Safety monitoring method for fused magnesium oxide production process based on supervision matrix regression

Abstract

The invention provides an electric smelting magnesium oxide production process safety monitoring method based on supervision matrix regression, and relates to the technical field of fault monitoring and diagnose.The method comprises the steps that firstly, a fixed camera is used for collecting furnace body image data of an electric smelting magnesium oxide furnace, and after graying and normalization processing, a furnace body image matrix is obtained; secondly, establishing and training an objective function model of the furnace body image matrix in a low-dimensional space through a public information extraction method, and solving a unique mapping matrix of each piece of sample data in the low-dimensional space; then, establishing a regression model of the mapping matrix of each sample and the corresponding class label vector by adopting a supervised matrix regression method; then, determining a hyper-spherical boundary and an angle boundary according to the category label of the sample; finally, furnace body image data are collected and processed in real time, the category of a new sample is judged according to the hyper-sphere boundary and the angle boundary, and then whether a fault occurs at the current moment or not is judged. According to the invention, the accuracy of industrial fault monitoring classification can be improved.

Description

Technical Field

[0001] The 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, which is widely used in chemical industry, aerospace, metallurgy and other fields. As the main equipment for producing magnesium oxide, the safety of the furnace body of the fused magnesium oxide furnace affects the entire production process. The fused magnesium oxide furnace is actually a submerged arc furnace. When it is energized, an arc will be generated between the electrodes, and arc heat will be generated at the same time. The heat generated by the arc can effectively heat the material to a temperature of 2800℃ or higher, which is conducive to the melting of magnesium oxide. During the production process, once the furnace wall is damaged by high temperature, the ultra-high temperature liquid in the furnace will flow out, which will reduce the performance and affect production, and even cause downtime, equipment damage, and even casualties. Fortunately, in the early stages of this process, the fault can be eliminated by spraying cooling water on the furnace wall or adjusting the position of the electrode. However, the current automation level of magnesium oxide smelting process in my country is low, and it mainly relies on workers' inspections to monitor faults. If the workers do not find it in time, it will lead to the occurrence of furnace leakage faults. Therefore, it is of great social benefit and economic significance to develop a safety monitoring method to monitor the fused magnesium oxide production process in order to detect faults in time. Summary of the invention

[0003] In view of the shortcomings of the prior art, 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 magnesium oxide 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 magnesium oxide, the furnace image data of the fused magnesium oxide furnace is collected by a fixed camera to obtain training samples under R working conditions, and the furnace image data is grayed 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] Where 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, 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: Order 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 formula (5) with respect to W is:

[0024]

[0025] Step 2.3.3: Order get:

[0026]

[0027] Where E is the identity matrix with data dimension of m×m;

[0028] Step 2.4: Fix H i , W, find H * , the specific steps are as follows:

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

[0030]

[0031] Step 2.4.2: Formula (8) for H * The guide is:

[0032]

[0033] Step 2.4.3: Order get

[0034]

[0035] Step 2.5: Repeat steps 2.2 to 2.4 for p iterations, and 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 * ;

[0036] Step 3: Obtain W and H from step 2 * , find the unique mapping matrix Z of each sample data in the low-dimensional space i for:

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

[0038] 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) ;

[0039] The regression model:

[0040]

[0041] Among them, u (r) 、v (r) They are left and right projection vectors, respectively, 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

[0042] set up

[0043]

[0044] 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;

[0045] The smallest c ω n The corresponding data labels constitute a set {Q}, {C n} is related to data Z n A collection of labels for data belonging to the same category;

[0046] definition

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

[0048]

[0049] σ is the coefficient parameter;

[0050] The specific steps of 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: Definition

[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 in 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 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: Definition

[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 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 category 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 surrounded 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 process of fused magnesium oxide online, and grayscale and normalize 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 method for safety monitoring of 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 the timeliness and accuracy of decision-making in manual monitoring.

