A method for dynamically changing model prediction parameters in a flotation pH adjustment process

Abstract

The application relates to the technical field of flotation process, and discloses a flotation pH adjustment process model prediction parameter identification method improved based on differential evolution and a partial least square method. The method is aimed at the key link of lead-zinc metal flotation, namely, dosing regulation, and pH of ore pulp is controlled through accurate process model analysis and parameter identification to realize efficient separation and extraction of lead-zinc metal. The process model is a mathematical tool for describing the dynamic behavior of the pH dosing regulation of the ore pulp, and the interaction and influence of internal and external variables in the dosing process are deeply analyzed. The model fuses a mechanism model and a data-driven model, simultaneously adopts an adaptive optimization mechanism, realizes closed-loop control, and thus can systematically understand and predict the dynamic trend of the pH value of the ore pulp with the change of the type, dosage and time of the dosing agent, and further realize accurate regulation of the dosing process, and ensure the efficiency and stability of the flotation process.

Description

Technical Field

[0001] This invention relates to the field of flotation technology, and in particular to a method for predicting the dynamic changes of parameters in a flotation pH adjustment process model. Background Technology

[0002] In the flotation process of metals such as lead and zinc, the control of reagent addition is a key step to achieve efficient separation and extraction. Traditional reagent addition control relies on manual experience and has disadvantages such as strong subjectivity, large reagent consumption and poor dynamic response.

[0003] To precisely control this process, a dynamic model must be established to describe the relationships between key variables and parameters in the flotation process, enabling precise control of the dosing process, thereby ensuring the efficiency and stability of the flotation process and achieving efficient separation and extraction of metals.

[0004] The dynamic characteristics of actual production processes are complex. When establishing a mathematical model of the controlled object, it is necessary to highlight key factors and ignore secondary factors. Sometimes, approximations are required, such as linearization, lumpedization, and model order reduction. This requires an understanding of the process and acceptance of errors. In conventional process control systems, the mathematical model of the controlled object is usually represented by a transfer function. This model, through parameter identification, quantitatively represents the dynamic relationship between the slurry pH value and the type, dosage, and reaction time of reagents, thereby achieving precise control of the dosing process and ensuring the efficiency and stability of the flotation process.

[0005] Differential evolution (DE) is a global optimization algorithm based on swarm intelligence, primarily used to solve optimization problems in multidimensional spaces. Partial least squares (PLS) is a multivariate statistical analysis method, mainly used to handle multivariate regression problems, especially when there is multicollinearity among independent variables or high data dimensionality. However, due to the complexity and nonlinearity of the flotation process, simple mechanistic PLS models suffer from insufficient modeling ability, poor dynamic adaptability, and poor anti-interference ability, and may be unable to fully and accurately describe the actual process. Currently, no relevant research has addressed these issues by applying the PLS scheme to the design of flotation models.

[0006] Therefore, how to combine the differential evolution algorithm with the partial least squares method, and on this basis improve the reliability and effectiveness of model analysis and parameter identification, has become a key research issue. Summary of the Invention

[0007] The technical problems to be solved by this invention include the complexity of flotation model data processing, insufficient PLS modeling capabilities, poor dynamic adaptability, and poor anti-interference ability. To address these issues, this invention provides a method for predicting dynamic changes in parameters during the flotation pH adjustment process, aiming to improve the reliability and effectiveness of flotation models.

[0008] The complexity and nonlinearity of the flotation process mean that simple mechanistic partial least squares models suffer from insufficient modeling capabilities, poor dynamic adaptability, and weak anti-interference ability, making it difficult to fully and accurately describe the actual process. Therefore, we introduce a data-driven modeling approach, utilizing a large amount of historical and real-time data accumulated during the flotation process, and employing advanced algorithms such as statistical analysis and machine learning to construct a mathematical model that more closely reflects reality. This method is independent of specific physical and chemical principles, can flexibly handle complex and nonlinear flotation processes, and its model updates and maintenance are relatively simple.

[0009] To achieve the above objectives, this invention provides a method for predicting dynamic changes in parameters of a flotation pH adjustment process model, comprising the following steps:

[0010] S1. Collect experimental parameters during the flotation pH adjustment process, perform physicochemical analysis, and fit a flotation pH adjustment process model; identify parameters for the flotation pH adjustment process model and calculate the gain of the identified parameters. 、 time constant and system lag time The characteristic correlation; the experimental parameters include pH value change data during the flotation pH adjustment process, flow rate data of pH adjustment reagents, pulp concentration and flow rate, pulp temperature, pulp volume in the flotation cell, and reagent dosage concentration parameters;

[0011] S2. The DE-PLS method is adopted. DE is the differential evolution algorithm, which performs population initialization, mutation evolution, differential crossover and selects the optimal feature. PLS is the partial least squares method, which accurately calculates the parameter identification of the flotation pH adjustment process model and outputs the parameter with the minimum identification error, thus obtaining the DE-PLS improved flotation pH adjustment process model.

[0012] S3. Using the DE-PLS improved flotation pH adjustment process model obtained in S2, the dynamic changes of pH during the flotation process are predicted based on the frequency of the variable frequency pump, the concentration and flow rate of the pulp, the pulp temperature and the real-time pH value, and the dosage of reagents is adjusted in real time.

