CN112016035A - Fault detection method of local tangent space arrangement algorithm based on global structure maintenance - Google Patents

Abstract

The invention provides a fault detection method based on a global structure-maintained local tangent space arrangement algorithm, which comprises the following steps: obtaining local coordinates of the sample points in the local cutting space; constructing a global coordinate according to the local coordinate; determining a target function maintained by a local structure according to the reconstruction error of the local coordinate; determining a mapping matrix of a local tangent space arrangement algorithm maintained by a global structure according to an objective function maintained by the local structure and an objective function maintained by the global structure; converting the online sample data after the standardization processing into dimension reduction data of a new feature space according to the mapping matrix; and establishing statistic of the dimension reduction data by a support vector data description method, and determining whether fault data exists in the online data according to the distance between the statistic and the central point of the hypersphere model of the online data feature space. The invention keeps the external shape of the data, prevents the failure report in the variance direction, ensures the accuracy of a failure detection model and improves the failure recognition rate.

Description

Fault detection method of local tangent space arrangement algorithm based on global structure maintenance

Technical Field

The invention relates to the technical field of fault diagnosis in a chemical process, in particular to a fault detection method based on a global structure-maintained local tangent space arrangement algorithm.

Background

GLTSA (Global-Local Structure vary Space Alignment, Local Tangent Space algorithm for Global Structure maintenance) makes definite constraint on the maintenance of Global Structure characteristics on the basis of LTSA (Local vary Space Alignment, Local Tangent Space arrangement algorithm), and provides a new Global-Local Structure analysis framework. The method is a new method combining the ideas of global maintenance and local maintenance, so that the projected low-dimensional space has not only a similar local structure but also a similar overall structure with the original variable space. Therefore, more comprehensive characteristic information can be contained, so that a more effective model is established, and the detection effect is improved.

At present, the chemical process structure in China is complex, and the chemical process has the characteristics of nonlinearity and coexistence of Gaussian and non-Gaussian characteristics. Although the GLTSA method is used for extracting the low-dimensional feature vector of the high-dimensional matrix and carrying out dimensionality reduction, the data after dimensionality reduction does not follow Gaussian distribution, and if T is constructed according to the traditional method²And SPE statistics, can greatly impact the establishment of fault detection models and the estimation of statistical limits.

Disclosure of Invention

Aiming at the defects in the prior art, the invention aims to provide a fault detection method based on a global structure-preserving local tangent space arrangement algorithm.

The invention provides a fault detection method based on a global structure-maintained local tangent space arrangement algorithm, which comprises the following steps:

step 1: extracting local information of offline sample data through a local tangent space algorithm maintained by a global structure to obtain a local tangent space;

step 2: obtaining local coordinates of the sample points in the local cutting space;

and step 3: constructing a global coordinate according to the local coordinate;

and 4, step 4: determining a target function maintained by a local structure according to the reconstruction error of the local coordinate;

and 5: determining a target function maintained by the global structure according to the overall structure of the global coordinate;

step 6: determining a mapping matrix of a local tangent space arrangement algorithm maintained by the global structure according to the target function maintained by the local structure and the target function maintained by the global structure;

and 7: converting the online sample data after the standardization treatment into dimension reduction data of a new feature space according to the mapping matrix;

and 8: and establishing statistic of the dimensionality reduction data through a support vector data description method, and determining whether fault data exists in the online data according to the distance between the statistic and the central point of the hypersphere model of the online data feature space.

Optionally, the step 1 includes:

step 1.1: for the offline sample data set X_a＝[x_a1，K，x_aN]Carrying out standardization processing to obtain a standardized data set X ═ X₁，K，x_N]；x_a1Representing an offline sample data set X_a1 st data of (1), x_aNRepresenting an offline sample data set X_aN-th data of (1), x₁Representing the 1 st data, X, in a normalized data set X_aNRepresenting the nth data in the normalized data set X, N being a natural number greater than 1;

step 1.2: construction of a proximity matrix X from a normalized data set X_i＝[x_i1，K，x_ik]；x_i1Representing the proximity matrix X_i1 st data of (1), x_ikRepresenting the proximity matrix X_iThe kth data of (1);

