Path optimization design method for concrete 3D printing based on graph theory

Abstract

The present invention discloses a path optimization design method for concrete 3D printing based on graph theory principles, comprising the following steps: step one: modeling a concrete 3D printed part; step two: establishing a weight information table; step three: finding the maximum Euler loop based on the weight information table and updating the weight information table, and finding the maximum Euler loop of the updated weight information table again until all printing paths are traversed; step four: finding the shortest printing shortest path using an ant colony algorithm. The present invention first establishes a concrete 3D printed component model as a digital model that is convenient for computer processing, and then establishes a weight information table based on the connection information of each point thereof. Find the maximum Euler loop therein based on the relevant information in the weight information table, then update the weight information table, and find the maximum Euler loop again until all printing paths are traversed.

Description

Technical Field

[0001] The present invention belongs to the technical field of concrete 3D printing path optimization, and in particular relates to a path optimization design method for concrete 3D printing based on graph theory principles. Background Art

[0002] Concrete 3D printing technology is a technology that uses computer layered modeling and program commands to control the printing nozzle to repeatedly lay materials layer by layer to build a free-form building structure. Compared with traditional construction technology, concrete 3D printing technology has the characteristics of intelligence, short construction period, zero pollution, ability to print nodes of complex structures, and low material cost.

[0003] However, the current concrete 3D printing technology is in the R&D trial stage, and its performance and application are still in the exploratory stage, so there are inevitably some problems. Due to the lack of intelligence in the operation path planning of the 3D printing nozzle, the printing time of concrete 3D printing technology is still too long. Moreover, the printing quality of the inflection point of concrete 3D printed components is still far behind that of traditional template fabrics. Summary of the invention

[0004] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a path optimization design method for concrete 3D printing based on graph theory principles. The method first establishes the concrete 3D printing component model as a digital model that is convenient for computer processing, and then establishes a weight information table based on the connection information of each point. According to the relevant information in the weight information table, the maximum Euler circuit is found, and then the weight information table is updated, and the maximum Euler circuit is found again until all printing paths are traversed.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] The path optimization design method of concrete 3D printing based on graph theory principle includes the following steps;

[0007] Step 1: Create a digital model of the concrete 3D printed part;

[0008] Step 2: Create a weight information table;

[0009] Step 3: Find the maximum Euler circuit according to the weight information table and update the weight information table, and then find the maximum Euler circuit of the updated weight information table again until all the printing paths are traversed;

[0010] Step 4: Use the ant colony algorithm to find the shortest printing path.

[0011] In the step 1, a concrete print made of bulk solid waste cementitious materials is selected, and the geometric data (length, width, height, etc.) of the print is first collected, and then a model is established on Sketch Up software according to the collected data, and then a printing model is established based on the collected data, and finally the established model is sliced ​​using Cura software.

[0012] Steps of step 2:

[0013] (1) When establishing the weight information table, it is first necessary to number the geometric points in the digital model established in step 1, in order of N1, N2, N3...N n , then create an n*n empty matrix T, where n is the number of geometric points;

[0014] (2) After the empty matrix T is established, the elements in the empty matrix T are assigned values ​​according to the connection information between the geometric points in the digital model. The connected elements are assigned a value of 1, and the unconnected elements are assigned a value of 0. When all elements are assigned values, it is recorded as the weight information table U.

[0015] The matrix U is:

[0016]

[0017] Steps of step three:

[0018] (1) In the process of finding the maximum Euler circuit in the weight information table U, first, it is necessary to copy the weight information table U and record it as U1, and then use the Euler circuit existence criterion to determine whether the elements in U1 meet the conditions for finding the Euler circuit. If not, perform an edge deletion operation (i.e., delete the non-maximum Euler circuit path in the table);

[0019] (2) After the preprocessing of the elements in U1 is completed, the elements in the table that are not 0 are found from top to bottom and from left to right as the initial points of the connection path to start looking for the maximum Euler circuit;

[0020] (3) After the maximum Euler circuit is found, an empty matrix T is created. The first row of elements in T stores the maximum Euler circuit that has been found, and its connection information is assigned to 0 in U.

[0021] (4) Repeat operations (1-3). Each time (3) is repeated, the maximum Euler circuit needs to be stored in the next row in T until all elements in the weight information table U are 0.

[0022] The judgment criteria are:

[0023] If and only if all vertex degrees (the number of non-zero elements in each row of the weight information table) in a digital model are even and the graph is a connected graph, then there is an Euler circuit in the graph;

[0024] If there is an Euler circuit in the printer nozzle, the path finding function can be directly applied to find its maximum Euler circuit; if it does not exist, the edge deletion operation is performed on U1. The specific edge deletion process is as follows:

[0025]

[0026] After the edge deletion process is completed, the maximum Euler circuit is searched for the first time. After the search is completed, the weight of the searched path is cleared in the weight information table U. The operation process is as follows:

[0027]

[0028] After all the Euler circuits are found, all the unfinded paths are connected and all elements in U are cleared.

