CN107092923A

CN107092923A - The electric melting magnesium furnace process monitoring method of method is locally linear embedding into based on improvement supervision core

Info

Publication number: CN107092923A
Application number: CN201710172013.0A
Authority: CN
Inventors: 张颖伟; 蔡营; 薛晓光
Original assignee: Northeastern University China
Current assignee: Northeastern University China
Priority date: 2017-03-22
Filing date: 2017-03-22
Publication date: 2017-08-25
Anticipated expiration: 2037-03-22
Also published as: CN107092923B

Abstract

The present invention provides a kind of based on the electric melting magnesium furnace process monitoring method that core is locally linear embedding into method of supervising is improved, and is related to Fault monitoring and diagnosis technical field.Sample data X is mapped to high-dimensional feature space Φ (X) by this method using kernel function；Regular terms is added by MKSLLE (Modified supervised kernel locally linear embedding) k Neighbor Points of algorithm picks, and in construction reconstruct weight matrix；Carry out dimension to combining KPCA global holding feature and the object function of the local holding feature composition of itself and about subtract, high-dimensional data space is obtained to the mapping matrix and coefficient matrix of low-dimensional feature space by approximate calculation；Construct Hotelling T²Statistic and SPE statistics simultaneously determine its control limit.The present invention can carry out real time on-line monitoring to the exception in the electric melting magnesium furnace course of work and failure, effectively improve the accuracy of malfunction monitoring, reduction wrong report and the generation of failing to report phenomenon, it is to avoid property loss, the life safety of safeguard work personnel.

Description

Electric smelting magnesium furnace process monitoring method based on improved supervision kernel local linear embedding method

Technical Field

The invention relates to the technical field of fault monitoring and diagnosis, in particular to a method for monitoring a process of an electro-fused magnesia furnace based on an improved supervision core local linear embedding method.

Background

The industrial fused magnesia furnace is mainly used for producing fused magnesia at the present stage, and the production process comprises the steps of firstly crushing solid fused magnesia into powder, then adding the powder into the fused magnesia furnace, inserting an electrode, melting the fused magnesia mainly by means of electrode arc heat after electrifying, lifting the electrode out after finishing melting, moving the fused magnesia out of the fused magnesia furnace after cooling the fused magnesia, and naturally crystallizing. The whole composition and the working principle of the electro-fused magnesia furnace device are shown in figure 1. At present, the automation degree of the smelting process of the electric smelting magnesium furnace in China is generally low, and faults and abnormal conditions are easy to occur, wherein due to the fact that an electrode actuator fails to work and the like, the electrode is too close to the furnace wall of the electric smelting magnesium furnace, the furnace temperature is changed abnormally, the furnace body of the electric smelting magnesium furnace is molten, once the furnace is smelted, a large amount of property loss can be caused, and more importantly, the personal safety is damaged. It is necessary to detect whether the abnormality and the failure occur in the working process of the electro-fused magnesia furnace in time.

The electric smelting magnesium furnace is divided into 3 stages of a furnace starting stage, a melting stage and a final crystallization stage, wherein electrode current and voltage must be well adjusted in each stage so as to ensure that furnace burden in the electric smelting magnesium furnace can be well melted and crystallized.

The temperature of the electro-fused magnesia furnace is generally selected to be monitored according to poor working conditions and faults which are easy to occur in the smelting process of the electro-fused magnesia furnace. The main reason is that the temperature not only affects the generation and discharge of impurities, but also affects the smelting process and the crystallization process of fused magnesia, so that the control of the temperature in the furnace is very reasonable and very important.

In the method for monitoring the smelting process of the electro-fused magnesia furnace, the neighborhood of the traditional non-linear dimension reduction method such as Local Linear Embedding (LLE) and the like is generally determined by adopting a K neighbor method, namely, each data point in a data set is subjected to Euclidean distance solving, and K points closest to the data point are selected as the neighbors of the data point. The selection of the neighboring point K is very important, if the value of K is too large, the algorithm cannot well reflect the local characteristics of the data, the calculation complexity is high, and the dimension reduction effect is not good, otherwise, the algorithm cannot well maintain the local topological structure of the data point in the low-dimensional space.

