Road crack repairing method and system based on dynamic planning

Abstract

According to the road crack repairing method and system based on dynamic planning, the crack repairing sequence is obtained by constructing the crack path planning model and using the dynamic planning algorithm for solving, repeated calculation of a large number of sub-problems can be reduced, the calculation time is shortened, and the planning efficiency is improved. According to the dynamic planning algorithm provided by the invention, whether the repair of a single crack or the overall planning of multiple cracks, the dynamic planning algorithm can ensure that a globally optimal scheme is found. According to the method, all possible path selection and repairing sequences are comprehensively considered, and the occurrence of a local optimal solution is avoided, so that the optimality of the overall repairing effect is ensured.

Description

Technical Field

[0001] This invention belongs to the field of path planning, and in particular relates to a method and system for repairing road cracks based on dynamic planning. Background Technology

[0002] With the acceleration of urbanization, the highway network is expanding rapidly. By the end of 2023, the total length of highways open to traffic nationwide had reached 5.441 million kilometers, an increase of over one million kilometers compared to ten years ago. However, at the same time, with the aging of infrastructure and the continuous increase in traffic load, road surface damage is becoming increasingly serious, resulting in numerous road surface defects that affect daily traffic and urban development, and even cause casualties. Therefore, road maintenance has become a top priority in the transportation sector, with maintenance mileage now accounting for as much as 99.4% of the total mileage, and the level and scale of highway maintenance are increasing daily. It is particularly necessary to address road surface defects, and road surface cracks are one of the most common defects. If road surface cracks are not repaired in time, they will accelerate road surface damage and shorten the life of highways. Traditional repair methods often suffer from low efficiency, high costs, and the possibility of decision-making errors. In recent years, the rapid development of computers and artificial intelligence has provided supporting means for intelligent repair of road surface cracks. How to quickly plan the optimal repair path after detecting cracks to minimize costs and time remains an urgent problem to be solved.

[0003] Currently, research on pavement crack detection and repair, both domestically and internationally, mainly focuses on the development of crack detection technologies and repair materials. In crack detection, various sensors and image processing technologies have been applied to automated detection systems. Regarding repair technology, new repair materials and processes are constantly emerging, improving repair effectiveness and durability. However, research on repair path planning is relatively limited. Summary of the Invention

[0004] The main problem addressed by this invention is how to optimize resource allocation and path selection to improve repair efficiency and reduce costs. It provides a road crack repair method and system based on dynamic programming.

[0005] To solve the above technical problems, the technical solution adopted is: A road crack repair method based on dynamic programming includes the following steps: Step 1: Obtain the set of road cracks; Step 2: Construct a crack path planning model based on the road crack set; Step 3: Solve the crack path planning model using a dynamic programming algorithm to obtain the repair planning result.

[0006] Furthermore, the crack path planning model is as follows: Objective function: (1) Constraints: (2) (3) (4) (5) (6) Equation (1) represents the shortest possible redundancy distance. Indicates the i-th crack The End With the j-th crack starting point The distance between them and Let be the decision variables, representing whether the i-th crack and the j-th crack are selected, where 1 indicates selection and 0 indicates non-selection, and n represents the number of cracks in the road crack set; Equation (2) indicates that each crack will be selected only once. Equations (3) and (4) indicate that the start and end points of a crack are connected to other cracks only once. Equation (5) indicates the possibility of a feasible solution. The sum and the sum in the equation indicate whether the start and end points of the crack are selected. Equation (6) is the decision variable.

[0007] Furthermore, the method for solving the crack path planning model is as follows: Step 3.1: Extract the set of endpoints of all cracks in the crack set. 1, 2, ..., n represent the nth crack; Step 3.2: Create an imaginary endpoint as the starting point for path planning, and make sure that the distance from this starting point to the endpoints of all cracks is zero; Step 3.3: Construct an endpoint distance matrix to store the distance between two endpoints in the endpoint set, and define the distance between two endpoints of the same crack as 0; Step 3.4: Use dynamic programming algorithm to find the global optimal solution for crack repair path, and output the optimal crack repair path and shortest distance.

[0008] Furthermore, the specific steps of the dynamic programming algorithm include: Step 3.4.1: Use the fictitious endpoint as the initial point i of the path; Step 3.4.2: Select the next repair endpoint s, which must conform to the state transition rules. , This represents the set of paths that have been repaired at time t-1. This indicates the set of endpoints selected at time t after the next repaired endpoint s. This represents the process from starting point i to completing the set. The shortest path distance from all endpoints to endpoint s. Indicates starting from the origin After completing the assembly Find the shortest distance of the path from all endpoints to endpoint s. Indicates the next endpoint to be repaired from the candidate. To any endpoint in the patched endpoint set The distance, j∈ .

