SALUD PÚBLICA

a. Increment or Decrement all OBS counters in dissents that mention xio = vij

b. Increment or Decrement all OBS counters in transitions that mention xio = vij

3. For each xic = vij∈ CMDS

a. Increment or Decrement all CMD counters in transitions that mention xic = vij

4. For each xim = vij∈ MODEPrev

a. Increment or Decrement all source mode counters in transitions that mention xim = vij

b. Increment or Decrement all mode counters for constraints in transitions that mention xim = vij

5. Determine which Dissents have ‘counter = 0’, and put them in DEN

6. Determine which Transitions have ‘counter = 0’ for the source, observations, command and mode variable counters, and put them in TEN

The above steps outline the Dissent and Transition triggering algorithms, creating the lists of enabled dissents, DEN, and enabled transitions, TEN. Along with the previous mode estimates, these outputs are used in the Constituent Diagnosis Generator to determine the constituent diagnoses, the reachable current modes and the enabled transitions.

followed by the mapping of enabled transitions and previous mode estimates to the set of reachable current modes.

The consequent of a dissent represents an infeasible space of assignments.

This can be turned around to describe the remaining feasible assignments.

The constituent diagnoses are generated by logically transforming the conflict. The logical transformation is as follows.

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

1 11 2 22 1 11 2 21 3 32

or by example

= = =

xo vl x o v l xm vl x m v l x m v l

bus-voltage nominal switch charger-1 charger-1 off

 = ∧ = ⇒  = ∧ = ∧ = 

   

 ⇒  ∧ 

   

¬

¬

Equation 6-1 - Logical Statement of a Dissent

Assuming that this dissent has been enabled, then the consequent is a conflict:

( ) ( ) ( )

( ) ( )

[ ]

1 1 2

1 1 2 2 3 3

or by example

= =

m l m l m l

x v x v x v

switch charger - 1 charger - 1 off

¬ = ∧ = ∧ = 

¬ ∧

In clausal form, these are equivalent to:

( ) ( ) ( )

( ) ( )

1 1 2

1 1 2 2 3 3

or by example

= =

m l m l m l

x v x v x v

switch charger - 1 charger - 1 off

¬ = ∨ ¬ = ∨ ¬ =

¬ ∨ ¬

These statements logically say that the variables cannot all have the values specified here. So, the ‘switch’ cannot have the value charger-1 at the same time that the ‘charger-1’ is off. However, the variables can take on any other value in its domain. So, the following is the logical equivalent of the above statements.

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )

2 2 3 1 3 3

1 1 2 2 2 2 3 3 3 3 1 1

or by example

=

m l m l m l m l m l m l

x v x v x v x v x v x v

switch charger - 2 charger - 1= full - on charger - 1= tri

= ∨ = ∨ = ∨ = ∨ = ∨ =

∨ ∨( ^ckle)∨^...

Equation 6-2 - Final Statement after Logical Transformation

The clause here is represented by the constituent diagnoses, defined as a set of component mode assignments in Equation 6-2. Each assignment in the set is referred to as a constituent diagnosis of the conflict because each

assignment resolves the conflict. The set of constituent diagnoses represents a single conflict, so the ‘Constituent Diagnoses’ is represented as a set of sets of constituent diagnoses of the form defined in Equation 6-2.

The final step of the Constituent Diagnosis Generator is to generate a list of reachable current modes using the enabled transitions, and to determine the likelihood of these assignments. This likelihood is taken from the transition probability specified on component mode assignments. After determining the enabled transitions, the set of reachable component modes is generated using the previous mode estimates and identifying the enabled transitions where a component mode assignment in the source is also in the previous mode estimate. A component mode assignment in the set of reachable component mode assignments is the target of these enabled transitions.

Figure 6-6 depicts the calculation.

S1(t)

x₁^m

x2m

S2(t)

Sn(t)

. .

. ^x1

m

x₂^m Time 't'

Previous Belief State

Time 't+1' Reachable Current Modes

Figure 6-6 – Calculation of the Reachable Current Modes

The figure denotes different component mode assignments in the previous mode estimate Si(t). Shown are the transitions from two different components in each mode estimate, and from two different mode estimates

in the previous belief state. The Constituent Diagnosis Generator then adds the component mode assignments on the right of the figure to the set of reachable current modes. So, the component mode assignments for x1m and x2m that are reachable from the previous mode estimates S1(t) and Sn(t) are added to the list of reachable current modes. There is a complication related to overlap of the reachable component modes generated from different previous mode estimates. In determining the reachable current modes, there is nothing to preclude two previous mode estimates from having transitions to the same current mode. When this occurs, the transitions are maintained separately. This enables the next phase of CME to compute the current belief state using the individually stored transitions.

The approach to dealing with the overlap of reachable component modes is addressed in the detailed algorithms of Chapter 7.

Similarly to Livingstone, the set of reachable component modes is computed from each previous mode estimate using the enabled transitions.

Each component mode assignment in the reachable current modes represents the transition using the probability of the transition and the previous mode estimate that is the source of this transition. The transition probability for the component mode assignment is given by the following equation:

(

)

₍

₎

(

(

) ^|

)

P x v P P x v S

Τ =

= = i Τ =

Equation 6-3 - Probability Equation for Assignment Estimation

Here, the probability of a component mode assignment is dependent on the transition probability, PT, and the guard probability, Pg. The guard probability is 1 or 0 depending on whether or not the guard is satisfied. The notation for ‘Pg’ is necessary to note that the transition probability is dependent on the entire state ‘Si(t)’, including all, commands and previous

component mode assignments. The union of the pairs of component mode assignments and the associated probabilities, 〈xim = vij, pij〉 where xim = vij is the target of the transition and pij represents the probability calculated in Equation 6-3 comprise the set of reachable current modes.

The following are the steps of the algorithm for the Constituent Diagnosis Generator.

1. For each ‘dissent’ in the Enabled Dissents

a. Transform the consequent of each dissent to a constituent diagnosis, and place in the set CD

2. For each ‘transition’ in the Enabled Transitions

a. Create a list of reachable current modes with the proper cost per Equation 6-3

3. Return the set CD, the Reachable Current Modes, and the Enabled Transitions

This completes the basic description of the Compiled Conflict Recognition algorithm design and computations that map the compiled knowledge to the set of constituent diagnoses, reachable current modes and the enabled transitions. The next step in the process of Online Mode Estimation is to use these to determine consistent mode estimates.