Adrien Leitold

Structure simplification of dynamic process models

Abstract Lumped process models derived from first engineering principles are usually too detailed for control purposes where only the major dynamic characteristics of the system should be captured. Two common steps of simplifying dynamic process models, the steady-state variable removal and the variable lumping simplification steps are investigated in this paper, in order to show if they preserve the key properties: the structural controllability, observability and stability of the models. In order to enable the formal analysis, these simplification steps are represented as context sensitive graph transformations acting on the structure graphs of the dynamic process models. It is shown that the simplification transformations above preserve the structural controllability and observability of process models. But only the steady-state variable removal transformation has been found not to destroy their structural stability. The variable lumping structure simplification transformation is further specialized to the case of cascade process models. It is shown that the inverse of this transformation does exist in this case, and both transformations preserve structural controllability and observability.

Structural solvability analysis of dynamic process models

Abstract The variable structure of dynamic process models is represented by a directed graph termed as the representation graph for the purpose of solvability analysis in this paper. Structural solvability analysis, the determination of the structural differential index and the structural decomposition of the differential–algebraic equations (DAE) model set can be performed using the representation graph. The characteristic features of the representation graph for both index 1 and high index semi-explicit DAE models are presented. Based on the above a novel index reduction procedure for high index models is proposed. The notions and methods are illustrated on simple process examples.

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.

Numerical method-independent structural solvability analysis of Dae models

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 of these models by using the so-called dynamic representation graph. The construction of the dynamic representation graphs that was originally proposed for the most simple, single-step, explicit numerical methods, has been extended in this paper to higher order explicit and implicit solution methods, that are used more frequently and efficiently for numerical solution of DAE-systems. It is shown here that the representation graph for both higher order explicit and implicit solution methods has similar properties to the case of explicit numerical solution procedures both for index one and higher index models. Thus it is proven that the important properties of the representation graph including the differential index of the models are independent of the assumption whether a single-step, explicit or implicit numerical method is used for the solution of the differential equations.

Structural analysis of the computational properties of QP-DAE systems

Many lumped dynamic models of process systems can be written without approximation in quasi-polynomial differential-algebraic equation (QP-DAE) form. We propose nonlinearity indices for QP-DAEs based on the system invariants. There are global (whole model) and local versions of the indices. The local ones are based on the implicit subsets (essential L-components) of the model. The indices are assessed against simulations of a vaporiser model with adjustable nonlinearity.