Multi-parameter matching method of crane power system considering load and dynamic characteristics

Abstract

The application belongs to the technical field of cranes, and particularly relates to a crane power system multi-parameter matching method considering load and dynamic characteristics, comprising S1. calculating motor torque speed basic demand and additional demand to obtain working condition power demand; S2. according to different motor power levels and speed reducer transmission ratios, different speed-torque level combinations, i.e. torque speed capability models, can be obtained; S3. taking motor power and speed reducer transmission ratio redundancy, motor-speed reducer system energy consumption, power system mass and minimum procurement cost as optimization targets, a multi-objective optimization function is constructed, a multi-objective differential evolution algorithm is improved based on a dynamic focusing strategy for iteration until an optimal solution is output; power system parameters are systematically matched and designed, so that multi-objective collaborative optimization of system redundancy, energy consumption and mass cost is considered while work efficiency is ensured.

Description

Technical Field

[0001] This application belongs to the field of crane technology, specifically relating to a multi-parameter matching method for a crane power system that considers load and dynamic characteristics. Background Technology

[0002] Cranes are responsible for loading and unloading cargo in port operations. During the operation, they usually need to perform actions such as lifting, slewing, luffing, and traveling.

[0003] In the traditional design of cranes, the core components of the power system, such as motors and reducers, are typically designed based on rated loads and experience under extreme conditions, with sufficient safety margins. However, in most actual operations, motors operate at lower load ranges for extended periods, resulting in lower energy efficiency and higher equipment costs, and making it difficult to meet the dynamic response requirements under different operating conditions.

[0004] However, with the increasing demand for automation, high efficiency, low energy consumption, and low cost in port equipment design, the key technical challenge facing port equipment design is how to match the parameters of the crane's power system while meeting the overall dynamic characteristics, swaying behavior, and loading and unloading cycle efficiency of the crane, so as to reduce energy consumption and costs while ensuring operational efficiency. Summary of the Invention

[0005] To address the above problems, this invention proposes a multi-parameter matching method system for crane power systems that considers load and dynamic characteristics. The technical solution is as follows: A multi-parameter matching method for a crane power system considering load and dynamic characteristics includes the following steps: S1. Calculate the basic and additional requirements of the mechanism's torque and speed to obtain the power requirements under working conditions; S2. Based on different motor power levels and reducer transmission ratios, different speed-torque level combinations can be obtained, i.e., torque-speed capability models; S3. With the optimization objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass and procurement cost, a multi-objective optimization function is constructed. The multi-objective differential evolution algorithm is improved based on dynamic focusing strategy and iterated until the optimal solution is output.

[0006] Preferably, it is assumed that the work area is divided into N discrete working conditions. Determine the torque and speed requirements for each power unit; The crane has a total of k power mechanisms. The speed and torque requirements of the k-th power mechanism under the i-th operating condition are as follows: ; in, Let the torque requirement of the k-th power mechanism be the torque requirement under the i-th operating condition. This represents the basic torque requirement of the k-th power mechanism under the i-th operating condition. This represents the additional torque requirement of the k-th power mechanism under the i-th operating condition. Let the k-th power mechanism be the speed requirement under the i-th operating condition. The base speed requirement of the k-th power mechanism under the i-th operating condition is given by [the relevant information]. This represents the additional speed requirement of the k-th power mechanism under the i-th operating condition. Together, these two constitute the power demand of the k-th power mechanism under the i-th operating condition. : ; in, Let the power requirement of the k-th power mechanism be the power demand under the i-th operating condition. Let the k-th power mechanism be the speed requirement under the i-th operating condition. Let represent the torque requirement of the k-th power mechanism under the i-th operating condition.

[0007] Preferably, assuming the work area is divided into N discrete working conditions, the power demand set is obtained by iterating through and solving for each working condition: ; in, Let k be the set of power demands of the k-th institution. Let i be the power demand of the k-th mechanism under the i-th working condition. Thus, the motion and load demand of the port crane within its operating range is transformed into a set of demands on a two-dimensional torque-speed plane.

