Multi-objective optimization method for pressure-flow characteristics of CDC electromagnetic pilot relief valve

Abstract

The present invention relates to a multi-objective optimization method for the pressure-flow characteristics of a CDC electromagnetic pilot relief valve, and belongs to the technical field of automobile suspension. The steps are as follows: (1) establishing a three-dimensional equivalent model of a CDC electromagnetic pilot relief valve; (2) building a dynamic model based on the built three-dimensional equivalent model and the working principle; (3) building a hydraulic simulation model based on the dynamic model; (4) forming training samples to train the neural network model; (5) initializing the ant colony algorithm parameters; (6) starting the ant colony algorithm iteration; (7) updating pheromones; (8) judging whether the termination condition is met; (9) outputting the optimal parameter combination and the optimized pressure-flow characteristic curve; (10) using the Pareto method to determine the importance of the influencing factors. The present invention combines the ant colony algorithm with the annealing algorithm, effectively avoiding the local optimal problem and accelerating global convergence.

Description

Technical Field

[0001] The invention relates to a multi-objective optimization method for pressure flow characteristics of a CDC electromagnetic pilot relief valve, and belongs to the technical field of automobile suspension. Background Art

[0002] The automobile suspension system working under various road conditions must have corresponding adaptability. Since the structural optimization and improvement of passive shock absorbers can no longer meet the development needs of today's automobiles, although they still occupy a large market share, it has become a general trend to gradually fade out of the automotive field. Active shock absorbers have certain disadvantages in practical applications due to high costs, high maintenance requirements, complexity, energy consumption and potential reliability issues. At present, there are still many problems that have not been well solved. The semi-active suspension system is a suspension that dynamically adjusts the damping and stiffness of the shock absorber according to the driving conditions of the car and the driving habits of the driver. Through the analysis of information such as the driving status of the car, road conditions and the driver's operation, the damping and stiffness of the shock absorber are automatically adjusted to achieve the optimal vibration reduction effect and smoothness of the suspension without manual intervention. The key technology of the semi-active shock absorber is the application of the CDC solenoid valve to achieve the above functions.

[0003] At present, there are some algorithms that can use machine learning and neural network technology to predict the performance of CDC solenoid valves. For example, Chinese patent CN117473838A discloses a multi-objective optimization design method for the electromagnetic force proportional characteristics of CDC solenoid valves. The cuckoo multi-objective search algorithm is used for the mathematical model of the electromagnetic force proportional characteristics of multi-objective optimization. Only the electromagnetic force proportional characteristics are multi-objective optimized, and the characteristic curve of the first overflow valve part is not optimized. The search strategy of the cuckoo algorithm simulates the parasitic behavior of the cuckoo bird, that is, the process of placing "eggs" in the nest. Although this method has certain advantages in global search, due to the strong jumping of the cuckoo algorithm, it will tend to explore local areas during the search process, resulting in falling into local optimality. For this reason, the present invention is proposed. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve, which combines an ant colony algorithm and an annealing algorithm to effectively avoid local optimal problems and accelerate global convergence.

[0005] The technical solution of the present invention is as follows:

[0006] A multi-objective optimization method for the pressure-flow characteristics of a CDC electromagnetic pilot relief valve, the steps are as follows:

[0007] (1) Establish a three-dimensional equivalent model of the CDC electromagnetic pilot relief valve;

[0008] Firstly, a three-dimensional model of a CDC electromagnetic pilot relief valve is established. The CDC electromagnetic pilot relief valve is an existing structure, including a pilot electromagnet, a pilot valve and a relief valve. A pilot valve is arranged on one side of the relief valve, and the relief valve and the pilot electromagnet are connected through a connecting seat.

[0009] The overflow valve includes a base, a valve seat, a main valve core, a main spring, a ball valve steel ball and an overflow spring. A valve seat is arranged on one side of the base, a stainless steel gasket is arranged between the base and the valve seat, a main valve core is arranged in the valve seat, a main spring is arranged in the main valve core, the main spring is connected to a pilot valve through a throttle valve plate, an O-ring is arranged on the outside of the base, a ball valve steel ball and an overflow spring matched therewith are arranged on one side of the valve seat, and the base, valve seat, main valve core and ball valve steel ball are spatially connected to form a hydraulic oil conduction path, such as Figure 2 The red route is shown;

[0010] The pilot valve comprises a valve sleeve, a pilot valve core, a pilot spring and a valve core push rod. The valve sleeve is provided with a pilot valve core, the outside of the pilot valve core is provided with a pilot spring, one end of the pilot valve core is connected to a valve core push rod, and the outside of the valve core push rod is provided with a pilot electromagnet;

[0011] The pilot electromagnet includes a magnetic isolation sleeve, an electromagnet cap, an armature and an electromagnet core. The bottom of the valve core push rod is equipped with the electromagnet core through a lubricating bearing, the middle of the valve core push rod is equipped with the armature, the top of the valve core push rod is connected to the electromagnet cap through a sliding bearing, and the lower part of the electromagnet cap is connected to the magnetic isolation sleeve.

[0012] (2) Build a dynamic model based on the constructed three-dimensional equivalent model and working principle, including the pilot valve dynamic model and the overflow valve dynamic model, and perform force analysis;

[0013] (3) Build a hydraulic simulation model based on the dynamic model;

[0014] Based on AMESim software and dynamics model, a hydraulic simulation model of CDC electromagnetic pilot relief valve is established. The model includes key parts such as pressure source, relief valve, pilot electromagnetic valve, one-way ball valve, etc. The physical properties of oil (density, viscosity, bulk modulus, etc.) and control parameters of electromagnetic valve (coil resistance, number of coil turns, initial air gap, etc.) are set. The inlet and outlet pressure and flow characteristics of the relief valve are measured through simulation, which provides basic data for neural network and optimization algorithm.

[0015] (4) Compose training samples to train the neural network model;

[0016] (5) Initialize the ant colony algorithm parameters;

[0017] In the optimization process, the ant colony algorithm combined with the double annealing local search strategy is used to solve the multi-objective optimization design of the CDC electromagnetic pilot relief valve. By initializing key parameters (such as the number of ants, the maximum number of iterations, the pheromone volatility, etc.), setting the local search mechanism, and balancing the efficiency of global search and local optimization, the convergence speed of the algorithm and the accuracy of the solution are significantly improved.

[0018] (6) Start the ant colony algorithm iteration;

[0019] (7) Update pheromones;

[0020] (8) Determine whether the termination conditions are met;

[0021] (9) Output the optimal parameter combination and the optimized pressure-flow characteristic curve;

[0022] (10) The Pareto method is used to determine the importance of influencing factors.

[0023] Preferably, in step (2) of the present invention, a dynamic model of the pilot valve is constructed, and the oil first enters the relief valve. When the inlet pressure of the relief valve is less than the opening pressure, the relief valve is in a closed state, and the oil enters the pilot valve through the relief valve. The pilot valve core and the valve sleeve are matched through the shaft hole. The gap between the pilot valve core and the valve sleeve changes to form a throttling hole effect. The pilot valve core includes three sections of diameter, so that it forms two throttling holes with the valve sleeve, generating a throttling effect at both ends. The relationship between the throttling effect at both ends and the damping force has been introduced above. After passing through the ball valve, the oil enters the compensation chamber to return oil. The formula of the constructed pilot valve dynamic model is:

[0024]

[0025] Among them, d K is the diameter of the relief valve spring seat hole (i.e. the seat hole where the main spring is located), d1 is the diameter of the pilot valve sleeve, d2 is the diameter of the middle section of the pilot valve core, d3 is the diameter of the front section of the pilot valve core, d4 is the diameter of the bottom section of the pilot valve core, and d5 is the diameter of the pilot valve connecting hole. is the displacement of the pilot valve core, , Q1 pilot valve inlet flow, Q a Q is the flow rate through the front section of the pilot valve core, b Q is the flow rate through the bottom section of the pilot valve core, c is the flow through the one-way ball valve, Q2 is the pilot valve outlet flow (i.e. the flow through the bottom section of the pilot valve core); △P in-1 △P is the pressure difference before and after the oil passes through the spring seat hole of the relief valve, 1-a △P is the pressure difference before and after the oil passes through the front section of the pilot valve core, a-b △P is the pressure difference before and after the oil passes through the bottom section of the pilot valve core, b-c△P is the pressure difference before and after the oil passes through the one-way ball valve, c-2 A is the pressure difference before and after the oil passes through the pilot valve connecting hole; K A is the cross-sectional area of ​​the relief valve spring seat hole; a A is the flow area of ​​the front section of the pilot valve core; b C is the flow area of ​​the bottom section of the pilot valve core; q is the flow coefficient, μ is the dynamic viscosity of the oil, ρ is the density of the oil, l is the length of the pilot valve connecting hole, F open1 It is the critical opening force of the one-way ball valve.

