A hydraulic control method and system for vertical mills based on an improved dung beetle optimization algorithm

Abstract

This invention discloses a hydraulic control method and system for a vertical mill based on an improved dung beetle optimization algorithm. The method includes: constructing a vertical mill hydraulic-mechanical coupling simulation model; introducing a fusion of optimal point set and reverse learning strategy, adaptive reproductive stealing strategy, and adaptive hybrid mutation strategy into the dung beetle algorithm; optimizing the quantization factor and proportional factor of the fuzzy PID controller using IDBO; and applying this optimization to the vertical mill hydraulic control system. This invention can dynamically adjust control parameters to adapt to different operating conditions and disturbances; effectively reducing the longitudinal fluctuation error of the grinding rollers; the fusion of optimal point set and reverse learning strategy to initialize the population improves the quality and diversity of the initial population solutions, effectively avoiding premature convergence, reducing the blank area in the search space, and improving algorithm performance; and the introduction of an adaptive reproductive stealing strategy increases the diversity of the search range, improving the algorithm's global search capability in the early stages of iteration and giving the algorithm stronger local fine-grained search capability in the later stages of iteration.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic control technology for vertical mills, and relates to a hydraulic control method and system for vertical mills based on an improved dung beetle optimization algorithm. Background Technology

[0002] The hydraulic system of a vertical mill provides a buffer for its lifting and lowering rollers; however, system instability can induce loading and unloading impacts on the mechanical body, causing unstable vibrations in the grinding system and damaging the mechanical structure and transmission system. Given the inherently complex mechanical-hydraulic coupling characteristics of vertical mills, and their complex dynamic characteristics and closed-loop instability in the face of varying operating conditions and parameter fluctuations, research on targeted control strategies in this field is still lacking and urgently needs in-depth exploration and optimization. Furthermore, existing technologies struggle to adjust the relevant parameters of fuzzy PID controllers, and simulation trial-and-error methods suffer from blindness, long processing times, and unsatisfactory control effects. The dung beetle algorithm, based on a "rolling-laying-foraging-stealing" simulation framework, can solve optimization problems. It is widely used in fluorographic inversion, vibration signal prediction, path planning, and fault diagnosis. Although the dung beetle search algorithm performs well in terms of global search capability and convergence speed, it suffers from problems such as insufficient population diversity, weak global search capability, and susceptibility to local optima when facing complex problems. Summary of the Invention

[0003] The purpose of this invention is to address the lack of research on control strategies for hydraulic systems of vertical mills in the existing technology, which urgently needs in-depth exploration and optimization; at the same time, the search efficiency and accuracy of fuzzy PID controllers are low, and the global search capability of the dung beetle algorithm is weak and prone to getting trapped in local optima. This invention provides a hydraulic control method and system for vertical mills based on an improved dung beetle optimization algorithm.

[0004] To achieve the above objectives, the present invention employs the following technical solution:

[0005] This invention proposes a hydraulic control method for vertical mills based on an improved dung beetle optimization algorithm, comprising:

[0006] Based on the structural stress data and Lagrange equations of the vertical mill, the system dynamic differential equations in various generalized coordinate systems are obtained.

[0007] Based on the dynamic differential equations, a joint simulation model of ADAMS-AMESim-Simulink is constructed;

[0008] The DBO algorithm is improved to obtain the IDBO algorithm;

[0009] The IDBO algorithm is applied to the co-simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, output the optimal control parameters, and optimize the hydraulic control system of the vertical mill.

[0010] This invention proposes a hydraulic control system for a vertical mill based on an improved dung beetle optimization algorithm, comprising:

[0011] The acquisition module obtains the system dynamic differential equations in various generalized coordinate systems based on the structural force data and Lagrange equations of the vertical mill.

[0012] The building module is based on the dynamic differential equation to construct the ADAMS-AMESim-Simulink joint simulation model;

[0013] The improvement module improves the DBO algorithm to obtain the IDBO algorithm;

[0014] The optimization module applies the IDBO algorithm to the co-simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, outputs the optimal control parameters, and optimizes the hydraulic control system of the vertical mill.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] This invention proposes a hydraulic control method for vertical mills based on an improved dung beetle optimization algorithm. It constructs a hydraulic-mechanical coupling simulation model of the vertical mill and incorporates a fusion of optimal point sets and a back-learning strategy, an adaptive breeding and stealing strategy, and an adaptive hybrid mutation strategy into the dung beetle algorithm. IDBO is used to optimize the quantization factor and proportional factor of the fuzzy PID controller, which is then applied to the hydraulic control system of the vertical mill. This invention can dynamically adjust control parameters to adapt to different operating conditions and disturbances. It effectively reduces the longitudinal fluctuation error of the grinding rollers and stabilizes the grinding force by fine-tuning the small-range fluctuations in the gap between the grinding rollers and the grinding disc. This invention integrates optimal point sets and a back-learning strategy to initialize the population, improving the quality and diversity of the initial population solutions, effectively avoiding premature convergence, reducing the blank areas in the search space, and improving algorithm performance. Simultaneously, the introduction of an adaptive breeding and stealing strategy increases the diversity of the search range, enhancing the algorithm's global search capability in the early stages of iteration and giving the algorithm stronger local fine-grained search capabilities in the later stages of iteration. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1This is a schematic flowchart of the hydraulic control method for vertical mills based on an improved dung beetle optimization algorithm according to the present invention.

[0019] Figure 2 This is a schematic diagram of the hydraulic control system for a vertical mill based on an improved dung beetle optimization algorithm, according to the present invention.

[0020] Figure 3 This is a technical roadmap for the hydraulic control method of a vertical mill based on an improved dung beetle optimization algorithm, as described in this invention.

[0021] Figure 4 The diagram shows the structural model of the vertical mill ((a) is a schematic diagram of the dynamic model of the vertical mill; (b) is a schematic diagram of the virtual prototype model of the vertical mill).

[0022] Figure 5 This is a schematic diagram of a closed-loop model of the hydraulic system of a vertical mill.

[0023] Figure 6 This is a schematic diagram of the control system structure of a vertical mill.

[0024] Figure 7 This is a flowchart illustrating the DBO algorithm.

[0025] Figure 8 A schematic diagram comparing the population distribution initialized for random initialization and initialization for optimal point sets.

[0026] Figure 9 This is a schematic diagram of a spiral search.

[0027] Figure 10 A comparison curve of the changing trends of nonlinear adaptive parameters.

[0028] Figure 11 The graph shows the probability density distributions of Cauchy, Gaussian, and t-distributions.

[0029] Figure 12 This is a trend chart of the adaptive factor.

[0030] Figure 13 A visualization of Kendall's coefficient.

[0031] Figure 14 This diagram illustrates the convergence curves of the IDBO, DBO, BOA, TSA, SSA, PSO, and WOA algorithms.

[0032] Figure 15 This is a schematic diagram showing the fitness value changes of the DBO and IDBO algorithms.

[0033] Figure 16 To optimize the curves for control parameters.

[0034] Figure 17The image shows the results of step signal tracking.

[0035] Figure 18 The result diagram is shown for step signal control.

[0036] Figure 19 The diagram shows the results of sinusoidal signal control.