[0013] To precisely control the pH adjustment process in flotation, a dynamic model must be established to describe the relationships between key variables and parameters in the flotation process. The system model must not only reflect the impact of production control parameters (such as reagent dosage, flotation time, and stirring speed) on flotation indicators (such as concentrate grade and recovery rate), but also consider the potential effects of disturbance variables (such as changes in ore properties and fluctuations in equipment performance). The controlled model, as a mathematical tool describing the dynamic behavior of the flotation process, comprises multiple aspects, including the flotation machine's operating model, reagent addition model, and pulp parameter model.

[0014] Preferably, the collection of experimental parameters during the flotation pH adjustment process, the physicochemical analysis, and the fitting of the flotation pH adjustment process model specifically include:

[0015] In an industrial test involving pH adjustment during flotation, data on pH changes during process control, reagent flow rate during pH adjustment, pulp concentration and flow rate, pulp temperature, pulp volume in the flotation cell, reagent concentration parameters, and system lag time were collected and analyzed. and parameter gain The characteristic correlation was determined by measuring the pH lag time and steady-state offset through a step response experiment. In the analysis and calculation of the dynamic response data characteristics, the gains of the three parameters of the first-order time-delay model were calculated. time constant Lag time As a task of identification methods;

[0016] Physicochemical analysis was conducted on the pH dosing control during the flotation process to obtain the pulp pH dosing adjustment process. The dynamic changes are as follows:

[0017] (0-1);

[0018] The motor frequency of the variable frequency pump is the control variable. / hz, slip , This represents the actual frequency control value of the variable frequency pump motor, and the number of pole pairs is... P The rotational speed is r / min, to obtain the motor speed of the variable frequency pump. for:

[0019] (0-2);

[0020] Diameter The cross-sectional area of ​​the variable frequency pump plunger is m 2 , The journey length is m, number of plungers The dosing flow rate of the variable frequency pump is m 3 / h, It is a complex frequency, where:

[0021] (0-3);

[0022] The control transfer function for variable frequency pump dosing, obtained through system mechanism modeling, is expressed as follows:

[0023] (0-4);

[0024] in, It is a complex frequency. The control transfer function for the variable frequency pump dosing. For flow transfer function, Frequency transfer function ， This is the proportionality coefficient; the above parameters can be calculated by referring to the nameplates of commonly available variable frequency pumps on the market.

[0025] Dosage concentration is pH adjustment reagents, pulp volume in flotation cell The pH of the flotation cell pulp is Hydrogen ion concentration in flotation cell pulp ore slurry H + concentration ore slurry flow rate Add pH flow rate The pH of the ore slurry is Concentration of ore pulp Ore slurry flow rate The dynamic relationship of the flotation cell adjustment process is as follows:

[0026] (0-5);

[0027] (0-6);

[0028] (0-7);

[0029] in, Indicates the dosage concentration is The dynamic relationship, Indicates the H of the ore slurry fed into the mine. + concentration The dynamic relationship;

[0030] The complex dynamic reaction process in the flotation cell is handled based on the principle of ion reaction conservation:

[0031] (0-8)

[0032] in, Indicates the hydrogen ion concentration in the flotation cell pulp. The dynamic relationship;

[0033] According to the Arrhenius formula, its calculation is as follows:

[0034] (0-9);

[0035] The Arrhenius equation is used to describe the rate constant of a chemical reaction. With absolute temperature The changing relationship;

[0036] In the formula, It is the coefficient of the rate of acid-base neutralization chemical reaction. Indicates pre-exponential factor, The apparent activation energy of a solution. Represents the molar gas constant. Indicates absolute temperature;

[0037] Secondly, the inlet and outlet flow rates of the slurry in the flotation cell are set constant. Since the concentration and flow rate of the slurry remain almost constant, they can be considered constant and regarded as the production condition parameters input to the flotation cell. Unchanged, based on the control quantity Post-state and the previous state After linearization, it becomes:

[0038] (0-10);

[0039] Nonlinear function of pH at the outlet of the flotation cell , Represented as:

[0040] (0-11);

[0041] In the formula, This indicates the input production condition parameters for the flotation cell. Indicates control variables;

[0042] pH control target desired control in pH regulation control system Controlling error for:

[0043] (0-12);

[0044] Equations 0-8 are simplified by transformation based on the principle of keeping the above parameters unchanged. The derivation of the formula is as follows:

[0045] (0-13);

[0046] make , , Before substitution , Substitute control quantity Simultaneously simplifying by combining 0-10 and 0-14, the transfer function of the pH reaction is obtained as follows:

[0047] (0-14);

[0048] In the formula, This is the proportionality coefficient for the pH reaction process. The time constant for the pH reaction process. Given the lag time in the pH reaction stage, and based on the control model of the frequency converter dosing described above, connecting them in series yields the overall control model for flotation dosing as follows:

[0049] (0-15);

[0050] in , and as well as These are the parameters to be fitted later;

[0051] For parameter identification of the transfer function of the flotation process control model, specifically the characteristic parameter identification of the transfer function of a first-order inertial element with time lag, taking the first-order inertial element transfer function with time lag as an example, the parameter gain... The value is obtained in the following way:

[0052] (0-16);

[0053] In the formula, The magnitude of the change in the step input excitation signal. The steady-state value of the step response output. The initial value for the step response output;

[0054] The tangent method, proposed by Ziegler and Nichols, is used to calculate the time constant. and lag time The core of this classic method lies in obtaining the controlled object model parameters through geometric analysis of the system's open-loop step response curve. In control model parameter identification, the two-point method significantly improves the lag time compared to the traditional tangent method. The identification accuracy is improved. Its core lies in extracting parameters using the time coordinate difference between the intersection points of the tangents at the inflection points of the step response curve, and determining the lag time using a two-point method. The parameter identification and the actual dynamic curve data of the system can be determined according to the relation 0-17. connect.