[0026] Preferably, according to the present invention, in step (2), when the inlet pressure of the overflow valve is greater than the opening pressure of the overflow valve, the overflow valve begins to overflow, and the dynamic model of the overflow valve is:

[0027]

[0028] Among them, A0 is the flow area of ​​the main valve core of the overflow valve. d A is the flow area of ​​the inner circle of the main valve core of the overflow valve, e A is the flow area of ​​the outer circle of the overflow valve main valve core, A4 is the flow area of ​​the overflow valve connecting hole, d6 is the inner circle radius of the overflow valve seat, d7 is the outer circle radius of the overflow valve seat, and d9 is the diameter of the overflow valve connecting hole; Q d Q is the flow rate of the overflow valve main valve core from the inner circle to the outer ring, e Q4 is the flow through the overflow valve connecting hole; △P in-d △P is the pressure difference before and after the oil passes through the inner circle of the main valve core of the overflow valve and enters the outer ring. d-e △P is the pressure difference before and after the oil passes through the outer ring of the main valve core of the relief valve, e-4 F is the pressure difference before and after the oil passes through the overflow valve connecting hole, open2 is the opening pressure of the relief valve.

[0029] Preferably, in step (2), assuming that the pressure in the compensation chamber is zero, the steady-state force equation when the main valve core of the overflow valve is opened and the force analysis of the valve core of the pilot valve are obtained:

[0030]

[0031] Among them, d9 represents the outer diameter of the main valve core of the overflow valve, d 10 Represents the diameter of the small circle outside the relief valve base, d 11 Represents the large circle diameter of the inner ring of the relief valve base; A 上represents the area of ​​the oil on the upper end of the main valve core of the relief valve, A1 represents the area of ​​the oil on the inner circle of the relief valve base, A2 represents the area of ​​the oil on the outer ring of the relief valve base, A3 represents the area of ​​the oil on the relief valve outlet cavity, x y0 is the pre-compression amount of the relief valve main spring, which is set to 0.3 mm in the present invention.

[0032]

[0033] This formula is the formula for the pilot valve core being affected by electromagnetic force, friction force, spring force, steady-state and transient fluid force. d is the thrust of the electromagnetic push rod, F w is the steady-state fluid force, f is the friction force on the pilot valve core, in N; G is the gravity of the pilot valve core, 0.038N, and the mass of the pilot valve core is m=3.8×10 -3 kg; B Z is the damping coefficient of the pilot valve core movement, which is 10N / (m / s); x is the displacement of the electromagnet core, with vertical downward being the positive direction; Indicates the pilot valve core speed in m / s; Indicates the pilot valve core acceleration in m / s 2 ;k x Indicates the spring stiffness of the pilot spring; x x0 Indicates the pre-compression amount of the pilot spring.

[0034] According to the preferred embodiment of the present invention, in step (4), the pilot valve sleeve diameter d1, the pilot valve valve core front section diameter d3, the pilot valve valve core bottom section diameter d4, the relief valve seat inner circle radius d6, the relief valve spring seat hole diameter d K , spring stiffness k of the pilot spring x , relief valve main spring stiffness k y As input variables, pressure P and flow rate Q are used as output variables to perform simulation and analysis, establish experimental data sets, and train neural network models.

[0035] Preferably, according to the present invention, in step (4), the neural network model is a five-layer artificial neural network: an input layer, three hidden layers and an output layer;

[0036] The input layer contains 7 neurons, each of which receives the optimization parameters (pilot valve sleeve diameter d1, pilot valve valve core front section diameter d3, pilot valve valve core bottom section diameter d4, relief valve seat inner circle radius d6, relief valve spring seat hole diameter d K , spring stiffness k of the pilot spring x , relief valve main spring stiffness k y ) as input, the role of the input layer is to pass these raw data to the hidden layer and prepare the data for subsequent processing;

[0037] Hidden layer 1 extracts features from input parameters through nonlinear activation functions (such as ReLU) to initially capture the nonlinear relationship between variables. Its function is to map the input to a higher-dimensional feature space, laying the foundation for more complex relationship modeling.

[0038] Hidden layer 2 further extracts hidden features and enhances the network’s expressiveness. This layer captures the deep dependencies between parameters by increasing the number of neurons or the strength of connections.

[0039] Hidden layer 3 integrates the features extracted by the first two layers to generate high-quality intermediate outputs, which are used to complete the final processing of the input features and provide them to the output layer to generate optimization targets;

[0040] The output layer contains two neurons, which output the two optimization target values ​​of pressure and flow respectively. This layer directly outputs the final result through a linear activation function for comparison with the true value;

[0041] The model training process is as follows:

[0042] First, the experimental data is divided into a training set and a test set in a ratio of 7:3. During the training process, the training data is input into the model for forward propagation, the output value is calculated, and the error between the predicted value and the true value is evaluated through the loss function (such as mean square error MSE). Then, the gradient is calculated through back propagation, and the weights and biases of the network are updated using the optimization algorithm to gradually reduce the error.

[0043] After each training, the model performance is verified using the test set. If the error between the predicted result of the test set and the actual result is less than 5%, the training is completed; otherwise, the model parameters (such as learning rate, number of neurons in the hidden layer) are adjusted or the number of training rounds is increased to retrain the model.

[0044] When the model error meets the requirements, the model is saved as a relationship model between input variables and output variables to support multi-objective optimization design. This process ensures that the model has good fitting ability and stable performance on the test set, thereby improving the accuracy and reliability of the optimization process.

[0045] According to the preferred embodiment of the present invention, step (5) is specifically as follows:

[0046] In the ant colony algorithm, the initialization phase is the key starting point, which determines the search behavior of the algorithm. The number of ants is set to 50. The number of ants affects the coverage of the search space. Too few ants may lead to insufficient search, and too many ants increase the computational complexity. The maximum number of iterations is set to 500 to ensure sufficient time for optimization and prevent the algorithm from terminating prematurely. The initial value of pheromone for each path is 0.1, which provides the algorithm with an initial search preference. The pheromone volatility rate is set to 0.2 to control the attenuation of pheromone concentration, maintain exploration and avoid early convergence. The pheromone gain coefficient is set to 1.0. The pheromone gain coefficient determines the impact of path quality on pheromone update. The heuristic information weight β=2, the pheromone weight α=1, balances the role of pheromone and heuristic information in path selection, and ensures that the search can take into account both global and local optimization. The local search frequency executes the double annealing algorithm every 5 generations to enhance the accuracy of the search.

[0047] In order to ensure the rationality of optimization, a constraint condition is given:

[0048] .

