CN116186993A - Flotation optimization control method based on online quality monitoring - Google Patents
Flotation optimization control method based on online quality monitoring Download PDFInfo
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Abstract
The invention relates to a flotation optimization control method based on online quality monitoring, which comprises the steps of collecting data collected by a plurality of links in the whole flotation process, processing the collected data to obtain a data set, extracting causal features of the data set by adopting a convergence cross mapping method, and obtaining a dynamic relation model of key operation variables and production index variables; designing an optimization target for realizing single-step optimization control based on Lyapunovo Barrier functions; searching for optimal actions by adopting a time forward rolling type finite time domain optimization strategy, and realizing a circular forward optimization control task; and 8, repeating the steps 5, 6 and 7, and optimally controlling the flotation process on line. The invention has the advantages that: the method effectively avoids the disconnection of a fixed global optimization target and actual production, reasonably optimizes target variables, and has better effects of reducing the tail floating grade and stabilizing the floating quality level.
Description
Technical Field
The invention belongs to the technical field of intelligent control of mineral separation processes, and particularly relates to an operation optimization control method for a flotation process.
Background
In recent years, with the development of science and technology, the demand for mineral resources has been increasing. Enterprises have to improve the economic benefit by ensuring the product quality, improving the production efficiency and reducing the production cost. Froth flotation is a highly efficient mineral separation technique that is commonly used in the modern mineral separation industry.
The traditional flotation process control is usually realized by on-site technicians adjusting parameters such as the dosage, the aeration quantity, the cone valve opening degree of a flotation machine and the like according to the past production experience. The control mode through subjective judgment has strong randomness, and the on-site process environment is bad, the process fluctuation is frequent, so that the product quality is poor and the stability is poor.
Since froth flotation is a complex process with multiple inputs and outputs and coupling and is affected by numerous parameters, the current methods have difficulty in establishing an accurate process model for the flotation process, and thus the automated control of the froth flotation process is difficult to implement.
The current automatic control research of flotation is mainly focused on the research of single links or single variable control strategies, but aiming at the flotation process with long production period, high internal coupling degree and multiple parameters, a plurality of data source data in the whole flotation process are required to be fully added into data modeling analysis, and a full-process operation optimization control model is established.
Disclosure of Invention
The invention aims to provide a flotation optimization control method based on online quality monitoring, which is characterized in that real-time flow data acquired by a sensor and an image characteristic value extracted by a foam analyzer are comprehensively modeled, a reliable predictive control model is established by considering causal characteristics among variables, and based on real-time prediction of monitoring variables and indexes, the operation variables such as the dosage, the aeration quantity, the cone valve opening degree and the like in the flotation process are optimally controlled.
The invention discloses a flotation optimization control method based on online quality monitoring, which is characterized by comprising the following steps of:
step 1, collecting data D collected by a plurality of links in the whole flotation process in real time, wherein the data D mainly comprises real-time monitoring data D collected by a sensor 1 Image characteristic value D extracted by foam analyzer 2 An operation control feedback value D 3 Adding the data into the subsequent data modeling analysis;
step 2, real-time monitoring data D 1 Control feedback data D 2 Respectively carrying out normalization processing to obtain dimensionless real-time monitoring data D 1 ' non-dimensional control feedback data D 2 ' image characteristic data D 3 Dummy variable processing is carried out to obtain pseudo-coded image characteristic data D 3 ′；
Step 3, adopting Kalman filtering to monitor dimensionless real-time data D 1 ' smoothing to obtain smoothed dimensionless real-time monitoring data D 1 ", the smoothed dimensionless real-time monitoring data D 1 "dimensionless control feedback data D 2 ' pseudo-encoded image characteristic data D 3 'combining to obtain a data set D';
step 4, extracting causal characteristics of the data set D' by adopting a convergence cross mapping method, and aiming at the operation variable
Sensor monitoring variable +.>
Is>
Is analyzed for causality of (a) and a key operation variable set is screened out +.>
Confirming production index variable according to actual demand>
Finally, the data set D' is set to remove the key operation variable T i And a production index variable T o Other than variables being other state variables T s ；
Step 5, using key operation variable T i And other state variables T s As input, build expansion time sequence convolution network, for production index variable T o Predicting to obtain key operation variable T i And production index variable T o Is a dynamic relationship model of (1);
step 6, designing an optimization target for realizing single-step optimization control based on Lyapunovo Barrier functions;
step 7, searching for an optimal action by adopting a time forward rolling type finite time domain optimization strategy, and realizing a circular forward optimization control task;
and 8, repeating the steps 5, 6 and 7, and optimally controlling the flotation process on line.
