model based sensor placement for component …...2014/05/22 · pratik pednekar west virginia...
TRANSCRIPT
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Model‐Based Sensor Placement for Component Condition Monitoring and Fault Diagnosis in Fossil Energy Systems
(PI) Raghunathan RengaswamyJeevan MaddalaParham Mobed
Texas Tech University
(CO‐PIs) Debangsu Bhattacharyya (Speaker) and Richard Turton Pratik Pednekar
West Virginia University
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Sensor Network Design Problem• Problem
– Which variables to measure and where (if spatial variation considered)
– Which physical sensors (with different properties, cost) should be used
– How many sensors (hardware redundancy) should be used for measuring a variable
– What should be the frequency of sampling (measurement) for different variables
– Maintenance policies
Design as well as a Retrofit problem
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Motivation
Sensor Placementfor Fault
Detection and Diagnosis
Early detection of faults
Green and safe
Monitoring
Fault‐tolerant control
Scheduling maintenance
‐ Emission standards‐Mitigating approaches‐ Avoid unsafe condition
Impact of Operatingconditions on equipment
Operation in presenceof fault
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Tier 1 – Plant level
Plant level model Cause and effect
Tier 2 – Equipment Level
a b
ba
Two‐tier approach
• Distributedmodel
• Estimator
• Distributedmodel
• Estimator
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Two‐tier approach
• Maximizing efficiency of sensor network
• Resolve component‐level faults while taking advantage of system‐
level interactions
• SP problem divided into two levels, solved, and then integrated.
• Use high fidelity models for component‐level fault simulation
Unresolvable faults
System‐level SP
Component‐level SP
Connectivity between units
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Component level and system level for an IGCC plant with CO2 Capture
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Approach
System‐level
1. SELEXOL unit2. Combined cycle
Component‐level
1. WGSR2. Gasifier
Integrated‐level
1. Gasification island
2. Plant‐wide model
Model development / enhancement
• System‐level units are modified for fault simulation
• Component‐level units are developed as high fidelity models
Fault simulation
• Commonly occurring faults are identified from open literature
• Responses of variables that can be measured by current technology are recoded
Sensor placement
• Quality / quantity based approaches are used depending upon the level
• Once selected, the process is validated by placing sensors and simulating faults again
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Tier 1: System Level Sensor Placement
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System‐level SP
Qualitative approach: Has a fault occurred? Take advantage of the flowsheet connectivity No quantitative information of fault magnitude available
Fault simulation
Qualitative model‐based approach
Integer Linear programming
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System‐Level SP: General Strategy
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Graph Based Approaches
11
DG Representation SDG Representation
z
DG• Change in variable > Threshold
→ Assign “1”• Otherwise → Assign “0”
SDG• Variable goes over threshold →
Assign “1”• Variable goes below threshold
→ Assign “‐1”• Otherwise→ Assign “0”
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Fault observability
• Observability→ Only response, not the direction → Matrix from DG
• SDG carries same information
• Faults must be observed by at least one sensor
→
12
1321 Nxxxx
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Fault resolution
• Add pseudo faults
• Pseudo‐fault: Symmetric difference of a pair of faults
• Symmetric difference: • From Venn diagram • Matrix from SDG
• Constraint matrix• A→ Augment observability and resolution• b → vector of ones
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2M
jijiij AAAAB
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Integer Programming
Objective function• Minimize sensor network cost
Constraint• Observability and resolution
Decision variables• Binary → “1”: Variable measured “0”: Variable not
measured• Weight → Cost of measuring sensor
14
N
jjj xw fmin
bAx T
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Fault SimulationFaults • Type: Process knowledge/experience/open literature• Magnitude: Designed/desired and tolerance
15
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Observability:Sensor: Make‐up solvent flow
Resolution:DG: 4 Temperature sensors + 2 Flow sensors
Irresolvable faults: 15 faults
SDG: 2 Temperature sensors + 2 Flow sensorsIrresolvable faults: 15 faults , same as DG
• Number of sensors reduced in SDG• All faults are not resolvable by DG/SDG
Enhancement to these algorithms helps in resolving more faults