[0037] Figure 20 This is a comparison curve of the longitudinal displacement error of the grinding roller. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0039] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0040] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0041] The present invention will now be described in further detail with reference to the accompanying drawings:

[0042] See Figure 1 This invention proposes a hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm, comprising:

[0043] S1: Based on the structural stress data and Lagrange equations of the vertical mill, obtain the system dynamic differential equations in various generalized coordinate systems;

[0044] The vertical mill includes a rocker arm, a swing arm, a grinding roller, a grinding roller shaft, and a hydraulic cylinder; the rocker arm and the swing arm of the vertical mill are connected by the grinding roller shaft; the swing arm of the vertical mill is connected to the grinding roller; and the hydraulic cylinder is connected to the rocker arm by a connecting rod.

[0045] Based on the structural stress data and Lagrange equations of the vertical mill, the differential equations of system dynamics in various generalized coordinate systems are derived, specifically:

[0046] Taking a hydraulic rod as an example, simplifying the center of mass, its kinetic energy... T液 Potential energy U 液 for

[0047] (1)

[0048] (2)

[0049] Based on formulas (1) and (2), the generalized coordinates are obtained. q The dynamic differential equation under condition 1 is:

[0050] (3)

[0051] in, It is the acceleration due to gravity. l 1 is the length of the hydraulic rod, α is the angle between the rocker arm and the Z-axis, β is the angle between the swing arm and the X-axis, δ is the angle between the hydraulic cylinder and the X-axis, m1 is the mass of the hydraulic cylinder, m2 is the mass of the rocker arm, m3 is the mass of the swing arm, m4 is the mass of the grinding roller, and c is the hydraulic cylinder damping.

[0052] The system dynamics differential equations in various generalized coordinate systems are shown in equation (4).

[0053] (4)

[0054] Among them, a generalized coordinate system is selected in the XOY plane. q 1. Describe the extension and retraction of the hydraulic rod, and select... θ Describe the rotation angles of the grinding roller, rocker arm, and swing arm about the grinding roller axis, and select... q 2 and q 3. Quantify the bending deformation of the rocker arm in the XOZ and YOZ planes respectively, and introduce [the following] into the XOZ plane. Ψ Describe the torsional deflection angle of the rocker arm; l 2 represents the length of the rocker arm. l 3 represents the length of the swing arm. l 4 represents the length of the grinding roller. m e2 The equivalent mass during rocker arm bending vibration. Let be the bending stiffness of the swing arm. The grinding force of the grinding roller on the material. This refers to the sliding friction between the material and the grinding roller.

[0055] S2: Based on the dynamic differential equations, construct the ADAMS-AMESim-Simulink joint simulation model;

[0056] Based on the dynamic differential equations, the parameters and material properties of each component of the vertical mill, and the force and constraint relationships applied according to the relationship between each relatively fixed and moving component, a rigid-flexible coupling dynamic model of the vertical mill is established.

[0057] Based on AMESim and following the principles of hydraulic and closed-loop control, a hydraulic system model for a vertical mill is constructed.

[0058] Based on the fuzzy PID controller, the error between the actual and desired displacement and its rate of change are selected as inputs, and the valve electrical signal of the vertical mill is used as the output to form a multi-input single-output Mamdani-type fuzzy controller.

[0059] Based on the rigid-flexible coupling dynamic model of the mill, the hydraulic system model of the vertical mill, and the Mamdani-type fuzzy controller with multiple inputs and single outputs, a joint simulation model of ADAMS-AMESim-Simulink is constructed.

[0060] S3: Improve the DBO algorithm to obtain the IDBO algorithm;

[0061] The population is initialized based on a fusion of a set of optimal points and a reverse learning strategy. The optimal point set is mapped to the solution space to obtain the initial population. Reverse learning is then implemented to generate the final population. After merging, fitness is evaluated, and selection is performed. N A new initial population is constructed using the optimal individuals;

[0062] A dynamic spiral search shape parameter is introduced into the initial population to endow dung beetles with diverse path adjustment capabilities; a nonlinear weighting factor is introduced to prevent premature convergence in the later stages of iteration. c t The positions of the egg masses and dung beetles are updated based on local and global optimality.

[0063] For adaptive t-distribution variation, an adaptive factor is used to constrain the degree of variation; and Kendall's rank correlation coefficient is introduced into the selective centroid back learning strategy to measure the correlation between two random variables. Negatively correlated and uncorrelated individuals are selected for back learning, and the optimal individual is subjected to mixed variation perturbation to complete the improvement of the DBO algorithm.

[0064] The population is initialized based on a fusion of a set of optimal points and a reverse learning strategy. The optimal point set is mapped to the solution space to obtain the initial population. Reverse learning is then implemented to generate the final population. After merging, fitness is evaluated, and selection is performed. N The optimal individuals are used to construct a new initial population, specifically:

[0065] By integrating the optimal point set with a reverse learning strategy to initialize the population, the convergence speed of the DBO algorithm is improved. The reverse learning formula is as follows:

[0066] (5)

[0067] In the formula, For reverse populations, k 1× D A random vector that follows a normal distribution. Ub and Lb Denotes the upper and lower bounds of the solution space. X This represents the initial population.

[0068] A dynamic spiral search shape parameter is introduced into the initial population to endow dung beetles with diverse path adjustment capabilities; a nonlinear weighting factor is introduced to prevent premature convergence in the later stages of iteration. c t The positions of the egg masses and dung beetles are updated based on local and global optimality, specifically as follows:

[0069] Introducing dynamic spiral search shape parameters p This endows dung beetles with diverse path adjustment capabilities, expressed as:

[0070] (6)

[0071] (7)

[0072] In the formula: The constant defining the spiral shape, g, is a dynamic adjustment coefficient that regulates the rate of exponential growth. β As a spiral search factor, r A random number in [0,1] t This represents the current iteration number. T This represents the maximum number of iterations.

[0073] To prevent premature convergence in the later stages of iteration, a nonlinear weighting factor is introduced. By optimizing the nonlinear adaptive decreasing parameter, the global optimization performance of the algorithm is improved. The expression is as follows:

[0074] (8)

[0075] In the formula: c t For iteration t The inertia weight of the second time, the maximum inertia weight c max =1, minimum inertia weight c min =0.001;

[0076] The positions of the egg masses and the dung beetle are updated based on local and global optimality, as shown below:

[0077] (9)

[0078] (10)

[0079] In the formula: X * This is the current local optimum. Bi ( t ) is the first t The generation i The position of each egg sphere is influenced by independent random vectors. b 1 and b 2 (1× D (dimensional) and the optimization dimension D constraint, located in [ Lb * , Ub * Within the spawning area, X i ( t ) is the first t The generation i The location of the dung beetle thief. X b This is the globally optimal solution. g 1× D Normal random vector, S It is a constant. Lb * This is the lower boundary of the spawning area. Ub * This is the upper boundary of the spawning area.

