Pipe network robot path and data station deployment joint optimization method

Abstract

The pipe network robot path and data station deployment joint optimization method disclosed by the application belongs to the technical field of smart city infrastructure operation and maintenance, and specifically comprises the following steps: firstly, a pipe network-robot-data station system model is constructed, and the pipe network topology is mapped into an undirected graph; secondly, combined with EPANET hydraulic simulation data, the pipe monitoring time is calculated under the conditions of downstream flow and upstream flow, and a hybrid graph with time weight is constructed; then, a weighted optimization mathematical model with the double objectives of minimizing the maximum monitoring time and minimizing the maximum data delay is established, and constraint conditions such as pipe full coverage and robot collision-free are defined; finally, the NSGA-II algorithm is used to generate a Pareto frontier, and the best compromise scheme is selected through weight distribution. The application solves the technical problems that the robot path planning and data station deployment lack cooperation in the existing pipe network monitoring technology, and the pipe network hydraulic characteristics are not coupled, so that the monitoring time and data delay are difficult to consider.

Description

Technical Field

[0001] This invention belongs to the field of smart city infrastructure operation and maintenance technology, specifically involving a method for joint optimization of pipeline robot paths and data station deployment. Background Technology

[0002] As a core component of smart city infrastructure, urban pipe networks encompass critical systems such as water supply, drainage, gas, and heating. Real-time monitoring and efficient operation and maintenance of these networks directly impact the stable functioning of the city. With the acceleration of urbanization, pipe network topologies are becoming increasingly complex and their coverage area is continuously expanding, placing stringent demands on the precision, intelligence, and efficiency of monitoring technologies.

[0003] Existing pipeline monitoring technologies are mainly divided into two categories: one is a monitoring scheme based on fixed sensors, which suffers from drawbacks such as high deployment costs, limited coverage, and insufficient fault location accuracy, making it difficult to adapt to the full-area monitoring needs of complex pipeline networks; the other is a scheme combining manual inspection and mobile robots, which, while improving coverage flexibility, still has significant technical bottlenecks: First, it fails to achieve joint optimization of robot path planning and data station deployment, often adopting a step-by-step decision-making mode of planning the path first and then deploying the data station, leading to an irreconcilable contradiction between the imbalance of monitoring task load and data transmission delay, thus limiting the overall system performance; Second, it ignores the impact of pipeline hydraulic characteristics on robot monitoring efficiency, failing to distinguish the difference in effective robot travel speed under downstream and upstream conditions, resulting in deviations in monitoring time calculations, which in turn affects the accuracy of path planning; Third, the multi-objective optimization model design is imperfect, lacking collaborative constraints on the dual objectives of minimizing the maximum monitoring time and minimizing the maximum data delay, and failing to establish a scientific weight allocation and compromise solution mechanism; Fourth, the collaborative constraints on robot path conflict avoidance and data station transmission coverage are insufficient, easily leading to monitoring blind spots or data transmission interruptions.

[0004] Furthermore, existing multi-objective optimization algorithms have limitations in the application of pipeline network monitoring scenarios. They fail to generate Pareto fronts through efficient population iteration and non-dominated sorting, making it difficult to select the optimal solution that balances monitoring efficiency and data real-time performance. Therefore, developing a monitoring method that integrates pipeline network hydraulic characteristics, jointly optimizes robot paths and data station deployment, and possesses a scientific multi-objective solution mechanism has become a key technological requirement for addressing current pain points in pipeline network monitoring and promoting the intelligent upgrade of urban pipeline network operation and maintenance. Summary of the Invention

[0005] The purpose of this invention is to provide a joint optimization method for pipeline robot path planning and data station deployment, which solves the technical problems in existing pipeline monitoring technologies where robot path planning and data station deployment lack coordination and are not coupled with the hydraulic characteristics of the pipeline network, making it difficult to balance monitoring time and data delay.

