A twostage optimization method for unmanned aerial vehicle inspection of an oil and gas pipeline network
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Abstract
Oil and gas pipeline networks are a key link in the coordinated development of oil and gas both upstream and downstream. To improve the reliability and safety of the oil and gas pipeline network, inspections are implemented to minimize the risk of leakage, spill and theft, as well as documenting actual incidents. In recent years, unmanned aerial vehicles have been recognized as a promising option for inspection due to their high efficiency. However, the integrated optimization of unmanned aerial vehicle inspection for oil and gas pipeline networks, including physical feasibility, the performance of mission, cooperation, realtime implementation and threedimensional (3D) space, is a strategic problem due to its largescale, complexity as well as the need for efficiency. In this work, a novel mixedinteger nonlinear programming model is proposed that takes into account the constraints of the mission scenario and the safety performance of unmanned aerial vehicles. To minimize the total length of the inspection path, the model is solved by a twostage solution method. Finally, a virtual pipeline network and a practical pipeline network are set as two examples to demonstrate the performance of the optimization schemes. Moreover, compared with the traditional genetic algorithm and simulated annealing algorithm, the selfadaptive genetic simulated annealing algorithm proposed in this paper provides strong stability.
Keywords
Pipeline network Unmanned aerial vehicle inspection Mixedinteger nonlinear programming Twostage solutionAbbreviations
 UAV
Unmanned aerial vehicle
 MINLP
Mixedinteger nonlinear programming
 GA
Genetic algorithm
 SA
Simulated annealing algorithm
 AGASA
Selfadaptive genetic simulated annealing algorithm
 PSO
Particle swarm optimization
 ACO
Ant colony optimization
List of symbols
 \(F\)
Total length of inspection path, m
 \(\alpha\)
Conversion coefficient of distance and time
 \(I = \left\{ {0,1, \ldots ,N} \right\}\)
Number of inspection nodes including the start node
 \(H = \left\{ {1, \ldots ,N} \right\}\)
Number of inspection nodes without start node
 \(L_{i,h}\)
Distance between inspection node \(i\) and node \(h\), m
 \(B_{i,h,k}\)
(A binary variable): If the inspection mission from node \(i\) to node \(h\) is performed by UAV \(k\), it is 1; otherwise it is 0
 \(R_{i,k}\)
(A binary variable): If node \(i\) is inspected by UAV \(k\), it is 1; otherwise it is 0
 \(\theta\)
Maximum turning angle of the UAV
 \(E_{k}\)
Endurance of UAV \(k\), h
 \(d\)
Minimum distance between the UAVs, m
 \(d_{\text{s}}\)
Minimum safe distance between the UAVs, m
 \(x_{0} ,y_{0}\)
Coordinate of the UAV base, m
 \(x_{i} ,y_{i}\)
Coordinate of node \(i\), m
 \(L_{m}\)
Chromosome of individual \(m\) in the species
 \(P\left( {L_{m} } \right)\)
Probability of selection of an individual
 \(p_{m}\)
Probability of mutation
 \(T_{0}\)
Initial temperature, °C
 \(w\)
Temperature update coefficient
 \(M\)
Size of population
 \(G_{\hbox{max} }\)
Maximum evolution generation
 \(T_{\text{end}}\)
Termination temperature, °C
1 Introduction
Oil and gas pipelines have features of high pressure and flammability, sometimes accompanied by leakage, fire and explosion (Zhang et al. 2018a). Accidents could result in great loss of lives and high economic costs, so it is of great significance to inspect the pipeline regularly to minimize the risks. In recent years, unmanned aerial vehicles (UAV) have attracted much attention due to the low cost, high efficiency as well as safety. There has been extensive research regarding the civil UAV applications for pipeline inspection (Tu and Yang 2003; Patle et al. 2018; Reddy et al. 2011; Sedighi et al. 2004; Tsai et al. 2011; Hu and Yang 2004). UAVs can carry relevant detection equipment (Gómez and Green 2017) for different targets, including pipeline infrastructure, leak detection and pipeline environmental condition monitoring. UAV inspection paths of pipeline networks should be optimized to reduce manpower and to use material resources effectively. Previous research on optimization of inspection path focused on power grids, railway networks (Zhang et al. 2018b) and other networks. However, oil and gas pipeline network topology is more complicated (Wang et al. 2018a, b; Zhang et al. 2017b, d) and difficult to work out. Even though previous algorithms are applied, the optimal solution cannot be obtained in many cases.
Currently, there are three approaches to plan the inspection path for pipeline networks. The first one is the graphbased algorithm, such as the Voronoi diagram, the probabilistic roadmap and the Dijkstra’s algorithm. The Voronoi diagram has been widely used in robot path planning (Bhattacharya and Gavrilova 2007; Candeloro et al. 2017; Chen and Chen 2014; Garrido et al. 2006). The inspection area is divided into points and these points are used to generate the Voronoi diagram. Then the Voronoi diagram divides the inspection area into many convex polygons which contain only one inspection point. When the graph contains the initial position and destination position, the optimal inspection path can be obtained. A probabilistic roadmap (Akbaripour and Masehian 2017; Geraerts and Overmars 2006; Wang and Cai 2018) is to convert the continuous space into discrete