[0008] Preferably, different speed-torque level combinations can be obtained based on different motor power ratings and reducer transmission ratios, i.e., torque-speed capability models. Based on these torque-speed capability models, the rated power of the motor can be used to determine the appropriate speed-torque level combinations. Rated speed Gearbox transmission ratio To obtain the maximum output speed of the power mechanism and maximum output torque When selecting a motor and reducer, both must meet the maximum allowable torque range; therefore, the driving capability must satisfy the boundary conditions. ; in, Let k be the set of allowable driving ranges for the k-th power mechanism. Let the k-th power mechanism be the speed requirement under the i-th operating condition. Let the torque requirement of the k-th power mechanism be the torque requirement under the i-th operating condition. This represents the maximum output speed of the power mechanism. This represents the maximum output torque of the power mechanism.

[0009] Preferably, step S3 uses a multi-objective differential evolution algorithm to search for the optimal motor-reducer parameter combination, specifically as follows: S31. Define a multi-objective optimization function: Objective function 1: Minimize the redundancy of motor power and reducer transmission ratio. ; in, The objective function is to minimize the redundancy of motor power and reducer transmission ratio. The rated torque of the motor. The rated speed of the motor. The gear ratio of the reducer. and These represent the torque and speed requirements of the k-th power mechanism under the i-th operating condition, respectively. Let be the maximum torque requirement of the k-th power mechanism across all N operating conditions. This represents the maximum speed requirement of the k-th power mechanism across all N operating conditions. Objective function 2: Minimizing the energy consumption of the motor-reducer system is the optimization objective. ; in, The objective function is to minimize the energy consumption of the motor-gearbox system. This refers to the rated power of the motor. To achieve the required operating efficiency of the k-th power mechanism under the i-th operating condition, by... and After determining the motor model, the operating efficiency is obtained based on the corresponding efficiency characteristic curve of the motor. For the reducer at the transmission ratio The transmission efficiency is reduced. The duration of the crane's operation under the i-th working condition is determined based on the working condition time sequence record; Objective function 3: The optimization objective is to minimize the power system quality and procurement cost. ; in, The objective function is to minimize the power system quality and procurement cost. ( )and ( ) are the cost functions for the motor and the reducer, respectively. ( )and ( ) are the mass functions of the motor and the reducer, respectively. , , , These are the weighting coefficients; To maintain the uniformity of numerical magnitude among objective functions 1, 2, and 3, a normalization transformation is first performed. The normalized objective functions 1, 2, and 3 are denoted as follows: , , ; With the optimization objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass, and procurement cost, a multi-objective optimization function is constructed: ; in, For a multi-objective optimization function, , , These are the weighting coefficients; S32. Initialize the candidate population: ; ; in, For iteration G, the candidate population is initialized. , There are M candidate solutions. It is the first The j-th candidate solution after the nth iteration. The first The rated power of the motor, the rated speed of the motor, and the transmission ratio of the reducer for the j-th candidate solution after the nth iteration. For the first The candidate population after the next iteration; For the Candidate solutions after the next iteration Perform driving capability judgment, that is, for candidate solutions All should meet the driving capability constraints. If a candidate solution does not meet the driving capability constraint, it should be discarded, and other candidate solutions should be judged to meet the driving capability constraint. For the Candidate population after the next iteration The process involves screening and searching for candidate solutions within the population. The parameters differ significantly, but the multi-objective optimization function can be used. Determine the candidate solution with better performance , and candidate solutions The parameter differences are small, but the multi-objective optimization function is used. Identify candidate solutions with poor performance And generate dynamically adjusted direction; ; in, Denotes the candidate solution after the g-th iteration. Dynamic adjustment of direction, Denotes the candidate solution after the g-th iteration. The weights with significantly different dynamic focusing parameters but superior performance Weights that represent parameters with small differences but poor performance. This is the scaling factor, used to control the step size; ; ; The dynamic focusing weights are adjusted during the iteration process. and They tend towards 1 and 0 respectively, so that dynamic adjustment directions with large differences can still be generated in the later stages of iteration, preventing them from getting trapped in local optima in the later stages of iteration; S33. Parameter optimization based on multi-objective differential evolution algorithm: Generate new candidate solutions after mutation: ; Determine new candidate solutions Does it meet the driving capability constraint? If the conditions are not met, then discard the new candidate solution. Retain candidate solutions If satisfied, then calculate and compare. and ,like Then use the new candidate solution. Replace candidate solutions Otherwise, retain the candidate solution. If new candidate solutions for several consecutive generations fail to meet the requirements for replacing candidate solutions, the scaling factor is gradually reduced. The process involves regenerating new candidate solutions until a new candidate solution meets the requirements for replacing the candidate solution while satisfying the driving capability constraints. The optimization objectives are to minimize motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, and power system mass and procurement cost. After G iterations, the optimal multi-objective optimization function is selected from the final retained candidate solutions. The candidate solution that yields the minimum value is taken as the optimal solution. = ; in, This represents the optimal solution obtained through iterative optimization, with the objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass, and procurement cost. This represents the parameter combination that minimizes the multi-objective optimization function. , , These are the optimal solutions for the rated power, rated speed, and reducer transmission ratio of the motor in the k-th group of mechanisms, respectively. S34. Perform parameter optimization processes on the four mechanisms of traveling, slewing, luffing, and hoisting respectively to obtain the configuration results of the overall machine power system: ; , , These are the optimal solutions for the rated power of the motor, the rated speed of the motor, and the transmission ratio of the reducer for the k-th mechanism.