[0006] The technical solution adopted in this invention is a joint optimization method for pipeline robot path and data station deployment, the specific steps of which are as follows: S1. Construct a pipeline-robot-data station system model: Map small areas in the pipeline network as nodes, and map the pipes connecting two small areas as edges to form an undirected graph; The system is configured with multiple autonomous monitoring robots that can move along the pipes, and multiple data stations deployed at the nodes to receive data collected by the robots; S2. Construct a hybrid graph with monitoring time weights: Obtain flow velocity and direction data in each pipe through hydraulic simulation, combine with the robot's constant travel speed, distinguish between downstream and upstream monitoring conditions, calculate the monitoring time of each pipe segment under the corresponding condition, and assign the monitoring time as a weight to the corresponding edge of the undirected graph to form a hybrid graph. S3. Establish a joint optimization mathematical model: Define the minimum monitoring time as the maximum time taken for all robots to complete their respective monitoring paths, and define the minimum data delay as the maximum time taken for all data stations to receive data from the corresponding robots; with the minimum weighted sum of the two indicators as the optimization objective, establish a mathematical model that includes constraints such as full pipeline coverage and no robot path collision. S4. Solving for the optimal solution: The NSGA-II algorithm is used to solve the above model. Pareto fronts are generated through population iteration. Then, based on the weights set according to actual needs, the best compromise solution for robot path planning and data station deployment is selected from the Pareto fronts.

[0007] The invention is further characterized by: The undirected graphs in S1 include: Each node, i.e., in the pipeline network A small area; Each edge, that is, the edge of the pipeline network Section of pipeline; A number of robots; A number of data stations; Furthermore, the absolute value of the robot's constant travel speed is greater than the absolute value of the maximum flow velocity inside the pipe.

[0008] The hydraulic simulation method in S2 is hydraulic simulation software; the input parameters include the diameter, length, and connection position of the pipe, as well as the water demand and elevation information of the nodes; the output parameters include the flow velocity, flow direction, and flow rate data in the pipe.

[0009] The hydraulic simulation software is specifically EPANET; The monitoring time for pipelines is calculated using the following formula:

[0010] In the formula: For monitoring the flow in or out of the pipeline; The length of the pipe; The robot's constant speed; The velocity in the pipe is represented by a minus sign for downstream flow and a plus sign for upstream flow.

[0011] The minimum monitoring time in S3 is calculated using the following formula:

[0012] In the formula: to These represent the monitoring path times for the 1st to the Kth robots, respectively. The minimum data latency in S3 is calculated using the following formula:

[0013] In the formula: to These represent the time taken for the 1st to the Kth robots to transmit data to their respective data stations.

[0014] The mathematical model in S3 is as follows:

[0015] In the formula: This is the weighted total time; The weight for the minimum monitoring time; The weight for minimizing data latency; The constraints also include: ,and, and The range of values ​​is .

[0016] The solution process of the NSGA-II algorithm in S4 includes: S4.1 Set algorithm parameters, including population size, maximum number of iterations, crossover probability, and mutation probability; S4.2 Randomly generate an initial parent population, and encode a complete solution containing all robot paths and all data station deployment locations for each individual, while satisfying the constraints of full pipeline coverage and collision-free robot paths; S4.3 Calculate the fitness of the parent population individuals, select the parent generation through the binary tournament selection method, perform three-level crossover operation and path-aware mutation operation, generate the offspring population and calculate the fitness; S4.4 Merge the parent and offspring populations, perform fast non-dominated sorting and crowding distance calculation, and select the best individuals to form the next generation population; S4.5 Repeat the iterations until the maximum number of iterations is reached to obtain the Pareto front.

[0017] The three-layer cross-operation includes robot path allocation cross-operation, data station deployment location cross-operation, and path and deployment location collaborative cross-operation; the path-aware mutation operation verifies the constraint satisfaction of the solution in real time after mutation to avoid invalid solutions.

[0018] The optimal compromise in S4 is to select the solution that minimizes the weighted total time from the Pareto front based on the preset weights for minimum monitoring time and minimum data delay.

