CN116904673B - Method for detecting abnormal furnace condition of blast furnace based on stable feature extraction - Google Patents
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Abstract
The invention provides a method for detecting abnormal furnace conditions of a blast furnace based on stable feature extraction, and belongs to the technical field of blast furnace smelting. The method comprises the following steps: establishing a Gaussian mixture model of historical data under normal furnace conditions in different time periods; based on the established Gaussian mixture model, a feature extraction matrix is constructed to extract stable features by minimizing the differences of feature distribution in different time periods; establishing a Gaussian mixture model of stable characteristics, and respectively constructing detection statistics based on Mahalanobis distance under each component; determining a threshold value of detection statistics under each component by using historical data under normal furnace conditions according to the confidence level; calculating stable characteristics of a sample to be detected by using the characteristic extraction matrix; judging the components of the Gaussian mixture model to which the stable characteristics belong, and calculating corresponding detection statistics; if the detection statistic is greater than the threshold value of the detection statistic under the corresponding component, the abnormal furnace condition is judged. By adopting the method, the abnormal furnace condition of the blast furnace can be effectively detected.
Description
Technical Field
The invention relates to the technical field of blast furnace smelting, in particular to a method for detecting abnormal furnace conditions of a blast furnace based on stable feature extraction.
Background
The abnormal furnace condition of the blast furnace can lead to the consequences of substandard quality of molten iron, increased energy consumption, increased damping down overhauling time and the like, thereby causing resource waste and increasing production cost. Therefore, the detection of the abnormal furnace condition as early as possible is helpful for reminding operators of timely countermeasures, so that the loss caused by the abnormal furnace condition is reduced. The raw material quality of the blast furnace ironmaking process is unstable, the operation condition and the environment are changeable, and the ironmaking process data has the characteristic of non-stability. Therefore, the conventional multivariate statistical process monitoring method is difficult to obtain a satisfactory effect in long-term application, and the main reason is that fluctuation caused by abnormal furnace conditions is covered in non-stationary data, so that normal data fluctuation and abnormal data fluctuation are difficult to distinguish, and many blast furnaces still rely on manual experience seriously in furnace condition judgment at present. Therefore, research on a monitoring method for a non-stationary process of a blast furnace has an important role in improving automation of a production process, reducing labor workload and ensuring safe production.
Currently, non-stationary process monitoring methods include adaptive strategy-based methods, trend analysis-based methods, and stationary subspace separation-based methods. The method based on the self-adaptive strategy automatically adapts to a non-stable process by continuously updating a process monitoring model, such as a recursive principal component analysis, a sliding window principal component analysis, a recursive Gaussian mixture model and the like. However, such methods may adapt the monitoring model to slowly occurring faults. The trend analysis-based method is a method for realizing abnormal detection, such as qualitative trend analysis, main trend analysis and the like, by analyzing whether the change trend of data is in a normal range. Detection by such methods tends to be relatively late, since the judgment of the trend requires a certain length of data. The method based on the stable subspace separation separates the original data space into a stable subspace and a non-stable subspace, and constructs detection statistics aiming at different subspaces. Common stationary spatial separation methods include collaborative analysis and stationary subspace analysis methods. Where the synergistic analysis assumes that the variables are homonymous, this is often difficult to satisfy for practical industrial data. The steady subspace analysis method utilizes the difference of the Kullback-Leible (KL) divergence of Gaussian distribution to measure the characteristic distribution of different time intervals, so that data is required to obey the Gaussian distribution, and the application range of the method is limited.
Disclosure of Invention
The embodiment of the invention provides a method for detecting the abnormal furnace condition of a blast furnace based on stable feature extraction, which can effectively detect the abnormal furnace condition of the blast furnace. The technical scheme is as follows:
in one aspect, a method for detecting abnormal furnace conditions of a blast furnace based on stationary feature extraction is provided, the method is applied to electronic equipment, and the method comprises the following steps: an off-line modeling process and an on-line detection process; wherein,
the offline modeling process includes:
establishing a Gaussian mixture model of historical data under normal furnace conditions in different time periods;
based on the established Gaussian mixture model, a feature extraction matrix is constructed to extract stable features of historical data by minimizing the differences of feature distribution in different time periods; the difference of the characteristic distribution of different time periods is measured by using the Wessentin distance;
establishing a Gaussian mixture model of the extracted stable characteristics, and respectively constructing detection statistics based on Mahalanobis distance under each component;
determining a threshold value of detection statistics under each component by using historical data under normal furnace conditions according to the confidence level;
the online detection process comprises the following steps:
calculating stable characteristics of a sample to be detected by using the characteristic extraction matrix;
judging the components of the Gaussian mixture model to which the stable characteristics belong, and calculating corresponding detection statistics;
if the detection statistic is greater than the threshold value of the detection statistic under the corresponding component, the abnormal furnace condition is judged.
