A method for optimizing control of flotation based on online quality monitoring

Abstract

The present application relates to a kind of based on online quality monitoring's flotation optimization control method, including time acquisition the data collected in the multiple links of entire flotation process, the data set is obtained by processing the data collected, the causal feature of data set is extracted using convergence cross mapping method, the dynamic relationship model of key operation variable and production index variable is obtained;Design the optimization objective of optimization control based on Lyapunovo Barrier function to realize single-step;Optimal action is searched using time forward rolling type finite time domain optimization strategy, and the optimization control task of cycle forward is realized;Step 8, repeat step 5, 6, 7, and the flotation process is controlled by online optimization.The advantages of the present application are: effectively avoid the disconnection of fixed global optimization target and actual production, and the target variable is reasonably optimized, such as reducing the grade of float tailings, and the grade of float fine product is stable, which has better effect.

Description

Technical Field

[0001] This belongs to the field of intelligent control technology for mineral processing, specifically a method for optimizing the operation and control of the flotation process. Background Technology

[0002] In recent years, with the development of science and technology, the demand for mineral resources has been increasing. Enterprises must improve their economic efficiency by ensuring product quality, increasing production efficiency, and reducing production costs. Foam flotation, as a highly efficient mineral separation technology, has been widely used in modern mineral processing industries.

[0003] Traditional flotation process control typically involves on-site process personnel adjusting parameters such as reagent dosage, aeration rate, and flotation machine cone valve opening degree based on past production experience. This subjective control method is highly arbitrary, and coupled with the harsh on-site process environment and frequent process fluctuations, it leads to poor product quality and instability.

[0004] Because froth flotation is a complex process with multiple inputs and outputs and is affected by many parameters, current methods are unable to establish an accurate process model for the flotation process, making it difficult to implement automated control of the froth flotation process.

[0005] Current research on automatic control of flotation mainly focuses on the study of control strategies for single links or single variables. However, for flotation processes with long production cycles, high internal coupling, and many parameters, it is necessary to fully incorporate data from multiple data sources in the entire flotation process into data modeling and analysis to establish a full-process operation optimization control model. Summary of the Invention

[0006] The purpose of this invention is to provide a flotation optimization control method based on online quality monitoring. This method integrates real-time process data collected by sensors with image feature values ​​extracted by a foam analyzer to form a comprehensive model. It considers the causal characteristics between variables and establishes a reliable predictive control model. Based on the real-time prediction of monitored variables and indicators, it optimizes the control of operational variables such as reagent dosage, aeration rate, and cone valve opening degree in the flotation process.

[0007] The present invention provides a flotation optimization control method based on online quality monitoring, characterized by comprising the following steps:

[0008] Step 1: Real-time acquisition of data from multiple stages throughout the entire flotation process. This mainly includes real-time monitoring data collected by sensors. Image feature data extracted by foam analyzer Control feedback data And incorporate it into subsequent data modeling and analysis;

[0009] Step 2: Real-time monitoring data Control feedback data Dimensionless real-time monitoring data were obtained by performing normalization processing on each data point. and dimensionless control feedback data For image feature data Dummy variable processing is performed to obtain pseudo-coded image feature data. ;

[0010] Step 3: Apply Kalman filtering to the dimensionless real-time monitoring data. Smoothing is performed to obtain smoothed dimensionless real-time monitoring data. The smoothed dimensionless real-time monitoring data Dimensionless control feedback data Pseudo-coded image feature data Combine to obtain the dataset ;

[0011] Step 4: Extract the dataset using the convergent cross-mapping method. The causal characteristics of the operands Sensor monitoring variables With foam state variables We will analyze the causal relationship and select a set of key operational variables. Confirm production indicator variables based on actual needs. Finally, set up the dataset. Remove key operational variables and production indicator variables Other variables are state variables. ;

[0012] Step 5: Using key operational variables Other state variables As input, an extended temporal convolutional network is established to process production index variables. Make predictions and obtain key operational variables. Production indicator variables A dynamic relationship model;

[0013] Step 6: Design an optimization objective based on the Lyapunovo Barrier function to achieve single-step optimization control;

[0014] Step 7: Use a time-forward rolling finite-time domain optimization strategy to search for the optimal action and realize the cyclic forward optimization control task;

[0015] Step 8: Repeat steps 5, 6, and 7 to optimize and control the flotation process online.