[0009] Step 3.4.3: Repeat the previous step until the set of unrepaired endpoints is empty, then output the crack endpoint repair order and the shortest repair distance.

[0010] Furthermore, when using the dynamic programming algorithm to solve the problem, the endpoint access status is represented in binary form, with 1 indicating that the endpoint has been visited and 0 indicating that it has not been visited.

[0011] The present invention also provides a road crack repair system based on dynamic programming, which is implemented using the steps of a road crack repair method based on dynamic programming.

[0012] By adopting the above technical solution, the present invention has the following beneficial effects: This invention provides a road crack repair method and system based on dynamic programming. By constructing a crack path planning model and using a dynamic programming algorithm to solve for the crack repair sequence, it reduces the amount of redundant calculation of sub-problems, shortens computation time, and improves planning efficiency. The dynamic programming algorithm of this invention guarantees finding the globally optimal solution, whether repairing a single crack or planning multiple cracks as a whole. It comprehensively considers all possible path choices and repair sequences, avoiding the occurrence of local optima, thereby ensuring the best overall repair effect. Attached Figure Description

[0013] Figure 1 This is a system flowchart of the present invention; Figure 2 This is a schematic diagram of the current optimal solution of the dynamic programming algorithm provided in this embodiment of the invention; Figure 3 A comparison chart of the running time of dynamic programming and enumeration methods provided in the embodiments of the present invention. Detailed Implementation

[0014] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] A road crack repair method based on dynamic programming includes the following steps: Step 1: Obtain the set of road cracks.

[0016] Step 2: Construct a crack path planning model based on the set of road cracks.

[0017] In this embodiment, the crack path planning model is: Objective function: (1) Constraints: (2) (3) (4) (5) (6) Equation (1) represents the shortest redundancy distance. Indicates the i-th crack The End With the j-th crack starting point The distance between them and Let be the decision variables, representing whether the i-th crack and the j-th crack are selected, where 1 indicates selection and 0 indicates non-selection, and n represents the number of cracks in the road crack set; Equation (2) indicates that each crack will be selected only once. Equations (3) and (4) indicate that the start and end points of a crack are connected to other cracks only once. Equation (5) indicates the possibility of a feasible solution. The sum and the sum in the equation indicate whether the start and end points of the crack are selected. Equation (6) is the decision variable.

[0018] Step 3: Solve the crack path planning model using a dynamic programming algorithm to obtain the repair planning result.

[0019] In this embodiment, the method for solving the crack path planning model is as follows: Step 3.1: Extract the set of endpoints of all cracks in the crack set. 1, 2, ..., n represent the nth crack.

[0020] Step 3.2: Create an imaginary endpoint as the starting point for path planning, and make sure that the distance between this starting point and the endpoints of all cracks is zero.

[0021] Step 3.3: Construct an endpoint distance matrix to store the distance between any two endpoints in the endpoint set, and define the distance between any two endpoints of the same crack as 0. Each crack has two endpoints. By setting the distance between any two endpoints of the same crack to 0, after selecting one endpoint of a crack, the starting endpoint and the ending endpoint are directly connected. After traversing the crack to the endpoint of the other end, the next endpoint of the crack is selected. Furthermore, from the perspective of the shortest path, the path from the starting point to the ending point is obviously the connection of the crack and is also the shortest path. This avoids the situation where the path only passes through one endpoint of the crack and then jumps to the endpoint of another crack, resulting in the previous crack only passing through one endpoint without being repaired.

[0022] A drawback of automated repair equipment is that it sometimes proceeds to repair the next crack before completing the previous one. This can lead to incomplete repairs and affect the overall repair quality. To prevent this, this embodiment employs an endpoint binding method. Specifically, during operation, when one endpoint of a crack is selected, according to a pre-defined rule, the next endpoint of the same crack will be selected. To implement this rule, the distance between the two endpoints of the same crack is defined as 0 during data processing. This ensures that the equipment completes the repair of only one crack at a time, preventing the premature repair of other cracks and effectively solving the potential problem of missed repairs.

[0023] In this embodiment, as Figure 2 As shown, the analysis is performed using data from five cracks: A crack path planning model is constructed based on the extracted crack images and the road crack set, resulting in the crack endpoint distance matrix D: ; Symbols in the matrix , ... ... , These represent the distance between the two endpoints, and the numbers in the subscripts represent the labels of the two endpoints.