[0055] (0-17);

[0056] First, the step response Convert to dimensionless form The conversion process is represented as follows:

[0057] (0-18);

[0058] After the response transformation, the transfer function that describes the dynamic behavior of the system is given. Represented as follows

[0059] (0-19);

[0060] Unit step response of the reverse system Under a unit step input, the system's output response is expressed as shown in Equation 0-20. This response characteristic reflects the system's delay and rise time. .

[0061] (0-20);

[0062] To calculate the two parameters in equation 0-20, it is only necessary to select two time points. and ,in And read the corresponding dimensionless response value from the curve data of the system response. and The calculation based on 0-20 is expressed as follows:

[0063] (0-21);

[0064] Then, further solving equation 0-21 yields... and The final value is as follows:

[0065] (0-22).

[0066] Preferably, step S2 employs the DE-PLS method, where DE performs population initialization, mutation evolution, differential crossover, and selection of the optimal feature, specifically including:

[0067] The core steps of DE mainly involve population initialization, mutation and evolution, differential crossover, and selection of the optimal feature. A mutation adaptive adjustment mechanism is constructed, represented as follows:

[0068] (0-23);

[0069] In the formula, It is the value updated by mutation and evolution. It is a random number. It is an individual within a population. It is the maximum value. It is the initial value for mutation and evolution. It is a random update coefficient for mutation and evolution;

[0070] In differential crossover operations A function definition can be represented as follows:

[0071] (0-24);

[0072] In the formula, These are the initial values ​​for the differential crossover. These are differential crossover random update coefficients.

[0073] Preferably, in step S2, the PLS performs precise calculations on the parameters of the flotation pH adjustment process model, outputs the parameter with the minimum identification error, and obtains the DE-PLS improved flotation pH adjustment process model, specifically including:

[0074] For the parameters of identification PLS is expressed using a recursive regression model as follows, where These are the parameters before the update. This is the actual value. These are samples of collected experimental data;

[0075] (0-25);

[0076] By orthogonally decomposing and extracting the input and output data, and suppressing the cumulative error caused by initial bias, the covariance matrix is ​​optimized. The recursive regression update is represented as follows:

[0077] (0-26);

[0078] The model updates its algorithm by calculating the error between the model's computational results and the actual data samples, and the model parameters are identified using the DE-PLS algorithm to construct the objective function. for:

[0079] (0-27);

[0080] in These are actual measured data. For the response of the parametric model, iterate Second-rate, The parameters identified;

[0081] After iterative updates, the error further decreases, and the final identification parameter with the smallest error is the final algorithm identification result. , means as follows:

[0082] (0-28);

[0083] To accurately identify the control model of the system's dynamic characteristics, further analysis and verification of errors and reliability are conducted.

[0084] To address the errors inherent in the aforementioned identification methods, the least squares method is employed to identify the control model parameters. The model identification parameter vector is derived from the transfer function of the first-order inertial element with time lag. The core steps of differential evolution are population initialization, mutation evolution, differential crossover, and optimal selection.

[0085] Partial Least Squares (PLS) is a widely used method for assessing the stability and accuracy of model parameter identification, enabling precise calculation of parameters for control system models. Given the strong coupling between model parameters, PLS corrects for these parameters through recursive regression with orthogonal latent variables. For the identified parameters, a recursive regression model represents the PLS approach.

[0086] An identification method was employed for parameter calculation experiments. An improved differential evolutionary partial least squares (DE-PLS) method was used to iteratively update the identified model parameters using pH-regulated control response data. Simultaneously, an adaptive mutation adjustment mechanism and nonlinear decay of the crossover rate were introduced to optimize the identified parameters. The error changes in model parameter identification were tracked in real time to achieve high-precision identification of model parameters. Finally, the identification results were substituted into a simulation system for testing. By verifying the response data of the identified model, the superiority and inferiority of various process control system model parameter identification algorithms were verified and compared.

[0087] Preferably, the flotation pH adjustment process is for lead-zinc metal flotation. This invention provides a solution for accurate reagent dosing in lead-zinc metal flotation by precisely controlling reagent dosing and establishing an effective reagent dosing control system.

[0088] Under the same technical concept, the present invention also provides a computer-readable storage medium storing a computer program for execution by a computer device to implement the method for predicting dynamic changes in parameters of the flotation pH adjustment process model.

[0089] Under the same technical concept, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0090] Under the same technical concept, the present invention also provides a computer program product, including a computer program / instructions; when the computer program / instructions are executed by a processor, they implement the steps of the above-described method.

