Supervised matrix regression-based safety monitoring method for fused magnesia production process

Abstract

The application provides a kind of safety monitoring method for electric smelting magnesium oxide production process based on supervision matrix regression, relating to fault monitoring and diagnosis technical field, first, the application uses fixed camera to collect the furnace body image data of electric smelting magnesium oxide furnace, after gray scale and normalization processing, the furnace body image matrix is obtained;Then, the target function model of furnace body image matrix in low-dimensional space is established and trained by public information extraction method, and the mapping matrix unique to each sample data in low-dimensional space is solved;Then, the regression model of the mapping matrix of each sample and its corresponding class label vector is established by using supervision matrix regression method;Next, the hyper-spherical boundary and angle boundary are determined according to the class label of sample;Finally, the furnace body image data is collected and processed in real time, and the class of new sample is judged according to the hyper-spherical boundary and angle boundary, and then it is judged whether the fault occurs at the current time or not.The application can improve the accuracy of industrial fault monitoring classification.

Description

Technical Field

[0001] The present invention relates to the technical field of fault monitoring and diagnosis, and in particular to a safety monitoring method for a fused magnesium oxide production process based on supervised matrix regression. Background Art

[0002] Magnesium oxide is an important refractory material widely used in chemical, aerospace, and metallurgical industries. As the primary equipment for magnesium oxide production, the safety of the fused magnesium oxide furnace itself is crucial to the entire production process. A fused magnesium oxide furnace is essentially a submerged arc furnace. When electricity is applied to it, an arc forms between the electrodes, generating arc heat. This arc heat effectively heats the material to temperatures of 2800°C or higher, facilitating the melting of the magnesium oxide. During the production process, if the furnace walls are damaged by high temperatures, the ultra-high-temperature liquid within the furnace will leak out. This can, at best, reduce performance and impact production, while at worst, it can cause downtime, equipment damage, and even casualties. Fortunately, faults can be corrected early in the process by spraying cooling water on the furnace walls or adjusting the electrode position. However, the current level of automation in my country's magnesium oxide smelting process relies primarily on worker inspections to detect faults. Failure to detect these faults in a timely manner can lead to furnace failures. Therefore, developing a safety monitoring method to monitor the fused magnesium oxide production process and detect faults promptly is of great social and economic significance. Summary of the Invention

[0003] In view of the shortcomings of the existing technology, the present invention provides a safety monitoring method for the fused magnesia production process based on supervised matrix regression, which can solve the problem of underreporting caused by incomplete monitoring of the magnesia furnace body and improve the accuracy of production data classification.

[0004] A safety monitoring method for a fused magnesium oxide production process based on supervised matrix regression comprises the following steps:

[0005] Step 1: In the industrial production process of fused magnesia, the image data of the fused magnesia furnace is collected by a fixed camera to obtain training samples under R working conditions. The furnace image data is grayscaled and normalized to obtain {X i |i=1,2,…,N}, where X i is the i-th image data, its image dimension is a×b, and N is the total number of training samples;

[0006] Step 2: Through the public information extraction method, establish the objective function model of the furnace image matrix of N training samples in low-dimensional space, solve the objective function model, and obtain W, {H i |i=1,2,…,N} and H * ;

[0007] The objective function model:

[0008]

[0009] Among them, W is the projection matrix with data dimension a×m, {H i |i=1,2,…,N} is the mapping matrix of N training samples in low-dimensional space, H * is the common mapping matrix of all furnace image matrices in low-dimensional space, its data dimension is m×b, and λ1 and λ2 are coefficient parameters;

[0010] The specific steps of solving the objective function model are as follows:

[0011] Step 2.1: Randomly generate the projection matrix W and the common mapping matrix H of all furnace image matrices in low-dimensional space * ;

[0012] Step 2.2: Fix W and H * , find H i , i=1,2,…,N, the specific steps are as follows:

[0013] Step 2.2.1: Convert the objective function model into:

[0014]

[0015] Step 2.2.2: Formula (2) for H i The guide is:

[0016]

[0017] Step 2.2.3: Make get:

[0018] H i =(W T W+λ1E) -1 (W T X i +λ1H * ) (4)

[0019] Where E is the identity matrix with data dimension of m×m;

[0020] Step 2.3: Fix H * 、H i , find W, the specific steps are as follows:

[0021] Step 2.3.1: Convert the objective function model into:

[0022]

[0023] Step 2.3.2: The derivative of (5) with respect to W is:

[0024]

[0025] Step 2.3.3: Let Get:

[0026]

[0027] where E is a unit matrix of dimension m x m;

[0028] Step 2.4: Fix H i , W, and solve H * . The specific steps are as follows:

[0029] Step 2.4.1: Convert the objective function model to:

[0030]

[0031] Step 2.4.2: The derivative of formula (8) with respect to H * is:

[0032]

[0033] Step 2.4.3: Let Get

[0034]

[0035] Step 2.5: Repeat steps 2.2 to 2.4 for p iterations, and finally get the projection matrix W, the mapping matrix of the training samples in the low-dimensional space {H i |i = 1, 2, …, N}, and the common mapping matrix H * of all furnace image matrices in the low-dimensional space.

[0036] Step 3: Solve the mapping matrix Z * unique to each sample data in the low-dimensional space using W and H i solved in step 2 as follows:

[0037] Z i = (W T W) -1 W T X i -H * (11)

[0038] Step 4: Establish a regression model of the mapping matrix of each sample and its corresponding class label vector by a supervised matrix regression method, and solve the regression model to obtain u (r) , v (r) and b (r) .

[0039] The regression model:

[0040]

[0041] where u (r) , v (r) are left and right projection vectors, and the data dimensions are m x 1 and b x 1, respectively, b (r) is a constant bias, and θ is a coefficient parameter; R is the number of sample categories; N is the number of training samples; is the category label of the nth sample in the rth regression model, if Z n belongs to the rth working condition, then otherwise

[0042] Let

[0043]

[0044] Define the parameter ω n = cos (y n , t n ) (14) represents the difference between the category label vector obtained by the sample through the regression model and its true value, that is: the greater the value of ω n , the better the regression effect;

[0045] where the smallest c ω n corresponding data label set {Q}, {C n} is the label set of data belonging to the same category as data Z n ;

[0046] Define

[0047] {G n} = {C n} - {Q} (15)

[0048]

[0049] σ is a coefficient parameter;

[0050] The specific steps for solving the regression model in step 4 are as follows:

[0051] Step 4.1: Decompose the above regression model (12) into R optimization problems, that is, rewrite it as:

[0052]

[0053] Step 4.2: Define

[0054] Ω (ij) = ω ij (18)

[0055] D=diag(d1,d2,…,d N )(19)

[0056] in

[0057] Step 4.3: Fix v (r) Find u (r) and b (r) , the specific steps are as follows:

[0058] Step 4.3.1: Definition

[0059]

[0060]

[0061] Depend on

[0062]

[0063] Ω (ij) is the element in row i and column j of Ω;

[0064] Formula (17) can be rewritten as

[0065]

[0066] Where e is a vector whose elements are all 1;

[0067] Step 4.3.2: By solving formula (24), we can get:

[0068] u (r) =(F (r) L c (F (r) ) T ) -1 F (r) L p (y (r) ) T (25)

[0069]

[0070] in, L c =L p +θ(D-Ω-Ω T ); Step 4.4: Fix u (r) Find v (r) and b (r) , the specific steps are as follows: Step 4.4.1: Define

[0071]

[0072] Formula (17) can be rewritten as

[0073]

[0074] Where e is a vector whose elements are all 1.

[0075] Step 4.4.2: By solving formula (30), we can get:

[0076] v (r) =((K (r) ) T L c K (r) ) -1 (K (r) ) T L p (y (r) ) T (31)

[0077]

[0078] in, L c =L p +θ(D-Ω-Ω T );

[0079] Step 4.5: Repeat the above formulas (13) to (16), and perform steps 4.2 to 4.4 for p iterations to finally obtain the left and right projection vectors u (r) 、v (r) , and a constant deviation b (r) .

[0080] Step 5: Determine the decision boundary based on the class label of the sample;

[0081] The decision boundary includes a hypersphere boundary and an angle boundary;

[0082] The hypersphere boundary is calculated based on the data category label, and the distance between any two labels is Then the hypersphere boundary is centered on the corresponding category label and has a radius of The area enclosed by the hypersphere.

[0083] The angle boundary is an area enclosed by a cone plane with the origin and the category label as the axis and the maximum angle between the categories as the vertex angle;

[0084] According to geometric knowledge, the expression of the maximum angle α is as follows:

[0085]

[0086] If the cosine value between the predicted sample label and the class label is less than Then the sample has the same category as the label.

[0087] Step 6: Conduct online safety monitoring of the fused magnesium oxide production process;

[0088] Step 6.1: Use a fixed camera to collect the image data of the fused magnesium furnace during the industrial production of fused magnesium oxide, and perform grayscale and normalization processing on the image data to obtain X new .