[0016] Preferably, the real-time monitoring data This includes underflow velocity and airflow rate for each process, liquid level, temperature, and pH value in each pump tank; and image feature values ​​extracted by the foam analyzer. This includes the RGB values ​​of the points in the image itself, as well as the size and color of the bubbles identified from the image; control feedback data. This includes the cone valve opening degree, the type and amount of chemical added, and the frequency of the feed pump.

[0017] Preferably, the collected real-time monitoring data and control feedback data Normalization was performed using the Min-Max standardization method, with a mapping range of [-1, 1], and the image feature data was then processed. The process involves using dummy variables to transform the data into m numerical features with values ​​of 0 and 1. The Min-Max standardization method is described in the following formula:

[0018] (1)

[0019] In the formula For the collected real-time monitoring data and control feedback data All data for each feature column, and They are respectively for Find the maximum and minimum values.

[0020] Preferably, in step 3, Kalman filtering is used to process the dimensionless real-time monitoring data. Smoothing is performed, and the Kalman filter time update formula is as follows:

[0021]

[0022]

[0023] The Kalman filter state update formula is as follows:

[0024]

[0025]

[0026]

[0027] In the formula and Let represent the posterior state estimates at time k-1 and time k, respectively. It is the prior state estimate at time k. and Let these represent the posterior estimated covariances at time k-1 and time k, respectively (i.e., and The covariance represents the uncertainty of the state. The prior estimate of the covariance at time k ( H is the transformation matrix from state variables to measurements (observations), representing the relationship between states and observations. It is the input to the filter, referring here to dimensionless real-time monitoring data. Dimensionless control feedback data , A is the filter gain matrix, A is the state transition matrix, Q is the process excitation noise covariance (the covariance of the system process), R is the measurement noise covariance, and B is the matrix that transforms the input into the state. It is the residual between actual observation and predicted observation.

[0028] Preferably, step 4, which involves screening key operational variables, includes the following steps;

[0029] Step 4-1: Determine production indicator variables based on actual production conditions. And based on production indicator variables and dataset Construct the dataset at time t Simultaneously construct the operation variables Sensor monitoring variables With foam state variables The feature set, excluding production indicator variables. , with dataset Forming a dataset at time t Then based on and Build and Corresponding shadow manifold , The formula is as follows:

[0030]

[0031]

[0032] Where E is the optimal embedding dimension;

[0033] Step 4-2: Calculate the distance between any two points in the shadow manifold of X and the distance between any two points in the shadow manifold of Y using Euclidean distance. and For each point in the manifold, find E+1 neighbor nodes, from the manifold Obtained through cross mapping The cross-mapping formula is as follows:

[0034]

[0035]

[0036]

[0037] in On the manifold and The Euclidean distance between them;

[0038] Step 4-3, Calculation and The correlation coefficient r is given by the following formula:

[0039]

[0040] As the length L of the input data sequence increases Gradually converges to If the correlation coefficient r converges to a value greater than 0, then it is determined that... arrive A causal relationship exists, that is, the causal relationship between the manipulated variable and the monitored variable is determined based on the value of the correlation coefficient r, and then the monitored variable that needs to be adjusted and its control priority are discovered so that the monitored variable can reach the target value.

[0041] Preferably, the search process for the optimal embedding dimension E includes the following steps:

[0042] The Akaike Information Criterion is used to determine the optimal embedding dimension. The Akaike Information Criterion is based on the concept of entropy and is used to balance the complexity of step 4 and the quality of the fitted data. The complexity of this process is defined as n, the loss function is defined as V, the number of samples is K, and the Akaike Information Criterion is defined as shown in equation (3):

[0043]

[0044] pass An autoregressive model is used to determine the optimal embedding dimension. The autoregressive model is shown in the following equation:

[0045]

[0046] loss function The model complexity is n=E, when The minimum value is the corresponding n, which is the optimal embedding dimension E.

[0047] Preferably, in step 5, key operational variables are used. Other state variables As input, an extended temporal convolutional network is trained on production indicator variables. Make predictions for the output.

