# Improving the Strategy of Maintaining Offshore Wind Turbines through Petri Net Modelling
## 3 A Brief Review of Petri Net-Based Modelling Technology  
To facilitate understanding of the PN models developed in this paper, the basics of the PN modelling method are briefly reviewed below. As shown in Figure 1, the bipartite graph of a PN model consists of four basic types of symbols, i.e., circles, rectangles, arrows, and tokens. The circles represent places, which are conditions or states of the system, such as component failure. In this paper, coloured patterns are used in order to differentiate between different places. The condition place, marked with yellow-horizontal-lines in the model, means that the model will perform predefined actions if the conditions in the place are met. The place filled by red-vertical-lines means that the simulation will be ended if a token is placed in it. Rectangles represent the transitions, which define the actions or events that cause the change in condition or state. It should be noted that when the time for completing the transition is zero, the rectangle is filled black. Otherwise, it will be blank. Arcs in the figure are used to set up the connections between places and transitions. To enhance the functions of the arcs, a slash and a number, n, next to the slash are used to represent a combination of n single arcs. In this case, it is said that the arc has weight n. When the weight is one, the slash will be absent from the arc for simplicity. In the PN models, small solid black circles are used to represent tokens in the places, which carry the information in the PNs. The dashed arcs mean the link between the connected places and transitions are conditional. The tokens will move via transitions once the enabling condition is satisfied, which offers the unique dynamic properties of the PNs. The transition will be enabled when the number of tokens contained in every input place is equal to, or greater than, the corresponding weight of the arc. The arc with a small solid circle on one end is known as inhibitor arc, which only links places to transitions. If the number of tokens in the place connecting the inhibitor arc is greater than or equal to the arc weight, the transition on the other end of the arc cannot fire even if the transition is already enabled. The marking of a PN, given by the position of the tokens in the net, at any particular time gives the instantaneous state of the system being modelled.  
To ease understanding, Figure 2 shows an example of the PN model, in which the movement of tokens in the places occurs after a delay, illustrating a transition through the net. In the figure, the net has two input places and one output place connected by a timed transition indicated by a blank rectangle with a time delay \(t\). There are two tokens in each input place. The two input places are connected by arcs of weight 1 and weight 2. The output place is connected by an arc of weight 1. As shown in the net on the left of the figure, the transition is enabled, hence after the delay of time t associated with the transition, the number of tokens indicated by the arc weights will be removed from the input places and  
Figure 1: Different symbols used in the Petri net (PN) models.  
placed in the output place. By following the rules outlined above, one token is taken out of the top input place and two from the lower and one token is placed in the output place as shown in the net on the right of the figure.