An online prediction method for the loss on ignition of calcined magnesite powder during the flash calcination process of magnesite.

Abstract

This invention discloses an online prediction method for the loss on ignition (LOI) of calcined magnesite powder during the flash calcination process of magnesite. The method includes: analyzing the flash calcination process of magnesite, measuring the LOI of calcined magnesite powder as the dominant variable, and establishing a training sample set using important parameters affecting the dominant variable as auxiliary variables; standardizing the training sample set data, using PCA to reduce the dimensionality of the input data, and eliminating redundant relationships between the auxiliary variables; establishing a prediction model based on the WOA-XGBoost method, and iteratively training it using the training sample set data to obtain an ideal model for predicting the LOI of calcined magnesite powder; and correcting the ideal model for the LOI of calcined magnesite powder using a combination of bias compensation correction and real-time learning. The prediction model of this invention can predict the LOI of calcined magnesite powder online, which can be used to predict the product quality of the flash calcination process of magnesite and to provide feedback for adjusting production process steps.

Description

Technical Field

[0001] This invention relates to the field of advanced control technology for the flash calcination process of magnesite, and in particular to an online prediction method for the loss on ignition of calcined magnesite powder in the flash calcination process of magnesite. Background Technology

[0002] The flash calcination process of magnesite uses magnesite with a particle size of 100-200μm as raw material. After drying and preheating, the magnesite is sent into the core equipment, the flash calcination furnace, by a blower. Combustion air generated by the blower and the finished product blower is sent into the flash calcination furnace. At the same time, natural gas is sent into the flash calcination furnace at different heights for multi-stage combustion. In the high-temperature gas in the flash calcination furnace, the magnesite undergoes a magnesite decomposition reaction and a magnesium oxide sintering reaction. Afterwards, the gas is collected by a cyclone separator and cooled to finally form the product, lightly calcined magnesia powder.

[0003] The quality indicator for light-burned magnesia powder is the loss on ignition (LOI). Currently, the method used by production enterprises employing the flash calcination process for magnesite to test the LOI of light-burned magnesia powder is as follows: inspectors manually sample the powder every two hours and then perform manual analysis to obtain the LOI. This method suffers from low sampling frequency and long time lag, making it difficult to provide timely guidance for production and seriously hindering product quality stability.

[0004] With the development of technology, process modeling and artificial intelligence technologies have provided a feasible solution for the online measurement of the loss on ignition (LOI) of light-burned magnesia powder. Establishing an online prediction model for the LOI of light-burned magnesia powder with strong generalization capabilities and performing online measurement of the LOI is of great significance for stabilizing the production of magnesite flash calcination and for implementing intelligent optimization control of the magnesite flash calcination process to improve the quality of light-burned magnesia powder. Summary of the Invention

[0005] In view of the problem that the loss on ignition of calcined magnesia powder during the flash calcination of magnesite cannot be detected online, this invention provides an online prediction method for the loss on ignition of calcined magnesite powder during the flash calcination of magnesite, which can continuously provide online measurement values ​​of the loss on ignition of calcined magnesite powder, has certain prediction accuracy, generalization ability and adaptability, and reduces the risk of overfitting.

[0006] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0007] A method for online prediction of the loss on ignition (LOI) of calcined magnesite powder during the flash calcination process of magnesite involves the following steps: obtaining a prediction model and performing online calibration; this model is used to predict the unknown product quality of the flash calcination process of magnesite; and the LIOI of the calcined magnesite powder is output as the result for evaluating the product quality of the flash calcination process of magnesite. The method includes the following steps:

[0008] The flash calcination process of magnesite was analyzed, and the loss on ignition of calcined magnesite powder was measured as the dominant variable. The important parameters affecting the dominant variable were used as auxiliary variables to establish a training sample set.

[0009] The training sample set data is standardized, and the input data is reduced in dimensionality using the PCA method to eliminate redundant relationships between various auxiliary variables.