[0080] For the adaptive t-distribution variation, an adaptive factor is used to constrain the degree of variation; and Kendall's rank correlation coefficient is introduced into the selective centroid back-learning strategy to measure the correlation between two random variables. Negatively correlated and uncorrelated individuals are selected for back-learning, and the optimal individual is subjected to mixed variation perturbation to complete the improvement of the DBO algorithm, specifically:

[0081] Introducing Adaptive t Distribution mutation strategy, mutation formula is

[0082] (11)

[0083] t Degrees of freedom parameters of distribution variation a Number of iterations T ,when T When the value is small, the curve exhibits a Cauchy distribution. C (0,1), when T As the value approaches infinity, the curve exhibits a Gaussian distribution. N (0,1);

[0084] Using adaptive factors α The degree of variation is constrained, and the calculation formula is as follows:

[0085] (12)

[0086] Sensitive parameters in the formula f=0.6, defining the local development accuracy during the iteration process;

[0087] Based on a selective centroid reverse learning strategy, Kendall's rank correlation coefficient is introduced to enhance the population's mutation capacity, defined as:

[0088] (13)

[0089] (14)

[0090] In the formula, N For individuals in a population, denoted as { x 1, x 2, ..., x N The search space dimension is d , M id The center of gravity of the group is in the first d The value of dimension, X id For individuals X i At d The position of the center of gravity of the dimension in the opposite direction; For individuals X i In the d Based on the center of gravity M id The opposite position;

[0091] Kendall's rank correlation coefficient is a nonparametric statistical method used to measure the correlation between two random variables; D 3D random variables Xi =[ x i1 , x i2 ..., x iD ]and X j =[ x j1 , x j2 ..., x jD The Kendall rank correlation coefficient is defined as follows:

[0092] (15)

[0093] In the formula, x i and x j The value of the first random variable. y i andy j The value of the second random variable;

[0094] Using selection probability P S Apply mixed mutation perturbation to the optimal individual; when P S When <0.5, adaptive method is used. t The distribution variation undergoes large-scale perturbation; when P S When the value is ≥0.5, selective centroid back-learning is used to perform small-scale perturbations; the relevant definitions are as follows:

[0095] (16)

[0096] (17)

[0097] In the formula, X best The optimal position for the dung beetle before the disturbance;

[0098] A greedy selection mechanism is employed, replacing the original solution with a mutated one based on its fitness, ensuring the algorithm evolves towards a better solution space. This mechanism is defined as follows:

[0099] (18)

[0100] In the formula, X best The optimal dung beetle position after greedy selection. This represents the fitness value of the optimal dung beetle position after the perturbation. This represents the fitness value of the optimal dung beetle position before the perturbation.

[0101] S4. The IDBO algorithm is applied to the co-simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, output the optimal control parameters, and optimize the hydraulic control system of the vertical mill.

[0102] The scaling coefficient of the fuzzy PID controller is changed, thereby altering the system error and the weights corresponding to the error rate of change at different stages.

[0103] Using the minimum integral of the absolute value of the time-multiplied error as the fitness criterion for optimization, the control system parameters are optimized to improve the steady-state accuracy of the hydraulic cylinder; the expression is:

[0104] (19)

[0105] in, t For system uptime, e (t This represents the difference in magnitude between the actual and target displacements. This is the fitness value.

[0106] See Figure 2 This invention discloses a hydraulic control system for a vertical mill based on an improved dung beetle optimization algorithm, comprising:

[0107] The acquisition module obtains the system dynamic differential equations in various generalized coordinate systems based on the structural force data and Lagrange equations of the vertical mill.

[0108] The building module is based on the dynamic differential equation to construct the ADAMS-AMESim-Simulink joint simulation model;

[0109] The improvement module improves the DBO algorithm to obtain the IDBO algorithm;

[0110] The optimization module applies the IDBO algorithm to the co-simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, outputs the optimal control parameters, and optimizes the hydraulic control system of the vertical mill.

[0111] Example:

[0112] See Figure 3 This invention discloses a hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm, comprising:

[0113] Step 1: Establish a simplified mechanical model of the vertical mill, select a generalized coordinate system, and derive the system dynamic differential equations under each generalized coordinate system based on the Lagrange equation method; implement the flexibility of the rocker arm using ANSYS software, set the connection parameters and material properties of each component in ADAMS / View, apply forces and constraints according to the relationship between the relatively fixed and moving components, and establish a rigid-flexible coupling dynamic model of the vertical mill; construct the hydraulic system model of the vertical mill using AMESim according to the hydraulic and closed-loop control principles; select the error between the actual and desired displacement using a fuzzy PID controller. E and its rate of change EC The input is the valve electrical signal, and the output is the valve electrical signal, forming a multi-input single-output Mamdani-type fuzzy controller. Based on this, an ADAMS-AMESim-Simulink co-simulation model is established.

[0114] Step 2: Improve the DBO algorithm by implementing a new strategy.

[0115] A) Initialize the population by fusing the set of best points with a reverse learning strategy. Map the set of best points to the solution space to obtain the initial population, perform reverse learning to generate the initial population, merge the best points, evaluate the fitness, and select the optimal population. NIndividuals construct a new initial population.

[0116] B) Adaptive breeding and theft strategy. Introducing dynamic spiral search shape parameters. p This endows dung beetles with diverse path adjustment capabilities. To prevent premature convergence in the later stages of iteration, a nonlinear weighting factor is introduced. c t The positions of the egg masses and the dung beetle are updated based on local and global optimality.

[0117] C) Adaptive hybrid mutation strategy, utilizing selection probability P S Alternate use of adaptive t Distribution variation and selective centroid inverse learning.

[0118] a. For adaptive t Distribution variation, using adaptive factors α Constraining the degree of variation;

[0119] b. For the selective centroid reverse learning strategy, Kendall's rank correlation coefficient is introduced to measure the correlation between two random variables. Then, based on the formula, negatively correlated and uncorrelated individuals are selected for reverse learning to enhance the algorithm's mutation ability.

[0120] Reuse P S The optimal individual is subjected to a hybrid mutation perturbation, with the two strategies complementing each other. This helps the algorithm escape local optima and achieve more efficient solution space exploration. A greedy selection mechanism is employed, replacing the original solution with a mutated one based on its fitness, ensuring the algorithm evolves towards a better solution space.

[0121] Finally, the CEC2005 benchmark function set was selected to solve the global optimal solution of the function for performance testing. At the same time, the IDBO algorithm was compared with the DBO algorithm, the Butterfly Algorithm (BOA), the Tree Species Algorithm (TSA), the Sparrow Search Algorithm (SSA), the Particle Swarm Optimization Algorithm (PSO), and the Whale Algorithm (WOA) to verify the convergence speed and accuracy of the IDBO algorithm.

[0122] Step 3: Based on the difference between the actual and target displacement amplitudes, the Time-Integral-Absolute-Error (ITAE) criterion is used as the optimization fitness criterion to update the individual fitness, achieving the preset fitness criterion requirements; the IDBO algorithm is applied to the co-simulation model to optimize the quantization factor of the fuzzy PID controller. K E , K EC With the scaling factor Δ K p Δ K i Δ Kd Optimization was performed; optimal control parameters were output to adjust the opening degree of the servo valve; this controller was compared with a Fuzzy-PID controller and a PID controller in terms of step tracking and anti-interference tests, and the fluctuation degree of hydraulic cylinder rod displacement was observed to verify the anti-interference capability and steady-state characteristics of the controller. Displacement response tests were conducted in a co-simulation model to verify its effectiveness and feasibility in responding to the displacement of the grinding roller.

