A method for predicting coal ash sintering temperature based on principal component regression

Abstract

The invention discloses a coal ash sintering temperature prediction method based on principal component regression, comprising: 1) collecting coal ash sintering test historical data; 2) using useless information variable elimination method to select variables, remove variables with useless information on coal ash sintering temperature, reduce the influence of irrelevant information on the prediction model, improve the prediction accuracy of the model, and reduce the number of variables to improve the efficiency of operation; 3) establishing a principal component regression model, taking coal quality test data as the input variable of the model, and coal ash sintering temperature as the output variable of the model, establishing a one-to-one mapping relationship between the two, and using the obtained optimal number of principal components to establish a principal component regression model, and the established prediction model is 4) substituting the coal quality test data into the model to obtain a predicted value. The invention establishes a prediction model according to the full analysis data of coal types and the coal ash component analysis data to predict the initial sintering temperature of other coal ashes.

Description

Technical Field

[0001] The invention belongs to a method for predicting the sintering temperature of coal ash, which is an indicator of the slagging and contamination characteristics of power coal, and is specifically a method for predicting the sintering temperature of coal ash based on principal component regression. Background Art

[0002] Boiler slagging and fouling affect the economy, environmental protection and safety of boiler operation. In serious cases, it will affect the normal operation of the boiler and even cause production safety accidents. At present, the indicators for judging boiler slagging and fouling include ash melting point, slagging index, alkali metal content, fouling index, ash sintering temperature, etc. The initial sintering temperature of high-alkali coal ash is very effective in judging the slagging and fouling characteristics.

[0003] The initial sintering temperature of coal ash is used to characterize the strength of coal ash contamination on the convection heating surface of the boiler, and the initial sintering temperature ts value of coal ash is used to judge the contamination characteristics of coal ash. The lower the initial sintering temperature, the stronger the contamination characteristics of coal ash; the higher the initial sintering temperature, the weaker the contamination characteristics of coal ash.

[0004] At present, the laboratory test method is used to ashed coal samples that meet certain coal powder fineness requirements at a set temperature and screen them according to the requirements to obtain coal ash samples; the coal ash sintering ratio is measured at different temperatures, and the coal ash sintering ratio curve is drawn according to the measurement results and the initial sintering temperature of the coal ash is calculated. The test results are greatly affected by the ashing conditions and test conditions.

[0005] Scholars have conducted a lot of research on the application of multivariate statistical methods in actual production processes. Currently, commonly used methods include BP neural network model building and multivariate statistical regression. BP neural network is relatively widely used, but the amount of historical data in this prediction model test is small. When using BP neural network and other types for prediction, the prediction accuracy is poor. Summary of the invention

[0006] In view of the limitations of existing measurement technology, the purpose of the present invention is to provide a coal ash sintering temperature prediction method based on principal component regression. This method establishes a prediction model based on the full analysis data of coal types and the coal ash composition analysis data to predict the initial sintering temperature of other coal ashes.

[0007] The present invention is achieved by adopting the following technical solutions:

[0008] A method for predicting coal ash sintering temperature based on principal component regression comprises the following steps:

[0009] 1) Collect historical data of coal ash sintering test, including coal quality industrial analysis, elemental analysis and coal ash sintering temperature test data;

[0010] 2) Use useless information variable elimination method to select variables, remove variables with useless information on coal ash sintering temperature, reduce the impact of irrelevant information on the prediction model, improve the prediction accuracy of the model, and reduce the number of variables while improving the efficiency of calculation;

[0011] 3) Establishment of principal component regression model. Coal quality test data is used as the input variable of the model, and coal ash sintering temperature is used as the output variable of the model. A one-to-one mapping relationship is established between the two. The principal component regression model is established using the optimal number of principal components. The established prediction model is

[0012] 4) Substitute coal quality test data into the model In the prediction value

[0013] A further improvement of the present invention is that in step 1), m tests are carried out on different types of coal to obtain m groups of input and output data, the input data selects the full analysis data and ash composition analysis data of the test coal types, a total of 33 variables, and the input data matrix X and the output data matrix Y are obtained. The output variable of the prediction model is the initial sintering temperature of the coal ash, X is an m×33 matrix, and Y is an m×1 matrix.

