CN113191615A - Polypropylene production process anomaly detection method based on analysis of multiple related components - Google Patents

Abstract

The invention discloses a polypropylene production process anomaly detection method based on multiple pieces of related component analysis. The method analyzes the correlation among the measured variables of a plurality of sub-production units by a multi-block correlation component analysis technology, thereby distinguishing the correlation and the non-correlation characteristics among blocks, and implementing distributed abnormality detection on the polypropylene production process on the basis. In other words, the method does not simply implement data-driven anomaly detection separately according to four reaction kettles, but extracts inter-block related characteristic components from each sub-block by a multi-block related analysis technology, so that the correlation among the sub-blocks is considered in the distributed modeling. Therefore, the method not only can carry out distributed anomaly detection on the polypropylene production process, but also realizes the purpose of correlation analysis among the subblocks.

Description

Polypropylene production process anomaly detection method based on analysis of multiple related components

Technical Field

The invention relates to an anomaly detection method, in particular to a polypropylene production process anomaly detection method based on analysis of multiple blocks of related components.

Background

As one of five common plastics, polypropylene has wide application in military and aerospace, industrial production and daily life, and is the most important downstream product of propylene. The data show that 50% of the propylene in the world and 65% of the propylene in our country are used to produce polypropylene. Among them, the melt index is the most important quality index of polypropylene, and is the key to guide and control the whole process in industrial production. In the production process of polypropylene, the main raw materials of polypropylene are propylene and hydrogen, so the hydrogen flow and the propylene flow entering a reaction kettle can certainly influence the measurement of the melt index; at the same time, the catalyst influences the speed of the polymerization reaction, so the melt index is also influenced by the flow rate of the catalyst in the reaction vessel.

In addition to the hydrogen and propylene flow rates affecting the quality of the final polypropylene product, conventional measurement variables such as temperature, pressure, level, etc. of the reactor in the polypropylene production process also affect the final polypropylene product. Therefore, to ensure the continuous stability of the polypropylene production process, it is necessary to detect abnormal conditions in real time. In recent years, due to the wide application of advanced measuring instruments and computing technologies, a polypropylene production process can acquire a large amount of information such as temperature, pressure, flow and the like in real time at high frequency, and the massive sampling data lays a full data foundation for implementing data-driven anomaly detection.

At present, most of domestic polypropylene production processes adopt a Hypol process with four reaction kettles connected in series, each reaction kettle can carry out a hydrogenation polymerization reaction, and a reflux device is arranged at the top of each reaction kettle. Thus, polypropylene production is actually a complex process flow resulting from the combination of multiple production units. Generally, for this type of production process, it is usually more convenient to implement distributed anomaly detection, which not only can reduce the complexity of modeling analysis, but also can perform anomaly detection in blocks and units. However, although the polypropylene production process comprises 4 production units, the mutual influence of the production units is mutually restricted, and the influence of the connection among the units is ignored by directly decomposing the production units into four independent subunits and respectively carrying out abnormality detection. Therefore, the technology for distributed detection of abnormal conditions in the polypropylene production process needs to be improved and improved.

Disclosure of Invention

The invention aims to solve the main technical problems that: how to implement distributed anomaly detection on the polypropylene production process by utilizing multi-block related component analysis on the premise of correlation among sub-production units. Specifically, the method analyzes the correlation among the measurement variables of a plurality of sub-production units by a multi-block correlation component analysis technology so as to distinguish correlation and non-correlation characteristics among blocks, and performs distributed abnormality detection on the polypropylene production process on the basis of the correlation and non-correlation characteristics.

The technical scheme adopted by the method for solving the problems is as follows: a polypropylene production process abnormity detection method based on multi-block related component analysis comprises the following steps:

step (1): determining measurement variables of the polypropylene production process, specifically comprising 28 measurement variables of four reaction kettles; wherein, every reation kettle all relates to 7 measured variables, is in proper order: reactor temperature, reactor pressure, reactor liquid level, hydrogen feed flow, propylene feed flow, catalyst feed flow, and reflux flow.

Step (2): continuously collecting sample data of N sampling moments according to the determined measurement variables, and storing the sample data corresponding to the measurement variables into an Nx 28-dimensional data matrix X e R^N×28Then, the column vectors z in X are respectively aligned according to the following formula₁，z₂，...，z₂₈Carrying out standardization processing to obtain data matrix

Wherein R is^N×28Representing a matrix of real numbers of dimension Nx 28, R representing a set of real numbers, mu_kAnd delta_kRespectively representing column vectors z_k∈R^N×1The mean and standard deviation of all elements in (k) e {1, 2., 28},

representing a matrix of data

The column vector of the k-th column.

And (3): according to the measured variable related to each reaction kettle, correspondingly combining the data matrix

Divided into four sub-block matrices X₁，X₂，X₃，X₄(ii) a Wherein, X_b∈R^N×7Is a subblock matrix R corresponding to the b-th reaction kettle in the production process of polypropylene^N×7Representing a matrix of real numbers of dimension N x 7, b ∈ {1, 2, 3, 4 }.

