Michael Russell Advisor: Dr. Shreekanth Mandayam August 30, 2010.

MS Thesis Defense:An Intelligent Valve Framework for Integrated Systems Health Management on Rocket Engine Test Stands

Michael Russell

Advisor:Dr. Shreekanth Mandayam

August 30, 2010

2

Overview Introduction Background Objectives Approach Results Conclusions

3

Introduction

B-1/B-2 Test StandA-2 Test Stand

A-1 Test Stand

E-2 Test Stands E-1 Test StandsE-3 Test Stands

NASA Stennis Space Center, Mississippi

Introduction Background Approach Results Conclusions

4

Introduction

• Over 1,500 sensors in a rocket engine test stand

• This results in an enormous volume of sensor information

• Utilize health analysis algorithms to reduce the amount of information for operators

• Predict anomalous conditions before they occur


5

IntroductionTest Stand Instrumentation • Large linear actuated valve• High-geared ball valves• Multi-sensor measurements –

Pressure, Temperature, Control, Feedback


6

IntroductionSmart Instrumentation Framework for NASA-SSC Ball Valves and Large Linear Actuator Valves


7

Objectives To design a framework for the detection of faults and failure

modes in the large linear actuated valve that are used on the rocket engine test stands at NASA-SSC.

To develop a diagnostic process that – Receives and stores incoming sensor data; Performs calculation of operating statistics; Compares with existing analytical models; and, Visualizes faults, failures and operating conditions in a 3D GUI

environment. To develop a suite of health analysis algorithms that can

detect anomalous behavior in the valve and other system components of the rocket engine test stand.

To expand the capability of the diagnostic algorithm to perform prognosis in specific contexts.

8

Background Health Analysis Framework

Background Approach Results ConclusionsIntroduction

9

Background - FMECA Failure Modes Effects and Criticality Analysis


10

Background – Types of diagnostics


11

Background - DiagnosticsAuthors Title Area of ResearchV. Puig, J. Quevedo, T. Escobet, F. Nejjari, and S. de las Heras, Automatic Control Department-Campus de Terrassa, Spain

Passive Robust Fault Detection of Dynamic Processes Using Interval Models

Model-based fault detection based on interval models that generate adaptive thresholds using three schemes (simulation, prediction, and observation)

H. Bassily, R. Lund, and J. Wagner,Clemson University

Fault Detection in Multivariate Signals With Applications to Gas Turbines

Compares multivariate autocovariance functions of two independently sampled signals in order to create a model-based algorithm to detect faults in a gas turbine

C. H. Lo, Eric H. K. Fung, and Y. K. Wong,Hong Kong Polytechnic University

Intelligent Automatic Fault Detection for Actuator Failures in Aircraft

Utilizes fuzzy-genetic algorithm to detect different types of actuator failures in a nonlinear F-16 aircraft model

G. Spitzlsperger, C. Schmidt, G. Ernst, H. Strasser, and M. Speil,Renesas Semiconductor Europe

Fault Detection for a Via Etch Process Using Adaptive Multivariate Methods

Uses an adaptive method to overcome false alarms in slowly degrading manufacturing processes that use Hotelling T2 and squared prediction errors.

W. R. A. Ibrahim, M. M. Morcos,Kansas State University

An Adaptive Fuzzy Self-Learning Techniquefor Prediction of Abnormal Operationof Electrical Systems

Details an intelligent adaptive fuzzy system with self-learning functions that monitors electrical equipment

S. Huang and K. K. Tan,National University of Singapore

Fault Detection and Diagnosis Based onModeling and Estimation Methods

Uses multiple Radial Basis Functions to estimate both the unknown nonlinear dynamics as well as the fault characteristics of a simulated system

J. Yun, K. Lee, K. Lee, S. B. Lee, J. Yoo,Electric Power Machinery Research Department, Hyundai Heavy Industries

Detection and Classification of Stator Turn Faultsand High-Resistance Electrical Connectionsfor Induction Machines

Proposes a stator-winding turn-fault detection algorithm using sensorless zero-sequence voltage or negative-sequence current measurements.


12

Background – Types of prognostics


13

Background - PrognosticsAuthors Title Area of ResearchF. Peysson, M. Ouladsine, R. Outbib, J.B. Leger, O. Myx, C. Allemand,University of Paul Cézanne

A Generic Prognostic Methodology Using Damage Trajectory Models

Presents a prognostic framework then decomposes a system into three levels: environment, mission, and process. Decision and data fusion between the three levels is used to create predictions.