Further, the establishing the Gaussian mixture model of the historical data under the normal furnace conditions of different time periods comprises the following steps:
step A1, acquiring historical data of q sections of normal furnace conditions in different periods as a training data setWherein the history data includes: cold air flow, hot air pressure, air permeability index, cold air pressure, full pressure difference, actual wind speed and resistance coefficient, and ith section data in training data set +.>Expressed as:
wherein the subscriptFor the number of sensors, < > for>For the number of samples in each piece of data;
step A2, for the acquired training data setPretreatment->Wherein,representing the mean value of the f-th sensor in the training data,representing the variance of the f-th sensor in the training data;
step A3, constructing an augmentation matrix according to the window length w for each piece of preprocessed data, and obtaining:
wherein X is (i) Is thatCorresponding augmentation matrix,/->Is a real number domain;
step A4, fitting the distribution of each piece of data by using a Gaussian mixture model with the component number of K, and estimating X by using an expectation maximization algorithm (i) Gaussian mixture model parameters of (c):and->Wherein (1)>And->Mean vector and covariance matrix of the (r) th Gaussian component respectively representing the (i) th segment data,/th Gaussian component>Representing the mixing weights of the ith gaussian component of the ith segment of data.
Further, the constructing the stationary feature of the feature extraction matrix extraction history data by minimizing the variability of the feature distribution of different time periods based on the established gaussian mixture model includes:
step H1, quantifying the differences among the extracted features of different data segments by using the Wessentin distance, and constructing an optimization target:
where i and i' represent the data segment numbers,and->Respectively representing the stability characteristics extracted from the ith section data and the ith' section data; b is a feature extraction matrix, and superscript T represents matrix transposition; />Is a unitary matrix->The number of the extracted stable features; />Representation->And->The differences between the distributions of (a), i.e.)>And->Wessentin distance between the distributions of +.>Expressed as:
wherein matrix W (i,i′) Representation ofAnd->I=1, 2, …, q, i' =1, 2, …, q, i.e. satisfying +.> As a matrix W (i,i′) The (r) 1 Line r 2 Elements of columns, r 1 And r 2 Respectively representAnd->Component numbering in the gaussian mixture distribution;
step H2, solving the optimization target to obtain a feature extraction matrix B, wherein W is required to be extracted (i,i′) And B joint estimation, which consists in fixing the matrix W first (i,i′) Updating the estimated value of matrix B, and then fixing matrix B to update matrix W (i,i′) And the like, iterative optimization is carried out until the result converges;
step H3, determining the stable characteristic S of the training data by utilizing the optimized matrix B tr BX, wherein matrix X is synthesized from a plurality of augmentation matrices,
further, the solving the optimization target to obtain the feature extraction matrix B includes:
step H21, initializing: let iteration number j=1 of joint estimation, initialize the first convergence threshold e B Sum matrix W (i,i′) Initial value of (1)
Step H22, fixing matrix W (i,i′) Updating the estimated value of matrix B:
(1) calculation ofAnd decomposing the characteristic value to minimize +.>Feature vectors corresponding to the feature values are stacked in rows in the order of the feature values from small to large into a matrix +.>I.e. < ->Wherein (1)>For matrix +.>The (r) 1 Line r 2 Elements of columns, b i″ Feature vectors corresponding to the i' th small feature value are normalized to be satisfied
(2) Computing a Wessertein distance matrixIts (r) 1 Line r 2 Column element->Representation->Is the (r) th 1 Individual components and->Is the (r) th 2 The Wessentin distances of the individual components are:
where Tr () represents the trace of the matrix;
step H23, updating matrix W by fixed matrix B (i,i′) Is a function of the estimated value of (a):
(1) let matrix W (i,i′) The optimization iteration number t=1, the second convergence threshold e is initialized W Constraint violation thresholdConstraint violation threshold updating coefficient>And beta, I>Penalty factor->Penalty factor update coefficient γ, lagrangian multiplier vector +.>Lagrangian multiplier vector->Lagrangian multiplier matrix->Relaxation factor matrix
(2) By solving the following formula, calculate W (i,i′) Estimated value obtained in the t-th iteration
Wherein,representing the Kronecker product, vec (·) representing the vectorization operator, I K Representing an identity matrix, 1 K Representing all elementsColumn vector of 1, +.>A mixing weight vector representing the gaussian component of the i-th segment of data;
(3) calculating constraint violation index v [t+1] ：
Wherein I 2 The number of 2-norms is indicated, I.I F Representing the Frobenius norm;
(4) if it isUpdating parameters using:
otherwise, let
(5) Calculating convergence indexUpdating the relaxation factor matrix->Its (r) 1 Line r 2 The elements of the columns are: />Wherein->And->Respectively as a matrixAnd->The (r) 1 Line r 2 Elements of a column;
(6) let t=t+1, ifReturning to step H23; no->
Step H24, calculating convergence index
Step H25, let j=j+1, ifReturning to step H22; no->
Further, the establishing the gaussian mixture model of the extracted stationary feature, and constructing the detection statistic based on the Mahalanobis distance under each component respectively includes:
step M1, fitting a stationary feature S by using a Gaussian mixture model with a component number of K tr Is estimated S using a expectation maximization algorithm tr Gaussian mixture model parameters of (c): mu' k Sum sigma' k The method comprises the steps of carrying out a first treatment on the surface of the Wherein μ' k Sum sigma' k Respectively representing a mean vector and a covariance matrix of the kth Gaussian component;
step M2, calculating detection statistic of sample in training data set, i.e. Mahalanobis distance, wherein detection statistic of first sample in training data set is T l 2 ＝(s l -μ′ k ) T (Σ′ k ) -1 (s l -μ′ k )，s l For stationary features of the first sample, i.e. S tr K is the gaussian component to which the plateau characteristic of the first sample belongs.
