Modelling and hierarchical diagnosis of timed discrete-event systems

Figures & data

Figure 1 The principal structure of model-based diagnosis.

Figure 2 Event generation in discrete-event systems.

Table

	Diagnostic Problem
Given:	Timed discrete-event model
	Timed input sequence V(0…th )
	Timed output sequence W(0…th )
Find:	Fault f

Figure 3 System to be diagnosed.

Figure 4 Overall system diagnosis.

Figure 5 Representation of the sequence of processes by a timed event graph.

Figure 6 Diagnosis at the component level.

Figure 7 Changes in signal V_s and corresponding dater x_i (k).

Figure 8 Part of a timed event graph and potential event sequence.

Figure 9 A timed automaton and one of its possible state sequences.

Table

	Fault detection problem for the overall system
Given:	Model of the overall system (6)
	Sequences of event times X(k − N…k) and U(k − N + 1…k)
Find:	Set of possibly faulty components

Table

Fault isolation and identification problem at the component level
Given:	Model (7) of the component Ci
	Timed input sequence v(t 0…th )
	Timed output sequence w(t 0…th )
Find:	Fault f

Figure 10 Batch process.

Figure 11 Timed event graph representing the overall behaviour of the batch process. All places where no holding time is displayed have the holding time 0.

Table 1. System parameters and elements of the timed event graph

Event and corresponding changes in Vi	Transition
New charge of substance becomes available for reactor 1 | 2
Open valve 1 | 2 (Change V 1 | V 2 from 1 to 0)	q 1  |  q 2
Open valve 4 | 5 (Change V 4 | V 5 from 1 to 0)	q 5 | q 6
Close valves (1,2) | (4,5) and start reaction in reactor 1 | 2 (Change (V 1,V 2) | (V 4,V 5) from 0 to 1)	q 3 | q 7
Reactor 1 | 2 gets empty, close valve 3 | 6 (Change V 3 | V 6 from 0 to 1)	q 4 | q 8
Open valve 7 and start filtering (Change V 7 from 1 to 0)	q 9
Solvent becomes available, close valve 7 (Change V 7 from 0 to 1)	q 10
Process	Holding time	Corresponding valve
Fill substance into reactor 1 | 2	τ31 | τ75	valve 1 | 4
Fill solvent into reactor 1 | 2	τ32 | τ76	valve 2 | 5
React and empty reactor 1 | 2	τ43 | τ87	valve 3 | 6
Filter	τ10 9	valve 7

Figure 12 Schematic structure of a valve.

Figure 13 Event sequences used at the upper process level.

Figure 14 Signals retrieved for diagnosis from the archive starting at t = 8 minutes.

Figure 15 Diagnostic results from lower process hierarchy.