[0010] A prediction model was established based on the WOA-XGBoost method, and an ideal model was obtained by iterative training using training sample set data, which was used to predict the loss on ignition of lightly calcined magnesium powder.

[0011] The ideal model for the loss on ignition of lightly calcined magnesium powder was corrected by combining deviation compensation correction with real-time learning.

[0012] The training sample set contains {auxiliary variables as inputs and dominant variables as outputs}, where the auxiliary variables are denoted as u1′~u1′. 11 ′ indicates that the following parameters are included as auxiliary variables: raw ore powder flow rate, main combustion natural gas flow rate, first-layer compensation natural gas flow rate, second-layer compensation natural gas flow rate, air supply volume, raw powder air supply volume, finished product conveying air volume, combustion chamber outlet temperature, first-layer supplementary combustion outlet temperature, second-layer supplementary combustion outlet temperature, and flash light-burning furnace outlet temperature.

[0013] It uses a normalization method to standardize the training samples.

[0014] The prediction model built based on the WOA-XGBoost method includes:

[0015] Set the model parameters for the prediction model, including the learning rate b1, the minimum loss threshold b2 caused by node splitting, the weight threshold b3 of the smallest node, the L1 regularization coefficient b4, the L2 regularization coefficient b5, and the threshold range for each parameter.

[0016] The vector [b1,b2,...,b5] consisting of b1 to b5 is used as the position of the individual whale. Several positions of individual whales are randomly generated within the range of the minimum to the maximum value of each parameter.

[0017] For parameters b1 to b5 at each individual whale location, a model was built using sample data and the XGBoost method, and WOA was used to iteratively optimize the parameters b1 to b5 in the model. After S iterations, the optimized parameters were... Substituting these values ​​into the XGBoost model yields the final prediction model.

[0018] In the s-th (s=1,2,...,S) iteration of the WOA optimization process, using the position of the k-th (k=1,2,...,K) whale individual, the XGBoost modeling method is used to establish an initial objective function that considers the loss function and model complexity. The objective function is transformed using a second-order Taylor expansion. A decision tree is defined, and the structure of the tree is introduced into the objective function. The optimal tree is constructed using a greedy algorithm. The above process is repeated t times, finally generating t decision trees. The outputs of these decision trees are summed together and multiplied by the learning rate as the predicted output of the light-burned magnesite powder loss on ignition prediction result obtained by the k-th whale individual in the s-th iteration.

[0019] The final prediction model is as follows:

[0020]

[0021] Among them, u I This represents the newly arrived input data u. I The result after standardization Indicates the k-th iteration of the S-th iteration. * The output of the a-th decision tree for each individual This represents the predicted loss on ignition of magnesite powder during the flash calcination process of magnesite, obtained based on the input data.

[0022] The method combining deviation compensation correction and real-time learning includes: calculating the root mean square error (RMSE) between the manually detected value and the predicted value of the loss on ignition of lightly burned magnesium powder within the latest consecutive sampling time period;

[0023] If RMSE < threshold 1, then keep the original prediction model unchanged;

[0024] If threshold 1 ≤ RMSE ≤ threshold 2, then the deviation compensation method is used for correction, and the actual error is added to the predicted result as the final prediction result.

[0025] If RMSE > threshold 2, then the real-time learning method is used for correction. The F samples with the highest similarity to the newly arrived input data are selected for preprocessing, added to the training sample set, and the WOA-XGBoost method is used to rebuild the prediction model.

[0026] The present invention has the following advantages and beneficial effects:

[0027] 1. It can measure online the important index of magnesium oxide loss on ignition in the flash calcination process of magnesite, which is difficult to detect online by traditional methods. This provides a prerequisite for the implementation of intelligent optimization control of the flash calcination process of magnesite and the stability of product quality.

[0028] 2. The WOA-XGBoost method was used to build the prediction model, which enhanced the model's generalization ability, overcame the risk of overfitting, and improved the model's prediction accuracy.

