CN113743489A - Process industrial process fault detection method based on data loss - Google Patents

Abstract

The invention relates to a process industrial process fault detection method based on data loss, which comprises the following steps: step S1: sampling and processing data of the process industrial process; step S2: filling missing data in the sampled data by using a kernel extreme learning machine KELM; step S3: performing low-dimensional feature extraction on the data by adopting a landmark equidistant mapping method L-ISOMAP; step S4: and calculating statistics and controlling the current situation in the feature space and the residual error space respectively, and performing fault detection. Compared with the prior art, the method has the advantages of high accuracy, time saving, computing resource saving and the like.

Description

Process industrial process fault detection method based on data loss

Technical Field

The invention relates to the field of process industrial process control, monitoring and safety production, in particular to a process industrial process fault detection method based on data loss.

Background

With the introduction of the industrial 4.0 concept and the increasing maturity of technologies such as industrial internet, internet of things and the like, the intelligent manufacturing transformation of the industrial production process has become a necessary trend of the traditional industrial development, and the industrial process has become increasingly integrated and large-scale as a result. The production process of the process industry such as oil refining, pharmacy and the like is increasingly complex, and the establishment of an accurate mechanism model for the process by a traditional mode becomes increasingly difficult. Under the wave of support of technologies such as a distributed control system, a data acquisition and monitoring control system and the like and machine/deep learning, process industrial process modeling and process monitoring based on data driving become indispensable links for industrial intelligent operation production.

Signals are unstable in the industrial data transmission process, data storage fails, a sensor loses packets during sampling, and data are lost due to the multiple sampling rates. When a large number of missing values appear in the historical process data applied to modeling, if a deletion rule is directly adopted, a large number of effective information can be removed, and a small amount of sample data used for constructing the model cannot embody the characteristics of the original process; if an unreasonable filling method is adopted, missing values can be predicted in a wrong mode, and the constructed fault detection model is low in accuracy.

Through retrieval, the Chinese patent publication No. CN109146004A discloses a dynamic process detection method based on an iterative missing data estimation strategy, and the invention uses an iterative missing data estimation method to estimate the estimated value of the missing data, thereby converting the assumed original data into an estimation error; and iteratively solving the estimation value of the missing variable by adopting a PCA (principal component analysis) model, and finally performing online fault detection by using the estimation error as a monitored object. However, the PCA model used in this method is slow and not highly accurate.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide a flow industrial process fault detection method based on data loss, which has high accuracy and saves time and computing resources.

The purpose of the invention can be realized by the following technical scheme:

a process industrial process fault detection method based on data loss comprises the following steps:

step S1: sampling and processing data of the process industrial process;

step S2: filling missing data in the sampled data by using a kernel extreme learning machine KELM;

step S3: performing low-dimensional feature extraction on the data by adopting a landmark equidistant mapping method L-ISOMAP;

step S4: and calculating statistics and controlling the current situation in the feature space and the residual error space respectively, and performing fault detection.

Preferably, the step S1 includes the steps of:

step S101: sampling data of a normally running process industrial process, simulating various industrial field reasons to perform deletion exception processing on the data, and obtaining an incomplete deletion data set X containing various deletion types_M，X_M∈R^{m ×n}Wherein R is^m×nRepresenting a real matrix with m samples and n dimensions;

step S102: for missing data set X_MCarrying out standardization processing to obtain a new data set X_SM；

Step S103: find dataset X_SMThe position of the missing data in (1) divides all sampling points containing the missing value into a data set X_SM-NCAnd dividing the complete sample point data into another data set X_SM-C。

