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Explain what the constraints are, generally spend

more time on this slide.

Explain what the constraints are, generally spend

more time on this slide.

Explain what the constraints are, generally spend

more time on this slide.

Explain what the constraints are, generally spend

more time on this slide.

Explain what the constraints are, generally spend

more time on this slide.

To
track the *n* most likely trajectories

For each new time step
until the end of time

Create full copy of the
model for the new time step

Assign command and
observation variables

Until *n *consistent
trajectories found

Enumerate the next best
t-length trajectory

Throw it out if
inconsistent

Report the t-length
trajectories

An
Algorithm with Only Two Problems!

Space - Representation grows linearly with
time

Time - Search space grows exponentially with
time - Checks an exponential number of
obviously wrong candidates

The
assignments to t capture every
possible trajectory

Trajectories
can be enumerated in prior probability order

P(trajectory) = S P(t
assignment)

Each
trajectory can be checked for agreement with observations

Avoid
committing to a small number of trajectories

Build
a structure that compactly represents all evolutions

Generate
additional trajectories in order as needed

To
track the *n* most likely trajectories

For each new time step
until the end of time

Create full copy of the
model for the new time step

Assign command and
observation variables

Until *n *consistent
trajectories found

Enumerate the next best
t-length trajectory

Throw it out if
inconsistent

Report the t-length
trajectories

An
Algorithm with Only Two Problems!

Space - Representation grows linearly with
time

Time - Search space grows exponentially with
time - Checks an exponential number of
obviously wrong candidates

The
assignments to t capture every
possible trajectory

Trajectories
can be enumerated in prior probability order

P(trajectory) = S P(t
assignment)

Each
trajectory can be checked for agreement with observations

Avoid
committing to a small number of trajectories

Build
a structure that compactly represents all evolutions

Generate
additional trajectories in order as needed

To
track the *n* most likely trajectories

For each new time step
until the end of time

Create full copy of the
model for the new time step

Assign command and
observation variables

Until *n *consistent
trajectories found

Enumerate the next best
t-length trajectory

Throw it out if
inconsistent

Report the t-length
trajectories

An
Algorithm with Only Two Problems!

Space - Representation grows linearly with
time

Time - Search space grows exponentially with
time - Checks an exponential number of
obviously wrong candidates

The
assignments to t capture every
possible trajectory

Trajectories
can be enumerated in prior probability order

P(trajectory) = S P(t
assignment)

Each
trajectory can be checked for agreement with observations

Avoid
committing to a small number of trajectories

Build
a structure that compactly represents all evolutions

Generate
additional trajectories in order as needed

To
track the *n* most likely trajectories

For each new time step
until the end of time

Create full copy of the
model for the new time step

Assign command and
observation variables

Until *n *consistent
trajectories found

Enumerate the next best
t-length trajectory

Throw it out if
inconsistent

Report the t-length
trajectories

An
Algorithm with Only Two Problems!

Space - Representation grows linearly with
time

The
assignments to t capture every
possible trajectory

Trajectories
can be enumerated in prior probability order

P(trajectory) = S P(t
assignment)

Each
trajectory can be checked for agreement with observations

Avoid
committing to a small number of trajectories

Build
a structure that compactly represents all evolutions

Generate
additional trajectories in order as needed

•Modeling
abrupt failure and gradual degradation

•Enable
automatic generation of fault symptom table, which is in turn automatically
compiled into a decision tree diagnoser.