step 1.3: constructing a local tangent space according to the proximity matrix and the high-dimensional to low-dimensional data mapping relation; the sample points in the local tangent space satisfy the following relationship:

x_i＝f(y_i)+_i，i＝1，K，N，

y_i∈R^d，x_i∈R^m，d＜m

where Q is the orthogonal basis vector matrix in tangent space, θ_jIs locally low-dimensional embedded data, x, corresponding to Q_iRepresenting the ith element, y, in the dataset matrix X_iRepresenting low dimensional feature momentsThe ith element in the matrix Y is,_irepresenting the i-th noise signal, R^dRepresenting a real matrix of dimension d, R^mRepresenting a data array of dimension m, d representing Y and m, X representing X and m_ijNeighbor matrix X representing a data set_iThe jth element of (a), x represents the optimal data, x^TThe transpose matrix representing the optimal data set and Θ represents the projected coordinate matrix of the sample point in the local tangent space.

Optionally, the step 2 includes:

a projection coordinate matrix Θ defining sample points in the local tangent space is ═ θ₁，...，θ_k]，θ₁Representing the 1 st element, theta, in the projection coordinate matrix theta_kRepresenting the kth element in the projection coordinate matrix Θ; wherein:

wherein, theta_iThe local coordinates of the ith sample point are represented,

a transpose matrix representing an ith orthogonal basis vector matrix, I an identity matrix, e an error, e^TIndicating errorsTransposed matrix, θ₁ ⁽ⁱ⁾Represents the ith local coordinate matrix theta_i1 st element of (1), theta_k ⁽ⁱ⁾Represents the ith local coordinate matrix theta_iThe kth element of (1), ξ_j ⁽ⁱ⁾A j-th element of the ith local coordinate matrix representing a j-th reconstruction error, Q_iRepresenting the ith orthogonal basis vector matrix, Q_i ^TTranspose matrix, x, representing the jth orthogonal basis vector matrix_ijNeighbor matrix X representing a data set_iThe (j) th element of (a),

denotes all x_ijAverage value of (1), H_kMapping parameter, θ, representing local k neighbors_j ⁽ⁱ⁾Represents the ith local coordinate matrix theta_iThe jth element in (a).

Optionally, the step 3 includes:

rearranging the local coordinates after linear affine transformation is carried out on the local coordinates to obtain global coordinates; wherein:

let Y_i＝[y_i1，K，y_ik]，E_i＝[₁ ⁽ⁱ⁾，...，_k ⁽ⁱ⁾](ii) a Then

Wherein: y is_ijThe ith sample is in low dimension spaceThe jth feature vector corresponding thereto,

denotes all of y_ijAverage value of (1), L_iThe optimal transformation matrix, θ, representing the ith sample_j ⁽ⁱ⁾Represents the ith local coordinate matrix theta_iThe (c) th element of (a),_j ⁽ⁱ⁾represents the ith local coordinate matrix theta_iLocal reconstruction error of the jth element in (1), E_iA reconstruction error matrix, Y, representing the ith local coordinate matrix_iLow-dimensional eigenvectors, y, representing the ith local coordinate matrix_i1The 1 st element, y, in the low-dimensional feature vector representing the ith local coordinate matrix_ikThe kth element in the low-dimensional feature vector representing the ith local coordinate matrix,₁ ⁽ⁱ⁾represents the ith local coordinate matrix theta_iThe local reconstruction error of the 1 st element in (a),_k ⁽ⁱ⁾represents the ith local coordinate matrix theta_iLocal reconstruction error of the kth element in (1).

