WO2017210894A1

WO2017210894A1 - Fault monitoring method for electric arc furnace based on operating video information

Info

Publication number: WO2017210894A1
Application number: PCT/CN2016/085280
Authority: WO
Inventors: 张颖伟; 王振帮; 杜文友; 樊云鹏
Original assignee: 东北大学
Priority date: 2016-06-08
Filing date: 2016-06-08
Publication date: 2017-12-14

Abstract

A fault monitoring method for electric arc furnace based on operating video information. Firstly, video information provided by a process monitoring device is used as a process variable. Then, a mapping Newton method is used for resolution, and an optimal solution of a target function of independent component analysis is obtained based on the Hilbert-Schmidt independence criteria. Finally, according to the solved mixture matrix and electric melting magnesium furnace production video information, the nonlinear characteristics of data in non-Gaussian distribution are realized, so that all the information about the data is fully used, and the adaptability of the data is enhanced in order to achieve the purpose of reducing the false alarm rate and the leakage alarm rate of furnace eruption faults.

Description

Electric arc furnace fault monitoring method based on running video information

Technical field

The invention belongs to the technical field of industrial process fault monitoring, and particularly relates to an electric arc furnace fault monitoring method based on running video information.

Background technique

With the rapid development of modern industry and science and technology, especially the wide application of computer technology and industrial control equipment, the structure of the process industry system is more and more complex, and the level of automation is getting higher and higher, gradually showing large-scale, continuous and intelligent. Characteristics. Once a complex and large system fails at an industrial site, it will cause huge loss of people and property. Therefore, industrial safety issues are receiving increasing attention. With the development of sensor technology and the popularization of industrial field monitoring equipment, a large amount of process variable data and audio and video information have been accumulated in the field, so data-based fault detection and diagnosis are getting more and more attention, especially to improve the accuracy of fault monitoring. It is even more important.

Fused magnesia is a kind of refractory material widely used in metallurgical industry, glass industry, cement industry, household heater, chemical industry and other industries. The fused magnesium furnace is one of the most widely used production equipment in the production of fused magnesium oxide. In order to ensure the normal operation of the fused magnesium furnace, we must ensure its safety. If any failure occurs during normal operation and the fault cannot be adjusted or predicted in time, the performance of the control system may be seriously impaired, and even the entire system may be paralyzed and cause huge losses. Therefore, it is necessary to perform fault detection and diagnosis on the fused magnesium furnace.

The fused magnesia furnace is a submerged arc furnace in which an electrode for generating a high temperature arc is inserted into a material composed of magnesium carbonate in the furnace. Through the outer surface material, the inside and outside of the furnace are thermally insulated, and a closed heat conducting space is formed inside the material to be heated. During the operation of the fused magnesium furnace, magnesium carbonate is decomposed into magnesium oxide and carbon dioxide gas. These gases are usually dissipated through the gap between the particles of the solid material; when some external conditions change, the gas discharge process is affected, for example, if the internal electrode is inserted too deeply or the internal temperature is too high, the generated gas cannot be immediately The release is exhausted, or the molten magnesium oxide blocks the gap between the solid materials and the like. Once the exhaust gas is not smooth, high pressure will be generated inside the fused magnesium furnace, which eventually causes the furnace failure to occur. When a furnace failure occurs, a large amount of high-temperature molten magnesium oxide that is ejected will pose a great safety hazard.

Conventional fused magnesia furnace monitoring process selects process data such as current and voltage as random variables of observation data set. However, for a non-linear, non-Gaussian process of fused magnesium furnace smelting, the above data often changes with the on-site environment. A large amount of data jitter occurs, which affects the monitoring effect. In view of the above nonlinear characteristics, some scholars have proposed Kernel Independence Component Analysis (KICA). However, in the process of using KPCA for dimensionality reduction, some secondary information is lost, and the objective function is established. The model is based on the maximization of negative entropy - this is an approximation. Therefore, once the model is established, the resulting de-mixing matrix will deviate significantly from the optimal solution, thus causing false positives or false negatives on the monitoring results. Dangerous, so an accurate and adaptable method is needed to solve the above nonlinear problem.

Summary of the invention

In view of the deficiencies of the prior art, the present invention provides an electric arc furnace fault monitoring method based on running video information, so as to achieve the purpose of reducing the false alarm rate and the leakage alarm rate of the furnace fault.

An electric arc furnace fault monitoring method based on running video information, comprising the following steps:

Step 1. Collecting a video image of the surface layer of the smelting material in the fused magnesium furnace;

Step 2: dividing each captured image into a plurality of viewpoints, obtaining an RGB color mean value of each viewpoint and storing the data as a sample data according to a row vector;

Step 3: Perform data preprocessing on the stored sample data, including standardization processing and whitening processing;

Step 4: Based on the Hilbert-Schmidt independence criterion, the estimated signal of the nonlinear independent element signal of the sample data is obtained by the improved FastKICA algorithm, and the specific steps are as follows:

Step 4-1, constructing an objective function based on the Hilbert-Schmidt independence criterion;

Step 4-2: According to the local parameterization process, obtain the objective function and constraint condition from the manifold space to the European space, and decompose the transformed target function to obtain the first stage sub-object optimization function and the second stage. The sub-objective optimization function is as follows:

Step 4-2-1: Perform local parameterization processing in the optimal solution neighborhood in the manifold space;

Step 4-2-2: obtaining a mapping function of the transformation of the manifold space to the European space according to the local parameterization processing, thereby obtaining a constraint condition;

Step 4-2-3. According to the mapping function, the objective function is converted from the manifold space to the European space, and the converted objective function is obtained;

Step 4-2-4. According to the mapping function, the constraint condition is converted from the manifold space to the European space, and the transformed constraint condition is obtained;

Step 4-2-5, decomposing the objective function to obtain a plurality of sub-objective functions;