[0123] 1.1 The steps to establish a simplified mechanical model of a vertical mill are as follows: The grinding system of a vertical mill consists of a grinding disc, grinding rollers, rocker arms, swing arms and hydraulic cylinders. The system is subjected to complex and variable forces, and there are significant interactions between the components. The bending deformation and torsional vibration of the rocker arms, the feeding motion of the hydraulic cylinders, the excitation of the grinding discs and the friction of the materials will all affect the motion state of the grinding rollers.

[0124] To construct the mechanical model, the system components are simplified as follows: 1) Each component is linearized; 2) The hydraulic cylinder is simplified to a mass. - Spring-damping element; 3) Rocker arms and swing arms are considered as mass elastic bodies, and grinding rollers are simplified as concentrated masses; 4) Constant force and static displacement terms in linear systems are ignored; 5) Setting F 1 represents the grinding force of the grinding roller on the material, that is, the excitation force on the grinding roller. F 2 represents the sliding friction between the material and the grinding roller.

[0125] Build as Figure 4 (a) shows the simplified dynamic model, in which a generalized coordinate system is selected in the XOY plane. q 1. Describe the extension and retraction of the hydraulic rod, and select... θ Describe the rotation angles of the grinding roller, rocker arm, and swing arm about the grinding roller axis, and select... q 2 and q 3. Quantify the bending deformation of the rocker arm in the XOZ and YOZ planes respectively, and introduce [the following] into the XOZ plane. Ψ Describes the torsional deflection angle of the rocker arm. Among them, α For rocker arm and Z The included angle of the axis, β For the swing arm and X The included angle of the axis, δ For hydraulic cylinder and X The included angle of the axis, m 1 represents the mass of the hydraulic cylinder. m 2 represents the mass of the rocker arm. m 3 represents the mass of the swing arm. m 4 represents the quality of the grinding roller. k For the stiffness of the hydraulic cylinder, c For hydraulic cylinder damping.

[0126] Taking a hydraulic rod as an example, with the center of mass simplified to the center of the rod, its kinetic energy... T 液 Potential energyU 液 for

[0127]

[0128] The generalized coordinates can be obtained from equations (1) and (2). q The dynamic differential equation under condition 1 is:

[0129]

[0130] In the formula, It is the acceleration due to gravity. l 1 represents the length of the hydraulic rod.

[0131] Similarly, the differential equations of system dynamics in each generalized coordinate system are shown in equation (4):

[0132]

[0133] In the formula: l 2 represents the length of the rocker arm. l 3 represents the length of the swing arm. l 4 represents the length of the grinding roller. m e2 The equivalent mass during rocker arm bending vibration. Let be the bending stiffness of the swing arm. The grinding force of the grinding roller on the material. This refers to the sliding friction between the material and the grinding roller.

[0134] Based on equations (3) and (4), the rocker arm is made flexible using ANSYS software. In ADAMS / View, the assembly parameters and material properties of each component of the model are set. Forces and constraints are applied according to the relationship between the relatively fixed and moving components. The virtual prototype model of the vertical mill is as follows: Figure 4 (b)

[0135] 1.2 Constructing a closed-loop model of the hydraulic system

[0136] Based on the hydraulic and closed-loop control principles of vertical mills, an AMESim hydraulic system model was established and the software interface was configured. The hydraulic system model is as follows: Figure 5 As shown in Table 1, the parameters of the hydraulic cylinder module are detailed based on the load and grinding pressure.

[0137] Table 1 AMEsim Simulation Parameters

[0138]

[0139] The control process based on the ADAMS-AMESim-Simulink co-simulation platform is as follows: The displacement target is preset, and the AMESim hydraulic position model outputs a force signal Vf to the ADAMS mechanical model; the feedback hydraulic rod displacement Vx is sent to the control system; the bias value is processed by the controller and used as a current input signal Vi to drive the opening of the electro-hydraulic proportional valve, thereby adjusting the hydraulic cylinder to push and pull the grinding roller load and realizing the closed-loop control strategy.

[0140] The vertical roller mill grinding system is a nonlinear system with complex dynamic characteristics and closed-loop instability. To adapt to different operating conditions and disturbances, a fuzzy controller and a PID controller are combined. Fuzzy inference is performed based on the hydraulic cylinder displacement deviation and its rate of change to dynamically adjust the PID parameter increment Δ. K p Δ K i Δ K d This enables intelligent parameter tuning. The structure of the control system is as follows: Figure 6 As shown.

[0141] Given the significant impact of quantization and scaling factors on control performance in fuzzy controllers, manual empirical methods are time-consuming and yield parameters with large accuracy errors. An improved dung beetle algorithm is used to optimize quantization and scaling factors to ensure optimal control performance.

[0142] A fuzzy PID controller adjusts the output current to drive an electro-hydraulic proportional valve, thereby controlling the roller displacement. This invention employs two inputs (error...) E and its rate of change EC Three outputs (PID parameter correction Δ) K p Δ K i Δ K d A Mamdani-type fuzzy controller is used. The fuzzy universe of discourse for the controller variables is [-6 -4 -2 0 2 4 6], and the fuzzy subsets are {NB, NM, NS, ZO, PS, PM, PB}, corresponding to {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}. The membership function adopts a triangular function. The output variable rule table is shown in Table 2.

[0143] The mathematical model of a fuzzy PID controller can be expressed as follows:

[0144]

[0145] In the formula: K p , K i , K d This is the initial setting value.U ( t () represents the output of the fuzzy PID controller. e ( t ) is the input for the fuzzy PID.

[0146] Table 2 Fuzzy Rule Table

[0147]

[0148] 2. DBO Optimization Strategy

[0149] See Figure 7 , Figure 7 The specific algorithm flowchart for the DBO optimization strategy includes the following steps:

[0150] a) Initialize algorithm parameters, determine the number of dung beetles N, the upper and lower limits of their positions, and the maximum number of iterations T;

[0151] b) Map the optimal point set to the solution space to obtain the initial population, and perform reverse learning according to equation (13) to generate the initial population;

[0152] c) Calculate the fitness value of each dung beetle individual, and record the global best position Xb and the global worst position Xb. w and the local optimal position X*;

[0153] d) The rolling dung beetle updates its position using formula (6), the dancing dung beetle updates its position using formula (7), and the dancing foraging dung beetle updates its position using formula (10).

[0154] e) Update the dynamic spiral search shape parameters for breeding and dung beetles. p The location of the breeding and robbing dung beetles is updated according to equations (17) and (18);

[0155] f) The optimal dung beetle is determined by the selection probability. P S The position is updated according to formula (25). The fitness values ​​of the dung beetle individuals before and after the update are compared, and the dung beetle individuals with larger fitness values ​​are retained.

[0156] g) Number of iterations t = t +1; if it is less than the maximum number of iterations, return to step b);

[0157] h) Otherwise, end the iteration and output the global optimum and the optimal path. Also, output the optimal control parameters. K E , K EC Δ K p Δ K i ΔK d .