[0029] 3. Predictive model calibration can perform online real-time calibration of the established predictive model, and has the ability to adapt to changes in operating conditions, which greatly reduces maintenance costs. Attached Figure Description

[0030] Figure 1 A schematic diagram illustrating the principle of the flash calcination process of magnesite.

[0031] Figure 2 This is a flowchart illustrating the process for predicting the loss on ignition of magnesium oxide powder during the flash calcination of magnesite. Detailed Implementation

[0032] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0033] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0034] This invention provides an online prediction method for the loss on ignition of magnesite powder during the flash calcination process. This method offers continuous online measurement of the loss on ignition of lightly calcined magnesite powder, possessing certain prediction accuracy, generalization ability, and adaptability, while reducing the risk of overfitting. The specific process is as follows: Figure 2 As shown, it includes the following steps.

[0035] 1. Selection of auxiliary variables:

[0036] Analysis of the flash calcination process of magnesite revealed 11 key parameters affecting the loss on ignition (y) of calcined magnesite powder: raw ore powder flow rate, main combustion natural gas flow rate, first-layer compensation natural gas flow rate, second-layer compensation natural gas flow rate, air supply volume, raw powder air supply volume, finished product conveying air volume, combustion chamber outlet temperature, first-layer supplementary combustion outlet temperature, second-layer supplementary combustion outlet temperature, and flash calcination furnace outlet temperature. Therefore, these 11 variables were used as auxiliary variables in the prediction model, and denoted by u1′~u 11 'express.

[0037] 2. Input data preprocessing:

[0038] The input data of the training samples is standardized and subjected to PCA dimensionality reduction.

[0039] (1) Standardization:

[0040] The training samples are standardized using a normalization method.

[0041]

[0042] In the formula, u ij Represents the i-th input variable u i The j-th sample value, For the i-th input variable

[0043] Quantity u i The sample mean, σ i For the i-th input variable u i The sample standard deviation, u ij For u ij The standardized values ​​are i = 1, 2, ..., 11; j = 1, 2, ..., N; N is the sample size.

[0044] (2) Input variable PCA dimensionality reduction:

[0045] Let the input data u ij The matrix U' formed by standardizing the data u ij The resulting matrix is ​​U∈R N ×11 Follow these steps:

[0046] Step 1: Calculate the covariance matrix

[0047] Step 2: Find the eigenvalues ​​and corresponding eigenvectors of the covariance matrix C, and arrange the eigenvalues ​​in descending order. Let the arranged eigenvalues ​​and their corresponding eigenvectors be θ. i and p i , i = 1, 2, ..., 11.

[0048] Step 3: Calculation The value of v. v is the number of new input variables obtained after dimensionality reduction of the input variables, and the specific value needs to be solved according to the inequality.

[0049] Step 4: Arrange the eigenvectors from left to right according to the size of their corresponding eigenvalues ​​to form an eigenmatrix P0, and take the first v columns of P0 to form matrix P.

[0050] Step 5: Calculate X = UP. X is the new input variable matrix after data preprocessing.

[0051] 3. Establishment of a prediction model based on the WOA-XGBoost method:

[0052] Follow these steps:

[0053] Step 1: Set the number of iterations s = 1, set the maximum number of iterations S = 30, and go to Step 2;

[0054] Step 2: Let k = 1, and assume the number of individual whales is K = 25. Let b i =b imin +rand ik (b imax -b imin ), where i = 1, 2, ..., 5, rand ik (i = 1, 2, ..., 5, k = 1, 2, ..., K) are uniformly distributed random numbers in the range [0, 1]. The minimum and maximum values ​​of each parameter are: b 1min =10 -6 b 2min =0.01, b 3min =0.01, b 4min =0.001, b 5min =0.001, b 1max =10 5 b 2max =10, b 3max =20, b 4max =1000, b 5max =1000. Randomly generate the positions of K individual whales, then the position of each individual whale is represented as L. s (k) = [b1,b2,...,b5] (k = 1,2,...,K), go to Step 3;

[0055] Step 3: Let t = 1, set the maximum number of trees to T = 15, then proceed to Step 4:

[0056] Step 4: Initialize and construct the target function.