[0048] The training of the dilated temporal convolutional network includes the following steps:

[0049] Step 5-1: Set the number of convolutional kernels, kernel size, stride parameters, and set the activation function of the convolutional layer to the ReLU function to establish an M-layer unidirectional causal convolutional network;

[0050] Step 5-2: Apply dilated convolution, with the kernel strided by a certain amount. Skip part of the input, where f is the dilation factor, c is the dilation coefficient, and l is the layer containing the convolution kernel;

[0051] Step 5-3: Add skip connections to residual convolutions and The convolution operation consists of two layers of dilated convolutions and ReLU nonlinear mappings in a residual block. WeightNorm and Dropout are added after each dilated convolution to achieve regularization.

[0052] Preferably, in step 6, an optimization objective is designed based on the Lyapunovo Barrier function.

[0053] The CLBF model based on the Lyapunovo Barrier function is determined by introducing the Lyapunovo Barrier function on top of the model predictive control strategy. The optimization problem based on CLBF-MPC is as follows:

[0054]

[0055]

[0056]

[0057]

[0058] in It is the predicted state trajectory, where S(∆) is a set of piecewise constant functions with period ∆. The number of sampling periods within the prediction range. It is used to represent Cost function satisfy , , This ensures that the cost function is minimized under stable system conditions, thus making Is the system optimization function within the prediction range? The optimal solution, in addition to the constraints mentioned above, also includes the Lyapunovo Barrier function condition.

[0059] Preferably, step 7 employs a time-forward rolling finite-time domain optimization strategy to search for the optimal action;

[0060] The iLQR algorithm is used for rolling optimization. Compared to the LQR algorithm, the dynamic function of iLQR is nonlinear. Therefore, it is necessary to perform Taylor approximate expansion on the local part of the function based on the LQR algorithm, and use Taylor expansion to estimate the local dynamic characteristics of a complex nonlinear function. and cost function The specific formula is as follows:

[0061]

[0062]

[0063] in, The current state parameter refers to the key operational variables selected in step 4. The control parameters at the current moment refer to the key operational variables selected in step 4. These are the actual sampled value and the estimated state parameter value at the current time, respectively. and control parameter estimates difference.

[0064] Dynamic function according to relevant definitions for:

[0065]

[0066] Cost function for:

[0067]

[0068] The control law at the current moment is obtained by using LQR inverse calculation. With control constant ; Perform the following iterative action until convergence:

[0069]

[0070] Compared with the prior art, the beneficial effects of the present invention are:

[0071] This invention overcomes the current production challenges posed by high-frequency noise and high latency in flotation processes. In the modeling process: 1) Kalman filtering is used to smooth the collected data, eliminating high-frequency noise; 2) a convergent cross-mapping method is employed to extract causal features from the data, preserving strong causal relationships, i.e., causal mechanisms; 3) dilated temporal convolutional networks are used for prediction. In predictive control: a time-forward rolling finite-domain optimization strategy is used to achieve online optimization control, effectively avoiding the disconnect between fixed global optimization objectives and actual production. Reasonable optimization of target variables, such as reducing tail grade and stabilizing float grade, has good results. Furthermore, this invention exhibits good robustness to deviations in the production environment from the model or actual environmental disturbances that cause a decline in control performance, and has both theoretical and practical significance for the optimized control of the flotation process. Attached Figure Description

[0072] Figure 1 This is a flowchart of the flotation optimization control method based on online quality monitoring according to the present invention;

[0073] Figure 2 Diagram of the extended temporal convolutional network structure;

[0074] Figure 3 Residual block structure diagram of dilated temporal convolutional network. Detailed Implementation

[0075] The invention will now be further described in conjunction with the accompanying drawings and the actual implementation in the field.

[0076] Reference Figure 1-3 The present invention provides a flotation optimization control method based on online quality monitoring, characterized by comprising the following steps:

[0077] Step 1: Real-time acquisition of data from multiple stages throughout the entire flotation process. This mainly includes real-time monitoring data collected by sensors. Image feature data extracted by foam analyzer Control feedback data And incorporate it into subsequent data modeling and analysis;

[0078] In an example, the real-time monitoring data described in this invention... Specifically, this includes, but is not limited to, the concentration, underflow velocity, and airflow rate of each process, the liquid level, temperature, and pH value of each pump tank; and the image feature values ​​extracted by the foam analyzer. Specifically, this includes, but is not limited to, the RGB values ​​of the points in the image itself, as well as the size and color of the bubbles identified from the image; control feedback data. This includes, but is not limited to, cone valve opening, type and amount of chemical dosing, and feed pump frequency.