Preferably, the step S2 is specifically:

step S201: determining KELM_iInput and output data of the model;

for the ith sampling point, finding the variable v to which the missing value belongs_{ms_i}V is to be_{ms_i}Corresponding data Nan_NCiAs a value to be predicted, the observed variable excluding the missing value in the sample point is defined as v_{ob_i}V is to be_{ob_i}Corresponding data X_NCiAs KELM_iTest input of the model;

complete data set X_SM-CAs KELM_iTraining data of the model-X_SM-CMiddle variable v_{ob_i}Corresponding data X_CiAs input, X_SM-CMiddle variable v_{ms_i}Corresponding data Y_CiAs model output, construct a model with P sampling pointsIs a data set of

Wherein X_Ci∈R^P×TRepresenting training input X_CiIs a data point of dimension T, Y_Ci∈R^P×KIndicating label Y_CiData points in K dimension, x_{Ci_t}Training data representing the t-th sample point, y_{Ci_t}A label representing the t-th sample point;

step S202: KELM for establishing ith sampling moment_iA model;

step S203: predicting missing data of the ith sample point;

step S204: mixing X_SM-NCFilling all the moments with missing values to obtain a complete data set X_f。

Preferably, the step S202 specifically includes:

the extreme learning machine ELM is a special single-hidden-layer feedforward neural network SLFNs, and aiming at the ith sampling moment, the SLFNs meet the following expression:

wherein L represents the number of nodes of the hidden layer, G (x)_{Ci_j},a_q,b_q) Representing the activation function, x_{Ci_j}Q represents a q-th layer hidden layer node for training data of the model; a is in the form of R^T×LFor inputting the weight matrix, b is an element of R^1×LTo imply layer bias, β ∈ R^{L ×K}As an output weight matrix, y^* _{Ci_j}An output value representing the model;

the parameters a and b in the extreme learning machine ELM model are randomly determined, only the output weight matrix parameter beta is required to be obtained, and the corresponding output of the extreme learning machine ELM is as follows:

Y_Ci ^*＝Hβ (2)

where H represents the feature mapping matrix:

wherein g (x)_{Ci_1},a_q,b_q) For activating a function matrix G (x)_{Ci_j},a_q,b_q) An element of (1);

obtaining an output weight matrix

Wherein H^TRepresenting the transposition of a characteristic mapping matrix H, C representing a regularization parameter, I representing an identity matrix, and P representing the number of samples;

the output function of the ELM is expressed as:

wherein h (x)_Ci) Is x_CiA mapping function of (a);

introducing Mercer theorem to construct KELM on the basis of ELM_iSaid KELM_iThe output function of (a) is as follows:

wherein omega_iThe kernel function matrix trained to fill the missing values of the ith sample point is expressed as:

K(x_{Ci_α},x_{Ci_β}) Is represented by X_CiTwo elements x in (1)_{Ci_α},x_{Ci_β}Constructed radial basis functionNumber:

where σ is a kernel width parameter, α and β represent the positions of the elements, respectively,

is x_{Ci_α},x_{Ci_β}An abbreviated form of the constructed kernel function.

Preferably, the step S203 specifically includes: mixing X_SM-NCData X at the ith time_NCiPredicting missing data Nan at that time as input to the model_NCi：

Preferably, the step S3 includes the steps of:

step S301: randomly selecting m' samples from m samples as landmark points;

step S302: constructing a neighbor neighborhood graph G;

calculating Euclidean distances between m' landmark point pairs, data point pairs (X)_fi,X_fj) Is recorded as d_Xm′(X_fi,X_fj) (ii) a Setting a distance threshold, selecting proper neighbors, and constructing a neighbor neighborhood graph G;

step S303: calculating the Dijkstra distance between the geodesic lines of the high-dimensional data, namely the shortest path;

by calculating X on the neighborhood map G_fi,X_fjGeodesic distance d between two points_Dm′(X_fi,X_fj) To approximate the geodesic distance of the original manifold, a geodesic distance matrix D_Dm′Consisting of the square of the geodesic distance;

step S304: determining an inner product matrix B_m′：

Wherein H_m′Is a centralized matrix;

