Overflow granularity optimization control method of cyclone

Abstract

The invention provides an overflow granularity optimization control method of a cyclone. The method comprises the steps of obtaining a data set; preprocessing the data set; a GDGMM-RBF neural network prediction model is built; the actual value of the overflow particle size of the cyclone is collected in real time, the set value of the overflow particle size of the cyclone is set, a dynamic adjustment factor is introduced, and the reference trajectory of the overflow particle size of the cyclone is calculated; calculating a control increment; the improved incremental PID controller is used for controlling the pressure of the cyclone and the feeding concentration of the cyclone, and the new pressure of the cyclone, the new feeding concentration of the cyclone and the new overflow particle size of the cyclone are obtained; obtaining a new predicted value of the overflow granularity of the cyclone; constructing an error compensation mechanism by comparing the difference between the actual value of the overflow granularity of the cyclone and the predicted value of the overflow granularity of the new cyclone; updating model parameters by using an adaptive gradient descent method; and iterative optimization is carried out. According to the method, the adaptability of the model to non-linear and time-varying working conditions is remarkably improved, and the problem of control lag caused by mechanism model deviation in a traditional method is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of grinding classification, and in particular to a method for optimizing control of overflow particle size of a cyclone. BACKGROUND

[0002] The ore dressing process mainly includes three processes of crushing, grinding and separation, wherein the grinding process is the most critical part of the whole ore dressing process and plays a role of connecting the previous and the next. The main task of grinding is to grind the ore particles from a larger size to a certain degree by using the physical grinding action of the mill and the classification action of the classification equipment, so that the mineral monomer is dissociated or close to dissociation, thereby realizing the mutual separation of useful minerals and gangue minerals. This process provides the qualified ore pulp in particle size for the subsequent separation process, thereby ensuring that the subsequent separation process can be carried out efficiently.

[0003] If the grinding particle size is too coarse, the useful minerals cannot be fully dissociated, resulting in a decrease in concentrate grade and metal recovery rate in the separation process; and if the grinding particle size is too fine, the energy consumption is increased, and at the same time, the useful minerals can be excessively crushed, which also affects the separation efficiency. The particle size, as a core quality index of the grinding process, will directly affect the quality of the concentrate grade and the metal recovery rate, and is a very important process index in the grinding process of the ore dressing plant. Therefore, the grinding process needs to be accurately controlled to ensure that the overflow particle size of the cyclone meets the requirements of the subsequent separation process. The cyclone is a key equipment in the mineral separation process, and its overflow particle size directly affects the efficiency of subsequent processes such as flotation and concentration. However, the traditional control method relies on manual experience or a PID controller to adjust the ore concentration and pressure, which has many problems and is difficult to meet the needs of modern industry for high precision and high robustness.

[0004] Moreover, the traditional control method has obvious model dependence. The dynamic characteristics of the cyclone are complex, and its internal flow field is affected by various factors such as ore composition, equipment structure, and operating parameters. The interaction of these factors makes the cyclone show strong nonlinearity and time-varying characteristics, and the traditional mechanism model is difficult to accurately describe this complexity. For example, the flow field distribution inside the cyclone will change significantly due to the change of ore composition, resulting in a decrease in separation efficiency. This model dependence makes the traditional control method appear to be inadequate when facing complex working conditions. At present, model predictive control (MPC) is introduced into the control of the cyclone to solve this problem. MPC can handle multivariable optimization problems by establishing a prediction model to optimize the control strategy. However, the performance of traditional MPC is highly dependent on the accuracy of the prediction model. In actual application, due to the dynamic change of working conditions, the model trained offline often cannot accurately reflect the actual running state.

[0005] Therefore, we also need an adaptive predictive control method that combines online model updating and optimization algorithms to improve the accuracy and robustness of cyclone control. This adaptive predictive control method can dynamically adjust control parameters by monitoring the operating state of the cyclone in real time, thereby better adapting to changes in operating conditions. SUMMARY

[0006] The set values of the cyclone feed concentration and feed pressure in the grinding process are currently given by the operator, which cannot set good set values, resulting in the inability to realize the safe operation of the grinding process; the dynamic characteristics of the cyclone are complex, and the traditional mechanism model is difficult to accurately describe the nonlinear and time-varying characteristics, and the performance of the traditional MPC is highly dependent on the accuracy of the prediction model; due to the dynamic changes of the working conditions, the model trained offline often cannot accurately reflect the actual operating state.

[0007] To solve the above problems, the present application provides a kind of overflow particle size optimization control method of cyclone of adaptive predictive model, realizes the optimization to cyclone feed concentration, feed pressure set value.

[0008] The technical scheme of the present application provides a kind of overflow particle size optimization control method of cyclone. The control method comprises: step S1: obtaining a data set;Wherein, the data set is a historical data set, and the historical data set includes: cyclone feed concentration, cyclone pressure and overflow particle size of cyclone;Step S2: pre-processing the data set, and then dividing the pre-processed data set into training set and test set according to the preset proportion;Step S3: building GDGMM-RBF neural network prediction model, training the GDGMM-RBF neural network prediction model based on the training set, and testing the prediction effect of the trained GDGMM-RBF neural network prediction model based on the test set;Wherein, the GDGMM-RBF neural network prediction model is composed of GMM model and RBF neural network model;The input of the GDGMM-RBF neural network prediction model is the cyclone feed concentration and the cyclone pressure, and the output of the GDGMM-RBF neural network prediction model is the overflow particle size of the cyclone;The GDGMM-RBF neural network prediction model calculates the parameters of the RBF neural network model using GMM algorithm, and optimizes the parameters by gradient descent method;Step S4: real-time acquisition of the actual value of the overflow particle size of the cyclone, setting the set value of the overflow particle size of the cyclone as y sp (t), and introducing a dynamic adjustment factor f(t) to calculate the reference trajectory y r (t+j) of the overflow particle size of the cyclone;Step S5: calculating the control increment Δu(t);Wherein, the control increment is the cyclone feed concentration and the cyclone pressure;In the prediction time domain H pIn the example, the prediction output of the GDGMM-RBF neural network prediction model is set to The control input is u(t); and the predicted output is calculated using the adaptive gradient descent method Jacobian matrix of control input u(t) In order to use the Jacobian matrix to calculate H in the control time domain u The control variable adjustment amount within; the control variable adjustment amount is the control increment Δu(t); Step S6: Calculate the new control setting value u by the control increment Δu(t) and the control amount u(t-1) at the previous moment sp (t), input the new control setting value into the PID control loop of the lower layer, and use the improved incremental PID controller to control the cyclone pressure and cyclone feed concentration to obtain new cyclone pressure, cyclone feed concentration and cyclone overflow particle size; wherein the cyclone pressure is controlled in real time by the pump frequency of the slurry pump, the cyclone feed concentration is controlled in real time by the pump pool water supply valve, and the cyclone overflow particle size is controlled in real time by the cyclone pressure and the cyclone feed concentration; step S7: input the new cyclone pressure and cyclone feed concentration into the GDGMM-RBF neural network prediction model to obtain a new predicted value of the cyclone overflow particle size; step S8: compare the actual value of the cyclone overflow particle size collected in real time with the predicted value of the new cyclone overflow particle size The difference in values ​​is calculated and an error compensation mechanism is constructed to dynamically correct the subsequent prediction trajectory of the overflow particle size of the cyclone; step S9: using the adaptive gradient descent method to adaptively update the parameters of the GDGMM-RBF neural network prediction model; wherein, when the error between the actual output and the predicted output of the GDGMM-RBF neural network prediction model is minimized and the parameter change of the GDGMM-RBF neural network prediction model is minimized, adjustable weight factors γ1 and γ2 are introduced, and a dynamic optimization mechanism under dual regularization constraints is designed to update the objective function to achieve online adjustment of the parameters of the GDGMM-RBF neural network prediction model; step S10: returning to step S4 to achieve the purpose of iterative optimization, thereby continuously optimizing the overflow particle size of the cyclone.