[0079] Step 2: Real-time monitoring data Control feedback data Dimensionless real-time monitoring data were obtained by performing normalization processing on each data point. and dimensionless control feedback data For image feature data Dummy variable processing is performed to obtain pseudo-coded image feature data. ;

[0080] This invention will collect real-time monitoring data and control feedback data Normalization was performed using the Min-Max standardization method, with a mapping range of [-1, 1], and the image feature data was then processed. The process involves using dummy variables to transform the data into m numerical features with values ​​of 0 and 1. The Min-Max standardization method is described in the following formula:

[0081]

[0082] In the formula For the collected real-time monitoring data and control feedback data All data for each feature column, and They are respectively for Find the maximum and minimum values.

[0083] Step 3: Apply Kalman filtering to the dimensionless real-time monitoring data. Smoothing is performed to obtain smoothed dimensionless real-time monitoring data. The smoothed dimensionless real-time monitoring data Dimensionless control feedback data and pseudo-coded image feature data Combine to obtain the dataset ;

[0084] In step 3, Kalman filtering is used to process the dimensionless real-time monitoring data. Smoothing is performed, and the Kalman filter time update formula is as follows:

[0085]

[0086]

[0087] The Kalman filter state update formula is as follows:

[0088]

[0089]

[0090]

[0091] In the formula and Let represent the posterior state estimates at time k-1 and time k, respectively. This is the prior state estimate at time k, which is also the output of the Kalman filter update. Here it is the smoothed, dimensionless real-time monitoring data. ;

[0092] and Let the posterior estimated covariances at time k-1 and time k be represented respectively. It is the prior estimate covariance at time k, and H is the transformation matrix from state variables to measurements;

[0093] It is the input to the filter, referring here to dimensionless real-time monitoring data. ;

[0094] A is the filter gain matrix, A is the state transition matrix, Q is the process excitation noise covariance, which is also the system process covariance, R is the measurement noise covariance, and B is the matrix that transforms the input into the state. It is the residual between actual observation and prior state estimation.

[0095] High-frequency noise was eliminated by smoothing the acquired data using Kalman filtering. The meanings of the variables remained unchanged.

[0096] Step 4: Extract the dataset using the convergent cross-mapping method. The causal characteristics of the operands Sensor monitoring variables With foam state variables We will analyze the causal relationship and select a set of key operational variables. Confirm production indicator variables based on actual needs. Finally, set up the dataset. Remove key operational variables and production indicator variables Other variables are state variables. Step 4, screening key operational variables, includes the following steps;

[0097] Step 4-1: Determine production indicator variables based on actual production conditions. Taking [the product name] as an example, production indicator variables include the grade of high-quality products, the grade of low-quality products, and the grade of high-quality products after initial cleaning. Based on these production indicator variables... and dataset Construct the dataset at time t Simultaneously construct the operation variables Sensor monitoring variables With foam state variables The feature set, excluding production indicator variables. , with dataset Forming a dataset at time t Then based on and Build and Corresponding shadow manifold , The formula is as follows:

[0098]

[0099]

[0100] Where E is the optimal embedding dimension.

[0101] Step 4-2: Calculate the distance between any two points in the shadow manifold of X and the distance between any two points in the shadow manifold of Y using Euclidean distance. and For each point in the manifold, find E+1 neighbor nodes, from the manifold Obtained through cross mapping The cross-mapping formula is as follows:

[0102]

[0103]

[0104]

[0105] in On the manifold and The Euclidean distance between them.

[0106] Step 4-3, Calculation and The correlation coefficient r is given by the following formula:

[0107]

[0108] As the length L of the input data sequence increases Gradually converges to If the correlation coefficient r converges to a value greater than 0, then it is determined that... arrive A causal relationship exists. This invention determines the causal relationship between key operational variables and production indicator variables based on the correlation coefficient r, and then identifies the key operational variables that need to be adjusted to achieve the target value of the production indicator variable. Taking the field as an example, this step can be used to screen out the sets of key operational variables that respectively enable the production indicator variable to reach the range of [64, 66] for the floating grade and the floating tail grade to be lower than 22.

