Miklós Gerzson

An intelligent diagnostic system based on Petri nets

Abstract An intelligent event-oriented diagnosis methodology and diagnostic system architecture is proposed in this paper. The dynamic behaviour of the process system in different faulty modes is described by cause-consequence event sequences represented by coloured Petri nets (CPNs). The dynamic model of the system is assumed to be partially unknown and it is refined using the observed event sequences by a learning method. The real-time diagnosis operates on the CPN model of the system and on the expected operating procedures comparing observed event sequences to the model-based prediction. The diagnostic system architecture consists of an event archivator, a data structure generator, a real-time diagnostic monitor and a learning subsystem.

Analysis of controlled technological systems using high level Petri nets

Abstract Based on the formal correspondence between constraint type qualitative differential equations (QDEs) with order of magnitude quantity space and colored Petri nets (CPNs) a formal relation is identified between 1. (i) the reachability tree of the stochastic CPNs and the behaviour tree of the related constraint type QDEs generated by the EQSIM method (Hangos et al ., 1992); 2. (ii) the reachability tree of deterministic CPNs and solution of constraint type QDEs generated by interval arithmetic methods. The behavioural properties of controlled technological systems, their reachability, boundedness and liveness, are investigated. It is shown that the technological subnet is live and bounded. The analysis of these properties in general case is based on the reachability tree of the CPN (Jensen and Rozenberg, 1991) which is of high computational time complexity. In contrary the structural properties of the overall CPN is analysed by the invariant method, which has polynomial time complexity. It is shown that places and transitions in the technological subnet are place and transition invariants of the overall net if the technological system has a steady state.

DISCRETE EVENT MODEL STRUCTURE IDENTIFICATION USING PROCESS MINING

A novel structure identification procedure for discrete event systems described by Petri nets are proposed in this paper for model-based diagnostic purposes that utilize the notions and tools of process mining. The identification of the structurally different discrete event system models describing a system in its normal and/or faulty modes was used for model-based isolation of the considered faulty modes. From the available process mining techniques that allow for the automatic construction of process models in Petri net form based on event logs, the genetic algorithmbased structure identification procedure has been found to be most capable of identifying the characteristic structural elements of the faulty models. The proposed procedures are illustrated on a simple example of an operated parking gate automaton with two faulty modes.

Structural Decomposition of Process Models Described by Higher Index DAE Systems

Abstract A graph-theoretical method for the structural analysis of dynamic lumped process models described by differential and algebraic equations (DAEs) is applied in this paper in order to determine the most important solvability properties (degree of freedom, structural solvability, model decomposition, dynamic degree of freedom, differential index, e.g.) of these models by using the so-called dynamic representation graph. The structure of the dynamic representation graph is suitable for the determination of the mentioned solvability properties. The aim of our work is to show a decomposition procedure in case of higher index models. This method shows the subpart which causes the higher index and the position of this part in the hierarchy of structurally solvable submodels. Using this procedure we can answer the generally not simple question that in case of large process models which submodel or submodels cause the higher index and what the positions of these submodels are in relation to the other, structurally solvable submodels in the model.

Diagnosis of Technological Systems Based on the Structural Decomposition of their Coloured Petri Net Model

Abstract Diagnosing faults during the operation of a system is an essential task when investigating technological systems. In this paper, a new online fault identification method is proposed which is based on the occurrence graph of the coloured Petri net model of the system. The model is able to simulate the normal and faulty operations of the system given in the form of event lists, so called traces. The diagnosis is based on the search for deviations between the traces of the normal and the actual operations. In the case of complex technological systems, the occurrence graph can contain hundreds of nodes; therefore, the computational effort and searching-time increase significantly. Our proposed structural decomposition method can manage these demands so it has a crucial impact on the practical application of diagnostic processes. The main idea of our method is that the complex systems can be decomposed into technological units. Therefore, the diagnosis can be done by components separately and the diagnostic result of a unit can be used for the diagnosis of the other units connected to it. Because of the structural decomposition, the diagnosis has to be performed on much smaller occurrence graphs but the effect of faults in previous units is taken into account. The proposed method is illustrated by a simple case study.

Monitoring and Diagnosis of Manufacturing Systems Using Timed Coloured Petri Nets

Novel fault modelling and integration method were applied in the case when the faultless operation of the system was modelled by a high-level, coloured Petri net. In order to achieve realistic investigations, a timed coloured Petri net model of the system was constructed, where faults can occur in the manufacturing lines. The faultless and fault containing models were implemented in CPNTools both for non-timed and timed cases. The resulted model was investigated both via simulation and using the occurrence graph. For efficient analysis of the occurrence graph a software module called OGAnalyser was developed.

Diagnosis of Technological Systems based on their Coloured Petri Net Model

Abstract A novel method for discrete event systems described by Petri nets are proposed in this paper for model-based diagnosis. The model of the investigated system was defined in hierarchical colored CP-net form. Both normal reference model describing the faultless operation and the extended model containing the different faults were developed. For the fault simulation we used the arc and transition inscriptions. In order to visualize the model in different faulty modes a converter program were developed. The proposed procedure was illustrated on a simple manufacturing process with different faulty modes.

Diagnostic Investigations Based on the Petri Net Model Generated from the Process Information

A novel structure comparison procedure for discrete event systems described by Petri nets are proposed in this paper for model-based diagnosis that utilizes the graph distance metric method. The model of the investigated system was defined in hierarchical colored CP-net form. Both normal reference model describing the faultless operation and the extended model containing the different faults were developed. For the fault simulation we used the arc and transition inscriptions. In order to visualize the model in different faulty modes a converter program were developed. The proposed procedure was illustrated on a simple manufacturing process with different faulty modes.

Investigating Energetic and Impedance Relations of Microwave Transmission Line Filled with Dielectric Material

During microwave treatment, microwave energy is transferred to a material sample placed in an applicator of given geometric parameters. As a result of the energy transfer, the sample absorbs energy from the microwave fleld depending on its dielectric properties. The degree of energy absorption is directly proportional to the dielectric loss and proportional to the square root of the dielectric constant. The temperature of the sample continuously increases due to the energy transfer and the dielectric properties of the sample also change with the rising temperature. Although the microwave energy supply is constant, time and temperature dependent energy impedance and dielectric relations are developed. A part of them is measurable, but the other part of them can not be directly measured, they can only be computed from the previously measured ones. In a closed model which contains the parameters of the sample and the waveguide, the continuously changing parameters can be determined in relation of the temperature. These parameters are as follows: Attenuation of the transmission line, temporal change of the sample temperature, dielectric properties of the sample, loss factor of the sample, penetration depth, impedance of the transmission line, standing wave ratio re∞ection factor. The above parameters can be modeled as a function of the samples temperature or as a function of time.

Invariant inheritance in structured operating procedures described by Petri nets

Abstract Place- and transition-invariants of structured operating procedures described by low level Petri nets containing a plant-level and embedded operating unit-level procedures are analysed in this paper. Place-invariants form a set of system states with conservation property while transition-invariants correspond to cyclical behaviour of the system. It is shown how the place and transition-invariants of the complete operating procedure can be determined from the invariants of the plant- ant unit-level procedures. The results are illustrated on a simple example.