Step 4-2-6, determining a sub-objective optimization function in the first stage of the solution process;

The specific formula is as follows:

Where H _i,j (·) represents the i-th, j sub-objective functions, b is the unmixed vector, and m is the dimension of the semi-orthogonal de-mixing matrix,

Representing the gradient of the sub-objective function H _i,j (b) at the local minimum point,

a Jacobian matrix representing a mapping function μ _B at a point u ^* corresponding to H _i,j (·);

After i is replaced by j, the following formula is obtained:

Where μ _B (·) represents a mapping function, u is a de-mixed vector in which b is mapped from a manifold space to a European space, and u _j represents a j-th unmixed vector in a European space;

As the difference between the sample and the l-th sample of the k-th _{post-whitening,} E _{k, l} represents about

Empirical expectation, E _k represents the empirical expectation of z _k , E _l represents the empirical expectation of z _l , φ (·) represents the Gaussian kernel function;

Step 4-2-7, determining a sub-objective optimization function of the second stage of the solution process;

The specific formula is as follows:

among them,

Optimize the function for the sub-target of the second stage;

Step 4-3. Under the constraint condition, the first-stage sub-objective optimization function and the second-stage sub-objective optimization function are solved by the mapping Newton method, as follows:

Step 4-3-1, randomly assigning an initial iteration point u ₁ and b ₁ , b ₁ is a unit vector;

Step 4-3-2, initializing i=1, t=0, and setting the maximum value of the iteration number t;

Step 4-3-3, obtaining the optimization direction of u _j in the first stage sub-objective function:

Where d _jt represents the t-th optimization direction when u _j is solved, and u _jt represents the t-th iteration result of the obtained u _j ,

Representing a Jacobian matrix mapping μ _B for the tth optimization of u _j ;

Step 4-3-4, performing a one-dimensional search on u _j according to the obtained optimization direction, and substituting the obtained b _j(t+1) into the sub-object optimization function of the first stage;

The specific formula is as follows:

j=i+1

Ω _jt = arg min{H(μ _B (u _jt +ω _jt d _jt ))|ω _jt >0}

(5)

u _j(t+1) =u _jt +ω _jt d _jt

b _j(t+1) =μ _B (u _j(t+1) )

Where ω _jt represents the step size in the t-th optimization direction with respect to u _j ;

Steps 4-3-5. Determine whether ||H _j (b)|| ₂ is close to 0 or whether the number of iterations reaches the maximum value. If yes, execute step 4-3-6. Otherwise, the number of iterations is increased by 1 and returned. Perform step 4-3-3;

Step 4-3-6, determining whether i is equal to m, and if so, performing step 4-3-7; otherwise, adding i to 1 and t=0, and returning to step 4-3-3;

Step 4-3-7, doing a Schmidt orthogonalization process on the semi-orthogonal de-mixing matrix B=(b ₁ , b ₂ , . . . , b _m ), and then normalizing the b _i The processed semi-orthogonal de-mixing matrix B is substituted into the second-stage sub-objective optimization function;

Step 4-3-8, judge

Whether it approaches 0, and if so, obtains the optimal semi-orthogonal de-mixing matrix B; otherwise, obtains the semi-orthogonal de-mixing matrix B and the de-mixing vector b ₂ ,..., b _m at this time, and gives b ₁ Search direction and then obtain updated b ₁ and return to step 4-3-2;

Step 4-4, obtaining an estimated signal of the non-Gaussian independent element signal of the sample data according to the whitened sample data and the obtained optimal semi-orthogonal demixing matrix B;

Step 5: Obtain a probability density of the T ² and SPE statistic of the sample data according to the estimated signal and perform a density curve fitting to obtain a control upper limit value corresponding to the T ² and the SPE under the confidence limit;

Step 6. Collect the surface video image of the molten material in the fused magnesium furnace in real time, and obtain the T ² and SPE statistics of the real-time working condition data according to steps 4-4 and 5;

Step 7. Determine whether the T ² and SPE statistics of the real-time working condition data exceed the control limit under the confidence limit. If yes, the fused magnesium furnace fails and alarms; otherwise, returns to step 6.

Constructing an objective function based on the Hilbert-Schmidt independence criterion as described in step 4-1;

The specific formula is as follows:

Where, H (B) as the objective function, B is a semi-orthogonal unmixing _{matrix, B = [b 1, b} 2, ... b m], b 1, b 2, ... b m is 1 to The mth unmixed vector, m is the dimension of the semi-orthogonal de-mixing matrix, m≤d, and d is the dimension of the sample data matrix;

For the difference between the kth sample and the lth sample after whitening, E _k,l indicates

The empirical expectation, E _k represents the empirical expectation of z _k , E _l represents the empirical expectation of z _l , and φ(·) represents the Gaussian kernel function.

The constraint conditions described in step 4-2-2 are as follows:

among them,

Represents the gradient of the objective function H(B) at the local minimum point B ^* ,

Representing the Jacobian matrix of the mapping function μ _B at point U ^* , and B ^* = μ _B (U ^* );

The converted constraint conditions described in Step 4-2-4 are as follows:

Among them, H(U) represents the objective function in the European space, u _i represents the i-th unmixed vector in the European space, and u _j represents the j-th unmixed vector in the European space.

The converted objective function described in step 4-2-3 is as follows:

Where H(U) represents the objective function in the European space, u ₁ ,..., u _m is b ₁ ,..., b _m is mapped from the manifold space to the unmixed vector of the European space; b ₁ ,b ₂ ,...b _m is the first to mth unmixed vector, m is the dimension of the semi-orthogonal demixing matrix, m≤d, and d is the dimension of the sample data matrix;

Converting the target function into multiple sub-objective functions as described in step 4-2-5;

The specific formula is as follows:

Where H(B) is the objective function, b is the unmixing vector, u is the de-mixing vector of b from the manifold space to the European space, m is the dimension of the semi-orthogonal de-mixing matrix, and H _ξ (·) For the sub-objective function of the first combination case, the value range of ξ is 1~i, the total number of j combinations; H _i,j (·) represents the i, j sub-objective functions, and μ _B (·) represents the mapping function.