Z. Sun, J. Wang, D. How, G. Jewell,The University of Sheffield

Analytical Prediction of the Short-Circuit Current in Fault-Tolerant Permanent-Magnet Machines

Describes an analytical technique to predict short-circuit current in a fault-tolerant permanent-magnet machine under partial-turn short-circuit fault conditions.

Y. Zhang, G. W. Gantt, M. J. Rychlinski, R. M. Edwards, J. J. Correia, C. E. Wolf,GM Research & Development,

Connected Vehicle Diagnostics and Prognostics, Concept, and Initial Practice

Presents a complete end-to-end framework of diagnostics and prognostics of General Motors vehicles. Presents initial result.

M. Baybutt, C. Minnella, A. E. Ginart, P. W. Kalgren, M. J. Roemer,Impact Technologies, LLC

Improving Digital System DiagnosticsThrough Prognostic and HealthManagement (PHM) Technology

Integrates prognostics and diagnostics from engineering disciplines to provide minimally invasive onboard monitoring of digital systems.

P. Lall, M. N. Islam, M. K. Rahim, J. C. Suhling,Auburn University

Prognostics and Health Management of Electronic Packaging

Investigates methods to determine material state in complex systems and subsystems to determine RUL.

S. K. Yang,Chin Yi Institute of Technology

A Condition-Based Failure-Prediction and Processing-Scheme for Preventive Maintenance

Uses an application-specific integrated circuit (ASIC) to perform preventive maintenance using Petri nets and Kalman filter prediction.

A. H. Al-Badi, S. M. Ghania, E. F. EL Saadany,University of Waterloo

Prediction of Metallic Conductor Voltage Owing to Electromagnetic Coupling Using Neuro Fuzzy Modeling

Presents a Fuzzy algorithm that can predict the level of a metallic conductor voltage. Provides simulation results and validation for three scenarios.


14

Background – System Identification


15

Background – LLAV


16

Background – LLAV

BonnetBonnetPacking

StemValve Plug Seating

Body


17

Approach Health Analysis Framework


Approach – Faults and failure modes

18

Function Failure Mode EffectsController for cryogenic fluid tank

Seat Wear cause leaking fluid Fluid can enter system during a test causing catastrophic failure

Monitor the feedback of the valve and downstream pressure

Faulty pressure sensor falsely indicate valve failure

Incorrect valve maintenance may be performed

Packing at the top of the valve prevents leaks and allows for balanced pressure

When frozen, the packing can crack and break apart, degrading the performance of the valve

Valve may not function properly or be able to maintain needed pressure for test

Actuator must transition from fully open to fully closed in a consistent amount of time.

If the valve does not open or close at consistent timings, valve maintenance must be performed

The valve’s remaining useful life without maintenance is reducing.

The controller of the valve sends a valve to full close.

If the PID controller is unstable or telling the valve to get to a value it cannot reach, the actuator may “bounce” on the seat causing degradation in the soft metal.

Seat wear (described above) can occur more quickly resulting in delays and increased maintenance costs.

The valve feedback must respond to the control signal in an appropriate time for effective test operations.

Excessive “deadtimes” create poor timing in test operations and can cause pressure or flow mixture errors.

If the mixture is not precise is certain test articles, undesired results can occur.


Approach – FMECA

19

0 1 2 3 4 5 6 7 8 9 10 110

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Criticality

Ris

k P

riorit

y N

umbe

r

Seat boucing

Transition Times

Sensor Failures

Extended Deadtimes

Frost Point

Seat Wear


20

Approach - Overall framework


21

Approach – Failure modes

Failure mode Fault Detection algorithmSeat Wear Operating StatisticsSensor Failures AANNFrost Point Thermal modelExtended Deadtimes Adaptive Threshold

Operating StatisticsTransition Times Adaptive Threshold

Operating StatisticsSeat bouncing Operating Statistics


22

Approach – Sensor Validation Pressure and temperature sensors are vital to the operations

of the test stands at NASA-SSC Specific mixtures of fluids and gas Chilldown

Failure modes in the sensors Characterized against faults found in frost line

Autoassociative neural networks Nonlinear principal component analysis Finds correlations of subsystem components Find faults based on residual values


