1
ActV1
0.046 0.048 0.05 0.052 0.0540.206
0.208
0.21
0.212
0.214
0.216
Sensor GEOV2
ActV2
0.042 0.044 0.046 0.048 0.050.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV3
ActV3
Figure 2.9: first version test results for Test 4
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score:
0 0 0 -3 0 0
GS-13 test Actuator Score
0 0 0 -3 -3 -3
Displacement Sensor Score:
0 0 0 -2 0 0
GS13- Seismometer Score:
0 0 0 -3 -3 -3
Disptest Actuator Score from NR:
0 0 0 -3 0 0
GS-13 test Actuator Score from NR
0 0 0 -3 0 0
Displacement Sensor Score from NR:
0 0 0 -1 0 0
GS-13- Seismometer Score from NR:
0 0 0 -1 0 0
Overall Disptest Actuator Score:
0 0 0 -6 0 0
Overall GS-13 test Actuator Score:
0 0 0 -6 -3 -3
Overall Displacement Sensor Score:
0 0 0 -3 0 0
Overall GS-13 Sensor Score:
0 0 0 -4 -3 -3
Test result: ACTV1 has the lowest score.
19
Test 5: Disconnect Displacement SensorH1
-0.02 -0.01 0 0.01-0.05
0
0.05
0.1
Sensor DispH1
ActH1
-0.015 -0.014 -0.0130.0855
0.086
0.0865
0.087
0.0875
0.088
Sensor DispH2
ActH2
-0.016 -0.015 -0.0140.087
0.088
0.089
0.09
Sensor DispH3
ActH3
0.011 0.0115 0.012 0.0125-0.0664
-0.0662
-0.066
-0.0658
-0.0656
Sensor DispV1
ActV1
0.011 0.0115 0.012 0.0125-0.067
-0.0665
-0.066
-0.0655
Sensor DispV2
ActV2
0.0105 0.011 0.0115 0.012-0.0655
-0.065
-0.0645
-0.064
-0.0635
Sensor DispV3
ActV3
0.011 0.0115 0.012 0.01250.072
0.0725
0.073
0.0735
0.074
Sensor GEOH1
ActH1
0.011 0.0115 0.012 0.01250.075
0.0755
0.076
0.0765
0.077
Sensor GEOH2
ActH2
0.01 0.012 0.0140.0745
0.075
0.0755
0.076
0.0765
0.077
Sensor GEOH3
ActH3
0.04 0.045 0.05 0.0550.2
0.205
0.21
0.215
0.22
Sensor GEOV1
ActV1
0.045 0.05 0.055 0.060.206
0.208
0.21
0.212
0.214
0.216
Sensor GEOV2
ActV2
0.04 0.045 0.05 0.0550.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV3
ActV3
Figure 2.10: first version test results for Test 5
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score:
-1 0 0 0 0 0
GS-13 test Actuator Score
0 0 0 -1 0 0
20
Displacement Sensor Score:
-3 0 0 0 0 0
GS-13- Seismometer Score:
0 0 0 -3 0 0
Disptest Actuator Score from NR:
-1 0 0 0 0 0
GS-13 test Actuator Score from NR
0 0 0 0 0 0
Displacement Sensor Score from NR:
-3 0 0 0 0 0
GS-13- Seismometer Score from NR:
0 0 0 0 0 0
Overall Disptest Actuator Score:
-2 0 0 0 0 0
Overall GS-13 test Actuator Score:
0 0 0 -1 0 0
Overall Displacement Sensor Score:
-6 0 0 0 0 0
Overall GS-13 Sensor Score:
0 0 0 -3 0 0
Test result: Displacement SensorH1 has the lowest score.