The plurality of viewpoints described in step 2 specifically include: 8, 10, and 12.

The advantages of the invention:

(1) Applying the improved FastKICA algorithm to the fault monitoring of the fused magnesium furnace smelting process, which can take into account all the data information of the fused magnesia furnace, so that the data characteristics of the nonlinear process can be analyzed more thoroughly and accurately;

(2) Because the Hilbert-Schmidt norm squared value of the covariance is non-negative, the present invention divides the complex high-dimensional feature space into several smaller spheres in the optimal solution domain in the mapping Newton method. Space, where each subspace contains each pair of unmixed vectors, so the high-dimensional feature space is transformed into a number of low-dimensional spherical vector spaces containing only two different deconvolution vectors, thus reducing the overall judgment of the independence equation scale;

(3) After considering the video information of the fused magnesium furnace and reasonably selecting the required multi-viewpoint to obtain the process variable, when applying the FastKICA algorithm to the furnace process, compared with KPCA and traditional KICA, the process monitoring results indicate that The method can effectively improve the accuracy of non-Gaussian process prediction and can reduce false positive rate and false negative rate.

DRAWINGS

1 is a flow chart of an electric arc furnace fault monitoring method based on running video information according to an embodiment of the present invention;

2 is a schematic view of a fused magnesium furnace with a monitoring device according to an embodiment of the present invention;

3 is a schematic diagram of a process monitoring image based on a multi-view method according to an embodiment of the present invention;

4 is a schematic diagram of comparison of monitoring indexes under different viewpoints according to an embodiment of the present invention, wherein (a) is a comparison chart of T ² statistics under 4, 5, 6, 8, 10, 12, 16, and 20 viewpoints, Figure (b) is a comparison chart of T ² statistics under 40, 250, 1000 viewpoints, and Figure (c) is a comparison chart of SPE statistics at 4, 5, 6, 8, 10, 12, 16, 20 viewpoints. (d) is a comparison chart of SPE statistics under 40, 250, 1000 viewpoints;

5 is a schematic diagram showing a distribution of RGB color values of a 3-2th viewpoint according to an embodiment of the present invention;

6 is a flowchart of a method for solving a semi-orthogonal demixing matrix by a mapping Newton method according to an embodiment of the present invention;

7 is a graph showing a probability density fit curve of T ² and SPE according to an embodiment of the present invention, wherein (a) is a T ² statistic probability density fitting curve, and (b) is a SPE statistic probability. Density fitting curve;

8 is a diagram showing an effect of monitoring a control limit obtained by using a fitting density curve according to an embodiment of the present invention, wherein (a) is a T ² monitoring diagram, and (b) is an SPE monitoring diagram;

FIG. 9 is a comparison diagram of T ² and SPE statistics of three different monitoring methods according to an embodiment of the present invention, wherein FIG. (a) is a comparison chart of T ² statistics of three different monitoring methods, and FIG. Comparison of SPE statistics for different monitoring methods;

FIG. 10 is a diagram showing the contribution of RGB variables when a fault occurs when monitored by the FastKICA method according to an embodiment of the present invention, wherein (a) is an RGB contribution diagram of the 89th sample point monitoring index, and (b) is 118th. A sample point monitors the RGB contribution map of the indicator.

detailed description

An embodiment of the present invention will be further described below with reference to the accompanying drawings.

In the embodiment of the present invention, an electric arc furnace fault monitoring method based on running video information, wherein the electric arc furnace is an fused magnesia furnace, and the method flow chart is as shown in FIG. 1 , and includes the following steps:

In order to avoid the occurrence of the accident of the spray furnace well, as shown in FIG. 2, the embodiment of the present invention installs the camera shown in the figure at the upper end of the electrode of the fused magnesium furnace, and is required to be able to reach a high temperature of 800 ° C and is in the camera. Externally installed with a protective cover made of high temperature refractory material;

As far as the control of the fused magnesium furnace is concerned, the temperature control should be placed in the first place; the reason is that the temperature of the entire molten pool is composed of the arc heat release and the molten magnesium oxide heat radiation, and the current and voltage changes are relative to The change in temperature is frequently fluctuating; in addition, the physical manifestation of temperature can be converted into different colored lights; therefore, the present invention achieves the goal of monitoring the fused magnesium furnace by analyzing the change in the color of the molten pool; using this method, real-time acquisition using a camera The image can effectively obtain the change of the color of the molten pool to monitor the temperature change, thus avoiding the occurrence of the furnace accident.

It can be seen from Fig. 3 that the frame image is relatively fuzzy, because the complicated smoke movement appears in the video; these smokes are caused by internal high temperature gas, arc and molten magnesium oxide; but still can be video Color change to judge the operation, and even the color change of the video caused by the change of smoke concentration can be analyzed to distinguish the degree of melting;

Any frame image, that is, the entire surface of the furnace, can be regarded as a whole, and the reference calculus idea can also be regarded as composed of a large number of pixels; that is, each pixel and image The adjacent pixels in it have the same contribution to the entire image. In order to simplify the complexity of the problem, the present invention only considers the complementarity between pixels; therefore, each image is artificially divided into a plurality of viewpoints, which can simulate multiple imaging devices in the monitoring process; The method can be referred to as video information failure monitoring based on a multi-view method. According to the experience of the work site, the area where the furnace accident occurs is shown in Figure 3. This part of the area can be separated into p × q viewpoints, and the obtained viewpoint can extract the corresponding RGB color values to be used as observation variables for process monitoring. Therefore, 3 × p × q variables can be obtained, which are composed of RGB values of respective regions;

