L15a model-based diagnosis - MITdspace.mit.edu/bitstream/handle/1721.1/36896/2/16-410... ·...

10/03/03 copyright Brian Williams, 2003 1Courtesy NASA/JPL-Caltech. http://www.jpl.nas.gov.

Model-based Diagnosis

Brian C. Williams16.410-13November 3rd & 5th 2003

Brian C. Williams, copyright 2000

10/03/03 copyright Brian Williams, 2003 2

Assignment

ReadingModel-based Diagnosis – Lecture notesPropositional Logic AIMA Chapter 6

Problem SetModel-based Diagnosis implementationPropositional Logic16.413: Hello World implementationDue Monday, November 17th


senseP(s)

WORLD

observations actions

AGENTDiagnostic Agent:

• Monitors & Diagnoses

• Repairs & Avoids

• Probes and Tests

Plant

act

Symptom-directed


Outline

Model-based diagnosisAccounting for failures

Explaining failuresHandling unknown failures


Hidden Failures Require Reasoning from a Model: STS-93

Symptoms:• Engine temp sensor high• LOX level low• GN&C detects low thrust• H2 level possibly low

Problem: Liquid hydrogen leak

Effect: • LH2 used to cool engine• Engine runs hot• Consumes more LOX

Image taken from NASA’s web site: http://www.nasa.gov.


Model-based DiagnosisGiven a system with symptomatic behavior and a model of the system, find diagnoses that accountfor symptoms.

12 Symptom6

6

O1

M2

M3

A1

A2

A

BCD

E

F

G

X

Y

Z

3

223

3

10

12

M1

6

12


Model-based DiagnosisGiven a system with symptomatic behavior and a model of the system, find diagnoses that accountfor symptoms.

12 Symptom6

6

M1

M2

M3

A1

A2

A

BCD

E

F

G

X

Y

Z

3

223

3

10

126

12


Diagnosis as Hypothesis Testing

1. Generate candidates, given symptoms.2. Test if candidates account for all symptoms.

• Set of diagnoses should be complete.• Set of diagnoses should consider all

available information.


Outline




How Should Diagnoses Account for Symptoms?Abductive Diagnosis: Given symptoms, find

diagnoses that predict observations.6

6

12 SymptomM1

M2

M3

A1

A2

A

BCD

E

3

223

3

F

G

X

Y

Z

10

12

Assume Exhaustive Fault Models:


How Should Diagnoses Account for Symptoms?Abductive Diagnosis: Given symptoms, find

diagnoses that predict observations.6

6

12 SymptomM1

M2

M3

A1

A2

A

BCD

E

3

223

3

F

G

X

Y

Z

10

12

Assume Exhaustive Fault Models:• O1 Drops low bit on A

A = 30011

A=20010

4 102

6

12


ModelStructureModel of normal behavior for each componentModel for every component failure mode

ObservationsInputs and Response

3

223

3

M1

M2

M3

A1

A2

A

BCD

E

F

G

X

Y

Z

Multiplier(i):G(i):Out(i) = In1(i)*In2(i)

Stuck_in1(i):Out(i) = . . .

10

12

Abductive,Model-based Diagnosis


X mode variables, one for each component cDc modes of component c = domain of xc XY model variablesM(X, Y) model constraintsO observable variables O Y

Partitioned into Inputs I and Response R

3

223

3

M1

M2

M3

A1

A2

A

BCD

E

F

G

X

Y

Z



10

12



In, Resp: Assignment to I and R, respectivelyCandidate Ci: Assignment of modes to XDiagnosis Di: A candidate such that

Di In C(X,Y) predicts (entails) Resp

Diagnosis = {A1=G, A2=S, O1=G, M2=G, M3=G}

M1

M2

M3

A1

A2

A

BCD

E

F

G

X

Y

Z




3

223

3

10

12

Candidate = {A1=G, A1=G, M1=G, A2=G, M3=G}


Abductive Diagnosis by Generate and Test

Given: Correct and exhaustive fault models for each component.

Generate: Consider each mode assignment as a candidate.

Test:1. Simulate candidate, given inputs.2. Compare to observations

• Disagree: Discard• Agree: Keep• No prediction: Discard

Problem:• Fault models are often incomplete• May incorrectly exonerate faulty components


Outline




• Mars Observer• Mars Climate Orbiter• Mars Polar Lander• Deep Space 2

Courtesy NASA/JPL-Caltech. http://www.jpl.nasa.gov.

Issue: Failures are Often Novel


Helium tank

Fuel tankOxidizer tank

MainEngines

Flow1 = zeroPressure1 = nominal

Pressure2= nominal

Acceleration = zero


How Should Diagnoses Account for Novel Symptoms?Consistency-based Diagnosis: Given symptoms,

find diagnoses that are consistent with symptoms.Suspending Constraints: Make no presumptions

about faulty component behavior.1

1

1 SymptomOr1

Or2

Or3

And1

And2

A

BCD

E

1

111

0

F

G

X

Y

Z

0

1


Consistency-based Diagnosis: Given symptoms, find diagnoses that are consistent with symptoms.

Suspending Constraints: Make no presumptions about faulty component behavior.

1

1

1 SymptomOr1

Or2

Or3

And1

And2

A

BCD

E

1

111

0

F

G

X

Y

Z

0

1

How Should Diagnoses Account for Novel Symptoms?


Consistency-based Diagnosis: Given symptoms, find diagnoses that are consistent with symptoms.

Suspending Constraints: Make no presumptions about faulty component behavior.

1

1

Or1

Or2

Or3

And1

And2

A

BCD

E

1

111

0

F

G

X

Y

Z

0

1

How Should Diagnoses Account for Novel Symptoms?


Consistency-based Diagnosis

And(i):G(i):Out(i) = In1(i) AND In2(i)

U(i):

Obs: Assignment to OCandidate Ci: Assignment of modes to XDiagnosis Di: A candidate such that

Di Obs C(X,Y) is satisfiable.

1

111

0

Or1

Or3

And1

A

BCD

E

F

G

X

Y

Z

0

1

Diagnosis = {A1=G, A2=U O1=G, O2=U, O3=G}

ALL components have “unknown Mode” U, Whose assignment isnever mentioned in C


Testing Consistency Propositional Logic• DPLL• Unit propagation (incomplete)

•Finite Domain Constraints• Backtrack w forward checking, …• Waltz constraint propagation (incomplete)

• Algebraic Constraints• Sussman/Steele Constraint Propagation:Propagate newly assigned values through equations mentioning variables.

• To propagate, use assigned values of constraint to deduce unknown value(s) of constraint.


X {1,0} X=1 X=0X=1 X=0

Encoding Models In Propositional Logic

(i=G) (In1(i)=1) Out(i)=1(i=G) (In2(i)=1) Out(i)=1(i=G) (In1(i)=0) (In2(i)=0) Out(i)=0

And(i):G(i):Out(i) = In1(i) AND In2(i)

U(i):

Or(i):G(i):Out(i) = In1(i) OR In2(i)

U(i):

(i=G) (In1(i)=0) Out(i)=0(i=G) (In2(i)=0) Out(i)=0(i=G) (In1(i)=1) (In2(i)=1) Out(i)=1


Summary:Model-based Diagnosis

• A failure is a discrepancy between the model and observations of an artifact.

• Diagnosis is symptom directed • Symptoms identify conflicting components as

initial candidates.• Test novel failures by suspending constraints

and testing consistency.• Newly discovered conflicts further prune

candidates.

L15a model-based diagnosis - MITdspace.mit.edu/bitstream/handle/1721.1/36896/2/16-410... ·...

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