Preferably, said real-time monitoring data
The underflow speed and air flow rate, the liquid level of each pump pool, the temperature and the PH value of each flow path are included; image characteristic value extracted by foam analyzer
The RGB values of the point locations of the image itself are included, as well as the foam size and color identified from the image; operation control feedback value +.>
Including cone valve opening, dosage type and quantity, and dosing pump frequency.
Preferably, the collected real-time monitoring data D 1 And an operation control feedback value D 3 Normalization processing and mapping are carried out by using Min-Max standardization methodIn the range of [ -1,1]And the image characteristic value D 2 Processing by means of dummy variables, converting into m numerical characteristics with 0,1 values, wherein the formula of the Min-Max standardization method is as follows:
in which x is i For the collected real-time monitoring data D 1 And operation control feedback data D 3 Is defined as the total data of each feature column, min (x i ) And max (x) i ) Is respectively to x i The maximum and minimum values are found.
Preferably, in the step 3, the real-time monitoring data D of dimensionless number is obtained by Kalman filtering 1 ' smoothing process, wherein the Kalman filter time update formula is as follows:
the Kalman filter state update formula is as follows:
in the middle of
And->
Posterior state estimation values respectively representing k-1 time and k time,/>
Is the prior state estimation value of k time, P k-1 And P k The a posteriori estimated covariance at time k-1 and time k respectively (i.e.)>
And->
Covariance of (c) representing uncertainty of state), +.>
Is the a priori estimated covariance of the k moment (+.>
Covariance of) H is the state variable to measurement (observation) transition matrix, representing the relationship connecting the states and observations, z k Is the filtered input, here dimensionless real-time monitoring data D 1 ' non-dimensional control feedback data D 2 ’，K k Is the filter gain matrix, a is the state transition matrix, and Q is the process excitation noise covariance (covariance of the system process). R is the measurement noise covariance, B is the matrix that converts the input into states, +.>
Is the residual of the actual observation and the predicted observation.
Preferably, the step 4 of screening the key operation variables includes the following steps;
step 4-1, determining a production index variable T according to production practice o And based on production index variable T o And data set D' construct data set Y (t) at time t;simultaneously constructing operating variables
Sensor monitoring variable +.>
Is>
Excluding the production index variable T therein o Forming a time-of-t dataset X (t) with dataset D'; then constructing a shadow manifold M corresponding to X (t) and Y (t) based on the X (t) and Y (t) X 、M Y The formula is as follows:
M X ＝{x (t) }x (t) ＝<X (t) ,X (t-τ) ,X (t-2τ) ,…,X (t-(E-1)τ) >
M Y ＝{y (t) }y (t) ＝<Y (t) ,Y (t-τ) ,Y (t-2τ) ,…,Y (t-(E-1)τ) >
wherein E is the optimal embedding dimension;
step 4-2, calculating the distance between any two points of the shadow manifold of X and the distance between any two points of the shadow manifold of Y by adopting Euclidean distance, and performing the calculation on the shadow manifold M X And M Y Finding E+1 neighbor nodes from manifold M Y Obtained by cross mapping
The cross-map formula is as follows:
w i ＝m i /∑m j
wherein the method comprises the steps of
Representing y on manifold (t) And->
Euclidean distance between them;
step 4-3, calculating
And x (t) The correlation coefficient r of (2) is as follows:
as the length L of the input data sequence increases,
gradually converge to x (t) I.e. the correlation coefficient r converges to a value greater than 0, then the decision is made from x (t) To y (t) And judging the causal relation between the operation variable and the monitoring variable according to the value of the correlation coefficient r, and further mining the monitoring variable and the control priority thereof which need to be regulated to enable the monitoring variable to reach the target value.
