Behavior Modes Meir Kalech Partially Based on slides of Brian Williams, Luca Console and Peter struss

Behavior Modes

Meir Kalech

Partially Based on slides of Brian Williams, Luca Console and Peter struss

Outline Last lecture:

1. Generation of tests/probes

2. Measurement Selection

3. Probabilities of Diagnoses

Today’s lecture:

1. Models of correct + faulty behavior

2. Sherlock engine

3. Abductive diagnosis

4. Qualitative models

Exploiting models of correct/faulty behaviorInitial proposal: using only models of correct behavior

They are those that are in strict accordance with the goals (easy to acquire, e.g., from design)

But unfortunately they are not always sufficient Need of exploiting also fault models of some form

predictive models [Struss, Dressler, 89] – GDE+[de Kleer, Williams 89] - SHERLOCK

“weak” models of physical impossibility [Friedrich et al. 90]

behavioral models [Console, Torasso, 91]

Diagnosis With Only the Unknown

Inverter(i): G(i): Out(i) = not(In(i)) U(i):

X YA B C0 00

Nominal and Unknown Modes

• Isolates surprises• Doesn’t explain

Diagnosis With Only the Known

Inverter(i): G(i): Out(i) = not(In(i)) S1(i): Out(i) = 1 S0(i): Out(i) = 0

X YA B C 00 0

Exhaustive Fault Modes

• No surprises• Explains

Solution: Diagnosis as Estimating Behavior Modes

Inverter(i): G(i): Out(i) = not(In(i)) S1(i): Out(i) = 1 S0(i): Out(i) = 0 U(i):

X YA B C 00 0

Nominal, Fault and Unknown Modes

• Isolates surprises• Explains

Measurement motivation to use Behavior modes Knowledge of failure modes is important to

decide what measurement to make next. If all faults were equally likely, measuring X or

Y provides equal information. Suppose:

Inverters A and B almost always fail by stuck-at-1. Inverter C almost always fails by stuck at-0.

It is unlikely that inverter A is failing. The likely failures of inverters B and C are

consistent with the symptom

Behavior Modes

• System comprises a (finite) set of components COMPS = { Ci }

• Each Ci has a (finite) set of behavior modes modes(Ci) = { mij

(Ci)}

• E.g.- (unique) correct behavior: ok(Ci)

- (any) faulty behavior: ok(Ci)

- a specific fault: stuck-closed(valvei)

• Behavior mode operating mode (of correct behavior)• E.g. blocking mode of a diode

• System comprises a (finite) set of components COMPS = { Ci }

• Each Ci has a (finite) set of behavior modes modes(Ci) = { mij

(Ci)}

• E.g.- (unique) correct behavior: ok(Ci)

- (any) faulty behavior: ok(Ci)

- a specific fault: stuck-closed(valvei)

• Behavior mode operating mode (of correct behavior)• E.g. blocking mode of a diode

Definition (Mode Assignment)• COMPS’ COMPS

• MA = {mij(Ci) Ci COMPS’ }

• or MA = Ci COMPS’ mij(Ci)

• MA complete: COMPS’=COMPS





Diagnoses as Assignments of Fault Modes

Definition (Diagnosis):• A complete mode assignment MA that is consistent with

the observations: SD MA OBS

Definition (Diagnosis):• A complete mode assignment MA that is consistent with

the observations: SD MA OBS









Yet Another Simple Example

Battery

RLight

HLight

Starter

Head lights work Starter and rear light don’t Obvious diagnosis:

Starter and rear light are broken

Head lights work Starter and rear light don’t Obvious diagnosis:

Starter and rear light are broken

Fault Localization for the Simple Example - Conflicts 1 and 2

Battery

RLight

HLight

Starter

• ok(Battery) ok(Wire1) ok(Wire2) ok(Starter) active(Starter)

• OBS active(Starter) Conflict

ok(Battery) ok(Wire1) ok(Wire2) ok(Starter)

• ok(Battery) ok(Wire1) ok(Wire2) ok(Starter) active(Starter)

• OBS active(Starter) Conflict

ok(Battery) ok(Wire1) ok(Wire2) ok(Starter)