During the monitoring process, the embodiment of the present invention divides the area shown in FIG. 3 into 5×2 viewpoints, and obtains 30 process variables in total, that is, 10 sets of RGB data; for every 5 frames of training data and real-time working condition data. Collect data at sampling intervals, The training data of the fault is composed of 200 sets of observation samples, and the real-time working condition data is composed of 130 sets of observation samples. The embodiment of the present invention gives partial sampling data, and the first 6 variables and 5 sets of data of the modeling data are shown in Table 1. The first 6 variables and 5 groups of data of the real-time working condition data are shown in Table 2:

Table 1

Table 2

The above block method can be proved by the following test:

In the embodiment of the present invention, the selected area is divided into 11 kinds of viewpoints shown in the figure according to a certain manner, as shown in (a), (b), (c) and (d) of FIG. 4, At 1000, 250, 40 viewpoints, due to too many variables, the robustness of the algorithm is weakened, resulting in a large number of false positives due to high sensitivity, which is not suitable for online detection; in addition, for 20, 16, 12, 10, 8 The comparison images at 6, 5, and 4 viewpoints can be found that their monitoring trends for T ² and SPE are generally the same, but the corresponding T ² statistic at 20 and 16 viewpoints is falsely reported; The corresponding monitoring results at 5 and 6 viewpoints are too robust for video and lack of sensitivity. At the same time, the present invention finds that the T ² value decreases as the viewpoint increases, and conversely, the SPE monitoring value increases as the viewpoint increases; therefore, the monitoring results under 8, 10, and 12 viewpoints can A satisfactory result is obtained. Therefore, in order to balance the robustness of the enhanced adaptive data and the sensitivity of detecting the fault and reducing the probability of false positives and false negatives during the detection, the above 10 viewpoint acquisition data are selected in the embodiment of the present invention.

In the embodiment of the present invention, since the multi-view method is applied, the data sets of the p×q group RGB are obtained and the data is stored in the manner of the row vector; any one of the viewpoints is defined as the pqth viewpoint according to the arrangement order; Each of the viewpoints has the same contribution to the color value of the entire image. Therefore, in this embodiment, the sub-images of any one of the viewpoints are randomly selected to display the RGB data distribution of the modeled samples and the faulty samples; Shown, that is, the modeled sample and test sample data distribution of the 3-2th viewpoint; by comparing the distribution of the test sample and the modeled sample, it is found that the test sample has fluctuations compared to the modeled sample, especially after 89 frames. Significant fluctuations occurred and it was observed that two abnormal peaks occurred at the 89th frame and the 118th frame, which is the point at which the fault occurred.

In the embodiment of the present invention, the sample data set may be represented by a random vector group x ₁ , x ₂ , . . . , x _d . For a nonlinear process, the set of data may be composed of non-Gaussian independent elements s ₁ , s ₂ , . , s _m , ( _m ≤ d) nonlinear combination is expressed;

Step 3-1: normalize the stored sample data, that is, remove the mean divided by the standard deviation;

In the embodiment of the present invention, the standardized sample data is represented as X'=[x' ₁ , x′ ₂ , . . . , x′ _d ];

Step 3-2: whitening the sample data;

The so-called whitening process, that is, applying a linear transformation to the observation data, removes the correlation between the acquired observation data, thereby simplifying the extraction process of the independent element; if the whitened data matrix satisfies E{zz ^T }=I, The covariance matrix of the zero mean vector z is a unit matrix, then z is a whitened vector;

The solution of the whitening vector is realized by singular value decomposition of the covariance matrix of the observed data, namely:

E{x'x' ^T }=UΛU ^T (11)

Where Λ is the eigenvalue diagonal matrix of the covariance matrix E{x'x' ^T }; U is the eigenvector matrix corresponding to the covariance matrix E{x'x' ^T };

If z=Qx', then E{zz ^T }=E{Qx'x' ^T Q ^T }=QE{x'x' ^T }Q ^T =QUΛU ^T Q ^T =I, so the whitening linear transformation can be expressed as:

z=Λ ^-1/2 U ^T x'=Qx' (12)

Where z is the whitening vector and Q = Λ - ^1/2 U ^T is the whitening matrix;

Under the assumption of no noise or low additive noise, there is an unknown mixing matrix A = [a ₁ , a ₂ , ..., a _m ] ∈ R ^{d × m} will observe the signal and independent source signal The following links have been established:

x=As (13)

In the above formula, once the mixing matrix is found, it can be determined directly from the above relationship using the observed variables. Independent source signal;

Therefore, the relationship between them can also be expressed as:

among them,

Is an estimate of the independent meta-signal s; and is estimated when the de-mixing matrix W is infinitely close to the inverse of the mixing matrix A

Will be closer to the real source signal s;

If

Then the de-mixing matrix W=B ^T Q, so the de-mixing matrix W can be obtained by the semi-orthogonal de-mixing matrix B (B is an orthogonal matrix between columns) and the whitened data matrix Z, and the source signal can be further estimated.