[0049] According to the preferred embodiment of the present invention, step (6) is specifically as follows:

[0050] (61) Path selection:

[0051] Based on the combination of pheromone concentration and heuristic information, ants choose the optimal path. The path selection formula is as follows:

[0052]

[0053] In the formula, τ ij is the pheromone concentration of path i to j; η ij is the heuristic information of path i to j, and the quality evaluation of the discrete parameter combination corresponding to each path, that is, the objective function value;

[0054] Heuristic information η ij It represents the influence of discrete parameter combination on the pressure-flow characteristic of the pilot relief valve, and obtains the target of the greater pressure and the smaller flow by calculating the objective function value of the current combination;

[0055] (62) Construct the solution:

[0056] After the ants select the discrete parameter combination, they optimize the continuous parameters through the double annealing algorithm. The specific steps of the double annealing algorithm include:

[0057] (621) Initialize the double annealing algorithm parameters: initial temperature, cooling strategy is that each round of temperature decays to 95% of the previous round;

[0058] (622) Double annealing algorithm iteration: Generate a new solution in the neighborhood of the current solution, calculate whether to accept the new solution based on the objective function value, and introduce randomness through the Metropolis criterion. The objective function is the mean square error (MSE) of the pressure-flow characteristic curve:

[0059]

[0060] Among them, P model (x i ) is the pressure-flow curve value calculated by the model, P target (x i ) is the target pressure-flow curve value, and N is the number of data points;

[0061] Decide whether to accept the new solution according to the Metropolis criteria:

[0062]

[0063] if , that is, the objective function value of the new solution is better, accept the new solution; if , then the probability of accepting the new solution is:

[0064]

[0065] According to probability, accept the worse solution with a certain probability to maintain the exploratory nature of the algorithm;

[0066] The double annealing algorithm is called to optimize the continuous parameters and the temperature is updated according to the cooling strategy:

[0067]

[0068] 𝑇 k : The temperature of the 𝑘th iteration, 𝛼=0.95 is the temperature attenuation coefficient (0<𝛼<1);

[0069] The double annealing algorithm continues to iterate until the termination condition is met, such as the temperature is lower than a certain threshold 𝑇min or the maximum number of iterations is reached;

[0070] (63) Evaluate the quality of the solution:

[0071] After each ant completes the process of path selection and solution construction, it needs to evaluate the solution and calculate the comprehensive objective function value;

[0072] The comprehensive objective function value is expressed as the weighted average of the objective function under the combination of discrete and continuous parameters:

[0073]

[0074] Among them, fdiscrete is the objective function value corresponding to the discrete parameter combination; f continuous is the objective function value corresponding to the continuous parameter combination optimized by the double annealing algorithm, and is the weight coefficient, which controls the influence of the discrete and continuous partial objective functions on the overall objective function;

[0075] (64) End the current ant's operation:

[0076] When each ant completes path selection, solution construction, objective function calculation, and solution evaluation, the operation on the current ant ends and the iteration of the next ant begins.

[0077] According to the preferred embodiment of the present invention, in step (7), specifically:

[0078] In each iteration of the ant colony algorithm, the ants will update the pheromone according to the quality of the solutions to the paths they find, ensuring that the paths with high-quality solutions can get more pheromone support, thereby guiding more ants to search along these paths;

[0079] (71) Pheromone update formula:

[0080] After each ant completes path selection and calculates the objective function, it will update the pheromone on the path. The update rules are as follows:

[0081]

[0082] is the pheromone concentration of the path 𝑖→𝑗 in the previous iteration;

[0083] is the pheromone concentration of the path 𝑖→𝑗 after this iteration;

[0084] ρ is the pheromone volatilization rate, which usually ranges from [0, 1] and is set to 0.2 here;

[0085] is the pheromone increment, and the calculation formula is:

[0086]

[0087] in, is the comprehensive objective function value calculated after the ant selects the path; Q is a constant that controls the increment of pheromone and can be set to 1.0;

[0088] The size of the pheromone increment is related to the objective function value of the path. The higher the path quality (i.e., the smaller the objective function value), the larger the pheromone increment, and vice versa. This ensures that high-quality paths get more pheromones, thus getting more choices in subsequent iterations.

[0089] (72) Pheromone Update:

[0090] Calculate path quality: After each ant completes path selection and constructs a solution, it calculates the objective function value (such as the error between the pressure-flow characteristic and the target curve);

[0091] Update path pheromone: According to the objective function value, use the formula to update the pheromone concentration on the path;

[0092] Pheromone volatilization: The volatilization of pheromone is controlled by the parameter ρ to avoid early convergence and keep a certain diversity in the search space.

[0093] According to the preferred embodiment of the present invention, step (8) is specifically as follows:

[0094] After each round of ant colony algorithm iteration, it is necessary to determine whether the termination condition is met. If the condition is met, the algorithm will terminate and output the optimal solution. If the condition is not met, the next round of iteration will be executed.

[0095] Set the maximum number of iterations to 500. When this number of iterations is reached, the algorithm stops;

[0096] The termination judgment formula is:

[0097]

[0098] and are the optimal solution objective function values ​​of the tth and t-1th generations, respectively. ε is the set accuracy threshold. If the objective function value of the optimal solution changes less than a certain threshold ε=1×10 in several consecutive generations (such as 10 iterations), -5 , the algorithm is considered to have converged and terminated.

[0099] According to the preferred embodiment of the present invention, step (9) is specifically as follows: when the termination condition is met, the optimal discrete and continuous parameter combination is output, and the optimized pressure-flow characteristic curve is given, and the output of the optimal solution is the optimal discrete and continuous parameter combination searched by the ant colony algorithm within the maximum number of iterations;

[0100] The optimal solution parameter combination is used to substitute into the dynamic model of the CDC electromagnetic pilot relief valve, and the optimized pressure-flow characteristic curve is calculated and plotted. The optimized pressure-flow characteristic curve shows the gradually decreasing relationship between flow and pressure, and the optimal solution is to minimize the mean square error of the pressure-flow curve.

[0101] Preferably, in step (10), a full-factor DOE technique is used to analyze the importance of influencing factors. DOE (Design of Experiments) is used to study how input variables of a system or process affect output variables. In the design and optimization of CDC solenoid valves, DOE can help identify and optimize key parameters to improve shock absorber performance.

[0102] The pilot valve core bottom section diameter, relief valve spring seat hole diameter, pilot valve sleeve diameter, relief valve main spring stiffness and pilot spring spring stiffness are taken as input parameters, and the pressure difference of the relief valve is selected as the output parameter. The full factorial technology is used to obtain The design matrix is ​​constructed, and finally the Pareto plot configuration is used to sort the parameters according to the degree of influence to obtain the parameters with the greatest and least influence.

[0103] The core technology of the present invention is to use fluid mechanics to build dynamics and AMESim models based on the three-dimensional model and working principle of the CDC electromagnetic pilot relief valve, so as to more rigorously verify the consistency between the theory and simulation of the CDC electromagnetic pilot relief valve, and determine 7 key structural parameters. By simulating the behavior of ant colonies, the optimal discrete parameter combination in the complex design space is searched to ensure the rationality of parameter selection. In order to optimize continuous parameters (such as valve opening, current control, etc.), a double annealing algorithm (DA) is adopted. The double annealing algorithm explores the best solution in the parameter space by simulating temperature changes and random search strategies, ensuring that the algorithm can effectively search for the optimal solution in the global range and prevent falling into the local optimum. The combination of the two ensures that discrete parameters and continuous parameters can be optimized collaboratively in multi-objective optimization problems, thereby improving the optimization efficiency. After the optimization is completed, the Pareto chart is used to post-process the optimization results, analyze the degree of influence of different parameter combinations on the target performance, and further clarify the key design parameters of the optimal solution. Through Pareto analysis, the priority of each influencing factor can be clearly seen, and a decision-making basis can be provided for further optimization.

[0104] Where the present invention is not exhaustive, prior art may be used.

[0105] The beneficial effects of the present invention are:

[0106] 1. In the field of multi-objective optimization of solenoid valves, the present invention combines simulation with data-driven optimization by establishing a simulation model of the solenoid valve and using a neural network to train the simulation data. This method demonstrates how to use simulation data to enhance the predictive ability of the optimization algorithm, and inspires the present invention to combine the fluid mechanics model with AMESim simulation during the optimization process to ensure the accuracy and reliability of the optimization results.

