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Kai Goebel, Ph.D.

kai.goebel@nasa.gov

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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2/2016

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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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Annual Conference of the Prognostics and Health Management Society 2009 28

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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