[0089] Step 6.2: Obtain the unique mapping matrix of the new sample data in the low-dimensional space:

[0090] Z new =(W T W) -1 W T X new -H * (35)

[0091] Step 6.3: Project vector u left and right (r) 、v (r) and a constant deviation b (r) Predict the class label of a new sample:

[0092]

[0093] Step 6.3: Determine the category of the new sample based on the hypersphere boundary and the angle boundary, and then determine whether a fault occurs at the current moment.

[0094] The beneficial effects of adopting the above technical solution are:

[0095] The present invention provides a safety monitoring method for the fused magnesium oxide production process based on supervised matrix regression, which has the following beneficial effects:

[0096] (1) The present invention uses a camera to replace worker inspections to collect furnace image data during the production process of fused magnesium oxide, and performs online fault monitoring of the fused magnesium oxide furnace body, thereby solving the problem of difficulty in ensuring timely and accurate decision-making in manual monitoring.

[0097] (2) The present invention grayscales the furnace image, preserving the light and dark features of the original image. It also uses a common information extraction method to reduce the dimensionality of the furnace image matrix, preserving the unique and significant features of the data, reducing the data dimension and thus improving the computational speed. A supervised matrix regression model is established, and furnace image data is collected and processed in real time during the production process. The hypersphere boundary and angle boundary are used to determine the category of new samples, thereby determining whether a fault has occurred at the current moment, thereby improving the accuracy of the monitoring results. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 Schematic diagram of the structure of the electric melting magnesium oxide furnace in this embodiment;

[0099] Figure 2 Flowchart of the safety monitoring method for the fused magnesium oxide production process based on supervised matrix regression in this embodiment;

[0100] Figure 3 is a classification result diagram of the hypersphere boundary in this embodiment;

[0101] Figure 4 is a classification result diagram of angle boundaries in this embodiment;

[0102] Figure 5 This is the decision boundary diagram when the category is 3 in this embodiment;

[0103] in Figure 5 (a) - Hypersphere boundary diagram when the sample category is 3, Figure 5 (b)-Angle boundary diagram when the sample category is 3. DETAILED DESCRIPTION

[0104] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0105] like Figure 1 The figure below shows the structure of a fused magnesium oxide furnace (hereinafter referred to as a fused magnesium furnace). The fused magnesium oxide furnace uses the material resistance heat generated by the passage of electric current through the molten material as its main heat source, accompanied by arc heat. This concentrated heat can effectively heat the material to a melting point above 2800°C, which is conducive to the smelting of fused magnesia.

[0106] A safety monitoring method for fused magnesia production process based on supervised matrix regression, such as Figure 2 As shown, the following steps are included:

[0107] Step 1: In the industrial production process of fused magnesia, the image data of the fused magnesia furnace is collected by a fixed camera to obtain training samples under R working conditions. The furnace image data is grayscaled and normalized to obtain {X i |i=1,2,…,N}, where X i is the i-th image data, its image dimension is a×b, and N is the total number of training samples;

[0108] In this embodiment, N=100, a×b is 691×500; there are 50 samples under normal working conditions and 50 samples under leaking furnace conditions.

[0109] Step 2: Through the public information extraction method, establish the objective function model of the furnace image matrix of N training samples in low-dimensional space, solve the objective function model, and obtain W, {H i |i=1,2,…,N} and H * ;

[0110] The objective function model:

[0111]

[0112] Among them, W is the projection matrix with data dimension a×m, {H i |i=1,2,…,N} is the mapping matrix of N training samples in low-dimensional space, H * is the common mapping matrix of all furnace image matrices in low-dimensional space, its data dimension is m×b, and λ1 and λ2 are coefficient parameters;

[0113] In this embodiment, W is a 691×100 matrix, {H i |i=1,2,…,N} and H * It is a 100×500 matrix, λ1=10, λ2=0.1.

[0114] The specific steps of solving the objective function model are as follows:

[0115] Step 2.1: Randomly generate the projection matrix W and the common mapping matrix H of all furnace image matrices in low-dimensional space * ;

[0116] Step 2.2: Fix W and H * , find H i , i=1,2,…,N, the specific steps are as follows:

[0117] Step 2.2.1: Convert the objective function model into:

[0118]

[0119] Step 2.2.2: Formula (2) for H i The guide is:

[0120]

[0121] Step 2.2.3: Make get:

[0122] H i =(W T W+λ1E) -1 (W T X i +λ1H * )(4)

[0123] Wherein, E is an identity matrix with a data dimension of m×m. In this embodiment, E is an identity matrix with a data dimension of 100×100.