Test 6: Disconnect GS-13 SeismometerV2
-0.018 -0.017 -0.016 -0.0150.089
0.09
0.091
0.092
Sensor DispH1
ActH1
-0.015 -0.014 -0.0130.0855
0.086
0.0865
0.087
0.0875
0.088
Sensor DispH2
ActH2
-0.016 -0.015 -0.0140.087
0.088
0.089
0.09
Sensor DispH3
ActH3
0.011 0.0115 0.012 0.0125-0.0664
-0.0662
-0.066
-0.0658
-0.0656
Sensor DispV1
ActV1
0.011 0.0115 0.012 0.0125-0.067
-0.0665
-0.066
-0.0655
Sensor DispV2
ActV2
0.0105 0.011 0.0115 0.012-0.0655
-0.065
-0.0645
-0.064
-0.0635
Sensor DispV3
ActV3
21
0.011 0.0115 0.012 0.01250.072
0.0725
0.073
0.0735
0.074
Sensor GEOH1
ActH1
0.011 0.0115 0.012 0.01250.075
0.0755
0.076
0.0765
0.077
Sensor GEOH2
ActH2
0.01 0.012 0.0140.0745
0.075
0.0755
0.076
0.0765
0.077
Sensor GEOH3
ActH3
0.04 0.045 0.05 0.0550.2
0.202
0.204
0.206
0.208
0.21
Sensor GEOV1
ActV1
-0.05 0 0.05 0.10
0.05
0.1
0.15
0.2
0.25
Sensor GEOV2
ActV2
0.04 0.045 0.05 0.0550.2
0.205
0.21
0.215
0.22
Sensor GEOV3
ActV3
Figure 2.11: first version test results for Test 6
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score:
0 0 0 0 0 0
GS-13 test Actuator Score
0 0 0 0 -3 -1
Displacement Sensor Score:
0 0 0 0 0 0
GS-13- Seismometer Score:
0 0 0 0 -3 -3
Disptest Actuator Score from NR:
0 0 0 0 0 0
GS-13 test Actuator Score from NR
0 0 0 0 0 0
Displacement Sensor Score from NR:
0 0 0 0 0 0
GS-13- Seismometer Score from NR:
0 0 0 0 -3 0
Overall Disptest Actuator Score:
0 0 0 0 0 0
Overall GS-13 test Actuator Score:
0 0 0 0 -3 -1
Overall Displacement Sensor Score:
0 0 0 0 0 0
Overall GS-13 Sensor Score:
0 0 0 0 -6 -3
Test result: GS-13 SeismometerV2 has the lowest score.
22
2.7 Conclusion
The test results show that using the primary indicators, transfer function, and the
secondary indicators, noise ratio, together can provide useful information about the
actuator and sensor health conditions. Especially when the measured system transfer
function is different from the reference system transfer function, it means the plant
definitely has some problems. However, the test results has the ambiguity because not
only the transfer function that contains disconnected actuators is affected, but also the
other transfer functions. In order to solve this ambiguity, in Chapter 3 a better method
will be introduced and the cause of the ambiguity will be discussed.
23
Chapter 3
HAM Chamber Test Method Second Version
3.1 Difference between First and Second Version
The major difference between the second version and the first version of the “watch-dog”
is that even when two actuators are disconnected, to search for broken actuators or
sensors and replace it by only using transfer functions won’t produce the ambiguity that
was produced by the first version. This ambiguity results from the configuration of the
damping loops. Due to the cross-coupling between different loops, the failure of one loop
will have a small but notable effect on the other loops. To achieve the goal without
having ambiguity, the basic assumption that the transfer function is simply derived from
(3-1)
has to be modified. In the following section, the block diagram of damping loops and
how the different loops affect each other will be discussed, also the algorithm which can
solve the ambiguity in the Test Method Version One.
3.2 Applying System Identification with Modification
The simple block diagram of the LIGO HAM chamber system is shown in Figure 3.1.
The output of the sensors in the LIGO HAM chamber system is feedback through the
damping loops, which generate the actuator input to drive the actuator in order to keep
the platform still.
24
Figure 3.1: block diagram of the LIGO HAM chamber system
Based on linear time-invariant property of the LIGO HAM chamber system, the equation
which links output Y(w), actuator inputs Ua(w), and ground force W(w) can be written as
(3-2)
Because the fact that vertical motion and horizontal motion are independent, the above
equation can be further written as
(3-3)
In equation (3-3), , , and are the actuator inputs for
horizontal actuators 1, 2, and 3. are
transfer functions for horizontal actuators 1, 2, and 3. is the transfer function from
the force to the displacement, and is the sensor transfer function for
horizontal GS-13H1. Similarly, the equations for GS-13H2, GS-13H3, GS-13V1, GS-13V2,
GS-13V3, and three horizontal displacement sensors and three vertical displacement
sensors can all be written in the same form as equation (3-3).