[0091] The above-described solution of the present invention has the following beneficial effects:

[0092] The flotation scheme of this invention combines differential evolution and partial least squares (PLS). Compared to PLS alone, the introduction of differential evolution leverages its strong global search capability. Through adaptive mutation and nonlinear decay mechanisms of crossover rate, it can efficiently explore the optimal solution in a complex parameter space, avoiding getting trapped in local optima. The combination of differential evolution and PLS significantly improves the model's noise resistance. The characteristics of differential evolution make it insensitive to initial values, adapting to nonlinear disturbances caused by fluctuations in ore properties and sensor noise during flotation. PLS, through recursive updates of the covariance matrix, suppresses the impact of data noise on parameter identification, ensuring model stability. Furthermore, the DE-PLS algorithm, through its iterative update mechanism, can track the dynamic changes in the flotation pH adjustment process in real time, rapidly adjusting model parameters. Compared to traditional single algorithms, this significantly shortens the parameter convergence time, meeting the real-time control requirements of industrial flotation scenarios.

[0093] Other beneficial effects of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0094] Figure 1 A schematic diagram of the model relating pulp pH to hydrogen ion concentration;

[0095] Figure 2 A schematic diagram of the structure for parameter identification of the tangent method control model;

[0096] Figure 3 A schematic diagram of the DE-PLS algorithm for identifying control model parameters;

[0097] Figure 4 This is a schematic diagram of the measured data curve of the flotation control response;

[0098] Figure 5 A schematic diagram of the DEPLS identification and calculation update error curve;

[0099] Figure 6 A schematic diagram comparing the effects of the DEPLS control model parameter identification method. Detailed Implementation

[0100] To make the technical problems, solutions, and advantages of this invention clearer, a detailed description will be provided below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0101] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0102] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a locking connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0103] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0104] The purpose of this invention is achieved through the following means: the flotation process of metallic minerals is controlled, especially the flotation of lead-zinc ore. During the separation and purification of flotation cells, reagents are added, and it is necessary to adjust the flotation reaction reagents such as collectors, inhibitors, and frothers, as well as the flotation reaction conditions such as pH and temperature, in order to achieve the optimal flotation effect, that is, to improve indicators such as lead-zinc recovery rate.

[0105] The acquisition of production data mainly adopts the method of historical data fusion training. Historical data fusion combines the historical flotation process database to extract pH adjustment response data under similar operating conditions, which is used for initial parameter training of the algorithm and model verification.

[0106] Example 1:

[0107] This invention provides a method for predicting dynamic changes in parameters in a DE-PLS-improved flotation pH adjustment process model, comprising the following steps:

[0108] S1. Collect experimental parameters during the pH adjustment process of flotation, perform physicochemical analysis, and fit a model of the pH adjustment process of flotation.

[0109] S2. Using the DE-PLS method, DE performs population initialization, mutation evolution, differential crossover, and selects the optimal features. PLS performs precise calculations on the parameter identification of the flotation pH adjustment process model and outputs the parameter with the minimum identification error, thus obtaining the DE-PLS improved flotation pH adjustment process model.

[0110] S3. Using the DE-PLS improved flotation pH adjustment process model obtained in S2, predict the dynamic changes of pH during the flotation pH adjustment process.

[0111] In one specific embodiment, the above process includes:

[0112] The physicochemical analysis of pH dosing control in the flotation process is as follows: First, pH = -lg[H+] + At normal temperature and pressure, the ionization constant of water is [H]. + ][OH - ]=10 -14 Therefore, the pH of the pulp during the flotation process corresponds to [OH-]. - The concentration is 10 ph -14 , where [H + ] and [OH - The concentration difference of ] is d[H] + ]=10 ph-14 -10 ph-14 Then, the pH adjustment process of the slurry by adding chemicals d[H] + Dynamic changes

[0113] (0-1);

[0114] Based on the formula relating concentration (0-1) to pH, the change curve of pH regulation in slurry can be obtained as follows: Figure 1 As shown;

[0115] The motor frequency of the variable frequency pump is the control variable. / hz, slip , This represents the actual frequency control value of the variable frequency pump motor, and the number of pole pairs is... P The rotational speed is r / min, to obtain the motor speed of the variable frequency pump. for:

[0116] (0-2);

[0117] Diameter The cross-sectional area of ​​the variable frequency pump plunger is m 2 , The journey length is m, number of plungers The dosing flow rate of the variable frequency pump is m 3 / h, It is a complex frequency, where:

[0118] (0-3)

[0119] For a given variable frequency pump, its flow rate can be simplified. ,in , The proportional coefficient is a constant parameter that can be calculated through system mechanism modeling or measurement data. For variable frequency pumps, the control input is frequency. The system output is the dosing flow rate of the variable frequency pump. transfer function It is the response, i.e., the system output. , and the stimulus, i.e., the system input The ratio of the Laplace transforms gives the control transfer function of the variable frequency pump for dosing as follows:

[0120] (0-4)

[0121] in, It is a complex frequency. The control transfer function for the variable frequency pump dosing. For flow transfer function, Frequency transfer function ， This is the proportionality coefficient;

[0122] The above parameters can be obtained by calculating the nameplate of a commonly available variable frequency pump on the market.