[0019] The beneficial effects of this invention are: This invention integrates EPANET hydraulic simulation data to accurately distinguish the effective travel speed of the robot under downstream and upstream conditions, and establishes a monitoring time calculation model based on the actual pipeline flow state. This avoids the path planning deviation caused by ignoring hydraulic characteristics in traditional methods, making the robot path allocation more in line with the actual working conditions, significantly reducing the monitoring time prediction error, and greatly improving the planning accuracy and feasibility. This invention establishes a mathematical model that includes dual-objective weighted optimization, clarifies core conditions such as full pipeline coverage, collision-free robot operation, and weight constraints, and through a flexible weight allocation mechanism, it can dynamically balance monitoring efficiency and data real-time performance according to different scenario requirements such as emergency monitoring and routine operation and maintenance, adapting to diverse pipeline monitoring needs and making it more practical. This invention completely eliminates the risk of collisions with monitoring blind spots by coordinating the design of collision-free robot paths and data station transmission coverage, while ensuring the continuity and stability of data transmission. Combined with mechanisms such as path perception variation and post-crossing constraint verification, it further ensures the effectiveness and feasibility of the optimization scheme, and significantly enhances the safety and reliability of system operation and maintenance. This invention employs the NSGA-II algorithm for multi-objective solutions. Through fast non-dominated sorting and crowding distance calculation, it efficiently generates the Pareto front, ensuring the diversity and convergence of solutions. The weight-based trade-off screening mechanism can quickly locate the optimal solution that takes into account multiple objectives, avoiding the defects of traditional algorithms getting stuck in local optima. The solution efficiency and solution quality are both at the leading level in the industry. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the method for joint optimization of pipeline robot path and data station deployment according to the present invention. Figure 2 This is a system model diagram of the joint optimization method for pipeline robot path and data station deployment of the present invention; Figure 3 This is a flowchart of the NSGA-II algorithm in the joint optimization method for pipeline robot path and data station deployment of the present invention; Figure 4 This is a schematic diagram of the optimization results of robot path and data station deployment in the joint optimization method of pipeline robot path and data station deployment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] Example 1 like Figure 1 and Figure 3 As shown in this embodiment, the joint optimization method for pipeline robot path and data station deployment includes the following specific steps: S1. Constructing a Pipeline-Robot-Data Station System Model: Based on the actual topology of the urban pipeline network, functionally independent small areas within the network (such as the pipeline coverage area corresponding to residential areas and commercial streets) are treated as nodes. The physical pipelines connecting two small areas and used for transmitting fluids (water, gas, etc.) are treated as edges. An undirected graph is formed through topological mapping, which fully reflects the connection relationships of the pipeline network. The autonomous monitoring robot configured in this system is an active device that provides continuous power, enabling it to move autonomously along the pipeline and collect pipeline status data (such as pressure, leakage, etc.). The data station is a fixed deployment device installed at the nodes of the undirected graph, possessing data receiving and storage functions, used to receive monitoring data transmitted by the robot in real time. S2. Constructing a hybrid graph with monitoring time weights: First, the actual flow state of the pipe network is simulated using hydraulic simulation methods to obtain the flow velocity and direction (with and against the main flow direction) data in each pipe. It is known that the robot maintains a constant speed during monitoring (except when receiving a stop command). Combined with the flow direction in the pipe, two monitoring conditions can be distinguished: with-flow (the robot's movement direction is consistent with the fluid flow direction) and against-flow (the robot's movement direction is opposite to the fluid flow direction). Based on the actual length of the pipe and the effective movement speed (the combined speed of the robot's speed and the flow velocity in the pipe) under the corresponding conditions, the monitoring time for each pipe segment (i.e., the total time it takes for the robot to move from one end of the pipe to the other and complete the monitoring) is calculated. This monitoring time is then used as a weight to assign to the corresponding edge in the undirected graph, forming a hybrid graph with time weights. This hybrid graph provides basic data support for subsequent path planning and optimization modeling. S3. Establish a joint optimization mathematical model: Define the minimum monitoring time as the maximum value among the times required for each robot to complete its assigned monitoring path (i.e., ensuring that the longest time for all robots to complete their tasks is minimized, achieving task load balancing); define the minimum data latency as the maximum value among the times required for all data stations to receive data transmitted by their corresponding robots (i.e., ensuring that the longest time for all monitoring data to be uploaded is minimized, improving data real-time performance); take the weighted sum of these two indicators as the core optimization objective, and establish two key constraints: first, all pipelines must be covered by the monitoring path of at least one robot (ensuring no monitoring omissions); second, the monitoring paths of any two robots at the same time do not overlap spatially (avoiding robot collisions), forming a complete joint optimization mathematical model; S4. Solving for the optimal solution: The second generation of the non-dominated sorting genetic algorithm (NSGA-II) is used to solve the above mathematical model. By initializing a population containing robot path and data station deployment schemes, Pareto fronts (i.e., a set of multiple non-dominated optimal solutions) are generated through multiple generations of genetic iteration (selection, crossover, and mutation). Weights are set according to actual monitoring needs (e.g., prioritizing shorter monitoring time during emergency fault diagnosis and prioritizing data real-time performance during routine monitoring). The solution with the smallest weighted sum is selected from the Pareto fronts as the best compromise between robot path planning and data station deployment. This solution can simultaneously balance monitoring efficiency and data transmission performance.