23

Approach – Sensor Validation Nonlinear principal component analysis (NPCA)

PCA: where P is the eigenvectors of the covariance matrix,Y is the sample set, and T is the transformed data

NPCA : Replace P by nonlinear vector function

In order to restore data, another nonlinear vector function is needed:

Cybenko (1989) showed that functions of the following form are capable of fitting any nonlinear function :

A sigmoid satisfies this

24

Approach – Sensor Validation

𝜎

𝜎

𝜎

𝜎

y1

y2

y3

T1

T2

𝜎

𝜎

𝜎

𝜎

y1'

y2’

y3’

T1

T2

G(Y) H(T)G(Y) H(T)

𝜎

𝜎

𝜎

𝜎

y1

y2

y3

𝜎

𝜎

𝜎

𝜎

y1’

y2’

y3’

T1

T2

Mapping Layer

InputLayer

BottleneckLayer

DemappingLayer

OutputLayer


25



26



27

Approach – Sensor Validation Data

Methane Thruster Testbed Project Trailer


28

Approach – Sensor Validation Metrics


Sensitivity – Measure of the amount of fault data points correctly identified

Sensitivity – Measure of the amount of nominal data points correctly identified

Positive Predictive Value – Measure of the fault data points correctly identified

Negative Predictive Value – Measure of the nominal data points correctly identified

F-measure – Measure of a tests accuracy

29

Approach – Adaptive Threshold PID controllers are used to operate valves

Stroke timings, input delays and gain factors can be contribute to failing health

A method to detect anomalous behavior of the valve A bank of ARMA filters can be used to create an

adaptive threshold based on the input of the set points and PID controller

ARMAX:


30

Approach – Adaptive Threshold

𝐹𝑖𝑡=100∗(1− 𝑛𝑜𝑟𝑚 ( h𝑦 − 𝑦 )𝑛𝑜𝑟𝑚 ( 𝑦−𝑚𝑒𝑎𝑛 ( 𝑦 ) ) )


31

Approach – Adaptive Threshold


32

Approach – Adaptive Threshold Data

Forward analytical model to simulate valve transfer function in Simulink with PID controller:

𝑉 𝑝𝑟𝑜𝑐𝑒𝑠𝑠=𝑔∗𝑒−𝑇 𝑠∗𝑠

𝑠2+2∗𝜁 ∗𝑇𝑤∗𝑠+𝑇𝑤2

: Gain: Unit delay: Natural frequency: Damping ratio: Valve response


0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (s)

Per

cent

age

open

(%

)

Transfer function with changing values of : damping coefficient

Step Signal = .2 = .4 = .6 = .8 = 1 = 1.2

33

Approach – Adaptive Threshold Data

Parameter Nominal Low Abnormal High Abnormal

Gain

Natural

Frequency

Damping Ratio

Delay


34

Approach – Diagnostic Process Requirements

Task 1: Development of the valve sensor interface to ActiveX controller

Task 2: Development of prototype immersive user interface for intelligent valve


35

Approach – Diagnostic Process


DDE Client

Virtual Reality Environment

G2 Diagnostic Environment

WonderWare .NET Plugin

NASA Data Acquistion

System (DDE Server)

Health Data

Health Data

Measurement Data

36

Approach – Diagnostic Process MS-SQLCE was used for database management and

persistent data storage


37

Approach – Class structure


38

Approach – Prognostics Goal of prognostics: Determine remaining

useful life (RUL) of a component or system Prognostic techniques are mathematical

predictions based on previous inputs and outputs AR and ARMA – Linear predictors Kalman Filter - State-space model

Prognostics rely heavily on diagnostic information as well as parameter calculation of key state variables


39

Approach – Prognostics Kalman Filter:

Time Update:

Measurement update:

−


Time(Predict)

Measurement(Correct)

40

Results – Sensor Validation





41


2.75 2.8 2.85 2.9 2.95

x 105

0

100

200

300

400

Elapsed Time (s)

Pre

ssu

re (

PS

IG)

Simulated data for sensor validation

Measured Data

Simulated Fault DataEstimated AANN Data

2.75 2.8 2.85 2.9 2.95

x 105

0

0.2

0.4

0.6

0.8

1

Elapsed Time (s)