[0158] 2.1 First, we introduce the DBO algorithm. The local and global search of the dung beetle algorithm are mainly achieved by simulating the dung beetle colony's behaviors of rolling balls, dancing, foraging, reproducing, and stealing. Assume the position of the i-th dung beetle is X. i =[ x i1 , x i2 ..., x iD ], where i = 1, 2, 3, ..., N, and D is the dimension of the search space. The dung beetle uses celestial information for navigation during its rolling process; its position update formula is:

[0159]

[0160] In the formula, t is the current iteration, Xi(t) is the position information of the i-th dung beetle at the t-th iteration, k is a constant value in (0, 0.2] representing the deflection coefficient; b is a constant value in (0, 1); α is the natural coefficient, with a value of 1 or -1; ∆x represents environmental changes; X W This is the worst position globally.

[0161] When a dung beetle encounters an obstacle and cannot move forward, it will find a new route by dancing. DBO uses a tangent function to mimic this behavior. Its position update formula is:

[0162]

[0163] In the formula, θ is the deflection angle, θϵ[0,Π]. If θ is 0, Π / 2, or Π, the position of the dung beetle will not be updated.

[0164] Reproductive dung beetles roll their dung balls to safe areas to provide a secure and protected environment for their offspring. DBO proposes a boundary selection strategy to simulate the oviposition area of ​​reproductive dung beetles, defined as:

[0165]

[0166] In the formula, X * This is the current local optimal position; Lb * , Ub * These are the lower and upper limits of the spawning area, respectively. R =1-t / T max , indicating the dynamic selection factor; T max t represents the maximum number of iterations; t represents the current number of iterations; Lb and Ub represent the lower and upper bounds of the optimization problem, respectively.

[0167] As shown in R, the area where dung beetles lay their eggs is dynamically adjusted with the number of iterations. The iterative dynamic change process of the egg ball's position is as follows:

[0168]

[0169] In the formula, B i (t) represents the position information of the i-th egg in the t-th iteration; b1 and b2 are independent random vectors of 1×D; D is the dimension of the optimization problem.

[0170] Foraging dung beetles seek out optimal foraging areas. DBO proposes a boundary selection strategy to simulate foraging areas, defined as:

[0171]

[0172] In the formula, Lb b , Ub b These represent the lower and upper limits of the optimal foraging area, respectively. X b This is the optimal position globally.

[0173] As shown in R, the optimal foraging area is dynamically adjusted with the number of iterations. Therefore, the position update process of the foraging dung beetle is as follows:

[0174]

[0175] In the formula, C1 is a random number that follows a normal distribution; C2 is a random number in the range (0, 1).

[0176] The thieving dung beetle, as a competitor, typically appears in the globally optimal location, and its position is updated as follows:

[0177] (12)

[0178] in, X i (t) represents the location information of the i-th dung beetle during the t-th iteration; g is a 1×D independent random vector following a normal distribution; D is the dimension of the optimization problem; and S is a constant value.

[0179] 2.2 Best Point Sets and Reverse Learning Strategies

[0180] The DBO algorithm, due to the high randomness and uncertainty of individual point generation, is prone to premature convergence to local optima. The optimal point set method, on the other hand, can efficiently utilize a small number of sample points to achieve uniform coverage of the search space. This invention integrates the optimal point set method with a back-learning strategy to initialize the population, thereby improving the convergence speed of the DBO algorithm. Figure 8As shown, the population size is 500, the dimension is 2, and the upper and lower bounds of the positions are 1 and 100, respectively. The optimal point set method can achieve a more uniform distribution of individual positions, improve the quality and diversity of the initial population solution, effectively avoid premature convergence, and reduce the blank areas in the search space, thereby improving the algorithm's optimization performance.

[0181] The optimal point set is mapped to the solution space to obtain the initial population, and reverse learning is performed to generate the initial population. After merging, the fitness is evaluated, and the optimal point is selected. N Each individual constructs a new initial population. The reverse learning formula is:

[0182] (13)

[0183] In the formula, For reverse populations, k 1× D A random vector that follows a normal distribution. Ub and Lb Denotes the upper and lower bounds of the solution space. X This represents the initial population.

[0184] 2.3 Adaptive Reproduction Stealing Strategy

[0185] The positions of the egg and the dung beetle are updated based on local and global optima, respectively. The algorithm initially has a wide search range, but it is prone to getting trapped in local optima when accelerating convergence.

[0186] This invention proposes a variable spiral search strategy based on the whale optimization algorithm, introducing dynamic spiral search shape parameters. p This endows dung beetles with diverse path adjustment capabilities. Figure 9 This is a schematic diagram of a spiral search. The expression is:

[0187] (14)

[0188] (15)

[0189] In the formula: The constant defining the spiral shape, g, is a dynamic adjustment coefficient that regulates the rate of exponential growth. β As a spiral search factor, r A random number in [0,1] t This represents the current iteration number. T This represents the maximum number of iterations.

[0190] To prevent premature convergence in the later stages of iteration, a nonlinear weighting factor is introduced. By optimizing the nonlinear adaptive decreasing parameter, the global optimization performance of the algorithm is improved; the expression is as follows:

[0191] (16)

[0192] In the formula: c t For iteration t The inertia weight of the second time, the maximum inertia weight c max =1, minimum inertia weight c min =0.001.

[0193] For example, the trend of nonlinear adaptive parameter changes Figure 10 As shown, the nonlinear adaptive parameters exhibit a nonlinear trend of rapid initial change followed by a slower decrease. Initially, the inertia weight factor adjusts with a higher value and a faster deceleration rate, enhancing the algorithm's global search capability. Later, the weight decreases to a lower level and maintains a gradual decreasing trend, giving the algorithm a stronger local fine-grained search capability.

[0194] The positions of the egg masses and the dung beetle are updated based on local and global optimality, as shown below:

[0195] (17)

[0196] (18)

[0197] In the formula: X * This is the current local optimum. B i ( t ) is the first t The generation i The position of each egg sphere is influenced by independent random vectors. b 1 and b 2 (1× D (dimensional) and the optimization dimension D constraint, located in [ Lb * , Ub * Within the spawning area, X i ( t ) is the first t The generation i The location of the dung beetle thief. X b This is the globally optimal solution. g 1× D Normal random vector, S It is a constant. Lb * This is the lower boundary of the spawning area. Ub * This is the upper boundary of the spawning area.

[0198] 2.4 Adaptive Hybrid Variation

[0199] When the DBO algorithm iteratively updates the optimal solution, it is prone to getting trapped in local extrema due to the lack of a perturbation mechanism for the optimal individual. This invention proposes an adaptive hybrid mutation strategy, which includes adaptive... t Backward learning of distribution variation and selective centroid, and iterative perturbation of the optimal solution.

[0200] Introducing Adaptive t Distribution mutation strategy, mutation formula is

[0201] (19)

[0202] Cauchy distribution and Gaussian distribution are t Distributional exception. t Degrees of freedom parameters of distribution variation a Number of iterations T ,when T When the value is small, the curve exhibits a Cauchy distribution. C (0,1), when T As the value approaches infinity, the curve exhibits a Gaussian distribution. N (0,1). The graphs of the three functions are as follows: Figure 11 As shown, with the increase of the degree of freedom parameter, the variation near the origin is significant. The probability of large perturbations is higher in the early stage of iteration, which is beneficial for global exploration. In the later stage of iteration, the probability of small perturbations increases, which strengthens the local development capability of the algorithm and achieves a balanced optimization of global and local search capabilities.