[0014] A further improvement of the present invention is that the input variables are selected as shown in Table 1:

[0015] Table 1 Prediction model input variables

[0016]

[0017]

[0018] A further improvement of the present invention is that in step 2), non-information variables are used to screen the variables of the coal ash sintering temperature prediction model, thereby filtering out variable information irrelevant to the coal ash sintering temperature modeling and regression analysis.

[0019] A further improvement of the present invention is that the specific implementation method of step 2) is as follows:

[0020] 1) Generate a random matrix S as the noise matrix. The S matrix takes the standard normal distribution and has the same dimension as the original sample set X. It is added to the matrix X to form a new matrix XS m×66 ;

[0021] 2) Use the root mean square error of prediction RMSEP as a criterion to determine the number of principal elements p of the input variable matrix X;

[0022]

[0023] In the formula, i is the number of principal elements, Y is the test value of the initial sintering temperature of coal ash, is the predicted value of the initial sintering temperature of coal ash, and N is the number of input variables;

[0024] 3) The regression coefficient matrix B of the prediction model is obtained by cross-validation with point removal, and the matrix B is an n×2p matrix;

[0025] 4) Calculate the standard deviation of each regression coefficient using the following formula:

[0026]

[0027] Where L is the number of trials, J is the number of variables, N is the number of input variables, B = [b1, b2, ... b n ] is the model regression coefficient parameter of principal variable regression;

[0028] 5) Take the absolute maximum value of the index of the random noise matrix in B as the threshold, that is, max(abs(cr)), and then remove the measurement point variables in B corresponding to the original input matrix that are less than the threshold max(abs(cr), considering that the information contained in these variables is useless like random noise. Finally, the remaining measurement data points form the new measurement matrix X new , X new is an m×l matrix;

[0029] Using the new input data matrix X new And the output data matrix Y is used to establish the principal component regression model.

[0030] A further improvement of the present invention is that in step 3), a multivariate statistical analysis method is used to rank the contribution rate of coal quality test data to the coal ash sintering temperature prediction model, and variables with low contribution rates are screened out during regression analysis, and a principal component regression analysis method is used to establish a coal ash sintering temperature prediction model.

[0031] A further improvement of the present invention is that the specific implementation method of step 3) is as follows:

[0032] Using X new As input to the multiple linear regression model for regression modeling, Before using X new The first k principal elements of the original data matrix X are used to replace new , as the input of the multiple linear regression model for regression modeling, E represents the error caused by deleting several principal components, and the principal component regression model can be obtained:

[0033] Y=a1t1+a2t2+…+a k t k =AT k (3)

[0034] Where k is the number of principal elements, A=[a1,a2,…a k ]Ask about the model parameters of principal component regression;

[0035] T k =[t1,t2,…t k ] is X new The principal component matrix of is fitted with the data to obtain an estimate of A;

[0036]

[0037] Since the principal components are orthogonal, the model overcomes the impact of multicollinearity;

[0038] Y=X new P k A (5)

[0039] Compared with formula (3), combined with formula (5), we get:

[0040]

[0041] The parameters of the principal component regression model are obtained through formula (6).

[0042] A further improvement of the present invention is that in step 4), the real-time operation data X of the unit of the verification set sample is substituted into , and obtain the predicted value.

[0043] The present invention has at least the following beneficial technical effects:

[0044] The present invention establishes a principal component regression prediction model of coal quality test data and coal ash initial sintering temperature by using a principal component regression analysis method, and uses the prediction model to predict the initial sintering temperature of coal ash of a new type of coal.

[0045] The principal component regression prediction model of the initial sintering temperature of coal ash is established through principal component regression analysis. Coal quality test data (ash melting point, ash content, ash composition, etc.) are selected. There is a strong correlation between these test data and the initial sintering temperature of coal ash. Principal component regression uses data analysis to project data with nonlinear relationships in low-dimensional space into high-dimensional space to obtain an approximate linear relationship. The relationship between the data does not change during the data projection process. The prediction model has good accuracy when modeling using principal component regression analysis.

[0046] The uninformative variable screening method is used to select variables and remove variables such as received basic hydrogen that have little influence on the initial sintering temperature of coal ash. This can reduce the impact of uninformative variables on the prediction model and improve the prediction accuracy of the model. In addition, the reduction in the number of variables can also improve the efficiency of the operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of the present invention.

[0048] Figure 2 Schematic diagram of a prediction model according to an embodiment of the present invention.