Optionally, the step 4 includes:

assuming an optimal transformation matrix

Wherein, theta_i ⁺Is theta_iMoore-Penrose generalized inverse of (1);

suppose S_iIs a selection matrix between 0 and 1, YS_i＝Y_iThen the objective function is converted into:

J(Y)＝min||YSW||＝min tr(YSWW^TS^TY^T)

wherein S ═ S₁...S_i，...S_N]Is a neighbor selection matrix, W ═ diag (W)₁，...W_i，...W_N)，S_iThe i-th element, W, of the neighbor selection matrix_iRepresenting an ith neighbor characterization matrix;

W_i＝H_k(I-V_iV_i ^T)

V_iis a matrix X_iH_kIn order to make Y a unique value, a constraint condition YY is added^T＝I_dIf A is the mapping matrix, then Y is equal to A^TXH_kThen, the objective function of local structure maintenance is converted into:

B＝SWW^TS^T

wherein: j (Y) represents the objective function for obtaining the feature space, YSW represents the specific mathematical expression of the objective function J (Y), tr (YSWW)^TS^TY^T) Traces, V, representing multiplication of the target function by its transpose_iRepresentation matrix X_iH_kRight singular vector, V, corresponding to the maximum singular value of_i ^TRepresents V_iTransposed matrix of (1), J (A)_localAn objective function representing local structure preservation, A^TXH_NRepresenting a mathematical expression of low-dimensional data characterized by high-dimensional data, B representing a matrix obtained by multiplying a local mapping matrix of a neighbor mapping matrix by its transpose, H_N ^TIndicating a local mapping parameter, X, when the number of neighbors takes N^TRepresenting the transpose of the original high-dimensional data.

Optionally, the global structure keeping objective function J (A) in the step 5_global，

All elements y representing a low-dimensional feature space_iAverage value of (a).

Optionally, the mapping matrix J (A) of the global structure-preserving local tangent space arrangement algorithm in the step 6_local-globalThe following were used:

optionally, in step 7, the formula for converting the normalized online sample data into the dimension reduction data of the new feature space is as follows:

Y_new＝A^TX_newH_k

wherein: y is_newReduced-dimension data representing a new feature space, A^TDenotes the transpose of the mapping matrix A, X_newRepresenting the online sample data after the normalization process.

Optionally, the step 8 includes:

the hypersphere model for establishing the online data feature space needs to solve the following optimization problems:

s.t.||Φ(Y_i)-a||²≤R²+ξ_i，ξ_i≥0

where R represents the radius of the hypersphere, C represents the trade-off of the hypersphere size and the normal sample error rate, ξ_iDenotes the relaxation coefficient, phi (Y)_i) The distance between the ith element in Y and the spherical center of the hypersphere is shown, and a represents the spherical center of the hypersphere;

converting the optimization problem into a Lagrange extreme value problem:

wherein alpha is_iAnd beta_iIs a Lagrange multiplier, Y_iFor the i-th support vector, Y, of the training data feature space_jIs the jth support vector in the training data feature space;

acceleration solving of Lagrange multiplier alpha by adopting sequential minimum optimization algorithm_iTo obtain a support vector Y_iAnd from support vectors toThe distance of the sphere centers is the radius R;

wherein, Y_oFor any support vector in the training data feature space, K represents the kernel function, alpha_jRepresents Y_iLagrange multiplier of, K (Y)_i，Y_j) Represents Y_iAnd Y_jThe kernel function expression of (1);

dimension reduction data Y of new feature space_newIs to calculate a sample data point phi (Y)_new) The distance from the center point a, and compared to R, is given by:

wherein, K (Y)_newi，Y_newo) Represents Y_newiAnd Y_newoExpression of kernel function of, Y_newiRepresenting support vectors, Y, in the ith online data feature space_newoRepresenting an arbitrary support vector, K (Y), in the online data feature space_newi，Y_newj) Represents Y_newiAnd Y_newjExpression of kernel function of, Y_newjRepresenting a support vector in a jth online data feature space;

if the sample data point Φ (Y)_new) And if the distance from the central point a is greater than R, detecting the data as fault data.

Compared with the prior art, the invention has the following beneficial effects:

the fault detection method based on the global structure-preserving local tangent space arrangement algorithm solves the problems of complex structure, high data dimension, more samples and complex relation between variables of a nonlinear chemical process, maintains the external shape of data, prevents the failure report in the variance direction, ensures the precision of a fault detection model and improves the fault recognition rate compared with the traditional fault detection method.

Drawings

Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:

fig. 1 is a schematic flow diagram of a fault detection method based on a global structure-preserving local tangent space arrangement algorithm according to the present invention.