Another conventional nonlinear dimension reduction method is that a supervised kernel local linear embedding algorithm (SKLLE) processes existing training sample data in a local reconstruction preserving manner, and the generalization problem of the newly measured sample data cannot be effectively solved, because the SKLLE cannot directly give reasonable embedding output to the input of the newly measured sample data by using low-dimensional embedded data extracted from the existing training sample, that is, so-called generalization capability is absent. Meanwhile, aiming at the problem that the SKLLE algorithm is very sensitive to data point noise, regularization processing is introduced on the premise that the representation coordinate of each data point in the neighborhood is kept unchanged. Namely, a regular term lambda | | w | | luminance is added in the calculation of the local reconstruction weight matrix²To reduce sensitivity to noise. On the basis, the embedded coordinates of the embedded low-dimensional target space are optimized, so that the algorithm can better keep the topological structure of nonlinear data and has better anti-noise capability. For the SKLLE method, the parameter k has a significant impact on the performance of the algorithm. The algorithm is sensitive to k selection, and the traditional method generally selects k points nearest to the k points as the neighbors by solving the Euclidean distance. If k is chosen too small, it is difficult to selectThe overall geometry of the data is guaranteed, otherwise points with a longer manifold space distance may be selected as neighborhoods, and the dimensionality reduction result is distorted. When the sample is a small sample, the correlation among the data is deteriorated due to improper selection of neighborhood data, and the data is distorted; the conventional Supervised Kernel Local Linear Embedding (SKLLE) algorithm only considers the local structure information of data, but ignores the global structure of the data, and non-adjacent points in a high-dimensional space should not be adjacent in a low-dimensional space.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a method for monitoring the process of an electro-fused magnesia furnace based on an improved supervision kernel local linear embedding method, which considers the advantages of the global European structure of KPCA (kernel-based language) capable of maintaining data and the class information of samples on the basis of maintaining the local structure of SKLLE, and solves the problems by constructing a new projection matrix objective function, so that the abnormity and the faults in the working process of the electro-fused magnesia furnace can be monitored on line in real time, the fault monitoring accuracy is effectively improved, the occurrence of false alarm and false alarm omission is reduced, the property loss is avoided, and the life safety of workers is guaranteed.

A method for monitoring the process of an electro-fused magnesia furnace based on an improved supervision kernel local linear embedding method comprises the following steps:

step 1, establishing a fault monitoring mathematical model of the fused magnesia furnace in an off-line state, wherein the method specifically comprises the following steps:

step 1.1, reading historical process data of normal work of the electro-fused magnesia furnace, forming a sample data set X, and carrying out centralized and standardized processing on the sample data set X;

step 1.2, introducing a kernel function, mapping the sample data after the standardization processing to a high-dimensional space, and obtaining a sample data set phi (X) of the high-dimensional space as [ phi (X) ]₁)，Φ(x₂)，…，Φ(x_n)]∈R^vWhere n is the number of samples and v is the dimension of the high dimensional space;

step 1.3, solving a low-dimensional space coordinate phi "(X) of high-dimensional data phi (X) by adopting an MKSLLE (modified super viewed kernel localization linear mapping) algorithm, and specifically comprising the following steps:

step 1.3.1, adjusting the distance between samples by adopting an MSKLLE algorithm, and searching k initial adjacent points, wherein the specific method comprises the following steps:

step 1.3.1.1, converting the sample data set Φ (X) in the high-dimensional space to [ Φ (X)₁)，Φ(x₂)，…，Φ(x_n)]Dividing the data into C subsets by adopting prior knowledge, wherein each subset represents one class;

step 1.3.1.2, calculating the distance between a sample data concentrated point and a point, wherein the distance calculation formula is shown as the following formula:

where M (i) represents the ith data Φ (x) in the sample data set_i) Average of the distances to its k neighbors, M (j) denotes the jth data Φ (x) in the sample data set_j) The average of the distances to its k neighbors is shown as follows:

wherein i, j is 1, 2, …, n,is phi (x)_i) P-th neighbor of (1, 2, …, k,is phi (x)_j) Q is 1, 2, …, k;

step 1.3.1.3, according to a distance calculation formula, considering data point type information, and adjusting a distance matrix into a nonlinear supervision distance matrix, as shown in the following formula:

where D is a non-linear supervised distance matrix, L_iAnd L_jα is an adjusting factor, is more than or equal to 0 and less than or equal to α and less than or equal to 1, and is used for controlling the distance between different types of data points and increasing the distance between different types of samples so as to classify the samples;

step 1.3.1.4, for each point in the sample data set, selecting k samples nearest to the point in the nonlinear supervision distance matrix D as the nearest neighbor points;

step 1.3.2, reconstructing a new neighborhood of a sample by adopting local KPCA (kernel-based principal component analysis), and optimizing the representation coordinates of a data point of an original high-dimensional feature space in the neighborhood, wherein the specific method comprises the following steps:

step 1.3.2.1, mixing phi (x)_i) And k neighborhood points constitute a k + 1-dimensional space S, which is considered as phi (x)_i) The specific non-linear data matrix in S space is phi (X)_k+1；

Step 1.3.2.2, find the data matrix phi (X)_k+1Where the r (r ═ 1, 2, …, k +1) th local nonlinear data Φ (x)_r) The covariance matrix of (a) is:

wherein,is a mean value matrix;

step 1.3.2.3, using KPCA method to covariance matrix C^FPerforming feature decomposition according to the following formula, then selecting a group of feature values,

C^FV＝λV

wherein V ═ V (V)₁，v₂，…，v_m) For the first m eigenvalues λ₁，λ₂，…，λ_mThe corresponding feature vector;

then the high dimensional data phi (x)_r) Has local low-dimensional coordinates ofThese new local low-dimensional coordinates are computed in turn and the local low-dimensional data matrix Φ ' (X) in a new neighborhood is reconstructed, where Φ ' (X) is [ Φ ' (X)₁)，Φ′(x₂)，...，Φ′(x_n)]；

Step 1.3.3, calculating a local reconstruction weight matrix of a new neighborhood phi' (X) of the sample point;

according to the reconstruction weight matrix, the reconstruction error of the data point is minimized, and the optimized reconstruction phi' (x) is calculated by combining the introduced regular term constraint_i) Weight W of_ijThe reconstruction error is:

the constraint conditions of the reconstruction error are as follows:

wherein e (W) is a cost function, mu is a weight coefficient, N_k(Φ′(x_i) Denotes Φ' (x)_i) A neighborhood point of (d);

solving the above formula least square problem with constraints to obtain all reconstruction weights W_ijObtaining a reconstructed weight matrix W ═ W_ij}_{i，j＝1，2，…，n}；

Step 1.3.4, according to the improved MSKLLE local characteristics, namely, the weight matrix is reconstructed to keep the property of the local structure information of the high-dimensional space, and the global characteristics of KPCA are combined to obtain a mapping matrix and a coefficient matrix thereof, and phi '(X) is mapped to the low-dimensional space to obtain the low-dimensional space coordinate phi' (X) ═ of original data (phi '(X)')₁)，Φ″(x₂)，...，Φ″(x_n))；

Let Φ "(X) be F^TΦ' (X), where F represents the mapping matrix projected from the high-dimensional space to the low-dimensional space, the constraint problem of Φ "(X) is solved as:

J＝min(αe(Φ″(X))+(1-α)J_KPCA)

s.t.F^TF＝I

calculating to obtain a result shown in the following formula;

wherein M is M^T＝(I-W)^T(I-W)；

The derivation by Lagrange multiplier method can obtain:

wherein γ represents a lagrangian coefficient;

after simplification, the following is obtained:

wherein K ═ Φ'^T(X) Φ' (X), Z is a coefficient matrix of the mapping matrix F;

thus to the matrixPerforming feature decomposition, wherein the feature vectors corresponding to the d minimum feature values obtained by the decomposition are coefficient matrixes Z of a mapping matrix F projected from a high dimension to a low dimension space, and F ═ phi '(X) Z, so as to obtain the coordinates of the low dimension space as phi' (X) ═ F-^TΦ′(X)＝Z^TΦ′^T(X)Φ′(X)；

Step 1.4, computing Hotelling T of sample data²The control limits of the statistic and the SPE statistic are respectively shown as the following two formulas;

T²＝Φ″^T(X)Λ^-1Φ″(X)

SPE＝||(Φ′^T(X)-Φ″^T(X)F^T)||²

step 2, carrying out online fault monitoring on the working process of the electro-fused magnesia furnace, and specifically comprising the following steps:

step 2.1, collecting the working process data of the electro-fused magnesia furnace in real time to form a new sample x_new；

Step 2.2, calculating T of a new sample according to the mathematical model established in the off-line state²Statistics and SPE statistics;

step 2.3, judging T of new sample²Whether the statistics or SPE statistics exceed their respective control limits if T²If the statistic or SPE statistic exceeds the respective control limit, a fault occurs; otherwise, the data that the new sample is normal is indicated, and the electric smelting magnesium furnaceAnd continuing normal production work.

