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Kai Goebel, Ph.D.
Prognostics Center of Excellence
Discovery and Systems Health (DaSH)
Intelligent Systems Division
NASA Ames Research Center, California USA
October 26, 2016
FPNI
http://prognostics.nasa.gov
When Will it Break? Prognostics and Health Management at NASA
Acknowledgement:
The slides represent work done by PCoE members who have contributed to this presentation. They include Abhinav Saxena,
Matt Daigle, Edward Balaban, George Gorospe, Chris Teubert, Sriram Narasimhan, Indranil Roychoudhury, Susan Frost,
Chetan Kulkarni, Shankar Sankararaman, Jose Celaya.
All details presented here are in the public domain and used for information purposes only.
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National Aeronautics and Space Administration
NASA
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t=100 s
19 kt
B-777
PA-23
Prognostics Definition
• Prognostics = A prediction of the occurrence of some event
of interest to the system
• This event could be
– Component failure
– Violation of functional or performance specifications
– Accomplishment of some system function
– End of a mission
– … anything of importance you want to predict, because
that knowledge is useful to a decision
• What this event represents does not matter to the
framework
Pump Degradation
Airspace Safety Margin
End of Flight
Completion of Fueling
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Prognostics Framework
Time (t)
Fa
ult D
ime
nsio
n (
a)
t0 tD tP
Complete Failure
EoL
Critical Fault
Level
End of Life point
Decision Risk Decision Risk
How soon is too soon and
how late is too late?
Model Uncertainty Model Uncertainty
Which model to trust? No
Model is perfect !
RUL
RUL
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The Science of Predicting RUL
• RUL: Remaining Useful Life
– Model underlying physics of a component/subsystem
– Model physics of damage propagation mechanisms
– Determine criteria for End-of-Life Threshold
– Develop algorithms to propagate damage into future
– Deal with uncertainty
Return Spring
Piston
Plug
Top
Pneumatic Port
Bottom
Pneumatic Port
Fluid Flow
0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3
3.5
4x 10
6
Time (cycles)
Friction C
oeff
icie
nt
(Ns/m
)
Damage Progression of Friction Coefficient
40 411.05
1.1
x 106
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Maintenance Management View Contingency Management View
Goals for Prognostics
• Prognostics goals should be defined from users’ perspectives
• Different solutions and approaches apply for different users
Increase Safety and Mission Reliability
Increase Safety and Mission Reliability
Improved mission planning; go-no go
decisions
Ability to reassess mission feasibility;
design for resilience
Decrease Collateral Damage
Decrease Collateral Damage
Avoid cascading effects onto healthy
subsystems
Maintain consumer confidence,
product reputation
Decrease Logistics Costs
Decrease Logistics Costs
More efficient maintenance
planning; optimal shop loading
Reduced spares
Decrease Unnecessary
Servicing
Decrease Unnecessary
Servicing
Reduce downtime
Service only when it is needed
What does prognostics aim to achieve?
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Setting up the Problem Prognostics
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Problem Formulation
• Interested in predicting
threshold condition E
• System starts at some state in
region A, eventually evolves to
some new state at which E
occurs and moves to region B
• TE defines the boundary
between A and B
• Must predict the time of event E,
kE, and the time until event E,
ΔkE
A B
Current
State at t
Future
State at t’
State Space
TE
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Problem Formulation
• System described by
– x: states, θ: parameters, u: inputs, y: outputs,
v: process noise, n: sensor noise
• Define system event of interest E
• Define threshold function, that evaluates to
true when E has occurred
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Problem Formulation
• Define kE
• Define ΔkE
• May also be interested in the values of some
system variables at kE
• Goal is to compute kE and its derived variables
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Uncertainty
• Goal of prognostics algorithm is to
predict true distribution of kE
– A misrepresentation of true
uncertainty could be disastrous
when used for decision-making
• Prognostics algorithm itself adds
additional uncertainty
– Initial state not known exactly
– Sensor and process noise
(stochastic processes with
unknown distributions)
– Model not known exactly
– System state at kP not known
exactly
– Future input trajectory distribution
not known exactly
p(kE)
p(kE)
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Prognostics Architecture
System receives inputs, produces outputs
System receives inputs, produces outputs
Estimate current state and parameter values Estimate current state and parameter values
Use surrogate variable distributions
Use surrogate variable distributions
Predict probability distributions for kE, ΔkE
Predict probability distributions for kE, ΔkE
1 1 2 2
3 3 4 4
• System gets input and produces output
• Estimation module estimates the states and parameters, given system
inputs and outputs
– Must handle sensor noise and process noise
• Prediction module predicts kE
– Must handle state-parameter uncertainty at kP
– Must handle future process noise trajectories and input trajectories
– A diagnosis module can inform the prognostics what model to use
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Modeling
What needs to be modeled?
