A multi-objective parameter design and scheme decision method for underwater electro-hydraulic actuators

Abstract

The application relates to a kind of underwater electro-hydraulic actuator multi-objective parameter design and scheme decision-making method, characterized in that, including determining design variable;Establish parameterized calculation model;Establish objective function;Establish constraint function;DOE sample calculation is carried out;AHP comprehensive decision-making is carried out;Weight sensitivity analysis and optimal scheme switching analysis are carried out;Original model back substitution check is carried out.The application is suitable for parameter screening, multi-objective optimization and scheme decision-making in the preliminary design stage of underwater electro-hydraulic actuator, by combining parameterized modeling, multi-objective optimization, comprehensive decision-making and back substitution check, to improve parameter screening efficiency and scheme recommendation reliability, at the same time, by hierarchical analysis method and weight sensitivity analysis, the candidate scheme is comprehensively sorted, and by original parameterized model back substitution check, the reliability of recommended scheme is improved, to solve the problem that underwater electro-hydraulic actuator parameter design depends on experience selection, it is difficult to coordinate quality, volume, power loss and engineering constraint simultaneously.

Description

Technical Field

[0001] This invention relates to the technical field of underwater electro-hydraulic actuator design and optimization methods, specifically a multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators. Background Technology

[0002] Underwater electro-hydraulic actuators are independent actuation units that integrate motor drive, hydraulic transmission, and mechanical execution functions. They offer advantages such as compact structure, high modularity, low leakage risk, and ease of electrical control integration, making them promising for applications in underwater robots, deep-sea operation equipment, and marine engineering actuators. Compared to airborne or land-based electro-hydraulic actuators, underwater electro-hydraulic actuators, in addition to meeting basic requirements such as output force, actuation time, and drive power, must also adapt to special constraints such as external seawater pressure, limited installation space, energy constraints, sealing compensation, and structural safety.

[0003] However, existing design methods mostly rely on experience-based selection or single-objective verification, making it difficult to coordinate the coupling relationship between parameters such as the system's rated working pressure, hydraulic cylinder diameter, piston rod diameter ratio, hydraulic pump displacement, and motor speed. It is also difficult to simultaneously consider multiple indicators such as system mass, total volume, and power loss. At the same time, the Pareto non-dominated solution set obtained from multi-objective optimization usually contains multiple candidate solutions, making it difficult to directly determine the final engineering solution. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators, addressing the shortcomings of existing technologies. This method is applicable to parameter screening, multi-objective optimization, and scheme decision-making in the preliminary design stage of underwater electro-hydraulic actuators. This invention combines parametric modeling, multi-objective optimization, comprehensive decision-making, and back-substitution verification to improve parameter screening efficiency and scheme recommendation reliability. Simultaneously, it uses the analytic hierarchy process (AHP) and weighted sensitivity analysis to comprehensively rank candidate schemes, and back-substitution verification of the original parametric model to improve the reliability of recommended schemes. This addresses the problems in existing technologies where underwater electro-hydraulic actuator parameter design relies on experience-based selection, struggles to simultaneously coordinate mass, volume, power loss, and engineering constraints, and the difficulty in directly determining the final scheme using Pareto non-dominated solution sets.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators includes the following steps: S1. Determine the design variables based on the operating requirements of the underwater electro-hydraulic actuator; S2. Establish a parametric calculation model based on design variables; S3. Calculate the total mass, total volume and power loss of the system using a parameterized calculation model, and use them as the objective function for multi-objective optimization. S4. Establish multiple constraint functions and perform feasibility filtering on design schemes that do not meet any of the constraint functions, so that they are not included as candidate recommended schemes in subsequent comprehensive decision-making. S5. Generate sample points within the range of design variable values, call the parameterized calculation model to calculate the objective function value and constraint function value corresponding to each sample point, and form a sample database; S6. Based on the sample database, construct an approximate mapping model between design variables and objective functions and constraint functions, and perform multi-objective optimization in the feasible solution space that satisfies the constraint functions to obtain a set of non-dominated candidate solutions with the objectives of total system mass, total system volume and power loss. S7. Normalize the cost-type indicators for the candidate solutions in the non-inferior candidate solution set, calculate the comprehensive score based on the indicator weight, obtain the candidate solution ranking results, and select the solution with the highest score as the recommended solution. S8. Change the weight of at least one of the indicators among the total system mass, total system volume and power loss, and recalculate the comprehensive score of the candidate schemes while keeping the sum of the indicator weights at 1. Record the candidate scheme number with the highest comprehensive score under different weight conditions, form the optimal scheme switching relationship, and determine the stable candidate scheme based on the optimal scheme switching relationship. S9. Substitute the recommended solution or stable candidate solution back into the parameterized calculation model for recalculation and verification, recalculate the objective function value and constraint function value, and use the recalculation and verification result satisfying all constraint functions as the determination condition for the final recommended solution.

[0006] Furthermore, in step S1, the design variables are determined as follows:

[0007] in, The system's rated operating pressure; The diameter of the hydraulic cylinder; This is the piston rod diameter ratio; This refers to the displacement of the hydraulic pump. This refers to the rated speed or operating speed of the motor.

[0008] Furthermore, in step S2, the parameterized calculation model includes a hydraulic cylinder model, a hydraulic pump model, a motor power model, a power loss model, a mass-volume model, and a structural constraint verification model.

[0009] Furthermore, in step S3, the objective function is as follows:

[0010] in, For multi-objective optimization, the objective function is... For the total mass of the system, The total volume of the system. This refers to power loss.