Detailed Description

The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.

The fault detection is carried out by constructing statistic through Support Vector Data Description (SVDD) (support Vector Data description), and the SVDD statistic does not need to meet the assumption that Data obeys Gaussian distribution, so that the monitoring performance is better. And the effect of applying the SVDD statistics is independent of the distribution of the process data, so that the process mixing information can be well processed. In addition, the SVDD statistic maps the process data to a high-dimensional feature space through a kernel method, so that the method has better processing nonlinear capacity.

However, there is a problem in that the computational complexity significantly increases when the sample data is large. In order to overcome the defect, the fault detection method based on the global structure maintenance local tangent space arrangement algorithm improves the effectiveness of observed data from the two aspects of reducing the number and the dimension of the data set samples. Specifically, firstly, a GLTSA algorithm is utilized to extract a feature space, the dimension of a sample is reduced, and then a support data vector description algorithm is introduced to directly establish an SVDD model according to the feature space; therefore, new statistics are constructed, and fault detection can be well realized.

Fig. 1 is a schematic flow chart of a fault detection method based on a global structure preserving local tangent space arrangement algorithm provided by the present invention, and with reference to fig. 1, the method in the present invention may include the following steps:

step 1: the local information is extracted by arranging the features. When the offline sample data set is X_a＝[x_a1，K，x_aN]The normalized data set is X ═ X₁，K，x_N]Then, using X to construct a neighbor matrix X_iFor each point in it, its neighbor matrix X can be used_i＝[x_i1，K，x_ik]A description is given. The high-dimensional to low-dimensional mapping may be represented as x_i＝f(y_i)+_iI is 1, K, N, wherein y_i∈R^d，x_i∈R^mAnd d is less than m, and the Euclidean distance is calculated. It should satisfy:

step 2: local coordinates are calculated. From all x_ijMean value of

And obtaining the optimal x. And the projection coordinate matrix theta of the sample point in the local tangent space is [ theta ═₁，...，θ_k]Can be defined as follows:

wherein the content of the first and second substances,

thus:

q is composed of Q_iIs derived from X_iH_kThe maximum d singular values of (a) are the corresponding left vectors, and the reconstruction error is:

and step 3: and arranging the local coordinates to construct global coordinates. Each sample point has a local coordinate system Θ_iArranging these local coordinates results in a global coordinate system, namely: y ═ Y₁，K，y_N]And after linear affine transformation is carried out on the local coordinates, the local coordinates are rearranged again to obtain global coordinates:

wherein

Represents the low dimensional coordinate center of X; l is_iRepresenting affine transformation relations;_j ⁽ⁱ⁾is the local reconstruction error. Remember Y_i＝[y_i1，K，y_ik]，E_i＝[₁ ⁽ⁱ⁾，...，_k ⁽ⁱ⁾]，

Then it is possible to obtain:

so reconstruction error E_iIt can be written as:

to preserve as many local geometric features as possible in a low-dimensional feature space, reconstruction errors are minimized_j ⁽ⁱ⁾The following can be obtained:

and 4, step 4: extracting low-dimensional sub-manifold. Optimal transformation matrix L_iIs composed of

Θ_i ⁺Is theta_iThe Moore-Penrose generalized inverse of (1). Let S_iIs a selection matrix between 0 and 1, YS_i＝Y_iThen the objective function is converted into:

J(Y)＝min||YSW||＝min tr(YSW^TS^TY^T)

wherein S ═ S₁...S_i，...S_N]Is a neighbor selection matrix, W ═ diag (W)₁，...W_i，...W_N)。

W_i＝H_k(I-V_iV_i ^T)

V_iIs a matrix X_iH_kIn order to make Y a unique value, a constraint condition YY is added^T＝I_dIf A is a linear mapping, then Y is equal to A^TXH_kThen, the objective function of local structure maintenance is converted into:

B＝SWW^TS^T

and 5: in order to extract more characteristic information and keep the overall structure similar to high-dimensional spatial data, a global objective function J (A) is introduced_global：