Fa

ult

De

tect

ed

Fault region detection


42


2.75 2.8 2.85 2.9 2.95

x 105

0

100

200

300

400

Elapsed Time (s)

Pre

ssu

re (

PS

IG)


Measured Data

Simulated Fault DataEstimated AANN Data

2.75 2.8 2.85 2.9 2.95

x 105

0

0.2

0.4

0.6

0.8

1

Elapsed Time (s)

Fa

ult

De

tect

ed



43


2.82 2.84 2.86 2.88 2.9 2.92 2.94 2.96

x 105

100

150

200

250

300

350

400

Elapsed Time (s)

Pre

ssu

re (

PS

IG)


Measured Data

Simulated Fault Data

Estimated AANN Data

2.82 2.84 2.86 2.88 2.9 2.92 2.94 2.96

x 105

0

0.2

0.4

0.6

0.8

1

Elapsed Time (s)

Fa

ult

De

tect

ed



44

Results – Sensor Validation Failure

0 1 2 3

x 104

0

200

400

600

AANN estimation for PE-1134-GO

Elapsed Time (ms)

Pre

ssur

e (P

SIG

)

0 1 2 3

x 104

0

100

200

300

Error signal and threshold for PE-1134-GO

Elapsed Time (ms)

Pre

ssur

e (P

SIG

)

0 1 2 3

x 104

0

50

100

150

200


Elapsed Time (ms)

Pre

ssur

e (P

SIG

)

0 1 2 3

x 104

0

50

100

150

200


Elapsed Time (ms)

Pre

ssur

e (P

SIG

)

0 1 2 3

x 104

0

200

400

600


Elapsed Time (ms)

Pre

ssur

e (P

SIG

)

0 1 2 3

x 104

0

100

200

300


Elapsed Time (ms)

Pre

ssur

e (P

SIG

)

0 1 2 3

x 104

0

50

100

AANN estimation for PC1

Elapsed Time (ms)

Pre

ssur

e (P

SIG

)

0 1 2 3

x 104

0

5

10

15

20

Error signal and threshold for PC1

Elapsed Time (ms)

Pre

ssur

e (P

SIG

)


45

Results – Sensor Validation Failure

0 1 2 3

x 104

0

20

40

60

AANN estimation for VPV-1139-FB

Elapsed Time (ms)

Perc

ent

Open (

%)

0 1 2 3

x 104

0

20

40

Error signal and threshold for VPV-1139-FB

Elapsed Time (ms)

Perc

ent

Open (

%)

0 1 2 3

x 104

0

20

40

AANN estimation for VPV-1139-CMD

Elapsed Time (ms)

Perc

ent

Open (

%)

0 1 2 3

x 104

0

10

20

30

40

Error signal and threshold for VPV-1139-CMD

Elapsed Time (ms)

Perc

ent

Open (

%)


46

Results – Sensor Validation Average Metrics

Sensitivity 99.89%

Specificity 74.76%

Positive Predictive Value 97.89%Negative Predictive Value 96.11%F-Measure 98.84%


47

Results – Adaptive Threshold





48

Results – Adaptive Threshold Setpoints

0 1000 2000 3000 40000

20

40

60

80

100

Samples

Ope

n P

erce

ntag

e (%

)

Setpoint transition 1

0 1000 2000 3000 40000

20

40

60

80

100

Samples

Ope

n P

erce

ntag

e (%

)


0 1000 2000 3000 40000

20

40

60

80

100

SamplesO

pen

Per

cent

age

(%)


0 1000 2000 3000 40000

20

40

60

80

100

Samples

Ope

n P

erce

ntag

e (%

)


0 1000 2000 3000 40000

20

40

60

80

100

Samples

Ope

n P

erce

ntag

e (%

)


0 1000 2000 3000 40000

20

40

60

80

100

Samples

Ope

n P

erce

ntag

e (%

)



49


1500 2000 2500 3000 3500 4000

60

80

100

Sample

Perc

ent

Open (

%)

G: 0.98 Tw

: 0.98 : 0.98 Ts: 2

Measured Values

Upper ThresholdLower Threshold

1500 2000 2500 3000 3500 4000

-1

0

1

Sample

Fault D

ete

ction:

Fault identification: 0 faults

Nominal operating conditions for Setpoint #1


50


1500 2000 2500 3000 3500 4000 450060

80

100

Sample

Per

cent

Ope

n (%

)