[0011] Furthermore, in step S4, the constraint functions include output force constraint, action time constraint, motor speed constraint, pump shaft torque constraint, motor power constraint, piston rod strength constraint, Euler stability constraint, and cylinder circumferential stress constraint. When all constraint functions are less than or equal to 0, the current design scheme is determined to be a feasible scheme; when any constraint function is greater than 0, the current design scheme is determined to be an infeasible scheme.

[0012] Furthermore, in step S5, the range of values ​​for the design variables is as follows:

[0013] in, These are DOE sample points; The minimum DOE sample point; The largest DOE sample point; The Latin hypercube sampling method is used to generate the design variables within the range. Group samples, represented as follows:

[0014] in, To design the variable sample matrix; The first The system's rated working pressure, hydraulic cylinder bore, piston rod diameter ratio, hydraulic pump displacement, and rated or operating speed of the motor are included in the sample. Each sample point was calculated using a parametric computational model, and the results are as follows:

[0015] in, Output the response matrix for the model; The first System mass, system volume, and power loss in the sample group; The first The constraints in the sample group include output force constraints, action time constraints, motor speed constraints, pump shaft torque constraints, motor power constraints, piston rod strength constraints, Euler stability constraints, and cylinder circumferential stress constraints. This leads to the formation of the DOE sample database. as follows: .

[0016] Furthermore, in step S6, the approximate mapping model is a radial basis function surrogate model as follows:

[0017] in, This is the predicted output of the radial basis function surrogate model; These are the weighting coefficients; These are radial basis functions.

[0018] Furthermore, in step S7, the NSGA-II algorithm is used for multi-objective optimization based on the radial basis function surrogate model, and the process is as follows: The initial population is randomly generated within the design variable range. as follows:

[0019] Among them, each individual This represents a design scheme; The radial basis function surrogate model is used to calculate the objective function value for each individual, and the constraint function is calculated at the same time. For individuals that violate the constraints, their selection probability is reduced according to the degree of constraint violation. Based on Pareto dominance relationships, the population is stratified for rapid non-dominated ordination. If the scheme... The following conditions must be met:

[0020] And at least one objective satisfies the following:

[0021] The plan is considered Domination Plan ; in, and These represent two candidate design schemes; Indicates the first One optimization objective function; These correspond to the total system mass, total system volume, and power loss, respectively. Based on the dominance relationship, the population is divided into multiple levels, with the first level being the current Pareto non-dominated solution set; The crowding distance is calculated for individuals in the same non-dominated layer as follows:

[0022] in, Indicate the optimization objective; Indicates the first The crowding distance of each option; Indicates according to the first After sorting the optimization objectives, the th optimization objective is... The objective function value corresponding to the next adjacent scheme in each scheme; Indicates according to the first After sorting the optimization objectives, the th optimization objective is... The objective function value corresponding to the preceding scheme of each scheme; and They represent the first The maximum and minimum values ​​of the optimization objective in the current undominated layer; The following new generation of candidate schemes are generated through selection, crossover, and mutation genetic operations:

[0023] in, Indicates the first The population of candidate solutions during the optimization process; This represents the first generation produced after selection, crossover, and mutation genetic operations. Population of candidate solutions; The selection is based on non-dominance level and crowding distance; For cross operations; This is a mutation operation; Repeat the non-dominated sorting, crowding distance calculation, and genetic operations until the maximum number of iterations is met, thus obtaining the Pareto non-dominated candidate solution set. .

[0024] Furthermore, in step S7, the normalization calculation formula is as follows:

[0025] in, For the first The first scheme is in the The original values ​​of each indicator; and These are the maximum and minimum values ​​of this indicator across all Pareto schemes; The normalized index score; Establish a judgment matrix , Indicators relative to indicators The importance of each eigenvalue is determined by weighting the eigenvalue with the largest eigenvalue, using the following formula:

[0026] in, This is the AHP judgment matrix; For indicator weight vectors; To determine the matrix The largest eigenvalue; The result is as follows:

[0027] in, These represent the weights corresponding to the three evaluation indicators: total system mass, total system volume, and power loss, respectively. Indicates matrix transpose; The consistency check is performed as follows:

[0028] when They consider the weights to be effective; in, The consistency ratio; As a consistency indicator; It is a random consistency indicator; No. The overall AHP score of the candidate solutions can be expressed as:

[0029] in, The first Normalized scores of the indicators corresponding to each candidate solution; The Pareto candidate solutions are ranked according to their comprehensive scores, and the solution with the highest score is selected as the recommended solution.

[0030] Furthermore, in step S9, the process of back-checking the recommended solution includes: S91. Write the design variables of the recommended scheme obtained by ranking the comprehensive scores into the input file; S92. Recalculate the objective function and constraint functions by calling the original parametric calculation model; S93. Extract the total mass of the system, the total volume of the system, the power loss, and the values ​​of each constraint function; S94. Determine whether the recommended solution satisfies all constraints; S95. If the recommended solution satisfies all constraints, output the final recommended solution; if the recommended solution does not satisfy all constraints, return the Pareto non-dominated candidate solution set, reselect the next candidate solution or adjust the index weights and perform back-substitution verification again.

[0031] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention incorporates five core parameters—rated working pressure, hydraulic cylinder diameter, piston rod diameter ratio, hydraulic pump displacement, and motor speed—into a unified design framework. It constructs a full-link parameterized calculation model covering the hydraulic cylinder, hydraulic pump, motor, power loss, mass, volume, and structural constraints. This model can quantitatively reflect the coupling relationship between output force, action time, mass, volume, and power consumption. It breaks through the limitations of traditional experience-based selection that relies on manual trial and error and has low parameter matching accuracy, effectively improving the systematicness and rationality of underwater electro-hydraulic actuator parameter design.