Step 6: and solving a mapping matrix of a local tangent space arrangement algorithm maintained by the global structure. The optimization objective for constructing the GLTSA is:

and 7, monitoring online data. In order to ensure the real-time effect of detection, online data X is available_anewAfter observed, normalization is performed to obtain X_newCalculating the low-dimensional feature space Y of the online data through the obtained A_newNamely:

Y_new＝A^TX_newH_k

and 8, establishing the statistic of the dimension reduction data by using an SVDD method. The hypersphere model for establishing the online data feature space needs to solve the following optimization problems:

s.t.||Φ(Y_i)-a||²≤R²+ξ_i，ξ_i≥0

wherein the parameter C is introduced to balance the size of the hyper-sphere and the normal sample error rate, ξ_iAnd the relaxation coefficient reflects the fault-tolerant capability of the SVDD model. The above problem translates into Lagrange extrema problem:

wherein alpha is_iAnd beta_iIs a Lagrange multiplier, Y_iIs the ith support vector of the training data feature space. Y is_jIs the jth support vector in the training data feature space.

Accelerated solution of Lagrange multiplier alpha by using Sequential Minimal Optimization (SMO)_iThereby obtaining a support vector Y_i. The distance from the support vector to the center of the sphere is the radius R.

Wherein, Y_oIs any support vector in the feature space of the training data.

On-line data feature space Y_newThe fault detection of (2) is to calculate the distance between the sample data point and the central point a and compare the distance with R. The formula is as follows:

if the above condition is satisfied, detecting as fault data, wherein Y_newiAnd Y_newjFor the support vectors in the ith and jth online data feature spaces, Y_newoIs an arbitrary support vector in the online data feature space.

For the further optimization scheme of the fault detection method of the global structure maintained local tangent space arrangement algorithm, in step 1, the euclidean distance can be defined as:

in step 8, when solving the Lagrange extremum problem, the method can convert the target into a dual function:

the invention utilizes the local structure of the LTSA stored sample to reduce the dimension of the high-dimensional data, and stores the local characteristics of the sample data as much as possible. The idea of global structure maintenance is added on the basis of local structure maintenance, so that the overall external characteristics of the original spatial data are retained to the maximum extent on the premise of extracting local feature information. The method establishes statistics on the dimension reduction data by constructing an SVDD model. The assumption that the data obeys Gaussian distribution is not required to be met, so that the monitoring performance is better.

The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (9)

1. A fault detection method based on a global structure-preserving local tangent space arrangement algorithm is characterized by comprising the following steps:

step 1: extracting local information of offline sample data through a local tangent space algorithm maintained by a global structure to obtain a local tangent space;

step 2: obtaining local coordinates of the sample points in the local cutting space;

and step 3: constructing a global coordinate according to the local coordinate;

and 4, step 4: determining a target function maintained by a local structure according to the reconstruction error of the local coordinate;

and 5: determining a target function maintained by the global structure according to the overall structure of the global coordinate;

step 6: determining a mapping matrix of a local tangent space arrangement algorithm maintained by the global structure according to the target function maintained by the local structure and the target function maintained by the global structure;

and 7: converting the online sample data after the standardization treatment into dimension reduction data of a new feature space according to the mapping matrix;

and 8: and establishing statistic of the dimensionality reduction data through a support vector data description method, and determining whether fault data exists in the online data according to the distance between the statistic and the central point of the hypersphere model of the online data feature space.

2. The method for detecting the fault based on the global structure preserving local tangent space arrangement algorithm according to claim 1, wherein the step 1 comprises:

step 1.1: for the offline sample data set X_a＝[x_a1，K，x_aN]Carrying out standardization processing to obtain a standardized data set X ═ X₁，K，x_N]；x_a1Representing an offline sample data set X_a1 st data of (1), x_aNRepresenting an offline sample data set X_aN-th data of (1), x₁Representing the 1 st data, X, in a normalized data set X_aNRepresenting the nth data in the normalized data set X, N being a natural number greater than 1;

step 1.2: construction of a proximity matrix X from a normalized data set X_i＝[x_i1，K，x_ik]；x_i1Representing the proximity matrix X_i1 st data of (1), x_ikRepresenting the proximity matrix X_iThe kth data of (1);