[0010] Compared to existing solutions, this application makes the following contributions:

[0011] 1. This invention obtains the working power requirements by calculating the basic and additional requirements of the torque and speed of the mechanism, thus avoiding the deviation caused by traditional methods that rely solely on the maximum load or empirical coefficients for estimation.

[0012] 2. This invention forms a set of speed-torque power requirements by traversing the operating range and matches it with the capacity range of the motor-reducer, so that the parameter selection can cover the power requirements under different operating positions and reduce the deviation caused by single working condition selection.

[0013] 3. The dynamic focusing strategy improves the multi-objective differential evolution algorithm to complete the system optimization of power system parameters. It adopts a hierarchical strategy based on the parameter difference with the largest but optimal performance and the parameter difference with the smallest but poor performance to avoid getting stuck in local optima during the optimization stage. This allows for the reduction of motor power level and transmission system specifications while meeting the operational capability requirements, thereby reducing equipment manufacturing costs and operating energy consumption. Attached Figure Description

[0014] Figure 1 This is the overall flowchart. Detailed Implementation

[0015] A multi-parameter matching method for a crane power system considering load and dynamic characteristics includes the following steps: S1. Calculate the basic and additional requirements of the mechanism's torque and speed to obtain the power requirements under working conditions; S2. Based on different motor power levels and reducer transmission ratios, different speed-torque level combinations can be obtained, i.e., torque-speed capability models; S3. With the optimization objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass and procurement cost, a multi-objective optimization function is constructed. The multi-objective differential evolution algorithm is improved based on dynamic focusing strategy and iterated until the optimal solution is output.

[0016] Assume that the work area is divided into N discrete working conditions. Determine the torque and speed requirements for each power unit; The crane has a total of k power mechanisms. The speed and torque requirements of the k-th power mechanism under the i-th operating condition are as follows: ; in, Let the torque requirement of the k-th power mechanism be the torque requirement under the i-th operating condition. This represents the basic torque requirement of the k-th power mechanism under the i-th operating condition. This represents the additional torque requirement of the k-th power mechanism under the i-th operating condition. Let the k-th power mechanism be the speed requirement under the i-th operating condition. The base speed requirement of the k-th power mechanism under the i-th operating condition is given by [the relevant information]. This represents the additional speed requirement of the k-th power mechanism under the i-th operating condition. Together, these two constitute the power demand of the k-th power mechanism under the i-th operating condition. : ; in, Let the power requirement of the k-th power mechanism be the power demand under the i-th operating condition. Let the k-th power mechanism be the speed requirement under the i-th operating condition. Let represent the torque requirement of the k-th power mechanism under the i-th operating condition.

[0017] Assuming the work area is divided into N discrete working conditions, the power demand set is obtained by iterating through and solving for each working condition: ; in, Let k be the set of power demands of the k-th institution. Let i be the power demand of the k-th mechanism under the i-th working condition. Thus, the motion and load demand of the port crane within its operating range is transformed into a set of demands on a two-dimensional torque-speed plane.

[0018] Based on different motor power ratings and reducer transmission ratios, different speed-torque level combinations can be obtained, i.e., torque-speed capability models. These torque-speed capability models can be used to determine the appropriate speed-torque capability based on the motor's rated power. Rated speed Gearbox transmission ratio To obtain the maximum output speed of the power mechanism and maximum output torque When selecting a motor and reducer, both must meet the maximum allowable torque range; therefore, the driving capability must satisfy the boundary conditions. ;

[0019] in, Let k be the set of allowable driving ranges for the k-th power mechanism. Let the k-th power mechanism be the speed requirement under the i-th operating condition. Let the torque requirement of the k-th power mechanism be the torque requirement under the i-th operating condition. This represents the maximum output speed of the power mechanism. This represents the maximum output torque of the power mechanism.