In the process of actual fault analysis, the measured data extracted in complex industrial production processes usually have outliers, nonlinearities, multi-scales, and dynamic characteristics. In order to solve the nonlinear problem of data, the present invention will be an independent meta-analysis method. Combined with the Hilbert-Schmidt Independence Criteria (HSIC), it provides an effective method for finding the semi-orthogonal de-mixing matrix B;

HSIC is based on the square of the Hilbert Schmidt norm mapped to the covariance between the variables of the regenerative kernel Hilbert space (RKHSs)

As a method of judging the independence of binary variables;

Assuming that the components s _i in the source signal S are statistically independent of each other, it is necessary to construct an ICA reference function based on the HSIC criterion that is far more than the binary random variable;

Therefore, the objective function based on the Hilbert-Schmidt independence criterion is:

Where H(B) is the objective function, B is the semi-orthogonal de-mixing matrix, B=[b ₁ , b ₂ ,...b _m ], b ₁ , b ₂ ,...b _m is the first The mth unmixed vector, m is the dimension of the semi-orthogonal de-mixing matrix, m≤d, and d is the dimension of the sample data matrix;

Step 4-2: According to the local parameterization process, obtain the objective function and constraint condition from the manifold space to the European space, and decompose the transformed target function to obtain the first stage sub-object optimization function and the second stage. Sub-objective optimization function;

The equality constraint optimization problem can be regarded as the optimization problem on the differential manifold. The algorithm can be summarized as follows:

First, attach a metric structure to the manifold to make it a Riemannian manifold; then define a vector field on the manifold and search for the zero point of the vector field through the geodesic; in addition, there are several points that need to be clearly stated for this algorithm. First, in addition to the purpose In addition to the special function, there is no intrinsic relationship between the objective function and the Riemannian geometry, and the manifold algorithm adds a metric structure. Secondly, when searching for the zero point of the vector field, the geodesic search is not the only path. Finally, it is found that under the condition of known manifold, the calculation of the optimal solution of the objective function along the geodesic direction is very large or cannot be calculated because the initial value is not good; there is local parameterization that can flow The shape optimization problem is transformed into an optimization problem in the European space;

details as follows:

In the embodiment of the present invention, before solving the semi-orthogonal demixing matrix B, local parameterization needs to be performed on the smooth manifold, and the conversion between the manifold space and the European space can be realized by local parameterization processing;

Let O(m) be a manifold space of m(m-1)/2-dimensional, and there is a smooth mapping for each point B∈O(m) in the manifold:

μ _B :R ^m(m-1)/2 →O(m), μ _B (0)=B (15)

The above mapping is a differential homeomorphic mapping at 0 ∈ R ^m(m-1)/2 , ie regardless of the mapping μ _B or its inverse mapping

It is locally smooth in the neighborhood of 0∈R ^m(m-1)/2 ; this mapping is called local parameterization in the B neighborhood;

In the embodiment of the present invention, for the second order and above real differentiable function H(B), if B ^* is the non-degenerate critical point of the target optimization function in the manifold space, then the domain of the local minimum point can be found.

And any differential homeomorphic mapping on M, then the smooth mapping μ _B in step 4-2-1 satisfies the following relationship:

among them,

In addition, if U ^* is the non-degenerate critical point of the objective function in the European space, and if and only if the matrix

At the point U ^* is positive, where

Is the Hessian matrix of function H,

Is the Hessian matrix of the function μ _B , then without loss of generality, B ^* = μ _B (U ^* ) is the absolute local minimum point of the function H(B);

In the embodiment of the present invention, the above optimization condition is combined with a HSIC based on a regenerated kernel Hilbert space, wherein the regenerative kernel Hilbert space has a Riemannian manifold structure;

Since the compact differential manifold is a non-degenerate critical point B ^* neighborhood in the manifold space, the mapping B = μ _B (U) can be used to establish mutual interaction between the European space and the reproducing kernel Hilbert space. Transformed bridge, where U∈R ^m(m-1)/2 is an element of local parameterization at point B ^* ; high-dimensional kernel space can be regarded as a high-dimensional sphere space of unit radius, so high-dimensional sphere is utilized in this embodiment The parametric equation represents the above mapping:

The converted objective function, the specific formula is as follows:

The converted constraints are as follows:

In the embodiment of the present invention, the following operator is defined to simplify the following expression:

Therefore, the first derivative of the function H(U) with respect to u _i is equation (20):

Similarly, the first derivative of u _j is obtained as shown in equation (21).

Obviously, the second derivative of the function H(U) with respect to u _i , u _j can be obtained by the same derivation method described above; therefore, the second-order partial derivative formula for solving H(U) is given by equation (22):

When formula (8) is used as the constraint condition for optimizing the optimal solution of objective function, the calculation scale of solving the whole semi-orthogonal deconvolution matrix is too large; because the HSIC-based ICA method is based on the Hilbert Schmidt of the covariance operator The square of the special norm

Non-negative criteria;

Therefore, in the embodiment of the present invention, the original optimization problem minH(B)=minH(μ _B (U)) is converted into m(m-1)/2 sub-objective optimization problems;

The specific proof is as follows:

According to HSIC, it can be seen that the closer the optimization result of the function H(B) is to zero, the stronger the mutual independence between the de-mixing vectors b _i and b _j in the semi-orthogonal de-mixing matrix B. H(B) is an accumulated result, and the optimal value of the objective function H(B) is zero, and the square value of the Hilbert Schmidt norm of the covariance operator

It is non-negative, so the optimal solution of the optimized function H(B) can be regarded as the accumulation of the optimal solution for each component.

According to the above decomposition method, the high-dimensional space where B is located is converted into m(m-1)/2 conventional three-dimensional spherical spaces at the non-degenerate critical point B ^* ; and the objective function H(B) can be rewritten into the following form. :

Where H(B) is the objective function, b is the unmixing vector, u is the de-mixing vector of b from the manifold space to the European space, m is the dimension of the semi-orthogonal de-mixing matrix, and H _ξ (·) The sub-objective function of the first combination case, the range of ξ is 1~i, the total number of j combinations; H _i,j (·) represents the i,j sub-objective functions, and the order of i,j is in accordance with i The order to j is arranged in ascending order, and μ _B (·) represents a mapping function;

Arbitrary sub-objective functions are non-negative, so when each component of the optimized function finds a minimum, then the global optimal solution is also obtained, that is, the entire matrix can be based on the search sub-objective function H _i,j (b) obtaining the optimal solution;