Wire1

Wire3

Wire5

Wire2

Wire4

Wire6Analogously: ok(Battery) ok(Wire1)

ok(Wire2) ok(Wire3) ok(Wire4) ok(RLight)

Analogously: ok(Battery) ok(Wire1)

ok(Wire2) ok(Wire3) ok(Wire4) ok(RLight)

Fault Localization for the Simple Example - Conflicts 3 and 4

Battery

RLight

HLight

Starter

• lit(HLight) ok(HLight) ok(Wire5) ok(Wire6) ok(RLight) lit(RLight)

• OBS lit(RLight) Conflict

ok(HLight) ok(Wire5)

ok(Wire6) ok(RLight)

• lit(HLight) ok(HLight) ok(Wire5) ok(Wire6) ok(RLight) lit(RLight)

• OBS lit(RLight) Conflict

ok(HLight) ok(Wire5)

ok(Wire6) ok(RLight)

Wire1

Wire3

Wire5

Wire2

Wire4

Wire6Analogously: ok(HLight) ok(Wire5)

ok(Wire6) ok(Wire3) ok(Wire4) ok(Starter)

Analogously: ok(HLight) ok(Wire5)

ok(Wire6) ok(Wire3) ok(Wire4) ok(Starter)

Fault Localization for the Simple Example - Hitting Sets

Battery

RLight

HLight

Starter

Wire1

Wire3

Wire5

Wire2

Wire4

Wire6

• {Battery, Wire1, Wire2, Starter}• {Battery, Wire1, Wire2, Wire3,

Wire4, Rlight}

• {HLight, Wire5, Wire6, Rlight} • {Hlight, Wire5, Wire6, Wire3,

Wire4, Starter}

• {Battery, Wire1, Wire2, Starter}• {Battery, Wire1, Wire2, Wire3,

Wire4, Rlight}

• {HLight, Wire5, Wire6, Rlight} • {Hlight, Wire5, Wire6, Wire3,

Wire4, Starter}

• {Starter, Rlight}• {Starter, Rlight}

• {Battery, HLight}• {Battery, HLight}

• {Wire1, Wire5}• {Wire1, Wire5}

• + 19 NONSENSES more!• + 19 NONSENSES more!!?

What Makes Most of the Fault Localizations Implausible?

Battery

RLight

HLight

Starter

Wire1

Wire3

Wire5

Wire2

Wire4

Wire6

• If the battery were broken, the headlights would not be lit

• Broken headlights cannot be lit Knowledge about faults can

reduce the set of fault localizations

• If the battery were broken, the headlights would not be lit

• Broken headlights cannot be lit Knowledge about faults can

reduce the set of fault localizations

• {Starter, Rlight}• {Starter, Rlight}

• {Battery, HLight}• {Battery, HLight}

• {Wire1, Wire5}• {Wire1, Wire5}

• + 19 more!• + 19 more!!?

Fault Models - “Physical Negation”

Fault models are neededpredictive: bulb(B) AB(B) voltageIn(B,X) light(B,off)

Fault models are neededpredictive: bulb(B) AB(B) voltageIn(B,X) light(B,off)





Today’s lecture:


2. Sherlock engine



Search Guided by Probabilities: SHERLOCK ([de Kleer- Williams 89])

• Basic Idea: Search for the most probable explanations of the observations

• Fault models for each component (type)• Possible: unknown fault mode

• Modes have prior probability Mode assignments have a probability • SHERLOCK: best first search for consistent mode assignments• termination criteria

• Basic Idea: Search for the most probable explanations of the observations

• Fault models for each component (type)• Possible: unknown fault mode

• Modes have prior probability Mode assignments have a probability • SHERLOCK: best first search for consistent mode assignments• termination criteria

Leading Diagnoses Complexity of diagnoses space:

n-#components, m-#modesGDE 2n SHERLOCK: mn

To reduce the high complexity, generate only leading diagnoses:

1. Diagnoses are those with the highest probabilities.2. No more than k1 (=5) leading diagnoses.3. Candidates with probability less than 1/k2(=100)

of the best diagnosis are not considered4. The diagnoses need not include more than k3

(=0.75) of the total probability mass of the candidates.

