System Failure Diagnosis for the Advanced LIGO HAM A ...pv002yn0780...1.1 LIGO Project Overview The idea of using gravitational waves to observe events such as black holes or compact

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



http://purl.stanford.edu/pv002yn0780

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 2.10 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 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-13V1 RV11 RV12 RV13



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



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


-3 -3 0 0 0 0


-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


17


H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3


-3 -3 -3 0 0 0


-3 -3 -3 0 0 0


-3 -3 -3 0 0 0


-3 -3 -3 0 0 0


-3 -3 0 0 0 0


-3 -3 0 0 0 0


-2 -2 0 0 0 0


-2 -2 0 0 0 0


-6 -6 -3 0 0 0


-6 -6 -3 0 0 0


-5 -5 -3 0 0 0


-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



H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3


0 0 0 -3 0 0


0 0 0 -3 -3 -3


0 0 0 -2 0 0

GS13- Seismometer Score:

0 0 0 -3 -3 -3


0 0 0 -3 0 0


0 0 0 -3 0 0


0 0 0 -1 0 0


0 0 0 -1 0 0


0 0 0 -6 0 0


0 0 0 -6 -3 -3


0 0 0 -3 0 0


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



H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3


-1 0 0 0 0 0


0 0 0 -1 0 0

20


-3 0 0 0 0 0


0 0 0 -3 0 0


-1 0 0 0 0 0


0 0 0 0 0 0


-3 0 0 0 0 0


0 0 0 0 0 0


-2 0 0 0 0 0


0 0 0 -1 0 0


-6 0 0 0 0 0


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



H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3


0 0 0 0 0 0


0 0 0 0 -3 -1


0 0 0 0 0 0


0 0 0 0 -3 -3


0 0 0 0 0 0


0 0 0 0 0 0


0 0 0 0 0 0


0 0 0 0 -3 0


0 0 0 0 0 0


0 0 0 0 -3 -1


0 0 0 0 0 0


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


H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3


0 0 0 0 0 0


0 0 0 0 0 0


0 0 0 0 0 0


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



H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3


30

-3 -3 0 0 0 0 -3 -3 0 0 0 0


-2 -2 0 0 0 0


-2 -2 0 0 0 0


-3 -3 0 -1 0 0


-3 -3 0 0 0 0


-3 -2 -3 -1 0 0


-2 -2 0 0 0 0


-6 -6 -2 -1 0 0


-6 -6 0 0 0 0


-5 -4 -3 -1 0 0


-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



H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3


32

0 0 0 -3 -3 0 0 0 0 -3 -3 0


0 0 0 -2 -2 0


0 0 0 -2 -2 0


0 0 0 -3 -3 0


0 0 0 -3 -3 0


0 0 0 -2 -2 0


0 0 0 -2 -2 0


0 0 0 -6 -6 0


0 0 0 -6 -6 0


0 0 0 -4 -4 0


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



H1 H2 H3 V1 V2 V3 H1 H2 H3 V1 V2 V3


-3 0 0 0 0 0


-3 0 0 0 0 0


-3 0 0 0 0 0


-1 0 0 0 0 0


-3 -2 -2 -1 0 0


-3 0 0 0 0 0


-3 -2 -2 -1 0 0


-1 0 0 0 0 0


-6 -2 -2 -1 0 0


-6 0 0 0 0 0


-6 -2 -2 -1 0 0


-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

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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,


[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.

http://www.eurospanbookstore.com/results.asp?aub=Peter%20Saulson&sort=sort_date/d&

http://www.eurospanbookstore.com/results.asp?aub=Mike%20Cruise&sort=sort_date/d&

Documents

System Failure Diagnosis for the Advanced LIGO HAM A ...pv002yn0780...1.1 LIGO Project Overview The idea of using gravitational waves to observe events such as black holes or compact