Further, step 2.2 calculates T for the new sample²The specific method of the statistics and SPE statistics is as follows:

step 2.2.1, for new sample x_newAfter being centralized and standardized, the data are mapped to a high-dimensional space to obtain high-dimensional space data phi (x)_new)；

Step 2.2.2, data phi (x) of high-dimensional space_new) Mapping to its local low-dimensional space phi' (x)_new) In the coordinates;

step 2.2.3, calculate the new kernel function k according to the following equation_new：

k_new＝k(x_new，x_j)＝Φ′^T(x_new)Φ′(x_j)

Wherein x is_iRepresenting raw data, k, during off-line modelling_newRepresents the kernel function under a new sample received on-line monitoring, j is 1, 2, …, n;

step 2.2.4, for the new kernel function k_newStandardized and centralized to obtain

Step 2.2.5, determining the coordinates of the low-dimensional space, as shown in the following formula:

Φ″(x_new)＝F^TΦ′(x_new)＝T^TΦ′^T(x_new)Φ′(x_new)

step 2.2.6, calculating high-dimensional space data phi (x)_new) T of²And SPE monitoring statistics, as shown in the following two equations.

T_o ²＝Φ^″T(x_new)A^-1Φ″(x_new)

SPE_o＝||(Φ′T(x_new)-Φ″^T(x_new)F^T)||²

According to the technical scheme, the invention has the beneficial effects that: according to the method for monitoring the process of the fused magnesia furnace based on the improved supervision kernel local linear embedding method, the advantages of the global European structure of KPCA (kernel-based correlation) capable of maintaining data and the class information of samples are considered on the basis of maintaining the local structure of SKLLE, and a new projection matrix objective function is constructed to solve, so that the real-time online detection of the faults in the working process of the fused magnesia furnace can be effectively carried out, the accuracy of fault monitoring is improved, the occurrence of false alarm and missing alarm phenomena is reduced, the property loss is avoided, and the life safety of workers is guaranteed. Mapping the sample data X to a high-dimensional characteristic space phi (X) by using a kernel function so as to solve the problem of 'out of sample', thereby improving the generalization capability; k neighbor points are selected through an MKSLLE (modified super seen kernel localization linear embedding) algorithm, and a regular term is added when a reconstruction weight matrix is constructed, so that the influence of data noise on the algorithm is effectively avoided; the MKSLLE algorithm can not only process the monitoring problem of the nonlinear process, but also be directly applied to the existing marked information for process monitoring, and can consider the integral correlation problem of data information distribution; performing dimensionality reduction on a target function consisting of global retention features combined with KPCA (kernel principal component analysis) and local retention features of the KPCA to store more nonlinear characteristics of the original system, and obtaining a coefficient matrix of a mapping matrix from a high-dimensional data space to a low-dimensional feature space through approximate calculation, so that the real-time performance of the algorithm is ensured; construction of HotellingT²And the statistic and the SPE statistic and the control limit of the SPE statistic are determined so as to effectively detect and identify the fault in the working process of the electro-fused magnesia furnace.

Drawings

FIG. 1 is a schematic structural view of an electro-fused magnesia furnace;

fig. 2 is a flowchart of a method for monitoring an electric smelting magnesium furnace process based on an improved supervision kernel local linear embedding method according to an embodiment of the present invention;

FIG. 3 is a set of statistical quantity charts of a failure 1 of an electro-fused magnesia furnace according to an embodiment of the present invention, wherein (a) is T at the time of the failure 1²A statistical quantity graph; (b) the SPE statistical quantity graph is a failure 1;

FIG. 4 is a set of statistical quantity charts of a defect 2 of an electro-fused magnesia furnace according to an embodiment of the present invention, wherein (a) is T at the time of the defect 2²A statistical quantity graph; (b) is SPE statistics graph at fault 2.