[0009] Preferably, the GMM algorithm is used to calculate the parameters of the RBF neural network prediction model, specifically comprising: step S3.1: determining the number of mixed components of the GMM model using the Bayesian information criterion; step S3.2: solving the parameters of the GMM model using the expectation-maximization algorithm; step S3.3: determining the number of neurons in the hidden layer, the initial center of the neurons, and the width of the neurons of the RBF neural network model by the solved parameters of the GMM model, and performing offline training on the GDGMM-RBF neural network prediction model; wherein the Gaussian distribution parameters in the GMM are mapped to the parameters of the RBF neural network model, the number of mixed components of the Gaussian distribution g is the number of RBF neurons, the mean μ g of the Gaussian distribution is the center c j of the RBF neuron, and the covariance Σ g is the width δ j of the RBF neuron; and step S3.4: performing parameter optimization on the width of the RBF neural network neurons, the center of the neurons, and the output weight of the neurons to the output layer by the GD gradient descent method.

[0010] Preferably, in step S4, the mathematical expression of the reference trajectory y r (t+j) of the overflow particle size of the cyclone is:

[0011]

[0012] In formula (1), y r (t) is the reference value of the overflow particle size of the cyclone to be tracked; y(t) is the actual value of the overflow particle size of the cyclone; the value range of f(t) is 0<f(t)<1;

[0013] wherein the mathematical expression of the dynamic adjustment factor f(t) is:

[0014]

[0015] In formula (2), e1(t) is the current error; k is a constant for adjusting the sensitivity of f(t) to the error; γ is a dynamic attenuation coefficient, which automatically reduces the error weight over time to prevent over-adjustment; λ is a nonlinear correction factor;

[0016] In formula (2), the mathematical expression of e1(t) is:

[0017] e1(t) = |y sp (t) - y(t)| (3).

[0018] Preferably, in step S5, the adaptive gradient descent method is used to calculate the prediction output The Jacobian matrix of the control input u(t) To achieve the control variable adjustment amount in the control time domain H u The step S5.1: selecting the current control input u(t) to minimize the objective function; wherein the mathematical expression of the objective function is:

[0019]

[0020] In formula (4), r(t) is the system reference trajectory; is the prediction output of the GDGMM-RBF neural network prediction model, r(t) and The dimension of is H p ×1; the dimension of Δu(t) is H u ×1; ρ1 and ρ2 are control weight factors;

[0021] In formula (4), r(t), The corresponding mathematical expressions of and Δu(t) are as follows:

[0022] r(t) = [r(t+1), r(t+2), …, r(t+H p )] T (5)

[0023]

[0024] Δu(t) = [Δu(t), Δu(t+1), …, Δu(t+H u -1)] T (7)

[0025] The step S5.2: updating the control input u(t) using the adaptive gradient descent method to minimize The corresponding mathematical expression of this step is:

[0026]

[0027] In formula (8), λ(t) is the dynamically adjusted step size, and the learning rate is adaptively adjusted by the gradient change threshold τ;

[0028] In formula (8), the update rule of the step size λ(t) is as follows:

[0029]

[0030] In formula (9), the fixed step size λ in gradient descent is replaced by an adaptive step size, τ is a gradient change threshold, and θ(t) is a parameter {c, ω, δ} in the GDGMM-RBF neural network prediction model; c is the center of the RBF neuron; ω is the output weight of the RBF neuron to the output layer; δ is the width of the RBF neuron; θ(t-1) is a parameter in the GDGMM-RBF neural network prediction model at the previous moment; when the gradient change is greater than the threshold, the step size is reduced by the ratio of the distance between adjacent iteration points to the gradient difference to avoid oscillation; ∈ t is a decreasing positive term sequence, and when the gradient change is not greater than the threshold, the step size is steadily increased until the threshold is exceeded again;

[0031] Step S5.3: A mathematical expression for the control increment Δu(t) is obtained by formula (8):

[0032]

[0033] Step S5.4: The objective function is differentiated with respect to u(t) to obtain:

[0034]

[0035] Step S5.5: Substituting formula (10) into formula (11) gives:

[0036]

[0037] In formula (13), is the Jacobian matrix, which is obtained from the GDGMM-RBF neural network prediction model.

[0038] Preferably, in step S6, an improved incremental PID controller is used to control the pressure of the cyclone and the feed concentration of the cyclone, specifically including: step S6.1: in the lower PID control loop, according to the size of the deviation e k , it is determined whether to introduce an integral element to achieve control of the pressure of the cyclone and the feed concentration of the cyclone using an improved incremental PID controller; wherein the mathematical expression of the improved incremental PID controller is:

[0039] Δu k = K p (e k -e k-1 )+ β·K i ·e k + K d (e k - 2e k-1 + e k-2 )(14)

[0040]

[0041] In formula (14) and formula (15), K p is a proportional coefficient; K i is an integral coefficient; K d is a differential coefficient; e k is a deviation of the kth set value and the control quantity; β is an integral open relation coefficient; and ε is a reference value.

[0042] Preferably, in step S8, the error compensation mechanism is constructed, specifically comprising: step S8.1: calculating a predicted value y p (t) of the overflow particle size of the new cyclone at the previous moment and an error err(t) of the predicted value y

[0043] (t) and an actual value y(t) of the overflow particle size of the cyclone collected in real time; wherein a mathematical expression of the error err(t) is as follows: p (t)(16)

[0044] Step S8.2: obtaining a corrected prediction result of the overflow particle size of the cyclone through the error err(t) and a dynamic adjustment factor f(t); wherein a mathematical expression of the corrected prediction result of the overflow particle size of the cyclone is as follows:

[0045]

[0046] In formula (17), y p (t+j) is the predicted value of the overflow particle size of the new cyclone.

[0047] Preferably, in step S9, a mathematical expression of the target function is as follows:

[0048]

[0049] Δθ a (t) = θ a (t) - θ a (t-1)(20)

[0050] In formula (18) and formula (20), γ1 and γ2 are both adjustable weight factors, and γ1 and γ2 are both greater than zero; Δθ a (t) is a parameter variation in the GDGMM-RBF neural network prediction model at the current moment; θ is a parameter {c, ω, δ} in the GDGMM-RBF neural network prediction model, c is a center of the RBF neuron; ω is an output weight of the RBF neuron to the output layer; δ is a width of the RBF neuron; n θwherein, a is the index of the GDGMM-RBF neural network prediction model parameter; and b is the number of the GDGMM-RBF neural network prediction model parameter.

[0051] in formula (19), φ j (·) is an activation function; x is an input vector, which is the cyclone pressure and the cyclone feed concentration; and c j is the center of the jth radial basis function; ω j is the output layer weight of the jth neuron; k is the total number of neurons; and j is the index of the number of neurons.

[0052] Preferably, in step S5 and step S9, the mathematical expression for variable updating using the adaptive gradient descent method is as follows:

[0053]

[0054] in formula (21), θ(t+1) is the GDGMM-RBF neural network prediction model parameter at the next time; L is the objective function of the GDGMM-RBF neural network prediction model optimization; and λ(t) is the dynamically adjusted step length.

