Petri net

Alesso, H. P., 1984, On the Relationship of Digraph Matrix Analysis to Petri Net Theory and Fault Trees, LLNL UCRL-90271 Preprint, January. 

Barthomieu, B. and Diaz, M. (1991) Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. Software Eng., 17(3), 259-273. 

I. Koch, B. H. Junker, and M. Heiner. Application of Petri net theory for modeling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics 21(7), 1219 1226 (2005). 

E. Grafahrend Belau, F. Schreiber, M. Heiner, A. Sackmann, B. H. Junker, S. Grunwald, A. Speer, K. Winder, and I. Koch, Modularization of biochemical networks based on classification of Petri net t invariants. BMC Bioinform. 9, 90 (2008). 

Development of a novel Petri net tool for process design selection based on inherent safety assessment method... 

Keywords Petri net, inherent safety, process design. 

Due to the importance of safety in process industries various safety and risk assessment methods have been developed to provide the opportunity of considering safety issues in early design stages. Meanwhile several studies have been undertaken to create appropriate implementation tools for developed assessment methodologies (Palaniappan et al, 2002a, Khan and Amyotte, 2004 and 2005). In this paper, inherent safety method and Petri nets modelling have been selected as the safety assessment and implementation tool, respectively. 

Development of a Novel Petri Net Tool for Process Design Selection Based on Inherent Safety Assessment Method... 

Petri net modelling tool can be considered as a suitable implementation tool for risk assessment due to its flexibility and process simulation ability (Vemez et al., 2004). In addition, different feasible process options can be modelled in a Petri net as a super model, and assessed from safety point of view. A Petri net is a directed bipartite graph including places (drawn as circles) and transitions (drawn as bars). Places contain tokens which are shown as dots. The set of arcs are divided into input and output arcs with an arrowhead on their destinations. A transition is called enabled if all input places have at least the same number of tokens as all its output places. An enabled transition fires by removing tokens from input places to output places. Places, transitions and arcs all can be weighted. Weight is an additional feature that can carry critical attribute of related node through the nets (Gu and Bahri, 2002)... 

In this paper, the first step has been to adapt a type of Petri net to model the process route(s). Initially, the basic route of producing a desired product is chosen. All possible combinations of process units to optimize the production yield and operating conditions of the basic route are considered as new routes. All the possible routes are then put together to create the supemet model of the system. This supemet is divided into various subnets based on the similarities and differences between production alternatives. Similar processing units of different routes build up subnets which are shared between some routes while unlike processing parts may create subnets which are used in one route only. Petri net model is able to automatically create different combinations of these subnets to define all possible process routes. 

The type of Petri net model used in this research is Place Weighted Petri net. Places represent equipment, transitions show starting and finishing of operations and tokens are raw material, semi-finished and finished products. The weights on places indicate Safety-Cost Ratios for equipment. 

The Petri net model of the supemet (Figure 2e) is implemented in Visual C++ and the total number of routes generated by Petri net is found to be 8. The results of Total Safety-Cost Ratio and Penalty factor estimations for these routes are presented in Table 1. 

Figure 2. Petri net model of aclyric acid production routes, a subnet A, b subnet B, c subnet C, d subnet D, e supemet.

Vemes, D., Buchs, D. R., Pierrehumbert, G. E. Bersour, A., 2004, MORM-A Petri net based model for assessing Oh S risks in industrial processes Modeling qualitative aspects. Risk Analysis, 24, 6, 1719-1735. 

Keywords Fault Detection and Isolation, Extended Kalman Filter, Dynamic Hybrid Simulation, Object Differential Petri nets. Distance. 

The last important evolution of PrODHyS is the integration of a dynamic hybrid simulation kernel (Ferret et al., 2004 Olivier et al., 2006, 2007). Indeed, the nature of the studied phenomena involves a rigorous description of the continuous and discrete dynamic. The use of Differential and Algebraic Equations (DAE) systems seems obvious for the description of continuous aspects. Moreover the high sequential aspect of the considered systems justifies the use of Petri nets model. This is why the Object Differential Petri Nets (ODPN) formalism is used to describe the simulation model associated with each component. It combines in the same structure a set of DAE systems and high level Petri nets (defining the legal sequences of commutation between states) and has the ability to detect state and time events. More details about the formalism ODPN can be found in previous papers (Ferret et al., 2004). 

In addition to the approaches described so far, mathematical formalisms hke Petri nets [770], state charts [718], and process algebra [551] have been developed which allow to describe the behavior of concurrent systems in an unambiguous, mathematically sound way, which makes up their suitability for computer-based applications. Petri nets, in particular, are an appropriate basis for work process automation by means of workflow systems [1014] or analysis by means of process simulation (cf. Sect. 5.2). 

Implementations of the languages are typically not based on Petri nets. 

Method definitions are integrated with tool models in environment models. These environment models are enriched with runtime semantics (e.g. Petri-Net extensions) and can get mechanically interpreted by the process engine, when method guidance is demanded. 

Fig. 3.20. Petri-Net based visualization of retrieved trace chunks in the method advisor s user interface... 

The Petri-Net based visualization depicts a sequential, flat view of the trace chunks consisting of the addressed situations and the contexts executed at each situation. The displayed trace chunks are sorted according to their Bayes factor calculated at the final step of the FIST algorithm, and annotated with values of their timestamp, similarity, frequency and Bayes factor. Moreover, the displayed situations that are similar to the current one are highlighted, and their exact similarity to the current situation can be shown by clicking on them. 

Two XML-based integration tools have been built in the area of process management. The first translates AHEAD (cf. Sect. 3.4) process definitions into the petri net dialect used as workflow language by the commercial workflow management tool COSA [615]. The second handles the import of workflow definitions made with WOMS (cf. Sect. 2.4) into AHEAD. Both made use of the XML transformation language XSLT [602]. 

Our research aims at the creation of an organizational simulation model, which is adequate for the participatory design of complex workflows and project structures (see Sect. 3.4) in the process industries. The research approach is based on the C3 notation. The notation s plain graphical basic elements and the consideration of an advanced methodical approach, e.g., for communication analysis, is an adequate foundation for simulation studies by means of high level Petri nets. 

The simulation model was implemented using the Java-based high level Petri net simulator Renew [796, 797]. Renew is a tool for the development and execution of object-oriented Petri nets. It provides synchronous channels and seamless Java integration for easy modeling. 

The entire Petri net model, according to the description of the PA6 design process, is composed of different sub-networks [constituent models). The core element is the Actmty Network, which connects i) the activities, ii) the employees, iii) the work tools or resources, and iv) the information to be processed. These four elements and their behavior are represented in more detail in four sub-networks that use different smaller networks for additional functionalities, such as the import and export of data or the visualization of the simulation progress. 

In C3, there are several possible relations between activities such as sequential activities, concurrent synchronized activities, and activities that model the communication between different organizational units or persons. Within the scope of the activity-driven approach, activities can be represented by places in a Timed Colored Petri Net thus, the tokens visualize the control flow, which again determines the activity sequence. 

Fig. 5.7. Transformation rules from C3 to the Activity Network (Petri net)...

Figure 5.7 shows the C3 example model on the left and the transformed Petri net (implemented in Renew), which represents the Activity Network, on the right. The underlying basic transformation rules are given at the bottom... 

The Activity Pool is an auxiliary network for the administration of the activities in a process. This comprises the import of the activities and their attributes from a database as well as the formatting into a new format adequate for the further processing in the Petri net simulator. All activities are initialized, imported, and managed by the Activity Pool. 

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