[0109] The search process for the optimal embedding dimension E described in step 4-1 of this invention includes the following steps:

[0110] The Akaike Information Criterion is used to determine the optimal embedding dimension. Based on the concept of entropy, the Akaike Information Criterion is used to balance the complexity of the model generated in step 4 with its goodness of fit to the data. Model complexity is defined as n, the loss function is defined as V, and the number of samples is K. The Akaike Information Criterion is defined as follows:

[0111]

[0112] pass An autoregressive model is used to determine the optimal embedding dimension. The autoregressive model is shown in the following equation:

[0113]

[0114] loss function The model complexity is n=E, when The minimum value is the corresponding n, which is the optimal embedding dimension E.

[0115] The convergent cross-mapping method described in step four is used to extract causal features from the data, preserving strong causal relationships, i.e., causal mechanisms. In practice, the key operational variables obtained from step four that enable the production index variable float quality level to reach the range of [64, 66] include dosage, opening degree of the three-stage sweeping cone valve, opening degree of the two-stage fine selection cone valve, and opening degree of the first-stage sweeping cone valve.

[0116] Step 5: Using key operational variables Other state variables As input, an extended temporal convolutional network is established to process production index variables. Make predictions and obtain key operational variables. Production indicator variables The dynamic relationship model; taking the field as an example, the extended temporal convolutional network is trained with two months of historical data to predict the production index variables, namely the floating quality grade, the floating tail grade and the first sweep quality grade, and predict the index changes in the half hour after the current moment.

[0117] The training of the dilated temporal convolutional network includes the following steps:

[0118] Step 5-1: Set the number of convolutional kernels, kernel size, stride parameters, and set the activation function of the convolutional layer to the ReLU function to establish an M-layer unidirectional causal convolutional network;

[0119] Step 5-2: Apply dilated convolution, with the kernel strided by a certain amount. Skip part of the input, where f is the dilation factor, c is the dilation coefficient, and l is the layer containing the convolution kernel;

[0120] Step 5-3: Add skip connections to residual convolutions and The convolution operation consists of two layers of dilated convolutions and ReLU nonlinear mappings in a residual block. WeightNorm and Dropout are added after each dilated convolution to achieve regularization.

[0121] Step 6: Design an optimization objective based on the Lyapunovo Barrier function to achieve single-step optimization control;

[0122] In step 6, an optimization objective based on the Lyapunovo Barrier function is designed.

[0123] The CLBF model based on the Lyapunovo Barrier function is determined by introducing the Lyapunovo Barrier function on top of the model predictive control strategy. The optimization problem based on CLBF-MPC is as follows:

[0124]

[0125]

[0126]

[0127]

[0128] in It is the predicted state trajectory, that is, the changing trend of the production indicator variables obtained in step five, where S(∆) is a set of piecewise constant functions with a period of ∆. The number of sampling periods within the prediction range. It is used to represent Cost function satisfy , , This ensures that the cost function is minimized under stable system conditions, thus making Is the system optimization function within the prediction range? The optimal solution, in addition to the constraints mentioned above, also includes the LyapunovoBarrier function condition.

[0129] Step 7: Using a time-forward rolling finite-time domain optimization strategy, search for the optimal action, i.e. the optimal control strategy, corresponding to the indicator change trend obtained in Step 5, to realize the cyclic forward optimization control task.

[0130] The aforementioned time-forward rolling finite-time domain optimization strategy searches for the optimal action;

[0131] The iLQR algorithm is used for rolling optimization. Compared to the LQR algorithm, the dynamic function of iLQR is nonlinear. Therefore, it is necessary to perform a Taylor approximation expansion on the local part of the function based on the LQR algorithm. The local characteristics of a complex nonlinear function are estimated by using the Taylor expansion. The specific formula is as follows:

[0132]

[0133]

[0134] in, The dynamic function is obtained according to the relevant definition. for:

[0135]

[0136] Cost function for:

[0137]

[0138] The control law at the current moment is obtained by using LQR inverse calculation. With control constant ; Execute the following loop until convergence.

[0139]

[0140] The convergence result of this step is the optimal control action obtained through the search.

[0141] Step 8: Repeat steps 5, 6, and 7 to optimize and control the flotation process online.

[0142] To further illustrate with an example of on-site control: Assuming the current concentrate grade is 65, step 5 predicts that the concentrate grade will be 60 half an hour later, and the production target concentrate grade is less than 64, which is below the normal range. According to the optimization target designed in step 6, the concentrate grade is adjusted in advance to keep it within the normal range in the second half hour. Step 7 obtains the optimal control action, such as starch dosage +300 and three-sweep cone valve opening degree -0.5. The flotation site is precisely controlled through this control command.