[0124] Step 2.3: Fix H * 、H i , find W, the specific steps are as follows:

[0125] Step 2.3.1: Convert the objective function model into:

[0126]

[0127] Step 2.3.2: The derivative of (5) with respect to W is:

[0128]

[0129] Step 2.3.3: Make get:

[0130]

[0131] Wherein, E is a unit matrix with a data dimension of m×m. In this embodiment, E is a unit matrix with a data dimension of 100×100.

[0132] Step 2.4: Fix H i , W, find H * , the specific steps are as follows:

[0133] Step 2.4.1: Convert the objective function model into:

[0134]

[0135] Step 2.4.2: Formula (8) for H * The guide is:

[0136]

[0137] Step 2.4.3: Make get

[0138]

[0139] Step 2.5: Repeat steps 2.2 to 2.4 for p iterations. In this embodiment, 50 iterations are performed to finally obtain the projection matrix W, the mapping matrix {H i |i=1,2,…,N}, the common mapping matrix H of all furnace image matrices in low-dimensional space * ;

[0140] Step 3: W and H obtained in step 2 * , find the unique mapping matrix Z of each sample data in the low-dimensional space i for:

[0141] Z i =(W T W) -1 W T X i -H * (11)

[0142] Step 4: Use the supervised matrix regression method to establish a regression model of the mapping matrix of each sample and its corresponding class label vector, and solve the regression model to obtain u (r) 、v (r) and b (r) ;

[0143] The regression model:

[0144]

[0145] Among them, u (r) 、v (r) They are left and right projection vectors, and the data dimensions are m×1, b×1, b (r) is a constant deviation, θ is a coefficient parameter; R is the number of sample categories; N is the number of training samples; is the category label of the nth sample in the rth regression model, if Z n Belongs to the rth working condition, then otherwise

[0146] set up

[0147]

[0148] Define parameter ω n =cos(y n ,t n )(14) represents the difference between the class label vector obtained by the regression model and its true value, that is: ω n The larger the value of , the better the regression effect;

[0149] In this embodiment, u (r) and v (r) They are matrices of 100×1 and 500×1 respectively, and θ=10000.

[0150] The smallest c ω n The corresponding data labels constitute the set {Q}, {C n} is related to data Z nA collection of labels for data belonging to the same category;

[0151] definition

[0152] {G n}={C n}-{Q}(15)

[0153]

[0154] σ is a coefficient parameter; in this embodiment, c=15, σ=1000.

[0155] The specific steps for solving the regression model in step 4 are as follows:

[0156] Step 4.1: Decompose the above regression model (12) into R optimization problems, which can be rewritten as:

[0157] Step 4.2: Definition

[0158] Ω (ij) =ω ij (18)

[0159] D=diag(d1,d2,…,d N )(19)

[0160] in Step 4.3: Fix v (r) Find u (r) and b (r) , the specific steps are as follows:

[0161] Step 4.3.1: Definition

[0162]

[0163] Depend on

[0164]

[0165] Ω (ij) is the element in row i and column j of Ω;

[0166] Formula (17) can be rewritten as

[0167]

[0168] Where e is a vector whose elements are all 1;

[0169] Step 4.3.2: By solving formula (24), we can get:

[0170] u (r) =(F (r) Lc (F (r) ) T ) -1 F (r) L p (y (r) ) T (25)

[0171]

[0172] in, L c =L p +θ(D-Ω-Ω T ). I is the identity matrix with data dimension of N×N.

[0173] Step 4.4: Fix u (r) Find v (r) and b (r) , the specific steps are as follows:

[0174] Step 4.4.1: Definition

[0175]

[0176] Formula (17) can be rewritten as

[0177]

[0178] Where e is a vector whose elements are all 1.

[0179] Step 4.4.2: By solving formula (30), we can get:

[0180] v (r) =((K (r) ) T L c K (r) ) -1 (K (r) ) T L p (y (r) ) T (31)

[0181]

[0182] in, L c =L p +θ(D-Ω-Ω T ); I is the identity matrix with data dimension of N×N.

[0183] Step 4.5: Repeat the above formulas (13) to (16), and perform steps 4.2 to 4.4 for p iterations to finally obtain the left and right projection vectors u (r) 、v (r) , and a constant deviation b (r) .