Damping Loop
Actuator
A(w)
Plant transfer
function P(w)
Sensor
S(w) Output Y(w)
Force from ground W(w)
Actuator input Ua(w)
25
Equation (3-3) shows the relationship between the method version 1 and the version
2. AGS-13H1(w)P(w)SGS-13H1(w), AGS-13H2(w)P(w)SGS-13H1(w), and AGS-13H3(w)P(w)
SGS-13H1(w) are GH11, GH12, and GH13 in Table 2.1 in the Chapter 2. To identify transfer
functions GH11, GH12, and GH13, the same drive input is sent through the horizontal
actuators 1, 2, and 3 during the different time segment as in the method version 1, and
then taking the Fourier Transform of the Actuator input Ua(w) of all three horizontal
actuators to form three equations for different time segments.
(3-4)
(3-5)
(3-6)
Equation (3-4), (3-5), and (3-6) are equations for time segments 1, 2, and 3 during which
the drive input with test frequencies is contained by horizontal actuator 1, 2, and 3
respectively.
Although in equations (3-4), (3-5), and (3-6), the number of unknowns is more than
the number of equations, the magnitude of the drive input signal at test frequencies is
much larger than the magnitude of the disturbances; therefore, the three disturbance
unknowns can be ignored, which leaves the equations with only three unknowns, GH11(w),
GH12(w), and GH13(w). Thus, the transfer function GH11(w), GH12(w), and GH13(w) can be
solved from equations (3-4), (3-5), and (3-6).
To simplify the notation of the equations (3-4), (3-5), and (3-6), we rewrite these
three equations as equations (3-7), (3-8), and (3-9), and the equation (3-10) is the matrix
form.
(3-7)
(3-8)
26
(3-9)
(3-10)
Then, we can form the equation (3-11)
(3-11)
where , and , to solve
horizontal transfer functions .
27
3.3 Test Result
Test Result Explantion:
The test results under normal conditions should be the same as the results shown in the
Chapter 2. However, the difference in here is that when the corresponding actuators or
sensors are disconnected, the other transfer fuctions shouldn’t be affected by the cross
coupling effect caused by the damping loops.
Test 1: Under Normal Conditions
-0.017 -0.016 -0.015-0.09
-0.0895
-0.089
-0.0885
-0.088
-0.0875
Sensor DispH1
ActH1
-0.016 -0.014 -0.012-0.086
-0.0855
-0.085
-0.0845
-0.084
-0.0835
Sensor DispH2
ActH2
-0.015 -0.0145 -0.014 -0.0135-0.0875
-0.087
-0.0865
-0.086
-0.0855
-0.085
Sensor DispH3
ActH3
0.011 0.012 0.0130.0656
0.0658
0.066
0.0662
0.0664
Sensor DispV1
ActV1
0.011 0.012 0.0130.0655
0.066
0.0665
0.067
0.0675
Sensor DispV2
ActV2
0.01 0.011 0.0120.064
0.0645
0.065
0.0655
Sensor DispV3
ActV3
28
0.018 0.019 0.02 0.021-0.0725
-0.072
-0.0715
-0.071
-0.0705
-0.07
Sensor GEOH1
ActH1
0.018 0.019 0.02 0.021-0.076
-0.075
-0.074
-0.073
Sensor GEOH2
ActH2
0.018 0.019 0.02 0.021-0.076
-0.075
-0.074
-0.073
Sensor GEOH3
ActH3
0.04 0.06 0.08-0.215
-0.21
-0.205
-0.2
-0.195
Sensor GEOV1
ActV1
0.04 0.06 0.08-0.22
-0.215
-0.21
-0.205
-0.2
Sensor GEOV2
ActV2
0.04 0.06 0.08-0.22
-0.215
-0.21
-0.205
-0.2
-0.195
Sensor GEOV3
ActV3
Figure 3.2: second version test results for Test 1
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score:
0 0 0 0 0 0
GS-13 test Actuator Score
0 0 0 0 0 0
Displacement Sensor Score:
0 0 0 0 0 0
GS13- Seismometer Score:
0 0 0 0 0 0
29
Test 2: Disconnect ACTUATORH1 and ACTUATORH2
-0.02 -0.01 0 0.01-0.1
-0.05
0
0.05
0.1
Sensor DispH1
ActH1
-0.02 -0.01 0 0.01-0.1
-0.05
0
0.05
0.1
Sensor DispH2
ActH2
-0.016 -0.014 -0.012-0.088
-0.087
-0.086
-0.085
-0.084