space and adopts a search algorithm to find the path on the roadmap to improve search efficiency. The Dijkstra’s algorithm is one of the shortest path algorithms from one vertex to the rest of the vertices, solving the shortest path problem in the directed graph. The main feature of this algorithm is to extend the outer layer centering on the starting point until it reaches the end. Chen et al. (2015) proposed a multiobjective optimization model for a wireless sensor network mobile agent problem, and the improved Dijkstra’s algorithm was applied to solve the model. The optimal mobile agent path between any two nodes could be obtained according to the network environment. However, it is very difficult to combine the motion constraints of a UAV with the graphbased algorithm, and the number of sampling points also has a great effect on the path search results.
The second approach is the classical heuristic search algorithms (Gammell et al. 2015; Li et al. 2017; Yu and LaValle 2016), such as the A* algorithm and Sparse A* Search (SAS). The A* algorithm was first described by Hart et al. (1968) and determined the optimal path from an initial node to a target node which evaluated each search position in the state space. In order to reduce the search space and realize the realtime path planning for the UAV (Szczerba et al. 2000), the constraints of the drone flight process are taken into account. However, the A* algorithm and the SAS algorithm can only plan the path when all environmental information is known. What is worse, the search space will be larger with an increase in the number of inspection points, and the computation time of the classical heuristic search algorithm will increase exponentially.
The third approach is the modern heuristic search algorithm that mainly includes a genetic algorithm (GA) (Tu and Yang 2003; Nazarahari et al. 2019; Patle, et al. 2018; Sedighi et al. 2004; Tsai, et al. 2011; Hu and Yang 2004), particle swarm optimization (PSO) (Zhang et al. 2017c) and an ant colony optimization (ACO) (Zhang et al. 2017a). Shen et al. (2016) developed a novel method for the path planning for an electricity distribution network patrol. The vehicle routing problem (VRP) model was established, and the improved ACO was adopted to obtain the optimum patrol path. In this way, the patrol programs became more scientific, reasonable and efficient. Guo et al. (2017) established an optimization model of the logistics network to minimize the overall cost of the circulationtype distribution vehicle routing, and a genetic algorithm and a particle swarm optimization algorithm are implemented to solve the model. However, the proposed optimization issue is so complex that the computation can easily to fall into a local optimum in the evolutionary process, which will lead to premature convergence and miss the optimal solution.
Given that oil and gas pipeline networks are more complex than electricity distribution networks, the selfadaptive genetic simulated annealing algorithm (AGASA) is introduced in this paper to improve the solution quality and efficiency of path planning. Moreover, based on the inspection demand of the pipeline network, taking the minimization of the total length of the inspection path as the objective, and through the establishment of constraints including the mission scenario and the safety performance of UAVs, a mixedinteger nonlinear programming (MINLP) model is proposed. By adopting the twostage solution methodology, the optimal inspection path is obtained.
2 Methodology
2.1 Preliminaries
In our path planner, all of the candidate routes are evaluated in the workspace. The pipelines are usually distributed linearly, so the pipeline is divided into multiple nodes and the twodimensional coordinates of these nodes are identified as deterministic parameters in the model. It should be noted that the flight path consists of straightline segments, e.g., a sequence of segments connecting the way nodes from the starting node to the goal node, and the starting node and goal node are the same.
2.2 Objective function
2.3 Constraints
3 Twostage solution methodology
In this paper, the twostage solution methodology is proposed to optimize the UAV inspection path. In the first stage, the pipeline is divided into some nodes according to the vision of UAV. In the second stage, the AGASA is adopted to solve the model and obtain the optimal patrol path for an oil and gas pipeline network.
3.1 Firststage solution
3.2 Secondstage solution
Genetic algorithm (GA) can search for the global optimal solution easily, but the local search optimization ability is poor and premature convergence could take place easily. As a stochastic optimization technique that simulates the annealing process of heating and melting metals proposed by Metropolis, the simulated annealing algorithm (SA) is able to get rid of the local optimal solution and inhibit the precocity of a genetic algorithm, but it evolves slowly. In this section, the global parallel search ability of GA and the strong local serial search ability of SA are combined. By introducing heuristic rules in the process of generating the initial population and crossover operation, the optimal solution is expected to be found.
3.2.1 Selfadaptive genetic algorithm
 (1)
Generation of the initial population
 (2)
Fitness function
 (3)
Selection of genetic operator
 (A)
Selection operator
 (1)
Roulette wheel selection