[0203] application t Distribution variation needs to be controlled in terms of its magnitude. In the early stages of iteration, variation is increased to facilitate global search, while in the later stages, it is gradually decreased to improve local exploration. This utilizes an adaptive factor. α The degree of variation is constrained, and the calculation formula is as follows:

[0204] (20)

[0205] Sensitive parameters in the formula f =0.6, defining the local development precision during the iteration process.

[0206] The iterative curve of the adaptive factor α is as follows Figure 12 As shown, α exhibits a non-linear decreasing trend. When the number of iterations is small, α is close to 1, which is beneficial for global search; when the number of iterations is large, α is close to 0, which is beneficial for local search, thereby accurately balancing the search strategy.

[0207] In the later stages of algorithm iteration, the back-learning strategy often leads to the solution space concentrating in a small region, making the algorithm prone to getting trapped in local optima. Therefore, a selective centroid back-learning strategy is proposed, incorporating Kendall's (…) Kendall The rank correlation coefficient, designed to enhance the population's ability to vary, is defined as follows:

[0208] (twenty one)

[0209] (twenty two)

[0210] In the formula: N For individuals in a population, denoted as { x 1, x 2, ..., x N The search space dimension is d , M id The center of gravity of the group is in the first d The value of dimension, X id For individuals X i At d The center of gravity of the dimension is in the opposite position. For individuals X i In the d Based on the center of gravity M id The opposite position.

[0211] Kendall The rank correlation coefficient is a nonparametric statistical method used to measure the correlation between two random variables. D 3D random variables Xi =[ x i1 , x i2 ..., x iD ]and X j =[ x j1 , x j2 ..., x jD ]of Kendall The rank correlation coefficient is defined as follows:

[0212] (twenty three)

[0213] In the formula: x i and x j The value of the first random variable. y i and y j Let be the value of the second random variable.

[0214] Assuming a 100×5 random data matrix is ​​generated, the Kendall coefficient matrix can be visualized as follows: Figure 13 As shown. τ The values ​​reveal the correlation between random variables. τ When = 1, it indicates that the two random variables are perfectly positively correlated and have the same trend of change; τ When the value is -1, it indicates that the two random variables are negatively correlated and have completely opposite trends; while τ When the value approaches 0, it indicates that the two variables are uncorrelated.

[0215] Will Kendall When the rank correlation coefficient is applied to the dung beetle optimization algorithm, this coefficient is used to measure the correlation between an individual and the best individual. Negatively correlated and uncorrelated individuals are selected for the reverse learning strategy to enhance the algorithm's mutation ability.

[0216] Using selection probability P S Apply a mixed mutation perturbation to the optimal individual. When P S When <0.5, adaptive method is used. t The distribution variation undergoes large-scale perturbation; when P S When the value is ≥0.5, selective centroid back-learning is used to perform small-scale perturbations. These two strategies complement each other, enabling the algorithm to escape local extrema and achieve more efficient solution space exploration. The relevant definitions are as follows:

[0217] (twenty four)

[0218] (25)

[0219] In the formula X best This represents the optimal dung beetle position before the disturbance.

[0220] A greedy selection mechanism is employed, replacing the original solution with a mutated one based on its fitness, ensuring the algorithm evolves towards a better solution space. This mechanism is defined as follows:

[0221] (26)

[0222] In the formula X best The optimal dung beetle position after greedy selection. The fitness value represents the optimal dung beetle position after the perturbation. This represents the fitness value of the optimal dung beetle position before the disturbance.

[0223] 2.5 Algorithm Testing

[0224] The CEC2005 benchmark dataset is used to evaluate the performance of the IDBO algorithm in finding the global optimum. The results are compared with those of the DBO algorithm, Butterfly Algorithm (BOA), Tree Specification Algorithm (TSA), Sparrow Search Algorithm (SSA), Particle Swarm Optimization (PSO), and Whale Algorithm (WOA) to examine convergence speed and accuracy. This includes single-peak (…) F 4. F 7) Multi-peak (F8, F10) and fixed multi-peak (F15, F23) function types.

[0225] Figure 14 For the iterative convergence curves of each test function, in test functions F4 and F10, the IDBO algorithm provides a favorable initial state for the population by leveraging the optimal point set and the reverse learning strategy. Combined with an adaptive hybrid mutation strategy, it converges quickly and accurately to the global optimum, effectively avoiding local extrema. F 7. F In section 8, the adaptive reproductive theft strategy enables the IDBO algorithm to intelligently adjust its search path, allowing it to escape local optima with fewer iterations. F In step 15, the iterative curve of the IDBO algorithm smoothly approaches the global optimum, effectively avoiding getting trapped in local optima and obtaining the optimal fitness value. F In 23, although the IDBO algorithm has slightly lower convergence accuracy, it can quickly escape local optima and its convergence speed is faster than that of the DBO algorithm. In summary, the three strategies significantly improve the convergence performance and accuracy of the DBO algorithm, while the IDBO algorithm has strong generalization ability.

[0226] 3. Optimization of controller parameters using the IDBO algorithm

[0227] The control performance of a fuzzy PID controller depends on its internal parameters. This invention utilizes the IDBO algorithm to optimize the quantization factor. K E , K EC With the scaling factor Δ K p Δ K i Δ K d This is to ensure optimal control performance.

[0228] 3.1 Optimizing Variables

[0229] By changing the scaling coefficient of the fuzzy PID controller, the system error and the weights corresponding to the error change rate at different stages can be altered. The value ranges of each optimization variable are shown in Table 2.

[0230] Table 3. Upper and lower limits of optimization variables

[0231]

[0232] 3.2 Fitness Function

[0233] The fitness criterion for optimization is to minimize the integral of the absolute value of the time-time error (ITAE). This is based on the fact that grinding force fluctuations during abrasive processing are short-cycled and large-amplitude, thus requiring the hydraulic system to have a rapid transient response to buffer the impact between the grinding roller and the grinding disc. This algorithm aims to optimize control system parameters and improve the steady-state accuracy of the hydraulic cylinder. The expression is as follows:

[0234] (27)

[0235] In the formula: t For system uptime, e ( t This represents the difference in magnitude between the actual and target displacements. This is the fitness value.

[0236] 3.3 Control Parameter Optimization Process

[0237] To ensure objectivity in the comparison, the IDBO and DBO algorithms were iteratively optimized using the same number of iterations, population size, and performance metrics. The fitness value change curves are shown below. Figure 15 The control parameter optimization curve is shown in [the image / description]. Figure 16 The specific parameter values ​​are shown in Table 4.

[0238] During the iteration process, the DBO algorithm prematurely entered the local solution space, causing premature convergence of the population. It converged to the optimal solution 4.9758 after 87 iterations. The IDBO algorithm, on the other hand, continuously escaped the local solution space with increasing iterations, converging to the optimal solution 4.9749 after 25 iterations, obtaining better control parameters and improving system performance. This indicates that the IDBO algorithm has better convergence speed and optimization capability in the parameter tuning process of this controller.

[0239] Table 4 Comparison of Iterative Optimization Results

[0240]

[0241] 4. Simulation Analysis and Results

[0242] To verify the control effect of the IDBO-Fuzzy-PID controller on the hydraulic system of the vertical mill, a comparative simulation was conducted with the Fuzzy-PID controller and the PID controller. The simulation duration was set to 20 seconds and the simulation step size was 0.01.

