Charging method of automatic charging equipment

Through the charging method of automatic charging equipment, the problem of insufficient accuracy of the blast hole position during tunnel excavation is solved, and the full automation of tunnel blasting and construction efficiency are improved.

CN119618005APending Publication Date: 2025-03-14CHINA RAILWAY 14TH BUREAU GRP NO 3 ENG CO LTD +1
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Patent Information

Application Number
CN202411980952.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-31
Publication Date
2025-03-14

AI Technical Summary

Technical Problem

In the construction of tunnel boring and drilling method in tunnel boring, the accuracy of the blast hole position is insufficient, resulting in the problem of tunnel over-excavation and the deviation of the line from the design route.

Method used

The charging method of automatic charging equipment is adopted to achieve full automation of tunnel blasting by designing blasting parameters, automatically drilling and cleaning the blasting hole, identifying the type of blasting hole, manually confirming the parameters, planning the loading sequence and performing loading operations.

Benefits of technology

It improves the accuracy of the blast hole position, realizes the full automation of tunnel blasting, reduces manual intervention, ensures process accuracy, and improves construction efficiency.

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Abstract

The invention discloses a charging method of automatic charging equipment. The charging method comprises the steps that S1, blasting parameters are designed; s2, shot holes are drilled on site; s3, identifying blast hole types; s4, manually confirming parameters; s5, planning a charging sequence: training the charging sequence according to the charging sequence of the peripheral holes and the auxiliary holes first and then the underholing holes; and S6, explosive loading operation is conducted, specifically, according to different explosive states, the drill jumbo carries different explosive loading devices to conduct explosive loading, whether explosive feeding is in place each time or not is determined through a sensor, explosive loading parameters are checked, and explosive loading is completed. The device can quickly identify the type of a field blast hole, quickly confirm specific charging parameters, realize whole-course automation of tunnel blasting, ensure the process accuracy and improve the construction efficiency.
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Description

Technical Field

[0001] The invention relates to the technical field of tunnel construction, and in particular to a charging method of automatic charging equipment. Background Art

[0002] In tunnel construction, engineers adopt different excavation methods to adapt to different types of geological conditions, such as the drilling and blasting method. The drilling and blasting method is to drill holes at the blasthole positions pre-set on the tunnel face, and then perform charging and blasting to achieve rock excavation. The preset blasthole positions on the tunnel face determine the blasting quality, which in turn affects the tunnel route.

[0003] At present, the method of combining total station with manual experience is usually used to determine the blasthole position of the tunnel face. Specifically, the total station is set up on a tripod and placed at the corresponding tunnel position. The position and parameters of the total station are constantly adjusted manually to measure and obtain the position of one blasthole. The positions of other blastholes are obtained based on the construction experience of the construction personnel. The method of judging the remaining blastholes based solely on construction experience is likely to result in large errors in the blasthole positions, reducing the accuracy of the blasthole positions, and making it easy for the tunnel to be over-excavated or under-excavated and the tunnel alignment to deviate from the designed route after blasting. Summary of the invention

[0004] In order to solve the above problems in the prior art, a charging method for an automatic charging device is provided.

[0005] The technical solution adopted by the present invention to solve its technical problem is:

[0006] The present invention provides a charging method for automatic charging equipment, comprising the following steps:

[0007] S1: Design blasting parameters: Design blasting parameters according to surrounding rock type and design section size, determine the location, depth and specific charging parameters of the cut hole, auxiliary hole and peripheral hole;

[0008] S2: On-site blasthole drilling: input the designed blasting parameters into the drilling rig for automatic drilling, and then clean the blasthole with high-pressure air or water;

[0009] S3: Identify the type of blasthole: After the drilling rig is in place, take photos of the tunnel face with a high-definition camera, and compare the coordinates of the blastholes with the input blasting parameters;

[0010] S4: Manual confirmation of parameters: After the blasthole type identification is completed, the technicians will confirm the results again, manually correct the possible deviations of individual blastholes, and complete the confirmation of the design charge parameters;

[0011] S5: Plan the charging sequence: Carry out charging sequence training, according to the charging sequence of peripheral holes and auxiliary holes first, and then the slot holes. Through repeated training, several mechanical arms of the rock drilling rig can operate at the same time without position collision in space;

[0012] S6: Charging operation: According to the different states of explosives, the drilling rig is equipped with different charging equipment to charge, and uses sensors to determine whether each charge is in place, check the charging parameters, and complete the charging.