step S305: obtaining a d-dimensional embedding matrix L of landmark points_d：

Solving to obtain a matrix B_m′Corresponding maximum d eigenvalues λ₁≥λ₂≥…λ_dD eigenvectors corresponding to the eigenvalues are [ v ]₁,v₂,…,v_d]Thus d-dimensional embedding matrix L of landmark points_dExpressed as:

wherein

Representing a feature vector corresponding to the first feature value;

step S306: obtaining a geodesic distance matrix D_Dm′Average vector of

Step S307: calculating the distance between the data point except the landmark point in the data set and the landmark point, namely the distance between a certain point r in the rest data points and the landmark point is marked as d_Dmm′(X_fr,X_fj) The distance squares form a matrix, and the vector formed by the columns of the data points r in the matrix is recorded as

Step S308: solving a matrix L_dIs pseudo-inverse transpose matrix L^# _d

Step S309: computing a d-dimensional embedding matrix L for the remaining data points_rd；

Step S310: adopting a Principal Component Analysis (PCA) algorithm to realize embedded coordinate alignment;

is calculated to obtaind-dimensional embedded matrix X_fd∈R^m×dRealizing coordinate alignment by using PCA (principal component analysis) standardization method to obtain aligned d-dimensional feature matrix Y ∈ R^m×d。

Preferably, the number of landmark samples in step S301 satisfies m' < m.

Preferably, the step S4 includes the steps of:

step S401: calculating a mapping matrix A;

solving a mapping matrix A of the original high-dimensional data projected to the low-dimensional space through a local linear regression idea:

Y＝AX_f (12)

A＝YX_f ^T(X_fX_f ^T)^-1 (13)

wherein X_fFor filling up the complete data set after missing data, Y is a feature matrix;

step S402: constructing an offline data fault detection statistic and a control limit;

step S403: and calculating the online data statistic for real-time monitoring.

Preferably, the step S402 specifically includes: for offline data X_fSeparately constructing feature space statistics

And residual spatial statistics SPE_f(ii) a And calculating respectively by adopting a kernel density estimation algorithm

And SPE_fControl limit of

And SPE_ucl。

Preferably, the step S403 specifically includes: standardizing observed real-time data x_tTo obtain x_rtObtaining a low-dimensional mapping y of the real-time data by the mapping matrix A_rtComprises the following steps:

y_rt＝Ax_rt (14)

computing real-time data statistics

And SPE_rtAnd if the online data statistic is larger than the control limit, indicating that the process has a fault.

Compared with the prior art, the invention has the following advantages:

1) when missing values are predicted, the difference of each sampling moment with the missing values is fully considered, and each sampling moment is sequentially filled in a model updating mode, so that the method is suitable for various missing types, and the accuracy of filling data is ensured;

2) the nuclear limit learning machine has the characteristics of strong generalization performance and high learning speed, and has less time consumption and computing resources by using the nuclear limit learning model to predict the missing value while ensuring the accuracy;

3) when a landmark equidistant mapping (L-ISOMAP) model is established to realize feature extraction, the low-dimensional feature data can keep the manifold structure of the original high-dimensional data, so that the low-dimensional data can keep effective information of the original data as much as possible;

4) compared with an equidistant mapping algorithm (ISOMAP), the landmark equidistant mapping algorithm (L-ISOMAP) has smaller operation amount when the distance matrix is calculated while the dimension reduction reliability is ensured, so the algorithm has higher operation speed.

Drawings

FIG. 1 is a flow chart of the overall steps of the present invention in implementing fault detection based on data loss;

FIG. 2 is a flow diagram of missing data padding implemented using a KELM model for model updating;

FIG. 3 is a flow chart for implementing feature extraction using the L-ISOMAP algorithm.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.

