## 5 Discussion: Industry 5.0 Framework and Complex Systems Simulations
### Industry 5.0 Workflow Design and Process Simulation
* _Actuator M3_: actuator relaying the sensing and actuation processing of _Machine 3_. * _Power Meter_M3_: power meter reading electrical power of _Machine 3_. * _Product_ (P): final product of the whole production line (output of _Machine 3_). * _Image Vision Product_: camera implementing image vision algorithms for detecting defects of in the final product;
* _Big Data_: internal big data collecting all production data (data from the whole production line). * _AI Edge Computing_: edge computing nodes processing all data collected into the internal big data system by AI algorithms; the AI algorithms are optimized by quantum calculus (_Quantum Computer_). * _Quantum Computer_: the quantum computer processing data collected in _Big Data_ and _External Big Data_. * _External Big Data_: dataset collected from the cloud by other third parties related to this specific production (external backend systems). * _Actuator Engine L1_: engine synchronizing all the actuators: _Actuator M1_, _Actuator R1_, _Actuator M2_, _Actuator M3_ (with synchronization supported by the AI algorithms). The complex network of Figure 3b is characterized by the parameters listed in Table 6.  
Figure 3: (**a**) Simplified Industry 5.0 framework differentiating three main levels of the processing of a manufacturing workpiece: production line level, sensing and actuation level, and Industry 5.0 level. (**b**) _Cytoscape_ complex model simulating the Industry 5.0 framework. The complexity of the operations of the network of Figure 3b can be simplified by the workflow of Figure 4, which sketches all the operations of the simulated Industry 5.0 framework and facilitates comprehension of the information flux trajectories. The workflow is sketched by a standard BPMN (standard ISO/IEC 19510:2013 [155]), typically adopted for process mapping in industrial applications such as predictive maintenance [156] and security [157]. The BPMN workflow of the analyzed model is structured into three pools (representing the three levels indicated in Figure 3a), and highlighted in red are the data processes of the Industry 5.0 level, which upgraded production processes. The BPMNs model integrating AI decision-making procedures are named BPMN Process Mining (PM) models. The adopted BPMN tool was illustrated with the open-source program, _draw.io_[158]. \ \begin{table}
\\begin{tabular}{c c} \\hline \\hline
**Parameter** & **Value** \\\\ \\hline Number of nodes & 28 \\\\ Number of edges & 51 \\\\ Avg. number of neighbors & 3.643 \\\\ Network diameter & 5 \\\\ Network radius & 3 \\\\ Characteristic path length & 2.370 \\\\ Clustering coefficient & 0.215 \\\\ Network density & 0.135 \\\\ Network heterogeneity & 0.645 \\\\ Network centralization & 0.413 \\\\ Analysis time \\(t\\) (s) & 0.038 \\\\ \\hline \\hline \\end{tabular}
\\end{table} 
Table 6: Summary statistics concerning the parameters of the complex network of Figure 3b. Figure 4: BPMN process modelling a simplification of the complex network of Figure 3b. Figure 5 illustrates the result of the simulation of the complex Industry 5.0 network of Figure 3b: the calculation of the diffusion heat parameters of the whole information flux is summarized by the heat map in Figure 5. In this map, it is possible to observe that the elements that majorly upgrade the industrial production processes are: _Big Data, Actuator Engine L1, Ai Edge Computing, and Quantum Computer_, which are all the elements highlighted in red in the BPMN workflow of Figure 4, which confirms these nodes belong to the Industry 5.0 level (upgrading level). The simulation was performed by the open source _Cytoscape_ tool [159]. The BPMN approach is then adopted to \"explode\" in detail the processes involving robot/machine control, predictive maintenance, and quality assessment.