[0029] The steps of step 4 are:

[0030] (1) Classifying the geometric points in the digital model according to the different Euler circuits being sought;

[0031] (2) Each time, a point is extracted from each category and the shortest path is found using the ant colony algorithm, where (x1, y1), (x2, y2), (x3, y3) ... (x n ,y n ) represent the coordinates of each point, and the relative distance d between each point is obtained by the following formula ij , add up each d ij The sum of the distances of each point is recorded as d k , each time a printed point is connected, a pheromone τ is left behind k , τ k The value of decreases with the length of the printing distance, and as time increases, τ k As τ decreases, k The calculation formula is as follows, and then use d according to the following formula k , τ k Calculate the probability p of printing the next point k , it can be seen from the formula that the smaller the distance between two points, the greater the probability of being printed next time. As time goes by, the larger the pheromone value left, and finally, under the positive feedback of the algorithm, the printing path will be concentrated on the optimal path;

[0032]

[0033]

[0034]

[0035]

[0036] Beneficial effects of the present invention:

[0037] The present invention aims at the problems of long printing time and poor molding quality in the running path of 3D printing nozzles in concrete printing, and proposes a path optimization method for concrete 3D printing based on graph theory. The method optimizes the trajectory sequence of the nozzle running in concrete 3D printing, reduces the empty stroke and head-up times of the nozzle running trajectory, and thus effectively reduces the related problems existing in concrete 3D printing. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flowchart of the path optimization design method for concrete 3D printing.

[0039] Figure 2 This is a digital model diagram of concrete 3D printed components.

[0040] Figure 3 This is the largest Euler circuit diagram in the concrete 3D printing model.

[0041] Figure 4 Simulation results of the path optimization design method for concrete 3D printing. DETAILED DESCRIPTION

[0042] The present invention is further described in detail below in conjunction with embodiments.

[0043] Reference Figure 1 , the specific steps of the present invention are described in detail.

[0044] Step 1: Modeling the concrete 3D printed part;

[0045] Step 1: This method uses the concrete prints required by the National Fund Project for the Application of Bulk Solid Waste Cementitious Materials in 3D Printed Buildings. First, collect the geometric data (length, width, height, etc.) of the prints, and then build a model on Sketch Up software based on the collected data. Figure 2 .

[0046] Step 2: Create a weight information table;

[0047] Step 2: According to the geometric point information in the generated print model, first establish an empty matrix U corresponding to the number of its geometric points; after the establishment is completed, assign values ​​to the elements in the matrix according to the geometric point connection information in the print model, assign 1 to the connected elements and 0 to the unconnected elements. The matrix U is as follows:

[0048]

[0049] Step 3: Find the maximum Euler circuit based on the weight information table and update the weight information table. Then, find the maximum Euler circuit of the updated weight information table again until all the printed paths are traversed.

[0050] In the said Step 3, when finding the maximum Euler circuit based on the weight information table U, first copy the weight information table and denote it as U1. Then, it is necessary to determine whether there is an Euler circuit in the running path of the printer nozzle. The determination rule is: if and only if all vertex degrees in a graph are even and the graph is a connected graph, then there is an Euler circuit in the graph. The vertex degree is the number of non-zero elements in each row of the weight information table.

[0051] If there is an Euler circuit in the printer nozzle, the function for finding the path can be directly applied to find its maximum Euler circuit; if not, edge deletion operations need to be performed on U1. That is, delete the common non-zero elements of the rows in the matrix where the number of non-zero elements is odd. The specific edge deletion process is as follows:

[0052]

[0053] After the edge deletion process is completed, start to find the maximum Euler circuit for the first time. After finding, clear the weights of the found paths in the weight information table U. The operation process is as follows:

[0054]

[0055] After all the Euler circuits are finally found, connect all the un-found paths and clear all the elements in U. The final connected graph is as Figure 3 .

[0056] Step 4: Use the ant colony algorithm to find the shortest printing path.

[0057] In the said Step 4: (1) Initialize various parameters, such as the number of ants μ, the importance factor α of pheromone, the evaporation factor β of pheromone, the maximum number of iterations itermax, etc.; (2) Construct the solution space, randomly place each ant at different starting points, and calculate the next printing point to be visited for each ant k (k = 1, 2, 3…n) until all ants have visited all printing points; (3) Update the pheromone, calculate the path length d k (k = 1, 2,…, n) of each ant passing through, and record the optimal solution (the shortest path) in the current iteration. At the same time, update the pheromone concentration on the connection paths of each printing point; (4) Determine whether to terminate. If iter < itermax, then set iter = iter + 1, clear the record table of the paths passed by the ants, and return to Step 2; otherwise, terminate the calculation and output the optimal solution. The final simulation results are as Figure 4 .