[0107] The present invention takes pressure and flow as targets, comprehensively considers multiple performance indicators, and realizes multi-objective optimization. This meets the comprehensive requirements of solenoid valves in pressure control, flow regulation and other aspects in actual engineering, so that the optimization results are evenly improved in various performance indicators, and the applicability of solenoid valves in complex application scenarios is enhanced.

[0108] 2. The ant colony algorithm of the present invention simulates the collaborative behavior of ant groups and efficiently searches for the optimal combination of discrete parameters on a global scale, avoiding the disadvantage that traditional optimization methods are prone to falling into local optimality. The double annealing algorithm, based on the optimization of discrete parameters, performs fine-grained optimization on continuous parameters and utilizes the temperature control mechanism to effectively avoid local optimality, further improving the global search capability.

[0109] 3. The present invention aims at the multi-objective optimization problem and transforms the two objective functions into a single-objective optimization problem through the weighted sum method. However, this method often has the problems of weight sensitivity and difficulty in describing the relationship between objectives. Therefore, a target optimization model of a double annealing weighted sum algorithm based on an ant colony algorithm is proposed here. The algorithm is based on the global search capability of the annealing algorithm and its sensitivity to nonlinear objectives, which effectively makes up for the shortcomings of using the weighted sum method alone. Before performing double annealing, the ant colony algorithm is first used to select the path. The algorithm determines the exploration of the model in space and then determines the quality of the prediction results. The update of pheromones in the ant colony algorithm is divided into two processes: pheromone volatilization and pheromone accumulation. The pheromone volatilization reduces the pheromone over time, which can avoid the premature appearance of local optimal solutions in space. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 It is the overall flow chart of the optimization method of the present invention;

[0111] Figure 2 A three-dimensional model diagram of the CDC electromagnetic pilot relief valve constructed for the present invention;

[0112] Figure 3 It is a schematic diagram of the cooperation between the pilot valve core and the valve sleeve of the CDC electromagnetic pilot relief valve of the present invention;

[0113] Figure 4 The overall dynamics model of the CDC electromagnetic pilot relief valve constructed for the present invention;

[0114] Figure 5 A schematic diagram of a dynamic model of a pilot valve constructed for the present invention;

[0115] Figure 6 A schematic diagram of a dynamic model of a relief valve constructed for the present invention;

[0116] Figure 7A schematic diagram of the force balance when the valve is opened for the three-dimensional model constructed by the present invention;

[0117] Figure 8 AMESim simulation model diagram of the CDC electromagnetic pilot relief valve built for the present invention;

[0118] Fig. 9 It is a comparison diagram between the optimization method of the present invention and the initial data;

[0119] Fig.10 The Pareto chart obtained by the present invention using the full factorial technique;

[0120] In the figure, 1-O-ring; 2-base; 3-valve seat; 4-main valve core; 5-valve sleeve; 6-pilot valve core; 7-pilot spring; 8-valve core push rod; 9-magnetic isolation sleeve; 10-connecting seat; 11-electromagnet pipe cap; 12-sliding bearing; 13-armature; 14-lubricating bearing; 15-electromagnet core; 16-overflow spring; 17-ball valve steel ball; 18-throttle valve plate; 19-main spring; 20-stainless steel gasket. DETAILED DESCRIPTION

[0121] The present invention will be further described below by way of embodiments in conjunction with the accompanying drawings, but is not limited thereto.

[0122] Embodiment 1:

[0123] like Figure 1 As shown, this embodiment provides a multi-objective optimization method for the pressure flow characteristics of a CDC electromagnetic pilot relief valve, and the steps are as follows:

[0124] (1) Establish a three-dimensional equivalent model of the CDC electromagnetic pilot relief valve;

[0125] First, a three-dimensional model of a CDC electromagnetic pilot relief valve is established. The CDC electromagnetic pilot relief valve is an existing structure, including a pilot electromagnet, a pilot valve and a relief valve. A pilot valve is provided on one side of the relief valve, and the relief valve and the pilot electromagnet are connected through a connecting seat 10.

[0126] The overflow valve includes a base 2, a valve seat 3, a main valve core 4, a main spring 19, a ball valve steel ball 17 and an overflow spring 16. A valve seat 3 is arranged on one side of the base 2, a stainless steel gasket 20 is arranged between the base 2 and the valve seat 3, a main valve core 4 is arranged in the valve seat 3, a main spring 19 is arranged in the main valve core 4, and the main spring 19 is connected to the pilot valve through a throttle valve plate 18. An O-ring 1 is arranged on the outside of the base 2, a ball valve steel ball 17 and an overflow spring 16 matched therewith are arranged on one side of the valve seat 3, and the base 2, the valve seat 3, the main valve core 4, and the ball valve steel ball 17 are spatially connected, which is a hydraulic oil conduction path, such as Figure 2 The red route is shown;

[0127] The pilot valve comprises a valve sleeve 5, a pilot valve core 6, a pilot spring 7 and a valve core push rod 8. The valve sleeve 5 is provided with a pilot valve core 6, the pilot spring 7 is sleeved on the outside of the pilot valve core 6, one end of the pilot valve core 6 is connected to the valve core push rod 8, and a pilot electromagnet is provided on the outside of the valve core push rod 8;

[0128] The pilot electromagnet includes a magnetic isolation sleeve 9, an electromagnet cap 11, an armature 13 and an electromagnet core 15. The electromagnet core 15 is mounted on the bottom of the valve core push rod 8 through a lubricating bearing 14, the armature 13 is mounted on the middle part of the valve core push rod 8, the top of the valve core push rod 8 is connected to the electromagnet cap 11 through a sliding bearing 12, and the lower part of the electromagnet cap 11 is connected to the magnetic isolation sleeve 9.

[0129] When the relief valve is closed, the total flow rate Q t The inlet flow rate Q1 of the pilot valve is equal to the outlet flow rate Q2 of the pilot valve. At this time, all the fluid only passes through the pilot valve and finally flows back into the liquid storage cylinder. The overall flow rate is small;

[0130] The schematic diagram of the cooperation between the pilot valve core and the valve sleeve is as follows Figure 3 As shown in the figure, when the driving current increases, the pilot valve core moves downward. Under the condition of small current, the lower part of the pilot valve (such as Figure 3 The lower red box) has a more obvious influence than the upper part, plays a leading role, and has a "dead zone". This structure determines that the flow area will increase, thereby reducing the difficulty of pilot flow. Therefore, under the same pilot flow, the pilot valve inlet pressure P in The pressure P1 in the lower chamber of the overflow valve decreases, and the overflow valve is easier to open or the opening degree increases (opening and closing characteristics of the overflow valve). The flow rate is Q3, then Q t It is the sum of Q2 and Q3, so the flow rate increases significantly and the damping force becomes "softer".

[0131] When the control current gradually increases, Figure 3 The force of the upper red frame is much greater than the force of the lower red frame. As the push rod pushes the pilot valve core downward, the gap between the pilot valve core and the valve sleeve continues to decrease, the damping hole becomes smaller and smaller, and the damping force becomes larger. Under the same flow rate, the pressure shows an upward trend. This phenomenon leads to a significant increase in the damping force, that is, the damping effect becomes "harder".