Further, the determining the threshold value of the detection statistic under each component using the historical data under the normal furnace condition according to the confidence level comprises:
from the significance level α, the 1- α samples are found by making them smaller than the control limitControl limit delta under each component k The method comprises the steps of carrying out a first treatment on the surface of the Wherein delta k For the control limit under the kth gaussian component, k=1, 2, …, K denotes the gaussian component number.
Further, the calculating the stationary feature of the sample to be detected by using the feature extraction matrix includes:
obtaining the latest w samples to be detected at the first moment to obtainAnd is about->Each column is formulated->Preprocessing, wherein μ and Σ are obtained in an offline modeling process step A2;
will be pretreatedGenerating vector->
Extracting stationary features s l′ ＝Bx l′ Wherein B is obtained in an off-line modeling process step H2.
Further, the judging the components of the gaussian mixture model to which the stationary feature belongs, and calculating the corresponding detection statistic includes:
respectively calculating s by using Gaussian mixture model l′ Probability density under each component, wherein the component k corresponding to the largest probability density is s l′ The Gaussian mixture model component;
calculating a sample to be detectedIs a detection statistic T of (a) l′ 2 ＝(s l′ -μ′ k ) T (Σ′ k ) -1 (s l′ -μ′ k ) Wherein μ' k Sum sigma' k Obtained in an off-line modeling process step M1.
Further, if the detection statistic is greater than the threshold value of the detection statistic under the corresponding component, determining that the furnace condition is abnormal comprises:
if it isAnd judging the furnace to be in an abnormal furnace condition, or judging the furnace to be in a normal furnace condition.
In one aspect, an electronic device is provided, the electronic device includes a processor and a memory, at least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to implement the method for detecting abnormal furnace conditions of the blast furnace based on stationary feature extraction.
In one aspect, a computer readable storage medium is provided, in which at least one instruction is stored, loaded and executed by a processor to implement the above method for detecting abnormal conditions of a blast furnace based on stationary feature extraction.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
1) Compared with KL divergence used by the traditional method, the Wassertein distance has symmetry, and when two distributions are not overlapped, the Wassertein distance can still reflect the difference, so that the Wassertein distance can process the non-Gaussian problem of process data, avoid gradient disappearance in the optimization process, better extract stable characteristics which are unchanged in the blast furnace process data, reduce false alarm caused by non-stationarity, be suitable for extracting the stable characteristics of non-Gaussian distribution, and be more suitable for complex actual data;
2) Compared with the traditional multivariate statistical process monitoring method, the blast furnace abnormal furnace condition detection method based on stable characteristic extraction can reduce false alarm caused by working state drift by extracting the stable characteristic, and simultaneously respectively construct detection statistics and control limits for different components of a Gaussian mixture model, thereby being applicable to industrial processes with working condition change, such as hot blast furnace switching of blast furnace ironmaking processes.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for detecting abnormal conditions of a blast furnace based on stationary feature extraction according to an embodiment of the present invention;
FIG. 2 is a schematic diagram showing a first detection result of an abnormal furnace condition of a blast furnace according to an embodiment of the present invention;
FIG. 3 is a schematic diagram II of a detection result of an abnormal furnace condition of a blast furnace according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, an embodiment of the present invention provides a method for detecting abnormal furnace conditions of a blast furnace based on stationary feature extraction, where the method may be implemented by an electronic device, and the electronic device may be a terminal or a server, and the method includes: an off-line modeling process and an on-line detection process; wherein,
1) The offline modeling process includes:
s101, establishing a Gaussian mixture model of historical data under normal furnace conditions in different time periods, wherein the method specifically comprises the following steps:
step A1, acquiring historical data of q sections of normal furnace conditions in different periods as a training data setWherein the history data includes: cold air flow, hot air pressure, air permeability index, cold air pressure, full pressure difference, actual wind speed and resistance coefficient, and ith section data in training data set +.>Expressed as:
wherein the subscriptFor the number of sensors, < > for>For the number of samples in each piece of data;
step A2, for the acquired training data setPretreatment->Wherein, representing the mean value of the f-th sensor in the training data,representing the variance of the f-th sensor in the training data;
step A3, constructing an augmentation matrix according to the window length w for each piece of preprocessed data, and obtaining:
wherein X is (i) Is thatCorresponding augmentation matrix,/->Is a real number domain;
step A4, fitting the distribution of each piece of data by using a Gaussian mixture model with the component number of K, and estimating X by using an expectation maximization algorithm (i) Gaussian mixture model parameters of (c):and->Wherein (1)>And->Mean vector and covariance matrix of the (r) th Gaussian component respectively representing the (i) th segment data,/th Gaussian component>Representing the mixing weights of the ith gaussian component of the ith segment of data.