[0143] This invention combines extended temporal convolutional networks for prediction. In predictive control, a time-forward rolling finite-domain optimization strategy is used to achieve online optimization control, effectively avoiding the disconnect between fixed global optimization objectives and actual production. It achieves good results in reasonably optimizing target variables, such as reducing the grade of the float tail and stabilizing the grade of the float. Furthermore, this invention exhibits good robustness to control performance degradation caused by deviations in the production environment and model, or by actual environmental disturbances, and has both theoretical and practical significance for the optimized control of the flotation process.

Claims

1. A flotation optimization control method based on online quality monitoring, characterized in that, Includes the following steps: Step 1: Real-time acquisition of data from multiple stages throughout the entire flotation process. This mainly includes real-time monitoring data collected by sensors. Image feature data extracted by foam analyzer Control feedback value data And incorporate it into subsequent data modeling and analysis; Step 2: Real-time monitoring data Control feedback data Dimensionless real-time monitoring data were obtained by performing normalization processing on each data point. and dimensionless control feedback data For image feature data Dummy variable processing is performed to obtain pseudo-coded image feature data. ; Step 3: Apply Kalman filtering to the dimensionless real-time monitoring data. Smoothing is performed to obtain smoothed dimensionless real-time monitoring data. The smoothed dimensionless real-time monitoring data Dimensionless control feedback data and pseudo-coded image feature data Combine to obtain the dataset ; Step 4: Extract the dataset using the convergent cross-mapping method. The causal characteristics of the operands Sensor monitoring variables With foam state variables We will analyze the causal relationship and select a set of key operational variables. Confirm production indicator variables based on actual needs. Finally, set up the dataset. Remove key operational variables and production indicator variables Other variables are state variables. ; Step 5: Using key operational variables Other state variables As input, an extended temporal convolutional network is trained on production indicator variables. Make predictions and obtain key operational variables. Production indicator variables A dynamic relationship model; Step 6: Design an optimization objective based on the Lyapunovo Barrier function to achieve single-step optimization control; Step 7: Use a time-forward rolling finite-time domain optimization strategy to search for the optimal action and realize the cyclic forward optimization control task; Step 8: Repeat steps 5, 6, and 7 to optimize and control the flotation process online.

2. The flotation optimization control method based on online quality monitoring according to claim 1, characterized in that, The real-time monitoring data This includes underflow velocity and airflow rate for each process, liquid level, temperature, and pH value in each pump tank; and image feature data extracted by a foam analyzer. This includes the RGB values ​​of the points in the image itself, as well as the size and color of the bubbles identified from the image; control feedback data. This includes the cone valve opening degree, the type and amount of chemical added, and the frequency of the feed pump.

3. The flotation optimization control method based on online quality monitoring according to claim 1, characterized in that, The collected real-time monitoring data and control feedback data Normalization was performed using the Min-Max standardization method, with a mapping range of [-1, 1], and the image feature data was then processed. The process involves using dummy variables to transform the data into m numerical features with values ​​of 0 and 1. The Min-Max standardization method is described in the following formula: In the formula For the collected real-time monitoring data and control feedback data All data for each feature column, and They are respectively for Find the maximum and minimum values.

4. The flotation optimization control method based on online quality monitoring according to claim 1, characterized in that, In step 3, Kalman filtering is used to process the dimensionless real-time monitoring data. Smoothing is performed, and the Kalman filter time update formula is as follows: The Kalman filter state update formula is as follows: In the formula and Let represent the posterior state estimates at time k-1 and time k, respectively. This is the prior state estimate at time k, which is also the output of the Kalman filter update. Here it is the smoothed, dimensionless real-time monitoring data. ; and Let the posterior estimated covariances at time k-1 and time k be represented respectively. It is the prior estimate covariance at time k, and H is the transformation matrix from state variables to measurements; It is the input to the filter, referring here to dimensionless real-time monitoring data. ; A is the filter gain matrix, A is the state transition matrix, Q is the process excitation noise covariance, which is also the system process covariance, R is the measurement noise covariance, and B is the matrix that transforms the input into the state. It is the residual between actual observation and prior state estimation.