Resultsfor plantwidesensorplacement
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Motivation
A = S1/S2 for F1B = S1/S2 for F2
A >>B
B>>A
AB1
Fault SensorS1 S2
F1 1 ‐1F2 1 ‐1
Magnitude Ratio Algorithm
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Magnituderatioisdefinedas:
Rij ispairofallvariablesandtreatedasapseudo‐sensors
Magnituderatioalgorithm: Define:Threshold() If,assign"1" If,assign"‐1" Otherwise,assign"0“
SSj,j
SSi,iij SS
SSR
λλRij
λ1Rij
Magnitude Ratio Algorithm
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pseudo sensors added to the decision variables
Cost of the pseudo‐sensors is set to zero
Constraints:
2N
1111
111
jij
iij
ijji
x)x(x)x(
x)x()x(
Magnitude Ratio Algorithm
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Fault evolution sequence algorithm
Fault response sequence
Comparing sequence of pairs can help in resolving faults
Fault Sequence Pairs
F1 S1 S3 S2 S4 {S1,S3}{S1,S2}{S1,S4}{S3,S2}{S3,S4}{S2,S4}
F2 S1 S2 S3 S4 {S1,S2}{S1,S3}{S1,S4}{S2,S3}{S2,S4}{S3,S4}
Further Enhancement to SDG Algorithm
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CSTR system
Five‐tank
Algorithms Sensors Irresolvable
SDG [Tc,VT,VP], CA 1fault
FES [Tc,VT,VP] 1fault⊆ SDG
MR [Tc,VT,VP] [ ]
FES&MR [Tc,VT,VP] []
Algorithms Sensors Irresolvable
SDG [L2,F10],L5,L4 1fault
FES [L2,F10],F12 []
MR [L2,F10],L5 [ ]
FES&MR [L2,F10]L5 []
Magnitude Ratio Results
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TE process
Alg. Sensors Irresolvable
SDG [F1,F9,F11,Tcs,VLs,VLp],F10,F2,Tcr
5Flow,2Temp. and2LevelSensors
10faultsets
FES [F1,F9,F11,Tcs,VLs,VLp],F10,Pr
4Flow,1Temp., 2Leveland1PressureSensors
6fault sets⊆ SDG
MR [F1,F9,F11,Tcs,VLs,VLp],Pr
3Flow,1Temp.,2Leveland1PressureSensors
SameasFES
FES&MR [F1,F9,F11,Tcs,VLs,VLp],Pr
3Flow,1Temp.,2Leveland1PressureSensors
Same asFES
Magnitude Ratio Results
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Tier II: Distributed Sensor Placement
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Component‐level SP
• Interested in condition monitoring• Faults cannot be resolved from a system‐level scope• Estimation of unmeasurable states
Component‐level SP algorithm
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Water gas shift reactor (WGSR)
• 1st principle, 1‐D, PDAE model developed using conservation equations in
MATLAB
• Reaction kinetics obtained by data reconciliation from erroneous / noisy
data from literature
• Simulate faults such as catalyst deactivation over time
syngas
steam
H2 richsyngas
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Model Summary
• Total equations : 76 – 53, differential – 23, algebraic
• Hence the system becomes a DAE system
• Total states are 76
• The equations are solved in MATLB with ODE15S
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Estimator
• State Estimation– Process models is nonlinear with a system of differential and algebraic equations (DAE)
Nonlinear estimator that can handle DAE systems is required Extended Kalman filter for DAE systems
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Summary of State Estimation
• DAE system is linearized at each time step as:
• Prediction and update steps of EKF for DAE systems:
zx
CBDCADBA
zx
DzCxBzAxx
0 11
kkx |1ˆ
kkz |1ˆ
kkP |1
1|1ˆ kkx1|1ˆ kkz1|1 kkP
0)ˆ,ˆ(:ˆ
1|11|1
1|1
kkkk
kk
zxgz
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Fault Simulations
• Porosity of the catalyst bed modify ɛ
• Catalyst deactivation change the pre‐exponential factor at specific location of the reactor
• Change in surface area of the catalyst leading to changes in the effectiveness factor
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Estimation of states in presence of noise
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• Catalystdeactivation
• State estimation
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Problem formulation for optimization• At each time step, a noisy measurement of the states are made:
• where, matrix is constructed from a binary vector
• The binary vector contains the sensors information:
− Location
− Number
− Type
• Search space for measurement model is huge (2400)
• Evolutionary algorithm can help us surf the space to find optimal model
• Genetic Algorithm!
kkk Hxy
110...1001
H
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Genetic Algorithm
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Simulation
• The nonlinear system is simulated with ramp disturbances which includes:
– 5% increase in inlet temperature (from 550 to 575.5 K)– 20% increase in syngas CO mole fraction (from 0.31 to 0.372)
• The system is simulated with the following specifications:
– Process noise: 10‐2
– Concentration, pressure and temperature measurement noise: 10‐2
– Error covariance: 10‐4
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Genetic Algorithm
• The fitness function, as reported previously, is calculated as:
• Fitness function is normalized by the fitness of the individual where all states are measured.