[0123] Based on the reference of commonly available variable frequency pump nameplates, with a maximum flow rate of 2600 L / h, a maximum frequency of 50 Hz, and a maximum head of 27 m, the following can be calculated:

[0124]

[0125] Dosage concentration is pH adjustment reagents, pulp volume in flotation cell The pH of the flotation cell pulp is Hydrogen ion concentration in flotation cell pulp ore slurry H + concentration ore slurry flow rate Add pH flow rate The pH of the ore slurry is Concentration of ore pulp Ore slurry flow rate The dynamic relationship of the flotation cell adjustment process is as follows:

[0126] (0-5);

[0127] (0-6);

[0128] (0-7);

[0129] in, Indicates the dosage concentration is The dynamic relationship, Indicates the H of the ore slurry fed into the mine. + concentration The dynamic relationship;

[0130] The dynamic reaction process in the flotation cell is complex, but it can be derived from the principle of ion reaction conservation:

[0131] (0-8)

[0132] in, Indicates the hydrogen ion concentration in the flotation cell pulp. The dynamic relationship;

[0133] in is the coefficient of the rate of acid-base neutralization chemical reaction, according to the Arrhenius equation. (0-9);

[0134] The Arrhenius equation is used to describe the rate constant of a chemical reaction. With absolute temperature The changing relationship;

[0135] In the formula, It is the coefficient of the rate of acid-base neutralization chemical reaction. Indicates pre-exponential factor, The apparent activation energy of a solution. Represents the molar gas constant. Indicates absolute temperature;

[0136] Secondly, the inlet and outlet flow rates of the slurry in the flotation cell are set to remain constant. Since the concentration and flow rate of the feed slurry, and other state parameters, change almost continuously, their dynamic changes in the short term are negligible and can be considered constants. These parameters are all dependent parameters. If unchanged, it is considered as the production condition parameter of the input flotation cell. Unchanged, based on the control quantity Post-state and the previous state After linearization, it becomes:

[0137] (0-10);

[0138] The outlet pH of the flotation cell is related to the system parameters and the input production condition parameters of the flotation cell. and control variables Nonlinear functions composed of isocorrelation , Represented as:

[0139] (0-11);

[0140] pH control target desired control in pH regulation control system Controlling error for:

[0141] (0-12)

[0142] Equations 0-9 are simplified by transformation based on the principle of keeping the above parameters unchanged. The derivation of the formulas is as follows:

[0143] (0-13);

[0144] make , , For system output, For system input, Before substitution , Substitute control quantity Simultaneously, simplification is performed using 0-10 and 0-14 equations, followed by linearization at the steady-state equilibrium point. Furthermore, there is a time delay between the complete reaction of the slurry reagents and the sensor measurement and data acquisition. Since it exhibits a time lag characteristic, the transfer function needs to include a time delay element to obtain the transfer function for the pH reaction. It is expressed as follows:

[0145] (0-14);

[0146] In the formula, This is the proportionality coefficient for the pH reaction process. The time constant for the pH reaction process. Given the lag time in the pH reaction stage, and based on the aforementioned control model for the frequency converter dosing, these components are connected in series to form the entire flotation dosing process. The control model is as follows:

[0147] (0-15);

[0148] in, , and as well as These are the parameters to be fitted later.

[0149] For parameter identification of the transfer function of the flotation process control model, specifically the characteristic parameter identification of the model of the first-order inertial element transfer function with time lag, this paper adopts a mathematical method. Commonly used mathematical methods include the tangent method and the two-point method. Taking the transfer function of the first-order inertial element with time lag as an example, it is usually necessary to input the excitation signal ut of the system step response, whose response is yt, and the magnitude of the change in the step input excitation signal is... Steady-state value of step response output and initial value The change is , obtain parameter gain The method for obtaining the value is as follows

[0150] (0-16);

[0151] like Figure 2 As shown, the tangent method can obtain the time values ​​of the positions of points A and B, and thus the two time parameters of the transfer function, the time constant. and lag time The time coordinate corresponding to point A is the system's pure delay time. The time difference between points A and B corresponds to the inertial time constant. In practice, the steepest part of the S-curve is often visually estimated for approximate positioning, but the accuracy of the response curve is also subject to error.

[0152] In the identification of control model parameters, the two-point method significantly improves the lag time compared to the traditional tangent method. The identification accuracy is improved. Its core lies in extracting parameters using the time coordinate difference between the intersection points of the tangents at the inflection points of the step response curve, and determining the lag time using a two-point method. The relationship between parameter identification and actual dynamic curve data of the system can be determined according to the following formula.

[0153] (0-17);

[0154] This allows us to deduce the system's control response. With the steady-state value of the system response Relatedly, for ease of calculation and analysis, the step response is first considered. Convert to dimensionless form The conversion process is represented as follows:

[0155] (0-18);

[0156] Now that the system response has become dimensionless, the transfer function that describes the system's dynamic behavior is... It can be expressed as follows, where the time constant is... and lag time These are the identified parameters.

[0157] (0-19);

[0158] The unit step response of the system can be deduced from the above formula. Under a unit step input, the system's output response is expressed as shown in Equation 0-21. This response characteristic reflects the system's delay and rise time. .

[0159] (0-20);

[0160] To calculate the two parameters in equation 0-20, it is only necessary to select two time points. and ,in And read the corresponding dimensionless response value from the curve data of the system response. and The calculation based on 0-21 can be expressed as follows:

[0161] (0-21);

[0162] Then, further solving equation 0-22 yields... and The value was finally calculated as follows:

[0163] (0-22);

[0164] Since the two-point method solves the problem by substituting the positions of two individual points, there is data that ignores the entire control response curve. Further analysis and verification of errors and reliability are needed to accurately identify the control model of the system's dynamic characteristics.