Preferably, the searching process of the optimal embedding dimension E includes the following steps:
judging the optimal embedding dimension by using a red pool information criterion, wherein the red pool information criterion is based on the concept of entropy and is used for balancing the complexity of the process of the step 4 and the superiority of fitting data; the complexity of the process is defined as n, a loss function V is defined, the number of samples is K, and the red pool information criterion is defined as shown in a formula (3):
by x (t) To determine the best embedding dimension, autoregressiveThe model is shown as follows:
loss function
Model complexity n=e, when AIC (n) And taking the minimum value, wherein the corresponding n is the optimal embedding dimension E.
Preferably, in the step 5, the key operation variable T is used i With other state variables T s As input, training the expansion time sequence convolution network for production index variable T o Predictions are made for the outputs.
The step of establishing the expansion time sequence convolution network comprises the following steps:
step 5-1: setting the number of convolution kernels, the size of the convolution kernels and step parameters, setting an activation function of a convolution layer as a relu function, and establishing a unidirectional causal convolution network of an M layer;
step 5-2: applying a dilation convolution, the convolution kernel is divided by a step f=c l Skipping part of input, wherein f is an expansion factor, c is an expansion coefficient, and l is a layer where a convolution kernel is located;
step 5-3: layer jump connection with residual convolution and 1×1 convolution operation are added, one residual block comprises two layers of expansion convolution and relu nonlinear mapping, and weight norm and Dropout are added after each hole convolution to realize regularization.
Preferably, the optimization objective based on Lyapunovo Barrier function is designed in the step 6,
the CLBF model based on Lyapunovo Barrier functions is determined by introducing Lyapunovo Barrier functions on the basis of model predictive control strategies, and the optimization problem based on the CLBF-MPC design is as follows:
wherein the method comprises the steps of
Is a predicted state trajectory, S (delta) is a piecewise constant function set with period delta, P N To predict the number of sampling cycles in the range, W c (x, u) is used to denote +.>
Cost function->
Satisfy L (0, 0) =0, +.>
So as to obtain the minimum value of the cost function under the condition of stable system, and thus, u (t) is the system optimization function in the prediction range P N The optimal solution on delta includes Lyapunovo Barrier function conditions in addition to the constraints described above.
Preferably, the step 7 searches for the optimal action by using a time forward scrolling type finite time domain optimization strategy;
the rolling optimization is carried out by adopting an iLQR algorithm, compared with the LQR algorithm, the dynamic function of the iLQR is nonlinear, so that the approximate expansion of Taylor is needed to be carried out on the function part on the basis of the LQR algorithm, and the local dynamic characteristic of a complex nonlinear function is estimated through the Taylor display
And cost function->
The specific formula is as follows:
wherein x is t The key operation variable filtered in the step 4 is the state parameter at the current moment, u t The key operation variables screened in step 4 are referred to herein as current time control parameters,
the actual sampling value at the current moment and the state parameter estimation value at the current moment are respectively +.>
And control parameter estimation +.>
Is a difference between (a) and (b).
From the correlation definition a dynamic function f (x t ,u t ) The method comprises the following steps:
cost function c (x t ,u t ) The method comprises the following steps:
obtaining a current moment control law K by using LQR reverse push t And control constant k t The method comprises the steps of carrying out a first treatment on the surface of the The following loop actions are performed until convergence:
for t＝1to T
x t+1 ＝f(x t ,u t )
compared with the prior art, the invention has the beneficial effects that:
the method overcomes the current production situation of complex dynamic characteristics such as high-frequency noise, high time delay and the like in the current flotation process. During the modeling process: 1) The Kalman filtering is utilized to carry out smoothing treatment on the acquired data, so that high-frequency noise is eliminated; 2) Extracting causal features of the data by adopting a convergence cross mapping method, and retaining a strong causal relationship, namely a causality mechanism; 3) Predicting by combining with a dilation time sequence convolution network; in predictive control: the online optimization control is realized by using a time forward rolling type finite time domain optimization strategy, the disconnection between a fixed global optimization target and actual production is effectively avoided, and the method has good effects on reasonable optimization of target variables, such as reduction of tail floating grade and stabilization of floating quality level. Meanwhile, the method has better robustness on the reduction of control performance caused by the deviation of the production environment and the model or the interference of the actual environment, and has theoretical and practical significance on the optimal control of the flotation process.
Drawings
FIG. 1 is a flow chart of the flotation optimization control method based on-line quality monitoring of the present invention;
FIG. 2 is a block diagram of a dilation timing convolutional network;
FIG. 3 is a diagram of a dilation timing convolutional network residual block structure.