As shown in fig. 1, the present invention provides a process industrial process fault detection method based on data loss, and the working principle of the method is as follows: firstly, collecting normal data when a process industrial process normally runs, processing to obtain a training data set containing a missing value, and filling the missing value through each sampling data of a Kernel Extreme Learning Machine (KELM) based on model updating to obtain a complete data set; on the basis, a Landmark equidistant mapping algorithm (Landmark-ISOMAP, L-ISOMAP) is adopted to realize low-dimensional feature extraction; finally, T is established in the feature space²And (4) statistics, namely establishing SPE statistics in the residual error space, and respectively calculating corresponding control limits, thereby realizing fault detection.

The embodiment is realized by the following specific technical scheme, which specifically comprises the following steps:

step S1: sampling data of a normally running process industrial process, simulating various reasons for data loss in an industrial field, and performing deletion exception processing on the data to obtain an incomplete missing data set X containing various deletion types_M，X_M∈R^m×nWherein R is^m×nRepresenting a real matrix with m samples and n dimensions;

step S2: for the missing data set X_MCarrying out standardization processing to obtain a new data set X_SM；

As shown in fig. 2, a flow chart of a data padding method is presented.

Here, for simplicity of illustration of the padding process, X_SMSetting a matrix with three missing values;

in which the coordinates (u) of the data are missing₁,v₁),(u₁,v₂),(u₂,v₃) Respectively represent the u-th₁V th of a sampling instant₁,v₂Individual variable and u₂V th of a sampling instant₃Data missing of each variable occurs;

step S3: find dataset X_SMThe position of the missing data is divided into data sets X by all sampling points containing the missing values_SM-NCDividing the complete sample point data into another data set X_SM-C；

Step S4: for data set X in turn_SM-NCFilling each sampling point;

as shown in FIG. 2, the variable v to which the missing value belongs is found for the ith sampling point of data padding_{ms_i}V is to be_{ms_i}Data Nan corresponding to variables_NCiThe observed variables in the sample points excluding the missing values are v as the values to be predicted_{ob_i}Data X corresponding thereto_NCiAs KELM_iTest input of the model;

complete data set X_SM-CAs KELM_iTraining data of the model, X_SM-CMiddle variable v_{ob_i}Corresponding data X_CiAs input, X_SM-CMiddle variable v_{ms_i}Corresponding data Y_CiAs a model output, a data set with P sample points is constructed as

Wherein X_Ci∈R^P×TRepresenting training input X_CiIs a data point of dimension T, Y_Ci∈R^P×KIndicating label Y_CiData points in the K dimension;

when X is present_SMHas three deficiency values as shown aboveFor the u-th example matrix, first₁Filling missing values of a sampling moment, wherein the variable to which the missing values belong is v₁,v₂Corresponding to missing data being

And

will miss data

And

the residual data after the missing value is removed at the sampling time is recorded as the prediction model output of the model

Will be

A prediction model input as a model; then selecting X_SM-CFind v in₁,v₂Data corresponding to variables

Output labels as model training data, X_SM-CThe rest of the data

As input for model training data;

to fill in u₁KeLM is a model of kernel limit learning machine with missing values at each moment_u1Training data sets of models

The specific data corresponding to the moment is

Extreme Learning Machines (ELM) are special single-hidden layer feedforward neural networks (SLFNs) for the u-th₁At each sampling instant, SLFNs satisfies the following expression:

where L represents the number of nodes of the hidden layer,

representing an activation function, the type of activation function represented by g (-), a ∈ R^T×LFor inputting the weight matrix, b is an element of R^1×LTo imply layer bias, β ∈ R^L×KTo output the weight matrix, the weight matrix is output,

an output value representing the model;

an Extreme Learning Machine (ELM) is a special SLFNs, parameters a and b in an ELM model are randomly determined, and only an output weight matrix parameter beta is required to be obtained; compared with the traditional SLFNs, the ELM has better generalization performance and learning speed; the corresponding outputs of ELM are:

where H represents the feature mapping matrix:

output weight matrix

The method of determination is as follows:

wherein H^TExpress characterThe transpose of the eigen-mapping matrix, C denotes the regularization parameter, and I denotes the identity matrix.