[0058] The algorithm used in the present invention was tested on the Windows 10 operating platform using the MATLAB R2018a development tool. The specific software and hardware environment is as follows:

[0059] Table 1. Software and hardware environment parameters

[0060]

[0061] This application proposes a concrete 3D printing path optimization design method based on graph theory principles. First, the concrete 3D printed component is modeled and sliced ​​to find all the paths that the print head needs to run. Then find the maximum Euler circuit in the printing path (Euler circuit: it does not need to return to the starting point, but must pass through each edge, and only once. It is also called the "one-stroke" problem), then extract the remaining path and find the maximum Euler circuit again until there is no circuit. Then use the ant colony algorithm to find the shortest path between each Euler circuit vertex, and finally find the shortest path for the print head to run. This reduces the number of times the 3D printer nozzle is raised, reduces the empty stroke during the 3D printing process, thereby improving the molding quality of concrete prints and shortening the 3D printing time.

Claims

1. A path optimization design method for concrete 3D printing based on graph theory, characterized in that: The steps include: Step 1: Create a digital model of the concrete 3D printed part; Step 2: Create a weight information table; Step 3: Find the maximum Euler circuit according to the weight information table and update the weight information table, and then find the maximum Euler circuit of the updated weight information table again until all the printing paths are traversed; Step 4: Use the ant colony algorithm to find the shortest printing path; Steps of step 2: (1) When establishing the weight information table, it is first necessary to number the geometric points in the digital model established in step 1, in order of N1, N2, N3...N n , then create an n*n empty matrix T, where n is the number of geometric points; (2) After the empty matrix T is established, the elements in the empty matrix T are assigned values ​​according to the connection information between the geometric points in the digital model. The connected elements are assigned a value of 1, and the unconnected elements are assigned a value of 0. When all elements are assigned values, it is recorded as the weight information table U; The matrix U is:

2. The path optimization design method for concrete 3D printing based on graph theory principle according to claim 1 is characterized in that: In the step 1, a concrete print made of bulk solid waste cementitious materials is selected, and first the geometric data of the print is collected, and then a model is established on Sketch Up software according to the collected data, and then a digital model is established based on the collected data, and finally the established model is sliced ​​using Cura software.

3. The path optimization design method for concrete 3D printing based on graph theory principle according to claim 1 is characterized in that: Steps of step three: (1) In the process of finding the maximum Euler circuit in the weight information table U, first, it is necessary to copy the weight information table U and record it as U1, and then use the Euler circuit existence criterion to determine whether the elements in U1 meet the conditions for finding the Euler circuit. If not, perform an edge deletion operation (i.e., delete the non-maximum Euler circuit path in the table); (2) After the preprocessing of the elements in U1 is completed, the elements in the table that are not 0 are found from top to bottom and from left to right as the initial points of the connection path to start looking for the maximum Euler circuit; (3) After the maximum Euler circuit is found, an empty matrix T is created. The first row of elements in T stores the maximum Euler circuit that has been found, and its connection information is assigned to 0 in U. (4) Repeat operations (1-3). Each time (3) is repeated, the maximum Euler circuit needs to be stored in the next row in T until all elements in the weight information table U are 0; The judgment criteria are: If and only if all vertex degrees (the number of non-zero elements in each row of the weight information table) in a digital model are even and the graph is a connected graph, then there is an Euler circuit in the graph; If there is an Euler circuit in the printer nozzle, the path finding function can be directly applied to find its maximum Euler circuit; if it does not exist, the edge deletion operation is performed on U1. The specific edge deletion process is as follows: After the edge deletion process is completed, the maximum Euler circuit is searched for the first time. After the search is completed, the weight of the searched path is cleared in the weight information table U. The operation process is as follows: After all the Euler circuits are found, all the unfinded paths are connected and all elements in U are cleared.

4. The path optimization design method for concrete 3D printing based on graph theory principle according to claim 1 is characterized in that: The steps of step 4 are: (1) Classifying the geometric points in the digital model according to the different Euler circuits being sought; (2) Each time, a point is extracted from each category and the shortest path is found using the ant colony algorithm, where (x1, y1), (x2, y2), (x3, y3) ... (x n ,y n ) represent the coordinates of each point, and the relative distance d between each point is obtained by the following formula ij , add up each d ij The sum of the distances of each point is recorded as d k , each time a printed point is connected, a pheromone τ is left behind k , τ k The value of decreases with the length of the printing distance, and as time increases, τ k As τ decreases, k The calculation formula is as follows, and then use d according to the following formula k , τ k Calculate the probability p of printing the next point k , it can be seen from the formula that the smaller the distance between two points, the greater the probability of being printed next time. As time goes by, the larger the pheromone value left behind, and finally, under the positive feedback of the algorithm, the printing path will be concentrated on the optimal path;

Images