Detailed Description
The invention will be further described with reference to the accompanying drawings and in the context of in-situ implementation.
Referring to fig. 1-3, the flotation optimization control method based on-line quality monitoring of the invention is characterized by comprising the following steps:
step 1, collecting data D collected by a plurality of links in the whole flotation process in real time, wherein the data D mainly comprises sensingReal-time monitoring data D collected by device 1 Image characteristic value D extracted by foam analyzer 2 An operation control feedback value D 3 Adding the data into the subsequent data modeling analysis;
in an example, the real-time monitoring data of the present invention
Specifically including, but not limited to, concentration, underflow speed and air flow, individual pump sump level, temperature and PH of each flow path; image characteristic value extracted by foam analyzer>
Specifically including, but not limited to, RGB values of the image's own points, and foam size and color identified from the image; operation control feedback value +.>
Including but not limited to cone valve opening, dosage type and amount, and dosing pump frequency.
Step 2, real-time monitoring data D 1 Control feedback data D 3 Respectively carrying out normalization processing to obtain dimensionless real-time monitoring data D 1 ' non-dimensional control feedback data D 3 ' image characteristic data D 2 Dummy variable processing is carried out to obtain pseudo-coded image characteristic data D 2 ′；
The invention monitors the collected real-time monitoring data D 1 And an operation control feedback value D 3 Normalization processing is carried out by using Min-Max standardization method, and the mapping range is [ -1,1]And the image characteristic value D 2 Processing by means of dummy variables, converting into m numerical characteristics with 0,1 values, wherein the formula of the Min-Max standardization method is as follows:
in which x is i For real-time monitoring data collectedD 1 And operation control feedback data D 3 Is defined as the total data of each feature column, min (x i ) And max (x) i ) Is respectively to x i The maximum and minimum values are found.
Step 3, adopting Kalman filtering to monitor dimensionless real-time data D 1 ' smoothing to obtain smoothed dimensionless real-time monitoring data D 1 "the smoothed dimensionless real-time monitoring data D 1 Non-dimensional control feedback data D 3 ' pseudo-encoded image characteristic data D 2 'combining to obtain a data set D';
in the step 3, kalman filtering is adopted to monitor the dimensionless real-time data D 1 ' smoothing process, wherein the Kalman filter time update formula is as follows:
the Kalman filter state update formula is as follows:
in the middle of
And->
Posterior state estimation values respectively representing k-1 time and k time,/>
Is the prior state estimation value at the moment k and is also the output of Kalman filtering update, and is the dimensionless real-time monitoring data D after smoothing 1 ″；
P k-1 And P k The a posteriori estimated covariance at k-1 and k times respectively,
is the prior estimated covariance at time k, H is the state variable to measured conversion matrix;
z k is the filtered input, here dimensionless real-time monitoring data D 1 ′；
K k Is the filter gain matrix, a is the state transition matrix, Q is the process excitation noise covariance, also the covariance of the system process, R is the measurement noise covariance, B is the matrix that converts the input into state,
is the residual of the actual observation and the prior state estimation.
The Kalman filtering is utilized to carry out smoothing treatment on the acquired data, so that high-frequency noise is eliminated, and the meaning of each variable D' is unchanged.
Step 4, extracting causal characteristics of the data set D' by adopting a convergence cross mapping method, and aiming at the operation variable
Sensor monitoring variable +.>
Is>
Is analyzed for causality of (2) and key is screened outSet of operating variables +.>
Confirming production index variable according to actual demand>
Finally, the data set D' is set to remove the key operation variable T i And a production index variable T o Other than variables being other state variables T s . The step 4 of screening the key operation variables comprises the following steps of;
step 4-1, determining a production index variable T according to production practice o For example, the production index variables include float grade, float tail grade, and sweep grade. Based on production index variable T o And data set D' construct data set Y (t) at time t; simultaneously constructing operating variables
Sensor monitoring variable +.>
Is>
Excluding the production index variable T therein o Forming a time-of-t dataset X (t) with dataset D'; then constructing a shadow manifold M corresponding to X (t) and Y (t) based on the X (t) and Y (t) X 、M Y The formula is as follows:
M X ＝{x (t) }x (t) ＝<X (t) ,X (t-τ) ,X (t-2τ) ,…,X (t-(E-1)τ) >
M Y ＝{y (t) }y (t) ＝<Y (t) ,Y (t-τ) ,Y (t-2τ) ,…,Y (t-(E-1)τ) >
where E is the optimal embedding dimension.