[0020] Step S3 uses a multi-objective differential evolution algorithm to search for the optimal combination of motor-reducer parameters, specifically: S31. Define a multi-objective optimization function: Objective function 1: Minimize the redundancy of motor power and reducer transmission ratio. ; in, The objective function is to minimize the redundancy of motor power and reducer transmission ratio. The rated torque of the motor. The rated speed of the motor. The gear ratio of the reducer. and These represent the torque and speed requirements of the k-th power mechanism under the i-th operating condition, respectively. Let be the maximum torque requirement of the k-th power mechanism across all N operating conditions. This represents the maximum speed requirement of the k-th power mechanism across all N operating conditions. Objective function 2: Minimizing the energy consumption of the motor-reducer system is the optimization objective. ; in, The objective function is to minimize the energy consumption of the motor-gearbox system. This refers to the rated power of the motor. To achieve the required operating efficiency of the k-th power mechanism under the i-th operating condition, by... and After determining the motor model, the operating efficiency is obtained based on the corresponding efficiency characteristic curve of the motor. For the reducer at the transmission ratio The transmission efficiency is reduced. The duration of the crane's operation under the i-th working condition is determined based on the working condition time sequence record; Objective function 3: The optimization objective is to minimize the power system quality and procurement cost. ; in, The objective function is to minimize the power system quality and procurement cost. ( )and ( ) are the cost functions for the motor and the reducer, respectively. ( )and ( ) are the mass functions of the motor and the reducer, respectively. , , , These are the weighting coefficients; To maintain the uniformity of numerical magnitude among objective functions 1, 2, and 3, a normalization transformation is first performed. The normalized objective functions 1, 2, and 3 are denoted as follows: , , ; With the optimization objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass, and procurement cost, a multi-objective optimization function is constructed: ; in, For a multi-objective optimization function, , , These are the weighting coefficients; S32. Initialize the candidate population: ; ; in, For iteration G, the candidate population is initialized. , There are M candidate solutions. It is the first The j-th candidate solution after the nth iteration. The first The rated power of the motor, the rated speed of the motor, and the transmission ratio of the reducer for the j-th candidate solution after the nth iteration. For the first The candidate population after the next iteration; For the Candidate solutions after the next iteration Perform driving capability judgment, that is, for candidate solutions All should meet the driving capability constraints. If a candidate solution does not meet the driving capability constraint, it should be discarded, and other candidate solutions should be judged to meet the driving capability constraint. For the Candidate population after the next iteration The process involves screening and searching for candidate solutions within the population. The parameters differ significantly, but the multi-objective optimization function can be used. Determine the candidate solution with better performance , and candidate solutions The parameter differences are small, but the multi-objective optimization function is used. Identify candidate solutions with poor performance And generate dynamically adjusted direction; ; in, Denotes the candidate solution after the g-th iteration. Dynamic adjustment of direction, Denotes the candidate solution after the g-th iteration. The weights with significantly different dynamic focusing parameters but superior performance Weights that represent parameters with small differences but poor performance. This is the scaling factor, used to control the step size; ; ; The dynamic focusing weights are adjusted during the iteration process. and They tend towards 1 and 0 respectively, so that dynamic adjustment directions with large differences can still be generated in the later stages of iteration, preventing them from getting trapped in local optima in the later stages of iteration; S33. Parameter optimization based on multi-objective differential evolution algorithm: Generate new candidate solutions after mutation: ; Determine new candidate solutions Does it meet the driving capability constraint? If the conditions are not met, then discard the new candidate solution. Retain candidate solutions If satisfied, then calculate and compare. and ,like Then use the new candidate solution. Replace candidate solutions Otherwise, retain the candidate solution. If new candidate solutions for several consecutive generations fail to meet the requirements for replacing candidate solutions, the scaling factor is gradually reduced. The process involves regenerating new candidate solutions until a new candidate solution meets the requirements for replacing the candidate solution while satisfying the driving capability constraints. The optimization objectives are to minimize motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, and power system mass and procurement cost. After G iterations, the optimal multi-objective optimization function is selected from the final retained candidate solutions. The candidate solution that yields the minimum value is taken as the optimal solution. = ; in, This represents the optimal solution obtained through iterative optimization, with the objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass, and procurement cost. This represents the parameter combination that minimizes the multi-objective optimization function. , , These are the optimal solutions for the rated power, rated speed, and reducer transmission ratio of the motor in the k-th group of mechanisms, respectively. S34. Perform parameter optimization processes on the four mechanisms of traveling, slewing, luffing, and hoisting respectively to obtain the configuration results of the overall machine power system: ; , , These are the optimal solutions for the rated power of the motor, the rated speed of the motor, and the transmission ratio of the reducer for the k-th mechanism.