[0049] Figure 3 Schematic diagram of the variable selection process of an embodiment of the present invention.

[0050] Figure 4 The scatter plot is a predicted output and expected output according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The present invention is described in detail below in conjunction with specific examples. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0052] like Figure 1 As shown, the present invention provides a method for predicting coal ash sintering temperature based on principal component regression, comprising the following steps:

[0053] Step 1. Data Collection

[0054] Carry out m tests on different types of coal respectively. To ensure the accuracy of the mathematical model, the test coal types cover as many types of coal as possible, so m groups of input and output data can be obtained. The input data selects the full analysis data and ash composition analysis data of the test coal types, a total of 33 variables, and obtains the input data matrix X (X is an m×33 matrix) and the output data matrix Y (Y is an m×1 matrix). The input variables are selected as shown in Table 1. The output variable of the prediction model is the initial sintering temperature of the coal ash.

[0055] Table 1 Prediction model input variables

[0056]

[0057]

[0058] Step 2. Variable selection

[0059] Before modeling, the input data matrix is ​​selected for variables, and variables carrying useless information are removed, which can reduce the impact of various non-target factors on the model and improve the prediction accuracy of the model. The reduction in the number of variables can also improve the efficiency of the operation. This model uses the useless information variable elimination method for variable selection. The useless information variable elimination method (Elimination of Uninformative Variables, UVE) is a variable selection method based on partial least squares regression. It achieves the purpose of variable selection by processing the regression coefficient. The calculation process is as follows:

[0060] 1) Generate a random matrix S as the noise matrix. The S matrix takes the standard normal distribution and has the same dimension as the original sample set X. It is added to the matrix X to form a new matrix XS m×66 .

[0061] 2) Use the root mean square error of prediction (RMSEP) as a criterion to determine the number of principal elements p of the input variable matrix X;

[0062]

[0063] In the formula, i is the number of principal elements;

[0064] 3) The regression coefficient matrix B of the prediction model is obtained by cross-validation with point removal, and the matrix B is an n×2p matrix;

[0065] 4) Calculate the standard deviation of each regression coefficient using the following formula:

[0066]

[0067] In the formula, l is the number of experiments, j is the number of regression coefficients;

[0068] 5) Take the absolute maximum value of the index of the random noise matrix in B as the threshold, that is, max(abs(cr)), and then remove the measurement point variables in B corresponding to the original input matrix that are less than the threshold max(abs(cr), considering that the information contained in these variables is useless like random noise. Finally, the remaining measurement data points form the new measurement matrix X new (X new is an m×l matrix).

[0069] Using the new input data matrix X new (X new is an m×l matrix) and the output data matrix Y (Y is an m×1 matrix) to establish a principal component regression model.

[0070] Step 3. Model building

[0071] Using X newAs input to the multiple linear regression model for regression modeling, Before using X new The first k principal components (k in the following table of formulas (3)-(6) represents the number of principal components) are used to replace the original data matrix X new , as the input of the multiple linear regression model for regression modeling, E represents the error caused by deleting several principal components, and the principal component regression model can be obtained:

[0072] Y=a1t1+a2t2+…+a k t k =AT k (3)

[0073] Where A=[a1,a2,…a k ] is the model parameter of principal component regression

[0074] The estimated value of A can be obtained by fitting the data.

[0075]

[0076] Since the principal components are orthogonal, the model can overcome the impact of multicollinearity.

[0077] Y=X new P k A (5)

[0078] Compared with formula (3), combined with formula (5), we can get:

[0079]

[0080] The parameters of the principal component regression model can be obtained through formula (6).

[0081] The principal component regression model overcomes the problem of correlation between variables, omits minor principal components and noise, retains the main information and simplifies the calculation process.

[0082] Step 4. Prediction of coal ash sintering temperature

[0083] Using the coefficient matrix B fitted by the principal component regression model, the prediction model is established as follows:

[0084]

[0085] Where:

[0086] —Prediction of initial sintering temperature of coal ash;

[0087] X—Full analysis data of coal type and ash composition analysis data;

[0088] B—PCR model regression coefficient.

[0089] Substituting the real-time operation data X of the validation set samples into model (7), the predicted value can be obtained.

[0090] Example

[0091] This embodiment involves the prediction of the sintering temperature of coal ash of typical domestic slagging and contaminated coal types. The main coal types include Shenhua coal, Binchang coal, Lu'an coal, Jin coal, Jingbian coal, Wucaiwan coal and kaolin at different blending ratios. The specific prediction model is established as follows: Figure 2 shown.