Step 4-2, calculating the distance between any two points of the shadow manifold of X by adopting Euclidean distance to obtainAnd the distance between any two points of the shadow manifold of Y, and the shadow manifold M X And M Y Finding E+1 neighbor nodes from manifold M Y Obtained by cross mapping
The cross-map formula is as follows:
w i ＝m i /∑m j
wherein the method comprises the steps of
Representing y on manifold (t) And->
Euclidean distance between them.
Step 4-3, calculating
And x (t) The correlation coefficient r of (2) is as follows:
as the length L of the input data sequence increases,
gradually converge to x (t) I.e. the correlation coefficient r converges to a value greater than 0, then the decision is made from x (t) To y (t) There is a causal relationship. The invention judges the causal relationship between the key operation variable and the production index variable according to the value of the correlation coefficient rAnd then excavating key operation variables which need to be adjusted to enable the production index variables to reach target values. Using this step, the production index variable float levels can be selected to achieve [64,66] respectively]The range and the float tail grade are lower than the key operation variable set corresponding to 22.
The searching process of the optimal embedding dimension E in the step 4-1 comprises the following steps:
judging the optimal embedding dimension by using a red pool information criterion, wherein the red pool information criterion is established on the basis of the concept of entropy and is used for balancing the complexity of the model generated in the step 4 and the superiority of the model fitting data; the model complexity is defined as n, the loss function V is defined, the sample number is K, and the red pool information criterion is defined as follows:
by x (t) The autoregressive model of (a) to determine the optimal embedding dimension is shown as:
loss function
Model complexity n=e, when AIC (n) And taking the minimum value, wherein the corresponding n is the optimal embedding dimension E.
And (3) extracting causal features of the data by adopting the convergence cross mapping method in the step four, and reserving strong causal relations, namely causality mechanisms. In practice, the key operation variables obtained in the fourth step for enabling the production index variable floating level to reach the range of [64,66] comprise dosing amount, three-scan cone valve opening degree, carefully selecting two-section cone valve opening degree, one-scan cone valve opening degree and the like.
Step 5, using key operation variable T i And other state variables T s As input, build up of a dilation time series convolutional network, refer to productionTarget variable T o Predicting to obtain key operation variable T i And production index variable T o Is a dynamic relationship model of (1); taking the site as an example, the production index variables, namely the float grade, the float tail grade and the one-sweep top grade are respectively predicted through the expansion time sequence convolution network trained by the two calendar history data, and the index change condition of the last half hour of the current moment is predicted.
The step of establishing the expansion time sequence convolution network comprises the following steps:
step 5-1: setting the number of convolution kernels, the size of the convolution kernels and step parameters, setting an activation function of a convolution layer as a relu function, and establishing a unidirectional causal convolution network of an M layer;
step 5-2: applying a dilation convolution, the convolution kernel is divided by a step f=c l Skipping part of input, wherein f is an expansion factor, c is an expansion coefficient, and l is a layer where a convolution kernel is located;
step 5-3: layer jump connection with residual convolution and 1×1 convolution operation are added, one residual block comprises two layers of expansion convolution and relu nonlinear mapping, and weight norm and Dropout are added after each hole convolution to realize regularization.
Step 6, designing an optimization target for realizing single-step optimization control based on Lyapunovo Barrier functions;
the optimization objective based on Lyapunovo Barrier function is designed in the step 6,
the CLBF model based on Lyapunovo Barrier functions is determined by introducing Lyapunovo Barrier functions on the basis of model predictive control strategies, and the optimization problem based on the CLBF-MPC design is as follows:
wherein the method comprises the steps of
Is a predicted state track, namely the change trend of the production index variable obtained in the step five, S (delta) is a piecewise constant function set with the period delta, and P N To predict the number of sampling cycles in the range, W c (x, u) is used to represent
Cost function->
Satisfy L (0, 0) =0, +.>
So as to obtain the minimum value of the cost function under the condition of stable system, and thus, u (t) is the system optimization function in the prediction range P N The optimal solution on delta includes Lyapunovo Barrier function conditions in addition to the constraints described above.
