La objeción de conciencia en la función pública

Grastien and Anbulagan [2009] proposed incremental diagnosis with the aim to up- date diagnosis when new observations arrive. Incremental diagnosis is an open re- search problem of on-line diagnosis. The incremental approach updates diagnostic results regularly. Grastien and Anbulagan [2009] proposedpreferred diagnosisto deal with the situation when it is not possible to retrieve precisely what behaviour gener- ated these observations. For systems that are not diagnosable, the sequence of faults that actually occurred on the system cannot always be precisely deduced from the

sequence of observations. Hence, several diagnoses can be returned to explain the observations. Grastien and Anbulagan [2009] defined the notion of preference such that the expected output of a diagnoser is the preferred diagnosis. The diagnosis preference is an ordering relationon a set of diagnoses. ∆ ∆0 denotes that diag- nosis∆is preferred to the diagnosis ∆0. Accordingly, p p0 denotes that a path pis preferred to pathp0, which means that the diagnosis of pis preferred to the diagnosis of p0. A Non-Exhaustive Diagnosis Engine (NEDE) is defined as a diagnostic engine such that a diagnoser only returns the preferred diagnosis, and this engine should re- turn an explanation of diagnosis. Therefore, preferred diagnosis saves computation, which avoids exponential numbers of all diagnoses.

Grastien and Anbulagan [2009] further argued that NEDE would be sufficient for a diagnoser since it only needs to consider the preferred diagnoses. This is because it is possible to turn an exhaustive diagnoser that returns explanations into an NEDE by determining the preferred diagnosis and extracting one of its explanations. Efficient computation is feasible if the search space is pruned as soon as the initial diagnosis is computed. For instance, SAT-based diagnoser is an instance of NEDE.

Incremental diagnosis means given a DES A, a sequence of observation obsj =

[o1,o2,o3, . . . ,oj] and a continuation obsj0 = [o₁,o₂,o₃, . . . ,o_j0] of obs_j such that j0 ≥ j, the incremental diagnosis is the computation of the diagnosis of obsj0 using the diagnosis of obsj. Grastien and Anbulagan [2009] proposed Algorithm 3 to compute

a path and the associated diagnosis.

Algorithm 3:Algorithm of Incremental Diagnosis with a NEDE

Input: prediction window µ, NEDEΩ, observation flowOF

Output: pu

1 S₀:= I 2 obs:= []

3 p:=∅

4 p_u:=∅

5 whileOF generates new_obs do 6 obs:=obs⊕new_obs

7 p0 :=Ω(obs,S₀)

8 if p0 not foundthen

9 p0 :=Ω(obs,Q)

10 pu:= p⊕p0

11 p:= p⊕remove_last(p0,µ)

12 obs:=keep_last(obs,µ)

13 S0:={last_state(p)}

§2.1 Existing Work of On-line Diagnosis of DES 21

A prediction window µindicates how many observations are required before a diagnosis is established. The input of NEDE, denoted asΩ, consists of a set of initial states and a sequence of observations. The output is a preferred explanation. An observation flowOF provides an ordered sequence of observations. This flow does not return all observations at once. Starting from Line 1, the established explanation of observations is stored inpand its final state is stored inS0. The path purepresents

the current explanation of all observations, which can be returned any time if the procedure is on-line. obs contains a list of observations that are not yet explained in p and its size is bounded by µ. Whenever new observations, denoted as new_obs, become available, new observations are added to the observations not explained and a path p0 is computed from a state ofS0. Both paths pu and p are updated, and the

lastµobservations are kept. Finally, the set of statesS0 is updated.

This algorithm allows a diagnoser to backtrack until the µprevious observations. The backtracking is limited to this position to avoid complexity explosion. However, this algorithm may return an incorrect diagnosis if the value µis set poorly, and the algorithm may return a diagnosis that is not the preferred one. One way to overcome this problem is to limit the backtracking until a bounded number of observations, and return a failure message. The alternative approach is to run the diagnostic algorithm from any system state Q in Line 9, which is called diagnosis reset. Diagnosis reset means that the state at the beginning of a prediction window abruptly jumps for no sensible reason. If the supervision system is able to recover the system state, the diagnosis will be incorrect around the diagnosis reset, but should be correct before and after. Finally, the incremental algorithm should warn a human agent of any incorrectness.

In summary, incremental diagnosis does not compute all diagnoses but only the preferred one. The benefit of the incremental approach is to simplify the problem as the number of possible diagnoses and their explanations is usually exponential to the number of system states. Furthermore, a human agent is usually more interested in the preferred diagnosis. Therefore, incremental diagnosis is advantageous when not all observations are known in the first place. On the other hand, the NEDE algorithm cannot ensure the completeness or consistency of diagnosis. Suggestions for future work include bounded preferred diagnoses, reusing conclusions from previous com- putations, and decomposition into sub-systems for diagnosis.