[0092] Step 1: Test sample collection: collect test coal quality data and laboratory coal ash initial sintering temperature test data. The test coal types are shown in Table 2, with a total of 26 coal samples.

[0093] Table 2 Test coal samples

[0094]

[0095]

[0096]

[0097] Step 2: Remove useless variables

[0098] Generate a random matrix S as the noise matrix. The S matrix takes the standard normal distribution and has the same dimension as the original correction sample set X. After being added to the matrix X, a new matrix XS is formed. The elements in the added noise matrix S should be selected with appropriate size according to the data in X. While ensuring the selection of variables, as many variables containing useful information as possible should be retained to ensure the accuracy of the model. Variable selection is performed on the new matrix XS, and the threshold max(abs(cr)) is determined. The measurement point variables corresponding to the c values ​​between +max(abs(cr)) and -max(abs(cr)) are calculated. The measurement information corresponding to these measurement point variables is considered to be noise for the overall data, and these measurement point variables are removed. After removing the useless information measurement point variables, the new matrix Xnew of the unit operation data is obtained. Xnew is a 26×22 matrix. Compared with the original matrix, the number of measurement point variables is reduced by 11, and the amount of data is greatly reduced. The variable selection process is as follows. Figure 3 shown.

[0099] After useless information variables were screened out, the variables involved in modeling became 22, as shown in Table 3.

[0100] Table 3 Input variables after variable screening

[0101]

[0102]

[0103] Step 3: Divide the test sample data into a calibration sample set Xc and a verification sample set Xv. Samples T1-T18 are calibration sample sets, and samples T19-T26 are verification sample sets. There are 18 samples in the calibration sample set and 8 samples in the verification set. Use the calibration sample set to establish a soft measurement model, use the real-time data of the verification sample set to perform calculations, and compare the calculation results with the coal quality parameters of the sample to obtain the error between the predicted value and the measured value. The error reflects the accuracy and stability of the measurement model.

[0104] Step 4: Prediction model building

[0105] The coal quality test data of the calibration sample set is used as the input variable of the model, and the initial sintering temperature of the coal ash of the calibration sample set is used as the output variable of the model. A one-to-one mapping relationship is established between the two to obtain a mathematical model. After a relatively accurate initial sintering temperature prediction model is established, the coal quality test data is input into the prediction model, and the output is the initial sintering temperature of the coal ash.

[0106] After calculation, the optimal number of principal components of coal quality data is R = 12. Using the principal component regression method to establish a prediction model, a 12×1 coefficient matrix B can be fitted, and the established prediction model is:

[0107]

[0108] Where:

[0109] —Prediction of initial sintering temperature of coal ash;

[0110] X v — Coal quality test data;

[0111] B—PCR model regression coefficient.

[0112] By bringing the coal quality test data Xv of the verification sample set into prediction models 3-4, the predicted value of the initial sintering temperature of the coal ash can be obtained.

[0113] Step 5: Prediction of sintering temperature of coal ash from validation set samples

[0114] Scatter plots are used as a method to test the prediction performance of the model. For each sample point in the validation sample set, its measured value has a corresponding model predicted value. The scatter plot uses the sample measured value as the X coordinate and the model predicted value / measured value as the Y coordinate to represent the sample point in a two-dimensional coordinate system. The best model result is when the predicted value and the measured value are equal. At this time, the sample point is Figure 4In the scatter plot, the data are distributed on a curve with a slope of 1. The distribution of points in the scatter plot can illustrate the prediction effect of the model.

[0115] Table 3 Prediction values ​​of prediction model

[0116] project unit T19 T20 T21 T22 T23 T24 T25 T26 Prediction of coal ash sintering temperature ℃ 982 981 998 1039 1014 1048 1080 1080 Test value of coal ash sintering temperature ℃ 975 983 986 1011 1022 1034 1076 1087

[0117] Although the present invention has been described in detail above with general descriptions and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements may be made thereto based on the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of protection claimed by the present invention.