And (4): four subblock matrices X according to steps (4.1) to (4.6) as shown below₁，X₂，X₃，X₄Carrying out multi-block correlation component analysis to obtain a correlation transformation matrix W corresponding to each sub-block matrix_bThe load matrix P_bCorrelation component matrix S_bAnd residual matrix E_b。

Step (4.1): the initialization d is 1.

Step (4.2): randomly initializing four transformation vectors w₁∈R^7×1，w₂∈R^7×1，w₃∈R^7×1And w₄∈R^7×1After that, b is set to 1.

Step (4.3): solving generalized eigenvalue problem

Medium maximum eigenvalue lambda_bCorresponding feature vector v_bThen according to the formula

Updating a transformation vector w_b(ii) a Wherein the upper symbol T represents the transpose of a matrix or vector, and the matrix theta_bThe calculation of (c) is as follows:

in the above formula, c is formed by {1, 2, 3, 4}, and when b is not equal to c, H is formed_b，cWhen b is c, H_b，c＝0。

Step (4.4): judging whether b is less than 4; if yes, after b is set to b +1, returning to the step (4.3); if not, obtaining the updated transformation vector w₁，w₂，w₃，w₄And then step (4.5) is executed.

Step (4.5): judging four transformation vectors w₁，w₂，w₃，w₄Whether both converge; if not, setting b to be 1 and then returning to the step (4.3); if yes, the correlation coefficient J ═ λ is calculated₁+λ₂+λ₃+λ₄) After/4, step (4.6) is performed.

Step (4.6): judging whether the correlation coefficient J is larger than a threshold value sigma; if yes, the formula s is firstly and respectively determined according to_b＝X_bw_bAnd

calculating a correlation component vector s_bAnd a load vector p_bThen according to the formula

Updating subblock matrix X_bAnd transforming the correlation matrix W₁，W₂，W₃，W₄The column vectors of the d-th column in the column are respectively set to w₁，w₂，w₃，w₄Will load the matrix P₁，P₂，P₃，P₄The column vectors of the d-th column are respectively set to p₁，p₂，p₃，p₄A matrix S of correlation components₁，S₂，S₃，S₄The column vectors of the d-th column are respectively set to s₁，s₂，s₃，s₄Then, after d is set to d +1, the step (4.2) is returned; if not, obtainingThe related transformation matrix W corresponding to each sub-block matrix_bThe load matrix P_bAnd a correlation component matrix S_bAnd by setting E_b＝X_bA residual matrix E can be obtained₁，E₂，E₃，E₄。

It is to be noted that, in the above step (4.6), the matrix W is transformed_bThe column vector of the d-th column in (d) is equal to w_bThe load matrix P_bThe column vector of the d-th column in (d) is equal to p_bThe correlation component matrix S_bThe column vector of the d-th column in (d) is equal to s_b，b∈{1，2，3，4}。

And (5): according to

Respectively for residual error matrix E₁，E₂，E₃，E₄Performing singular value decomposition with retention of decomposition matrix

Where b is ∈ {1, 2, 3, 4}, diagonal matrix Λ_bThe elements on the diagonal being composed of non-zero singular values, U_bAnd V_bAre two unitary matrices of a singular value decomposition,

is represented by_bThe inverse matrix of (c).

And (6): according to the formula respectively

And

calculating an anomaly detection index vector psi_bAnd Q_bThen respectively transferring psi_bAnd Q_bThe maximum value of the element in (1) is recorded as

And

where diag () denotes an operation of converting the elements of the matrix diagonal in brackets into column vectors.

And (7): calculating an abnormal comprehensive detection index vector D according to a formula shown in the specification, and recording the maximum value in the D as the D_lim：

And (8): at the latest sampling time t, sample data x corresponding to the measured variable is collected_t(1)，x_t(2)，...，x_t(28) And respectively normalizing them according to the following formula to obtain data vectors

Wherein k ∈ {1, 2,..., 28},

representing input vectors

The kth element in (1).

And (9): according to the measured variable related to each reaction kettle, correspondingly calculating the data vector

Division into four sub-block vectors

Then, again according to

And

respectively calculating related feature vectors

And residual vector e_b。

Step (10): according to

And

respectively calculating abnormality detection indexes

And q is_bThen, the abnormal comprehensive detection index D corresponding to the latest sampling time t is calculated according to the formula shown in the specification_t：

Step (11): judging whether the conditions are met: d_t≤D_lim(ii) a If yes, the polypropylene production process at the current sampling moment is not abnormal, and the step (8) is returned to continue to carry out the abnormal detection of the latest sampling moment; if not, executing step (12) to decide whether to trigger an abnormal alarm.

Step (12): returning to the step (8) to continue to carry out the abnormal detection of the latest sampling time until the abnormal comprehensive detection indexes of the continuous 6 latest sampling times are obtained, and then judging whether the 6 abnormal comprehensive detection indexes are all larger than D_lim(ii) a If yes, triggering an abnormal alarm; if not, the abnormal alarm is not triggered, and the step (8) is returned to continue to detect the abnormality of the latest sampling time.