[0023] Example 2 Based on Example 1, this example provides supplementary explanations regarding the undirected graph structure and robot velocity constraints in S1: The undirected graphs in S1 specifically include: Each node uniquely corresponds to a small area in the pipeline network (such as the pipeline coverage area of ​​a certain area in a city). The value is determined based on the actual scale of the pipeline network (for example, a water supply network in a small to medium-sized city can be divided into 8 small areas, i.e. =8); There are 9 edges, each edge uniquely corresponding to a segment of a physical pipe connecting two small regions. The value of |E| is consistent with the actual number of pipes in the pipe network (for example, the water supply network mentioned above contains 9 pipe segments, i.e., ...). =9); An autonomous monitoring robot, The value is determined based on the pipeline network scale, monitoring efficiency requirements, and cost budget (for example, the above-mentioned water supply network is equipped with 2 robots, i.e., ...). =2); One data station, The value must meet data transmission coverage requirements and cost constraints (for example, the above-mentioned water supply network deploys 2 data stations, i.e.) =2).

[0024] Meanwhile, the robot's constant travel speed must satisfy the constraint that its absolute value is greater than the absolute value of the maximum flow velocity in the pipe: since the robot is an active device, it can be powered by its built-in power system. This speed setting ensures that the robot can still move normally under reverse flow conditions (avoiding the robot being unable to move forward due to excessive flow velocity in the pipe). For example, setting a constant travel speed for the robot... =1m / s, the maximum flow velocity in the pipe network is 0.3m / s, which satisfies... > Constraints.

[0025] Example 3 Based on Example 1, this example provides a detailed supplement to the hydraulic simulation methods in S2: The hydraulic simulation method in S2 specifically adopts professional hydraulic simulation software (EPANET), which must have the ability to simulate the hydraulic characteristics of urban pipe networks. The input parameters are obtained as follows: the diameter, length, connection position and other parameters of the pipe are the design data or field survey data during the construction of the pipe network (for example, the pipe diameter is uniformly 200mm, and the length is obtained by measuring the actual laying distance); the water demand data of the nodes comes from urban water supply statistics (such as the average daily water consumption of residential areas and commercial facilities); and the elevation data of the nodes is obtained through topographic surveying tools (such as GPS elevation measurement).

[0026] After importing the above input parameters into the hydraulic simulation software, the software simulates the steady-state or transient flow state of the pipe network by solving hydraulic equations (such as the continuity equation and the energy equation), and outputs the flow velocity, flow direction (clockwise / counterclockwise or a specific direction indicator) and flow rate data in each pipe. This output data can accurately reflect the actual flow situation in the pipe, providing a reliable basis for subsequent differentiation of downstream / countercurrent conditions and calculation of monitoring time, and avoiding errors in monitoring time calculation caused by unknown flow state in the pipe.

[0027] The monitoring time for pipelines is calculated using the following formula:

[0028] In the formula: For monitoring the flow in or out of the pipeline; The length of the pipe; The robot's constant speed; The velocity in the pipe is represented by a minus sign for downstream operation (the robot uses fluid assistance and has a faster effective speed) and a plus sign for upstream operation (the robot needs to overcome fluid resistance and has a slower effective speed).