[0165] To address the errors inherent in the two identification methods mentioned above, the least squares method is adopted to identify control model parameters, thereby reducing the overall identification error. Furthermore, differential evolution (DE) is not only robust but also highly versatile in system parameter identification, effectively addressing complex signal identification tasks. It avoids the problem of poor adaptability during particle iteration, improves mutation and crossover algorithm operations, and incorporates an adaptive random factor. Traditional methods are susceptible to initial value shifts and nonlinear coupling interference; therefore, the improved least squares method combined with differential evolution, compared to the traditional tangent and two-point methods, enhances overall identification accuracy and iteration convergence speed, achieves higher pH control precision, and is better suited to the precise control requirements of flotation industrial scenarios.

[0166] Model identification parameter vector of a first-order inertial element transfer function with time lag The core steps of differential evolution mainly include population initialization, mutation evolution, differential crossover, and optimal selection. A mutation adaptive adjustment mechanism is constructed, with a high mutation rate in the early stage to enhance global exploration, and cosine decay combined with random perturbation in the later stage to improve local development capabilities. The formal representation is as follows:

[0167] (0-23);

[0168] In the formula, It is the value updated by mutation and evolution. It is a random number. It is an individual within a population. It is the maximum value. It is the initial value for mutation and evolution. It is a random update coefficient for mutation and evolution;

[0169] In differential crossover operations, a nonlinear decay of the crossover rate is required to balance local solution and population diversity. Parabolic decay is used to balance population diversity and avoid premature convergence. A function definition can be represented as follows:

[0170] (0-24);

[0171] in These are the initial values ​​for the differential crossover. These are differential crossover random update coefficients.

[0172] In terms of the stability and accuracy of model parameter identification, the Partial Least Squares (PLS) method is a widely used approach, capable of accurately calculating parameters for control system models. Based on the candidate model parameter identification generated by the dynamic DE algorithm, an improved differential evolution approach is introduced to incorporate Partial Least Squares (DE-PLS) for error decoupling and local correction. Since model parameters exhibit strong coupling, PLS corrects these parameters through orthogonal latent variable recursive regression. First, PLS orthogonally decomposes the given data matrix, extracting principal component weight vectors that satisfy the covariance maximization criterion, thus eliminating redundant parameter information. Then, for the identified parameters... PLS is expressed using a recursive regression model as follows, where These are the parameters before the update. This is the actual value. These are samples of collected experimental data;

[0173] (0-25);

[0174] By orthogonally decomposing and extracting the input and output data, and suppressing the cumulative error caused by initial bias, the covariance matrix is ​​optimized. The recursive regression update is represented as follows:

[0175] (0-26);

[0176] The parameter identification problem is transformed into optimal fitting of a low-dimensional latent space, effectively reducing the joint variance of parameter identification. The model updates the error between the model's calculation results for identified parameters and the actual data samples, adjusting the algorithm coefficients to form a global optimal solution. The DE-PLS algorithm is used to construct the objective function for model parameter identification. for:

[0177] (0-27);

[0178] in These are actual measured data. For the response of the parametric model, iterate Second-rate, The parameters identified;

[0179] After iterative updates, the error further decreases, and the identification parameters with the minimum error are the final algorithm identification results. , means as follows:

[0180] (0-28);

[0181] For model identification of the transfer function of a time-lag first-order inertial element, the computational process of the improved differential evolution algorithm introducing partial least squares (DE-PLS) is as follows: Figure 3 .

[0182] The improved differential evolutionary partial least squares (DE-PLS) method is used to iteratively update the identification results of model parameters using pH-regulated control response data.

[0183] Specifically, this invention simultaneously utilizes an adaptive mutation adjustment mechanism and a nonlinear decay of the crossover rate. The adaptive mutation adjustment mechanism dynamically adjusts the mutation factor F, causing it to adapt to the evolutionary process. In the initial iterations, the mutation factor is brought close to its maximum value for global search, avoiding getting trapped in local optima. Later iterations bring the mutation factor close to its minimum value, focusing on fine-tuning within the neighborhood of potential optimal solutions to balance global search and local optimization. The nonlinear decay of the crossover rate dynamically adjusts the crossover rate. The algorithm utilizes a nonlinear decay function to converge to the optimal solution. Initially, the crossover rate is adjusted to its maximum value to explore the crossover effects of multiple factors / combinations. Later, the crossover rate is adjusted to 0 to reduce the disruption to the current optimal solution and focus on local optimization. These two methods work together to optimize the identified parameters, thereby tracking the error changes in model parameter identification in real time and achieving high-precision identification of model parameters.

[0184] A high-precision transfer function model is generated based on model parameters and embedded into a flotation control simulation system. This system receives data from field sensors and outputs control commands such as pump frequency and reagent dosage. The simulation system predicts dynamic pH changes and adjusts pump frequency and reagent dosage in real time, forming a closed loop of "identification-simulation-control" from high-precision parameter identification, transfer function model, flotation control simulation system, real-time dynamic prediction, pump frequency and reagent dosage adjustment to new pH response data. This effectively reduces the error in fitting the flotation control model. pH adjustment is characterized by high nonlinearity, time-varying nature, and strong interference. Traditional models suffer from the drawback of applying linear or time-invariant models. The variability adaptive adjustment mechanism and crossover rate nonlinear decay mechanism introduced in this invention overcome the shortcomings of traditional models and effectively improve the accuracy of pH adjustment control in the flotation process.