[0024] Specifically, in this embodiment, there are five cracks and a dummy starting point, and a distance matrix between the crack endpoints of the two endpoints. The value is: ; In the distance matrix, inf represents infinity. The modified crack endpoint distance matrix is ​​obtained by binding the two endpoints of a crack and adding a dummy starting point. .

[0025] ; The optimized path is [8, 7, 3, 4, 10, 9, 6, 5, 1, 2], where the numbers in the path are the crack endpoint numbers, and the shortest distance of the optimized path is 399m.

[0026] Step 3.4: Use dynamic programming algorithm to find the global optimal solution for crack repair path, and output the optimal crack repair path and shortest distance.

[0027] In this embodiment, the specific steps of the dynamic programming algorithm include: Step 3.4.1: Use the fictitious endpoint as the initial point i of the path, and define the initial point as 0.

[0028] Step 3.4.2: Select the next repair endpoint s, which must conform to the state transition rules. , This represents the set of paths that have been repaired at time t-1. This indicates the set of endpoints selected at time t after the next repaired endpoint s. This represents the process from starting point i to completing the set. The shortest path distance from all endpoints to endpoint s. Indicates starting from the origin After completing the assembly Find the shortest distance of the path from all endpoints to endpoint s. Indicates the next endpoint to be repaired from the candidate. To any endpoint in the patched endpoint set The shortest distance, j∈ .

[0029] At time t=0, the set of endpoints The set of endpoints that have been repaired at time t-1 The set of unpatched endpoints is The method for finding the next repair endpoint s is as follows: (1) ,but ; (2) ,but ; ......; (10) , ; At time t=1, Then we will discuss the following cases.

[0030] (1) If the set of endpoints that have been repaired for The next patch endpoint ,but: ① If the next endpoint to be repaired, s, is selected as 2, ; ; ②If the next endpoint to be repaired, s, is selected as 3, ; ; ......; ⑩ If the next endpoint to be repaired, s, is selected as 10, ; ; (2) If the set of endpoints that have been repaired for The next patch endpoint : ① If the next endpoint to be repaired, s, is selected as 1, , ; ②If the next endpoint to be repaired, s, is selected as 3, , ; ......; ⑩ If the next endpoint to be repaired, s, is selected as 10, , ; ......; (10) If the set of endpoints that have been repaired for The next patch endpoint : ① If the next endpoint to be repaired, s, is selected as 1, , ; ②If the next endpoint to be repaired, s, is selected as 2, , ; ......; ⑩ If the next endpoint to be repaired, s, is selected as 9, , ; At time t=2, Then we will discuss the following cases.

[0031] (1) If the set of endpoints that have been repaired for The next patch endpoint : ① If the next endpoint to be repaired, s, is selected as 3, , ; When j=2 The minimum value is found, and the repair path at the crack endpoint is [3, 2, 1, 0]. ②If the next endpoint to be repaired, s, is selected as 4, , ; When j=2 The minimum value is found, and the repair path at the crack endpoint is [4, 2, 1, 0]. ......; ⑩ If the next endpoint to be repaired, s, is selected as 10, , ; When j=2 The minimum value is found, and the repair path at the crack endpoint is [10, 2, 1, 0]. (2) If the set of endpoints that have been repaired for The next patch endpoint : ① If the next endpoint to be repaired, s, is selected as 2, , ; When j=1 The minimum value is found, and the repair path at the crack endpoint is [2, 1, 3, 0]. ②If the next endpoint to be repaired, s, is selected as 4, , ; When j=3 The minimum value is found, and the repair path at the crack endpoint is [4, 3, 1, 0]. ......; ⑩ If the next endpoint to be repaired, s, is selected as 10, , ; When j=3 The minimum value is found, and the repair path at the crack endpoint is [10, 3, 1, 0]. ......; (10) If the set of endpoints that have been repaired for The next patch endpoint : ① If the next endpoint to be repaired, s, is selected as 1, , ; When j=9 The minimum value is found, and the repair path at the crack endpoint is [1, 9, 10, 0]. ②If the next endpoint to be repaired, s, is selected as 2, , ; When j=9 The minimum value is found, and the repair path at the crack endpoint is [2, 9, 10, 0]. ......; ⑩ If the next endpoint to be repaired, s, is selected as 8, , ; When j=9 The minimum value is found, and the repair path at the crack endpoint is [8, 9, 10, 0]. ......; At time t=9, the set of repaired endpoints Then we will discuss the following cases.