The output function of the ELM can be expressed as:

in order to avoid the influence of the selection of the number L of nodes of the hidden layer on the model training result, Mercer theorem construction is introduced on the basis of ELM

The output function of (a) is as follows:

the kernel function matrix trained to fill the missing value at the ith time is shown in the form:

K(x_{Ci_α},x_{Ci_β}) Shown in the specification

Two elements of

Constructed radial basis kernel function:

is represented by X_CiTwo of (1)An element

Constructed radial basis kernel function:

where σ is the kernel width parameter.

To sum up, it can be determined that the padding u₁Model of temporal missing values

Mixing X_SM-NCMiddle u₁Data X of time_NCiPredicting missing data at that time as input to the model

Is filled up with u₁After the missing value of the moment, the u-th order₂Predicting and filling missing values of sampling time, wherein the variable to which the missing values of the sampling time belong is v₃Corresponding to missing data being

Will miss data

The residual data after the missing value is removed at the sampling time is recorded as the prediction model output of the model

Will be

Prediction model output as a modelEntering; then selecting X_SM-CFind v in₃Data corresponding to variables

Output labels as model training data, X_SM-CThe rest of the data

As input for model training data;

to fill in u₂The kernel limit learning machine model of the missing value at each moment is recorded as

Data set for training model

At u₂The specific data corresponding to the time is

After confirming the input and output data of the model, training according to the above

Same step training

Finally obtaining the predicted missing value

X_SM-NCAfter all the missing values are filled up, a complete data set X is finally obtained_f。

Step S5: utilizing L-ISOMAP algorithm to carry out pair on filled data set X_fCarrying out feature extraction;

high-dimensional training data set X by L-ISOMAP algorithm_f∈R^m×nMapping to a low-dimensional matrix Y ∈ R^m×dWherein X is_fThe method comprises the following steps of (1) obtaining a matrix with m sample numbers and n dimension; y is a matrix with the sample number of m and the dimension of d; in-process industrial processesThe dimension represents the number of variables in the process.

As shown in FIG. 2, the dimension reduction process of the L-ISOMAP algorithm is as follows:

1) selecting m' landmark points;

in the traditional ISOMAP algorithm, no matter the distance between every two m sample points needs to be calculated when the Euclidean distance is calculated, when the value of m is large, the algorithm has high calculation complexity; the L-ISOMAP algorithm randomly selects m ' samples from m samples as landmark points, wherein m ' < m, and only the distance between the m ' landmark points needs to be calculated, so that the complexity is greatly reduced;

2) constructing a neighbor neighborhood graph G;

calculating Euclidean distances between m' landmark point pairs, data point pairs (X)_fi,X_fj) Is recorded as d_Xm′(X_fi,X_fj) The calculation formula is as follows:

setting a distance threshold, selecting proper neighbors, and constructing a neighbor neighborhood graph G;

3) calculating the geodesic distance (Dijkstra distance) between the high-dimensional data, namely the shortest path;

by calculating X on the neighborhood map G_fi,X_fjGeodesic distance d between two points_Dm′(X_fi,X_fj) To approximate the geodesic distance of the original manifold, if X_fi,X_fjThe two points are shared, and then:

d_Dm′(X_fi,X_fj)＝d_Xm′(X_fi,X_fj) (13)

otherwise, there are:

d_Dm′(x_fi,x_fj)＝min{d_Dm′(x_fi,x_fj),d_Dm′(x_fi,x_fp)+d_Dm′(x_fp,x_fj)} (14)

wherein d is_Dm′(X_fi,X_fj)＝∞，i,j＝1,2,…,m′，p＝1,2,…,m′；

Geodesic distance matrix D_Dm′The method is composed of the square of geodesic distance, and the concrete form is as follows:

4) determining an inner product matrix B_m′；

Wherein H_m′Is a centralized matrix, which is specifically defined as follows:

δ_ij＝[D_Dm′]_ij (18)

wherein delta_ijRepresents X_fi,X_fjThe square of the distance between the two points;

5) d-dimensional embedding of landmark points is obtained;

solving to obtain a matrix B_m′Corresponding maximum d eigenvalues λ₁≥λ₂≥…λ_dD eigenvectors corresponding to the eigenvalues are [ v ]₁,v₂,…,v_d]Thus d-dimensional embedding matrix L of landmark points_dCan be expressed as:

6) obtaining a geodesic distance matrix D_Dm′Average vector of

Known as D_Dm′Is composed of m' vectors, and the vector is,

average vector

As follows:

7) calculating the distance between the data point except the landmark point in the data set and the landmark point, namely the distance between a certain point r in the rest data points and the landmark point is marked as d_Dmm′(X_fr,X_fj) The distance squares form a matrix, and the vector formed by the columns of the data points r in the matrix is recorded as

8) Solving a matrix L_dIs pseudo-inverse transpose matrix L^# _d；

9) Computing a d-dimensional embedding matrix L for the remaining data points_rd；

L_rdNeutralization

Correlated embedding vector

The expression is as follows:

from this, a d-dimensional embedding matrix L of the remaining data points can be determined_rd。

10) A Principal Component Analysis (PCA) algorithm realizes embedded coordinate alignment;

obtaining the d-dimensional embedded matrix X through the steps_fd∈R^m×dRealizing coordinate alignment by using PCA (principal component analysis) standardization method to obtain aligned d-dimensional feature matrix Y ∈ R^m×d。

Step S6: calculating a mapping matrix A;

in order to calculate real-time statistics conveniently, a mapping matrix A of original high-dimensional data projected to a low-dimensional space is solved through a local linear regression idea:

Y＝AX_f(23)

A＝YX_f ^T(X_fX_f ^T)^-1 (24)

step S7: constructing an offline data fault detection statistic and a control limit;

for offline data X_fSeparately constructing feature space statistics

And residual spatial Statistics (SPE)_f)：

T_f ²＝YS^-1Y (25)

SPE_f＝||(I-A^TA)X_f||² (26)

Where S is the covariance matrix and,

S＝YY^T/(m-1) (27)

separately computing using a kernel density estimation method

And SPE_fA control limit of (d); if the confidence coefficient is 0.99, α is 0.01, and therefore the control limit can be derived by the following equation

And SPE_ucl：

Step S8: calculating online data statistics to realize real-time detection;

if real-time data x is observed_tNormalized to obtain x_rtObtaining a low-dimensional mapping y of the real-time data by the mapping matrix A_rt：

y_rt＝Ax_rt (30)

Calculating real-time data statistics:

T_rt ²＝y_rtS^-1y_rt (31)

SPE_rt＝||(I-A^TA)X_rt||² (32)

the online detection is realized through two statistics, if the online data statistics is larger than the control limit, the process is indicated to have a fault, namely the fault occurs when the following conditions occur:

in an industrial field of process industrial production, data loss can occur in the process of collecting, transmitting, storing and the like of process industrial process data due to various reasons such as equipment aging, wrong operation, technical bottlenecks and the like. The invention provides a fault detection method under the condition of data deficiency, which comprises the steps of firstly, effectively predicting the deficient data through a kernel limit learning machine model updated by the model, after obtaining a complete training data set, utilizing a landmark equidistant mapping algorithm to carry out feature extraction, establishing corresponding statistics and control limits, and realizing fault detection.

While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. A process industrial process fault detection method based on data loss is characterized by comprising the following steps:

step S1: sampling and processing data of the process industrial process;

step S2: filling missing data in the sampled data by using a kernel extreme learning machine KELM;

step S3: performing low-dimensional feature extraction on the data by adopting a landmark equidistant mapping method L-ISOMAP;

step S4: and calculating statistics and controlling the current situation in the feature space and the residual error space respectively, and performing fault detection.