step 1.3: constructing a local tangent space according to the proximity matrix and the high-dimensional to low-dimensional data mapping relation; the sample points in the local tangent space satisfy the following relationship:

x_i＝f(y_i)+_i，i＝1，K，N，

y_i∈R^d，x_i∈R^m，d＜m

where Q is the orthogonal basis vector matrix in tangent space, θ_jIs locally low-dimensional embedded data, x, corresponding to Q_iRepresenting the ith element, y, in the dataset matrix X_iRepresenting the ith element in the low-dimensional feature matrix Y,_irepresenting the i-th noise signal, R^dRepresenting a real matrix of dimension d, R^mRepresenting a data array of dimension m, d representing Y and m, X representing X and m_ijNeighbor matrix X representing a data set_iThe jth element of (a), x represents the optimal data, x^TThe transpose matrix representing the optimal data set and Θ represents the projected coordinate matrix of the sample point in the local tangent space.

3. The method for fault detection based on the global structure preserving local tangent space arrangement algorithm as claimed in claim 2, wherein the step 2 comprises:

a projection coordinate matrix Θ defining sample points in the local tangent space is ═ θ₁，...，θ_k]，θ₁Representing the 1 st element, theta, in the projection coordinate matrix theta_kRepresenting the kth element in the projection coordinate matrix Θ; wherein:

wherein, theta_iThe local coordinates of the ith sample point are represented,

a transpose matrix representing an ith orthogonal basis vector matrix, I represents an identity matrix,e denotes an error, e^TTransposed matrix, theta, representing the error₁ ⁽ⁱ⁾Represents the ith local coordinate matrix theta_i1 st element of (1), theta_k ⁽ⁱ⁾Represents the ith local coordinate matrix theta_iThe kth element of (1), ξ_j ⁽ⁱ⁾A j-th element of the ith local coordinate matrix representing a j-th reconstruction error, Q_iRepresenting the ith orthogonal basis vector matrix, Q_i ^TTranspose matrix, x, representing the jth orthogonal basis vector matrix_ijNeighbor matrix X representing a data set_iThe first element of (a) is,

denotes all x_ijAverage value of (1), H_kMapping parameter, θ, representing local k neighbors_j ⁽ⁱ⁾Represents the ith local coordinate matrix theta_iThe jth element in (a).

4. The method for fault detection based on the global structure preserving local tangent space arrangement algorithm as claimed in claim 3, wherein the step 3 comprises:

rearranging the local coordinates after linear affine transformation is carried out on the local coordinates to obtain global coordinates; wherein:

let Y_i＝[y_i1，K，y_ik]，E_i＝[₁ ⁽ⁱ⁾，...，_k ⁽ⁱ⁾](ii) a Then

Wherein: y is_ijThe ith sample corresponds to the jth eigenvector in the low-dimensional space,

denotes all of y_ijAverage value of (1), L_iThe optimal transformation matrix, θ, representing the ith sample_j ⁽ⁱ⁾Represents the ith local coordinate matrix theta_iThe (c) th element of (a),_j ⁽ⁱ⁾represents the ith local coordinate matrix theta_iLocal reconstruction error of the jth element in (1), E_iA reconstruction error matrix, Y, representing the ith local coordinate matrix_iLow-dimensional eigenvectors, y, representing the ith local coordinate matrix_i1The 1 st element, y, in the low-dimensional feature vector representing the ith local coordinate matrix_ikThe kth element in the low-dimensional feature vector representing the ith local coordinate matrix,₁ ⁽ⁱ⁾represents the ith local coordinate matrix theta_iThe local reconstruction error of the 1 st element in (a),_k ⁽ⁱ⁾represents the ith local coordinate matrix theta_iLocal reconstruction error of the kth element in (1).