What features do models need?
What are the modeling trade-offs?
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What Kind of Models?
• Models for prognostics require the following features
– Describe dynamics in nominal case (no aging/degradation)
– Describe dynamics in the faulty/degraded/damaged case
– Describe dynamics of aging/degradation
Time
Health
• What are the dynamics
describing discharge?
• What model parameters
change as a result of
aging?
• How do the aging
parameters change in
time?
Aging
Failure Threshold
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Estimation Algorithms
How can the system state be estimated?
How does fault diagnosis fit in?
How is uncertainty in estimation handled?
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Estimation Problem
• First problem of prognostics is state-parameter estimation
– What is the current system state and its associated uncertainty?
– Input: system outputs y from k0 to k, y(k0:k)
– Output: p(x(k),θ(k)|y(k0:k))
• There are several algorithms that accomplish this, e.g.,
– Kalman filter (linear systems, additive Gaussian noise)
– Extended Kalman filter (nonlinear systems, additive Gaussian noise)
– Unscented Kalman filter (nonlinear systems, additive Gaussian
noise)
– Particle filter (nonlinear systems)
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Prediction Algorithms
How is uncertainty represented concisely?
How is uncertainty folded into prediction?
What algorithms are used for prediction?
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Prediction Problem
• Most algorithms operate by simulating samples forward
in time until E
• Algorithms must account for several sources of
uncertainty besides that in the initial state
– A representation of that uncertainty is required for the selected
prediction algorithm
– A specific description of that uncertainty is required (e.g., mean,
variance)
– Usually no closed-form solution
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Prediction
• The P function takes an initial state,
and a parameter, an input, and a
process noise trajectory
– Simulates state forward using f until E is
reached to compute kE for a single
sample
• Top-level prediction algorithm calls P
– These algorithms differ by how they compute samples upon which to call P
• Monte Carlo algorithm (MC) takes as
input
– Initial state-parameter estimate
– Probability distributions for the surrogate
variables for the parameter, input, and
process noise trajectories
– Number of samples, N
• MC samples from its input distributions,
and computes kE
• The “construct” functions describe
how to construct a trajectory given
surrogate variable samples
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It’ll Break at this Time:
• Damage progression, EOL prediction
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Application Example
How is this done in practice?