[0097] (2) The present invention grayscales the furnace image, retains the light and dark features of the original image, and uses a common information extraction method to reduce the dimension of the furnace image matrix, retains the unique and significant features of the data, reduces the data dimension and thus improves the computing speed. A supervised matrix regression model is established, and the furnace image data is collected and processed in real time during the production process. The category of the new sample is determined by the hypersphere boundary and the angle boundary, and then it is determined whether a fault occurs 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 Flow chart of the safety monitoring method of 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 It 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 specific implementation of the present invention is further described in detail below in conjunction with 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 shows the schematic diagram of the structure of the fused magnesium oxide furnace (hereinafter referred to as the fused magnesium furnace). The fused magnesium oxide furnace mainly uses the material resistance heat generated by the current passing through the material in the molten state as the main heat source, accompanied by arc heat. Its heat is concentrated and can effectively heat the material to a melting point of more than 2800℃, which is conducive to smelting fused magnesia.

[0106] A safety monitoring method for fused magnesium oxide 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 magnesium oxide, the furnace image data of the fused magnesium oxide furnace is collected by a fixed camera to obtain training samples under R working conditions, and the furnace image data is grayed 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] Where 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, 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: Order get:

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

[0123] 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.

[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 formula (5) with respect to W is:

[0128]

[0129] Step 2.3.3: Order 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: Order 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: Obtain W and H from 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, respectively, 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 100×1 and 500×1 matrices respectively, and θ=10000.

[0150] The smallest c ω n The corresponding data labels constitute a 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 of solving the regression model in step 4 are as follows:

[0156] Step 4.1: Decompose the above regression model (12) into R optimization problems, that is, rewrite it 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 in 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 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 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 ), where I is the unit 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 category 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 a cone plane 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 process of fused magnesium oxide online, and grayscale and normalize 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 better classification effect on normal data and fault data.

[0200] In the overall monitoring process of this embodiment, the classification accuracy of samples at the hypersphere boundary and the angle boundary is 99.5%. It can be seen that the present invention can accurately classify data under normal working conditions and abnormal working conditions, and then determine whether a fault occurs at the current moment, thereby improving the accuracy of industrial fault monitoring in the fused magnesium oxide production process.

[0201] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. 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 cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form a technical solution.

Claims

1. A safety monitoring method for fused magnesium oxide production process based on supervised matrix regression, characterized in that: The following steps are involved: Step 1: In the industrial production process of fused magnesium oxide, the furnace image data of the fused magnesium oxide furnace is collected by a fixed camera to obtain training samples under R working conditions, and the furnace image data is grayed 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 common 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 * ; 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 ; 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) ; Step 5: Determine the decision boundary based on the category label of the sample; Step 6: Conduct online safety monitoring of the fused magnesium oxide production process.

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 objective function model in step 2 is: Where 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 * It is the common mapping matrix of all furnace image matrices in the low-dimensional space. Its data dimension is m×b, and λ1 and λ2 are coefficient parameters.

3. The 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: Order 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 formula (5) with respect to W is: Step 2.3.3: Order 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: Order get Step 2.5: Repeat steps 2.2 to 2.4 for p iterations, and 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 * .

4. The method for safety monitoring of fused magnesium oxide production process based on supervised matrix regression according to claim 1 is characterized in that: The mapping matrix Z described in step 3 i for: Z i =(W T W) -1 W T X i -H * 。 (11)。 5. The method for safety monitoring of fused magnesium oxide production process based on supervised matrix regression according to claim 1, characterized in that: 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 a 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.

6. The 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, that is, rewrite it 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 in 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 get: u (r) =(F (r) L c (F (r) ) T ) -1 F (r) L p (y (r) ) T (25) Among them, 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: Definition 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 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) .

7. The method for safety monitoring of fused magnesium oxide production process based on supervised matrix regression according to claim 1, characterized in that: 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 surrounded 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.

8. The method for safety monitoring of fused magnesium oxide production process based on supervised matrix regression according to claim 1, characterized in that: The step 6 specifically comprises the following steps: Step 6.1: Use a fixed camera to collect the image data of the fused magnesium furnace during the industrial production process of fused magnesium oxide online, and grayscale and normalize 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.

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