S102, based on the established Gaussian mixture model, constructing a feature extraction matrix to extract stable features of historical data by minimizing differences of feature distribution in different time periods; the difference of the characteristic distribution of different time periods is measured by using the Wessentin distance; the method specifically comprises the following steps:
step H1, in order to extract stationary features in the data, should minimize the variability between the distribution of features extracted by the data segments of different periods, in particular: the difference between the extracted features of different data segments is quantified by using the Wessertein distance, and an optimization target is constructed:
where i and i' represent the data segment numbers,and->Respectively representing the stability characteristics extracted from the ith section data and the ith' section data; b is a feature extraction matrix, and superscript T represents matrix transposition; />Is a unitary matrix->For the number of stationary features extracted, +.>The ADF test setup can be passed; />Representation->And->The differences between the distributions of (a), i.e.)>Andwessentin distance between the distributions of +.>Expressed as:
wherein the matrixRepresentation->And->I=1, 2, …, q, i' =1, 2, …, q, i.e. satisfying +.> As a matrix W (i,i′) The (r) 1 Line r 2 Elements of columns, r 1 And r 2 Respectively indicate->And->Component numbering in the gaussian mixture distribution;
step H2, solving the optimization target to obtain a feature extraction matrix B, wherein W is required to be extracted (i,i′) And B joint estimation, which consists in fixing the matrix W first (i,i′) Updating the estimated value of matrix B, and then fixing matrix B to update matrix W (i,i′) And the like, iterative optimization is carried out until the result converges; the method specifically comprises the following steps:
step H21, initializing: let iteration number j=1 of joint estimation, initialize the first convergence threshold e B Sum matrix W (i,i′) Initial value of (1)
Step H22, fixing matrix W (i,i′) Updating the estimated value of matrix B:
(1) calculation ofAnd decomposing the characteristic value to minimize +.>Feature vectors corresponding to the feature values are stacked in rows in the order of the feature values from small to large into a matrix +.>I.e. < ->Wherein (1)>For the matrix in the jth iterationThe (r) 1 Line r 2 Elements of columns, b i″ Feature vectors corresponding to the i' th small feature value are normalized to be satisfied
(2) Computing a Wessertein distance matrixIts (r) 1 Line r 2 Column element->Representation->Is the (r) th 1 Individual components and->Is the (r) th 2 The Wessentin distances of the individual components are:
where Tr () represents the trace of the matrix;
step H23, updating matrix W by fixed matrix B (i,i′) Is a function of the estimated value of (a):
(1) let matrix W (i,i′) The optimization iteration number t=1, the second convergence threshold e is initialized W Constraint violation thresholdConstraint violation threshold updating coefficient>And beta, I>Penalty factor->Penalty factor update coefficient γ, lagrangian multiplier vector +.>Lagrangian multiplier vector->Lagrange multiplier matrixRelaxation factor matrix->
(2) By solving the following formula, calculate W (i,i′) Estimated value obtained in the t-th iteration
Wherein,representing the Kronecker product, vec (·) representing the vectorization operator, ++>Representing the identity matrix of the cell,column vector representing all elements 1, < ->A mixing weight vector representing the gaussian component of the i-th segment of data;
(3) calculating constraint violation index v [t+1] ：
Wherein I 2 The number of 2-norms is indicated, I.I F Representing the Frobenius norm;
(4) if it isUpdating parameters using:
otherwise, let
(5) Calculating convergence indexUpdating the relaxation factor matrix->Its (r) 1 Line r 2 The elements of the columns are: />Wherein->And->Respectively as a matrixAnd->The (r) 1 Line r 2 Elements of a column;
(6) let t=t+1, ifReturning to step H23; no->
Step H24, calculating convergence index
Step H25, let j=j+1, ifReturning to step H22; no->
Step H3, determining the stable characteristic S of the training data by utilizing the optimized matrix B tr ＝BX，Wherein the matrix X is synthesized by a plurality of augmentation matrices,
s103, establishing a Gaussian mixture model of the extracted stable characteristics, and respectively constructing detection statistics based on Mahalanobis distance (Mahalanobis distance) under each component, wherein the method specifically comprises the following steps:
step M1, fitting a stationary feature S by using a Gaussian mixture model with a component number of K tr Is estimated S using a expectation maximization algorithm tr Gaussian mixture model parameters of (c): mu' k Sum sigma' k The method comprises the steps of carrying out a first treatment on the surface of the Wherein μ' k Sum sigma' k Respectively representing a mean vector and a covariance matrix of the kth Gaussian component;
step M2, calculating detection statistic of sample in training data set, i.e. Mahalanobis distance, wherein detection statistic of first sample in training data set is T l 2 ＝(s l -μ′ k ) T (Σ′ k ) -1 (s l -μ′ k )，s l For stationary features of the first sample, i.e. S tr K is the gaussian component to which the plateau characteristic of the first sample belongs.
S104, determining a threshold value of the detection statistic under each component by using the historical data under the normal furnace condition according to the confidence level.