[0184] Step 5: Determine the decision boundary based on the class label of the sample;

[0185] The decision boundary includes a hypersphere boundary and an angle boundary;

[0186] The hypersphere boundary is the largest non-intersecting hypersphere with the category label as the decision center; according to the data category label, the distance between any two labels is calculated as Then the hypersphere boundary is centered on the corresponding category label and has a radius of The area enclosed by the hypersphere.

[0187] The angle boundary is an area surrounded by cone planes with the origin and the category label as the axis and the maximum angle between the categories as the vertex angle. The decision boundary diagram when the number of sample categories is 3 is as follows: Figure 5 As shown, Figure 5 (a) is the hypersphere boundary diagram, Figure 5 (b) is the angle boundary diagram.

[0188] According to geometric knowledge, the expression of the maximum angle α is as follows:

[0189]

[0190] In this embodiment, R=2.

[0191] If the cosine value between the predicted sample label and the class label is less than In this embodiment, Then the sample has the same category as the label.

[0192] Step 6: Conduct online safety monitoring of the fused magnesium oxide production process;

[0193] Step 6.1: Use a fixed camera to collect the image data of the fused magnesium furnace during the industrial production of fused magnesium oxide, and perform grayscale and normalization processing on the image data to obtain X new .

[0194] Step 6.2: Obtain the unique mapping matrix of the new sample data in the low-dimensional space:

[0195] Z new =(W T W) -1 W T Xnew -H * (35)

[0196] Step 6.3: Project vector u left and right (r) 、v (r) and a constant deviation b (r) Predict the class label of a new sample:

[0197]

[0198] Step 6.3: Determine the category of the new sample based on the hypersphere boundary and the angle boundary, and then determine whether a fault occurs at the current moment.

[0199] Figure 3 、 Figure 4 They are the sample classification diagrams under the hypersphere boundary and angle boundary respectively. Figure 3 、 Figure 4 It can be seen that the present invention achieves a good classification effect on normal data and fault data.

[0200] During the overall monitoring process, the classification accuracy of samples within both the hypersphere boundary and the angle boundary reached 99.5%. This demonstrates that the present invention can accurately classify data under normal and abnormal operating conditions, thereby determining whether a fault has occurred at the current moment, thereby improving the accuracy of industrial fault monitoring in the fused magnesia production process.

[0201] The above description is merely a preferred embodiment of the present disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also encompass other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the above-mentioned inventive concept. For example, a technical solution formed by mutually replacing the above-mentioned features with (but not limited to) technical features with similar functions disclosed in the embodiments of the present disclosure.

Claims

1. A safety monitoring method for the production process of fused magnesium oxide based on supervised matrix regression, characterized in that: The following steps are involved: Step 1: In the industrial production process of fused magnesia, the image data of the fused magnesia furnace is collected by a fixed camera to obtain training samples under R working conditions. The furnace image data is grayscaled and normalized to obtain {X i |i=1,2,…,N}, where X i is the i-th image data, its image dimension is a×b, and N is the total number of training samples; Step 2: Through the public information extraction method, establish the objective function model of the furnace image matrix of N training samples in low-dimensional space, solve the objective function model, and obtain the projection matrix W and the mapping matrix {H i |i=1,2,…,N} and the common mapping matrix H * ; The objective function model in step 2 is: Among them, W is the projection matrix with data dimension a×m, {H i |i=1,2,…,N} is the mapping matrix of N training samples in low-dimensional space, H * is the common mapping matrix of all furnace image matrices in low-dimensional space, its data dimension is m×b, and λ1 and λ2 are coefficient parameters; Step 3: The projection matrix W and the common mapping matrix H obtained in step 2 * , find the unique mapping matrix Z of each sample data in the low-dimensional space i ;. The mapping matrix Z described in step 3 i for: Z i =(W T W) -1 W T X i -H * (11); Step 4: Use the supervised matrix regression method to establish a regression model of the mapping matrix of each sample and its corresponding class label vector, and solve the regression model to obtain the left and right projection vectors u (r) 、v (r) , and a constant deviation b (r) ; The regression model described in step 4: Among them, u (r) 、v (r) They are left and right projection vectors, and the data dimensions are m×1, b×1, b (r) is a constant deviation, θ is a coefficient parameter; R is the number of sample categories; N is the number of training samples; is the category label of the nth sample in the rth regression model, if Z n Belongs to the rth working condition, then otherwise set up Define parameter ω n =cos(y n ,t n )(14) represents the difference between the class label vector obtained by the regression model and its true value, that is: ω n The larger the value of , the better the regression effect; The smallest c ω n The corresponding data labels constitute the set {Q}, {C n } is related to data Z n A collection of labels for data belonging to the same category; definition {G n }={C n }-{Q}(15) σ is the coefficient parameter; Step 5: Determine the decision boundary based on the class label of the sample; Step 6: Conduct online safety monitoring of the fused magnesium oxide production process; The step 6 specifically includes the following steps: Step 6.1: Use a fixed camera to collect the image data of the fused magnesium furnace during the industrial production of fused magnesium oxide, and perform grayscale and normalization processing on the image data to obtain X new ; Step 6.2: Obtain the unique mapping matrix of the new sample data in the low-dimensional space: Z new =(W T W) -1 W T X new -H * (35) Step 6.3: Project vector u left and right (r) 、v (r) and a constant deviation b (r) Predict the class label of a new sample: Step 6.3: Determine the category of the new sample based on the hypersphere boundary and the angle boundary, and then determine whether a fault occurs at the current moment.