[0013] Preferably, the optimization of blasting parameters based on the Kuz-Ram model comprises the following steps:

[0014] S11: Collect basic data, including rock properties, explosive properties and blasting site conditions;

[0015] S12: Predict block size distribution, the formula is as follows:

[0016]

[0017] In the formula, is the average size of rock fragments after blasting, K is a constant related to rock properties, E is the blasting energy of explosives, Q is the charge per hole, and S is the distance between blast holes;

[0018] Based on the determined initial blasting parameters, substitute them into formula (1) to calculate the average block size of the rock after blasting;

[0019] S13: According to the predicted block size distribution and engineering requirements, the blasting parameters are adjusted. The blasting parameters include blasthole diameter, blasthole spacing, charge amount, and a wide hole narrow row hole arrangement method is adopted;

[0020] S14: Establish an optimization model with the goal of minimizing the drilling and blasting cost and the constraints of large block rate, blasting volume and blasting parameters meeting the prescribed values.

[0021] Preferably, optimizing the Kuz-Ram model based on the optimization model comprises the following steps:

[0022] S21: Initialize the population: randomly generate N individuals in the feasible domain, each individual represents a set of blasting parameter vectors, the formula is as follows:

[0023] X i =X min +(X max -X min )·rand(n) (2);

[0024] Where i = 1, 2, ..., N, rand(n) is an n-dimensional random vector whose elements are uniformly distributed between 0 and 1;

[0025] The blasting parameter vector includes blasthole diameter D, blasthole depth H, blasthole spacing S, charge amount Q, and plugging length L;

[0026] S22: Define the objective function, take a set of blasting parameter vectors as input, and output a cost value. The objective function is the weighted sum of blasting cost, fragmentation effect, and safety distance. The formula is as follows:

[0027]

[0028] Where, X i is the blow-up parameter vector, C i (x) is the i-th cost item, and n is the total number of cost items;

[0029] S23: Search for the optimal solution. In each iteration, the position of each individual is updated according to the current optimal solution X*. The update formula is as follows:

[0030] X i (t+1)=X * (t)+A·(X * (t)-X i (t)) (4);

[0031] In the formula, A is a coefficient that decreases linearly with the number of iterations. t is the current iteration number, T is the total iteration number;

[0032] S24: Update the position of the optimal solution X* found, the formula is as follows:

[0033] X i (t+1)=X * (t)-A·C·(X i (t)-X * (t)) (5);

[0034] Where C is a random number, C∈[0,1];

[0035] Perform spiral update, the formula is as follows:

[0036] X i (t+1)=D * ·e B·l (6);

[0037] In the formula, D* is the distance between the optimal solution and the individual, B is the shape parameter, and l is a random number uniformly distributed in the range of [-1,1];

[0038] S25: Update the optimal solution if the new position X i (t+1) produces a better objective function value, then the current optimal solution formula is updated as follows:

[0039] X * (t+1)=X i (t+1), if, f(X i (t+1))<f(X * (t)) (7);

[0040] Through the iterative process, when the maximum number of iterations is reached or the value of the objective function is lower than the threshold, the algorithm stops, and the optimal solution at this time is the blasting parameter group with the minimum cost.

[0041] Preferably, during the drilling process, the drilling trolley automatically collects the hardness and softness of the rock formation at the blasthole location, and automatically calculates and adjusts the single-hole design blasting parameters.