In the present embodiment, the control limit δ for each component is found by making the samples of 1- α smaller than the control limit based on the significance level α k The method comprises the steps of carrying out a first treatment on the surface of the Wherein delta k For the control limit under the kth gaussian component, k=1, 2, …, K denotes the gaussian component number.
2) The online detection process comprises the following steps:
s105, calculating stable characteristics of a sample to be detected by using the characteristic extraction matrix, wherein the method specifically comprises the following steps:
obtaining the latest w samples to be detected at the first moment to obtainAnd is about->Each column is formulated->Preprocessing, wherein μ and Σ are obtained in an offline modeling process step A2;
will be pretreatedGenerating vector->
Extracting stationary features s l′ ＝Bx l′ Wherein B is obtained in an off-line modeling process step H2.
S106, judging the components of the Gaussian mixture model to which the stable characteristics belong, and calculating corresponding detection statistics, wherein the method specifically comprises the following steps:
respectively calculating s by using Gaussian mixture model l′ Probability density under each component, wherein the component k corresponding to the largest probability density is s l′ The Gaussian mixture model component;
calculating a sample to be detectedDetection statistics of->Wherein μ' k Sum sigma' k Obtained in an off-line modeling process step M1.
And S107, if the detection statistic is larger than the threshold value of the detection statistic under the corresponding component, judging that the furnace is in an abnormal condition.
In the present embodiment, ifAnd judging the furnace to be in an abnormal furnace condition, or judging the furnace to be in a normal furnace condition.
In order to better understand the method for detecting the abnormal furnace condition of the blast furnace based on the stable characteristic extraction, the method is described in detail by using blast furnace operation process data and MATLAB software.
1) Offline modeling process
(1) Historical data is collected for q=6 periods of normal furnace conditions, taken from the first 5000 sampling moments (sampling interval of 10 s) of each day of 2015, 11-1, 1-10, 2016, 4-1, 2016, 10-1, 2017, 7-1 and 2017-10 respectively, the variables include cold air flow, hot air pressure 1, hot air pressure 2, air permeability index, cold air pressure 1, cold air pressure 2, full pressure difference, actual wind speed and resistance coefficient, and a training data set is establishedWherein, the ith section data in the training data set +.>Expressed as:
wherein,for the number of sensors, < > for>Is the number of samples in each piece of data.
(2) Order theData preprocessing is performed, wherein ∈> Mean value of f-th sensor in training data, < >> Representing the variance of the f-th sensor in the training data.
(3) For each piece of data, an augmentation matrix is constructed with a window length w=10:
wherein X is (i) Is thatCorresponding augmentation matrix,/->Is the real number domain.
(4) Fitting the distribution of each piece of data using a gaussian mixture model with a group score of k=5, estimating X using a expectation maximization algorithm (i) Is used for the parameters of the Gaussian mixture model,and->Wherein (1)>And->Mean vector and covariance matrix of the (r) th Gaussian component respectively representing the (i) th segment data,/th Gaussian component>Representing the mixing weights of the ith gaussian component of the ith segment of data.
(5) To extract stationary features in the data, the variability between the distribution of features extracted by different periods of data segments should be minimized, in particular: the difference between the extracted features of different data segments is quantified by using the Wessertein distance, and the following optimization targets are constructed:
where i and i' represent the data segment numbers,and->Respectively representing the stability characteristics extracted from the ith section data and the ith' section data; b is a feature extraction matrix, and superscript T represents matrix transposition; />Is a unitary matrix->For the number of stationary features extracted, +.>The ADF test setup can be passed; />Representation->And->The differences between the distributions of (a), i.e.)>And->Wessentin distance between the distributions of +.>Expressed as: />
Wherein the matrixRepresentation->And->Wherein i=1, 2, …, q; i' =1, 2, …, q, i.e. satisfy +.> As a matrix W (i,i′) The (r) 1 Line r 2 Elements of columns, r 1 And r 2 Respectively indicate->And->In a Gaussian mixture distribution of (2)Component numbers.
(6) Solving the optimization problem to obtain a feature extraction matrix B, wherein W is required to be extracted (i,i′) And B joint estimation, which consists in fixing the matrix W first (i,i′) Updating the estimated value of matrix B, and then fixing matrix B to update matrix W (i,i′) And so on, iteratively optimizing until the result converges, wherein the steps are as follows:
6.1 initializing: let iteration number j=1 of joint estimation, initialize convergence threshold e B Sum matrix W (i,i′) Initial value of (1)
6.2 fixed matrix W (i,i′) Updating the estimated value of matrix B:
(1) calculation ofAnd decomposing the characteristic value, wherein +_>For matrix->The (r) 1 Line r 2 The element of the column stacks the eigenvectors corresponding to the m least eigenvalues into a matrix according to the order of the eigenvalues from small to large>I.e.Wherein b i″ The feature vector corresponding to the i' th small feature value is satisfied by normalization>
(2) Computing a Wessertein distance matrixIts kth 1 Line k 2 Element of row->Representation ofIs the (r) th 1 Individual components and->Is the (r) th 2 The Wessentin distances of the individual components are:
where Tr () represents the trace of the matrix;
6.3 fixed matrix B update matrix W (i,i′) Is a function of the estimated value of (a):
(1) let matrix W (i,i′) The optimization iteration number k=1, and the parameter convergence threshold epsilon is initialized W Constraint violation thresholdConstraint violation threshold updating coefficient>And beta (satisfy->) The method comprises the steps of carrying out a first treatment on the surface of the Penalty factor->Penalty factor update coefficient γ, lagrangian multiplier vector +.>Lagrangian multiplier vector->Lagrange multiplier matrixRelaxation factor matrix->
(2) By solving the following formula, calculate W (i,i′) Estimated value obtained in the t-th iteration/>
Wherein,representing the Kronecker product, vec (·) representing the vectorization operator, ++>Matrix representing all 1 diagonal elements, +.>Column vector representing all elements 1, < ->A mixing weight vector representing the gaussian component of the i-th segment of data;
(3) calculating constraint violation index v [t+1] ：
Wherein I 2 The number of 2-norms is indicated, I.I F Indicating the Frobenius norm.