[0055] Advantages of the present application:

[0056] (1) The present application introduces a data-driven adaptive prediction model method, which replaces the traditional control strategy based on mechanism model or fixed parameter model, and significantly improves the adaptability and accuracy of the control system.

[0057] (2) The present application introduces a Gaussian Mixture Model (GMM) algorithm based on gradient descent method (GD) and a Radial Basis Function (RBF) neural network, determines the RBF model parameters according to the GMM algorithm, reduces the uncertainty caused by random initial parameters, and optimizes the model parameters by the gradient descent method, thereby improving the fitting ability of the model to complex dynamic processes.

[0058] (3) The present application introduces an online adaptive updating mechanism of the prediction model, dynamically adjusts the model parameters of the GDGMM-RBF prediction model according to real-time data, gradient descent method and GMM algorithm, so that it can quickly adapt to system dynamic changes and external disturbances, and significantly improves the real-time performance and robustness of the control system.

[0059] (4) The present application introduces a feedback correction model of the prediction model, adjusts the new prediction result according to the prediction model error at the previous time and the error change adjustment factor of the system, and enhances the dynamic adaptability of the model.

[0060] (5) The application introduces an adaptive gradient descent method, dynamically adjusts the size of the step length, minimizes the deviation of the actual value of the overflow particle size of the cyclone from the set value, considers the constraint conditions of the control input, and effectively solves the problem of insufficient adaptability of the traditional control method under complex working conditions.

[0061] Additional aspects and advantages of the application will become apparent in the description which follows, or will be apparent from the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 A schematic flow chart of the overflow particle size optimization control method of the cyclone of one embodiment of the application is shown.

[0063] Figure 2 A grinding classification process flow chart of one embodiment of the application is shown.

[0064] Figure 3 An adaptive optimization control strategy diagram of the overflow particle size of the cyclone of one embodiment of the application is shown.

[0065] Figure 4 A network topology diagram of the intelligent regulation and control system of the overflow particle size of the cyclone of one embodiment of the application is shown.

[0066] Figure 5 A comparison diagram of the prediction effects of different modeling methods of the overflow particle size of the cyclone of one embodiment of the application is shown.

[0067] Figure 6 A comparison diagram of the control effects of different models of the overflow particle size of the cyclone of one embodiment of the application is shown. DETAILED DESCRIPTION

[0068] In order to more clearly understand the above-mentioned purposes, features and advantages of the application, as Figures 1 to 6 shown in the accompanying drawings and specific embodiments, the application will be further described in detail below. It should be noted that the embodiments of the application and the features in the embodiments can be combined with each other without conflict.

[0069] In the following description, many specific details are set forth in order to provide a thorough understanding of the application, but the application can also be implemented in other ways different from those described herein, therefore, the scope of protection of the application is not limited to the specific embodiments disclosed below.

[0070] Figure 1 A schematic flow chart of the overflow particle size optimization control method of the cyclone of one embodiment of the application is shown. As Figure 1 shown, the overflow particle size optimization control method of the cyclone comprises:

[0071] Step S1: obtaining a data set; wherein the data set is a historical data set, and the historical data set comprises a cyclone feed concentration, a cyclone pressure, and an overflow particle size of the cyclone;

[0072] Step S2: preprocessing the data set, and then dividing the preprocessed data set into a training set and a test set according to a preset proportion;

[0073] Step S3: building a GDGMM-RBF neural network prediction model, training the GDGMM-RBF neural network prediction model based on the training set, and then testing the prediction effect of the trained GDGMM-RBF neural network prediction model based on the test set; wherein the GDGMM-RBF neural network prediction model is composed of a GMM model and a RBF neural network model; the input of the GDGMM-RBF neural network prediction model is the cyclone feed concentration and the cyclone pressure, and the output of the GDGMM-RBF neural network prediction model is the overflow particle size of the cyclone; the GDGMM-RBF neural network prediction model calculates the parameters of the RBF neural network model by using a GMM algorithm, and optimizes the parameters by using a gradient descent method;

[0074] Step S4: collecting an actual value of the overflow particle size of the cyclone in real time, setting a set value of the overflow particle size of the cyclone as y sp (t), and introducing a dynamic adjustment factor f(t) to calculate a reference trajectory y r (t+j) of the overflow particle size of the cyclone;

[0075] Step S5: calculating a control increment Δu(t); wherein the control increment is the cyclone feed concentration and the cyclone pressure; within a prediction time domain H p of the GDGMM-RBF neural network prediction model, setting the prediction output of the GDGMM-RBF neural network prediction model as , and setting the control input as u(t); and using an adaptive gradient descent method to calculate the prediction output and the Jacobian matrix of the control input u(t) , so as to calculate a control variable adjustment amount within a control time domain H u by using the Jacobian matrix; the control variable adjustment amount is the control increment Δu(t);

[0076] Step S6: calculating a new control set value u sp(t), input the new control set value into the lower PID control loop, and use the improved incremental PID controller to control the cyclone pressure and the cyclone feed concentration to obtain a new cyclone pressure, a new cyclone feed concentration and a new overflow particle size of the cyclone; wherein the cyclone pressure is controlled by the pump frequency of the slurry pump in real time, the cyclone feed concentration is controlled by the pump pool water valve in real time, and the overflow particle size of the cyclone is controlled by the cyclone pressure and the cyclone feed concentration in real time;

[0077] Step S7: input the new cyclone pressure and the new cyclone feed concentration into the GDGMM-RBF neural network prediction model to obtain a new predicted value of the overflow particle size of the cyclone;

[0078] Step S8: by comparing the difference between the actual value of the overflow particle size of the cyclone collected in real time and the predicted value of the overflow particle size of the cyclone, and constructing an error compensation mechanism, the subsequent prediction trajectory of the overflow particle size of the cyclone is dynamically corrected;

[0079] Step S9: the adaptive gradient descent method is used to adaptively update the parameters of the GDGMM-RBF neural network prediction model; wherein in the case that the error between the actual output and the predicted output of the GDGMM-RBF neural network prediction model is minimum and the change of the parameters of the GDGMM-RBF neural network prediction model is minimum, adjustable weight factors γ1, γ2 are introduced, and a dynamic optimization mechanism under double regularization constraints is designed to update the objective function, so as to realize online adjustment of the parameters of the GDGMM-RBF neural network prediction model;

[0080] Step S10: return to step S4 to achieve the purpose of iterative optimization, so as to continuously optimize the overflow particle size of the cyclone.

[0081] In the embodiment, the application proposes a method for optimizing the overflow particle size of a cyclone. First, historical data of the grinding and classification process is collected, a GDGMM-RBF neural network prediction model of the overflow particle size of the cyclone is established, the GMM algorithm is used to determine the initial model parameters of the RBF network, and the gradient descent method is used for parameter optimization; secondly, according to the error, the prediction result obtained by the prediction model is corrected to improve the accuracy of the model; at the same time, according to real-time data, the adaptive gradient descent method is used to update the parameters of the prediction model online; and then an incremental PID controller is used to control the cyclone pressure and the cyclone feed concentration. Finally, the adaptive gradient descent method is used to solve the optimal cyclone feed concentration and cyclone pressure at each moment.