5. The flotation optimization control method based on online quality monitoring according to claim 1, characterized in that, Step 4, which involves screening key operational variables, includes the following steps; Step 4-1: Determine production indicator variables based on actual production conditions. And based on production indicator variables and dataset Construct the dataset at time t Simultaneously construct the operation variables Sensor monitoring variables With foam state variables The feature set, excluding production indicator variables. , with dataset Forming a dataset at time t Then based on and Build and Corresponding shadow manifold , The formula is as follows: Where E is the optimal embedding dimension; Step 4-2: Calculate the distance between any two points in the shadow manifold of X and the distance between any two points in the shadow manifold of Y using Euclidean distance. and For each point in the manifold, find E+1 neighbor nodes, from the manifold Obtained through cross mapping The cross-mapping formula is as follows: in On the manifold and The Euclidean distance between them; Step 4-3, Calculation and The correlation coefficient r is given by the following formula: As the length L of the input data sequence increases Gradually converges to If the correlation coefficient r converges to a value greater than 0, then it is determined that... arrive A causal relationship exists, that is, the causal relationship between the manipulated variable and the monitored variable is determined based on the value of the correlation coefficient r, and then the monitored variable that needs to be adjusted and its control priority are discovered so that the monitored variable can reach the target value.

6. The flotation optimization control method based on online quality monitoring according to claim 5, characterized in that, The search process for the optimal embedding dimension E includes the following steps: The Akaike Information Criterion is used to determine the optimal embedding dimension. Based on the concept of entropy, the Akaike Information Criterion is used to balance the complexity of step 4 and the quality of the fitted data. The complexity of this process is defined as n, the loss function is defined as V, and the number of samples is K. The Akaike Information Criterion is defined as follows: pass An autoregressive model is used to determine the optimal embedding dimension. The autoregressive model is shown in the following equation: loss function The model complexity is n=E, when The minimum value is the corresponding n, which is the optimal embedding dimension E.

7. The flotation optimization control method based on online quality monitoring according to claim 1, characterized in that, In step 5, the key operational variables are... Other state variables As input, an extended temporal convolutional network is trained on production indicator variables. To predict the output, training the dilated temporal convolutional network includes the following steps: Step 5-1: Set the number of convolutional kernels, kernel size, stride parameters, and set the activation function of the convolutional layer to the ReLU function to establish an M-layer unidirectional causal convolutional network; Step 5-2: Apply dilated convolution, with the kernel strided by a certain amount. Skip part of the input, where f is the dilation factor, c is the dilation coefficient, and l is the layer containing the convolution kernel; Step 5-3: Add skip connections to residual convolutions and The convolution operation consists of two layers of dilated convolutions and ReLU nonlinear mappings in a residual block. WeightNorm and Dropout are added after each dilated convolution to achieve regularization.

8. The flotation optimization control method based on online quality monitoring according to claim 1, characterized in that, In step 6, an optimization objective based on the Lyapunovo Barrier function is designed. The CLBF model based on the Lyapunovo Barrier function is determined by introducing the Lyapunovo Barrier function on top of the model predictive control strategy. The optimization problem based on CLBF-MPC is as follows: in It is the predicted state trajectory, where S(∆) is a set of piecewise constant functions with period ∆. The number of sampling periods within the prediction range. It is used to represent Cost function satisfy , , This ensures that the cost function is minimized under stable system conditions, thus making Is the system optimization function within the prediction range? The optimal solution, in addition to the constraints mentioned above, also includes the Lyapunovo Barrier function condition.

9. The flotation optimization control method based on online quality monitoring according to claim 1, characterized in that, Step 7 describes the use of a time-forward rolling finite-time domain optimization strategy to search for the optimal action. The iLQR algorithm is used for rolling optimization. Compared to the LQR algorithm, the dynamic function of iLQR is nonlinear. Therefore, it is necessary to perform Taylor approximate expansion on the local part of the function based on the LQR algorithm, and use Taylor expansion to estimate the local dynamic characteristics of a complex nonlinear function. and cost function The specific formula is as follows: in, The current state parameter refers to the key operational variables selected in step 4. The control parameters at the current moment refer to the key operational variables selected in step 4. These are the actual sampled value and the estimated state parameter value at the current time, respectively. and control parameter estimates difference; Dynamic function according to relevant definitions for: Cost function for: The control law at the current moment is obtained by using LQR inverse calculation. With control constant ; Perform the following iterative action until convergence; 。

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