(4) If it isUpdating parameters using
Otherwise, let
(5) Calculating convergence indexUpdating the relaxation factor matrix->Its (r) 1 Line r 2 The elements of the columns are: />Wherein->And->Respectively as a matrixAnd->The (r) 1 Line r 2 Elements of a column;
(6) let t=t+1, ifReturn to 6.3. (1); no->/>
D. Calculating a convergence index
E. Let j=j+1, ifReturn to 6.2; no->
(7) The matrix B is used to obtain the stable characteristic S of the training data tr BX, wherein matrix X is synthesized from a plurality of augmentation matrices,
(8) Fitting a stationary feature S using a gaussian mixture model with a group score of k=5 tr Is estimated S using a expectation maximization algorithm tr Gaussian mixture model parameters, μ' k Sum sigma' k The method comprises the steps of carrying out a first treatment on the surface of the Wherein μ' k Sum sigma' k The mean vector and covariance matrix of the kth gaussian component are represented, respectively.
(9) Calculating detection statistic of samples in the training data set, namely Mahalanobis distance, wherein the detection statistic of the first sample is T l 2 ＝(sl-μ′ k ) T (Σ′ k ) -1 (sl-μ′ k )，s l For stationary features of the first training sample, i.e. S tr K is the gaussian component to which the stationary characteristic of the first training sample belongs.
(10) Based on the significance level alpha, the control limit delta for each component is obtained by making training samples of 1-alpha smaller than the control limit k Wherein delta k For the control limit under the kth gaussian component, k=1, 2, …, K denotes the component number.
2) On-line detection process
(1) The last 10 test samples were taken at time l',and initialize +.>Wherein μ and Σ are obtained in an offline modeling process step (2).
(2) Will be pretreatedGenerating vector->
(3) Extracting stationary features s l′ ＝Bx l′ Wherein B is obtained in an offline modeling process step (6).
(4) Respectively calculating s by using Gaussian mixture model l′ Probability density under each component, wherein the component k corresponding to the largest probability density is s l′ The Gaussian mixture model component.
(5) The training test statistic is calculated and the test data is obtained,wherein μ' k Sum sigma' k Obtained in an off-line modeling process step (8).
(6) If it isAnd judging the furnace to be in an abnormal furnace condition, or judging the furnace to be in a normal furnace condition.
Fig. 2 and fig. 3 respectively show detection results of a method for detecting abnormal furnace conditions of a blast furnace based on stable feature extraction on two sets of blast furnace test data containing abnormal furnace conditions according to an embodiment of the present invention; the result shown in fig. 2 shows that the method for detecting the abnormal furnace condition of the blast furnace based on stable feature extraction provided by the invention detects the abnormal furnace condition 50s earlier than manual operation; the result shown in fig. 3 shows that the method for detecting the abnormal furnace condition of the blast furnace based on stable feature extraction provided by the invention detects the abnormal furnace condition 10s earlier than manual work. Meanwhile, as can be seen from fig. 2 and 3, the detection statistics using the gaussian mixture model have time-varying thresholds, so that they can cope with non-gaussian problems of process data, thereby reducing false positives.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
1) Compared with KL divergence used by the traditional method, the Wassertein distance has symmetry, and when two distributions are not overlapped, the Wassertein distance can still reflect the difference, so that the Wassertein distance can process the non-Gaussian problem of process data, avoid gradient disappearance in the optimization process, better extract stable characteristics which are unchanged in the blast furnace process data, reduce false alarm caused by non-stationarity, be suitable for extracting the stable characteristics of non-Gaussian distribution, and be more suitable for complex actual data;
2) Compared with the traditional multivariate statistical process monitoring method, the blast furnace abnormal furnace condition detection method based on stable characteristic extraction can reduce false alarm caused by working state drift by extracting the stable characteristic, and simultaneously respectively construct detection statistics and control limits for different components of a Gaussian mixture model, thereby being applicable to industrial processes with working condition change, such as hot blast furnace switching of blast furnace ironmaking processes.