Step 7, searching an optimal action corresponding to the index change trend, namely an optimal control strategy, based on the step five by adopting a time forward rolling type finite time domain optimization strategy, so as to realize a circular forward optimization control task;
the limited time domain optimization strategy adopting time forward scrolling searches for the optimal action;
the rolling optimization is carried out by adopting an iLQR algorithm, compared with the LQR algorithm, the dynamic function of the iLQR is nonlinear, so that the approximate expansion of Taylor is needed to be carried out on the function part on the basis of the LQR algorithm, and the local characteristic of a complex nonlinear function is estimated by Taylor display, wherein the specific formula is as follows:
wherein,,
from the correlation definition a dynamic function f (x t ,u t ) The method comprises the following steps:
cost function c (x t ,u t ) The method comprises the following steps:
obtaining a current moment control law K by using LQR reverse push t And control constant k t The method comprises the steps of carrying out a first treatment on the surface of the The following loop actions are performed until convergence.
for t＝1to T
x t+1 ＝f(x t ,u t )
The convergence result of the step is the optimal control action obtained by searching.
And 8, repeating the steps 5, 6 and 7, and optimally controlling the flotation process on line.
Further described in the field control example: assuming that the concentrate grade at the current moment is 65, predicting that the concentrate grade in the second half hour of the current state is 60 through the step 5, wherein the concentrate grade of the production index is less than 64 and is lower than the normal range; designing an optimization target according to the step 6, and regulating in advance to ensure that the concentrate grade is still in a normal range in the latter half hour; and 7, obtaining optimal control actions, such as adding the starch with the dosage of +300 and opening the three-scan cone valve to be-0.5, and implementing precise regulation and control on the flotation site through the control instruction.
The invention predicts by combining with the expansion time sequence convolution network; in predictive control: the online optimization control is realized by using a time forward rolling type finite time domain optimization strategy, the disconnection between a fixed global optimization target and actual production is effectively avoided, and the method has good effects on reasonable optimization of target variables, such as reduction of tail floating grade and stabilization of floating quality level. Meanwhile, the method has better robustness on the reduction of control performance caused by the deviation of the production environment and the model or the interference of the actual environment, and has theoretical and practical significance on the optimal control of the flotation process.
Claims (9)
1. The flotation optimization control method based on-line quality monitoring is characterized by comprising the following steps of:
step 1, collecting data D collected by a plurality of links in the whole flotation process in real time, wherein the data D mainly comprises real-time monitoring data D collected by a sensor 1 Image characteristic value D extracted by foam analyzer 2 An operation control feedback value D 3 Adding the data into the subsequent data modeling analysis;
step 2, real-time monitoring data D 1 Control feedback data D 2 Respectively carrying out normalization processing to obtain dimensionless real-time monitoring data D 1 ' non-dimensional control feedback data D 2 ' image characteristic data D 3 Dummy variable processing is carried out to obtain pseudo-coded image characteristic data D 3 ′；
Step 3, adopting Kalman filtering to monitor dimensionless real-time data D 1 ' smoothing to obtain smoothed dimensionless real-time monitoring data D 1 "the smoothed dimensionless real-time monitoring data D 1 Non-dimensional control feedback data D 2 ' pseudo-encoded image characteristic data D 3 'combining to obtain a data set D';
step 4, extracting causal characteristics of the data set D' by adopting a convergence cross mapping method, and aiming at the operation variable
Sensor monitoring variable +.>
Is>
Is analyzed for causality of key operation variable set
Confirming production index variable according to actual demand>
Finally, the data set D' is set to remove the key operation variable T i And a production index variable T o Other than variables being other state variables T s
Step 5, using key operation variable T i And other state variables T s As input, training the expansion time sequence convolution network for production index variable T o Predicting to obtain key operation variable T i And production index variable T o Is a dynamic relationship model of (1);
step 6, designing an optimization target for realizing single-step optimization control based on Lyapunovo Barrier functions;
step 7, searching for an optimal action by adopting a time forward rolling type finite time domain optimization strategy, and realizing a circular forward optimization control task;
and 8, repeating the steps 5, 6 and 7, and optimally controlling the flotation process on line.