[0057] Let the initial objective function of the t-th decision tree for the k-th whale individual in the s-th iteration be as follows:

[0058]

[0059] Wherein, the loss function for the i-th (i = 1, 2, ..., N) sample is: y i This represents the value of the i-th sample in the output; Let represent the prediction value of the first t decision trees for the k-th whale individual in the s-th iteration for the i-th sample; Let represent the model complexity of the a-th tree for the k-th whale individual in the s-th iteration. Proceed to Step 5;

[0060] Step 5: Objective function transformation.

[0061] Substituting equation (5) into equation (4), we get

[0062]

[0063] Where, x i This represents the i-th row of X. And it is a constant. Expanding equation (6) using Taylor series, we get...

[0064]

[0065] in They are all constants. After simplification and removal of the constant terms, the objective function is equation (8). Proceed to Step 6.

[0066]

[0067] Step 6: Define a decision tree and incorporate the tree into the objective function.

[0068] The representation of a decision tree is defined as follows:

[0069] Bundle Defined as in This represents the result of a tree, and its function is to transform the input x i ∈R s Mapped to a leaf node (assuming the tree has...) (a leaf node), It is a length of A one-dimensional vector represents the weight of the leaf node (i.e., the predicted value of the decision tree).

[0070] The complexity of a tree is measured using the following formula:

[0071]

[0072] in, for The There are several components. Therefore, the objective function is transformed into:

[0073]

[0074] All samples x belonging to the j-th leaf nodei , is assigned to a leaf node sample set, mathematically represented as: The loss for all leaf node samples is calculated as follows: make

[0075] The objective function then becomes To minimize the objective function, let right The partial derivatives are zero, therefore... Determine if it satisfies or If satisfied, then maintain. If it does not satisfy the condition, then let it remain unchanged; if not, then let it remain unchanged. or Proceed to Step 7;

[0076] Step 7: Construct the optimal tree.

[0077] Determining candidate split points: For each new input variable, select quartiles based on the number of samples, and each quartile is a candidate split point;

[0078] Use a greedy algorithm to split tree nodes:

[0079] Starting at a tree depth of 0, each leaf node in the tree is subjected to one round of splitting. This involves considering all new input variables and splitting at each candidate split point for each new input variable. After each split, the original leaf node is further split into two child leaf nodes (left and right). The sample set from the original leaf node is then distributed to the left and right leaf nodes according to the node's judgment rule (compared to the values ​​at the candidate split points). After each new split, it is checked whether this split contributes a gain to the loss function. The gain is defined as follows:

[0080]

[0081] Where L represents the optimal value of the objective function when partitioning to the left subtree, and R represents the optimal value of the objective function when partitioning to the right subtree. If Gain < b2, stop the split; if the number of samples in any leaf node is less than the threshold Nu... min To stop this split, among which Nu min Positive integers within the range [1, 5]; if the depth of the tree reaches the maximum value dep max To stop this split, among which dep maxThe value range is a positive integer within the interval [2, 7]; otherwise, after splitting at all candidate split points, the candidate split point with the largest Gain ≥ b2 is selected as the best split point for this round of splitting. Then, at the next leaf node, consider all candidate split points for all new input variables, repeat the above process, and perform the next round of splitting on that leaf node until the condition for stopping splitting is met. The final number of leaf nodes is [the number of nodes in the original text]. Proceed to Step 8;

[0082] Step 8: Determine if t reaches T. If it does, go to Step 9; otherwise, let t = t + 1 and go to Step 4.

[0083] Step 9: Based on the position parameters of the kth individual whale, obtain the kth model. Among them, u I This represents the newly arrived input data u. I The result after standardization This represents the output of the a-th decision tree for the k-th individual in the s-th iteration. This represents the output of the k-th model. The fitness function is used. Calculate the fitness of the model. Where x i Let k represent the i-th row of X. Determine if k reaches K. If it does, go to Step 10; otherwise, let k = k + 1 and go to Step 3.