Fig. 4 is a schematic structural diagram of an electronic device 600 according to an embodiment of the present invention, where the electronic device 600 may have a relatively large difference due to different configurations or performances, and may include one or more processors (central processing units, CPU) 601 and one or more memories 602, where at least one instruction is stored in the memories 602, and the at least one instruction is loaded and executed by the processors 601 to implement the above-mentioned method for detecting abnormal conditions of a blast furnace based on stable feature extraction.
In an exemplary embodiment, a computer readable storage medium, such as a memory including instructions executable by a processor in a terminal to perform the above-described method for detecting abnormal furnace conditions of a blast furnace based on stationary feature extraction is also provided. For example, the computer readable storage medium may be ROM, random Access Memory (RAM), CD-ROM, magnetic tape, floppy disk, optical data storage device, etc.
It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program for instructing relevant hardware, where the program may be stored in a computer readable storage medium, and the storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (9)
1. The method for detecting the abnormal furnace condition of the blast furnace based on the stable characteristic extraction is characterized by comprising the following steps of: an off-line modeling process and an on-line detection process; wherein,
the offline modeling process includes:
establishing a Gaussian mixture model of historical data under normal furnace conditions in different time periods;
based on the established Gaussian mixture model, a feature extraction matrix is constructed to extract stable features of historical data by minimizing the differences of feature distribution in different time periods; the difference of the characteristic distribution in different time periods is measured by using Wasserstein distance;
establishing a Gaussian mixture model of the extracted stable characteristics, and respectively constructing detection statistics based on Mahalanobis distance under each component;
determining a threshold value of detection statistics under each component by using historical data under normal furnace conditions according to the confidence level;
the online detection process comprises the following steps:
calculating stable characteristics of a sample to be detected by using the characteristic extraction matrix;
judging the components of the Gaussian mixture model to which the stable characteristics belong, and calculating corresponding detection statistics;
if the detection statistic is greater than the threshold value of the detection statistic under the corresponding component, the abnormal furnace condition is judged.
2. The method for detecting abnormal furnace conditions of a blast furnace based on stable feature extraction according to claim 1, wherein the establishing a gaussian mixture model of historical data under normal furnace conditions in different time periods comprises:
step A1, acquiring q segments of positive values in different periodsHistorical data under normal furnace conditions as training data setWherein the history data includes: cold air flow, hot air pressure, air permeability index, cold air pressure, full pressure difference, actual wind speed and resistance coefficient, and ith section data in training data set +.>Expressed as:
wherein the subscriptFor the number of sensors, < > for>For the number of samples in each piece of data;
step A2, for the acquired training data setPretreatment->Wherein, representing the mean value of the f-th sensor in the training data, representing the variance of the f-th sensor in the training data;
step A3, constructing an augmentation matrix according to the window length w for each piece of preprocessed data, and obtaining:
wherein X is (i) Is thatCorresponding augmentation matrix,/->Is a real number domain;
step A4, fitting the distribution of each piece of data by using a Gaussian mixture model with the component number of K, and estimating X by using an expectation maximization algorithm (i) Gaussian mixture model parameters of (c):and->Wherein (1)>And->Mean vector and covariance matrix of the (r) th Gaussian component respectively representing the (i) th segment data,/th Gaussian component>Representing the mixing weights of the ith gaussian component of the ith segment of data.
3. The method for detecting abnormal furnace conditions of a blast furnace based on stationary feature extraction according to claim 2, wherein the constructing stationary features of feature extraction matrix extraction history data by minimizing differences in feature distribution of different time periods based on the established gaussian mixture model comprises:
step H1, quantifying the differences among the extracted features of different data segments by using Wasserstein distance, and constructing an optimization target:
where i and i' represent the data segment numbers,and->Respectively representing the stability characteristics extracted from the ith section data and the ith' section data; b is a feature extraction matrix, and superscript T represents matrix transposition; />Is a unitary matrix->The number of the extracted stable features; />Representation->And->The differences between the distributions of (a), i.e.)>And->Wasserstein distance between distributions of +.>Expressed as:
wherein matrix W (i,i′) Representation ofAnd->I=1, 2, …, q, i' =1, 2, …, q, i.e. satisfy As a matrix W (i,i′) The (r) 1 Line r 2 Elements of columns, r 1 And r 2 Respectively indicate->And->In a Gaussian mixture distribution of (2)Component numbering;
step H2, solving the optimization target to obtain a feature extraction matrix B, wherein W is required to be extracted (i,i′) And B joint estimation, which consists in fixing the matrix W first (i,i′) Updating the estimated value of matrix B, and then fixing matrix B to update matrix W (i,i′) And the like, iterative optimization is carried out until the result converges;
step H3, determining the stable characteristic S of the training data by utilizing the optimized matrix B tr BX, wherein matrix X is synthesized from a plurality of augmentation matrices,