[0032] 2. This invention uses minimizing the total system mass, minimum total volume, and minimum power loss as three optimization objectives. Simultaneously, it transforms eight engineering requirements—output force, action time, motor speed, pump shaft torque, motor power, piston rod strength, Euler stability, and cylinder circumferential stress—into constraint functions. Feasibility filtering pre-emptively eliminates infeasible design schemes, completing multi-objective trade-off optimization within the feasible solution space. This approach ensures that the final solution meets the rigid performance and structural safety requirements for underwater operation while simultaneously coordinating the three conflicting design demands of lightweighting, miniaturization, and low energy consumption, achieving optimal overall performance.

[0033] 3. This invention employs Latin hypercube sampling to generate a DOE sample library, constructs a radial basis function surrogate model based on the samples, establishes a nonlinear approximate mapping from design variables to objective and constraint functions, and then combines this with the NSGA-II algorithm to perform evolutionary multi-objective optimization. This architecture significantly reduces the number of calls to the high-precision parameterized model and substantially improves the efficiency of optimization iteration; simultaneously, through fast non-dominated sorting and crowding distance mechanisms, it ensures that the output Pareto non-dominated candidate solution set is evenly distributed and comprehensively covered, providing sufficient high-quality alternative solutions for subsequent decisions.

[0034] 4. This invention introduces the Analytic Hierarchy Process (AHP) based on the Pareto nondominated solution set. By constructing a judgment matrix to determine the index weights, it performs normalized weighted scoring and ranking of candidate solutions. The preference weights for mass, volume, and power consumption can be flexibly adjusted according to the actual design requirements of underwater equipment, outputting the optimal recommended solution for the corresponding scenario. Furthermore, by conducting optimal solution switching analysis through weight scanning, it can identify robust solutions with stable performance within a wide weight range, helping designers understand the sensitivity of the recommendation results to changes in preferences, significantly improving the interpretability and engineering adaptability of decisions.

[0035] 5. This invention incorporates a back-substitution verification step using the original parametric model. Instead of using the prediction results of the surrogate model as the final judgment criterion, the recommended solution is re-input into the high-precision original model for recalculation. The recalculated objective function and constraint function values ​​are used as the feasibility judgment criteria. This mechanism effectively eliminates the approximation error of the surrogate model, avoids misjudgment of constraints in boundary solutions, and ensures that the final output recommended solution fully meets all engineering constraints, significantly improving the reliability and engineering feasibility of the recommended solution.

[0036] 6. This invention adopts a loosely coupled data interaction mode of input file + output file. The optimization scheduling platform and parameterized calculation model are independent of each other, requiring no complex secondary development interface. It is compatible with various optimization software and calculation programs, facilitating rapid integration with existing design processes. At the same time, the range of design variables, constraint thresholds, and optimization objectives can be flexibly expanded. It is suitable for rapid iteration of preliminary design of underwater electro-hydraulic actuators and can also be extended to multi-objective optimization design of other types of electro-hydraulic actuators, possessing good versatility and engineering application value. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the overall process of the multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators in this invention; Figure 2 This is a schematic diagram illustrating the calculation process of the objective function and constraint function in this invention; Figure 3 This is a schematic diagram illustrating the calling relationship between the optimized scheduling platform and the input / output files of the parameterized calculation model in this invention; Figure 4 This is a schematic diagram of the DOE sample calculation process in this invention; Figure 5 This is a schematic diagram of the Pareto solution set and AHP decision-making process in this invention; Figure 6 This is a schematic diagram of the back-substitution verification process of the recommended scheme in this invention. Detailed Implementation

[0038] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0039] Example 1 For easier understanding, please refer to Figures 1 to 6This embodiment provides a multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators, including the following steps: S1. Determine the design variables.

[0040] Based on the operating requirements of the underwater electro-hydraulic actuator, the system's rated working pressure, hydraulic cylinder diameter, piston rod diameter ratio, hydraulic pump displacement, and motor speed are determined as design variables as follows:

[0041] in, The rated operating pressure of the system is expressed in MPa. This refers to the cylinder diameter of the hydraulic cylinder, in mm. The piston rod diameter ratio is defined as the ratio of the piston rod diameter to the cylinder diameter. This refers to the hydraulic pump displacement, expressed in mL / r. The rated speed or operating speed of the motor is given in r / min. The above design variables reflect the main coupling relationships between the output force, action time, mass, volume, and power loss of the underwater electro-hydraulic actuator.

[0042] In this embodiment, the rated working pressure of the system ranges from 15MPa to 20MPa, the cylinder diameter of the hydraulic cylinder ranges from 45mm to 65mm, the piston rod diameter ratio ranges from 0.4 to 0.6, the hydraulic pump displacement ranges from 0.5mL / r to 0.8mL / r, and the motor speed ranges from 2300r / min to 2900r / min.

[0043] S2. Establish a parameterized calculation model.

[0044] Based on the above design variables, a dedicated parametric calculation model for underwater electro-hydraulic actuators is established, including a hydraulic cylinder model, a hydraulic pump model, a motor power model, a power loss model, a mass and volume model, and a structural constraint verification model.

[0045] Specifically, the hydraulic cylinder model is used to calculate the piston rod diameter. Effective area of ​​rodless cavity Piston rod cross-sectional area Effective area of ​​rod cavity Output force Action speed and action time .in, For the mechanical efficiency of the hydraulic cylinder, To ensure the effective flow rate entering the hydraulic cylinder, This refers to the stroke of the hydraulic cylinder.

[0046] Hydraulic pump model used to calculate theoretical flow rate Effective traffic Pump shaft torque and hydraulic power .in, This refers to the leakage flow rate of the hydraulic pump. This refers to the overall efficiency of the hydraulic pump.