[0185] Based on this, an actual pH adjustment process experiment was conducted in a flotation stirred tank, and the experimentally measured response data were obtained as follows: Figure 4 As shown in the figure, the response curve obtained from the measured data is typical of a first-order time-delay control system model, making the DE-PLS identification algorithm suitable for parameter identification of the flotation dosing control system model. Furthermore, the model presented in this application can also identify parameters from simulation data.

[0186] The recognition algorithm result curve is as follows Figure 6 Experiments show that this method can effectively identify the model parameters of the flotation dosing control system. Furthermore, the improved DEPLS identification algorithm exhibits the smallest error compared to other model fitting methods, as shown in the iteration error curve. Figure 5 As shown, the mean absolute error after iteration is as low as 0.01418, which improves the model prediction accuracy compared to other methods. Through dual-driven modeling and identification using both mechanism and data algorithms, the final flotation process control model identification method can accurately characterize the flotation process control system, laying a control data foundation for the implementation of advanced control strategies in the flotation control system.

[0187] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for predicting dynamic changes in parameters in a flotation pH adjustment process model, characterized in that, Includes the following steps: S1. Collect experimental parameters during the flotation pH adjustment process, perform physicochemical analysis, fit a flotation pH adjustment process model, identify parameters of the flotation pH adjustment process model, and calculate the gain of the identified parameters. 、 time constant and system lag time The characteristic correlation; the experimental parameters include pH value change data during the flotation pH adjustment process, flow rate data of pH adjustment reagents, pulp concentration and flow rate, pulp temperature, pulp volume in the flotation cell, and reagent dosage concentration parameters; S2. The DE-PLS method is adopted. DE is the differential evolution algorithm, which performs population initialization, mutation evolution, differential crossover and selects the optimal feature. PLS is the partial least squares method, which accurately calculates the parameter identification of the flotation pH adjustment process model and outputs the parameter with the minimum identification error, thus obtaining the DE-PLS improved flotation pH adjustment process model. S3. Using the DE-PLS improved flotation pH adjustment process model obtained in S2, the dynamic changes of pH during the flotation process are predicted based on the frequency of the variable frequency pump, the concentration and flow rate of the pulp, the pulp temperature and the real-time pH value, and the dosage of reagents is adjusted in real time. The collection of experimental parameters during the flotation pH adjustment process, the physicochemical analysis, and the fitting of the flotation pH adjustment process model specifically include: In an industrial test involving pH adjustment during flotation, data on pH changes during process control, reagent flow rate during pH adjustment, pulp concentration and flow rate, pulp temperature, pulp volume in the flotation cell, reagent concentration parameters, and system lag time were collected and analyzed. and parameter gain The characteristic correlation was determined by measuring the pH lag time and steady-state offset through a step response experiment. In the analysis and calculation of the dynamic response data characteristics, the gains of the three parameters of the first-order time-delay model were calculated. time constant Lag time As a task of identification methods; Physicochemical analysis was conducted on the pH dosing control during the flotation process to obtain the changes in hydrogen ion concentration during the pH dosing adjustment of the pulp. The dynamic changes are as follows: （0-1）； The motor frequency of the variable frequency pump is the control variable. Unit is Hz, slip ratio , This represents the actual frequency control value of the variable frequency pump motor, and the number of pole pairs is... P The rotational speed is The unit is r / min, which gives the motor speed of the variable frequency pump. for: （0-2）； Diameter The cross-sectional area of ​​the variable frequency pump plunger is The unit is m 2 , The journey length is The unit is meters (m), representing the number of plungers. The dosing flow rate of the variable frequency pump is The unit is m 3 / h, It is a complex frequency, where: （0-3）； The control transfer function for variable frequency pump dosing, obtained through system mechanism modeling, is expressed as follows: （0-4）； in, It is a complex frequency. The control transfer function for the variable frequency pump dosing. For flow transfer function, Frequency transfer function ， This is the proportionality coefficient; Dosage concentration is pH adjustment reagents, pulp volume in flotation cell The pH of the flotation cell pulp is Hydrogen ion concentration in flotation cell pulp ore slurry H + concentration ore slurry flow rate Add pH flow rate The pH of the ore slurry is Concentration of ore pulp Ore slurry flow rate The dynamic relationship of the flotation cell adjustment process is as follows: （0-5）； （0-6）； （0-7）； in, Indicates the dosage concentration is The dynamic relationship, Indicates the H of the ore slurry fed into the mine. + concentration The dynamic relationship; The complex dynamic reaction process in the flotation cell is handled based on the principle of ion reaction conservation: （0-8）； in, Indicates the hydrogen ion concentration in the flotation cell pulp. The dynamic relationship; According to the Arrhenius formula, its calculation is as follows: （0-9）； The Arrhenius equation is used to describe the rate constant of a chemical reaction. With absolute temperature The changing relationship; In the formula, It is the coefficient of the rate of acid-base neutralization chemical reaction. Indicates pre-exponential factor, The apparent activation energy of a solution. Represents the molar gas constant. Indicates absolute temperature; Secondly, the inlet and outlet flow rates of the slurry in the flotation cell are set to remain constant. Since the concentration and flow rate of the slurry entering the cell are almost constant, they are considered constant and thus regarded as the production condition parameters input to the flotation cell. Unchanged, based on the control quantity Post-state and the previous state After linearization, it becomes: （0-10）； Nonlinear function of pH at the outlet of the flotation cell , Represented as: （0-11）； In the formula, This indicates the input production condition parameters for the flotation cell. Indicates control variables; pH control target desired control in pH regulation control system Controlling error for: （0-12）； Equations 0-8 are simplified based on the principle of keeping the parameters unchanged. The derivation of the formula is as follows: （0-13）； make , , For system output, For system input, Before substitution , Substitute control quantity Simultaneously simplifying by combining 0-10 and 0-14, we obtain the transfer function for the pH reaction. It is expressed as follows: （0-14）； In the formula, This is the proportionality coefficient for the pH reaction process. The time constant for the pH reaction process. Given the lag time in the pH reaction stage, and based on the control model of the variable frequency pump dosing described above, the entire flotation dosing process can be obtained by connecting these components in series. The control model is as follows: （0-15）； in, , and as well as These are the parameters to be fitted later; For parameter identification of the transfer function of the flotation process control model, specifically the characteristic parameter identification of the transfer function of a first-order inertial element with time lag; taking the transfer function of a first-order inertial element with time lag as an example, then the parameter gain... The value is obtained in the following way: （0-16）； In the formula, The magnitude of the change in the step input excitation signal. The steady-state value of the step response output. The initial value for the step response output; The tangent method, proposed by Ziegler and Nichols, is used to calculate the time constant. and lag time The core of this classic method lies in obtaining the controlled object model parameters through geometric analysis of the system's open-loop step response curve. In the identification of control model parameters, the two-point method significantly improves the lag time compared to the traditional tangent method. The core of the identification accuracy lies in extracting parameters by using the time coordinate difference between the intersection points of the tangents at the inflection points of the step response curve and determining the lag time using the two-point method. The parameter identification and the actual dynamic curve data of the system can be determined according to the relation 0-17. connect: （0-17）； First, the step response Convert to dimensionless form The conversion process is represented as follows: （0-18）； After the response transformation, the transfer function that describes the dynamic behavior of the system is given. It can be expressed as follows: （0-19）； Unit step response of the reverse system Under a unit step input, the system's output response is expressed as shown in Equation 0-20. This response characteristic reflects the system's delay and rise time. : （0-20）； To calculate the two parameters in equation 0-20, it is only necessary to select two time points. and ,in And read the corresponding dimensionless response value from the curve data of the system response. and The calculation based on 0-20 is expressed as follows: （0-21）； Then, further solving equation 0-21 yields... and The final value is as follows: （0-22）。 2. The method as described in claim 1, characterized in that, Step S2 describes the use of the DE-PLS method, where DE performs population initialization, mutation evolution, differential crossover, and selection of the optimal feature. Specifically, this includes: The core steps of DE mainly involve population initialization, mutation and evolution, differential crossover, and selection of the optimal feature. A mutation adaptive adjustment mechanism is constructed, represented as follows: （0-23）； In the formula, It is the value updated by mutation and evolution. It is a random number. It is an individual within a population. It is the maximum value. It is the initial value for mutation and evolution. It is a random update coefficient for mutation and evolution; In differential crossover operations A function definition can be represented as follows: （0-24）； In the formula, These are the initial values ​​for the differential crossover. These are differential crossover random update coefficients.