[0243] 4.1 System Step Tracking Test

[0244] When the grinding pressure of the system is constant and the working displacement of the equilibrium point is set to 50 mm, the simulation experiment uses a step input signal, introducing a step external load signal at the 10th second to simulate the sudden increase in grinding pressure caused by the presence of hard material during the abrasive process, resulting in a sudden increase in the displacement of the hydraulic rod. The step response curves of the three controllers are shown below. Figure 13 As shown, the response results are compared in Table 5.

[0245] from Figure 17 As shown in Table 5, the PID controller has a settling time of 5.294s and an overshoot of 8.568%, indicating that it is not suitable for time-varying systems with these parameters. The Fuzzy-PID controller outperforms the PID controller in both overshoot and settling time. In contrast, the IDBO-Fuzzy-PID controller has a settling time of only 0.743s, achieving near-zero overshoot to the target displacement. For step-load disturbances, the IDBO-Fuzzy-PID controller exhibits the best anti-interference capability, followed by the Fuzzy-PID controller, while the PID controller shows the worst anti-interference performance. In conclusion, the IDBO-Fuzzy-PID controller demonstrates a clear advantage in both response speed and control accuracy, exhibiting strong robustness.

[0246] Table 5 Comparison of simulation results for the three controllers

[0247]

[0248] 4.2 System Anti-interference Test

[0249] The hydraulic control system of a vertical mill is subject to various interference factors during actual operation, such as component aging, grinding pressure fluctuations caused by hard material adhesion during grinding, and noise interference in sensor feedback signals. To verify the feasibility of the controller, anti-interference tests need to be conducted on the system to ensure its stable operation under complex working conditions.

[0250] 4.2.1 Simulation of Step Signal

[0251] When the grinding pressure of the system is constant and the working displacement of the equilibrium point is 50 mm, the simulation results obtained by applying random white noise to the feedback are as follows: Figure 18 As shown, after the controller is disturbed, the hydraulic rod displacement oscillation amplitude of the PID controller is 0.879 mm, the displacement oscillation amplitude of the Fuzzy-PID controller is 0.463 mm, while the IDBO-Fuzzy-PID controller is significantly reduced to 0.252 mm, greatly improving the anti-interference ability and thus improving the longitudinal displacement error of the grinding roller.

[0252] 4.2.2 Sine Signal Simulation

[0253] The above-mentioned object is a linear model based on a step signal, limited to performance testing near a specific operating point. Given that system parameters dynamically change with the grinding process under actual operating conditions, it is necessary to conduct anti-interference tests on the nonlinear model. Experimental results obtained by applying random white noise to the feedback using a sinusoidal input signal are shown below. Figure 19 As shown, compared to Fuzzy-PID controllers and PID controllers, the IDBO-Fuzzy-PID controller's stability is not significantly affected by disturbances, and its sine wave tracking performance is optimal. This indicates that it has a significant advantage in steady-state accuracy, good robustness, and meets the high standards required for control systems.

[0254] 4.3 Displacement Response Test

[0255] Actual operating conditions require the vertical mill's hydraulic system to achieve self-stabilizing balance and maintain a constant grinding force during the grinding process. Fluctuations in grinding force trigger a response in the hydraulic system, which in turn affects the dynamic changes in the gap between the grinding rollers and the grinding disc. This gap needs to be within a reasonable range to avoid drastic fluctuations in the grinding rollers that could affect the stability of the grinding process. The designed controller was applied to a co-simulation model of the vertical mill to verify its effectiveness and feasibility in responding to grinding roller displacement.

[0256] like Figure 20 As shown, the displacement error generated by the Fuzzy-PID controller is 0.3 mm, while the IDBO-Fuzzy-PID controller reduces the displacement error to 0.1 mm. This indicates that the IDBO-Fuzzy-PID controller effectively suppresses the longitudinal fluctuation of the grinding roller, and at the same time, it stabilizes the grinding force by finely adjusting the small fluctuations in the gap between the grinding roller and the grinding disc.

[0257] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm, characterized in that, include: Based on the structural stress data and Lagrange equations of the vertical mill, the system dynamic differential equations in various generalized coordinate systems are obtained. Based on the dynamic differential equations, a joint simulation model of ADAMS-AMESim-Simulink is constructed; The DBO algorithm is improved to obtain the IDBO algorithm; The IDBO algorithm is applied to the co-simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, output the optimal control parameters, and optimize the hydraulic control system of the vertical mill. The construction of the ADAMS-AMESim-Simulink joint simulation model based on the dynamic differential equation is as follows: Based on the dynamic differential equations, the parameters and material properties of each component of the vertical mill, and the force and constraint relationships applied according to the relationship between each relatively fixed and moving component, a rigid-flexible coupling dynamic model of the vertical mill is established. Based on AMESim and following the principles of hydraulic and closed-loop control, a hydraulic system model for a vertical mill is constructed. Based on the fuzzy PID controller, the error between the actual and desired displacement and its rate of change are selected as inputs, and the valve electrical signal of the vertical mill is used as the output to form a multi-input single-output Mamdani-type fuzzy controller. Based on the rigid-flexible coupling dynamic model of the mill, the hydraulic system model of the vertical mill, and the Mamdani-type fuzzy controller with multiple inputs and single outputs, a joint simulation model of ADAMS-AMESim-Simulink is constructed. The strategy improvement of the DBO algorithm to obtain the IDBO algorithm specifically involves: The population is initialized based on a fusion of a set of optimal points and a reverse learning strategy. The optimal point set is mapped to the solution space to obtain the initial population. Reverse learning is then implemented to generate the final population. After merging, fitness is evaluated, and selection is performed. N A new initial population is constructed using the optimal individuals; A dynamic spiral search shape parameter is introduced into the initial population to endow dung beetles with diverse path adjustment capabilities; a nonlinear weighting factor is introduced to prevent premature convergence in the later stages of iteration. c t The positions of the egg masses and dung beetles are updated based on local and global optimality. For adaptive t The distribution variation is constrained by an adaptive factor; and the Kendall rank correlation coefficient is introduced into the selective centroid back learning strategy to measure the correlation between two random variables. Negatively correlated and uncorrelated individuals are selected for back learning, and the optimal individual is subjected to mixed variation perturbation to complete the improvement of the DBO algorithm. The optimization of the quantization factor and proportional factor of the fuzzy PID controller to output optimal control parameters and optimize the hydraulic control system of the vertical mill is specifically as follows: The scaling coefficient of the fuzzy PID controller is changed, thereby altering the system error and the weights corresponding to the error rate of change at different stages. The fitness criterion for optimization is based on minimizing the integral of the absolute value of the time-multiplied error. This optimizes the control system parameters and improves the steady-state accuracy of the hydraulic cylinder. The expression is: （19） Where t is the system running time, and e(t) represents the difference in amplitude between the actual and target displacements; This is the fitness value.

2. The hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm according to claim 1, characterized in that, The vertical mill includes a rocker arm, a swing arm, a grinding roller, a grinding roller shaft, and a hydraulic cylinder; the rocker arm of the vertical mill is connected to the swing arm; the swing arm of the vertical mill is connected to the grinding roller; and the hydraulic cylinder is connected to the rocker arm via a connecting rod.