[0032] (1) If the set of endpoints that have been repaired for The next patch endpoint s is 10: When j=9 The minimum value is reached, and the repair path at the crack endpoint is [10,9,4,3,7,8,6,5,2,1,0]. (2) If the set of endpoints that have been repaired for The next patch endpoint s is 9: When j=10 The minimum value is reached, and the repair path at the crack endpoint is [9,10,4,3,7,8,6,5,2,1,0]. ......; (10) If the set of endpoints that have been repaired for The next patch endpoint s is 1: ; When j=2 The minimum value is reached, and the repair path at the crack endpoint is [1,2,4,3,7,8,6,5,9,10,0]. At time t=10, The optimal solution can then be obtained. , When j=8 The minimum value is found, and the repair path at the crack endpoint is {8, 7, 3, 4, 10, 9, 6, 5, 1, 2}.

[0033] Define node 0 as the initial starting point for solving this problem. Using the flowchart shown, obtain the value stored in the path, and find the optimal path [8, 7, 3, 4, 10, 9, 6, 5, 1, 2], where the shortest distance of the optimal path is 399m. For example... Figure 2 As shown, the optimal path for crack repair is visualized. This excludes the case where there are 5 cracks. Figure 3 The solution time of the dynamic programming algorithm and the enumeration algorithm are shown when there are 5, 6, 7 and 8 cracks. As the number of cracks increases, the solution time optimization of the dynamic programming algorithm becomes more obvious.

[0034] This embodiment addresses the problem of automated crack repair path planning by employing state compression (to avoid redundant calculations): binary representation is used to indicate the access status, with 1 representing visited and 0 representing unvisited. For example, representing five cracks with ten endpoints, 1100110000, means endpoints 1, 2, 5, and 6 have been visited, while endpoints 3, 4, 7, 8, 9, and 10 have not. This reduces the computational complexity from n! to... For example, to repair the crack endpoints 1→2→3→4 and 1→2→3→5, the enumeration algorithm has a computational cost of 6; the dynamic programming algorithm will store 1→2→3 as dp[1110000000][3] when calculating 1→2→3→4, and directly add the distance of 3→5 to the stored result when calculating 1→2→3→5, with a computational cost of 4.

[0035] Subproblem reuse (reducing redundant computation): Dynamic programming may contain repeated subproblems. For example, the crack endpoint repair sequence 0→3→1→4→2 and 0→1→3→4→2 both contain the subproblem of repairing crack endpoints 3, 1, and 4. Storing the path distances to endpoints 3, 1, and 4 reduces computational complexity. Solve using dynamic programming: For 0→3→1→4→2: ; For 0→1→3→4→2: ; Both of the above cases have subproblems involving repairing endpoints 0, 1, 3, and 4. The algorithm is consistent and only requires one calculation, with a computation cost of 5; while the enumeration algorithm has a computation cost of 8.

[0036] Both of these methods can significantly reduce the solution size, decrease the amount of redundant calculations of a large number of subproblems (referring to the minimum path distance after visiting all unvisited crack endpoints once from a certain endpoint of a crack), shorten the computation time, and improve computational efficiency. A time comparison between dynamic programming and enumeration algorithms is shown below. Figure 3 As shown. By using the state transition rules of this embodiment, global optimality is ensured. All possible path selections and repair sequences are comprehensively considered, avoiding the occurrence of local optima, thereby ensuring the best overall repair effect.

[0037] Step 3.4.3: Repeat the previous step until the set of unrepaired endpoints is empty, then output the crack endpoint repair order and the shortest repair distance.

[0038] at this time, The optimal solution can be obtained by following this process. At this point, the repair path at the crack endpoint is {8, 7, 3, 4, 10, 9, 6, 5, 1, 2}, and the shortest redundant distance is 399m.

[0039] This embodiment also provides the following proof of the accuracy of the dynamic algorithm.

[0040] Step 1 When the number of cracks At that time, the set of endpoints In this scenario, the starting and ending points are directly connected. Clearly, the path from the starting point to the ending point is the connection of this crack, which is the shortest path. Therefore, the dynamic programming algorithm will also consider this crack connection as the shortest path, and the algorithm holds true.

[0041] Step 2: Assuming the number of cracks n=k, dynamic programming can be used to find the exact solution for the optimal path. That is... ; This represents the distance between endpoints i and j; This represents the shortest distance to repair k cracks; and Let be the decision variables, representing the selection of the i-th endpoint and the j-th endpoint.