[0029] Example 4 Based on Example 1, this example provides supplementary explanations regarding the calculation formulas and parameter meanings for minimum monitoring time and minimum data delay: The minimum monitoring time in S3 is calculated using the following formula:

[0030] In the formula: to These represent the monitoring path times for the 1st to the Kth robots, respectively. The minimum data latency in S3 is calculated using the following formula:

[0031] In the formula: to These represent the time taken for the 1st to the Kth robots to transmit data to their respective data stations.

[0032] Furthermore, this embodiment provides supplementary explanations regarding the objective function and constraints of the joint optimization mathematical model: The mathematical model in S3 is specifically as follows:

[0033] In the formula: The weighted total time is a comprehensive indicator that measures monitoring efficiency and data real-time performance. The weight for the minimum monitoring time; The weight for minimizing data latency; and The values ​​of both can be flexibly adjusted according to actual monitoring needs.

[0034] The constraints also include: ,and, and The range of values ​​is .

[0035] Example 5 Based on Example 1, this example provides a detailed supplement to the solution process of the NSGA-II algorithm in S4: The solution process of the NSGA-II algorithm in S4 includes: S4.1 Set algorithm parameters, including population size. Maximum number of iterations Crossover probability Probability of mutation ; Set algorithm parameters: Set parameters according to problem complexity and solution efficiency requirements. Specific values ​​are as follows: Population size =10 (Balancing search efficiency with solution diversity) Too large a value will increase computational cost, while too small a value will result in insufficient solution coverage; maximum number of iterations. =20 (to ensure algorithm convergence; too few iterations will result in not finding the optimal solution, while too many will increase redundant calculations); crossover probability (Promoting population gene recombination and preserving the characteristics of high-quality solutions); mutation probability (Introducing random mutations to avoid the algorithm getting trapped in local optima).

[0036] S4.2 Randomly generate the initial parent population: Each individual adopts a binary encoding method of robot path + data station deployment, for example, encoding length = K × number of path pipelines + M × node index; two constraints must be met during generation: first, all |E| segment pipelines are assigned to K robots (verified by pipeline allocation matrix); second, there is no time-space conflict between the paths of any two robots (verified by path conflict detection). S4.3 Fitness Calculation and Genetic Operations: For each individual in the parent population, calculate... and Two objective function values ​​are used as fitness; a binary tournament selection method is adopted (two individuals are randomly selected, and the individual with better fitness is selected as the parent); a three-layer crossover operation is performed (crossover is performed on robot path allocation, data station deployment location, and the cooperative relationship between path and deployment location respectively) to ensure that the offspring inherit the superior characteristics of the parent; a path-aware mutation operation is performed (randomly modifying a section of a robot's path or a deployment node of a data station), and after generating the offspring population, the fitness of each offspring is calculated in the same way.

[0037] S4.4 Population Update: Update the parent population ( Individuals) and offspring populations Individuals were merged into a temporary population. (Individuals); perform fast non-dominated sorting on the temporary population, dividing individuals into multiple non-dominated fronts (the first front represents the optimal solution set, the second front the next, and so on); calculate the crowding distance for each individual (measures the distribution density of individuals within the fronts; a larger distance indicates better solution diversity in that region); filter by front priority + crowding distance. The best individuals form the next generation of parent population.

[0038] S4.5, Iteration Termination: Repeat S4.3-S4.4 until the number of iterations is reached. =20, at which point the first non-dominated front is the Pareto front, which contains multiple non-dominated optimal solutions (each solution corresponds to a set of robot paths and data station deployment schemes).

[0039] Example 6 Based on Example 5, this example provides supplementary explanations of the three-layer crossover operation and the path-aware mutation operation: Three-level crossover operation: Robot path allocation crossover: For two parent individuals, a crossover point is randomly selected (such as the middle section of robot 1's path), and the pipeline allocation scheme after the crossover point is swapped. For example, if the path of robot 1 in parent 1 is (1,2), (2,5), (5,8), and the path of robot 1 in parent 2 is (1,2), (2,3), (3,5), the path of robot 1 in child 1 after the crossover is (1,2), (2,5), (3,5). After the crossover, it is necessary to check whether the pipeline is reassigned or omitted.