G: 0.9 Tw

: 0.85 : 0.85 Ts: 4

Measured Values

Upper Threshold

Lower Threshold

1500 2000 2500 3000 3500 4000

-1

0

1

Sample

Fau

lt D

etec

tion:


Abnormal operating conditions for Setpoint #1:Low Damping coefficient


51


Abnormal operating conditions for Setpoint #3:High input delay

1500 1600 1700 1800 1900 2000 2100 2200 2300

0

20

40

60

Sample

Per

cent

Ope

n (%

)

G: 0.9 Tw

: 0.9 : 0.95 Ts: 5

Measured Values

Upper ThresholdLower Threshold

1500 1600 1700 1800 1900 2000 2100 2200 2300-1

-0.5

0

0.5

1

Sample

Fau

lt D

etec

tion:



52


Abnormal operating conditions for Setpoint #5:Low gain

100 200 300 400 500 600 700 800 900

0

50

100

Sample

Per

cent

Ope

n (%

)

G: 0.9 Tw

: 1.15 : 0.85 Ts: 5

Measured Values

Upper Threshold

Lower Threshold

100 200 300 400 500 600 700 800 900

-1

-0.5

0

0.5

Sample

Faul

t Det

ectio

n:



53

Results – Adaptive Threshold Metrics

0.9 1 1.1 1.2 1.3100

150

200

250Gain

Avg

. N

umbe

r of

Fau

lts

Parameter value0.8 1 1.2 1.40

200

400

600Natural Frequency

Avg

. N

umbe

r of

Fau

lts

Parameter value

0.8 1 1.2 1.4120

140

160

180

200Damping Coefficient

Avg

. N

umbe

r of

Fau

lts

Parameter value2 3 4 5

100

150

200

250Input Delay

Avg

. N

umbe

r of

Fau

lts

Parameter value


54

Results – Adaptive Threshold on LLAV

0 50 100 150-20

0

20

40

60

80

100

120

Time (s)

Perc

enta

ge C

losed (

%)

Adaptive Threshold Training Data

Upper Values

Lower ValuesActual Values


55

Results – Adaptive Threshold on LLAV

0 50 100 150

0

20

40

60

80

100

Elapsed Time (s)

Per

cent

age

Clo

sed

(%)

Valve Feedback with Simulated Obstruction

Upper Threshold

Lower TresholdMeasured Valve Feedback

0 50 100 150-0.2

0

0.2

0.4

0.6

0.8

1

Upper Faults

Elapsed Time (s)

Fau

lt D

etec

ted

0 50 100 150-0.2

0

0.2

0.4

0.6

0.8

1

Lower Faults

Elapsed Time (s)

Fau

lt D

etec

ted


56

Results – Diagnostic Process


57



58



59



60

Results – Prognostics for LLAV


61


0

10

20

30-50-40-30-20-10010

500

1000

1500

2000

2500

3000

3500

4000

4500

SNR

Prediction performance of Kalman model for LLAV signal

Prediction Steps

RM

SE


62

Contributions Validation of a thermal model for the determination of the

frost line on the LLAV. The development of an auto-associative neural network

algorithm for validation of sensors. An adaptive threshold algorithm for fault detection and

trending of degradation in the LLAV. A survey of AR, ARMA and Kalman filter techniques for the

prediction of time series data. Operating statistic algorithm that provides historical context

for maintenance personnel. Development of a diagnostic process for data acquisition,

data storage and visualization of the LLAV.


Conclusions

An intelligent valve framework has been designed and implemented that gives NASA-SSC test operators ability to diagnosis key faults and monitor a valve’s health degradation at the E complex test stands.

Three diagnostic algorithms assist in detecting and diagnosing the faults outlined in the FMECA

A diagnostic process was developed that acquires, stores and analyzes data from the valves on the E complex test stands


64

Future Work

Further develop the diagnostic process Complete prognostics section of the

framework to provide maintenance personnel with three types of data: Determination of remaining useful life (RUL) of a

valve for predictive maintenance Initiation of “what if?” queries Comprehensive risk analysis of every test

procedure


65

Acknowledgements

The support of my MS program by the NASA Graduate Student Researchers Program (GSRP) award No. NNX07AO92H in 2008 and 2009 is gratefully acknowledged. The research work presented in this thesis was also supported by NASA Stennis Space Center under Grant/Cooperative Agreement No. NNX08BA19A


69

Approach – Operational Statistics Seven key statistics were identified that

provide historical context for the valve’s health: Transitions - The amount of times the valve has

traveled from a completely open to a completely closed with non-cryogenic fluid flow.