Summing up the fitness function values of all individuals in the population and getting the \(f_{\text{total}} ;\)

A random number \(f_{\text{random}}\) is generated in the interval \(\left[ {0,f_{\text{total}} } \right];\)

The fitness function values are incremented one by one starting from the first individual. The chromosome \(L_{m}\) will be chosen if \(q_{m} \ge f_{\text{random}} ;\)
 (2)
Elitist model

Identify the individuals with the highest fitness value \(f_{\text{best}}^{m}\) and the lowest fitness value \(f_{\text{worst}}^{m}\) in the current population.

If \(f_{\text{best}}^{m} > f_{\text{best}}^{\text{all}}\), take the individual with the highest fitness value \(f_{\text{best}}^{m}\) as the best individuals in all populations, i.e., \(f_{\text{best}}^{\text{all}} = f_{\text{best}}^{m} .\)

Replace the individual with the lowest fitness value \(f_{\text{worst}}^{m}\) in the current population with the best individuals \(f_{\text{best}}^{m}\) in all populations, i.e., \(f_{\text{worst}}^{m} = f_{\text{best}}^{\text{all}} .\)
 (B)
Crossover
 (1)
Set the number of intersections to \(W\) and select the intersection range \(p \in [p,p + W]\) randomly. Meanwhile, set \(r = 1.\)
 (2)
Search the position of the intersection in the individuals \(C_{1}\) and \(C_{2}\), and record it as \(x\) and \(y.\)
 (3)
Switch the position of individuals \(C_{1} \left( {1,p} \right)\) and \(C_{2} \left( {1,p} \right).\)
 (4)
Switch the position of individuals \(C_{1} \left( {1,x} \right)\) and \(C_{2} \left( {1,y} \right)\), \(r = r + 1.\)
 (5)
If \(r < W\), go back to Step 2, otherwise, the crossover operation is finished.
 (C)
Mutation
 (1)
A random mutation probability \(p_{m}\) is generated in the interval \(\left[ {0,1} \right].\)
 (2)
A random two elements on the chromosome \(L_{m}\) will switch position if \(0 \le p_{m} \le 0.5\), otherwise, a random three elements on the chromosome \(L_{m}\) will switch position if \(0.5 < p_{m} \le 1.\)
 (3)
The new individuals \(F_{1}\) and \(F_{2}\) are generated after a mutation operation.
3.2.2 Simulated annealing algorithm
 (1)
Initial temperature
 (2)
Temperature update function
 (3)
Acceptance function
3.2.3 Path planning steps
 (1)
Initialize a group of paths with the size of \(M\) and set the parameters of the initial temperature \(T_{0}\), maximum evolution generations \(G_{\hbox{max} }\), and termination temperature \(T_{\text{end}} .\)
 (2)
Initialize the genetic algebra counter \(g = 0\) and evaluate the fitness of each path.
 (3)
According to the crossover probability and mutation probability, the individuals selected from each subpopulation to undergo the operations of selection, crossover as well as mutation are decided, then the fitness value of each new individual is calculated.
 (4)
Decide whether to replace the old individual with the new individual according to the Metropolis criterion.
 (5)
If \(g < G_{\text{max}}\), \(g = g + 1\), go back to Step 3, Otherwise, go to Step 6.
 (6)
