## 4 Materials and Methods
### Extenics-Based Identification Primitive Modeling of Coil Manufacturing Process Information
#### 4.4.1 All Elements Information Fusion Based on Extensible Petri Net Model  
By deeply integrating identification resolution code, expandable information element modeling, and Petri nets, the coil manufacturing process is modeled and simulated to achieve high-fidelity modeling of process information propagation paths and process traceability. The identification resolution expandable Petri net for coil production process traceability can be considered as a septuple composed of the finite sets of places \(P\) and transitions \(T\), the directed arcs set \(F\), the expandable element sets (\(Q_{m}\), \(Q_{a}\), \(Q_{r}\)), and the mapping set f as follows:  
\[\sum\
olimits_{\text{ Petri}}=\{P,T,F,Q_{m},Q_{a},Q_{r},f\} \tag{5}\]  
where \(P\) = {\(P_{1}\), \(P_{2}\), \(\ldots\), \(P_{i}\)} represents all the variations of information surrounding the coil product manufacturing process. \(T\) = {\(t_{1}\), \(t_{2}\), \(\ldots\), \(t_{i}\)} represents the processes where changes occur in the position, quality, and form of the coil product. \(F\subseteq(P\times T)\cup(T\times P)\) represents the directed arcs connecting \(P\) and \(T\). \(Q_{m}\), \(Q_{a}\), and \(Q_{r}\), respectively, denote the information resource entity elements, process event elements, and process relationship elements revolving around coil product manufacturing. \(f\) = {\(f\),\(f\),\(f\),\(f\)},\(f\),\(f\),\(f\),\(f\),\(f\) are mappings of place \(P\) to element \(Q_{m}\), transition \(T\) to element \(Q_{a}\), and directed arc \(F\) to element \(Q_{r}\), respectively. The identification-resolving expandable Petri net for traceability of coil production processes simulates and analyzes system behavior through the interaction of four basic elements: places \(P\), transitions \(T\), directed arcs \(F\), and token. \(P\) represents the system's states, depicted by circles; transitions represent events in the system, depicted by short rectangles; directed arcs define the causal relationships between states and events, depicted by arrows; while tokens indicate whether states satisfy the transition conditions. The specific symbols are illustrated in Figure 5.  
The transformation process of coil production involves four possible forms: sequence, selection, parallel, and loop. In the modeling process of identification-resolving expandable Petri nets, these forms can be achieved by adjusting the connections between transitions and places. Sequential structure uses a concatenation between places and transitions to represent the sequential execution of tasks. The selection structure employs multiple output places to represent different branching paths, thus implementing decision-making functionality. The parallel structure reflects the simultaneous execution of multiple tasks through branching transitions. The loop structure simulates repetitive activities by using closed-loop directed arcs returning to input places. The representations of these four relationships and their corresponding expandable transformations in Petri nets are illustrated in Table 7:  
Figure 5: Related Symbols of Petri Net. Based on the modeling method described above, a dynamic system model of the coil product manufacturing process is constructed by closely integrating the business flow, data flow, and information flow of coil production. This formalizes descriptions of the physical-temporal processes, event response mechanisms, unit behavior rules, operational transformation logic, etc., in coil manufacturing. This, in turn, provides a theoretical foundation for information traceability in coil production. The identification resolution and expandable Petri net construction process for transformer coil production involve the following three steps:  
1. Define the sets of places and transitions of the system model based on the technological processes and business operational flows of coil production. 2.