[0042] Preferably, the charging sequence training method comprises:

[0043] Define k i represents the charge of the ith blasthole, t i represents the charging time of the ith blasthole, O i represents the role of the i-th turret;

[0044] Define the objective function, the formula is as follows:

[0045]

[0046] Where K is the charge vector, t is the charge time vector, C i (x i ) is the cost function of the ith blasthole, λ is the penalty coefficient used to increase the value of the objective function when the charging sequence is violated, δ(Q i ,Q j ) is the indicator function, when O i and O j When the charging sequence is incorrect, it takes a positive value, otherwise it takes a 0 value. By minimizing the objective function, the minimum cost charging scheme that satisfies the charging sequence constraints is found.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The present application is provided with a drilling rig, blasting parameters are input into the drilling rig, and holes are drilled by the drilling rig. At the same time, the blast holes can be automatically cleaned after drilling, and during the drilling process, the drilling rig can automatically collect the softness and hardness of the rock strata at the blast hole position, automatically calculate and adjust the single-hole design blasting parameters, and realize the differentiation of blast hole spacing and charging. After that, the drilling rig carries out charging, and the drilling rig recognizes the coordinates of the drilled hole position for image coordinate comparison, which can quickly identify the type of blast hole on site, quickly confirm the specific charging parameters, and realize the full automation of tunnel blasting. No human intervention is required throughout the process, which can ensure process accuracy and improve construction efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0050] Figure 1 is an overall top view of the present invention;

[0051] Figure 2 It is the overall front view of the present invention;

[0052] Figure 3 is an overall side view of the present invention;

[0053] Figure 4 It is the overall flow chart of the present invention.

[0054] Description of reference numerals:

[0055] 1. Six-axis robotic arm; 2. Telescopic industrial arm; 3. Working platform; 4. Walking tracks; 5. High-definition camera. DETAILED DESCRIPTION

[0056] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0057] like Figure 1-Figure 4 As shown, this embodiment proposes a charging method for automatic charging equipment, comprising the following steps:

[0058] S1: Design blasting parameters: Design blasting parameters according to surrounding rock type and design section size, determine the location, depth and specific charging parameters of the cut hole, auxiliary hole and peripheral hole;

[0059] S2: On-site blast hole drilling: The designed blasting parameters are input into the drilling trolley, and the telescopic industrial arm 2 can drive the six-axis robotic arm 1 to move, and the six-axis robotic arm 1 drives the drilling mechanism to move in the space to perform automatic drilling. After drilling, the blast hole is cleaned by high-pressure air or high-pressure water;

[0060] S3: Identify the type of blasthole: After the drilling rig is in place, the high-definition camera 5 is used to take photos of the tunnel face, and the coordinate position of the blasthole is compared by inputting the blasting parameters. Due to certain construction errors on site, a certain position deviation allowance standard is set, and the on-board computer automatically calculates and outputs the preliminary comparison results;

[0061] The high-definition camera 5 is arranged on the working platform 3, the working platform 3 is connected with a rotatable walking crawler 4, the walking crawler 4 is connected with a driving mechanism, and the crawler walking mode is adopted to adapt to various complex terrains;

[0062] S4: Manual confirmation of parameters: After the blasthole type identification is completed, the technicians will confirm the results again, manually correct the possible deviations of individual blastholes, and complete the confirmation of the designed charging parameters. At this time, the computer has clearly defined the specific charging parameters for each hole position, including the number of explosives, whether the charging is dispersed, etc.

[0063] S5: Plan the charging sequence: Carry out charging sequence training, according to the charging sequence of peripheral holes and auxiliary holes first, and then the slot holes. Through repeated training, several mechanical arms of the drilling rig can work at the same time without position collision in space, and can work at the highest efficiency;

[0064] S6: Charging operation: According to the different states of explosives, the drilling rig is equipped with different charging equipment for charging. Sensors are used to determine whether the explosives are delivered in place each time, and the charging parameters are checked to avoid operational errors and complete the charging.

[0065] The optimization of blasting parameters based on the Kuz-Ram model includes the following steps:

[0066] S11: Collect basic data, including rock properties, explosive properties and blasting site conditions;

[0067] Rock properties: Obtain the physical and mechanical properties of rocks, such as the compressive strength, elastic modulus, Poisson's ratio, etc. These parameters can be obtained through laboratory tests or field tests. At the same time, determine relevant indicators such as the rock's strength coefficient for subsequent model calculations.

[0068] Explosive performance: clarify the performance parameters of the explosives used, such as detonation velocity, detonation heat, and intensity. The performance of explosives directly affects the release and transfer of blasting energy and has an important impact on the blasting effect.