[0040] Cross-deployment of data stations: For two parent individuals, the deployment node indices of the data stations are exchanged. For example, the data stations of parent 1 are deployed on nodes 2 and 5, and the data stations of parent 2 are deployed on nodes 4 and 5. After the cross-deployment, the data stations of child 1 are deployed on nodes 2 and 4. After the cross-deployment, it is necessary to ensure that the deployment locations of the data stations are reasonable (such as avoiding centralized deployment that may lead to insufficient transmission coverage).

[0041] Coordination and intersection of path and deployment location: Adjust the robot path endpoint according to the data station deployment location to ensure that the robot can quickly transmit data after completing the monitoring. For example, if the data station of child 1 is deployed at nodes 2 and 4, adjust the path endpoint of robot 1 to the pipe (2,5) close to node 2, and adjust the path endpoint of robot 2 to the pipe (1,4) close to node 4.

[0042] Path-aware mutation operation: During mutation, a specific encoding segment of an individual is randomly selected for modification. For example, a path segment of robot 2 is randomly modified (replacing pipe (4,6) with pipe (4,5)), or the deployment node of a data station is adjusted (changing the data station of node 5 to node 7). After mutation, two constraints need to be verified in real time: first, all pipes are still fully covered; second, there are no collisions on the robot path. If the constraints are not met after mutation, the mutation operation is repeated until a valid solution that meets the constraints is generated, thus preventing invalid solutions from entering the next generation of the population.

[0043] Example 7 Based on Example 5, this example provides a supplementary explanation of the selection process for the optimal compromise solution: In S4, the optimal compromise solution is selected from the Pareto front that minimizes the weighted total time based on the preset weights of minimum monitoring time and minimum data delay.

[0044] The following is based on Figure 2 and Figure 4 Specific implementation examples are provided: Figure 2The diagram shows a city's pipeline network system. This model system can be divided into two parts: above ground and underground. Each small building on the surface represents an independent small area, while each small black dot underground corresponds to a pipeline node within that area. Nodes are connected by underground pipelines represented by black lines. Robots move along the pipeline lines to collect data, and data stations at the nodes collect the data from the robots.

[0045] The first step is to treat a small area in the pipeline network as a node and the pipeline connecting two areas as an edge, thus mapping the pipeline network into an undirected graph. Figure 2 The network diagram below is the undirected graph mapped from this model. The pipeline system diagram includes 8 small regions and 9 pipelines. Additionally, 2 robots and 2 data stations were deployed. The second step involves obtaining the flow velocity and flow rate information within the pipe using hydraulic simulation software. Utilizing the pipe length and flow velocity, and combining this with the robot's own movement speed, the monitoring status of each pipe is categorized into upstream and downstream flow, depending on the situation. This allows for the acquisition of the monitoring time for each individual pipe's upstream or downstream flow. These times are then weighted and added to the graph to create a hybrid graph. The specific details are as follows: When deploying urban pipe networks, the diameter, length, and connection locations of each pipe in the system are already known, allowing for the acquisition of length and adjacency information. Combined with information such as water demand and elevation for each small area, this data is imported into simulation software for hydraulic simulation, yielding data on flow rate, velocity, and direction within each pipe. Furthermore, considering the robot's ability to move at a certain speed... This speed remained constant throughout the monitoring process, except when a stop command was given. Combined with the flow direction within the pipe, this was categorized into two cases: downstream and upstream. Therefore, in... At that time, two velocities, one for downstream and one for upstream, can be obtained. Then, using the pipe length and these two velocities, the monitoring time for downstream and upstream flow in each pipe can be calculated. Then, this time is weighted and added to the undirected graph to form a hybrid graph.

[0046] exist Figure 2 In the example, the known pipeline data is shown in Tables 1 and 2: Table 1

[0047] Table 2

[0048] Given the length matrix and the adjacency matrix:

[0049]

[0050] This data and connection information can be imported into EPANET hydraulic simulation software to obtain the velocity matrix;

[0051] Assumption Therefore, according to the formula The downstream monitoring time matrix can then be calculated:

[0052] Countercurrent monitoring time matrix:

[0053] These monitoring times are weighted and added to the undirected graph to form a time-weighted hybrid graph.