It is difficult to find each unmixed vector by optimizing all sub-objective functions to zero; to simplify the problem The operation scale of the present invention, the combination hypothesis of some sub-objective functions is designed into a new optimization index;

In the embodiment of the present invention, an approximate solution is proposed in this step;

First, select (m-1) components in the original optimization function H(B) as the sub-objective function group of the first stage, where the components can be expressed as H _i,j (b)| _{j=i+1,1≤ i ≤ (m-1)} ; then construct a relatively simple second-stage sub-objective function

As the next optimization goal; therefore, the optimization functions of these two stages are specifically as step 4-2-6 and step 4-2-7;

The specific formula is as follows:

After i is replaced by j, the following formula is obtained:

Step 4-2-7, determining a sub-objective optimization function in the first stage of the solution process;

After the optimization solution obtains each of the de-mixing vectors, the orthogonalization of the columns between the de-mixed vectors is performed to obtain the semi-orthogonal de-mixing matrix B, and is substituted into the second-stage sub-objective function to check whether the condition is satisfied. Therefore, Two-stage sub-objective optimization The specific formula is as follows:

among them,

Optimize the function for the sub-target of the second stage;

Step 4-3. Under the constraint condition, the first-stage sub-objective optimization function and the second-stage sub-objective optimization function are solved by the mapping Newton method. The specific flow chart is shown in Figure 6, as follows:

In the embodiment of the present invention, u ₁ ∈R ^m(m-1)/2 , b ₁ ∈O(m), and b ₁ is a unit vector and satisfies b ₁ =μ _B (u ₁ );

In the embodiment of the present invention, t _max = 10000;

Representing a Jacobian matrix mapping μ _B for the tth optimization of u _j ;

The specific formula is as follows:

j=i+1

Ω _jt = arg min{H(μ _B (u _jt +ω _jt d _jt ))|ω _jt >0}

(5)

u _j(t+1) =u _jt +ω _jt d _jt

b _j(y+1) =μ _B (u _j(t+1) )

Steps 4-3-5. Determine whether ||H _j (b)|| ₂ is close to 0 or whether the number of iterations reaches the maximum value. If yes, perform step 4-3-6. Otherwise, the number of iterations t=t+ 1 and return to step 4-3-3;

Step 4-3-8, judge

Whether it approaches 0, and if so, obtains the optimal semi-orthogonal de-mixing matrix B; otherwise, obtains the semi-orthogonal de-mixing matrix B and the de-mixing vector b ₂ ,..., b _m at this time, and gives b ₁ Search direction

Further obtaining the updated b ₁ and returning to step 4-3-2;

It should be noted that the objective function constructed in the embodiment of the present invention is required.

It should contain all the sub-objective functions related to the unmixing vector b ₁ so that there will be a great probability of finding the optimal b ₁ . Therefore, if you can give a good initial iteration value, it will make the calculation easier and the result more accurate. Therefore, according to this conclusion, in the embodiment of the present invention, the near-optimal solution b ₁ obtained each time can be continuously optimized, thereby obtaining a set of more perfect global optimal solutions.

For step 4-3, if you want to obtain a more accurate semi-orthogonal de-mixing matrix, you need to traverse all the components; divide the sub-optimal targets into (m-1) groups respectively; then the first-stage sub-goals at this time The function group is:

i=1,minH _1,2 (b),minH _2,3 (b),...,minH _(m-1),m (b)

i=2,minH _2,3 (b),minH _3,4 (b),...,minH _(m-1),m (b)

(25)

...

i=(m-1), minH _{(m-1), m} (b)

The r-th sub-objective function of the second stage is:

And the first phase and the second phase are matched.

In the embodiment of the present invention, the sample z and the semi-orthogonal de-mixing matrix B are whitened by the fused magnesium furnace industrial process to obtain a potential independent meta-signal;

For a new whitened sample z, it can get an estimate of the source signal in the feature space.

That is, the independent element is sought:

Therefore, the T ² and SPE statistics are:

Where D is the variance matrix of the high dimensional samples,

An estimate of the whitened sample;

Step 5: Obtain a probability density of the T ² and SPE statistics of the sample data according to the estimated signal and perform a density curve fitting to obtain a control upper limit value corresponding to the T ² and the SPE under the confidence limit;

In the embodiment of the present invention, the T ² and SPE control limits of the new sample are determined by the respective T ² and SPE values corresponding to the fitted probability density obtained by the standard modeling samples, and the set of control limits corresponds to 95% confidence of the density function. Limit, as shown in Figure 7 (a) and Figure (b);

In Figure 7, the present invention constructs a fitted curve to approximate the distribution of probability densities of all modeling data T ² and SPE; as shown, the distribution of observed samples T ² and SPE is represented by blue splines Observing the distribution of samples T ² and SPE represented by splines, it is generally considered that the statistical indicators of normal data obey the non-Gaussian distribution, so that it can be inferred that the original modeling data or observation data used are consistent with non-Gaussian distribution. This is another reason why KPCA is not suitable for monitoring the failure of the furnace; in addition, in the figure (a) and (b) of Fig. 7, in the embodiment of the present invention, T ^{2 is} inferred by calculation. When the probability value of SPE is 95%, it corresponds to T ² of 20 and SPE of 2.8 respectively. The T ² and SPE statistics of 89th sample point of real-time working condition data are 379.78 and 38.27, which are greater than the control limit. Therefore, fused The magnesium furnace fails and alarms; the present invention refers to the probability value of 95% as the fault control limit with a 95% confidence limit, and uses this control limit for fault monitoring as shown in Fig. 8 (a) and (b). As shown, the value of the test data T ² and SPE can be monitored by the above-described confidence limits to diagnose whether a fault has occurred. Here, for convenience of drawing, in FIG. 8, the two-norm value of each sample is selected as the abscissa;

In the embodiment of the present invention, the KPCA and KICA algorithms are applied to compare with the algorithm proposed by the present invention, and the monitoring results are as follows:

In this section, the above variables for monitoring the process are extracted into 10-dimensional row vectors in the same manner as R, G, and B as variables, respectively. Then, the present invention uses abnormal data to test the fault monitoring performance of different algorithms. The statistical indicators T ² and SPE after fault detection and diagnosis are shown in Fig. 9 (a) and (b), and Fig. 10 (a) and (b).