[0132] (2) Build a dynamic model based on the constructed three-dimensional equivalent model and working principle, such as Figure 4 As shown, it includes the pilot valve dynamics model and the overflow valve dynamics model, and performs force analysis;

[0133] according to Figure 3The dynamic model diagram of the pilot valve is shown in the figure. The dynamic model of the pilot valve is constructed. The oil first enters the relief valve. When the inlet pressure of the relief valve is less than the opening pressure, the relief valve is in a closed state, and the oil enters the pilot valve through the relief valve; then the oil enters the gap between the pilot valve core and the axial hole of the valve sleeve. The gap will change under the action of the push rod force, forming a throttling hole effect, through Figure 2 From the structure, it can be seen that the pilot valve core includes three sections of diameter, so that it forms two throttling holes with the valve sleeve, producing a two-end throttling effect. The relationship between the two-end throttling effect and the damping force has been introduced above. Finally, after passing through the one-way ball valve, the oil enters the compensation chamber through the pilot valve connecting hole and returns to the oil. Figure 5 Schematic diagram of the dynamic model. The formula of the pilot valve dynamic model is:

[0134]

[0135] Among them, d K is the diameter of the relief valve spring seat hole (i.e. the seat hole where the main spring is located), d1 is the diameter of the pilot valve sleeve, d2 is the diameter of the middle section of the pilot valve core, d3 is the diameter of the front section of the pilot valve core, d4 is the diameter of the bottom section of the pilot valve core, and d5 is the diameter of the pilot valve connecting hole. is the displacement of the pilot valve core, , Q1 pilot valve inlet flow, Q a Q is the flow rate through the front section of the pilot valve core, b Q is the flow rate through the bottom section of the pilot valve core, c is the flow through the one-way ball valve, Q2 is the pilot valve outlet flow (i.e. the flow through the bottom section of the pilot valve core); △P in-1 △P is the pressure difference before and after the oil passes through the spring seat hole of the relief valve, 1-a △P is the pressure difference before and after the oil passes through the front section of the pilot valve core, a-b △P is the pressure difference before and after the oil passes through the bottom section of the pilot valve core, b-c △P is the pressure difference before and after the oil passes through the one-way ball valve, c-2 A is the pressure difference before and after the oil passes through the pilot valve connecting hole; K A is the cross-sectional area of ​​the relief valve spring seat hole; a A is the flow area of ​​the front section of the pilot valve core; b C is the flow area of ​​the bottom section of the pilot valve core; q is the flow coefficient, μ is the dynamic viscosity of the oil, ρ is the density of the oil, l is the length of the pilot valve connecting hole, F open1 It is the critical opening force of the one-way ball valve.

[0136] according to Figure 6 The dynamic model of the overflow valve is established by analyzing the oil circuit structure. When the inlet pressure of the overflow valve is greater than the opening pressure of the overflow valve, the overflow valve begins to overflow. The dynamic model of the overflow valve is:

[0137]

[0138] Among them, A0 is the flow area of ​​the main valve core of the overflow valve. d A is the flow area of ​​the inner circle of the main valve core of the overflow valve, e A is the flow area of ​​the outer circle of the overflow valve main valve core, A4 is the flow area of ​​the overflow valve connecting hole, d6 is the inner circle radius of the overflow valve seat, d7 is the outer circle radius of the overflow valve seat, and d9 is the diameter of the overflow valve connecting hole; Q d Q is the flow rate of the overflow valve main valve core from the inner circle to the outer ring, e Q4 is the flow through the overflow valve connecting hole; △P in-d △P is the pressure difference before and after the oil passes through the inner circle of the main valve core of the overflow valve and enters the outer ring. d-e △P is the pressure difference before and after the oil passes through the outer ring of the main valve core of the relief valve, e-4 F is the pressure difference before and after the oil passes through the overflow valve connecting hole, open2 is the opening pressure of the relief valve.

[0139] Assuming that the pressure in the compensation chamber is zero, the steady-state force equation when the overflow valve main valve core is opened and the force analysis of the pilot valve core are obtained. The specific force conditions can be seen Figure 7 :

[0140]

[0141] Among them, d9 represents the outer diameter of the main valve core of the overflow valve, d 10 Represents the diameter of the small circle outside the relief valve base, d 11 Represents the large circle diameter of the inner ring of the relief valve base; A 上 represents the area of ​​the oil on the upper end of the main valve core of the relief valve, A1 represents the area of ​​the oil on the inner circle of the relief valve base, A2 represents the area of ​​the oil on the outer ring of the relief valve base, A3 represents the area of ​​the oil on the relief valve outlet cavity, x y0 is the pre-compression amount of the relief valve main spring, which is set to 0.3 mm in the present invention.

[0142] Figure 7 In, P1×A 上 Represents the downward pressure generated by the oil on the upper end face of the main valve core of the relief valve, k y (x+x y0 ) represents the spring force generated by the main spring of the relief valve when the main valve core of the relief valve moves upward by a distance x, P in ×A1 represents the upward pressure generated by the oil acting on the inner circle of the relief valve base, P d ×A2 represents the upward pressure generated by the oil acting on the outer ring of the relief valve base, Pe ×A3 represents the upward pressure generated by the oil acting on the outlet cavity of the relief valve;

[0143]

[0144] This formula is the formula for the pilot valve core being affected by electromagnetic force, friction force, spring force, steady-state and transient fluid force. d is the thrust of the electromagnetic push rod, F w is the steady-state fluid force, f is the friction force on the pilot valve core, in N; G is the gravity of the pilot valve core, 0.038N, and the mass of the pilot valve core is m=3.8×10 -3 kg; B Z is the damping coefficient of the pilot valve core movement, which is 10N / (m / s); x is the displacement of the electromagnet core, with vertical downward being the positive direction; Indicates the pilot valve core speed in m / s; Indicates the pilot valve core acceleration in m / s 2 ;k x Indicates the spring stiffness of the pilot spring; x x0 Indicates the pre-compression amount of the pilot spring.

[0145] (3) Build a hydraulic simulation model based on the dynamic model;

[0146] AMESim's HCD library, namely the Hydraulic Component Design library, contains a wealth of basic hydraulic modeling components and is a supplement to the standard hydraulic library;

[0147] Based on the above-mentioned dynamic model, AMESim model is constructed, such as Figure 8 As shown in the figure, the model is mainly divided into the pressure source, relief valve, pilot solenoid valve, one-way ball valve and pilot valve connecting hole. The physical properties of the hydraulic oil are set to a density of 845 kg / m 3 , dynamic viscosity 0.04Pa·s, kinematic viscosity 21.4mm 2 / s, bulk modulus 1700MPa, the electromagnetic core uses the EMLtrans module to input different excitation currents to generate electromagnetic force and then push the pilot valve core to obtain different displacements. The module's drive coil resistance is set to 4.7Ω, the number of coils is 420 turns, the initial working air gap is 0.46mm, and the minimum inductance is 100μH. The control power supply is set to a constant current, and the pressure source output flow is set to , the slope is The inlet and outlet pressures of the CDC solenoid pilot relief valve and the flow rate (inlet flow rate) passing through the valve are measured. Since the compensation chamber pressure is assumed to be 0 MPa, the CDC solenoid valve outlet is set to return oil to the oil tank so that the outlet pressure of the pilot relief valve in AMESim is zero, that is, the inlet pressure value can represent the inlet and outlet pressure difference of the CDC solenoid pilot relief valve.

[0148] (4) Compose training samples to train the neural network model;

[0149] The diameter of the pilot valve sleeve d1, the front section diameter of the pilot valve core d3, the bottom section diameter of the pilot valve core d4, the inner circle radius of the relief valve seat d6, the spring seat hole diameter d K , spring stiffness k of the pilot spring x , relief valve main spring stiffness k y As input variables, pressure P and flow rate Q are used as output variables to perform simulation and analysis, establish experimental data sets, and train neural network models.

[0150] The neural network model is an artificial neural network with five layers: input layer, three hidden layers and output layer;

[0151] The input layer contains 7 neurons, each of which receives the optimization parameters (pilot valve sleeve diameter d1, pilot valve valve core front section diameter d3, pilot valve valve core bottom section diameter d4, relief valve seat inner circle radius d6, relief valve spring seat hole diameter d K , spring stiffness k of the pilot spring x , relief valve main spring stiffness k y ) as input, the role of the input layer is to pass these raw data to the hidden layer and prepare the data for subsequent processing;

[0152] Hidden layer 1 extracts features from input parameters through nonlinear activation functions (such as ReLU) to initially capture the nonlinear relationship between variables. Its function is to map the input to a higher-dimensional feature space, laying the foundation for more complex relationship modeling.

[0153] Hidden layer 2 further extracts hidden features and enhances the network’s expressiveness. This layer captures the deep dependencies between parameters by increasing the number of neurons or the strength of connections.