[0084] Step 10: Select The maximum value in the range is used as the optimal whale position in the s-th iteration, and denoted as L. * (s) and The serial number of this individual whale is denoted as k. * Determine if s = S is satisfied, then proceed to Step 11;

[0085] Step 11: If satisfied, position L of the optimal whale individual. * (s) is output as the final result and substituted into the XGBoost model. The resulting model is the prediction model for the loss on ignition of magnesite powder during the flash calcination process of magnesite. The model is now established. When new input data u I When it arrives, This is the final prediction model output, where u I This represents the newly arrived input data u. I The result after standardization Indicates the k-th iteration of the S-th iteration. * The output of the a-th decision tree for each individual (i.e., the optimal individual). This represents the predicted loss on ignition of calcined magnesite powder during the flash calcination process of magnesite, obtained based on the input data; if it does not meet the requirements, let D... k (s)=C k (s)L * (s)-L k (s) represents the position vector between the k-th individual whale and a random individual whale; Let A represent the distance vector between the k-th individual whale and the optimal individual whale (i.e., the optimal solution); k (s)=2a(s)r 1k (s)-a(s), where a(s) is a parameter that decreases linearly from 2 to 0, expressed as: r 1k (s) is a random number in the range [0,1], C k (s)=2r 2k (s), r 2k (s) is a random number in the range [0,1]; generate a random number β(s) in the range [0,1], determine whether β(s)≤0.5, and go to Step 12;

[0086] Step 12: If β(s) ≤ 0.5, then determine whether |A k (s)|<1, if satisfied, then use L k (s+1)=L * (s)-A k (s)D k (s) Update the position of the kth individual whale; if |A k (s)|≥1, then use L k (s+1)=L rand (s)-A k (s)D k (s) Update the position of the kth individual whale, L rand (s) represents the location of a randomly selected individual whale. Proceed to Step 13.

[0087] Step 13: If β(s) > 0.5, then utilize... Update the position of the kth individual whale; where b is the spiral shape parameter, with a value in the range [0.2, 0.5]; l represents a random number uniformly distributed in the interval [-1, 1], go to Step 14;

[0088] Step 14: Let s = s + 1, then go to Step 2.

[0089] 4. Correction of the prediction model:

[0090] A method combining bias compensation correction and real-time learning was used to correct the prediction model for the loss on ignition of light-burned magnesium powder. The manually detected loss on ignition value of light-burned magnesium powder was compared with the predicted value. If the RMSE (Root Mean Square Error) for the latest consecutive 4 hours was less than a predefined threshold 1, the original prediction model remained unchanged. If the RMSE was greater than threshold 1 but less than threshold 2, bias compensation was used for correction, that is, the actual error was added to the predicted result as the final prediction result. If the RMSE was greater than threshold 2, the F samples with the highest similarity to the newly arrived input data were selected, the newly arrived input data were preprocessed, and the prediction model was rebuilt using the WOA-XGBoost method. The newly arrived input and output data were then added to the training samples.

[0091] Among them, the threshold 1 range of the loss on ignition rate of lightly calcined magnesium powder is between [0.1% and 0.2%], the threshold 2 range is between (0.2% and 0.3%), and the similarity is calculated using formula (12). The value of F is between 300 and 500.