Sensor DispH3
ActH3
0.011 0.0115 0.012 0.01250.0655
0.066
0.0665
0.067
Sensor DispV1
ActV1
0.011 0.0115 0.012 0.01250.0655
0.066
0.0665
0.067
0.0675
Sensor DispV2
ActV2
0.0105 0.011 0.0115 0.0120.064
0.0645
0.065
0.0655
Sensor DispV3
ActV3
-0.01 0 0.01 0.02-0.08
-0.06
-0.04
-0.02
0
0.02
Sensor GEOH1
ActH1
-0.02 0 0.02 0.04-0.08
-0.06
-0.04
-0.02
0
0.02
Sensor GEOH2
ActH2
0.018 0.019 0.02 0.021-0.076
-0.075
-0.074
-0.073
Sensor GEOH3
ActH3
0.04 0.06 0.08-0.215
-0.21
-0.205
-0.2
-0.195
Sensor GEOV1
ActV1
0.04 0.06 0.08-0.22
-0.215
-0.21
-0.205
-0.2
Sensor GEOV2
ActV2
0.04 0.06 0.08-0.22
-0.215
-0.21
-0.205
-0.2
-0.195
Sensor GEOV3
ActV3
Figure 3.3: second version test results for Test 2
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score: GS-13 test Actuator Score
30
-3 -3 0 0 0 0 -3 -3 0 0 0 0
Displacement Sensor Score:
-2 -2 0 0 0 0
GS-13- Seismometer Score:
-2 -2 0 0 0 0
Disptest Actuator Score from NR:
-3 -3 0 -1 0 0
GS-13 test Actuator Score from NR
-3 -3 0 0 0 0
Displacement Sensor Score from NR:
-3 -2 -3 -1 0 0
GS-13- Seismometer Score from NR:
-2 -2 0 0 0 0
Overall Disptest Actuator Score:
-6 -6 -2 -1 0 0
Overall GS-13 test Actuator Score:
-6 -6 0 0 0 0
Overall Displacement Sensor Score:
-5 -4 -3 -1 0 0
Overall GS-13 Sensor Score:
-4 -4 0 0 0 0
Test result: ACTH1 and ACTH2 both have the lowest score.
In this test, the ACTH1 and ACTH2 are intentionally disconnected. The test result shows
that only the plots related to ACTH1 and ACTH2 are affected. Therefore, we can
successfully conclude that the failure is caused by ACTH1 and ACTH2. In order to verify if
the Test Method Second Version can successfully solve the ambiguity, several additional
tests are presented below and none of them have the ambiguity.
31
Test 3: Disconnect ACTUATORV1 and ACTUATORV2
-0.0165 -0.016 -0.0155 -0.015-0.09
-0.0895
-0.089
-0.0885
-0.088
-0.0875
Sensor DispH1
ActH1
-0.015 -0.014 -0.013 -0.012-0.086
-0.0855
-0.085
-0.0845
-0.084
-0.0835
Sensor DispH2
ActH2
-0.015 -0.0145 -0.014 -0.0135-0.0875
-0.087
-0.0865
-0.086
-0.0855
-0.085
Sensor DispH3
ActH3
-5 0 5 10 15
x 10-3
-0.02
0
0.02
0.04
0.06
0.08
Sensor DispV1
ActV1
-0.01 0 0.01 0.02-0.02
0
0.02
0.04
0.06
0.08
Sensor DispV2
ActV2
0.0105 0.011 0.0115 0.0120.064
0.0645
0.065
0.0655
Sensor DispV3
ActV3
0.018 0.019 0.02 0.021-0.0725
-0.072
-0.0715
-0.071
-0.0705
-0.07
Sensor GEOH1
ActH1
0.018 0.019 0.02 0.021-0.076
-0.0755
-0.075
-0.0745
-0.074
-0.0735
-0.073
Sensor GEOH2
ActH2
0.018 0.019 0.02 0.021-0.076
-0.0755
-0.075
-0.0745
-0.074
-0.0735
-0.073
Sensor GEOH3
ActH3
-0.05 0 0.05 0.1 0.15-0.25
-0.2
-0.15
-0.1
-0.05
0
Sensor GEOV1
ActV1
-0.05 0 0.05 0.1 0.15-0.3
-0.2
-0.1
0
0.1
Sensor GEOV2
ActV2
0.04 0.05 0.06 0.07 0.08-0.22
-0.215
-0.21
-0.205
-0.2
-0.195
Sensor GEOV3
ActV3
Figure 3.4: second version test results for Test 3
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score: GS-13 test Actuator Score
32
0 0 0 -3 -3 0 0 0 0 -3 -3 0
Displacement Sensor Score:
0 0 0 -2 -2 0
GS-13- Seismometer Score:
0 0 0 -2 -2 0
Disptest Actuator Score from NR:
0 0 0 -3 -3 0
GS-13 test Actuator Score from NR
0 0 0 -3 -3 0
Displacement Sensor Score from NR:
0 0 0 -2 -2 0
GS-13- Seismometer Score from NR:
0 0 0 -2 -2 0
Overall Disptest Actuator Score:
0 0 0 -6 -6 0
Overall GS-13 test Actuator Score:
0 0 0 -6 -6 0
Overall Displacement Sensor Score:
0 0 0 -4 -4 0
Overall GS-13 Sensor Score:
0 0 0 0 0 0
Test result: ACTV1 and ACTV2 both have the lowest score.