[0154] Hidden layer 3 integrates the features extracted by the first two layers to generate high-quality intermediate outputs, which are used to complete the final processing of the input features and provide them to the output layer to generate optimization targets;

[0155] The output layer contains two neurons, which output the two optimization target values ​​of pressure and flow respectively. This layer directly outputs the final result through a linear activation function for comparison with the true value;

[0156] The model training process is as follows:

[0157] First, the experimental data is divided into a training set and a test set in a ratio of 7:3. During the training process, the training data is input into the model for forward propagation, the output value is calculated, and the error between the predicted value and the true value is evaluated through the loss function (such as mean square error MSE). Then, the gradient is calculated through back propagation, and the weights and biases of the network are updated using the optimization algorithm to gradually reduce the error.

[0158] After each training, the model performance is verified using the test set. If the error between the predicted result of the test set and the actual result is less than 5%, the training is completed; otherwise, the model parameters (such as learning rate, number of neurons in the hidden layer) are adjusted or the number of training rounds is increased to retrain the model.

[0159] When the model error meets the requirements, the model is saved as a relationship model between input variables and output variables to support multi-objective optimization design. This process ensures that the model has good fitting ability and stable performance on the test set, thereby improving the accuracy and reliability of the optimization process.

[0160] (5) Initialize the ant colony algorithm parameters;

[0161] In the ant colony algorithm, the initialization phase is the key starting point, which determines the search behavior of the algorithm. The number of ants is set to 50. The number of ants affects the coverage of the search space. Too few ants may lead to insufficient search, and too many ants increase the computational complexity. The maximum number of iterations is set to 500 to ensure sufficient time for optimization and prevent the algorithm from terminating prematurely. The initial value of pheromone for each path is 0.1, which provides the algorithm with an initial search preference. The pheromone volatility rate is set to 0.2 to control the attenuation of pheromone concentration, maintain exploration and avoid early convergence. The pheromone gain coefficient is set to 1.0. The pheromone gain coefficient determines the impact of path quality on pheromone update. The heuristic information weight β=2, the pheromone weight α=1, balances the role of pheromone and heuristic information in path selection, and ensures that the search can take into account both global and local optimization. The local search frequency executes the double annealing algorithm every 5 generations to enhance the accuracy of the search.

[0162] In order to ensure the rationality of optimization, a constraint condition is given:

[0163] ;

[0164] (6) Start the ant colony algorithm iteration;

[0165] (61) Path selection:

[0166] Based on the combination of pheromone concentration and heuristic information, ants choose the optimal path. The path selection formula is as follows:

[0167]

[0168] In the formula, τ ij is the pheromone concentration of path i to j; η ij is the heuristic information of path i to j, and the quality evaluation of the discrete parameter combination corresponding to each path, that is, the objective function value;

[0169] Heuristic information η ij It represents the influence of discrete parameter combination on the pressure-flow characteristic of the pilot relief valve, and obtains the target of the greater pressure and the smaller flow by calculating the objective function value of the current combination;

[0170] (62) Construct the solution:

[0171] After the ants select the discrete parameter combination, they optimize the continuous parameters through the double annealing algorithm. The specific steps of the double annealing algorithm include:

[0172] (621) Initialize the double annealing algorithm parameters: initial temperature T0 = 100, the cooling strategy is that the temperature in each round decays to 95% of the previous round;

[0173] (622) Double annealing algorithm iteration: Generate a new solution in the neighborhood of the current solution. Assuming the current solution is x, the new solution It can be generated by perturbation operation:

[0174]

[0175] Here, △x is a randomly generated perturbation.

[0176] Whether to accept the new solution is calculated based on the objective function value, and randomness is introduced through the Metropolis criterion. The objective function is the mean square error (MSE) of the pressure-flow characteristic curve:

[0177]

[0178] Among them, P model (x i ) is the pressure-flow curve value calculated by the model, P target (x i ) is the target pressure-flow curve value, and N is the number of data points;

[0179] Decide whether to accept the new solution according to the Metropolis criteria:

[0180]

[0181] if , that is, the objective function value of the new solution is better, accept the new solution; if , then the probability of accepting the new solution is:

[0182]

[0183] According to probability, accept the worse solution with a certain probability to maintain the exploratory nature of the algorithm;

[0184] The double annealing algorithm is called to optimize the continuous parameters and the temperature is updated according to the cooling strategy:

[0185]

[0186] 𝑇 k : The temperature of the 𝑘th iteration, 𝛼=0.95 is the temperature attenuation coefficient (0<𝛼<1);

[0187] The double annealing algorithm continues to iterate until the termination condition is met, such as the temperature is lower than a certain threshold 𝑇min or the maximum number of iterations is reached;

[0188] (63) Evaluate the quality of the solution:

[0189] After each ant completes the process of path selection and solution construction, it needs to evaluate the solution and calculate the comprehensive objective function value;

[0190] The comprehensive objective function value is expressed as the weighted average of the objective function under the combination of discrete and continuous parameters:

[0191]

[0192] Among them, f discrete is the objective function value corresponding to the discrete parameter combination; f continuous is the objective function value corresponding to the continuous parameter combination optimized by the double annealing algorithm, and is the weight coefficient, which controls the influence of the discrete and continuous partial objective functions on the overall objective function;

[0193] (64) End the current ant's operation:

[0194] When each ant completes path selection, solution construction, objective function calculation, and solution evaluation, the operation on the current ant ends and the iteration of the next ant begins.

[0195] (7) Update pheromones;

[0196] In each iteration of the ant colony algorithm, the ants will update the pheromone according to the quality of the solutions to the paths they find, ensuring that the paths with high-quality solutions can get more pheromone support, thereby guiding more ants to search along these paths;

[0197] (71) Pheromone update formula:

[0198] After each ant completes path selection and calculates the objective function, it will update the pheromone on the path. The update rules are as follows:

[0199]

[0200] is the pheromone concentration of the path 𝑖→𝑗 in the previous iteration;

[0201] is the pheromone concentration of the path 𝑖→𝑗 after this iteration;

[0202] ρ is the pheromone volatilization rate, which usually ranges from [0, 1] and is set to 0.2 here;

[0203] is the pheromone increment, and the calculation formula is:

[0204]

[0205] in, is the comprehensive objective function value calculated after the ant selects the path; Q is a constant that controls the increment of pheromone and can be set to 1.0;

[0206] The size of the pheromone increment is related to the objective function value of the path. The higher the path quality (i.e., the smaller the objective function value), the larger the pheromone increment, and vice versa. This ensures that high-quality paths get more pheromones, thus getting more choices in subsequent iterations.

[0207] (72) Pheromone Update:

[0208] Calculate path quality: After each ant completes path selection and constructs a solution, it calculates the objective function value (such as the error between the pressure-flow characteristic and the target curve);

[0209] Update path pheromone: According to the objective function value, use the formula to update the pheromone concentration on the path;

[0210] Pheromone volatilization: The volatilization of pheromone is controlled by the parameter ρ to avoid early convergence and keep a certain diversity in the search space.

[0211] (8) Determine whether the termination conditions are met;

[0212] After each round of ant colony algorithm iteration, it is necessary to determine whether the termination condition is met. If the condition is met, the algorithm will terminate and output the optimal solution. If the condition is not met, the next round of iteration will be executed.

[0213] Set the maximum number of iterations to 500. When this number of iterations is reached, the algorithm stops;

[0214] The termination judgment formula is:

[0215]

[0216] and are the optimal solution objective function values ​​of the tth and t-1th generations, respectively. ε is the set accuracy threshold. If the objective function value of the optimal solution changes less than a certain threshold ε=1×10 in several consecutive generations (such as 10 iterations), -5 , the algorithm is considered to have converged and terminated.