[0054] The third step is to define the maximum time required for monitoring the paths of multiple robots as the minimum monitoring time, and the maximum time required for multiple data stations to obtain robot data as the minimum data delay. Therefore, a mathematical model for jointly optimizing the minimum monitoring time and the minimum data delay can be constructed. The maximum time required for monitoring paths by multiple robots is defined as the minimum monitoring time. The maximum time among multiple data stations to obtain robot data is defined as the minimum data latency. Therefore, a mathematical model can be constructed to jointly optimize the minimum monitoring time and the minimum data latency. Based on this mathematical model, an optimization problem is established. The constraints are as follows: Constraint 1: All pipes must be covered by the robot path; Restriction 2: There must be no collisions or conflicts on the robot's path at the same time; Restriction 3: ; The fourth step involves using the NSGA-II algorithm to find a solution for multi-robot path planning and data station deployment that minimizes monitoring time, while ensuring all pipelines are monitored. This solution is then optimized to achieve a weighted minimum of both minimum monitoring time and minimum data latency. However, the NSGA-II algorithm typically finds the optimal Pareto front, which includes many possible solutions. Therefore, we identify the best compromise solution among these.

[0055] Using the NSGA-II algorithm, the specific flowchart is as follows: Figure 3 As shown. Under the premise of ensuring all pipelines are monitored, find a solution for multi-robot path planning and data station deployment that achieves minimal monitoring time.

[0056] The first step is to set the parameters related to the algorithm, including the population size. Maximum number of iterations Crossover probability Probability of mutation Then generate randomly. An initial set of individuals satisfying the constraints, each encoded with a sequence containing... Robot path and The complete solution for the deployment locations of each data station is obtained, satisfying all constraints, such as all pipelines being assigned to robots and no path conflicts among robots. Then, for each individual in the initial population, its corresponding objective function value is calculated. and As the initial fitness.

[0057] Through iterative loops, a binary tournament selection is performed in the current population, followed by three-level crossover and path-aware mutation operations based on problem characteristics to generate a new generation. After merging the parent and offspring populations, a fast non-dominated sort is performed to partition all solutions into non-dominated fronts. Next, the crowding distance for each individual is calculated. Based on the level of the non-dominant front and the crowding distance, the next generation of the population is selected to ensure better convergence and greater diversity. This process continues until the maximum number of iterations is reached. At this point, the Pareto front is a non-dominated front. .

[0058] The Pareto front includes multiple solutions. We customize the weights. and Representing the two objective function values ​​respectively and The importance of each factor is considered, and then a compromise solution is chosen, finding an optimal compromise solution on the Pareto front.

[0059] exist Figure 2 In the example, we set the population size to 10, the maximum number of iterations to 20, the crossover probability to 0.8, the mutation probability to 0.2, and the weighting coefficient to... Then, 10 initial individuals are randomly generated. Each chromosome contains a complete solution with 2 robot paths and 2 data station deployment locations, satisfying all constraints, such as all pipelines being assigned to robots and no path conflicts. Then, the NSGA-II algorithm is executed.

[0060] The optimized result is shown in the figure below. Figure 4 As shown, this indicates the final compromise solution. The monitoring path for robot 1 is... The monitoring path of robot 2 is Their monitoring times were 156.21s and 138.27s, respectively. The data stations are deployed at nodes 2 and 5. .final, This result achieves minimal monitoring time and data latency.