Test 4: Disconnect ACTUATORH1 and Displacement SensorH1
-0.02 0 0.02-0.1
-0.05
0
0.05
0.1
Sensor DispH1
ActH1
-0.016 -0.014 -0.012-0.086
-0.085
-0.084
-0.083
Sensor DispH2
ActH2
-0.016 -0.014 -0.012-0.088
-0.087
-0.086
-0.085
-0.084
Sensor DispH3
ActH3
0.011 0.012 0.0130.065
0.0655
0.066
0.0665
0.067
Sensor DispV1
ActV1
0.011 0.012 0.0130.0655
0.066
0.0665
0.067
0.0675
Sensor DispV2
ActV2
0.01 0.011 0.0120.064
0.0645
0.065
0.0655
Sensor DispV3
ActV3
33
-0.01 0 0.01 0.02-0.08
-0.06
-0.04
-0.02
0
0.02
Sensor GEOH1
ActH1
0.018 0.019 0.02 0.021-0.076
-0.075
-0.074
-0.073
Sensor GEOH2
ActH2
0.018 0.019 0.02 0.021-0.076
-0.075
-0.074
-0.073
Sensor GEOH3
ActH3
0.04 0.06 0.08-0.215
-0.21
-0.205
-0.2
-0.195
Sensor GEOV1
ActV1
0.04 0.06 0.08-0.22
-0.215
-0.21
-0.205
-0.2
Sensor GEOV2
ActV2
0.04 0.06 0.08-0.22
-0.215
-0.21
-0.205
-0.2
-0.195
Sensor GEOV3
ActV3
Figure 3.5: second version test results for Test 4
Final Scores for Sensors and Actuators
H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3
Disptest Actuator Score:
-3 0 0 0 0 0
GS-13 test Actuator Score
-3 0 0 0 0 0
Displacement Sensor Score:
-3 0 0 0 0 0
GS13- Seismometer Score:
-1 0 0 0 0 0
Disptest Actuator Score from NR:
-3 -2 -2 -1 0 0
GS-13 test Actuator Score from NR
-3 0 0 0 0 0
Displacement Sensor Score from NR:
-3 -2 -2 -1 0 0
GS-13- Seismometer Score from NR:
-1 0 0 0 0 0
Overall Disptest Actuator Score:
-6 -2 -2 -1 0 0
Overall GS-13 test Actuator Score:
-6 0 0 0 0 0
Overall Displacement Sensor Score:
-6 -2 -2 -1 0 0
Overall GS-13 Sensor Score:
-2 0 0 0 0 0
Test result: ACTH1 and Displacement SensorH1 both have the lowest score.
The minus scores of noise ratio for actuators and displacement sensors H1, H2, and V1
are caused by the disturbances. The measured system transfer functions are still within
34
the uncertainty range of the reference system transfer functions.
3.4 Conclusion
From the test result, the Second Version test successfully solve the ambiguity generated
by the cross coupling effects from damping loops. In addition, the measured system
transfer functions of weekly-based inspection are recorded which can be plotted in order
to observe any trend in the change of the transfer function history. Therefore, the operator
can identify not only sudden failures such as the test results shown in Chapter 2 and
Chapter 3, but also possibly observe gradual degrading before components completely
fail.