In the figure: 1. a transformer; 2. a short network; 3. an electrode holder; 4. an electrode; 5. a furnace shell; 6. a vehicle body; 7. an electric arc; 8. charging materials; 9. an operation platform.

Detailed Description

The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.

An electric smelting magnesium furnace process monitoring method based on an improved supervision kernel local linear embedding method is shown in fig. 2, and the method of the embodiment is as follows.

Step 1, establishing a fault monitoring mathematical model of the fused magnesia furnace in an off-line state. In this embodiment, 600 sampling data under normal operating conditions are collected as modeling data of a monitoring mathematical model, and a sampling data 600 group containing fault information is selected to establish a comparison model in online monitoring. The specific method comprises the following steps:

step 1.1, reading historical process data of normal work of the electro-fused magnesia furnace, forming a sample data set X, and carrying out centralized and standardized processing on the sample data set X to obtain X_m＝[x₁，x₂，…，x_n]∈R^m×nWherein n is the number of samples, n is 600, m is the number of testing variables at a certain time, and in the specific implementation, the value of m depends on the type of the collected data samples.

Step 1.2, introducing a kernel function, and standardizing the processed sample data set X_m＝[x₁，x₂，…，x_n]∈R^m×nMapping the data to a high-dimensional feature space F to obtain a sample data set phi (X) of the high-dimensional feature space₁)，Φ(x₂)，…，Φ(x_n)]∈R^vWhere n is the number of samples and v is the dimension of the high dimensional feature space.

Step 1.3, obtaining a local low-dimensional coordinate phi' (X) of the high-dimensional data phi (X) by adopting an MKSLLE (modified super viewed kernel localization linear mapping) algorithm. The method specifically comprises the following steps:

step 1.3.1.1, converting the sample data set Φ (X) of the high-dimensional feature space into [ Φ (X)₁)，Φ(x₂)，…，Φ(x_n)]Dividing the data into C subsets by adopting prior knowledge, wherein each subset represents one class;

in the formula, the distance between heterogeneous data points increases exponentially, the distance in the homogeneous data points increases slowly, and the ratio of the inter-class distance to the intra-class distance increases along with the increase of the distance, so that the effects of inter-class dispersion and intra-class aggregation are achieved, the precision of high-dimensional mapping is finally enhanced, and the classification of embedded data is facilitated.

And 1.3.1.4, for each point in the sample data set, selecting k samples closest to the point in the nonlinear supervision distance matrix D as the adjacent points.

wherein,is a mean value matrix;

C^FV＝λV

then high dimensional data phi (X)_r) Has local low-dimensional coordinates ofThese new low-dimensional coordinates are computed in turn and the local low-dimensional data matrix Φ ' (X) in a new neighborhood is reconstructed, where Φ ' (X) is [ Φ ' (X)₁)，Φ′(x₂)，...，Φ′(x_n)]。

And 1.3.3, calculating a local reconstruction weight matrix of the new neighborhood phi' (X) of the sample point.

the constraint conditions of the reconstruction error are as follows:

solving the above formula least square problem with constraints to obtain all reconstruction weights W_ijObtaining a reconstructed weight matrix W ═ W_ij}_{i，j＝1，2，…，n}。

When all the reconstruction weights W are obtained_ijThe low-dimensional space coordinates can be calculated according to the property of the local structure information of the high-dimensional space maintained by the reconstructed weight matrix W.

Step 1.3.4, according to the improved MSKLLE local characteristics, namely, the weight matrix is reconstructed to keep the property of the local structure information of the high-dimensional space, and the global characteristics of KPCA are combined to obtain a mapping matrix and a coefficient matrix thereof, and phi '(X) is mapped to the low-dimensional space to obtain the low-dimensional space coordinate phi' (X) ═ of original data (phi '(X)')₁)，Φ″(x₂)，...，Φ″(x_n))。