[0082] In one embodiment of the present application, the GMM algorithm is used to calculate the parameters of the RBF neural network prediction model, specifically comprising: step S3.1: determining the number of mixed components of the GMM model using the Bayesian information criterion; step S3.2: solving the parameters of the GMM model using the expectation-maximization algorithm; step S3.3: determining the number of neurons in the hidden layer, the initial center of the neurons, and the width of the neurons of the RBF neural network model by the solved parameters of the GMM model, and performing offline training on the GDGMM-RBF neural network prediction model; wherein the Gaussian distribution parameters in the GMM are mapped to the parameters of the RBF neural network model, the number of mixed components of the Gaussian distribution g is the number of RBF neurons, the mean μ g of the Gaussian distribution is the center c j of the RBF neuron g , and the covariance Σ j is the width δ of the RBF neuron; and step S3.4: performing parameter optimization on the width of the RBF neural network neurons, the center of the neurons, and the output weight of the neurons to the output layer by the GD gradient descent method.

[0083] In one embodiment of the present application, in step S4, the mathematical expression of the reference trajectory y r (t+j) of the overflow particle size of the cyclone is:

[0084]

[0085] In formula (1), y r (t) is the reference value of the overflow particle size of the cyclone to be tracked; y(t) is the actual value of the overflow particle size of the cyclone; the value range of f(t) is 0<f(t)<1; wherein the mathematical expression of the dynamic adjustment factor f(t) is:

[0086]

[0087] In formula (2), e1(t) is the current error; k is a constant for adjusting the sensitivity of f(t) to the error; γ is a dynamic attenuation coefficient, which automatically reduces the error weight over time to prevent over-adjustment; λ is a nonlinear correction factor; in formula (2), the mathematical expression of e1(t) is:

[0088] e1(t) = |y sp (t) - y(t)| (3).

[0089] In one embodiment of the present application, in step S5, the adaptive gradient descent method is used to calculate the prediction output Jacobian matrix of the control input u(t) to realize the calculation of the control time domain Hu The control variable adjustment amount inside the control input u(t) is adjusted, specifically including: step S5.1: selecting the current control input u(t) to minimize the objective function; wherein the mathematical expression of the objective function is:

[0090]

[0091] In formula (4), r(t) is a system reference trajectory; is the prediction output of the GDGMM-RBF neural network prediction model, r(t) and The dimension of is H p ×1; the dimension of Δu(t) is H u ×1; ρ1 and ρ2 are control weight factors;

[0092] In formula (4), r(t), and Δu(t) correspond to the mathematical expressions respectively as follows:

[0093] r(t) = [r(t+1), r(t+2), …, r(t+H p )] T (5)

[0094]

[0095] Δu(t) = [Δu(t), Δu(t+1), …, Δu(t+H u -1)] T (7)

[0096] Step S5.2: updating the control input u(t) using the adaptive gradient descent method to achieve minimization The mathematical expression corresponding to this step is:

[0097]

[0098] In formula (8), λ(t) is a dynamically adjusted step size, and the learning rate is adaptively adjusted by the gradient change threshold τ;

[0099] In formula (8), the update rule of the step size λ(t) is as follows:

[0100]

[0101] In formula (9), the fixed step size λ in the gradient descent is replaced by an adaptive step size, τ is the gradient change threshold, and θ(t) is the parameters {c, ω, δ} in the GDGMM-RBF neural network prediction model; c is the center of the RBF neuron; ω is the output weight of the RBF neuron to the output layer; δ is the width of the RBF neuron; θ(t-1) is the parameters in the GDGMM-RBF neural network prediction model at the previous moment; when the gradient change When the step is larger than the threshold, the step is reduced by the ratio of the distance between adjacent iteration points and the difference of the gradient to avoid oscillation; ∈ t is a positive term sequence, when the gradient change does not exceed the threshold, the step is steadily increased until the threshold is exceeded again;

[0102] Step S5.3: the mathematical expression of the control increment Δu(t) is obtained by formula (8):

[0103]

[0104] Step S5.4: the objective function is After differentiating u(t), we get:

[0105]

[0106] Step S5.5: formula (10) is substituted into formula (11), and then we get:

[0107]

[0108] In formula (13), is the Jacobian matrix, which is obtained from the GDGMM-RBF neural network prediction model.

[0109] In an embodiment of the present application, in step S6, the cyclone pressure and the cyclone feed ore concentration are controlled by using an improved incremental PID controller, specifically including: step S6.1: in the lower PID control loop, according to the size of the deviation e k , it is determined whether to introduce an integral element to realize the control of the cyclone pressure and the cyclone feed ore concentration by using the improved incremental PID controller; wherein the mathematical expression of the improved incremental PID controller is:

[0110] Δu k = K p (e k -e k-1 )+ β·K i ·e k + K d (e k -2e k-1 +e k-2 )(14)

[0111]

[0112] In formula (14) and formula (15), K p is a proportional coefficient; K i is an integral coefficient; K d is a differential coefficient; ek is the deviation of the kth set value and the control variable; β is the integral opening coefficient; and ε is the reference value.

[0113] In one embodiment of the present application, in step S8, the error compensation mechanism is constructed, specifically comprising: step S8.1: calculating the predicted value y p of the overflow particle size of the new cyclone at the previous moment

[0114] err(t) = y(t) - y p (t) (16)

[0115] Step S8.2: obtaining the corrected prediction result of the overflow particle size of the cyclone through the error err(t) and the dynamic adjustment factor f(t); wherein the mathematical expression of the corrected prediction result of the overflow particle size of the cyclone is:

[0116]

[0117] In formula (17), y p (t+j) is the predicted value of the overflow particle size of the new cyclone.

[0118] In one embodiment of the present application, in step S9, the mathematical expression of the target function is:

[0119]

[0120] Δθ a (t) = θ a (t) - θ a (t-1) (20)

[0121] In formula (18) and formula (20), γ1 and γ2 are both adjustable weight factors, and γ1 and γ2 are both greater than zero; Δθ a (t) is the parameter variation amount in the GDGMM-RBF neural network prediction model at the current moment; θ is the parameter {c, ω, δ} in the GDGMM-RBF neural network prediction model, c is the center of the RBF neuron; ω is the output weight of the RBF neuron to the output layer; δ is the width of the RBF neuron; n θ is the number of parameters of the GDGMM-RBF neural network prediction model; a is the index of the parameter of the GDGMM-RBF neural network prediction model;

[0122] In formula (19), φ j (·) is an activation function; x is an input vector, which is the cyclone pressure and the cyclone ore concentration; c jis the center of the j-th radial basis function; ω j is the output layer weight of the jth neuron; k is the total number of neurons; j is the index of the number of neurons.

[0123] In one embodiment of the present invention, in step S5 and step S9, the mathematical expression for updating the variables using the adaptive gradient descent method is:

[0124]

[0125] In formula (21), θ(t+1) is the GDGMM-RBF neural network prediction model parameter at the next moment; L is the objective function of the GDGMM-RBF neural network prediction model optimization; λ(t) is the step size of dynamic adjustment.

[0126] Figure 2 FIG1 shows a process flow chart of grinding and classification according to an embodiment of the present invention. Figure 2 As shown in the figure, the slurry, after processing through the previous steps, first enters the pump sump, where the pump sump water level is controlled by the pump sump fill valve to adjust the slurry concentration. Further, the slurry, pressurized by the slurry pump, enters the hydrocyclone tangentially at a specific pressure, where the centrifugal field separates the slurry into particle size fractions. After classification, the coarse product (underflow) is discharged through the grit nozzle and returned to the ball mill for regrinding. The fine product (overflow) passes through the top of the cyclone and enters the online particle size analysis system for real-time monitoring. The fine-grade product that meets the process requirements enters the subsequent sorting system for sorting.