2. The method for fault detection of process industrial process based on data loss according to claim 1, wherein the step S1 comprises the following steps:

step S101: sampling data of a normally running process industrial process, simulating various industrial field reasons to perform deletion exception processing on the data, and obtaining an incomplete deletion data set X containing various deletion types_M，X_M∈R^m×nWherein R is^m×nRepresenting a real matrix with m samples and n dimensions;

step S102: for missing data set X_MCarrying out standardization processing to obtain a new data set X_SM；

Step S103: find dataset X_SMThe position of the missing data in (1) divides all sampling points containing the missing value into a data set X_SM-NCAnd dividing the complete sample point data into another data set X_SM-C。

3. The method for detecting the fault of the process industrial process based on the data missing as claimed in claim 1, wherein the step S2 is specifically as follows:

step S201: determining KELM_iInput and output data of the model;

for the ith sampling point, finding the variable v to which the missing value belongs_{ms_i}V is to be_{ms_i}Corresponding data Nan_NCiAs a value to be predicted, the observed variable excluding the missing value in the sample point is defined as v_{ob_i}V is to be_{ob_i}Corresponding data X_NCiAs KELM_iTest input of the model;

complete data set X_SM-CAs KELM_iTraining data of the model, X_SM-CMiddle variable v_{ob_i}Corresponding data X_CiAs input, X_SM-CMiddle variable v_{ms_i}Corresponding data Y_CiAs a model output, a data set with P sample points is constructed as

Wherein X_Ci∈R^P×TRepresenting training input X_CiIs a data point of dimension T, Y_Ci∈R^P×KIndicating label Y_CiData points in K dimension, x_{Ci_t}Training data representing the t-th sample point, y_{Ci_t}A label representing the t-th sample point;

step S202: KELM for establishing ith sampling moment_iA model;

step S203: predicting missing data of the ith sample point;

step S204: mixing X_SM-NCFilling all the moments with missing values to obtain a complete data set X_f。

4. The method for detecting process industrial process faults based on data loss according to claim 3, wherein the step S202 specifically comprises:

the extreme learning machine ELM is a special single-hidden-layer feedforward neural network SLFNs, and aiming at the ith sampling moment, the SLFNs meet the following expression:

wherein L represents the number of nodes of the hidden layer, G (x)_{Ci_j},a_q,b_q) Representing the activation function, x_{Ci_j}Is the training data for the model and is,_qis shown as_qA layer implies a layer node; a is in the form of R^T×LFor inputting the weight matrix, b is an element of R^1×LTo imply layer bias, β ∈ R^L×KAs an output weight matrix, y^* _{Ci_j}An output value representing the model;

the parameters a and b in the extreme learning machine ELM model are randomly determined, only the output weight matrix parameter beta is required to be obtained, and the corresponding output of the extreme learning machine ELM is as follows:

Y_Ci ^*＝Hβ (2)

where H represents the feature mapping matrix:

wherein g (x)_{Ci_1},a_q,b_q) For activating a function matrix G (x)_{Ci_j},a_q,b_q) An element of (1);

obtaining an output weight matrix

Wherein H^TRepresenting the transposition of a characteristic mapping matrix H, C representing a regularization parameter, I representing an identity matrix, and P representing the number of samples;

the output function of the ELM is expressed as:

wherein h (x)_Ci) Is x_CiA mapping function of (a);

introducing Mercer theorem to construct KELM on the basis of ELM_iSaid KELM_iThe output function of (a) is as follows:

wherein omega_iThe kernel function matrix trained to fill the missing values of the ith sample point is expressed as:

K(x_{Ci_α},x_{Ci_β}) Is represented by X_CiTwo elements x in (1)_{Ci_α},x_{Ci_β}Constructed radial basis kernel function:

where σ is a kernel width parameter, α and β represent the positions of the elements, respectively,

is x_{Ci_α},x_{Ci_β}An abbreviated form of the constructed kernel function.