2. The method for optimizing control of flotation based on-line quality monitoring according to claim 1, wherein the real-time monitoring data
The underflow speed and air flow rate, the liquid level of each pump pool, the temperature and the PH value of each flow path are included; image characteristic value extracted by foam analyzer>
The RGB values of the point locations of the image itself are included, as well as the foam size and color identified from the image; operation control feedback value +.>
Including cone valve opening, dosage type and quantity, and dosing pump frequency.
3. The flotation optimization control method based on online quality monitoring according to claim 1, wherein the collected real-time monitoring data D 1 And an operation control feedback value D 3 Normalization processing is carried out by using Min-Max standardization method, and the mapping range is [ -1,1]And the image characteristic value D 2 Processing by means of dummy variables, converting into m numerical characteristics with 0,1 values, wherein the formula of the Min-Max standardization method is as follows:
in which x is i For the collected real-time monitoring data D 1 And operation control feedback data D a Is defined as the total data of each feature column, min (x i ) And max (x) i ) Is respectively to x i The maximum and minimum values are found.
4. The method for optimizing and controlling flotation based on-line quality monitoring according to claim 1, wherein the step 3 uses Kalman filtering to monitor dimensionless real-time data D 1 ' smoothing process, wherein the Kalman filter time update formula is as follows:
the Kalman filter state update formula is as follows:
in the middle of
And->
Posterior state estimation values respectively representing k-1 time and k time,/>
Is the prior state estimation value at the moment k and is also the output of Kalman filtering update, and is the dimensionless real-time monitoring data D after smoothing 1 ″；
P k-1 And P k The a posteriori estimated covariance at k-1 and k times respectively,
is the a priori estimated covariance at time k, H is the state variable to measurement rotationChanging a matrix;
z k is the filtered input, here dimensionless real-time monitoring data D 1 ′；
K k Is the filter gain matrix, a is the state transition matrix, Q is the process excitation noise covariance, also the covariance of the system process, R is the measurement noise covariance, B is the matrix that converts the input into state,
is the residual of the actual observation and the prior state estimation.
5. The flotation optimization control method based on-line quality monitoring according to claim 1, wherein the step 4 of screening key operation variables comprises the following steps of;
step 4-1, determining a production index variable T according to production practice o And based on production index variable T o And data set D' construct data set Y (t) at time t; simultaneously constructing operating variables
Sensor monitoring variable +.>
Is>
Excluding the production index variable T therein o Forming a time-of-t dataset X (t) with dataset D'; then constructing a shadow manifold M corresponding to X (t) and Y (t) based on the X (t) and Y (t) X 、M Y The formula is as follows:
M x ＝{x (t) }x (t) ＝<X (t) ，X (t-τ) ，X (t-2τ) ，…，X (t-(E-1)τ) >
M Y ＝{y (t) }y (t) ＝<Y (t) ，Y (t-τ) ，Y (t-2τ) ，…，Y (t-(E-1)τ) >
wherein E is the optimal embedding dimension;
step 4-2, calculating the distance between any two points of the shadow manifold of X and the distance between any two points of the shadow manifold of Y by adopting Euclidean distance, and performing the calculation on the shadow manifold M X And M Y Finding E+1 neighbor nodes from manifold M Y Obtained by cross mapping
The cross-map formula is as follows:
w i ＝m i /∑m j
wherein the method comprises the steps of
Representing y on manifold (t) And->
Euclidean distance between them.
Step 4-3, calculating
And x (t) The correlation coefficient r of (2) is as follows:
as the length L of the input data sequence increases,
gradually converge to x (t) I.e. the correlation coefficient r converges to a value greater than 0, then the decision is made from x (t) To y (t) And judging the causal relation between the operation variable and the monitoring variable according to the value of the correlation coefficient r, and further mining the monitoring variable and the control priority thereof which need to be regulated to enable the monitoring variable to reach the target value.
6. The flotation optimization control method based on-line quality monitoring according to claim 5, wherein the searching process of the optimal embedding dimension E comprises the following steps:
judging the optimal embedding dimension by using a red pool information criterion, wherein the red pool information criterion is based on the concept of entropy and is used for balancing the complexity of the process of the step 4 and the superiority of fitting data; the complexity of the process is defined as n, a loss function V is defined, the number of samples is K, and the red pool information criterion is defined as follows:
by x (t) The autoregressive model of (a) to determine the optimal embedding dimension is shown as follows:
loss function
Model complexity n=e, when AIC (n) And taking the minimum value, wherein the corresponding n is the optimal embedding dimension E.