[0127] The technical solution of the present invention will be demonstrated below with a specific embodiment. Figure 3 As shown, the overflow particle size optimization control method of the cyclone in this specific embodiment is achieved by the following steps:

[0128] (1) Step S1: Acquire a data set; wherein the data set is a historical data set, and the historical data set includes: cyclone feed concentration, cyclone pressure, and cyclone overflow particle size;

[0129] (2) Step S2: preprocessing the data set, and then dividing the preprocessed data set into a training set and a test set according to a preset ratio; preprocessing the data set includes: normalizing the data set; the mathematical expression corresponding to the normalization process is:

[0130]

[0131] Where x norm is the normalized value; x is the original value of the data; x min , x maxrespectively the maximum and minimum values of the data.

[0132] (3) Step S3: building a GDGMM-RBF neural network prediction model, training the GDGMM-RBF neural network prediction model based on the training set, and testing the prediction effect of the trained GDGMM-RBF neural network prediction model based on the test set; wherein the GDGMM-RBF neural network prediction model is composed of a GMM model and a RBF neural network model; the input of the GDGMM-RBF neural network prediction model is the cyclone feed concentration and the cyclone pressure, and the output of the GDGMM-RBF neural network prediction model is the overflow particle size of the cyclone; the GDGMM-RBF neural network prediction model uses a GMM algorithm to calculate the parameters of the RBF neural network model, and a gradient descent method is used for parameter optimization;

[0133] The GMM model is a classical unsupervised probability model, and any Gaussian distribution can be composed of a series of Gaussian components. Generally, given a sufficient number of Gaussian distributions, the GMM algorithm can smoothly approach any given non-Gaussian probability density, that is, multiple Gaussian distributions are used to effectively approximate the probability distribution of a complex process.

[0134]

[0135] In the formula, G is the total number of Gaussian distributions; θ g ={μ g ,∑g} respectively represent the mean and deviation of the gth Gaussian distribution; π g represents the mixing weight of x i belonging to the gth Gaussian distribution.

[0136]

[0137] The probability density function of the gth Gaussian distribution C g is:

[0138]

[0139] Wherein, the GMM algorithm is used to calculate the parameters of the RBF neural network prediction model, and specifically includes: step S3.1: using the Bayesian information criterion (BIC) to determine the number of mixed components of the GMM model; step S3.2: using the expectation maximization algorithm (EM) to solve the parameters of the GMM model; step S3.3: determining the number of neurons in the hidden layer, the initial center of the neurons, and the width of the neurons of the RBF neural network model by the solved parameters of the GMM model, and performing offline training on the GDGMM-RBF neural network prediction model; wherein the Gaussian distribution parameters in the GMM are mapped to the parameters of the RBF neural network model, the number of mixed components of the Gaussian distribution g is the number of RBF neurons, the mean μ g of the Gaussian distribution is the center c j of the RBF neuron g , the covariance Σ j is the width δ of the RBF neuron Step S3.4: using the GD gradient descent method to optimize the parameters of the width of the RBF neural network neurons, the center of the neurons, and the output weight of the neurons to the output layer.

[0140] For a given initial parameter, the following two steps are used for iterative calculation,

[0141] E-step: in the lth iteration, use θ (l) to calculate the posterior probability of the training sample with respect to the gth Gaussian distribution.

[0142]

[0143] M-step: recalculate the model parameters using the current posterior probability.

[0144]

[0145] Repeat the E-step and the M-step until the parameters converge. Wherein are the mean, covariance and prior probability of the gth Gaussian distribution in the (l+1)th iteration, the number of neurons and the initial center of the RBF hidden layer have a greater impact on the modeling effect, the adaptive GMM algorithm is used to iteratively calculate and determine the number of neurons and the initial center of the RBF neural network hidden layer, and the GDGMM-RBF neural network prediction model is trained offline. The prior probability π g is the output weight ω j of the RBF neuron.

[0146] The RBF neural network model is a typical three-layer feedforward network architecture, including a data input layer, a hidden layer, and a result output layer. The activation function of the hidden layer node uses a Gaussian function:

[0147]

[0148] The network output is:

[0149]

[0150] where X = (x1, x2, …, x m ) T is the l-dimensional input variable, hc represents the number of hidden layer neurons, y p represents the output of the network when the input is x, ω j is the weight from the jth neuron of the hidden layer to the output layer, c j and δ j are the center vector and width of the jth neuron, respectively. Gradient descent is used to adjust the network parameters, and in order to improve the optimization speed of the algorithm, an inertia link is introduced in the process of parameter adjustment.

[0151] For the tth sample, the error e(t) between the actual output and the expected output of the network is defined as:

[0152]

[0153] where y is the actual value, and N is the number of samples. The center c j , width δ j and output weight ω j of the jth neuron of the hidden layer are updated as follows:

[0154]

[0155] where η1 is the learning rate, and α is the inertia coefficient. The specific gradient formula is as follows:

[0156]

[0157] (4) Step S4: The actual value of the overflow particle size of the cyclone is collected in real time, the set value of the overflow particle size of the cyclone is set as y sp (t), and a dynamic adjustment factor f(t) is introduced to calculate the reference trajectory y r (t+j) of the overflow particle size of the cyclone.

[0158] In order to smoothly guide the current output to the set value y sp (t), the mathematical expression of the reference trajectory y r (t+j) of the overflow particle size of the cyclone is:

[0159]

[0160] In formula (1), y r(t) is a reference value of the overflow particle size of the cyclone to be tracked; y(t) is an actual value of the overflow particle size of the cyclone; f(t) is a dynamic adjustment factor according to real-time performance or error change of the system; the value range of f(t) is 0 < f(t) < 1;

[0161] The mathematical expression of the dynamic adjustment factor f(t) is as follows:

[0162]

[0163] In formula (2), e1(t) is a current error; k is a constant for adjusting the sensitivity of f(t) to the error, which can control the speed and amplitude of the reference value adjustment; γ is a dynamic attenuation coefficient, which automatically reduces the error weight over time to prevent over-adjustment; λ is a nonlinear correction factor, which functions to suppress exponential growth when the error is large and increase the adjustment sensitivity when the error is small, thereby realizing a smoother adjustment process;

[0164] The mathematical expression of e1(t) in formula (2) is as follows:

[0165] e1(t) = |y sp (t) - y(t) | (3).

[0166] (5) Step S5: calculating a control increment Δu(t); wherein the control increment is a cyclone feed concentration and a cyclone pressure; within a prediction time domain H p of the GDGMM-RBF neural network prediction model, setting the prediction output of the GDGMM-RBF neural network prediction model as the control input u(t); and using an adaptive gradient descent method to calculate the prediction output the Jacobian matrix of the control input u(t) to realize the calculation of a control variable adjustment amount within a control time domain H u using the Jacobian matrix; the control variable adjustment amount is the control increment Δu(t);

[0167] The prediction output calculated by the adaptive gradient descent method is as follows: The Jacobian matrix of the control input u(t) is as follows: to realize the calculation of a control variable adjustment amount within a control time domain H u using the Jacobian matrix, specifically including:

[0168] Step S5.1: selecting a current control input u(t) to minimize a target function; wherein the mathematical expression of the target function is as follows:

[0169]

[0170] In formula (4), r(t) is a system reference trajectory; is a prediction output of the GDGMM-RBF neural network prediction model, r(t) and The dimension of r(t) is H p × 1; the dimension of Δu(t) is H u × 1; ρ1 and ρ2 are control weight factors;

[0171] In formula (4), r(t), and Δu(t) correspond to the following mathematical expressions, respectively:

[0172] r(t) = [r(t+1), r(t+2), …, r(t+H p )] T (5)

[0173]

[0174] Δu(t) = [Δu(t), Δu(t+1), …, Δu(t+H u -1)] T (7)