5. The method for fault detection based on the global structure preserving local tangent space arrangement algorithm as claimed in claim 4, wherein the step 4 comprises:

assuming an optimal transformation matrix

Wherein, theta_i ⁺Is theta_iMoore-Penrose generalized inverse of (1);

suppose S_iIs a selection matrix between 0 and 1, YS_i＝Y_iThen the objective function is converted into:

J(Y)＝min||YSW||＝min tr(YSWW^TS^TY^T)

wherein S ═ S₁...S_i，...S_N]Is a neighbor selection matrix, W ═ diag (W)₁，...W_i，...W_N)，S_iThe i-th element, W, of the neighbor selection matrix_iRepresenting an ith neighbor characterization matrix;

W_i＝H_k(I-V_iV_i ^T)

V_iis a matrix X_iH_kIn order to make Y a unique value, a constraint condition YY is added^T＝I_dIf A is the mapping matrix, then Y is equal to A^TXH_kThen, the objective function of local structure maintenance is converted into:

B＝SWW^TS^T

wherein: j (Y) represents the objective function for obtaining the feature space, YSW represents the specific mathematical expression of the objective function J (Y), tr (YSWW)^TS^TY^T) Traces, V, representing multiplication of the target function by its transpose_iRepresentation matrix X_iH_kRight singular vector, V, corresponding to the maximum singular value of_i ^TRepresents V_iTransposed matrix of (1), J (A)_localAn objective function representing local structure preservation, A^TXH_NRepresenting a mathematical expression of low-dimensional data characterized by high-dimensional data, B representing a matrix obtained by multiplying a local mapping matrix of a neighbor mapping matrix by its transpose, H_N ^TIndicating a local mapping parameter, X, when the number of neighbors takes N^TRepresenting the transpose of the original high-dimensional data.

6. The method for detecting faults based on the local tangent space arrangement algorithm of global structure maintenance as claimed in claim 5, wherein the objective function J (A) of global structure maintenance in the step 5_global，

All elements y representing a low-dimensional feature space_iAverage value of (a).

7. The method for detecting faults based on global structure preserving local tangent space arrangement algorithm of claim 6, wherein the mapping matrix J (A) of the global structure preserving local tangent space arrangement algorithm in the step 6_local-globalThe following were used:

8. the method according to claim 7, wherein the formula for converting the normalized online sample data into the dimension-reduced data of the new feature space in step 7 is as follows:

Y_new＝A^TX_newH_k

wherein: y is_newReduced-dimension data representing a new feature space, A^TDenotes the transpose of the mapping matrix A, X_newRepresenting the online sample data after the normalization process.

9. The method for fault detection based on the global structure preserving local tangent space arrangement algorithm as claimed in claim 8, wherein the step 8 comprises:

the hypersphere model for establishing the online data feature space needs to solve the following optimization problems:

s.t.||Φ Y_i)-a||²≤R²+ξ_i，ξ_i≥0

where R represents the radius of the hypersphere, C represents the trade-off of the hypersphere size and the normal sample error rate, ξ_iDenotes the relaxation coefficient, phi (Y)_i) The distance between the ith element in Y and the spherical center of the hypersphere is shown, and a represents the spherical center of the hypersphere;

converting the optimization problem into a Lagrange extreme value problem:

wherein alpha is_iAnd beta_iIs a Lagrange multiplier, Y_iFor the i-th support vector, Y, of the training data feature space_jIs the jth support vector in the training data feature space;

acceleration solving of Lagrange multiplier alpha by adopting sequential minimum optimization algorithm_iTo obtain a support vector Y_iAnd the distance from the support vector to the center of the sphere is the radius R;

wherein, Y_oFor any support vector in the training data feature space, K represents the kernel function, alpha_jRepresents Y_iLagrange multiplier of, K (Y)_i，Y_j) Represents Y_iAnd Y_jThe kernel function expression of (1);

dimension reduction data Y of new feature space_newIs to calculate a sample data point phi (Y)_new) The distance from the center point a, and compared to R, is given by:

wherein, K (Y)_newi，Y_newo) Represents Y_newiAnd Y_newoExpression of kernel function of, Y_newiRepresenting support vectors, Y, in the ith online data feature space_newoRepresenting an arbitrary support vector, K (Y), in the online data feature space_newi，Y_newj) Represents Y_newiAnd Y_newjExpression of kernel function of, Y_newjRepresenting a support vector in a jth online data feature space;

if the sample data point Φ (Y)_new) And if the distance from the central point a is greater than R, detecting the data as fault data.

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