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GA Results• Value 1, shown as a bar, indicates that a sensor has to be placed at thespecified location of the reactor
• The figure is prepared with information from current generation of the GAalgorithm.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Dimensionless reactor length
CO
Sen
sor L
ocat
ion
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Dimensionless reactor length
H2O
Sen
sor L
ocat
ion
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Dimensionless reactor length
CO
2 Se
nsor
Loc
atio
n
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Dimensionless reactor lengthH
2 Se
nsor
Loc
atio
n
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Dimensionless reactor lengthTem
pera
ture
Sen
sor L
ocat
ion
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Dimensionless reactor lengthPres
sure
Sen
sor L
ocat
ion
Sensor locations on the dimensionless reactor length after 470 generations
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GA results• A fixed number of sensors (=100) is assumed and the genetic algorithm is
run to find best combination of the sensors.
• The fitness is normalized with the case that all measureable states are measured.
0 200 400 600 800 1000 1200 1400 1600 18000.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Generation
Nor
mal
ized
Fitn
ess
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Distributed Sensor Placement In Gasifier
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Gasifier‐Model• Gasifier operates at temperatures of
about 1200‐1600°C
• Liquid slag flows on walls and is
collected at bottom
• Gasifier model developed at WVU
does not consider slagging
phenomenon
• Slag penetration mainly responsible
for refractory degradation
Two‐stage model for slag deposition
1. Slag formation and detachment
2. Slag deposition and flow
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Model Development
Carbon consumed inreactions;
Ash skeleton exposed on surface
Slag droplet being formed at different
locations along particle
Rejuvenated coal particle surface goes through the process again
Separated slag dropletmove Into the bulk gas phase
Co‐current gas flow
Coal particle
Slag droplet
Slag formation on char particle Slag deposition
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Reaction Models Used in Non‐Slagging and Slagging Gasifier Section
40
Devolatilization &water evaporation
Gasification section
Shrinking core model
Shrinking particle model
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Integration of Continuum and Discrete Particle Phase
41
Continuum phaseMass, momentum and energy conservation;
PDE‐based
Discrete particle phaseTracks number density
of char particles, slag dropletsand mass of slag attached;
algebraic eqns.
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Gasifier Fault - Refractory Degradation
Spalling Tensile Spalling Compressive Spalling
www.netl.doe.gov
Bennett, J. “Failure Mechanisms in High Chrome Oxide Gasifier Refractories”; Metallurgical and Materials Transactions; 2011, 42, 4, pp. 888 ‐ 904
Slag penetration
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Compressive Spalling
Fe3+/Cr3+ substitution• Results in Buckling
Slag flow
Slag affected region
Buckle
Slag free region
Tensile Spalling
Cr3+ migration Cracked structure
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Results : Gasifier Steady state temperature profile
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Testing: Base, Thermal Cycling, High and Low Case
• Coal slurry SP was oscillated using sinusoidal function with period of 1 hour
• Slag model wall temperature was found for this input and fit
• Wall temperature was used as boundary condition for Refractory Degradation model
• Gasifier model and Degradation model operate at different time scales
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Results : Refractory Spalling time
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Future work
• Develop a reduced order gasifier model for estimation
• Implement distributed sensor placement algorithms on the gasifier
• Integrating the gasifier model into the gasification Island
• Perform two tier sensor placement algorithm
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System
‐level SELEXOL
Model enhancement
Fault simulation
Sensor placement
Combined cycle
Model enhancement
Fault simulation
Sensor Placement
Compo
nent‐le
vel
SWGSR
Model development
Fault simulation
Sensor placement
Gasifier
Model enhancement
Fault simulation
Sensor Placement
Integration Gasification island
Model enhancement
Fault simulation
Sensor placement
Plant‐wide model
Model enhancement
Fault simulation
Sensor Placement
Current status
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System
‐level SELEXOL
Model enhancement
Fault simulation
Sensor placement
Combined cycle
Model enhancement
Fault simulation
Sensor Placement
Compo
nent‐le
vel
SWGSR
Model development
Fault simulation
Sensor placement
Gasifier
Model enhancement
Fault simulation
Sensor Placement
Integration Gasification island
Model enhancement
Fault simulation
Sensor placement
Plant‐wide model
Model enhancement
Fault simulation
Sensor Placement
Current status
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Acknowledgment The authors gratefully acknowledge support from NETL DOE through grant no. DE‐FE0005749 titled "Model‐Based Sensor Placement for Component Condition Monitoring and Fault Diagnosis in Fossil Energy Systems”
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