[0175] Step S5.2: updating the control input u(t) using the adaptive gradient descent method to achieve minimization The mathematical expression corresponding to this step is as follows:

[0176]

[0177] In formula (8), λ(t) is a dynamically adjusted step size, and the learning rate is adaptively adjusted through a gradient change threshold τ;

[0178] In formula (8), the update rule of the step size λ(t) is as follows:

[0179]

[0180] In formula (9), the fixed step size λ in the gradient descent is replaced by an adaptive step size, τ is a gradient change threshold, and θ(t) is a parameter {c, ω, δ} in the GDGMM-RBF neural network prediction model; c is the center of the RBF neuron; ω is the output weight of the RBF neuron to the output layer; δ is the width of the RBF neuron; θ(t-1) is the parameter in the GDGMM-RBF neural network prediction model at the previous moment; when the gradient change is severe and exceeds the threshold, the step size is reduced by the ratio of the distance between adjacent iteration points to the gradient difference to avoid oscillation; ∈ t is a decreasing positive term sequence, and when the gradient change does not exceed the threshold, the step size is stably increased until it exceeds the threshold again;

[0181] Step S5.3: By formula (8), the mathematical expression of the control increment Δu(t) is obtained as:

[0182]

[0183] Step S5.4: By the objective function Differentiating u(t), we have:

[0184]

[0185] Step S5.5: Substituting formula (10) into formula (11), we have:

[0186]

[0187] In formula (13), is the Jacobian matrix obtained from the GDGMM-RBF neural network prediction model.

[0188] Further, let:

[0189]

[0190] We have:

[0191]

[0192] For the RBF network:

[0193]

[0194] When the control time domain H u is 1, the calculation amount of the predictive controller is less, which can overcome the problem that a large matrix operation is required when the control method solves the optimization problem, and satisfactory control effect is obtained. Therefore, setting H u to 1, Δu(t) can be expressed as:

[0195] Δu(t) = ε(g T (t)E(t));

[0196] In the formula,

[0197]

[0198] Wherein, the mathematical expression of variable update by using the adaptive gradient descent method is:

[0199]

[0200] In formula (21), θ(t+1) is the GDGMM-RBF neural network prediction model parameter at the next moment; L is the objective function of the GDGMM-RBF neural network prediction model optimization.

[0201] (6) Step S6: Calculate the new control setting value u from the control increment Δu(t) and the control amount u(t-1) at the previous moment sp (t), the new control set value is input into the lower PID control loop, and the improved incremental PID controller is used to control the cyclone pressure and cyclone feed concentration to obtain the new cyclone pressure, cyclone feed concentration and cyclone overflow particle size; the cyclone pressure is controlled in real time by the slurry pump frequency, the cyclone feed concentration is controlled in real time by the pump pool water supply valve, and the cyclone overflow particle size is controlled in real time by the cyclone pressure and cyclone feed concentration;

[0202] The original purpose of the integral term in the PID control algorithm was to overcome the system's steady-state error, thereby improving control system accuracy. However, its introduction can easily lead to significant control deviations during the system's initial operation, during operating mode changes, or when the setpoint fluctuates dramatically. In such cases, the continuous cumulative effect of the integral term can quickly generate excessive control signals, exceeding the actuator's operating threshold and causing system oscillation. To address this issue, the incremental PID algorithm has been modified to incorporate an integral term when the deviation is sufficiently large.

[0203] The improved incremental PID controller is used to control the cyclone pressure and cyclone feed concentration, including:

[0204] Step S6.1: In the lower PID control loop, according to the deviation e k The size of determines whether to introduce an integral link to achieve the control of the cyclone pressure and cyclone feed concentration using an improved incremental PID controller; wherein the mathematical expression corresponding to the improved incremental PID controller is:

[0205] Δu k =K p (e k -e k-1 )+β·K i ·e k +K d (e k -2e k-1 +e k-2 )(14)

[0206]

[0207] In formula (14) and formula (15), K p is the proportional coefficient; K i is the integral coefficient; Kd is the differential coefficient; e k is the deviation of the kth setting value and the control variable; β is the integral open relation coefficient; and ε is the reference value.

[0208] The mathematical expression for updating the variables using the adaptive gradient descent method is as follows:

[0209]

[0210] In formula (21), θ(t+1) is the GDGMM-RBF neural network prediction model parameter at the next time; L is the objective function for optimizing the GDGMM-RBF neural network prediction model

[0211] (7) Step S7: input the new cyclone pressure and cyclone feed concentration into the GDGMM-RBF neural network prediction model to obtain the predicted value of the overflow particle size of the new cyclone;

[0212] (8) Step S8: compare the difference between the actual value of the overflow particle size of the cyclone collected in real time and the predicted value of the overflow particle size of the new cyclone in real time, and build an error compensation mechanism to realize dynamic correction of the subsequent prediction trajectory of the overflow particle size of the cyclone;

[0213] In order to improve the accuracy of model prediction, the error err(t) between the predicted output y p (t) at the previous time and the actual output y(t) is calculated, and then the prediction result is corrected through err(t) and the system adjustment factor f(t) to build an error compensation mechanism;

[0214] The error compensation mechanism is built, and specifically includes:

[0215] Step S8.1: calculate the error err(t) between the predicted value y p (t) of the overflow particle size of the new cyclone at the previous time and the actual value y(t) of the overflow particle size of the cyclone collected in real time; wherein the mathematical expression of the error err(t) is as follows:

[0216] err(t) = y(t) - y p (t) (16)

[0217] Step S8.2: obtain the corrected prediction result of the overflow particle size of the cyclone through the error err(t) and the dynamic adjustment factor f(t); wherein the mathematical expression of the corrected prediction result of the overflow particle size of the cyclone is as follows:

[0218]

[0219] In formula (17), y p(t+j) is a predicted value of the overflow particle size of the new cyclone.

[0220] (9) Step S9: adaptive update the parameters of the GDGMM-RBF neural network prediction model by using adaptive gradient descent method; wherein, in the case that the error between the actual output and the predicted output of the GDGMM-RBF neural network prediction model is minimum and the parameter change of the GDGMM-RBF neural network prediction model is minimum, adjustable weight factors γ1, γ2 are introduced, and a dynamic optimization mechanism under double regularization constraints is designed to update the objective function, so as to realize online adjustment of the parameters of the GDGMM-RBF neural network prediction model;

[0221] Wherein, the mathematical expression of the objective function is:

[0222]

[0223] Δθ a (t)=θ a (t)-θ a (t-1)(20)

[0224] In formula (18) and formula (20), γ1 and γ2 are both adjustable weight factors, and γ1 and γ2 are both greater than zero; Δθ a (t) is the parameter change amount in the GDGMM-RBF neural network prediction model at the current moment; θ is the parameter {c, ω, δ} in the GDGMM-RBF neural network prediction model, c is the center of the RBF neuron; ω is the output weight of the RBF neuron to the output layer; δ is the width of the RBF neuron; n θ is the number of parameters of the GDGMM-RBF neural network prediction model; a is the index of the parameter of the GDGMM-RBF neural network prediction model;

[0225] In formula (19), φ j (·) is an activation function, which is a Gaussian kernel function here; x is an input vector, which is the cyclone pressure and the cyclone ore concentration; c j is the center of the jth radial basis function; ω j is the output layer weight of the jth neuron; k is the total number of neurons; j is the index of the number of neurons.

[0226] The adaptive gradient descent strategy is also used to update the variable in the above formula:

[0227]

[0228] In formula (21), θ(t+1) is the GDGMM-RBF neural network prediction model parameter at the next moment; L is the objective function of the GDGMM-RBF neural network prediction model optimization; λ(t) is the step size of dynamic adjustment.