If \(T < T_{\text{end}}\), update the temperature and go back to Step 2, otherwise, the optimal or nearoptimal routes are found.
4 Computational studies
The parameters and configuration of UAV
Flying altitude  Low (< 100 m) 
Velocity  5–15 km/h 
Endurance  5 h 
Payload  < 7 kg 
Platform  Fixed wing 
Sensor  Optical or IR camera, LIDAR 
4.1 Example 1
Influence of population size on calculation results
Population size  Best fitness value 

50  19,811 
100  19,787 
150  18,937 
200  18,891 
250  18,696 
300  17,819 
350  16,250 
400  16,250 
450  16,250 
500  16,250 
Influence of temperature update coefficient on calculation results
Temperature update coefficient  Best fitness value 

0.90  18,932 
0.91  18,067 
0.92  17,406 
0.93  16,858 
0.94  16,826 
0.95  16,250 
0.96  16,250 
0.97  16,250 
0.98  16,250 
0.99  16,250 
4.2 Example 2
During the generation of the initial solution and crossover operation, the nodes on the pipeline segment remain unchanged, which means that the size of the model is largely related to the number of segments divided. For the sake of simplification, pipelines of less than 1.5 km in length will not be divided and considered as segments directly. In contrast, pipelines with a length greater than 1.5 km will be divided into segments at a distance of 1.5 km. This can greatly reduce the model scale and accelerate the convergence speed, thereby finding the optimal solution quickly.
5 Conclusions
In this paper, a new inspection path optimization method for oil and gas pipeline networks is proposed. A mixedinteger nonlinear programming model is established by setting the minimum length of the inspection path as the objective function, which also takes the mission scenario and the safety performance of UAVs into account. In model solving part, a twostage solution methodology is proposed. In the first stage, the pipeline is divided into some nodes according to the vision capability of the UAV. In the second stage, the AGASA that introduces heuristic rules is adopted to solve the model. Finally, three algorithms (GA, SA and AGASA) are employed for calculation, and the results show that the AGASA proposed in this paper has great stability and convergence. What is more, it can be applied to the inspection path planning optimization problem of most oil and gas pipeline networks. This paper considered the importance of each inspection node is the same, ignoring the difference in the inspection of highleakage danger zones, densely populated areas and noman’s land. Therefore, further research can add the requirement for the number of inspection times in each area and solve the optimization problem of inspection path planning.
Notes
Acknowledgements
This work was part of the Program of “Study on Optimization and Supplyside Reliability of Oil Product Supply Chain Logistics System” funded under the National Natural Science Foundation of China, Grant Number 51874325. The authors are grateful to all study participants.
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