4. the method for detecting abnormal furnace conditions of a blast furnace based on stable feature extraction according to claim 3, wherein the solving the optimization objective to obtain the feature extraction matrix B comprises:
step H21, initializing: let iteration number j=1 of joint estimation, initialize the first convergence threshold e B Sum matrix W (i,i′) Initial value of (1)
Step H22, fixing matrix W (i,i′) Updating the estimated value of matrix B:
(1) calculation ofAnd decomposing the characteristic value to minimize +.>Feature vectors corresponding to the feature values are stacked in rows in the order of the feature values from small to large into a matrix +.>I.e. < ->Wherein (1)>For matrix +.>The (r) 1 Line r 2 Elements of columns, b i″ Feature vectors corresponding to the i' th small feature value are normalized to be satisfied
(2) Computing Wasserstein distance matrixIts (r) 1 Line r 2 Column element->Representation->Is the (r) th 1 Individual components and->Is the (r) th 2 The Wasserstein distance of the individual components is:
where Tr () represents the trace of the matrix;
step H23, updating matrix W by fixed matrix B (i,i′) Is a function of the estimated value of (a):
(1) let matrix W (i,i′) The optimization iteration number t=1, the second convergence threshold e is initialized W Constraint violation thresholdConstraint violation threshold updating coefficient>And beta, I>Penalty factor->Penalty factor update coefficient γ, lagrangian multiplier vector +.>Lagrangian multiplier vector->Lagrangian multiplier matrix->Relaxation factor matrix->
(2) By solving the following formula, calculate W (i,i′) Estimated value obtained in the t-th iteration
Wherein,representing the Kronecker product, vec (·) representing the vectorization operator, I K Representing an identity matrix, 1 K Column vector representing all elements 1, < ->A mixing weight vector representing the gaussian component of the i-th segment of data;
(3) calculating constraint violation index v [t+1] ：
Wherein I 2 The number of 2-norms is indicated, I.I F Representing the Frobenius norm;
(4) if it isUpdating parameters using:
otherwise, let
(5) Calculating convergence indexUpdating the relaxation factor matrix->Its (r) 1 Line r 2 The elements of the columns are: />Wherein->And->Respectively as a matrixAnd->The (r) 1 Line r 2 Elements of a column;
(6) let t=t+1, ifReturning to step H23; no->
Step H24, calculating convergence index
Step H25, let j=j+1, ifReturning to step H22; no->
5. The method for detecting abnormal furnace conditions of a blast furnace based on stable feature extraction according to claim 4, wherein the establishing a gaussian mixture model of the extracted stable features and constructing detection statistics based on Mahalanobis distance under each component respectively comprises:
step M1, fitting a stationary feature S by using a Gaussian mixture model with a component number of K tr Is estimated S using a expectation maximization algorithm tr Gaussian mixture model parameters of (c): mu' k Sum sigma' k The method comprises the steps of carrying out a first treatment on the surface of the Wherein μ' k Sum sigma' k Respectively representing a mean vector and a covariance matrix of the kth Gaussian component;
step M2, calculating detection statistics of samples in the training data set, i.e. Mahalanobis distance, wherein the detection statistic of the first sample in the training data set is T l 2 ＝(s l -μ′ k ) T (Σ′ k ) -1 (s l -μ′ k )，s l For stationary features of the first sample, i.e. S tr K is the gaussian component to which the plateau characteristic of the first sample belongs.
6. The method for detecting abnormal furnace conditions of a blast furnace based on stationary feature extraction according to claim 5, wherein the determining the threshold value of the detection statistic under each component using the history data under the normal furnace conditions according to the confidence level comprises:
from the significance level α, a control limit δ for each component is found by making a sample of 1- α smaller than the control limit k The method comprises the steps of carrying out a first treatment on the surface of the Wherein delta k For the control limit under the kth gaussian component, k=1, 2, …, K denotes the gaussian component number.
7. The method for detecting abnormal furnace conditions of a blast furnace based on stationary feature extraction according to claim 6, wherein calculating stationary features of a sample to be detected using a feature extraction matrix comprises:
obtaining the latest w samples to be detected at the first moment to obtainAnd is about->Each column is formulated->Preprocessing, wherein μ and Σ are obtained in an offline modeling process step A2;
will be pretreatedGenerating vector->
Extracting stationary features s l′ ＝Bx l′ Wherein B is obtained in an off-line modeling process step H2.
8. The method for detecting abnormal furnace conditions of a blast furnace based on stable feature extraction according to claim 7, wherein the judging the components of the gaussian mixture model to which the stable feature belongs and calculating the corresponding detection statistics comprises:
respectively calculating s by using Gaussian mixture model l′ Probability density under each component, wherein the component k corresponding to the largest probability density is s l′ The Gaussian mixture model component;
calculating a sample to be detectedIs a detection statistic T of (a) l′ 2 ＝(s l′ -μ′ k ) T (Σ′ k ) -1 (s l′ -μ′ k ) Wherein μ' k Sum sigma' k Obtained in an off-line modeling process step M1.
9. The method for detecting abnormal furnace conditions of a blast furnace based on stationary feature extraction according to claim 8, wherein the determining that the abnormal furnace condition is determined if the detection statistic is greater than a threshold value of the detection statistic under the corresponding component comprises:
if T l′ 2 >δ k And judging the furnace to be in an abnormal furnace condition, or judging the furnace to be in a normal furnace condition.
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| CN108595380A (en) * | 2018-03-14 | 2018-09-28 | 山东科技大学 | A kind of Blast Furnace Abnormal Conditions Judgement detection method |
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