[0047] The motor power model is used to calculate the motor angular velocity. Motor mechanical power and input power Demand. Among them, For the motor output torque, This refers to the overall efficiency of the motor.

[0048] The power loss model adopts a decompositional loss model, which divides the system power loss into internal leakage loss. viscous oil churning loss Mechanical friction loss Motor copper loss and driver losses The mapping relationships between each power loss component and the system's rated working pressure, hydraulic pump displacement, motor speed, and pump shaft torque were established to characterize the effects of the system's rated working pressure, hydraulic pump displacement, motor speed, and pump shaft torque on power loss.

[0049] The mass-volume model uses a component stacking method to calculate the total system mass and total system volume. The formula for calculating the total system mass is as follows:

[0050] in, For the quality of the hydraulic cylinder, For the quality of the hydraulic pump, For motor quality, For the mass of the power electronic unit, For integrated circuit quality.

[0051] The formula for calculating the total system volume is as follows:

[0052] in, For the volume of the hydraulic cylinder, For the volume of the hydraulic pump, For motor volume, For the volume of the power electronic unit, This refers to the integrated block volume.

[0053] The structural constraint verification model is used to calculate the compressive stress of the piston rod. Euler stability and cylinder circumferential stress .in, This is the required output load for the hydraulic cylinder. The elastic modulus of the piston rod material. Let the moment of inertia of the piston rod section be . This is the length coefficient. The effective length of the piston rod. The thickness is the cylinder wall thickness.

[0054] The aforementioned parametric calculation model establishes an algebraic solution chain through the matching relationships of flow rate, pressure, and torque among various components, directly mapping the input design variables to physical characteristics at each level, thereby eliminating the limitations of conflicting multiple indicators in traditional empirical design. Simultaneously, to ensure the convergence and computational robustness of the optimization process under complex underwater conditions (such as high pressure resistance and ultimate load), the parametric calculation model introduces a piecewise numerical processing mechanism. This mechanism automatically identifies critical states (such as Euler critical load or circumferential stress limit) during the calculation process, performs constraint filtering on the design space, eliminates invalid design spaces, and outputs the filtering results as a sample database or feasible states during the optimization iteration process. This ensures that the calculation process meets physical feasibility requirements at each optimization iteration point, while also ensuring the convergence of the entire optimization design framework and avoiding the generation of invalid samples due to model divergence.

[0055] It should be noted that the pressure compensation boundary model uses the external seawater pressure as the external pressure boundary of the actuator and the pressure compensation-related structures as the low-pressure side compensation boundary, which is used to correct the effective pressure difference of the hydraulic cylinder, the pump inlet pressure state, and the structural pressure-bearing verification conditions. The hydraulic cylinder, hydraulic pump, motor, power electronics unit, and integrated circuit are the main calculation objects of the parametric calculation model.

[0056] S3. Establish the objective function.

[0057] The total system mass, total system volume, and power loss are calculated using the aforementioned parameterized calculation model. These factors are then used as objective functions for multi-objective optimization, as shown below:

[0058] in, For multi-objective optimization, the objective function is... For the total mass of the system, The total volume of the system. This refers to power loss.

[0059] S4. Establish constraint functions.

[0060] Constraint functions are established based on the performance, driving capability, and structural safety requirements of underwater electro-hydraulic actuators. Sample points or iteration points that do not meet any constraint function are filtered for feasibility, preventing them from participating in subsequent comprehensive decision-making as candidate recommended solutions. The constraint functions are expressed as follows:

[0061] When all constraint functions are less than or equal to 0, the current solution is determined to be a feasible solution; when any constraint function satisfies... At that time, the current design scheme was determined to be an infeasible scheme.

[0062] Specifically, the constraint functions include the following: Output force constraint This is used to ensure that the output force of the hydraulic cylinder meets the load requirements; Action time constraints This is used to ensure that the hydraulic cylinder completes its action within a specified time. Motor speed constraint This is used to limit the maximum operating speed of a motor or hydraulic pump. Pump shaft torque constraint This is used to ensure that the motor has sufficient driving torque; Motor power constraints This is used to ensure that the motor power does not exceed the allowable upper limit; Piston rod strength constraint This is used to ensure that the compressive stress on the piston rod does not exceed the allowable stress. Euler stability constraints This is used to ensure that the piston rod does not experience rod instability during compression. Cylinder circumferential stress constraint It is used to ensure the safety of the hydraulic cylinder barrel under pressure.

[0063] S5. Perform DOE sample calculation.

[0064] Within the range of design variable values, DOE sample points are generated. The optimization scheduling platform writes the design variables corresponding to the current DOE sample point or optimization iteration point into the input file, calls the parametric calculation model to read the input file and calculate the objective function value and constraint function value corresponding to each sample point, and then writes the calculation results (total system mass, total system volume, power loss, constraint function value and feasibility status) into the output file. The optimization scheduling platform reads the output file and forms a DOE sample database or updates the optimization calculation results. That is, the parametric calculation model interacts with the optimization scheduling platform through the input file and the output file.

[0065] Specifically, the design variable range is as follows:

[0066] in, These are DOE sample points; The minimum DOE sample point; This represents the largest DOE sample point.

[0067] The Latin hypercube sampling method was used to generate the design variables within the aforementioned range. Group samples, represented as follows:

[0068] in, The design variable sample matrix, also known as the input sample matrix, is a matrix in which each row represents a combination of design variables corresponding to a design scheme. The first The sample group includes the system's rated working pressure, hydraulic cylinder diameter, piston rod diameter ratio, hydraulic pump displacement, and motor rated speed or working speed.