Claims

1. A multi-parameter matching method for a crane power system considering load and dynamic characteristics, characterized in that, Includes the following steps: S1. Calculate the basic and additional requirements of the mechanism's torque and speed to obtain the power requirements under working conditions; S2. Based on different motor power levels and reducer transmission ratios, different speed-torque level combinations can be obtained, i.e., torque-speed capability models; S3. With the optimization objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass and procurement cost, a multi-objective optimization function is constructed. The multi-objective differential evolution algorithm is improved based on dynamic focusing strategy and iterated until the optimal solution is output.

2. The multi-parameter matching method for a crane power system considering load and dynamic characteristics according to claim 1, characterized in that, Assume that the work area is divided into N discrete working conditions. Determine the torque and speed requirements for each power unit; The crane has a total of k power mechanisms. The speed and torque requirements of the k-th power mechanism under the i-th operating condition are as follows: ； in, Let the torque requirement of the k-th power mechanism be the torque requirement under the i-th operating condition. This represents the basic torque requirement of the k-th power mechanism under the i-th operating condition. This represents the additional torque requirement of the k-th power mechanism under the i-th operating condition. Let the k-th power mechanism be the speed requirement under the i-th operating condition. The base speed requirement of the k-th power mechanism under the i-th operating condition is given by [the relevant information]. This represents the additional speed requirement of the k-th power mechanism under the i-th operating condition. Together, these two constitute the power demand of the k-th power mechanism under the i-th operating condition. : ； in, Let the power requirement of the k-th power mechanism be the power demand under the i-th operating condition. Let the k-th power mechanism be the speed requirement under the i-th operating condition. Let represent the torque requirement of the k-th power mechanism under the i-th operating condition.

3. The multi-parameter matching method for a crane power system considering load and dynamic characteristics according to claim 2, characterized in that, Assuming the work area is divided into N discrete working conditions, the power demand set is obtained by iterating through and solving for each working condition: ； in, Let k be the set of power demands of the k-th institution. Let i be the power demand of the k-th mechanism under the i-th working condition. Thus, the motion and load demand of the port crane within its operating range is transformed into a set of demands on a two-dimensional torque-speed plane.

4. The multi-parameter matching method for a crane power system considering load and dynamic characteristics according to claim 3, characterized in that, Based on different motor power ratings and reducer transmission ratios, different speed-torque level combinations can be obtained, i.e., torque-speed capability models. These torque-speed capability models can be used to determine the appropriate speed-torque capability based on the motor's rated power. Rated speed Gearbox transmission ratio To obtain the maximum output speed of the power mechanism and maximum output torque When selecting a motor and reducer, both must meet the maximum allowable torque range; therefore, the driving capability must satisfy the boundary conditions. ； in, Let k be the set of allowable driving ranges for the k-th power mechanism. Let the k-th power mechanism be the speed requirement under the i-th operating condition. Let the torque requirement of the k-th power mechanism be the torque requirement under the i-th operating condition. This is the maximum output speed of the power mechanism. This represents the maximum output torque of the power mechanism.