Claims

1. A method for predicting coal ash sintering temperature based on principal component regression, characterized in that: The following steps are involved: 1) Collect historical data of coal ash sintering test, including coal quality industrial analysis, elemental analysis and coal ash sintering temperature test data; Carry out m tests on different types of coal respectively, and obtain m groups of input and output data. The input data selects the full analysis data and ash composition analysis data of the test coal, with a total of 33 variables, and obtains the input data matrix X and the output data matrix Y. The output variable of the prediction model is the initial sintering temperature of coal ash. X is an m×33 matrix, and Y is an m×1 matrix. The input variables include: total moisture content on received basis, aluminum oxide, ash deformation temperature DT, moisture content on air-dried basis, iron oxide, ash softening temperature ST, ash content on received basis, calcium oxide, ash flow temperature FT, volatile matter on dry ash-free basis, magnesium oxide, Rtj, carbon content on received basis, sodium oxide, alkali-acid ratio, hydrogen content on received basis, potassium oxide, silicon ratio, nitrogen content on received basis, titanium dioxide, FA index, oxygen content on received basis, sulfur trioxide, FKNA index, total sulfur, manganese dioxide in ash, S / A, lower calorific value on received basis, phosphorus pentoxide in ash, Fe, silicon dioxide, characteristic ash melting temperature and Rz; 2) Use the useless information variable elimination method to select variables, remove variables with useless information on the coal ash sintering temperature, reduce the impact of irrelevant information on the prediction model, and improve the prediction accuracy of the model. In addition, the reduction in the number of variables also improves the efficiency of the operation; Among them, the variables of the coal ash sintering temperature prediction model are screened by using non-information variables to screen out variable information that is irrelevant to the coal ash sintering temperature modeling and regression analysis. The specific implementation method is as follows: 201) Generate a random matrix S as the noise matrix. The S matrix takes the standard normal distribution and has the same dimension as the original sample set X. It is added to the matrix X to form a new matrix XS m×66 ; 202) Using the root mean square error of prediction RMSEP as a criterion to determine the number of principal elements p of the input variable matrix X; In the formula, i is the number of principal elements, Y is the test value of the initial sintering temperature of coal ash, is the predicted value of the initial sintering temperature of coal ash, and N is the number of input variables; 203) The regression coefficient matrix B of the prediction model is obtained by removing the point cross validation, and the matrix B is an n×2p matrix; 204) Calculate the standard deviation of each regression coefficient using the following formula: Where L is the number of trials, J is the number of variables, N is the number of input variables, B = [b1, b2, ... b n ] is the model regression coefficient parameter of principal variable regression; 205) Take the absolute maximum value of the index of the random noise matrix in B as the threshold, that is, max(abs(cr)), and then remove the measurement point variables in B corresponding to the original input matrix that are less than the threshold max(abs(cr)). It is believed that the information contained in these variables is useless like random noise. Finally, the remaining measurement data points form the new measurement matrix X new , X new is an m×l matrix; Using the new input data matrix X new Establish a principal component regression model with the output data matrix Y; 3) Establishment of principal component regression model. Coal quality test data is used as the input variable of the model, and coal ash sintering temperature is used as the output variable of the model. A one-to-one mapping relationship is established between the two. The principal component regression model is established using the optimal number of principal components. The established prediction model is The multivariate statistical analysis method is used to rank the contribution rate of coal quality test data to the coal ash sintering temperature prediction model, and the variables with low contribution rate are screened out during regression analysis. The principal component regression analysis method is used to establish the prediction model of coal ash sintering temperature. The specific implementation method is as follows: Using X new As input to the multiple linear regression model for regression modeling, Using X new The first k principal elements of the original data matrix X are used to replace new , as the input of the multivariate linear regression model for regression modeling, E represents the error caused by deleting several principal components, and the principal component regression model can be obtained: Y=a1t1+a2t2+…+a k t k =AT k (3) Where k is the number of principal elements, A=[a1,a2,…a k ] are the model parameters of principal variable regression; T k =[t1,t2,…t k ] is X new The principal component matrix of is fitted with the data to obtain an estimate of A; Since the principal components are orthogonal, the model overcomes the impact of multicollinearity; Y=X new P k A(5) Compared with formula (3), combined with formula (5), we get: The parameters of the principal component regression model are obtained through formula (6); 4) Substitute coal quality test data into the model The predicted value is obtained 2. The method for predicting coal ash sintering temperature based on principal component regression according to claim 1 is characterized in that: In step 4), substitute the real-time operation data X of the verification set sample into , and obtain the predicted value.

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