35
Chapter 4
HAM Chamber Test Method by Sending Horizontal
and Vertical Test Signals Simultaneously
In chapter 3, the HAM Chamber Test Method is executed by sending the test signals
through the actuators one by one. In this chapter, the data from the experiment shows that
the test method can be done by sending test signals through the horizontal and the vertical
actuators simultaneously. From Figure 4.1, 4.2, 4.3, and 4.4, the data indicate that when
horizontal and vertical actuators are excited simultaneously, the responses from the
GS-13 seismometer and the displacement sensor at test frequencies are similar to the
responses of those sensors with only one actuator excited. Therefore, by using the same
method in chapter 3 with different test frequencies for horizontal motion and vertical
motion, we can decrease the time for executing the test.
Figure 4.1: H1 displacement sensor output comparison
36
Figure 4.2: V1 displacement sensor output comparison
Figure 4.3: H1 GS13 seismometer output comparison
37
Figure 4.4: V1 GS13 seismometer output comparison
The test signal for generating the plots above contains 0.2 Hz and 0.5 Hz test frequencies
for horizontal and vertical displacement sensors and 5 Hz and 7 Hz test frequencies for
vertical and horizontal GS-13 seismometer.
38
Chapter 5
Future Work
There are still several improvements for the test method. First, with the linearity
assumption [14], it’s possible to reduce the time for inspection by sending the drive signal
with different test frequencies into the actuators simultaneously. Second, the current
method hasn’t been tested when the detector is in “science mode” which means the
detector is detecting gravitational wave. It’s possible that the current test signal
magnitude may be too high to keep the detector staying at the “science mode”. Therefore,
to optimize the test signal magnitude and duration in order to run the test method while
the detector is in “science mode” is also a potential improvement. Third, the future
system may include the feed-forward control loops which use the information from the
ground seismometers to generate the control input. To further identify the health
condition of the ground seismometers, we can incorporate the control input in the test
method.
Chapter 6
Final Conclusion
We started with a test method calculating the system transfer function from input to
output to and advanced to the more sophisticated algorithm which can solve the cross
coupling effects caused by the damping loops. Although both first and second methods
won’t perfectly identify every mailfunctions of the plant, the test method in Chapter 3 can
successfully solve the cross coupling problem and provide the operator correct
information about the health condition of sensors and actuators. Furthermore, in Chapter
4 the response of the sensors of the HAM chamber platform are investigated while the
test signal is sent through the horizontal and the vertical actuators simultaneously. The
result indicates that the test method can be executed by sending the test signal through the
horizontal and the vertical actuators at the same time. This decreases the time needed for
39
the test. In the end, several ways that may further decrease the testing time or keep the
detector in “science mode” while running the test are presented.
40
Bibliography
[1] Barish and R. Weiss (1999). LIGO and the Detection of Gravitational Waves, Phys.
Today, 52:44–50.
[2] Sigg (for the LIGO Scientific Collaboration) (2008). Status of the LIGO Detectors,
Classical and Quantum Gravity, 25(11):114041.
[3] Grote (for the LIGO Scientific Collaboration) (2008). The Status of GEO 600,
Classical and Quantum Gravity, 25(11):114043.
[4] Acernese et al. (2008). Status of Virgo, Classical and Quantum Gravity,
25(11):114045.
[5] Tatsumi et al. (2007). Current Status of Japanese Detectors, Classical and Quantum
Gravity, 24(19):S399–S403.
[6] Barriga et al. (2005). Technology Developments for ACIGA High Power Test
Facility for Advanced Interferometry, Classical and Quantum Gravity,
22(10):S199–S208.
[7] Kuroda and the LCGT Collaboration (2006). The Status of LCGT, Classical and
Quantum Gravity, 23(8):S215–S221.
[8] A. Shaddock (2008). Space-based Gravitational Wave Detection with LISA,
Classical and Quantum Gravity, 25(11):114012.
[9] Peter Saulson and Mike Cruise, Gravitational-wave Detection.
ISBN-10: 0819446351
[10] Jeff Kissel, Brian Lantz. Enhanced LIGO HAM ISI Prototype Preliminary
Performance Review, T-080251-01.
[11] W Hua et al. Low Frequency Active Vibration Isolation for Advanced LIGO
LIGO-P040022-00-R
[12] Jeffrey Kissel et al. Performance of eLIGO Prototype HAM ISIs and improvements
for aLIGO HAM ISIs
[13] Rik Pintelon, Johan Schoukens. System Identification, A Frequency Domain
Approach.
[14] Brad Osgood. Fourier Transform Lecture Notes.