# Colored Petri Net Modelling and Evaluation of Drone Inspection Methods for Distribution Networks
###### Abstract  
The UAV industry is developing rapidly and drones are increasingly used for monitoring industrial facilities. When designing such systems, operating companies have to find a system configuration of multiple drones that is near-optimal in terms of cost while achieving the required monitoring quality. Stochastic influences such as failures and maintenance have to be taken into account. Model-based systems engineering supplies tools and methods to solve such problems. This paper presents a method to model and evaluate such UAV systems with coloured Petri nets. It supports a modular view on typical setup elements and different types of UAVs and is based on UAV application standards. The model can be easily adapted to the most popular flight tasks and allows for estimating the monitoring frequency and determining the most appropriate grouping and configuration of UAVs, monitoring schemes, air time and maintenance periods. An important advantage is the ability to consider drone maintenance processes. Thus, the methodology will be useful in the conceptual design phase of UAVs, in monitoring planning, and in the selection of UAVs for specific monitoring tasks. U  
A 2022 2  
Moreover, applications that involve multiple UAVs that operate in a common setup or cooperatively obviously involve additional design choices that are even more complex to decide. This often involves questions of how many UAVs are necessary as minimum equipment to fulfil the required tasks, how many ground stations are necessary and where to place them, which UAV should be assigned to what task, etc. Apart from such strategic system design questions, other decisions have to be made online during run time, similar to scheduling or flight path issues and decisions about whether a UAV should continue its task or return to a base. These are classic optimization questions in systems design under uncertainty, which should be supported by models, evaluation methods, and software tools. In this paper, we propose a method for modelling and evaluating multidrone inspection systems for distribution networks. Such networks can include oil and gas pipelines, electricity distribution networks, or even roads. We consider as UAVs fixed-wing aircraft (planes), vertical take-off and landing (VTOL) aircraft, such as multirotor systems (quadcopters or multicopters) and convertiplanes, which are combinations of planes and multicopters. Models for such systems should be easy to understand and thus visual while also being capable enough to cover the necessary object types and attributes as well as their behaviour. For these reasons, we chose stochastic coloured Petri nets [6] as the basic description. Petri nets allow for modelling systems containing parallel running processes naturally. They are represented as bipartite graphs with directed arcs and visualize systems and processes. The behaviour of a system using drones is influenced by many stochastic factors, such as weather, the probability of breakdown, the need of maintenance and others. Stochastic Petri nets [7] allow us to take such factors into account and simulate the nature of the model as closely as necessary to reality. Abstracting away from task-specific algorithms, almost any drone mission comes down to the most efficient flight path. For the type of networks to be monitored that we consider here, routes have to follow the network connections and do not have to cover areas, i.e., linear objects. Consequently, mission performance is most influenced by speed and range. The actual scientific task, the solution of which is presented in this paper, is to develop and implement a unified model using Petri nets to evaluate the feasibility of a particular drone model for monitoring linear objects. The described modelling method will allow for achieving the required level of abstraction. A modular system will be created that can be adapted to many typical tasks.