[0092]

[0093] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for online prediction of the loss on ignition of calcined magnesite powder during the flash calcination process of magnesite, characterized in that, The following steps are performed to obtain a prediction model and perform online calibration, which is used to predict the product quality of the unknown magnesite flash calcination process. The loss on ignition rate of calcined magnesite powder is output as the result to evaluate the product quality of the magnesite flash calcination process. The method includes the following steps: The flash calcination process of magnesite was analyzed, and the loss on ignition of calcined magnesite powder was measured as the dominant variable. A training sample set was established using important parameters affecting the dominant variable as auxiliary variables. In the training sample set, {auxiliary variables are inputs, and dominant variables are outputs}, with auxiliary variables denoted as u1′~u 11 ′ indicates that the following parameters are included as auxiliary variables: raw ore powder flow rate, main combustion natural gas flow rate, first-layer compensation natural gas flow rate, second-layer compensation natural gas flow rate, air supply volume, raw powder air supply volume, finished product conveying air volume, combustion chamber outlet temperature, first-layer supplementary combustion outlet temperature, second-layer supplementary combustion outlet temperature, and flash light-burning furnace outlet temperature. The training sample set data is standardized, and the input data is reduced in dimensionality using the PCA method to eliminate redundant relationships between various auxiliary variables. A prediction model was established based on the WOA-XGBoost method, and an ideal model was obtained by iterative training using training sample set data, which was used to predict the loss on ignition of lightly calcined magnesium powder. The ideal model of loss on ignition of lightly calcined magnesium powder is corrected by a combination of deviation compensation correction and real-time learning. The method of combining deviation compensation correction and real-time learning includes: calculating the root mean square error (RMSE) between the manually detected value and the predicted value of loss on ignition of lightly calcined magnesium powder within the latest continuous sampling time. If RMSE < threshold 1, then keep the original prediction model unchanged; If threshold 1 ≤ RMSE ≤ threshold 2, then the deviation compensation method is used for correction, and the actual error is added to the predicted result as the final prediction result. If RMSE > threshold 2, then the real-time learning method is used for correction. The F samples with the highest similarity to the newly arrived input data are selected for preprocessing, added to the training sample set, and the WOA-XGBoost method is used to rebuild the prediction model.

2. The method for online prediction of the loss on ignition of calcined magnesite powder during the flash calcination process of magnesite according to claim 1, characterized in that, It uses a normalization method to standardize the training samples.

3. The method for online prediction of the loss on ignition of calcined magnesite powder during the flash calcination process of magnesite according to claim 1, characterized in that, The prediction model built based on the WOA-XGBoost method includes: Set the model parameters for the prediction model, including the learning rate b1, the minimum loss threshold b2 caused by node splitting, the weight threshold b3 of the smallest node, the L1 regularization coefficient b4, the L2 regularization coefficient b5, and the threshold range for each parameter. The vector [b1,b2,...,b5] consisting of b1 to b5 is used as the position of the individual whale. Several positions of individual whales are randomly generated within the range of the minimum to the maximum value of each parameter. For parameters b1 to b5 at each individual whale location, a model was built using sample data and the XGBoost method, and WOA was used to iteratively optimize the parameters b1 to b5 in the model. After S iterations, the optimized parameters were... Substituting these values ​​into the XGBoost model yields the final prediction model.

4. The method for online prediction of the loss on ignition of calcined magnesite powder during the flash calcination process of magnesite according to claim 3, characterized in that, In the s-th iteration of the WOA optimization process, using the position of the k-th whale individual, the XGBoost modeling method is used to establish an initial objective function that considers the loss function and model complexity. The objective function is transformed using a second-order Taylor expansion. A decision tree is defined, and the structure of the tree is introduced into the objective function. The optimal tree is constructed using a greedy algorithm. The above process is repeated t times, and finally t decision trees are generated. The outputs of these decision trees are summed together and multiplied by the learning rate as the predicted output of the light-burned magnesite powder loss on ignition prediction result obtained by the k-th whale individual in the s-th iteration; where s = 1, 2, ..., S; k = 1, 2, ..., K.

5. A method for online prediction of the loss on ignition of calcined magnesite powder during the flash calcination process of magnesite according to any one of claims 1-4, characterized in that, The final prediction model is: Among them, u I This represents the newly arrived input data u. I The result after standardization Indicates the k-th iteration of the S-th iteration. * The output of the a-th decision tree for each individual This represents the predicted loss on ignition of magnesite powder during the flash calcination process of magnesite, obtained based on the input data.

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