[0069] Each sample is calculated using a parametric model, resulting in the following:

[0070] in, The model outputs a response matrix, also known as an output sample matrix. Each row corresponds to the objective function value and constraint function value obtained by parametrically calculating the model for a design scheme. The first System mass, system volume, and power loss in the sample group; The first The constraints in the sample group include output force constraints, action time constraints, motor speed constraints, pump shaft torque constraints, motor power constraints, piston rod strength constraints, Euler stability constraints, and cylinder circumferential stress constraints.

[0071] This leads to the formation of the DOE sample database. as follows:

[0072] S6. Construct a proxy model and perform multi-objective optimization.

[0073] Based on DOE sample database An approximate mapping model is constructed between design variables and objective functions and constraint functions to establish the nonlinear mapping relationship between design variables and objective functions and constraint functions. Then, the NSGA-II evolutionary multi-objective optimization algorithm is used to perform multi-objective optimization within the feasible solution space that satisfies the constraint functions. This results in a set of non-dominated candidate solutions with the objectives of total system mass, total system volume, and power loss as objectives within the feasible solution space that satisfies the constraint functions. Each candidate solution corresponds to a set of design variable, objective function, and constraint function values.

[0074] Specifically, the approximate mapping model is a radial basis function surrogate model, and its expression is as follows:

[0075] in, For the predicted output of the surrogate model, These are the weighting coefficients; These are DOE sample points; For radial basis functions, Gaussian radial basis functions are used as follows:

[0076] in, The distance between the point to be predicted and the DOE sample points is the Euclidean distance. represents the shape parameter of the radial basis function.

[0077] Predicting using a Gaussian radial basis function surrogate model , , The multi-objective optimization problem is as follows:

[0078] in, The total system mass predicted by the surrogate model; The total system volume predicted by the surrogate model; The system power loss predicted by the surrogate model; The input design variable sample matrix.

[0079] Based on the Gaussian radial basis function surrogate model, the NSGA-II multi-objective optimization algorithm is used, and the process is as follows: The initial population was randomly generated within the design variable range as follows:

[0080] Each individual This represents a design scheme for an underwater EHA (Electronic Harbor Automation).

[0081] The objective function value for each individual is calculated using a Gaussian radial basis function surrogate model. Simultaneously, the constraint function is calculated, and for individuals that violate the constraints, their selection probability is reduced according to the degree of constraint violation.

[0082] Based on Pareto dominance relationships, the population is stratified for rapid non-dominated ordination. If the scheme... The following conditions must be met:

[0083] And at least one objective satisfies the following:

[0084] The plan is considered Domination Plan .

[0085] in, and These represent two candidate design schemes; Indicates the first One optimization objective function; These correspond to the total mass of the system, the total volume of the system, and the power loss, respectively.

[0086] Based on dominance relationships, the population is divided into: The first layer This is the current Pareto non-dominated solution set.

[0087] To maintain a uniform distribution of the Pareto solution set, the crowding distance is calculated for individuals in the same non-dominated layer as follows:

[0088] in, Indicate the optimization objective; Indicates the first The crowding distance of each scheme is considered, with individuals having a greater crowding distance having a higher retention priority; Indicates according to the first After sorting the optimization objectives, the th optimization objective is... The objective function value corresponding to the next adjacent scheme in each scheme; This represents the objective function value corresponding to the preceding adjacent solution; and They represent the first The optimization objective is to find the maximum and minimum values ​​in the current undominated layer.

[0089] Then, through selection, crossover, and mutation genetic operations, a new generation of candidate schemes is generated as follows:

[0090] in, Indicates the first The candidate solution population in the optimization process, i.e. the current solution set consisting of multiple sets of design variables; This represents the first generation produced after selection, crossover, and mutation operations. Population of candidate solutions; The selection is based on non-dominance level and crowding distance; For cross operations; This is a mutation operation.

[0091] Finally, repeat the non-dominated sorting, crowding distance calculation, and genetic operations until the maximum number of iterations is met (i.e., ...). This will yield the Pareto non-dominated solution set. .

[0092] S7. Perform AHP integrated decision-making.

[0093] The candidate solutions in the Pareto non-dominated solution set are normalized using cost-type indicators. The weights of the indicators are determined by the analytic hierarchy process (AHP) in the multi-indicator decision-making method. The total system mass, total system volume, and power loss are all treated as cost-type evaluation indicators and processed to be dimensionless. Based on the indicator weights, the comprehensive score of each non-dominated candidate solution is calculated. This score is used to determine the recommended solution under the current weight preference in the set of non-dominated candidate solutions that meet the constraints, and thus obtain the ranking result of the candidate solutions.

[0094] Since the total system mass, total system volume, and power loss are all cost-related indicators, and smaller values ​​are better, a cost-based normalization method is adopted, and the calculation formula is as follows:

[0095] in, For the first The first scheme is in the The original values ​​of each indicator and These are the maximum and minimum values ​​of this indicator across all Pareto schemes, respectively. This is the normalized indicator score.

[0096] Establish a judgment matrix , Indicators relative to indicators The importance of each eigenvalue is determined by weighting the eigenvalue with the largest eigenvalue, using the following formula:

[0097] in, This is the AHP judgment matrix; For indicator weight vectors; To determine the matrix The largest eigenvalue is used to calculate the weight vector and perform consistency checks.

[0098] The result is as follows:

[0099] in, These represent the weights corresponding to the three evaluation indicators: total system mass, total system volume, and power loss, respectively. This indicates matrix transpose, which converts the weight vector from a row vector to a column vector.

[0100] The consistency check is performed as follows:

[0101] when They believe the weights are effective.