SHERLOCK - Example: Two Inverters

A B0 1

Model of Inverter X

Mode Behavior Prior

XN: Normal Out =In .99X1: Stuck at 1 Out = 1 .006

X0: Stuck at 0 Out = 0 .003XU: Unknown .001


A B0 1

Model of Inverter X

Mode Behavior Prior

XN: Normal Out =In .99X1: Stuck at 1 Out = 1 .006

X0: Stuck at 0 Out = 0 .003XU: Unknown .001

• Conflicts: {AN, BN}, {B0}, {A1, BN}


In slide 25 see how to generate conflicts and diagnoses


A B0 1



• Inspired by GDE + modes• Diagnosis is an explanation: SDMAOBS ┴ , where

MA=CiCOMPSmij(Ci), (rather than a set of faulty components)

• I.E., the diagnosis set contains all the combinations of the components’ modes except of conflicts.

• Inspired by GDE + modes• Diagnosis is an explanation: SDMAOBS ┴ , where

MA=CiCOMPSmij(Ci), (rather than a set of faulty components)

• I.E., the diagnosis set contains all the combinations of the components’ modes except of conflicts.


A B0 1

[[AN , B1]] .00594 [[AN , BU]] .00099

[[A1 , B1]] .00004 [[A1 , BU]] .00001

[[A0 , BN]] .00297 [[A0 , B1]] .00002 [[A0 , BU]] .000003

[[AU , BN]] .00099 [[AU , B1]] .00001 [[AU , BU]] .000001

Conflicts: {AN, BN}, {B0}, {A1, BN}Conflicts: {AN, BN}, {B0}, {A1, BN}

Diagnoses set does not contain:{AN, BN}, {A1, BN}, and supersets of {B0}

Diagnoses set does not contain:{AN, BN}, {A1, BN}, and supersets of {B0}

Generated by ATMS

Full diagnostic explanations with probabilities:


A B0 1

[[AN , B1]] .00594 [[AN , BU]] .00099

[[A1 , B1]] .00004 [[A1 , BU]] .00001

[[A0 , BN]] .00297 [[A0 , B1]] .00002 [[A0 , BU]] .000003

[[AU , BN]] .00099 [[AU , B1]] .00001 [[AU , BU]] .000001

Conflicts: {AN, BN}, {B0}, {A1, BN}Conflicts: {AN, BN}, {B0}, {A1, BN}

Generated by ATMS

Full diagnostic explanations with probabilities:

• Exhaustive search impossible• Perform best first search

• Exhaustive search impossible• Perform best first search

SHERLOCK - Example: Search Strategy

{ } 1.0 1

{An,B1} .00594 5

{An,Bn} .98010 3 x

{An,B0} .00297 8 x

{An,Bu} .00099

{A0,Bn} .00297 9

{A0,B1} .00002

{A0,B0} .000009 x{A0,Bu} .000003

{A1,B1} .00004

{A1,Bn} .00594 6 x

{A1,B0} .00002 x

{A1,Bu} .00001

{An} .99 2

{A1} .006 4

{A0} .003 7

{Au} .001

0 1A B

Legend:

x inconsistent

Legend:

x inconsistentMA Probability Step # Consistent ?

Generate the next explanation with the highest probability

Generate the next explanation with the highest probability

SHERLOCK, Process in details:1. Find Symptoms & Conflicts

Conflict:

not (G(A) and G(B) and G(C))

Finding conflict through ATMS, but generate focus environments

X YA B C0 0

1 0G G

G0

01

0

More Symptoms & Conflicts

not (S1(A) and G(B) and G(C)

X YA B C0 0

1 0S1 G

G0

01

0

not (S0(B) and G(C))

X YA B C0 0

0S0

G0

01


0

not S1(C)

X YA B C0 0

1S10

0


All Minimal Conflicts < S1(C) >

< S0(B), G(C) >

< S1(A), G(B), G(C) >

< G(A), G(B), G(C) >

2. Constituent Diagnoses from Conflicts

Diagnosis is an explanation, so it must contains no conflict:

< S1(C) >: not S1(C):=> G(C) or S0(C) or U(C)