3. The method as described in claim 2, characterized in that, As described in step S2, PLS performs precise calculations on the parameters of the flotation pH adjustment process model, outputs the parameter with the minimum identification error, and obtains the DE-PLS improved flotation pH adjustment process model, specifically including: For the parameters of identification PLS is expressed using a recursive regression model as follows, where These are the parameters before the update. This is the actual value. These are samples of collected experimental data; （0-25）； By orthogonally decomposing and extracting the input and output data, and suppressing the cumulative error caused by initial bias, the covariance matrix is ​​optimized. The recursive regression update is represented as follows: （0-26）； The model updates its algorithm by calculating the error between the model's computational results and the actual data samples, and the model parameters are identified using the DE-PLS algorithm to construct the objective function. for: （0-27）； in These are actual measured data. For the response of the parametric model, iterate Second-rate, The parameters identified; After iterative updates, the error further decreased, eventually yielding the result with the minimum error. The identification parameters are the final algorithm identification result. , means as follows: （0-28）。 4. The method as described in claim 1, characterized in that, The flotation pH adjustment process is for lead-zinc metal flotation operations.

5. A computer-readable storage medium, characterized in that, The computer-readable medium stores a computer program that can be executed by a computer device to implement the method for predicting dynamic changes in parameters of a flotation pH adjustment process model as described in any one of claims 1 to 4.

6. A computer device, characterized in that, The device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method for predicting dynamic changes in parameters of the flotation pH adjustment process model as described in any one of claims 1 to 4.

7. A computer program product, comprising a computer program / instructions; characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the method for predicting dynamic changes in parameters of the flotation pH adjustment process model as described in any one of claims 1 to 4.

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