[0069] Blasting site: Understand the topography, geological structure, surrounding environment and other information of the blasting area. For example, whether there are buildings, roads and other objects that need to be protected in the surrounding area, which will affect the safety and feasibility of the blasting design.

[0070] S12: Predict block size distribution, the formula is as follows:

[0071]

[0072] In the formula, is the average size of rock fragments after blasting, K is a constant related to rock properties, E is the blasting energy of explosives, Q is the charge per hole, and S is the distance between blast holes;

[0073] Based on the determined initial blasting parameters, the average rock fragment size after blasting is calculated by substituting them into formula (1). At the same time, the rock fragment size distribution in different particle size ranges can be further analyzed based on the model.

[0074] S13: According to the predicted block size distribution and engineering requirements, the blasting parameters are adjusted. The blasting parameters include blasthole diameter, blasthole spacing, charge amount, and a wide hole narrow row hole arrangement method is adopted;

[0075] S14: Establish an optimization model with the goal of minimizing the drilling and blasting cost and the constraints of large block rate, blasting volume and blasting parameters meeting the prescribed values.

[0076] At the same time, the blasting effect should be evaluated in time: according to the calculated rock fragmentation distribution and the actual needs of the project, the effect of the current blasting design should be evaluated. For example:

[0077] Degree of crushing: Determine whether the degree of rock crushing meets the requirements of subsequent construction, such as the efficiency of excavation, transportation and other operations. If the blocks are too large, it may increase the difficulty and cost of construction.

[0078] Explosion pile shape: Analyze whether the shape and size of the blast pile meet expectations and whether it is conducive to subsequent operations. Unreasonable blast pile shape may lead to uneven rock accumulation and affect construction progress.

[0079] Impact on the surrounding environment: Consider the impact of vibrations, flying rocks, etc. caused by blasting on the surrounding environment. If they exceed the safe allowable range, appropriate measures need to be taken to make adjustments.

[0080] According to the evaluation results, the blasting parameters are adjusted and optimized. The optimization directions usually include:

[0081] Adjust the charge: Increase or decrease the charge per hole to change the input of blasting energy, thereby affecting the degree of rock crushing and fragmentation distribution.

[0082] Change the spacing and row spacing of blastholes: adjust the distance between blastholes to change the propagation and superposition of blasting stress waves, thereby optimizing the rock crushing effect.

[0083] Optimize the detonation sequence: By changing the detonation sequence, the time and space effects of blasting can be controlled to make the rock breakage more uniform and reduce the rate of large blocks.

[0084] After each parameter adjustment, the Kuz-Ram model is re-substituted for calculation and evaluation until a satisfactory blasting effect is obtained.

[0085] Field test and verification: In actual projects, field tests are carried out according to the optimized blasting parameters. Through actual observation and data collection of the on-site blasting effect, such as actual measurement of rock block size, recording of blast pile morphology, monitoring of blasting vibration and flying rocks, further verification is made as to whether the optimized blasting design meets the requirements.

[0086] If there is a difference between the field test results and the expected effects, it is necessary to analyze the reasons and adjust and optimize the blasting parameters again until the best blasting effect is achieved.

[0087] Throughout the blasting process, data is continuously collected and analyzed, and lessons learned are summarized. As the project progresses and geological conditions change, the blasting design is continuously optimized and improved to ensure the efficiency, safety, and economy of the blasting project. Through the above steps, the application of the Kuz-Ram model can achieve scientific optimization of blasting design, improve blasting effects, reduce engineering costs, and ensure the safety of blasting operations and minimize the impact on the surrounding environment.