<S0(B) and G(C)>:not (S0(B) and G(C)) => not S0(B) or not G(C) => G(B) or S1(B) or U(B) or S1(C) or S0(C) or U(C)

< S1(A), G(B), G(C) >=> G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C) or U(C)

< G(A), G(B), G(C) >=> S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C) or U(C)

3. Generating Kernel Diagnoses

[U(C)]

[G(C),S0(C),U(C)]

[G(B),S1(B),U(B),S1(C),S0(C),U(C)]

[G(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]

[S1(A),S0(A),U(A),S1(B),S0(B),U(B),S1(C),S0(C),U(C)]

[U(C)] [S0(C)]

[G(C),S0(C),U(C)]

[G(B),S1(B),U(B),S1(C),S0(C),U(C)]




[U(C)] [S0(C)]

[U(B),G(C)]

[G(C),S0(C),U(C)]

[G(B),S1(B),U(B),S1(C),S0(C),U(C)]




[U(C)] [S0(C)]

[U(B),G(C)]

[G(C),S0(C),U(C)]

[G(B),S1(B),U(B),S1(C),S0(C),U(C)]



[S1(B),G(C)]


[U(C)] [S0(C)]

[U(B),G(C]

[S1(B),G(C)]

[U(A),G(B),G(C)]

[G(C),S0(C),U(C)]

[G(B),S1(B),U(B),S1(C),S0(C),U(C)]




[U(C)] [S0(C)]

[U(B),G(C]

[S1(B),G(C)]

[U(A),G(B),G(C)]

[S0(A),G(B),G(C)]

[G(C),S0(C),U(C)]

[G(B),S1(B),U(B),S1(C),S0(C),U(C)]



3. Generate Kernel Diagnoses

These are the kernel diagnoses But for [U(C)] (for instance), what are the modes of A and B? The best first search finds the most likely modes of A and B.

Candidate Initial (prior) Probabilities

p(c) p(m)mc

A B C

p(G) .99 .99 .99

p(S1) .008 .008 .001

p(S0) .001 .001 .008

p(U) .001 .001 .001

No observations With no observations Sherlock finds the single leading diagnosis

The unfocused Sherlock finds 43 diagnoses

Input I=0 Sherlock computes the following environments:

The focused Sherlock finds no label for X=0 as it does not hold in the single leading diagnosis.

00.20.40.60.8

11.2

X YA B C0

Suppose O=0 Minimal conflicts are:1. < S1(C) >2. < S0(B), G(C) >3. < S1(A), G(B), G(C) >4. < G(A), G(B), G(C) > Leading candidates:

X YA B C0 0

Next highest probability:

For instance:These are the most likely modes of A and B, beyond the kernel diagnosis U(C)

Now, the posterior behavior modes probabilities are:

ATMS labels are:

X YA B C0 0

0

0.1

0.2

0.3

0.4

0.5

X YA B C0 0

Top 6 of 64 = 98.6% of P





Today’s lecture:


2. Sherlock engine



Abductive diagnosis The definition above is based on consistency:

explanation consistent with the observations Weak notion of explanation A diagnosis D explains an observation m if it does not

contradict m (D does not support not m). Abductive diagnosis:

A stronger notion of explanation Explanation implies the observations A diagnosis D explains an observation m if it supports

m (D m). Abductive diagnosis [Poole 87][Console, Torasso, 89]

Abductive diagnosis – Poole et al. 87

A different concept:

A diagnosis is not a logical consequence of our

observations.

Exactly the opposite:

The observation should be shown to be logical

consequences of our knowledge and diagnosis.