J＝min(αe(Φ″(x))+(1-α)J_KPCA)

s.t.F^TF＝I

calculating to obtain a result shown in the following formula;

wherein M is M^T＝(I-W)^T(I-W)；

The derivation by Lagrange multiplier method can obtain:

wherein, gamma represents Lagrange coefficient, and the specific value is obtained by the following characteristic decomposition; l is a code number introduced for deriving the formula;

after simplification, the following is obtained:

thus to the matrixPerforming feature decomposition, wherein the feature vectors corresponding to the d minimum feature values obtained by the decomposition are coefficient matrixes T, F ═ phi '(X) Z of a mapping matrix F projected from a high-dimensional space to a low-dimensional space, and thus obtaining coordinates of the low-dimensional space as phi' (X) ═ F-^TΦ′(X)＝Z^TΦ′^T(X)Φ′(X)。

Step 1.4, computing Hotelling T of sample data²Statistics and SPE statistics control limits, respectivelyThe following two formulas are shown.

T²＝Φ″^T(X)A^-1Φ″(X)

SPE＝||(Φ′^T(X)-Φ″^T(X)F^T)||²

And 2, carrying out online fault monitoring on the working process of the electro-fused magnesia furnace. The method comprises the following specific steps.

Step 2.1, collecting the working process data of the electro-fused magnesia furnace in real time to form a new sample x_new. In this embodiment, two sets of 400 samples of data are collected and faults are introduced at the 175 th and 225 th sample points, respectively.

Step 2.2, calculating T of a new sample according to the mathematical model established in the off-line state²Statistics and SPE statistics, the specific method is as follows:

k_new＝k(x_new，x_j)＝Φ′^T(x_new)Φ′(x_j)

Wherein x is_jRepresenting raw data, k, during off-line modelling_newRepresents the kernel function under a new sample received on-line monitoring, j is 1, 2, …, n;

Φ″(x_new)＝F^TΦ′(x_new)＝T^TΦ^′T(x_new)Φ′(x_new)

T_o ²＝Φ″^T(x_new)A^-1Φ″(x_new)

SPE_o＝||(Φ′^T(x_new)-Φ″^T(x_new)F^T)||²

Step 2.3, taking the statistic calculated in the off-line modeling as the control limit of the statistic calculated during on-line monitoring, comparing the control limit with the statistic calculated during on-line monitoring, and judging the T of the new sample²Whether the statistics or SPE statistics exceed their respective control limits if T²And if the statistic or SPE statistic exceeds the respective control limit, a fault occurs, otherwise, the new sample is normal data.

In the present embodiment, the failure data has failures 1 and 2. In the production process, when the current set value is unchanged and the length change of raw material particles is large, the electrodes are caused to move, gaps generated among the raw materials are not proper in size, the gas pressure in the furnace is unbalanced due to the discharge of gas, the liquid level of the electrode and the molten pool in the furnace is caused to fluctuate violently, the arc resistance is caused to change violently, and the phenomenon that molten liquid is sprayed out of the furnace along with the gas occurs. Molten bath liquid level rises fast when the raw materials melting point reduces, leads to arc resistance to reduce, and the current value risees very fast, if the current setting value is unchangeable this moment, then the current is followed the error and is great or very big, when the molten bath liquid level lasts fast rising for a long time, can lead to the impurity in the molten bath can't thoroughly separate out, causes the product quality to descend, and single ton energy consumption risees, and in this embodiment, this kind of overheating operating mode is trouble 2.

For failure 1, fig. 3 shows that T of mksle proposed in this embodiment²Statistics and SPE statistics show that a process internal fault occurs when the control limit is exceeded from about 175 th sampling, and the time is consistent with the actual fault, and after the fault occurs, T of each sampling point²And the SPE curve is basically above the control limit, and no point below the control limit exists in the curve after the fault is monitored, which indicates that no report missing phenomenon occurs. Through T²The statistical quantity and the SPE statistical quantity can accurately monitor the fault 1 added in the data set, and the method can effectively avoid the phenomena of misinformation and missing report, so that the performance of fault monitoring is greatly improved.

With respect to failure 2, FIG. 4 shows that T of MKSLLE proposed by the present invention²Statistics and SPE statistics show that a failure occurs inside the process starting from about 225 th sample, coinciding with the time of actual added failure, and after monitoring for failure, T of each sample point²And SPE statistics are substantially above the control limit, thereby indicating a pass through T²The fault 2 in the data set can be monitored by the statistic and the SPE statistic, and the method can effectively avoid the phenomena of misinformation and missing report and well improve the performance of fault monitoring.