[0102] in, This is the consistency ratio, used to evaluate the degree of consistency of the judgment matrix; As a consistency index, its calculation results reflect the degree to which the judgment matrix deviates from complete consistency; It is a random consistency index used to represent the consistency level of random judgment matrices of the same order.

[0103] Finally, the first The overall AHP score of the candidate solutions can be expressed as:

[0104] in, These are the weights for total system mass, total system volume, and power loss, respectively. The first The normalized score of the corresponding indicator for each candidate solution.

[0105] The Pareto candidate solutions are ranked according to their comprehensive scores, and the solution with the highest score is selected as the recommended solution.

[0106] S8. Perform weight sensitivity analysis and optimal solution switching analysis.

[0107] Change the weight of at least one of the indicators, namely power loss, total system mass, and total system volume, and recalculate the comprehensive score of the candidate schemes while keeping the sum of the indicator weights at 1. Record the candidate scheme number with the highest comprehensive score under different weight conditions, form the optimal scheme switching relationship, and determine the stable candidate scheme based on the optimal scheme switching relationship.

[0108] Specifically, in this embodiment, the power loss weight is changed according to a preset step size, and other index weights are adjusted accordingly while keeping the sum of the system total mass weight, system total volume weight, and power loss weight at 1. The comprehensive score of the candidate scheme under different weight conditions is calculated, and the candidate scheme number with the highest comprehensive score under different power loss weights is recorded to form the optimal scheme switching relationship. The optimal scheme switching relationship is used to determine the sensitivity of the recommended scheme to changes in engineering preferences. When the same candidate scheme maintains the highest comprehensive score under multiple consecutive power loss weight values, the candidate scheme is output as a stable candidate scheme.

[0109] More specifically, the power loss weight is changed, and the calculation formula is as follows:

[0110] in, This indicates the weight of the power loss index after weight adjustment. This indicates the initial power loss index weights before weight adjustment. This indicates the step size for weight adjustment, used to simulate changes in the level of attention paid to energy consumption indicators during the engineering design process.

[0111] Simultaneously satisfying the following:

[0112] in, These represent the weights of the system's total mass, total system volume, and power loss indicators after weight adjustment.

[0113] Recalculate the weighted overall score The calculation formula is as follows:

[0114] Record the candidate solution number with the highest overall score. as follows:

[0115] Record the candidate solution number with the highest comprehensive score under different weight conditions, obtain the optimal solution switching relationship, and analyze the impact of weight changes on the recommended solution.

[0116] S9. Perform back-substitution verification of the original model.

[0117] The recommended or stable candidate solutions in the ranking results are substituted back into the original parameterized calculation model for recalculation and verification. The objective function value and constraint function value are recalculated, and the final recommended solution is determined by the recalculation and verification results satisfying all constraint functions.

[0118] Specifically, the AHP recommended solution Substitute back to the original parameterized computational model A recalculation was performed, recalculating the output force, action time, motor power, pump shaft torque, piston rod compressive stress, Euler stability, cylinder circumferential stress, total system mass, total system volume, and power loss. The calculation results from the original model were used as the basis for judging the feasibility of the final solution.

[0119] More specifically, the process of back-verifying the recommended solution includes the following: S91. Write the design variables of the recommended scheme obtained by ranking the comprehensive scores into the input file; S92. Recalculate the objective function and constraint functions by calling the original parametric calculation model; S93. Extract the total mass of the system, the total volume of the system, the power loss, and the values ​​of each constraint function; S94. Determine whether the recommended solution satisfies all constraints; S95. If the recommended solution satisfies all constraints, output the final recommended solution. S96. If the recommended solution does not meet all constraints, return to the Pareto non-dominated solution set, reselect the next candidate solution, or adjust the index weights and perform back-substitution verification again.

[0120] The final recommended solution is determined based on the recalculation results of the original parametric calculation model, rather than using the prediction results of the surrogate model as the sole criterion.

[0121] Example 2 For easier understanding, please refer to Figure 3 This embodiment provides a file-call-based Python-Isight joint optimization implementation. It should be noted that this embodiment uses Python-Isight file-call joint optimization as an example to illustrate the implementation of the invention, but the invention is not limited to this software combination. Other optimization scheduling platforms and computing programs with external program calls, DOE sample generation, surrogate model construction, and multi-objective optimization functions can also be used to implement the invention.

[0122] like Figure 3 As shown, Isight, as the optimization scheduling platform, is responsible for DOE sample generation, surrogate model construction, and multi-objective optimization. Python, as the parameterized computation model, is responsible for calculating the objective function and constraint functions. Data is transferred between the two through input and output files.

[0123] At the start of each calculation, Isight writes the current design variables to an input file. The input file includes the system's rated operating pressure, hydraulic cylinder bore, piston rod diameter ratio, hydraulic pump displacement, and motor speed. Isight then calls a batch file via the Simcode module, which launches a Python parametric calculation program. After reading the input file, the Python program sequentially performs calculations for the hydraulic cylinder model, hydraulic pump model, motor power model, power loss, mass and volume, and constraint functions.

[0124] After the calculations are complete, the Python program writes the objective function and constraint functions to an output file. The output file includes the total system mass, total system volume, power loss, values ​​of the eight constraint functions, and feasibility states. Isight reads the output file and passes the results to the DOE database, a surrogate model, or a multi-objective optimization module.

[0125] This approach does not rely on complex secondary development interfaces, making it easy to modify the model, adjust the variable range, and expand the objective function. It is suitable for rapid iterative optimization in the preliminary design phase.

[0126] Example 3 For easier understanding, please refer to Figure 5 This embodiment provides a Pareto candidate scheme comprehensive decision-making method based on AHP.