2. A method for safety monitoring of fused magnesium oxide production process based on supervised matrix regression according to claim 1, characterized in that: The specific steps for solving the objective function model described in step 2 are as follows: Step 2.1: Randomly generate the projection matrix W and the common mapping matrix H of all furnace image matrices in low-dimensional space * ; Step 2.2: Fix W and H * , find H i , i=1,2,…,N, the specific steps are as follows: Step 2.2.1: Convert the objective function model into: Step 2.2.2: Formula (2) for H i The guide is: Step 2.2.3: Make get: H i =(W T W+λ1E) -1 (W T X i +λ1H * ) (4) Where E is the identity matrix with data dimension of m×m; Step 2.3: Fix H * 、H i , find W, the specific steps are as follows: Step 2.3.1: Convert the objective function model into: Step 2.3.2: The derivative of (5) with respect to W is: Step 2.3.3: Make get: Where E is the identity matrix with data dimension of m×m; Step 2.4: Fix H i , W, find H * , the specific steps are as follows: Step 2.4.1: Convert the objective function model into: Step 2.4.2: Formula (8) for H * The guide is: Step 2.4.3: Make get Step 2.5: Repeat steps 2.2 to 2.4 for p iterations to finally obtain the projection matrix W, the mapping matrix {H i |i=1,2,…,N}, the common mapping matrix H of all furnace image matrices in low-dimensional space * .

3. A method for safety monitoring of fused magnesium oxide production process based on supervised matrix regression according to claim 1, characterized in that: The specific steps for solving the regression model described in step 4 are as follows: Step 4.1: Decompose the above regression model (12) into R optimization problems, which can be rewritten as: Step 4.2: Definition Oh (ij) =ω ij (18) D=diag(d1,d2,…,d N )(19) in Step 4.3: Fix v (r) Find u (r) and b (r) , the specific steps are as follows: Step 4.3.1: Definition Depend on Ω (ij) is the element in row i and column j of Ω; Formula (17) can be rewritten as Where e is a vector whose elements are all 1; Step 4.3.2: By solving formula (24), we can get: in, L c =L p +θ(D-Ω-Ω T ); Step 4.4: Fix u (r) Find v (r) and b (r) , the specific steps are as follows: Step 4.4.1: Define Formula (17) can be rewritten as Where e is a vector whose elements are all 1; Step 4.4.2: By solving formula (30), we can get: v (r) =((K (r) ) T L c K (r) ) -1 (K (r) ) T L p (y (r) ) T (31) Among them, L c =L p +θ(D-Ω-Ω T ); Step 4.5: Repeat the above formulas (13) to (16), and perform steps 4.2 to 4.4 for p iterations to finally obtain the left and right projection vectors u (r) 、v (r) , and a constant deviation b (r) .

4. The method for safety monitoring of fused magnesium oxide production process based on supervised matrix regression according to claim 1, wherein: The decision boundary in step 5 includes a hypersphere boundary and an angle boundary; The hypersphere boundary is calculated based on the data category label, and the distance between any two labels is Then the hypersphere boundary is centered on the corresponding category label and has a radius of The area enclosed by the hypersphere; The angle boundary is an area enclosed by a cone plane with the origin and the category label as the axis and the maximum angle between the categories as the vertex angle; According to geometric knowledge, the expression of the maximum angle α is as follows: If the cosine value between the predicted sample label and the class label is less than Then the sample has the same category as the label.

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