The statistical information for monitoring two faults in this embodiment is shown in table 5, and includes a monitoring accuracy, a false alarm rate, and a missing report rate. According to the test result, the fault 1, T²The statistic has high accuracy, few false alarm conditions exist, no report missing condition occurs, the SPE statistic accuracy is low, the report missing condition exists, and T is adopted for the type of the fault 1²The statistic is better monitored; for fault 2, T²Statistics SPE statistics all have and have very high rate of accuracy, SPE has individual false alarm condition in the aspect of false alarm rate, and the phenomenon of failing to report does not exist in both statistics. In conclusion, T is preferably used when the scheme is adopted²The statistics are monitored.

TABLE 5 statistical data of two kinds of fault data in MSKLLE method-based fused magnesia furnace mode

According to the analysis, the method for monitoring the process of the electric smelting magnesium furnace based on the improved supervision kernel local linear embedding method can effectively perform real-time online detection on the faults in the working process of the electric smelting magnesium furnace, improve the fault monitoring accuracy, reduce the occurrence of false alarm and missing alarm, avoid property loss and guarantee the life safety of workers.

Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims

1. A method for monitoring the process of an electro-fused magnesia furnace based on an improved supervision kernel local linear embedding method is characterized by comprising the following steps: the method comprises the following steps:

step 1.2, introducing a kernel function, and mapping the sample data after the standardization processing to a high levelDimension space, obtaining a sample data set phi (X) of high dimension space as phi (X)₁)，Φ(x₂)，…，Φ(x_n)]∈R^vWhere n is the number of samples and v is the dimension of the high dimensional space;

step 1.3, solving a low-dimensional space coordinate phi "(X) of high-dimensional data phi (X) by adopting an MKSLLE (modified super viewed kernel localization linear embedding) algorithm, and specifically comprising the following steps:

<mrow> <mi>M</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <mo>|</mo> <mo>|</mo> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mi>p</mi> <mi>i</mi> </msubsup> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mi>k</mi> </mfrac> </mrow>

<mrow> <mi>M</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <mo>|</mo> <mo>|</mo> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mi>q</mi> <mi>j</mi> </msubsup> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mi>k</mi> </mfrac> </mrow>

wherein i, j is 1, 2, …, n,is phi (x)_i) The p-th neighbor of (1, 2, …, k,is phi (x)_j) Q is 1, 2, …, k;

<mrow> <mi>D</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msup> <mi>d</mi> <mn>2</mn> </msup> <mo>/</mo> <mi>&beta;</mi> </mrow> </msup> </mrow> </msqrt> <mo>,</mo> <msub> <mi>L</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>L</mi> <mi>j</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msqrt> <msup> <mi>e</mi> <mrow> <msup> <mi>d</mi> <mn>2</mn> </msup> <mo>/</mo> <mi>&beta;</mi> </mrow> </msup> </msqrt> <mo>-</mo> <mi>&alpha;</mi> <mo>,</mo> <msub> <mi>L</mi> <mi>i</mi> </msub> <mo>&NotEqual;</mo> <msub> <mi>L</mi> <mi>j</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

<mrow> <msup> <mi>C</mi> <mi>F</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>&Phi;</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>r</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>&Phi;</mi> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mi>r</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mi>&Phi;</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>r</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>&Phi;</mi> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mi>r</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mrow>

wherein,is a mean value matrix;

C^FV＝λV

then the high dimensional data phi (x)_r) Has local low-dimensional coordinates ofThese new local low-dimensional coordinates are computed in turn and the local low-dimensional data matrix phi 'in a new neighborhood is reconstructed'(X), wherein Φ '(X) ═ Φ' (X)₁)，Φ′(x₂)，...，Φ′(x_n)]；

<mrow> <mi>min</mi> <mi> </mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>W</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <msup> <mi>&Phi;</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> </mrow> <mi>k</mi> </munderover> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msup> <mi>&Phi;</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mi>&mu;</mi> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> </mrow> <mi>k</mi> </munderover> <msubsup> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow>

the constraint conditions of the reconstruction error are as follows:

<mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> </mrow> <mi>k</mi> </munderover> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>,</mo> <msup> <mi>&Phi;</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>&NotElement;</mo> <msub> <mi>N</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>&Phi;</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

solving the above formula least square problem with constraints to obtain all reconstruction weights W_iObtaining a reconstructed weight matrix W ═ W_ij}_{i，j＝1，2，…，n}；

J＝min(αe(Φ″(X))+(1-α)J_KPCA)

s.t.F^TF＝I

calculating to obtain a result shown in the following formula;

<mrow> <mi>t</mi> <mi>r</mi> <mi>a</mi> <mi>c</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>(</mo> <mrow> <msup> <mi>F</mi> <mi>T</mi> </msup> <msup> <mi>&Phi;</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <msup> <mi>M&Phi;</mi> <mrow> <mo>&prime;</mo> <mi>T</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mi>F</mi> </mrow> <mo>)</mo> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>&alpha;</mi> </mrow> <mi>n</mi> </mfrac> <msup> <mi>F</mi> <mi>T</mi> </msup> <msup> <mi>&Phi;</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <mi>X</mi> <mo>)</mo> <msup> <mi>&Phi;</mi> <mrow> <mo>&prime;</mo> <mi>T</mi> </mrow> </msup> <mo>(</mo> <mi>X</mi> <mo>)</mo> <mi>F</mi> <mo>)</mo> </mrow> </mrow>2

wherein M is M^T＝(I-W)^T(I-W)；

The derivation by Lagrange multiplier method can obtain:

<mrow> <mi>L</mi> <mo>=</mo> <mi>t</mi> <mi>r</mi> <mi>a</mi> <mi>c</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>(</mo> <mrow> <msup> <mi>F</mi> <mi>T</mi> </msup> <msup> <mi>&Phi;</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <msup> <mi>M&Phi;</mi> <mrow> <mo>&prime;</mo> <mi>T</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mi>F</mi> </mrow> <mo>)</mo> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>&alpha;</mi> </mrow> <mi>n</mi> </mfrac> <msup> <mi>F</mi> <mi>T</mi> </msup> <msup> <mi>&Phi;</mi> <mo>&prime;</mo> </msup> <mo>(</mo> <mi>X</mi> <mo>)</mo> <msup> <mi>&Phi;</mi> <mrow> <mo>&prime;</mo> <mi>T</mi> </mrow> </msup> <mo>(</mo> <mi>X</mi> <mo>)</mo> <mi>F</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>&gamma;</mi> <mrow> <mo>(</mo> <msup> <mi>F</mi> <mi>T</mi> </msup> <mi>F</mi> <mo>-</mo> <mi>I</mi> <mo>)</mo> </mrow> </mrow>

wherein γ represents a lagrangian coefficient;

after simplification, the following is obtained:

<mrow> <mi>&alpha;</mi> <mi>K</mi> <mi>M</mi> <mi>K</mi> <mi>Z</mi> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>&alpha;</mi> </mrow> <mi>n</mi> </mfrac> <mi>K</mi> <mi>K</mi> <mi>Z</mi> <mo>=</mo> <mi>&gamma;</mi> <mi>K</mi> <mi>Z</mi> </mrow>

Step 1.4, computing HotellingT of sample data²The statistic and the SPE statistic control limit are respectively shown as the following two formulas;

T²＝Φ″^T(X)A^-1Φ″(X)

SPE＝||(Φ′^T(X)-Φ″^T(X)F^T)||²

step 2.3, judging T of new sample²Whether the statistics or SPE statistics exceed their respective control limits if T²Statistic or SIf the PE statistic exceeds the respective control limit, a fault occurs, otherwise, the new sample is indicated to be normal data, and the electric smelting magnesium furnace continues to perform normal production work.

2. The method for monitoring the process of the electro-fused magnesia furnace based on the improved supervision kernel local linear embedding method according to claim 1, is characterized in that: said step 2.2 calculating T of the new sample²The specific method of the statistics and SPE statistics is as follows:

k_new＝k(x_new，x_j)＝Φ′^T(x_new)Φ′(x_j)

Φ″(x_new)＝F^TΦ′(x_new)＝T^TΦ′^T(x_new)Φ′(x_new)

T_o ²＝Φ″^T(x_new)A^-1Φ″(x_new)

SPE_o＝||(Φ′^T(x_new)-Φ″^T(x_new)F^T)||²。