[0127] First, the total system mass, total system volume, and power loss in the Pareto non-dominated solution set are used as evaluation indicators. Since all three are cost-based indicators, smaller values ​​indicate a better solution; therefore, a cost-based normalization method is used to convert them into dimensionless scores. An AHP judgment matrix is ​​established based on engineering preferences, and the weights of the three indicators—total system mass, total system volume, and power loss—are calculated. If a particular underwater equipment prioritizes energy utilization, the weight of power loss can be increased; if more emphasis is placed on installation space and overall layout, the weight of volume or mass can be increased.

[0128] Subsequently, the normalized scores of the candidate schemes are weighted and summed according to the weights of each indicator to obtain the AHP comprehensive score for each candidate scheme. The higher the comprehensive score, the better the overall performance of the scheme under the current engineering preferences. The power loss weight is changed and the comprehensive scores of the candidate schemes are calculated repeatedly to obtain the optimal scheme number under different weight conditions. If a scheme remains optimal or close to optimal within a wide weight range, it indicates that the scheme has good decision stability; if the optimal scheme changes frequently with weight changes, it indicates that the differences between the candidate schemes are small, and the final scheme needs to be further determined by combining component selection, manufacturing feasibility, and structural layout.

[0129] By using the above method, multiple candidate solutions in the Pareto non-dominated solution set can be transformed into recommended solutions with engineering preference interpretations, thereby improving the interpretability and engineering applicability of the optimization results.

[0130] Example 4 For easier understanding, please refer to Figure 6 This embodiment provides a recommended method for back-substitution verification.

[0131] After the recommended solution is obtained through AHP decision-making, the prediction results of the surrogate model are not directly used as the final solution. Instead, the design variables of the recommended solution are re-input into the original Python parametric calculation model. The original model recalculates the hydraulic cylinder output force, action time, motor speed, pump shaft torque, motor power, piston rod compressive stress, Euler stability, cylinder circumferential stress, total system mass, total system volume, and power loss.

[0132] If all constraint functions of the recommended solution are satisfied If so, the solution is deemed to satisfy the engineering constraints. If a constraint function exists... If the answer is no, the solution is deemed infeasible and needs to be returned to the Pareto candidate solution set to select the next high-scoring solution or to adjust the optimization weights.

[0133] By using back-substitution verification, we can avoid misjudgment of boundary solutions caused by surrogate model errors, and ensure that the final recommended solution is determined based on the calculation results of the original parameterized model.

[0134] Example 5 This embodiment provides a system for multi-objective parameter design and scheme decision-making of underwater electro-hydraulic actuators, including: Design a variable input module for inputting the system's rated working pressure, hydraulic cylinder bore, piston rod diameter ratio, hydraulic pump displacement, and motor speed; The parametric calculation module integrates hydraulic cylinder model, hydraulic pump model, motor power model, power loss model, mass and volume model, pressure compensation boundary model, and structural constraint verification model. It is used to perform performance calculations, structural strength verification, and overall component superposition based on the input design variables, and output the total system mass, total system volume, power loss, and constraint function values. The sample generation module is used to generate sample points within the range of design variable values; The proxy model building module is used to construct nonlinear mapping relationships between design variables and objective functions and constraint functions based on a sample database. A multi-objective optimization module is used to obtain a set of non-dominated candidate solutions under the objectives of total system mass, total system volume, and power loss. The comprehensive decision-making module is used to perform comprehensive scoring and ranking of candidate solutions in the non-inferior candidate solution set based on indicator weights, weight sensitivity analysis, and optimal solution switching analysis. The back-substitution verification module is used to substitute the recommended solution back into the original parameterized calculation model for recalculation and verification, and output the final recommended solution.

[0135] Although the present invention has been described using the above preferred embodiments, it is not intended to limit the scope of protection of the present invention. Any changes and modifications made by those skilled in the art to the above embodiments without departing from the spirit and scope of the present invention shall still fall within the scope of protection of the present invention.

Claims

1. A multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators, characterized in that, Includes the following steps: S1. Determine the design variables based on the operating requirements of the underwater electro-hydraulic actuator; S2. Establish a parametric calculation model based on design variables; S3. Calculate the total mass, total volume, and power loss of the system using a parameterized calculation model, and use these as the objective function for multi-objective optimization. S4. Establish multiple constraint functions and perform feasibility filtering on design schemes that do not meet any of the constraint functions, so that they are not included as candidate recommended schemes in subsequent comprehensive decision-making. S5. Generate sample points within the range of design variable values, call the parameterized calculation model to calculate the objective function value and constraint function value corresponding to each sample point, and form a sample database; S6. Based on the sample database, construct an approximate mapping model between design variables and objective functions and constraint functions, and perform multi-objective optimization in the feasible solution space that satisfies the constraint functions to obtain a set of non-dominated candidate solutions with the objectives of total system mass, total system volume and power loss. S7. Normalize the cost-type indicators for the candidate solutions in the non-inferior candidate solution set, calculate the comprehensive score based on the indicator weight, obtain the candidate solution ranking results, and select the solution with the highest score as the recommended solution. S8. Change the weight of at least one of the indicators among the total system mass, total system volume and power loss, and recalculate the comprehensive score of the candidate schemes while keeping the sum of the indicator weights at 1. Record the candidate scheme number with the highest comprehensive score under different weight conditions, form the optimal scheme switching relationship, and determine the stable candidate scheme based on the optimal scheme switching relationship. S9. Substitute the recommended solution or stable candidate solution back into the parameterized calculation model for recalculation and verification, recalculate the objective function value and constraint function value, and use the recalculation and verification result satisfying all constraint functions as the determination condition for the final recommended solution.

2. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 1, characterized in that, In step S1, the design variables are determined as follows: ， in, The system's rated operating pressure; The diameter of the hydraulic cylinder; This is the piston rod diameter ratio; This refers to the displacement of the hydraulic pump. This refers to the rated speed or operating speed of the motor.

3. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 2, characterized in that, In step S2, the parameterized calculation model includes a hydraulic cylinder model, a hydraulic pump model, a motor power model, a power loss model, a mass and volume model, and a structural constraint verification model.

4. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 3, characterized in that, In step S3, the objective function is as follows: ， in, For multi-objective optimization, the objective function is... For the total mass of the system, The total volume of the system. This refers to power loss.

5. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 4, characterized in that, In step S4, the constraint functions include output force constraint, action time constraint, motor speed constraint, pump shaft torque constraint, motor power constraint, piston rod strength constraint, Euler stability constraint, and cylinder circumferential stress constraint. When all constraint functions are less than or equal to 0, the current design scheme is determined to be a feasible scheme; when any constraint function is greater than 0, the current design scheme is determined to be an infeasible scheme.

6. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 5, characterized in that, In step S5, the range of values ​​for the design variables is as follows: ， in, These are DOE sample points; The minimum DOE sample point; The largest DOE sample point; The Latin hypercube sampling method is used to generate the design variables within the range. Group samples, represented as follows: ， in, To design the variable sample matrix; The first The system's rated working pressure, hydraulic cylinder bore, piston rod diameter ratio, hydraulic pump displacement, and rated or operating speed of the motor are included in the sample. Each sample point was calculated using a parametric computational model, and the results are as follows: ， in, Output the response matrix for the model; The first System mass, system volume, and power loss in the sample group; The first The constraints in the sample group include output force constraints, action time constraints, motor speed constraints, pump shaft torque constraints, motor power constraints, piston rod strength constraints, Euler stability constraints, and cylinder circumferential stress constraints. This leads to the formation of the DOE sample database. as follows: 。 7. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 6, characterized in that, In step S6, the approximate mapping model is a radial basis function surrogate model as follows: ， in, This is the predicted output of the radial basis function surrogate model; These are the weighting coefficients; These are radial basis functions.

8. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 7, characterized in that, In step S7, the NSGA-II algorithm is used for multi-objective optimization based on the radial basis function surrogate model. The process is as follows: The initial population is randomly generated within the design variable range. as follows: ， Among them, each individual This represents a design scheme; The radial basis function surrogate model is used to calculate the objective function value for each individual, and the constraint function is calculated at the same time. For individuals that violate the constraints, their selection probability is reduced according to the degree of constraint violation. Based on Pareto dominance relationships, the population is stratified for rapid non-dominated ordination. If the scheme... The following conditions must be met: ， And at least one objective satisfies the following: ， The plan is considered Domination Plan ; in, and These represent two candidate design schemes; Indicates the first One optimization objective function; These correspond to the total system mass, total system volume, and power loss, respectively. Based on the dominance relationship, the population is divided into multiple levels, with the first level being the current Pareto non-dominated solution set; The crowding distance is calculated for individuals in the same non-dominated layer as follows: ， in, Indicate the optimization objective; Indicates the first The crowding distance of each option; Indicates according to the first After sorting the optimization objectives, the th... The objective function value corresponding to the next adjacent scheme in each scheme; Indicates according to the first After sorting the optimization objectives, the th... The objective function value corresponding to the preceding adjacent scheme of each scheme; and They represent the first The maximum and minimum values ​​of the optimization objective in the current undominated layer; The following new generation of candidate schemes are generated through selection, crossover, and mutation genetic operations: ， in, Indicates the first The population of candidate solutions during the optimization process; This represents the first generation produced after selection, crossover, and mutation genetic operations. Population of candidate solutions; The selection is based on non-dominance level and crowding distance; For cross operations; This is a mutation operation; Repeat the non-dominated sorting, crowding distance calculation, and genetic operations until the maximum number of iterations is met, thus obtaining the Pareto non-dominated candidate solution set. .

9. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 8, characterized in that, In step S7, the normalization calculation formula is as follows: ， in, For the first The first scheme is in the The original values ​​of each indicator; and These are the maximum and minimum values ​​of this indicator across all Pareto schemes; The normalized index score; Establish a judgment matrix , Indicators relative to indicators The importance of each element is determined by weighting it using the largest eigenvalue. The calculation formula is as follows: ， in, This is the AHP judgment matrix; For indicator weight vectors; To determine the matrix The largest eigenvalue; The result is as follows: ， in, These represent the weights corresponding to the three evaluation indicators: total system mass, total system volume, and power loss, respectively. Indicates matrix transpose; The consistency check is performed as follows: ， when They consider the weights to be effective; in, The consistency ratio; As a consistency indicator; It is a random consistency indicator; No. The overall AHP score of the candidate solutions can be expressed as: ， in, The first The normalized scores of the indicators corresponding to each candidate solution; The Pareto candidate solutions are ranked according to their comprehensive scores, and the solution with the highest score is selected as the recommended solution.

10. The multi-objective parameter design and scheme decision-making method for underwater electro-hydraulic actuators according to claim 9, characterized in that, In step S9, the process of back-substituting the recommended solution for verification includes: S91. Write the design variables of the recommended scheme obtained by ranking the comprehensive scores into the input file; S92. Recalculate the objective function and constraint functions by calling the original parametric calculation model; S93. Extract the total mass of the system, the total volume of the system, the power loss, and the values ​​of each constraint function; S94. Determine whether the recommended solution satisfies all constraints; S95. If the recommended solution satisfies all constraints, output the final recommended solution; if the recommended solution does not satisfy all constraints, return the Pareto non-dominated candidate solution set, reselect the next candidate solution or adjust the index weights and perform back-substitution verification again.

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