3. The hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm according to claim 1, characterized in that, Based on the structural stress data and Lagrange equations of the vertical mill, the differential equations of system dynamics in various generalized coordinate systems are derived as follows: Simplifying the center of mass of the hydraulic rod, its kinetic energy... T 液 Potential energy U 液 for: （1） （2） Based on formulas (1) and (2), the generalized coordinates are obtained. q The dynamic differential equation under condition 1 is: （3） in, It is the acceleration due to gravity. l 1 is the length of the hydraulic rod, α is the angle between the rocker arm and the Z-axis, β is the angle between the swing arm and the X-axis, δ is the angle between the hydraulic cylinder and the X-axis, m1 is the mass of the hydraulic cylinder, m2 is the mass of the rocker arm, m3 is the mass of the swing arm, m4 is the mass of the grinding roller, and c is the hydraulic cylinder damping. The differential equations of system dynamics in various generalized coordinate systems are shown in equation (4): （4） Among them, a generalized coordinate system is selected in the XOY plane. q 1. Describe the extension and retraction of the hydraulic rod, and select... θ Describe the rotation angles of the grinding roller, rocker arm, and swing arm about the grinding roller axis, and select... q 2 and q 3. Quantify the bending deformation of the rocker arm in the XOZ and YOZ planes respectively, and introduce [the following] into the XOZ plane. Ψ Describe the torsional deflection angle of the rocker arm; l 2 represents the length of the rocker arm. l 3 represents the length of the swing arm. l 4 represents the length of the grinding roller. m e2 The equivalent mass during rocker arm bending vibration. Let be the bending stiffness of the swing arm. The grinding force of the grinding roller on the material. This refers to the sliding friction between the material and the grinding roller.

4. The hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm according to claim 1, characterized in that, The population is initialized based on a fusion of the best point set and a reverse learning strategy; the best point set is mapped to the solution space to obtain the initial population, reverse learning is implemented to generate the initial population, the fitness is evaluated after merging, and N optimal individuals are selected to construct a new initial population. Specifically: By integrating the optimal point set with the reverse learning strategy to initialize the population, the convergence speed of the DBO algorithm is improved. The reverse learning formula is as follows: （5） In the formula, It is a reverse population. k 1× D A random vector that follows a normal distribution. Ub and Lb Denotes the upper and lower bounds of the solution space. X This represents the initial population.

5. The hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm according to claim 1, characterized in that, The method involves introducing a dynamic spiral search shape parameter into the initial population to endow dung beetles with diverse path adjustment capabilities; and introducing a nonlinear weighting factor to prevent premature convergence in the later stages of iteration. c t The positions of the egg masses and dung beetles are updated based on local and global optimality, specifically as follows: Introducing dynamic spiral search shape parameters p This endows dung beetles with diverse path adjustment capabilities, expressed as: （6） （7） In the formula: The constant defining the spiral shape, g, is a dynamic adjustment coefficient that regulates the rate of exponential growth. β As a spiral search factor, r A random number in [0,1] t This represents the current iteration number. T This represents the maximum number of iterations. To prevent premature convergence in the later stages of iteration, a nonlinear weighting factor is introduced. By optimizing the nonlinear adaptive decreasing parameter, the global optimization performance of the algorithm is improved. The expression is: （8） In the formula: c t For iteration t The inertia weight of the second time, the maximum inertia weight c max =1, minimum inertia weight c min =0.001; The positions of the egg masses and the dung beetle are updated based on local and global optimality, as shown below: （9） （10） In the formula: X * This is the current local optimum. B i ( t ) is the first t The generation i The position of each egg sphere is determined by an independent random vector. b 1 and b 2 (1× D (dimensional) and the optimization dimension D constraint, located in [ Lb * , Ub * Within the spawning area, X i ( t ) is the first t The generation i The location of the dung beetle thief. X b This is the globally optimal solution. g 1× D Normal random vector, S It is a constant. Lb * This is the lower boundary of the spawning area. Ub * This is the upper boundary of the spawning area.

6. The hydraulic control method for a vertical mill based on an improved dung beetle optimization algorithm according to claim 1, characterized in that, For the adaptive t-distribution variation, an adaptive factor is used to constrain the degree of variation; and in the selective centroid back-learning strategy, Kendall's rank correlation coefficient is introduced to measure the correlation between two random variables. Negatively correlated and uncorrelated individuals are selected for back-learning, and the optimal individual is subjected to mixed variation perturbation to complete the improvement of the DBO algorithm, specifically: Introducing Adaptive t Distribution mutation strategy, mutation formula is: （11） t Degrees of freedom parameters of distribution variation a Number of iterations T ,when T When the value is small, the curve exhibits a Cauchy distribution. C (0,1), when T As the value approaches infinity, the curve exhibits a Gaussian distribution. N (0,1); Using adaptive factors α The degree of variation is constrained, and the calculation formula is as follows: （12） Sensitive parameters in the formula f =0.6, defining the local development accuracy during the iteration process; Based on a selective centroid reverse learning strategy, Kendall's rank correlation coefficient is introduced to enhance the population's mutation capacity, defined as: （13） （14） In the formula, N For individuals in a population, denoted as { x 1, x 2, ..., x N The search space dimension is d , M id The center of gravity of the group is in the first d The value of dimension, X id For individuals X i At d The position of the center of gravity of the dimension in the opposite direction; For individuals X i In the d Based on the center of gravity M id The opposite position; Kendall's rank correlation coefficient is a nonparametric statistical method used to measure the correlation between two random variables; two D 3D random variables Xi =[ x i1 , x i2 ..., x iD ]and X j =[ x j1 , x j2 ..., x jD The Kendall rank correlation coefficient is defined as follows: （15） In the formula, x i and x j The value of the first random variable. y i and y j The value of the second random variable; Using selection probability P S Apply mixed mutation perturbation to the optimal individual; when P S When <0.5, adaptive method is used. t The distribution variation undergoes large-scale perturbation; when P S When the value is ≥0.5, selective centroid back-learning is used to perform small-scale perturbations; the relevant definitions are as follows: （16） （17） In the formula, X best The optimal position for the dung beetle before the disturbance; A greedy selection mechanism is adopted, which replaces the original solution when the fitness of the mutated solution is better, to ensure that the algorithm evolves towards a better solution space, as defined below: （18） In the formula, X best The optimal dung beetle position after greedy selection. This represents the fitness value of the optimal dung beetle position after the perturbation. This represents the fitness value of the optimal dung beetle position before the perturbation.

7. A hydraulic control system for a vertical mill based on an improved dung beetle optimization algorithm, characterized in that: The vertical mill hydraulic control method based on the improved dung beetle optimization algorithm according to any one of claims 1 to 6 includes: The acquisition module obtains the system dynamic differential equations in various generalized coordinate systems based on the structural force data and Lagrange equations of the vertical mill. The building module is based on the dynamic differential equation to construct the ADAMS-AMESim-Simulink joint simulation model; The improvement module improves the DBO algorithm to obtain the IDBO algorithm; The optimization module applies the IDBO algorithm to the co-simulation model to optimize the quantization factor and proportional factor of the fuzzy PID controller, outputs the optimal control parameters, and optimizes the hydraulic control system of the vertical mill.

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