Cryogenic Transitions - The amount of times the valve has traveled from a completely open to a completely closed with cryogenic fluid flow.


70

Approach – Operational Statistics Distance Traveled - The linear distance the valve has

traveled in inches. Last transition time - The time it took for a valve to

go from completely open to completely closed. Average transition time - The average of the last ten

transitions from completely open to completely closed.

Direction changes - The amount of times the valve has changed motion from either opening to closing or closing to opening.

Number of closings - The amount of times the valve has come to a completely closed state.


71

Approach – Operational Statistics


72

175”

11”

Approach – Frost Line Packing at the top the LLAV is used to keep

offset pressures for pneumatic and hydraulic valves Freezing the packing causes degradation Valve length is increased to prevent

freezing Every inch added to these valves

increases cost Performed test to analyze frost

line

Predicted Locationfor 32° F

Actual Frost Line


73

Approach – Frost LineThe test was completed with the following protocol: A simulated valve was programmed into the WonderWare

control environment When the simulated valve opened, liquid nitrogen (LN) was

poured into the box containing the valve. During the next several hours, the liquid nitrogen was kept at a

constant level in order to simulate the passing of fluid through an open valve.

The temperature and frost line was monitored after the body reached a steady state temperature of -322oF (boiling point of LN).

There was a thermocouple at the base of the valve and a thermocouple about 3 inches up the stem of the valve, both were monitored and stored in a data file.


74

Approach – Frost Line


75

Approach – Frost LineThe following sensor faults were injected into the DAQ system: Faulty connection in amplifier input Amplifier power down Tustin input disconnect Input disconnection on the digitizer Frost insulation Temperature junction reference Thermocouple and power disconnection Thermocouple disconnections and shorts Transmitter power and failure Unaccounted thermocouple junction


76

Approach – Frost Line AlgorithmUse physical model to estimate base and stem temperatures:

Estimated base temperatureAmbient Temperature

𝑇 𝑓𝑙𝑢𝑖𝑑:Boiling temperature of fluid𝑡𝑜𝑝𝑒𝑛 :Time the valvehas beenopen𝑚 : Steady state time

𝐿𝑇𝐶 :Distanceof thermocouple ¿ base

𝑇 𝑒𝑠𝑡 :Estimated temperature of thermocoupleat LtcLength of the stem of the valve𝑇 𝑎𝑚𝑏: Ambient temperature𝑚𝑡 : material constant


Approach – Frost Line Algorithm

77

Used least squares curve fitting on base run to determine and :

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 104

-350

-300

-250

-200

-150

-100

-50

0

50

Time (s)

De

gre

ss (

F)

Base Run

Top ThermocoupleTop SimulationBottom ThermocoupleBottom Simulation

M – Chill Down M – Warm Up mt – Chill Down mt – Warm up

659.80s 4672s .36 .32


78

Results – Prognostics

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

120Time series with 0 mean and 1 variance

Time (s)

Am

plitu

de


79


0 20 40 60 80 1000

20

40

60

80

100

120

Time (s)

Am

plitu

de

AR prediction at 1 prediction step and SNR = 25dB

AR Prediction

Actual Signal

0 20 40 60 80 1000

20

40

60

80

100

120

Time (s)

Am

plitu

de

AR prediction at 5 prediction steps and SNR = 25dB

AR Prediction

Actual Signal

0 20 40 60 80 1000

20

40

60

80

100

120

Time (s)

Am

plit

ude

AR prediction at 5 prediction steps and SNR = -5dB

AR Prediction

Actual Signal


80


0 20 40 60 80 1000

20

40

60

80

100

120

Time (s)

Am

plit

ude

ARMA prediction at 1 prediction steps and SNR = 25dB

ARMA Prediction

Actual Signal

0 20 40 60 80 100-20

0

20

40

60

80

100

120

Time (s)

Am

plit

ude

ARMA prediction at 1 prediction steps and SNR = -5dB

ARMA Prediction

Actual Signal

0 20 40 60 80 1000

20

40

60

80

100

120

Time (s)