[0229] Adaptively adjust the learning rate by gradient change threshold τ to avoid local optimality and oscillation, and introduce a decreasing sequence ∈ t Control the step size growth well and balance the convergence speed and accuracy. as follows:

[0230]

[0231] When the set accuracy requirement or the update termination condition of the maximum number of iterations is met, the adaptively adjusted prediction model parameters at time t can be obtained.

[0232] (10) Step S10: Return to step S4 to achieve the purpose of iterative optimization, so as to realize continuous optimization of the overflow particle size of the cyclone.

[0233] In this specific embodiment, before step S1, the following steps are also included: selecting appropriate parameters, including RBF neural network parameters such as learning rate η1, network weights, etc.; control parameters such as prediction time domain H p , control time domain H u , adjustment factor k, control weight factors ρ1, ρ2, initial control input learning rate λ(t) and model parameter adaptive update learning rate λ.

[0234] This method is applied to industrial sites, such as Figure 4 As shown, the system utilizes an edge-cloud architecture. The edge is deployed on the industrial site, forming a closed loop of various sensors and actuators. These include measuring instruments such as pump sump sensors, pressure sensors, and particle size analyzers, as well as PLC controllers, slurry pump inverters, and pump sump water replenishment valves. These collect physical quantities and feed them back to the central control system, where they are then optimized by algorithms to drive dynamic adjustments. Industrial servers, switches, and data servers are deployed on the edge in the central control room, responsible for data collection, monitoring, and host computer interface interaction. They leverage 5G communication technology for high-speed data transmission. The cloud, based on an artificial intelligence platform, features an algorithm server and monitoring equipment in the laboratory. These systems integrate core algorithm modules such as online prediction and calibration, adaptive model parameter updates, and reference trajectory calculation, and display the system's operational status in real time through a visual interface. Through the integrated linkage between the laboratory, central control room, and field equipment, precise control of the cyclone overflow particle size is achieved.

[0235] In order to illustrate the effectiveness and superiority of the overflow particle size optimization control method of the cyclone proposed in the present application, the present application method is compared with some models, and the prediction models are introduced as follows: (1) GDGMM-RBF, which is the modeling algorithm proposed in the present application. The GDGMM-RBF neural network prediction model calculates the parameters of the RBF neural network model by using the GMM algorithm, and the parameters are optimized by the gradient descent method. (2) FCM-RBF, which calculates the parameters of the RBF neural network model by using the FCM algorithm, and the parameters are optimized by the gradient descent method. (3) RBF, which randomly initializes the parameters of the RBF neural network model, and the parameters are optimized by the gradient descent method.

[0236] 960 groups of data are selected as the data set, and are divided according to the ratio of 4:1, 768 groups of data are used as the training set, 192 groups of data are used as the test set, the target error of the prediction model is set to 0.001, the learning rate η1 is 0.01, the maximum number of iterations is 200 times, the optimal Gaussian component number obtained by the GMM algorithm is 5, and the number of RBF network neurons is set. The prediction effects of different models are shown in Figure 5 In order to further verify the effectiveness of the GDGMM-RBF neural network prediction model in predicting the overflow particle size, the root mean square error (RMSE for short), the mean absolute percentage error (MAPE for short), the determination coefficient (R 2 ) and the mean absolute error (MAE for short) are used to evaluate the prediction performance, and the average values of the prediction performance indicators of different models running independently for 20 times are listed in Table 1, wherein the prediction performance indicators of the GDGMM-RBF neural network prediction model are obviously improved.

[0237] Table 1 Comparison of prediction evaluation indicators of different prediction models

[0238]

[0239] In order to verify the effectiveness of the GDGMM-RBF-MPC method, the overflow particle size control effects of different RBF neural network prediction models are compared. The prediction time domain H p is 5, the control time domain H u is 1, the adjustment factor k is 0.8, the control weight factor p1 is 5, p2 is 1, the learning rate of the initial control input is 1, and the model parameter adaptive updating learning rate is 0.01. Due to the complex working conditions of the grinding process, in order to simulate this situation, a disturbance with a value of 0.4 is applied at the time period of 150, and the control effects of different models are shown in Figure 6The absolute error integral (IAE), the absolute error and time product integral (ITAE) and the average absolute error (MAE) are used to evaluate the control effect. Table 2 lists the evaluation index comparison of the overflow particle size of different model controllers. The GDGMM-RBF-MPC method has better anti-interference and adaptive capacity, and can more accurately control the overflow particle size of the cyclone.

[0240] Table 2: Evaluation index comparison of different model controllers

[0241]

[0242] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. The present application can be variously changed and modified by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for optimizing the overflow particle size of a cyclone, characterized in that: include: Step S1: Acquire a data set; wherein the data set is a historical data set, and the historical data set includes: cyclone feed concentration, cyclone pressure, and cyclone overflow particle size; Step S2: preprocessing the data set, and then dividing the preprocessed data set into a training set and a test set according to a preset ratio; Step S3: building a GDGMM-RBF neural network prediction model, training the GDGMM-RBF neural network prediction model based on the training set, and then testing the prediction effect of the trained GDGMM-RBF neural network prediction model based on the test set; wherein the GDGMM-RBF neural network prediction model is mainly composed of a GMM model and an RBF neural network model; the input of the GDGMM-RBF neural network prediction model is the cyclone feed concentration and the cyclone pressure, and the output of the GDGMM-RBF neural network prediction model is the overflow particle size of the cyclone; the GDGMM-RBF neural network prediction model uses a GMM algorithm to calculate the parameters of the RBF neural network model, and the parameters are optimized by a gradient descent method; Step S4: Collect the actual value of the overflow particle size of the cyclone in real time, and set the overflow particle size of the cyclone to y sp (t), and introduce the dynamic adjustment factor f(t) to calculate the reference trajectory y of the overflow particle size of the cyclone r (t+j); Step S5: Calculate the control increment Δu(t); wherein the control increment is the cyclone feed concentration and the cyclone pressure; in the prediction time domain H of the GDGMM-RBF neural network prediction model p In the example, the prediction output of the GDGMM-RBF neural network prediction model is set to The control input is u(t); and the predicted output is calculated using the adaptive gradient descent method Jacobian matrix of control input u(t) In order to use the Jacobian matrix to calculate H in the control time domain u The control variable adjustment amount within; the control variable adjustment amount is the control increment Δu(t); Step S6: Calculate the new control setting value u from the control increment Δu(t) and the control amount u(t-1) at the previous moment sp (t), input the new control set value into the lower-layer PID control loop, and use the improved incremental PID controller to control the cyclone pressure and cyclone feed concentration to obtain new cyclone pressure, cyclone feed concentration and cyclone overflow particle size; wherein the cyclone pressure is controlled in real time by the slurry pump frequency, the cyclone feed concentration is controlled in real time by the pump pool water supply valve, and the cyclone overflow particle size is controlled in real time by the cyclone pressure and cyclone feed concentration; Step S7: inputting the new cyclone pressure and cyclone feed concentration into the GDGMM-RBF neural network prediction model to obtain a new predicted value of the overflow particle size of the cyclone; Step S8: comparing the real-time collected actual value of the overflow particle size of the cyclone with the predicted value of the overflow particle size of the new cyclone in real time, and establishing an error compensation mechanism to dynamically correct the subsequent predicted trajectory of the overflow particle size of the cyclone; Step S9: Adaptively updating the parameters of the GDGMM-RBF neural network prediction model using an adaptive gradient descent method; wherein, when the error between the actual output and the predicted output of the GDGMM-RBF neural network prediction model is minimized and the parameter change of the GDGMM-RBF neural network prediction model is minimized, adjustable weight factors γ1 and γ2 are introduced, and a dynamic optimization mechanism under dual regularization constraints is designed to update the objective function, so as to achieve online adjustment of the parameters of the GDGMM-RBF neural network prediction model; Step S10: Return to step S4 to achieve the purpose of iterative optimization, so as to realize continuous optimization of the overflow particle size of the cyclone.