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• Models developed include
– Centrifugal Pumps
– Cryo Valves (RO* valves)
– Current/Pressure Transducers
– Filters
– Pressure Regulators
– Solenoid Valves
– Batteries
– Composites Structures
– Electronics (power semiconductors)
– Motors
– Electro-Mechanical Actuators
Model Development
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Propellant Loading System
Prognostics Center of Excellence
Liquid
Hydrogen
(LH2) Tank
Launch
Tower
Cross-Country
Lines
Pneumatic
Valves
Centrifugal
Pumps
Thrust
Vector
Control
Pneumatic
Valves
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Discrete Control (DV) Valve
• Apply framework to pneumatic valve in propellant loading system – Complex mechanical devices used in many domains including
aerospace
– Failures of critical valves can cause significant effects on system function
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• Valve operation The valve is opened by filling the
chamber with gas up to the
supply pressure
Evacuating the chamber above
the piston down to atmospheric
pressure
Return spring ensures valve will
close upon loss of supply
pressure
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Fault Matrix
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Pneumatic Valve Modeling
• Piston movement governed by sum of forces, including – Friction
– Spring force
– Contact forces
– Gas pressures
– Fluid pressures
• Mass flows determined by choked and non-choked gas flow equations for orifices
• Nominal operation – Opens and closes within 15
seconds
– Valve closes completely upon loss of supply pressure
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Valve Modeling Some equations
– Pressures pt(t) and pb(t)
– Gas flows
– Choked flow
– Fluid flow through valve
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Modeling Damage
Increase in friction
•Based on sliding wear equation
•Describes how friction coefficient changes as function of friction force, piston velocity, and wear coefficient
Degradation of spring
•Based on sliding wear equation
•Describes how spring constant changes as function of spring force, piston velocity, and wear coefficient
Growth of internal leak
•Based on sliding wear equation
•Describes how leak size changes as function of friction force, piston velocity, and wear coefficient
Growth of external leak
•Based on environmental factors such as corrosion
•Assume a linear change in absence of known model
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Damage Progression
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0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3
3.5
4x 10
6
Time (cycles)
Friction C
oeff
icie
nt
(Ns/m
)
Damage Progression of Friction Coefficient
40 411.05
1.1
x 106
0 20 40 60 80 1004
5
6
7
8
9
10x 10
4
Time (cycles)
Spring C
onsta
nt
(N/m
)
Damage Progression of Spring Constant
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6.846.866.886.9
6.926.94
x 104
0 20 40 60 80 1000
0.5
1
1.5
2x 10
-6
Time (cycles)
Inte
rnal Leak A
rea (
m2)
Damage Progression of Internal Leak
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6.8
6.9
7
x 10-7
0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3x 10
-5
Time (cycles)
Top E
xte
rnal Leak A
rea (
m2)
Damage Progression of Top External Leak
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Failure Injection Testbed
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y
NI DAQ
Power Supply
DAQ
Control Room
Supply pressure
To Atm
DIO
AIO
Temperature
DV
Supply Current
Supply Current
Supply pressure
CV
LAN
Outlet
pressure
Battery/Test Supply
Test Supply
SV
Electrical Signals
Pneumatic Lines
IPT
External Supply
Battery
DAQ Lines
Schematic
Testbed
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Atmospheric Leak Fault
• Fault emulates a leak at the
solenoid cylinder port or, when
energized, a leak across the
NO seat
• Fault injected using
proportional valve V1 (at 1%
per cycle)
• Affects the closing time of RO
due to decreased supply
pressure.
y
RO
Supply pressure
To Atm
Leak at Supply
Input port
Pneumatic gas leak
at valve port
Leak across Normally
Open (NO) seat
Solenoid Valve
V1V2
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Experiments and results
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Leak from Signal
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CV open times CV steady state position
times
• Steady state position threshold detected at 38th cycle
• Relatively no change observed in the open time values
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Leak from Supply
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CV open times CV steady state position times
• Open time changes and fault detected at 43rd cycle
• Relatively no change observed in the steady state values
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RUL Estimation α-λ Plot
• a-l is a performance metric for prognostics
• After fault detection within couple of cycles prediction in cone
• Model prediction accurate for both injected faults
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CV Signal fault CV Supply fault
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Summary • Predicting Time to Failure
– Promises to have significant benefit
– Rigorous Modeling required
– Dealing with uncertainties important
– Validation difficult
• Decision-Making
– Act on remaining life information
– Based on Prognostic horizon:
• Fail-Safe Mode
• Controller Reconfiguration
• Mission Re-planning
• Maintenance Scheduling
• Resources – Run-to-Failure Data Sets
• Data repository – https://ti.arc.nasa.gov/tech/dash/pcoe/prognostic-data-repository/
– Algorithms & Models • Open Source
– https://github.com/nasa/PrognosticsModelLibrary
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Prognostics in Action
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Last slide