[0217] (9) Output the optimal parameter combination and the optimized pressure-flow characteristic curve;

[0218] When the termination conditions are met, the optimal discrete and continuous parameter combination is output, and the optimized pressure-flow characteristic curve is given, such as Figure 8 As shown, the output of the optimal solution is the optimal discrete and continuous parameter combination searched by the ant colony algorithm within the maximum number of iterations;

[0219] (1) Discrete parameters: pilot valve sleeve diameter / 2.8mm, pilot valve core front section diameter / 1.6mm, pilot valve core bottom section diameter / 3.2mm, relief valve spring seat hole diameter / 0.7mm, pilot spring spring stiffness / 11.8N / mm, relief valve main spring stiffness / 35.5N / mm, relief valve seat inner radius / 7mm.

[0220] (2) The optimal values ​​of the optimized continuous parameters obtained by the double annealing algorithm are: pilot valve opening / 0.8 mm, relief valve opening / 1 mm, solenoid valve drive current / 1.6 A, and valve port control pressure / 6.0 MPa.

[0221] Use the optimal solution parameter combination to substitute into the dynamic model of the CDC electromagnetic pilot relief valve, calculate and draw the optimized pressure-flow characteristic curve, according to Fig. 9 By comparing the results of the above, we can draw the following conclusions: the optimization method of this embodiment significantly reduces pressure loss, improves flow control accuracy and system stability, and the optimized pressure-flow curve is smoother, with faster dynamic response speed, and can more accurately adapt to changes in working conditions and meet complex application requirements. Compared with the initial data, the method of this embodiment shows obvious advantages in efficiency and performance, and has high engineering application value.

[0222] (10) The Pareto method is used to determine the importance of influencing factors.

[0223] The full-factor DOE technology is used to analyze the importance of influencing factors. DOE (Design of Experiments) is used to study how the input variables of a system or process affect the output variables. In the design and optimization of CDC solenoid valves, DOE can help identify and optimize key parameters to improve shock absorber performance.

[0224] The pilot valve core bottom section diameter, relief valve spring seat hole diameter, pilot valve sleeve diameter, relief valve main spring stiffness and pilot spring spring stiffness are used as input parameters, represented by I, K, XD, YT and XT respectively. The pressure difference of the relief valve is selected as the output parameter. The full factorial technology is used to obtain The design matrix is ​​then plotted using Pareto, as Fig.10 As shown in the figure, the horizontal axis is the positive / negative impact on the pressure difference, and the vertical axis is the various parameters and the combination of parameters. From the figure, it can be seen that the order of influence is K, I, XD, YT, and XT, that is, the diameter of the valve seat hole of the overflow valve spring has the greatest impact, and the spring stiffness of the pilot spring has the smallest impact.

Claims

1. A multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve, characterized in that: Here are the steps: (1) Establish a three-dimensional equivalent model of the CDC electromagnetic pilot relief valve, including the pilot electromagnet, pilot valve and relief valve; (2) Build a dynamic model based on the constructed three-dimensional equivalent model and working principle, including the pilot valve dynamic model and the overflow valve dynamic model, and perform force analysis; (3) Build a hydraulic simulation model based on the dynamic model; (4) Compose training samples to train the neural network model; (5) Initialize the ant colony algorithm parameters; In the optimization process, the ant colony algorithm combined with the double annealing local search strategy is used to solve the multi-objective optimization design of the CDC electromagnetic pilot relief valve. By initializing key parameters and setting the local search mechanism, the efficiency of global search and local optimization is balanced. (6) Start the ant colony algorithm iteration; (7) Update pheromones; (8) Determine whether the termination conditions are met; (9) Output the optimal parameter combination and the optimized pressure-flow characteristic curve; (10) The Pareto method is used to determine the importance of influencing factors.

2. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve as claimed in claim 1, characterized in that: In step (2), a dynamic model of the pilot valve is constructed. The oil first enters the relief valve. When the inlet pressure of the relief valve is less than the opening pressure, the relief valve is in a closed state, and the oil enters the pilot valve through the relief valve. The pilot valve core and the valve sleeve are matched through the shaft hole. The gap between the pilot valve core and the valve sleeve changes to form a throttling hole effect. The pilot valve core includes three sections of diameter, so that it forms two throttling holes with the valve sleeve, producing a throttling effect at both ends. After passing through the ball valve, the oil enters the compensation chamber and returns. The formula of the constructed pilot valve dynamic model is: Among them, d K is the diameter of the relief valve spring seat hole, d1 is the diameter of the pilot valve sleeve, d2 is the diameter of the middle section of the pilot valve core, d3 is the diameter of the front section of the pilot valve core, d4 is the diameter of the bottom section of the pilot valve core, and d5 is the diameter of the pilot valve connecting hole. is the displacement of the pilot valve core, , Q1 pilot valve inlet flow, Q a Q is the flow rate through the front section of the pilot valve core, b Q is the flow rate through the bottom section of the pilot valve core, c is the flow through the one-way ball valve, Q2 is the pilot valve outlet flow; △P in-1 △P is the pressure difference before and after the oil passes through the spring seat hole of the relief valve, 1-a △P is the pressure difference before and after the oil passes through the front section of the pilot valve core, a-b △P is the pressure difference before and after the oil passes through the bottom section of the pilot valve core, b-c △P is the pressure difference before and after the oil passes through the one-way ball valve, c-2 A is the pressure difference before and after the oil passes through the pilot valve connecting hole; K A is the cross-sectional area of ​​the relief valve spring seat hole; a A is the flow area of ​​the front section of the pilot valve core; b C is the flow area of ​​the bottom section of the pilot valve core; q is the flow coefficient, μ is the dynamic viscosity of the oil, ρ is the density of the oil, l is the length of the pilot valve connecting hole, F open1 It is the critical opening force of the one-way ball valve.

3. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve as claimed in claim 2, characterized in that: In step (2), when the inlet pressure of the overflow valve is greater than the opening pressure of the overflow valve, the overflow valve begins to overflow, and the dynamic model of the overflow valve is: Among them, A0 is the flow area of ​​the main valve core of the overflow valve. d A is the flow area of ​​the inner circle of the main valve core of the overflow valve, e A is the flow area of ​​the outer circle of the overflow valve main valve core, A4 is the flow area of ​​the overflow valve connecting hole, d6 is the inner circle radius of the overflow valve seat, d7 is the outer circle radius of the overflow valve seat, and d9 is the diameter of the overflow valve connecting hole; Q d Q is the flow rate of the overflow valve main valve core from the inner circle to the outer ring, e Q4 is the flow through the overflow valve connecting hole; △P in-d △P is the pressure difference before and after the oil passes through the inner circle of the main valve core of the overflow valve and enters the outer ring. d-e △P is the pressure difference before and after the oil passes through the outer ring of the main valve core of the relief valve, e-4 F is the pressure difference before and after the oil passes through the overflow valve connecting hole, open2 is the opening pressure of the relief valve.

4. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve as claimed in claim 3, characterized in that: In step (2), assuming that the pressure in the compensation chamber is zero, the steady-state force equation when the overflow valve main valve core is opened and the force analysis of the pilot valve core are obtained: Among them, d9 represents the outer diameter of the main valve core of the overflow valve, d 10 Represents the diameter of the small circle outside the relief valve base, d 11 Represents the large circle diameter of the inner ring of the relief valve base; A 上 represents the oil action area on the upper end of the relief valve main valve core, A1 represents the oil action area on the inner circle of the relief valve base, A2 represents the oil action area on the outer ring of the relief valve base, A3 represents the oil action area on the relief valve outlet cavity, x y0 is the pre-compression of the relief valve main spring; This formula is the formula for the pilot valve core being affected by electromagnetic force, friction force, spring force, steady-state and transient fluid force. d is the thrust of the electromagnetic push rod, F w is the steady-state fluid force, f is the friction force on the pilot valve core, in N; G is the gravity of the pilot valve core, 0.038N, and the mass of the pilot valve core is m=3.8×10 -3 kg; B Z is the damping coefficient of the pilot valve core movement, which is 10N / (m / s); x is the displacement of the electromagnet core, with vertical downward being the positive direction; Indicates the pilot valve core speed in m / s; Indicates the pilot valve core acceleration in m / s 2 ;k x Indicates the spring stiffness of the pilot spring; x x0 Indicates the pre-compression amount of the pilot spring.

5. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve as claimed in claim 4, characterized in that: In step (4), the pilot valve sleeve diameter d1, the pilot valve valve core front section diameter d3, the pilot valve valve core bottom section diameter d4, the relief valve seat inner circle radius d6, the relief valve spring seat hole diameter d K , spring stiffness k of the pilot spring x , relief valve main spring stiffness k y As input variables, pressure P and flow rate Q as output variables, simulation and analysis are performed, experimental data sets are established, and neural network models are trained; The neural network model is an artificial neural network with five layers: input layer, three hidden layers and output layer; The input layer contains 7 neurons, each of which receives the optimization parameters as input. The role of the input layer is to pass these raw data to the hidden layer and prepare the data for subsequent processing; Hidden layer 1 extracts features of input parameters through nonlinear activation functions, preliminarily capturing the nonlinear relationship between variables. Its function is to map the input to a higher-dimensional feature space. Hidden layer 2 further extracts hidden features and enhances the network’s expressiveness. This layer captures the deep dependencies between parameters by increasing the number of neurons or the strength of connections. Hidden layer 3 integrates the features extracted by the first two layers to generate intermediate outputs, which are used to complete the final processing of the input features and provide them to the output layer to generate optimization targets; The output layer contains two neurons, which output the two optimization target values ​​of pressure and flow respectively. This layer directly outputs the final result through a linear activation function for comparison with the true value; The model training process is as follows: First, the experimental data is divided into a training set and a test set in a ratio of 7:

3. During the training process, the training data is input into the model for forward propagation, the output value is calculated, and the error between the predicted value and the true value is evaluated through the loss function. Then, the gradient is calculated through backpropagation, and the weights and biases of the network are updated to gradually reduce the error. After each training, the test set is used to verify the model performance. If the error between the predicted result of the test set and the actual result is less than 5%, the training is completed; Otherwise, adjust the model parameters or increase the number of training rounds to retrain the model.

6. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve as claimed in claim 5, characterized in that: Step (5) is specifically as follows: In the ant colony algorithm, the number of ants is set to 50, the maximum number of iterations is set to 500, the initial pheromone value of each path is 0.1, the pheromone volatility rate is set to 0.2, the pheromone gain coefficient is set to 1.0, the heuristic information weight β=2, the pheromone weight α=1, and the local search frequency is performed once every 5 generations. Double annealing algorithm; In order to ensure the rationality of optimization, a constraint condition is given: 。 7. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve as claimed in claim 6, characterized in that: Step (6) is as follows: (61) Path selection: Based on the combination of pheromone concentration and heuristic information, ants choose the optimal path. The path selection formula is as follows: In the formula, τ ij is the pheromone concentration of path i to j; η ij is the heuristic information of path i to j, and the quality evaluation of the discrete parameter combination corresponding to each path, that is, the objective function value; (62) Construct the solution: After the ants select the discrete parameter combination, they optimize the continuous parameters through the double annealing algorithm. The specific steps of the double annealing algorithm include: (621) Initialize the double annealing algorithm parameters: initial temperature, cooling strategy is that each round of temperature decays to 95% of the previous round; (622) Double annealing algorithm iteration: Generate a new solution in the neighborhood of the current solution, calculate whether to accept the new solution based on the objective function value, and introduce randomness through the Metropolis criterion. The objective function is the mean square error of the pressure-flow characteristic curve: Among them, P model (x i ) is the pressure-flow curve value calculated by the model, P target (x i ) is the target pressure-flow curve value, and N is the number of data points; Decide whether to accept the new solution according to the Metropolis criteria: if , that is, the objective function value of the new solution is better, accept the new solution; if , then the probability of accepting the new solution is: According to probability, accept the worse solution with a certain probability to maintain the exploratory nature of the algorithm; The double annealing algorithm is called to optimize the continuous parameters and the temperature is updated according to the cooling strategy: 𝑇 k : The temperature of the 𝑘th iteration, 𝛼=0.95 is the temperature attenuation coefficient (0 < 𝛼< 1); The double annealing algorithm continues to iterate until the termination condition is met; (63) Evaluate the quality of the solution: After each ant completes the process of path selection and solution construction, it needs to evaluate the solution and calculate the comprehensive objective function value; The comprehensive objective function value is expressed as the weighted average of the objective function under the combination of discrete and continuous parameters: Among them, f discrete is the objective function value corresponding to the discrete parameter combination; f continuous is the objective function value corresponding to the continuous parameter combination optimized by the double annealing algorithm, and is the weight coefficient, which controls the influence of the discrete and continuous partial objective functions on the overall objective function; (64) End the current ant's operation: When each ant completes path selection, solution construction, objective function calculation, and solution evaluation, the operation on the current ant ends and the iteration of the next ant begins.

8. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve as claimed in claim 7, characterized in that: In step (7), specifically: In each iteration of the ant colony algorithm, the ants will update the pheromone according to the quality of the solutions to the paths they find, ensuring that the paths with high-quality solutions can get more pheromone support, thereby guiding more ants to search along these paths; (71) Pheromone update formula: After each ant completes path selection and calculates the objective function, it will update the pheromone on the path. The update rules are as follows: is the pheromone concentration of the path 𝑖→𝑗 in the previous iteration; is the pheromone concentration of the path 𝑖→𝑗 after this iteration; ρ is the pheromone volatilization rate, usually in the range of [0, 1]; is the pheromone increment, and the calculation formula is: in, is the comprehensive objective function value calculated after the ant selects the path; Q is a constant that controls the increment of pheromone; The size of the pheromone increment is related to the objective function value of the path. The higher the path quality, the larger the pheromone increment, and vice versa. (72) Pheromone Update: Calculate path quality: After each ant completes path selection and builds a solution, calculate the objective function value; Update path pheromone: Update the pheromone concentration on the path according to the objective function value; Pheromone volatilization: The volatilization of pheromone is controlled by the parameter ρ.

9. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve as claimed in claim 8, characterized in that: Step (8) is specifically as follows: After each round of ant colony algorithm iteration, it is necessary to determine whether the termination condition is met. If the condition is met, the algorithm will terminate and output the optimal solution. If the condition is not met, the next round of iteration will be executed. Set the maximum number of iterations to 500. When this number of iterations is reached, the algorithm stops; The termination judgment formula is: and are the optimal solution objective function values ​​of the tth generation and the t-1th generation, respectively. ε is the set accuracy threshold. If the objective function value of the optimal solution changes less than a certain threshold ε=1×10 in several consecutive generations, -5 , the algorithm is considered to have converged and terminated.

10. The multi-objective optimization method for the pressure and flow characteristics of a CDC electromagnetic pilot relief valve according to claim 9, characterized in that: Step (9) is specifically as follows: when the termination condition is met, the optimal discrete and continuous parameter combination is output, and the optimized pressure-flow characteristic curve is given, and the output of the optimal solution is the optimal discrete and continuous parameter combination searched by the ant colony algorithm within the maximum number of iterations; The optimal solution parameter combination is used to substitute into the dynamic model of the CDC electromagnetic pilot relief valve, and the optimized pressure-flow characteristic curve is calculated and drawn. The optimized pressure-flow characteristic curve shows the gradually decreasing relationship between flow and pressure, and the optimal solution is to minimize the mean square error of the pressure-flow curve. In step (10), the full factor DOE technology is used to analyze the importance of the influencing factors. The pilot valve core bottom section diameter, the relief valve spring seat hole diameter, the pilot valve sleeve diameter, the relief valve main spring stiffness and the pilot spring spring stiffness are used as input parameters, and the pressure difference of the relief valve is selected as the output parameter. The full factor technology is used to obtain The design matrix is ​​constructed, and finally the Pareto plot configuration is used to sort the parameters according to the degree of influence to obtain the parameters with the greatest and least influence.

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