[0061] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0062] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0063] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A joint optimization method for pipeline robot path and data station deployment, characterized in that, The specific steps are as follows: S1. Construct a pipeline-robot-data station system model: Map small areas in the pipeline network as nodes, and map the pipes connecting two small areas as edges to form an undirected graph; The system is configured with multiple autonomous monitoring robots that can move along the pipes, and multiple data stations deployed at the nodes to receive data collected by the robots; S2. Construct a hybrid graph with monitoring time weights: Obtain flow velocity and direction data in each pipe through hydraulic simulation, combine with the robot's constant travel speed, distinguish between downstream and upstream monitoring conditions, calculate the monitoring time of each pipe segment under the corresponding condition, and assign the monitoring time as a weight to the corresponding edge of the undirected graph to form a hybrid graph. S3. Establish a joint optimization mathematical model: Define the minimum monitoring time as the maximum time taken for all robots to complete their respective monitoring paths, and define the minimum data delay as the maximum time taken for all data stations to receive data from the corresponding robots; with the minimum weighted sum of the two indicators as the optimization objective, establish a mathematical model that includes constraints such as full pipeline coverage and no robot path collision. S4. Solving for the optimal solution: The NSGA-II algorithm is used to solve the above model. Pareto fronts are generated through population iteration. Then, based on the weights set according to actual needs, the best compromise solution for robot path planning and data station deployment is selected from the Pareto fronts.

2. The method for joint optimization of pipeline robot path and data station deployment according to claim 1, characterized in that, The undirected graphs in S1 include: Each node, i.e., in the pipeline network A small area; Each edge, that is, the edge of the pipeline network Section of pipeline; A number of robots; A number of data stations; Furthermore, the absolute value of the robot's constant travel speed is greater than the absolute value of the maximum flow velocity inside the pipe.

3. The method for joint optimization of pipeline robot path and data station deployment according to claim 1, characterized in that, The hydraulic simulation method in S2 is hydraulic simulation software; the input parameters include the diameter, length, and connection position of the pipe, as well as the water demand and elevation information of the nodes; the output parameters include the flow velocity, flow direction, and flow rate data in the pipe.

4. The method for joint optimization of pipeline robot path and data station deployment according to claim 3, characterized in that, The hydraulic simulation software is specifically EPANET; The monitoring time for pipelines is calculated using the following formula: In the formula: For monitoring the flow in or out of the pipeline; The length of the pipe; The robot's constant speed; The velocity in the pipe is represented by a minus sign for downstream flow and a plus sign for upstream flow.

5. The method for joint optimization of pipeline robot path and data station deployment according to claim 1, characterized in that, The minimum monitoring time in S3 is calculated using the following formula: In the formula: to These represent the monitoring path times for the 1st to the Kth robots, respectively. The minimum data latency in S3 is calculated using the following formula: In the formula: to These represent the time taken for the 1st to the Kth robots to transmit data to their respective data stations.

6. The method for joint optimization of pipeline robot path and data station deployment according to claim 5, characterized in that, The mathematical model described in S3 is as follows: In the formula: This is the weighted total time; The weight for the minimum monitoring time; The weight for minimizing data latency; The constraints also include: ,and, and The range of values ​​is .

7. The method for joint optimization of pipeline robot path and data station deployment according to claim 1, characterized in that, The solution process of the NSGA-II algorithm in S4 includes: S4.1 Set algorithm parameters, including population size, maximum number of iterations, crossover probability, and mutation probability; S4.2 Randomly generate an initial parent population, and encode a complete solution containing all robot paths and all data station deployment locations for each individual, while satisfying the constraints of full pipeline coverage and collision-free robot paths; S4.3 Calculate the fitness of the parent population individuals, select the parent generation through the binary tournament selection method, perform three-level crossover operation and path-aware mutation operation, generate the offspring population and calculate the fitness; S4.4 Merge the parent and offspring populations, perform fast non-dominated sorting and crowding distance calculation, and select the best individuals to form the next generation population; S4.5 Repeat the iterations until the maximum number of iterations is reached to obtain the Pareto front.

8. The method for joint optimization of pipeline robot path and data station deployment according to claim 7, characterized in that, The three-layer cross operation includes robot path allocation cross, data station deployment location cross, and path and deployment location collaborative cross; the path-aware mutation operation verifies the constraint satisfaction of the solution in real time after mutation to avoid invalid solutions.

9. The method for joint optimization of pipeline robot path and data station deployment according to claim 7, characterized in that, The optimal compromise in S4 is to select the solution that minimizes the weighted total time from the Pareto front based on the preset weights for minimum monitoring time and minimum data delay.

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