[0042] Step 3 When the number of cracks At that time, the set of crack endpoints ; Time t=2k: This represents the set of possible crack endpoints to be repaired in the previous moment and the current stage. This represents the set of crack endpoints that have been repaired in the current stage; In the following formulas , This indicates that the collection has been traversed. Finally arrived The shortest redundancy distance, i.e., the shortest distance for this stage, is: ; The following are the formulas. , This indicates that the collection has been traversed. Finally arrived The shortest redundancy distance, i.e., the shortest distance for this stage, is: ; Similarly, we can obtain when hour, The values ​​are all minimum values; Time t=2k+1: ,but Consider each situation individually; The following are the formulas. , This indicates that the collection has been traversed. Finally arrived The shortest redundancy distance, i.e., the shortest distance for this stage, is: ; The following are the formulas. , This indicates that the collection has been traversed. Finally arrived The shortest redundancy distance, i.e., the shortest distance for this stage, is: ; Similarly, we can obtain when hour, All values ​​are minimum values; Time t=2k+2: This is the final solution obtained by the dynamic programming algorithm. The desired result is the optimal result when the number of cracks is k+1.

[0043] As can be seen from the above proof, for any non-zero positive integer... Dynamic programming algorithms can find the shortest path from the starting point to the ending point and will traverse every crack.

[0044] The mathematical symbols in the above formula have the following meanings: Indicates the crack endpoint number selected in the current stage; This represents the set of crack endpoint repairs at the current stage; Indicates the distance between endpoints; This indicates that the final repaired crack endpoint is... And traversal The shortest distance between the endpoints; The endpoint of the last repaired crack is indicated as And traversal The shortest distance between each endpoint.

[0045] The present invention also provides a road crack repair system based on dynamic programming, which is implemented using the steps of a road crack repair method based on dynamic programming.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A road crack repair method based on dynamic programming, characterized in that, Includes the following steps: Step 1: Obtain the set of road cracks; Step 2: Construct a crack path planning model based on the road crack set; Step 3: Solve the crack path planning model using a dynamic programming algorithm to obtain the repair planning result.

2. The road crack repair method based on dynamic programming according to claim 1, characterized in that, The crack path planning model is as follows: Objective function: (1) Constraints: （2） （3） （4） （5） （6） Equation (1) represents the shortest redundancy distance. Indicates the i-th crack The End With the j-th crack starting point The distance between them and Let be the decision variables, representing whether the i-th crack and the j-th crack are selected, where 1 indicates selection and 0 indicates non-selection, and n represents the number of cracks in the road crack set; Equation (2) indicates that each crack will be selected only once. Equations (3) and (4) indicate that the start and end points of a crack are connected to other cracks only once. Equation (5) indicates the possibility of a feasible solution. The sum and the sum in the equation indicate whether the start and end points of the crack are selected. Equation (6) is the decision variable.

3. The road crack repair method based on dynamic programming according to claim 2, characterized in that, The method for solving the crack path planning model is as follows: Step 3.1: Extract the set of endpoints of all cracks in the crack set. 1, 2, ..., n represent the nth crack; Step 3.2: Create an imaginary endpoint as the starting point for path planning, and make sure that the distance from this starting point to the endpoints of all cracks is zero; Step 3.3: Construct an endpoint distance matrix to store the distance between two endpoints in the endpoint set, and define the distance between two endpoints of the same crack as 0; Step 3.4: Use dynamic programming algorithm to find the global optimal solution for crack repair path, and output the optimal crack repair path and the shortest redundant distance.

4. The road crack repair method based on dynamic programming according to claim 3, characterized in that, The specific steps of the dynamic programming algorithm include: Step 3.4.1: Use the fictitious endpoint as the initial point i of the path; Step 3.4.2: Select the next repair endpoint s, which must conform to the state transition rules. , This represents the set of paths that have been repaired at time t-1. This indicates the set of endpoints selected at time t after the next repaired endpoint s. Indicates starting point From start to finish walking the assembly The shortest distance of the path that reaches all endpoints in the given path and ultimately reaches endpoint s. Indicates starting from the origin After completing the assembly Find the shortest path distance from all endpoints in the path to endpoint j. Indicates the next endpoint to be repaired from the candidate. To any endpoint in the patched endpoint set The distance, j∈ . Step 3.4.3: Repeat the previous step until the set of unrepaired endpoints is empty, then output the crack endpoint repair order and the shortest repair distance.

5. A road crack repair method based on dynamic programming according to claim 4, characterized in that, When using dynamic programming to solve the problem, binary representation is used to indicate the endpoint access status, where 1 indicates that the endpoint has been visited and 0 indicates that it has not been visited.

6. A road crack repair system based on dynamic programming, characterized in that, The method for repairing road cracks based on dynamic programming, as described in any one of claims 1 to 5, is implemented using each step.

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