7. The method for optimizing and controlling flotation based on-line quality monitoring according to claim 1, wherein in the step 5, the following is performedKey operation variable T i With other state variables T s As input, training the expansion time sequence convolution network for production index variable T o The method for predicting the output comprises the following steps:
the step of establishing the expansion time sequence convolution network comprises the following steps:
step 5-1: setting the number of convolution kernels, the size of the convolution kernels and step parameters, setting an activation function of a convolution layer as a relu function, and establishing a unidirectional causal convolution network of an M layer;
step 5-2: applying a dilation convolution, the convolution kernel is divided by a step f=c l Skipping part of input, wherein f is an expansion factor, c is an expansion coefficient, and 1 is a layer where a convolution kernel is located;
step 5-3: layer jump connection with residual convolution and 1×1 convolution operation are added, one residual block comprises two layers of expansion convolution and relu nonlinear mapping, and weight norm and Dropout are added after each hole convolution to realize regularization.
8. The method for optimizing and controlling flotation based on-line quality monitoring according to claim 1, wherein the optimization objective based on Lyapunovo Barrier function is designed in the step 6,
the CLBF model based on Lyapunovo Barrier functions is determined by introducing Lyapunovo Barrier functions on the basis of model predictive control strategies, and the optimization problem based on the CLBF-MPC design is as follows:
wherein the method comprises the steps of
Is a predicted state trajectory, S (delta) is a piecewise constant function set with period delta, P N To predict the number of sampling cycles in the range, W c (x, u) is used to denote +.>
Cost function->
Satisfying the condition that L (0, 0) =0,
so as to obtain the minimum value of the cost function under the condition of stable system, and thus, u (t) is the system optimization function in the prediction range P N The optimal solution on delta includes Lyapunovo Barrier function conditions in addition to the constraints described above.
9. The method for optimizing control of flotation based on-line quality monitoring according to claim 1, wherein the step 7 searches for an optimal action by using a time-forward rolling finite time domain optimization strategy;
the rolling optimization is carried out by adopting an iLQR algorithm, compared with the LQR algorithm, the dynamic function of the iLQR is nonlinear, so that the approximate expansion of Taylor is needed to be carried out on the function part on the basis of the LQR algorithm, and the local dynamic characteristic of a complex nonlinear function is estimated through the Taylor display
And cost function->
The specific formula is as follows:
wherein x is t The key operation variable filtered in the step 4 is the state parameter at the current moment, u t The key operation variables screened in step 4 are referred to herein as current time control parameters,
the actual sampling value at the current moment and the state parameter estimation value at the current moment are respectively +.>
And control parameter estimation +.>
Is the difference between (1);
from the correlation definition a dynamic function f (x t ，u t ) The method comprises the following steps:
cost function c (x t ，u t ) The method comprises the following steps:
obtaining a current moment control law K by using LQR reverse push t And control constant k t The method comprises the steps of carrying out a first treatment on the surface of the Performing the following cyclic actions until convergence;
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| CN116611522A (en) * | 2023-06-02 | 2023-08-18 | 中南大学 | Foam flotation process working condition deterioration tracing method based on probability ash number fuzzy Petri net |
| CN117193025A (en) * | 2023-11-07 | 2023-12-08 | 矿冶科技集团有限公司 | Control method and device of dosing machine, electronic equipment and storage medium |
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| CN116611522A (en) * | 2023-06-02 | 2023-08-18 | 中南大学 | Foam flotation process working condition deterioration tracing method based on probability ash number fuzzy Petri net |
| CN116611522B (en) * | 2023-06-02 | 2024-04-30 | 中南大学 | Foam flotation process working condition deterioration tracing method based on probability ash number fuzzy Petri net |
| CN117193025A (en) * | 2023-11-07 | 2023-12-08 | 矿冶科技集团有限公司 | Control method and device of dosing machine, electronic equipment and storage medium |
| CN117193025B (en) * | 2023-11-07 | 2024-02-02 | 矿冶科技集团有限公司 | Control method and device of dosing machine, electronic equipment and storage medium |
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