5. The method for detecting process industrial process faults based on data loss according to claim 4, wherein the step S203 specifically comprises: mixing X_SM-NCData X at the ith time_NCiPredicting missing data Nan at that time as input to the model_NCi：

6. The method for fault detection of process industrial process based on data loss according to claim 1, wherein the step S3 comprises the following steps:

step S301: randomly selecting m' samples from m samples as landmark points;

step S302: constructing a neighbor neighborhood graph G;

calculating Euclidean distances between m' landmark point pairs, data point pairs (X)_fi,X_fj) Is recorded as d_Xm′(X_fi,X_fj) (ii) a Setting a distance threshold, selecting proper neighbors, and constructing a neighbor neighborhood graph G;

step S303: calculating the Dijkstra distance between the geodesic lines of the high-dimensional data, namely the shortest path;

by calculating X on the neighborhood map G_fi,X_fjGeodesic distance d between two points_Dm′(X_fi,X_fj) To approximate the geodesic distance of the original manifold, a geodesic distance matrix D_Dm′Consisting of the square of the geodesic distance;

step S304: determining an inner product matrix B_m′：

Wherein H_m′Is a centralized matrix;

step S305: obtaining a d-dimensional embedding matrix L of landmark points_d：

Solving to obtain a matrix B_m′Corresponding maximum d eigenvalues λ₁≥λ₂≥…λ_dD eigenvectors corresponding to the eigenvalues are [ v ]₁,v₂,…,v_d]Thus d-dimensional embedding matrix L of landmark points_dExpressed as:

wherein

Representing a feature vector corresponding to the first feature value;

step S306: obtaining a geodesic distance matrix D_Dm′Average vector of

Step S307: calculating the distance between the data point except the landmark point in the data set and the landmark point, namely the distance between a certain point r in the rest data points and the landmark point is marked as d_Dmm′(X_fr,X_fj) The distance squares form a matrix, and the vector formed by the columns of the data points r in the matrix is recorded as

Step S308: solving a matrix L_dIs pseudo-inverse transpose matrix L^# _d

Step S309: computing a d-dimensional embedding matrix L for the remaining data points_rd；

Step S310: adopting a Principal Component Analysis (PCA) algorithm to realize embedded coordinate alignment;

d-dimension embedded matrix X is obtained through calculation_fd∈R^m×dRealizing coordinate alignment by using PCA (principal component analysis) standardization method to obtain aligned d-dimensional feature matrix Y ∈ R^m×d。

7. The method for detecting faults of process industrial process based on data loss according to claim 6, wherein the number of landmark sample samples in step S301 satisfies m' < m.

8. The method for fault detection of process industrial process based on data loss according to claim 1, wherein the step S4 comprises the following steps:

step S401: calculating a mapping matrix A;

solving a mapping matrix A of the original high-dimensional data projected to the low-dimensional space through a local linear regression idea:

Y＝AX_f (12)

A＝YX_f ^T(X_fX_f ^T)^-1 (13)

wherein X_fFor filling up the complete data set after missing data, Y is a feature matrix;

step S402: constructing an offline data fault detection statistic and a control limit;

step S403: and calculating the online data statistic for real-time monitoring.

9. The method for detecting process industrial process faults based on data loss according to claim 8, wherein the step S402 specifically comprises: for offline data X_fSeparately constructing feature space statistics

And residual spatial statistics SPE_f(ii) a And calculating respectively by adopting a kernel density estimation algorithm

And SPE_fControl limit of

And SPE_ucl。

10. The method for detecting process industrial process faults based on data loss according to claim 8, wherein the step S403 specifically includes: standardizing observed real-time data x_tTo obtain x_rtObtaining a low-dimensional mapping y of the real-time data by the mapping matrix A_rtComprises the following steps:

y_rt＝Ax_rt (14)

computing real-time data statistics T_rt ²And SPE_rtAnd if the online data statistic is larger than the control limit, indicating that the process has a fault.

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