Given SD Modes Observations, with the distinction between

contextual data (Cxt) and observations (Obs) Determine

An assignment of behavior modes to components = {mi(ci) | mi Modes(ci) }

such that:

1. SD Cxt |= Obs 2. (SD Cxt consistent)

Abductive diagnosis - definition

Cxt: inputs. The data that let the diagnoser to make prediction about the behavior of the system

A continuum of definitionsConsole and Torasso 91Given OBS, partition it into Obs1 Obs2

SD Cxt D Obs2 |= Obs1 SD Cxt D Obs1 Obs2 consistentSince Abduction diagnosis is more restrict than

consistency:Abduction provides a subset of the solutions provided by consistency-based diagnosis

Varying Obs1 we have a continuum of definitions:Obs1=OBS,Obs2= Ø abduction diagnosis of Poole86Obs1=Ø, Obs2=OBS consistency based diagnosis

Criteria to select the most appropriate definition abduction and consistency are the two extremes of

a spectrum of alternatives abduction is the most restrictive definition

it requires “complete” models it provides a strong (physical) notion of

explanation consistency-based is less restrictive

less constraints on the models weaker notion of explanation

Abductive or Consistency?

oil_cup

normal holed

oil_level

normal low

oil_loss

oil_below_car

oil_gauge

normal red

radiatornormal holed

water_levelnormal low

water_tempnormal high

engine_tempnormal high

engine_on

Computing abductive diagnoses: an example

Obs1 = {engine_temp(high)}Two minimal candidate explanations E1 = { oil_cup(holed) } E2 = {radiator(holed)}

Model:

oil_cup(normal) oil_level(normal)oil_cup(holed) oil_loss(present)oil_loss(present) oil_below_car(present)oil_loss(present) oil_level(low)oil_level(normal) oil_gauge(normal)oil_level(low) oil_gauge(red)oil_level(normal) water_level(normal)

engine(on) engine_temp(normal)...





Today’s lecture:


2. Sherlock engine



Qualitative models in MBD

Instead of educate quantity model give qualitative values

In many cases qualitative models are sufficient for

diagnostic purposes.

They are close to the way expert diagnosticians

operate.

In many cases imprecise knowledge makes numerical

models useless.

Usually imprecision in the observations.

Easier to use (in some cases).

New problems: choosing the “right” qualitative models

choosing the right form of qualitative reasoning choosing the “right” qualitative abstractions

mapping quantities into qualitative values (e.g., for observations)

dealing with the ambiguities that arise as a result of the abstraction

Qualitative models in MBD (2)

A simple example

Pump: interface variables:

Pout, Fout (0, +) constraints (pump ON)

Pump OK Pout= + Fout=0, Pout=0 Fout=+ Pump blocked Fout=0

pipe tankpump

Pipe (flow direction from 1 to 2): interface variables:

P1, P2, F1, F2 (0, +) constraints

Pipe Ok F2= F1 P1=P2

Pipe occluded F2=0, P1=+ Pipe leaking F2=0, P1=0

Tank: interface variables: Fin, Ltank, Ptank

(0, +) internal variable dLtank (0, +, -)

constraints Tank Ok Ptank=Ltank, dLtank= Fin

Pipe leaking Ptank=0, dLtank= -

1 2

Structure:Fout= F1, Pout= P1 , P2= Ptank ,

F2= Fin

Diagnosis (using pump and pipe only, we will return later to considering the tank) Obs {F2=0, P2=0 } the set of assumptions {ok(pump), ok(pipe)} is a conflict

from P2=0 and ok(pipe) we predict P1=0 and from the structure Pout=0 (for the pump)

then from ok(pump) we predict Fout=+ i.e., F1=0 (for the pipe) and finally using again ok(pipe) we predict F2=+ (CONFLICT!!!!)

Three set of assumptions explain the observations (are candidate diagnoses)

D1 { blocked(pump) } D2 { occluded(pipe)} D3 { leaking(pipe)}

A simple example (2)

A second example

Join interface variables:

Pout, Fout, Pin1, Fin1

Pin2, Fin2 (0, +) constraints

Pump OK Pin1= Pin2= Pout

Fout= Fin1 Fin2

( qualitative add)

pipe1pump1

pipe2pump2

join Diagnosis if: Obs = {Fout=0, Pout=0 } Then several minimal

explanations D1 { blocked(pump1) } D2 { occluded(pipe1)} D3 { leaking(pipe1)} D1 { blocked(pump2) } D2 { occluded(pipe2)} D3 { leaking(pipe2)}

- 0 +- - - ??0 - 0 ++ ?? + +

Documents

Behavior Modes Meir Kalech Partially Based on slides of Brian Williams, Luca Console and Peter struss