[0088] The Kuz-Ram model is optimized based on the optimization model, including the following steps:

[0089] S21: Initialize the population: randomly generate N individuals in the feasible domain, each individual represents a set of blasting parameter vectors, the formula is as follows:

[0090] X i =X min +(X max -X min )·rand(n) (2);

[0091] Where i = 1, 2, ..., N, rand(n) is an n-dimensional random vector whose elements are uniformly distributed between 0 and 1;

[0092] The blasting parameter vector includes blasthole diameter D, blasthole depth H, blasthole spacing S, charge amount Q, and plugging length L;

[0093] S22: Define the objective function, take a set of blasting parameter vectors as input, and output a cost value. The objective function is the weighted sum of blasting cost, fragmentation effect, and safety distance. The formula is as follows:

[0094]

[0095] Where, X i is the blow-up parameter vector, C i (x) is the i-th cost item, and n is the total number of cost items;

[0096] S23: Search for the optimal solution. In each iteration, the position of each individual is updated according to the current optimal solution X*. The update formula is as follows:

[0097] X i (t+1)=X * (t)+A·(X * (t)-X i (t)) (4);

[0098] In the formula, A is a coefficient that decreases linearly with the number of iterations. t is the current iteration number, T is the total iteration number;

[0099] S24: Update the position of the optimal solution X* found, the formula is as follows:

[0100] X i (t+1)=X * (t)-A·C·(X i (t)-X * (t)) (5);

[0101] Where C is a random number, C∈[0,1];

[0102] Perform spiral update, the formula is as follows:

[0103] X i (t+1)=D * ·e B·l (6);

[0104] In the formula, D* is the distance between the optimal solution and the individual, B is the shape parameter, and l is a random number uniformly distributed in the range of [-1,1];

[0105] S25: Update the optimal solution if the new position X i (t+1) produces a better objective function value, then the current optimal solution formula is updated as follows:

[0106] X * (t+1)=X i (t+1), if, f(X i (t+1))<f(X * (t)) (7);

[0107] Through the iterative process, when the maximum number of iterations is reached or the value of the objective function is lower than the threshold, the algorithm stops, and the optimal solution at this time is the blasting parameter group with the minimum cost.

[0108] In S2, during the drilling process, the drilling rig automatically collects the hardness and softness of the rock formation at the blasthole location, automatically calculates, and adjusts the single-hole design blasting parameters.

[0109] In S5, the charging sequence training method includes:

[0110] Define k i represents the charge of the ith blasthole, t i represents the charging time of the ith blasthole, O i represents the role of the i-th turret;

[0111] Define the objective function, the formula is as follows:

[0112]

[0113] Where K is the charge vector, t is the charge time vector, C i (x i ) is the cost function of the ith blasthole, λ is the penalty coefficient used to increase the value of the objective function when the charging sequence is violated, δ(Q i ,Q j ) is the indicator function, when O i and O j When the charging sequence is incorrect, it takes a positive value, otherwise it takes a 0 value. By minimizing the objective function, the minimum cost charging scheme that satisfies the charging sequence constraints is found.

[0114] In practical applications, intelligent optimization algorithms such as genetic algorithms and particle swarm optimization algorithms can be used to solve this optimization problem. Through the above steps, the designed algorithm can optimize the charging sequence to make the blasting operation more efficient and safe.

[0115] The drilling rig can realize automatic drilling and automatic cleaning of the blastholes after drilling. After identifying the blasthole type, the drilling rig can automatically collect the hardness of the rock formation at the blasthole location during the drilling process, automatically calculate and adjust the single-hole design blasting parameters, and realize the differentiation of blasthole spacing and charging. It can quickly identify the type of blastholes on site, quickly confirm the specific charging parameters, and realize the full automation of tunnel blasting. No human intervention is required throughout the process, which can ensure process accuracy and improve construction efficiency.

[0116] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A charging method for automatic charging equipment, characterized in that: The following steps are involved: S1: Design blasting parameters: Design blasting parameters according to surrounding rock type and design section size, determine the location, depth and specific charging parameters of the cut hole, auxiliary hole and peripheral hole; S2: On-site blasthole drilling: input the designed blasting parameters into the drilling rig for automatic drilling, and then clean the blasthole with high-pressure air or water; S3: Identify the type of blasthole: After the drilling rig is in place, take photos of the tunnel face with a high-definition camera, and compare the coordinates of the blastholes with the input blasting parameters; S4: Manual confirmation of parameters: After the blasthole type identification is completed, the technicians will confirm the results again, manually correct the possible deviations of individual blastholes, and complete the confirmation of the design charge parameters; S5: Plan the charging sequence: Carry out charging sequence training, according to the charging sequence of peripheral holes and auxiliary holes first, and then the slot holes. Through repeated training, several mechanical arms of the rock drilling rig can operate at the same time without position collision in space; S6: Charging operation: According to the different states of explosives, the drilling rig is equipped with different charging equipment to charge, and uses sensors to determine whether each charge is in place, check the charging parameters, and complete the charging.