2. The method for optimizing the overflow particle size of a cyclone according to claim 1, characterized in that: The GMM algorithm is used to calculate the parameters of the RBF neural network prediction model, specifically including: Step S3.1: Determine the number of mixture components of the GMM model using the Bayesian Information Criterion; Step S3.2: Use the maximum expectation algorithm to solve the parameters of the GMM model; Step S3.3: Determine the number of neurons in the hidden layer of the RBF neural network model, the initial center of the neurons, and the width of the neurons by using the parameters of the solved GMM model, and perform offline training on the GDGMM-RBF neural network prediction model; wherein, the Gaussian distribution parameters in the GMM are mapped to the parameters of the RBF neural network model, the number of mixed components of the Gaussian distribution g is the number of RBF neurons, and the mean value μ of the Gaussian distribution is g is the center c of RBF neuron j , covariance Σ g is the width of the RBF neuron δ j ; Step S3.4: Optimize the parameters of the width of the RBF neural network neurons, the center of the neurons, and the output weights of the neurons to the output layer by using the GD gradient descent method.

3. The method for optimizing the overflow particle size of a cyclone according to claim 1, characterized in that: In step S4, the reference trajectory y of the overflow particle size of the cyclone r The mathematical expression of (t+j) is: In formula (1), y r (t) is the reference value of the overflow particle size of the cyclone to be tracked; y(t) is the actual value of the overflow particle size of the cyclone; the value range of f(t) is 0 <f(t)<1; Among them, the mathematical expression of the dynamic adjustment factor f(t) is: In formula (2), e1(t) is the current error; k is a constant used to adjust the sensitivity of f(t) to the error; γ is a dynamic attenuation coefficient that automatically reduces the error weight over time to prevent over-adjustment; λ is a nonlinear correction factor; In formula (2), the mathematical expression of e1(t) is: e1(t)=|y sp (t)-y(t)| (3)。 4. The method for optimizing the overflow particle size of a cyclone according to claim 1, characterized in that: In step S5, the adaptive gradient descent method is used to calculate the predicted output Jacobian matrix of control input u(t) In order to use the Jacobian matrix to calculate H in the control time domain u The control variable adjustment amount within includes: Step S5.1: Select the current control input u(t) to minimize the objective function; wherein the mathematical expression of the objective function is: In formula (4), r(t) is the system reference trajectory; is the predicted output of the GDGMM-RBF neural network prediction model, r(t) and The dimension is H p ×1; the dimension of Δu(t) is H u ×1; ρ1 and ρ2 are control weight factors; In formula (4), r(t), The mathematical expressions corresponding to and Δu(t) are: r(t)=[r(t+1),r(t+2)…r(t+H p )] T (5) Δu(t)=[Δu(t),Δu(t+1),…,Δu(t+H u -1)] T (7) Step S5.2: Update the control input u(t) using adaptive gradient descent to minimize The mathematical expression corresponding to this step is: In formula (8), λ(t) is the dynamically adjusted step size, and the learning rate is adaptively adjusted through the gradient change threshold τ; In formula (8), the update rule of step size λ(t) is as follows: In formula (9), the fixed step size λ in the gradient descent is changed to an adaptive step size, τ is the gradient change threshold, θ(t) is the parameter {c, ω, δ} in the GDGMM-RBF neural network prediction model; c is the center of the RBF neuron; ω is the output weight of the RBF neuron to the output layer; δ is the width of the RBF neuron; θ(t-1) is the parameter in the GDGMM-RBF neural network prediction model at the previous moment; when the gradient changes / / ▽L(θ(t)) / / violently and exceeds the threshold, the step size is reduced by the ratio of the distance between adjacent iteration points to the gradient difference to avoid oscillation; ∈ t It is a decreasing positive sequence. When the gradient change does not exceed the threshold, the step size increases steadily until it exceeds the threshold again. Step S5.3: Through formula (8), the mathematical expression of the control increment Δu(t) is obtained as follows: Step S5.4: Through the objective function Differentiating u(t), we can get: Step S5.5: Substitute equation (10) into equation (11), and we get: In formula (13), is the Jacobian matrix obtained from the GDGMM-RBF neural network prediction model.

5. The method for optimizing the overflow particle size of a cyclone according to claim 1, characterized in that: In step S6, the improved incremental PID controller is used to control the cyclone pressure and the cyclone feed concentration, specifically including: Step S6.1: In the lower PID control loop, according to the deviation e k The size of determines whether to introduce an integral link to achieve the control of the cyclone pressure and cyclone feed concentration using an improved incremental PID controller; wherein the mathematical expression corresponding to the improved incremental PID controller is: Thu k =K p (e k -e k-1 )+β·K i ·e k +K d (e k -2e k-1 +e k-2 (14) In formula (14) and formula (15), K p is the proportional coefficient; K i is the integral coefficient; K d is the differential coefficient; e k is the deviation between the kth set value and the controlled quantity; β is the integral switching coefficient; ε is the reference value.

6. The method for optimizing the overflow particle size of a cyclone according to claim 1, characterized in that: In step S8, an error compensation mechanism is constructed, specifically including: Step S8.1: Calculate the predicted value y of the overflow particle size of the new cyclone at the previous moment p The error err(t) between the actual value y(t) of the overflow particle size of the cyclone collected in real time is: err(t)=y(t)-y p (t)(16) Step S8.2: Obtain a corrected prediction result of the overflow particle size of the cyclone using the error err(t) and the dynamic adjustment factor f(t); wherein the mathematical expression of the corrected prediction result of the overflow particle size of the cyclone is: In formula (17), y p (t+j) is the predicted value of the overflow particle size of the new cyclone.

7. The method for optimizing the overflow particle size of a cyclone according to claim 1, characterized in that: In step S9, the mathematical expression of the objective function is: Dth a (t)=θ a (t)-θ a (t-1) (20) In formula (18) and formula (20), γ1 and γ2 are both adjustable weight factors, and both γ1 and γ2 are greater than zero; Δθ a (t) is the parameter change in the GDGMM-RBF neural network prediction model at the current moment; θ is the parameter {c, ω, δ} in the GDGMM-RBF neural network prediction model, where c is the center of the RBF neuron; ω is the output weight of the RBF neuron to the output layer; δ is the width of the RBF neuron; n θ is the number of GDGMM-RBF neural network prediction model parameters; a is the index of the GDGMM-RBF neural network prediction model parameter; In formula (19), φ j (·) is the activation function; x is the input vector, which is the cyclone pressure and the cyclone feed concentration; c j is the center of the j-th radial basis function; ω j is the output layer weight of the jth neuron; k is the total number of neurons; j is the index of the number of neurons.

8. The method for optimizing the overflow particle size of a cyclone according to any one of claims 1 to 7, characterized in that: In step S5 and step S9, the mathematical expression for updating the variables using the adaptive gradient descent method is: In formula (21), θ(t+1) is the GDGMM-RBF neural network prediction model parameter at the next moment; L is the objective function of the GDGMM-RBF neural network prediction model optimization; λ(t) is the step size of dynamic adjustment.

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