Am

plitu

de

ARMA prediction at 5 prediction steps and SNR = -5dB

ARMA Prediction

Actual Signal


81


0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Time (s)

Am

plit

ude

Kalman prediction at 1 prediction steps and SNR = 25dB

Kalman Prediction

Actual Signal

0 20 40 60 80 1000

20

40

60

80

100

120

Time (s)

Am

plit

ude

Kalman prediction at 5 prediction steps and SNR = 25dB

Kalman Prediction

Actual Signal

0 20 40 60 80 100-20

0

20

40

60

80

100

120

Time (s)

Am

plitu

de

Kalman prediction at 5 prediction steps and SNR = -5dB

Kalman Prediction

Actual Signal


82


0

5

10

15

-50510152025

0

500

1000

1500

2000

2500

3000

3500

SNR (dB)

Prediction performance of AR model for = 0 and = 1 signal

Prediction Steps

MS

E

0

5

10

15

-100

1020

30

0

500

1000

1500

SNR (dB)

Prediction performance of ARMA model for = 0 and = 1 signal

Prediction Steps

MS

E


83


0

5

10

15

-50

510

1520

25

0

500

1000

1500

2000

SNR (dB)

Prediction performance of Kalman filter model for = 0 and = 1 signal

Prediction Steps

MS

E


84


85 90 95 100 105 110 115 120 125 130

-20

0

20

40

60

80

100

120

Time (s)

Per

cent

age

Ope

n(%

)

30 step prediction of process variable using ARX model

Previous Process

Predicted ProcessActual Process

Control Input

85 90 95 100 105 110 115 120 125 130-20

0

20

40

60

80

100

120

Time (s)

Per

cent

age

Ope

n(%

)

30 step prediction of process variable using ARMAX model

Previous Process

Predicted ProcessActual Process

Control Input


85


0

10

20

30

-50-40

-30-20

-100

10

0

2000

4000

6000

8000

10000

SNR

Prediction performance of ARMA model for LLAV signal

Prediction Steps

RM

SE

0

10

20

30

-50-40-30-20-10010

0

2000

4000

6000

8000

10000

12000

SNR

Prediction performance of AR model for LLAV signal

Prediction Steps

RM

SE


86

Results – Thermal Modeling

0.5 1 1.5 2 2.5

x 104

-500

-400

-300

-200

-100

0

100

200

Time (s)

De

gre

ss (

F)

Amplifier Power Down and Tustin Input Disconnect


0.5 1 1.5 2 2.5

x 104

0

0.2

0.4

0.6

0.8

1

Time (s)

Fa

ult

Cla

ssifi

catio

n

Top Thermocouple Fault Detection

0.5 1 1.5 2 2.5

x 104

0

0.2

0.4

0.6

0.8

1

Time (s)

Fa

ult

Cla

ssifi

catio

n

Bottom Thermocouple Fault Detection


87


0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

-350

-300

-250

-200

-150

-100

-50

0

50

Time (s)

De

gre

ss (

F)

Faulty Connection in Amplifier Input


0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

0

0.2

0.4

0.6

0.8

1

Time (s)

Fau

lt C

lass

ifica

tion

Top Thermocouple Fault Detection

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

0

0.2

0.4

0.6

0.8

1

Time (s)

Fau

lt C

lass

ifica

tion

Bottom Thermocouple Fault Detection


88


350 400 450 500 550 600 650

-3

0

3

5

7

9

11

13

X: 417.2Y: 3.006

Fro

st L

ine

(in

che

s)

Elapsed Time (s)

Frost line model comparison with actual thermocouple data

350 400 450 500 550 600 650

-20

-10

0

10

20

30

40

50

60

40

X: 359.8Y: 31.97

Te

mp

era

ture

(F

)

Thermocouple reading at 3 inches

Actual time of frost point at 3 inchesPredicted time of frost point at 3 inches

Predicted frost line


89

Results – Thermal Modeling Average Metrics

Sensitivity 98.80%Specificity 81.07%Positive Predictive Value 86.13%Negative Predictive Value 91.39%F-Measure 89.32%


90

Approach – PrognosticsARX:

ARMAX:


Michael Russell Advisor: Dr. Shreekanth Mandayam August 30, 2010.

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