2. A charging method for automatic charging equipment according to claim 1, characterized in that: The optimization of blasting parameters based on the Kuz-Ram model includes the following steps: S11: Collect basic data, including rock properties, explosive properties and blasting site conditions; S12: Predict block size distribution, the formula is as follows: In the formula, is the average size of rock fragments after blasting, K is a constant related to rock properties, E is the blasting energy of explosives, Q is the charge per hole, and S is the distance between blast holes; Based on the determined initial blasting parameters, substitute them into formula (1) to calculate the average block size of the rock after blasting; S13: According to the predicted block size distribution and engineering requirements, the blasting parameters are adjusted. The blasting parameters include blasthole diameter, blasthole spacing, charge amount, and a wide hole narrow row hole arrangement method is adopted; S14: Establish an optimization model with the goal of minimizing the drilling and blasting cost and the constraints of large block rate, blasting volume and blasting parameters meeting the prescribed values.

3. A charging method for automatic charging equipment according to claim 2, characterized in that: The Kuz-Ram model is optimized based on the optimization model, including the following steps: S21: Initialize the population: randomly generate N individuals in the feasible domain, each of which represents a set of blasting parameter vectors. The formula is as follows: X i =X min +(X max -X min )·rand(n) (2); Where i = 1, 2, ..., N, rand(n) is an n-dimensional random vector whose elements are uniformly distributed between 0 and 1; The blasting parameter vector includes blasthole diameter D, blasthole depth H, blasthole spacing S, charge amount Q, and plugging length L; S22: Define the objective function, take a set of blasting parameter vectors as input, and output a cost value. The objective function is the weighted sum of blasting cost, fragmentation effect, and safety distance. The formula is as follows: In the formula, X i is the blow-up parameter vector, C i (x) is the i-th cost item, and n is the total number of cost items; S23: Search for the optimal solution. In each iteration, the position of each individual is updated according to the current optimal solution X*. The update formula is as follows: X i (t+1)=X * (t)+A·(X * (t)-X i (t)) (4); In the formula, A is a coefficient that decreases linearly with the number of iterations. t is the current iteration number, T is the total iteration number; S24: Update the position of the optimal solution X* found, the formula is as follows: X i (t+1)=X * (t)-A·C·(X i (t)-X * (t)) (5); Where C is a random number, C∈[0,1]; Perform spiral update, the formula is as follows: X i (t+1)=D * ·e B·l (6); In the formula, D* is the distance between the optimal solution and the individual, B is the shape parameter, and l is a random number uniformly distributed in the range of [-1,1]; S25: Update the optimal solution if the new position X i (t+1) produces a better objective function value, then the current optimal solution formula is updated as follows: X * (t+1)=X i (t+1),if,f(X i (t+1))<f(X * (t)) (7); Through the iterative process, when the maximum number of iterations is reached or the value of the objective function is lower than the threshold, the algorithm stops, and the optimal solution at this time is the blasting parameter group with the minimum cost.

4. The charging method of the automatic charging equipment according to claim 1, characterized in that: In S2, during the drilling process, the drilling trolley automatically collects the hardness and softness of the rock formation at the blasthole location, automatically calculates, and adjusts the single-hole design blasting parameters.

5. The charging method of the automatic charging equipment according to claim 1, characterized in that: In S5, the charging sequence training method includes: Define k i represents the charge of the ith blasthole, t i represents the charging time of the ith blasthole, O i represents the role of the i-th turret; Define the objective function, the formula is as follows: Where K is the charge vector, t is the charge time vector, C i (x i ) is the cost function of the ith blasthole, λ is the penalty coefficient used to increase the value of the objective function when the charging sequence is violated, δ(Q i ,Q j ) is the indicator function, when O i and O j When the charging sequence is incorrect, it takes a positive value, otherwise it takes a 0 value. By minimizing the objective function, the minimum cost charging scheme that satisfies the charging sequence constraints is found.