In order to compare several statistical charts with large numerical values in the same graph, and to show the respective trend of change so as to compare the respective features, in the embodiment of the present invention, the relative degree of dispersion is defined here (Relative Discrete Degree). , RDD) as a relative trend between the description data, which is defined as the ratio of each sample data to the sample mean, using RDD(·) Indicates:

Where n is the number of samples collected;

In Fig. 9 (a) and (b), the present invention compares the monitoring results of FastKICA, KICA and KPCA in the same coordinate system; from Fig. 9 (a) and (b) Among them, the performance of the algorithm FastKICA and KICA is significantly better than KPCA;

When the SPE statistic of the red value and the green value of Fig. 9(b) is shown, KPCA clearly fails to indicate the occurrence of the fault at the 89th sample point compared to FastKICA and KICA. This is due to the fact that KPCA ignores high-order statistics information, and KPCA is in a false positive state for KPCA's SPE monitoring for red values; therefore, for KPCA, using KPCA algorithm to monitor furnace failure is Very difficult; but fortunately, the other two algorithms are able to detect faults well throughout the process; however, compared to FastKICA, for the T ² and SPE statistics for blue values, the KICA algorithm is at frame 95 to A false alarm occurred during the 115-frame monitoring process, as shown in Figure (a) and Figure (b) of Figure 9;

KICA also cannot clearly distinguish the two fault conditions of the red value T ² ; the reason why KICA provides false positive information is that the independence constraint function is based on negative entropy, which is approximate and is included in the traditional KICA algorithm. KPCA, its dimensionality reduction of data makes some data lost, and it also makes the application of observation information incomplete;

Based on all of the above reasons, the present invention concludes that FastKICA has strong data adaptability and more accurate diagnostic capabilities. Based on the above analysis, it is possible to determine that FastKICA has many advantages for application to the field of fault diagnosis. Therefore, as shown in (a) and (b) of FIG. 10, the present invention only considers the contribution of the red value, the green value, and the blue value change to the occurrence of the fault under the FastKICA method; in FIG. 10, the figure (a) And Figure (b) is a comparison of the contribution of RGB values to the T ² and SPE statistics at frames 89 and 118; respectively, according to the two figures, the green variable values are decisive for these two statistics; Therefore, in order to reduce the size of the observed data, it is possible to analyze only all the green variables.

Summary: In order to more accurately provide the ability to predict and monitor dynamic and complex industrial processes in fused magnesium furnaces, especially in the presence of nonlinear, non-Gaussian variables, the improved FastKICA method can effectively improve the fused furnace furnace monitoring process. The false positive phenomenon existing in the KICA method and the defect that the KPCA cannot diagnose the non-Gaussian variable; through the above test, the present invention proves the improved vitality and great application value of the improved FastKICA in the field of fault monitoring, and also shows the application video information. Great prospects for fault monitoring; based on the improved video information of the fused magnesium furnace, the FastKICA method can provide accurate and reliable alarm information, which can effectively reduce the unnecessary parking maintenance loss; therefore, the improved FastKICA method is based on Multi-view video information The production operation monitoring of fused magnesium furnace furnace failures will provide full support and assistance to the factory, whether it is accuracy, adaptability or economic budget for the factory.

Claims

An electric arc furnace fault monitoring method based on running video information, characterized in that the method comprises the following steps:

Step 1. Collecting a video image of the surface layer of the smelting material in the fused magnesium furnace;

Step 2: dividing each captured image into a plurality of viewpoints, obtaining an RGB color mean value of each viewpoint and storing the data as a sample data according to a row vector;

Step 3: Perform data preprocessing on the stored sample data, including standardization processing and whitening processing;

Step 4: Based on the Hilbert-Schmidt independence criterion, the estimated signal of the nonlinear independent element signal of the sample data is obtained by the improved FastKICA algorithm, and the specific steps are as follows:

Step 4-1, constructing an objective function based on the Hilbert-Schmidt independence criterion;

Step 4-2: According to the local parameterization process, obtain the objective function and constraint condition from the manifold space to the European space, and decompose the transformed target function to obtain the first stage sub-object optimization function and the second stage. The sub-objective optimization function is as follows:

Step 4-2-1: Perform local parameterization processing in the optimal solution neighborhood in the manifold space;

Step 4-2-2: obtaining a mapping function of the transformation of the manifold space to the European space according to the local parameterization processing, thereby obtaining a constraint condition;

Step 4-2-3. According to the mapping function, the objective function is converted from the manifold space to the European space, and the converted objective function is obtained;

Step 4-2-4. According to the mapping function, the constraint condition is converted from the manifold space to the European space, and the transformed constraint condition is obtained;

Step 4-2-5, decomposing the objective function to obtain a plurality of sub-objective functions;

Step 4-2-6, determining a sub-objective optimization function in the first stage of the solution process;

The specific formula is as follows:

Where H i,j (·) represents the i-th, j sub-objective functions, b is the unmixed vector, and m is the dimension of the semi-orthogonal de-mixing matrix,
Representing the gradient of the sub-objective function H i,j (b) at the local minimum point,
a Jacobian matrix representing a mapping function μ B at a point u * corresponding to H i,j (·);

After i is replaced by j, the following formula is obtained:

Where μ B (·) represents a mapping function, u is a de-mixed vector in which b is mapped from a manifold space to a European space, and u j represents a j-th unmixed vector in a European space;
For the difference between the kth sample and the lth sample after whitening, E k,l indicates
Empirical expectation, E k represents the empirical expectation of z k , E l represents the empirical expectation of z l , φ (·) represents the Gaussian kernel function;

Step 4-2-7, determining a sub-objective optimization function of the second stage of the solution process;

The specific formula is as follows:

among them,
Optimize the function for the sub-target of the second stage;

Step 4-3. Under the constraint condition, the first-stage sub-objective optimization function and the second-stage sub-objective optimization function are solved by the mapping Newton method, as follows:

Step 4-3-1, randomly assigning an initial iteration point u 1 and b 1 , b 1 is a unit vector;

Step 4-3-2, initializing i=1, t=0, and setting the maximum value of the iteration number t;

Step 4-3-3, obtaining the optimization direction of u j in the first stage sub-objective function:

Where d jt represents the t-th optimization direction when u j is solved, and u jt represents the t-th iteration result of the obtained u j ,
Representing a Jacobian matrix mapping μ B for the tth optimization of u j ;

Step 4-3-4, performing a one-dimensional search on u j according to the obtained optimization direction, and substituting the obtained b j(t+1) into the sub-object optimization function of the first stage;

The specific formula is as follows:

Where ω jt represents the step size in the t-th optimization direction with respect to u j ;

Steps 4-3-5. Determine whether ||H j (b)|| 2 is close to 0 or whether the number of iterations reaches the maximum value. If yes, execute step 4-3-6. Otherwise, the number of iterations is increased by 1 and returned. Perform step 4-3-3;

Step 4-3-6, determining whether i is equal to m, and if so, performing step 4-3-7; otherwise, adding i to 1 and t=0, and returning to step 4-3-3;

Step 4-3-7, doing a Schmidt orthogonalization process on the semi-orthogonal de-mixing matrix B=(b 1 , b 2 , . . . , b m ), and then normalizing the b i The processed semi-orthogonal de-mixing matrix B is substituted into the second-stage sub-objective optimization function;

Step 4-3-8, judge
Whether it approaches 0, and if so, obtains the optimal semi-orthogonal de-mixing matrix B; otherwise, obtains the semi-orthogonal de-mixing matrix B and the de-mixing vector b 2 ,..., b m at this time, and gives b 1 Search direction and then obtain updated b 1 and return to step 4-3-2;

Step 4-4, obtaining an estimated signal of the non-Gaussian independent element signal of the sample data according to the whitened sample data and the obtained optimal semi-orthogonal demixing matrix B;

Step 5: Obtain a probability density of the T 2 and SPE statistic of the sample data according to the estimated signal and perform a density curve fitting to obtain a control upper limit value corresponding to the T 2 and the SPE under the confidence limit;

Step 6. Collect the surface video image of the molten material in the fused magnesium furnace in real time, and obtain the T 2 and SPE statistics of the real-time working condition data according to steps 4-4 and 5;

Step 7. Determine whether the T 2 and SPE statistics of the real-time working condition data exceed the control limit under the confidence limit. If yes, the fused magnesium furnace fails and alarms; otherwise, returns to step 6.
An electric arc furnace fault monitoring method based on running video information according to claim 1, wherein the objective function is constructed based on the Hilbert-Schmidt independence criterion according to step 4-1;

The specific formula is as follows:

Where H(B) is the objective function, B is the semi-orthogonal de-mixing matrix, B=[b 1 , b 2 ,...b m ], b 1 , b 2 ,...b m is the first to The mth unmixed vector, m is the dimension of the semi-orthogonal de-mixing matrix, m≤d, and d is the dimension of the sample data matrix;
For the difference between the kth sample and the lth sample after whitening, E k,l indicates
The empirical expectation, E k represents the empirical expectation of z k , E l represents the empirical expectation of z l , and φ(·) represents the Gaussian kernel function.
The electric arc furnace fault monitoring method based on running video information according to claim 1, wherein the constraint condition described in step 4-2-2 is as follows:

among them,
Represents the gradient of the objective function H(B) at the local minimum point B * ,
Representing the Jacobian matrix of the mapping function μ B at point U * , and B * = μ B (U * );

The converted constraint conditions described in Step 4-2-4 are as follows:

Among them, H(U) represents the objective function in the European space, u i represents the i-th unmixed vector in the European space, and u j represents the j-th unmixed vector in the European space.
The electric arc furnace fault monitoring method based on running video information according to claim 1, wherein the converted objective function described in step 4-2-3 has the following specific formula:

Where H(U) represents the objective function in the European space, u 1 ,..., u m is b 1 ,..., b m is mapped from the manifold space to the unmixed vector of the European space; b 1 ,b 2 ,...b m is the first to mth unmixed vector, m is the dimension of the semi-orthogonal demixing matrix, m≤d, and d is the dimension of the sample data matrix;
For the difference between the kth sample and the lth sample after whitening, E k,l indicates
The empirical expectation, E k represents the empirical expectation of z k , E l represents the empirical expectation of z l , and φ(·) represents the Gaussian kernel function.
An electric arc furnace fault monitoring method based on running video information according to claim 1, wherein the objective function is converted into a plurality of sub-objective functions as described in step 4-2-5;

The specific formula is as follows:

Where H(B) is the objective function, b is the unmixing vector, u is the de-mixing vector of b from the manifold space to the European space, m is the dimension of the semi-orthogonal de-mixing matrix, and H ξ (·) For the sub-objective function of the first combination case, the value range of ξ is 1~i, the total number of j combinations; H i,j (·) represents the i, j sub-objective functions, and μ B (·) represents the mapping function.
The method according to claim 1, wherein the plurality of viewpoints in the step 2 include: 8, 10, and 12.