5. The multi-parameter matching method for a crane power system considering load and dynamic characteristics according to claim 4, characterized in that, In step S3, the multi-objective optimization function is defined: Objective function 1: Minimize the redundancy of motor power and reducer transmission ratio. ； in, The objective function is to minimize the redundancy of motor power and reducer transmission ratio. The rated torque of the motor. The rated speed of the motor. The gear ratio of the reducer. and These represent the torque and speed requirements of the k-th power mechanism under the i-th operating condition, respectively. Let be the maximum torque requirement of the k-th power mechanism across all N operating conditions. This represents the maximum speed requirement of the k-th power mechanism across all N operating conditions. Objective function 2: Minimizing the energy consumption of the motor-reducer system is the optimization objective. ； in, The objective function is to minimize the energy consumption of the motor-gearbox system. This refers to the rated power of the motor. To achieve the required operating efficiency of the k-th power mechanism under the i-th operating condition, by... and After determining the motor model, the operating efficiency is obtained based on the corresponding efficiency characteristic curve of the motor. For the reducer at the transmission ratio The transmission efficiency is reduced. The duration of the crane's operation under the i-th working condition is determined based on the working condition time sequence record; Objective function 3: The optimization objective is to minimize the power system quality and procurement cost. ； in, The objective function is to minimize the power system quality and procurement cost. ( )and ( ) are the cost functions of the motor and the reducer, respectively. ( )and ( ) are the mass functions of the motor and the reducer, respectively. , , , These are the weighting coefficients.

6. The multi-parameter matching method for a crane power system considering load and dynamic characteristics according to claim 5, characterized in that, To maintain the uniformity of numerical magnitude among objective functions 1, 2, and 3, a normalization transformation is first performed. The normalized objective functions 1, 2, and 3 are denoted as follows: , , ; With the optimization objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass, and procurement cost, a multi-objective optimization function is constructed: ； in, For a multi-objective optimization function, , , These are the weighting coefficients; Initialize candidate population: ； ； in, For iteration G, the candidate population is initialized. , There are M candidate solutions. It is the first The j-th candidate solution after the nth iteration. The first The rated power of the motor, the rated speed of the motor, and the transmission ratio of the reducer for the j-th candidate solution after the nth iteration. For the first The candidate population after the next iteration; For the Candidate solutions after the next iteration Perform driving capability judgment, that is, for candidate solutions All should meet the driving capability constraints. If a candidate solution does not meet the driving capability constraint, it should be discarded, and other candidate solutions should be judged to meet the driving capability constraint. For the Candidate population after the next iteration The process involves screening and searching for candidate solutions within the population. The parameters differ significantly, but the multi-objective optimization function can be used. Determine the candidate solution with better performance , and candidate solutions The parameter differences are small, but the multi-objective optimization function is used. Identify candidate solutions with poor performance And generate dynamically adjusted direction; ； in, Denotes the candidate solution after the g-th iteration. Dynamic adjustment of direction, Denotes the candidate solution after the g-th iteration. The weights with significantly different dynamic focusing parameters but superior performance Weights that represent parameters with small differences but poor performance. This is the scaling factor, used to control the step size; ； ； The dynamic focusing weights are adjusted during the iteration process. and They tend towards 1 and 0 respectively, so that dynamic adjustment directions with large differences can still be generated in the later stages of iteration, preventing them from getting trapped in local optima in the later stages of iteration.

7. The multi-parameter matching method for a crane power system considering load and dynamic characteristics according to claim 6, characterized in that, Parameter optimization based on multi-objective differential evolution algorithm: Generate new candidate solutions after mutation: ； Determine new candidate solutions Does it meet the driving capability constraint? If the conditions are not met, then discard the new candidate solution. Retain candidate solutions If satisfied, then calculate and compare. and ,like Then use the new candidate solution. Replace candidate solutions Otherwise, retain the candidate solution. If new candidate solutions for several consecutive generations fail to meet the requirements for replacing candidate solutions, the scaling factor is gradually reduced. The process involves regenerating new candidate solutions until a new candidate solution meets the requirements for replacing the candidate solution while satisfying the driving capability constraints. The optimization objectives are to minimize the redundancy of motor power and reducer transmission ratio, the energy consumption of the motor-reducer system, and the mass and procurement cost of the power system. After G iterations, the multi-objective optimization function is selected from the final retained candidate solutions. The candidate solution that yields the minimum value is taken as the optimal solution. = ； in, This represents the optimal solution obtained through iterative optimization, with the objectives of minimizing motor power and reducer transmission ratio redundancy, motor-reducer system energy consumption, power system mass, and procurement cost. This represents the parameter combination that minimizes the multi-objective optimization function. , , These are the optimal solutions for the rated power, rated speed, and reducer transmission ratio of the motor in the k-th group of mechanisms, respectively. The parameter optimization process was performed on the four mechanisms of traveling, slewing, luffing, and hoisting to obtain the configuration result of the overall machine power system: ； , , These are the optimal solutions for the rated power of the motor, the rated speed of the motor, and the transmission ratio of the reducer for the k-th mechanism.

Images