The implementation step (4) of the method of the invention utilizes a multi-block correlation component analysis algorithm to implement the correlation analysis among four sub-block matrixes, and the algorithm aims at respectively finding out corresponding transformation vectors w for each sub-block matrix₁，w₂，w₃，w₄So that the objective function shown below is satisfied:

the above-described constrained objective function aims to maximize the sum of squares of correlation coefficients between feature components. In other words, the objective function is intended to pass through the transform vector w₁，w₂，w₃，w₄And extracting the characteristic component with the maximum correlation.

The lagrange function L is defined by the lagrange multiplier method as follows:

by setting L relative to w_bThe partial differential equation of (a) is equal to 0, the following reasoning process can be obtained:

on both sides of the upper equal sign, the left multiplication is carried out simultaneously

Then, can obtain

Thus, the maximized objective function is equivalent to maximizing the sum of the eigenvalues, i.e., λ₁+λ₂+λ₃+λ₄。

In order to avoid using different technical terms for the same symbol, the problem of the generalized eigenvalues in step (4.3) of the method of the invention is actually to fit w in the above equation_bIs replaced by a feature vector v_b. And further by formula

Satisfy the constraint condition

By carrying out the steps described above, the advantages of the method of the invention are presented below.

When the method is used for detecting the quality abnormity of the polypropylene product, the technical means of directly measuring the melt index of the polypropylene, namely long and serious hysteresis, is not relied on, and the characteristic variable or component which is most relevant to the melt index of the polypropylene and is obtained by double-layer relevant characteristic analysis of a neighbor component analysis algorithm and a typical relevant analysis algorithm is used for indirectly detecting the abnormity. The method can detect whether the quality of the polypropylene product is abnormal in real time according to the sampling frequency of the measured variable, and overcomes the problem of hysteresis of the traditional method.

Drawings

FIG. 1 is a schematic flow chart of the method of the present invention.

FIG. 2 is a schematic flow diagram of a polypropylene process

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

Referring to fig. 1, the present invention discloses a method for detecting quality abnormality of polypropylene product based on double-layer correlation characteristic analysis, and the following describes a specific embodiment of the method according to the present invention with reference to a specific application example.

As shown in fig. 2, the production flow of a polypropylene process object comprises four reactors, respectively referred to as a first reactor, a second reactor, a third reactor, and a fourth reactor; wherein the first reactor and the second reactor are liquid phase continuous stirred reactors and the third reactor and the fourth reactor are gas phase fluidized bed reactors. Each reactor had a feed of propylene and hydrogen and a feed of catalyst. In addition, the product at the outlet of the fourth reactor is a polypropylene product.

Step (1): the measured variables of the polypropylene production process are determined, and specifically comprise 28 measured variables of four reactors.

Step (2): continuously collecting sample data of N sampling moments by using a measuring instrument installed in the production process of polypropylene; meanwhile, the melt index of the polypropylene product in the fourth reactor is obtained by sampling and analyzing every 2 hours; and then storing the sample data corresponding to the measurement variable into an Nx 28-dimensional data matrix X, and storing N data corresponding to the melt index into an N X1-dimensional data vector y.

And (3): element filling is carried out on the data vector Y according to the formula (i), and thus a column vector Y epsilon R is obtained^N×1. In the present embodiment, the sampling period of the measured variable is 6 minutes, i.e. the sampling frequency is equal to 1/(6 × 60), while the sampling frequency of the melt index is equal to 1/(120 × 60). Therefore, f in formula (i) is (120 × 60)/(6 × 60) is 20.

And (4): according to the formula 2, respectively aligning the column vectors z in X₁，z₂，...，z₂₈And standardizing the column vector Y to obtain an input matrix

And outputting the vector

And (5): obtaining the weight vector w according to the optimization of the steps (5.1) to (5.6)₀∈R^28×1Thereby obtaining a direct correlation feature matrix X₁∈R^N×mAnd uncorrelated feature matrix X₂∈R^N×(28-m)。

And (6): solving generalized eigenvalue problem

The feature vector beta corresponding to the middle maximum feature value eta is calculated according to

Calculating a correlation projection vector q ∈ R^(28-m)×1Then according to the formula

Computing indirect correlation feature vectors

And (7): mixing X₁And

combined into an input correlation feature matrix

Then, the above steps (7.1) to (7.4) are executed to determine the upper limit D of the abnormality detection index_lim。

And (8): at the latest sampling time t, sample data x corresponding to the measured variable is collected_t(1)，x_t(2)，...，x_t(28) And normalizing them according to the formula (R) to obtain input vectors

And (9): according to the weight vector w₀∈R^1×28The column where the maximum m elements are located corresponds to the input vector

Elements in the same column constitute directly related feature vectors

Then will be

The remaining 28-m elements in the set constitute uncorrelated feature vectors

Step (10): according to the formula

Calculating an indirect correlation feature s_tThen, the mixture is mixed with

And s_tCombined into an input-dependent feature vector

Step (11): calculating an abnormality detection index D according to the aforementioned steps (11.1) to (11.2)_t。

Step (12): judging whether the conditions are met: d_t≤D_lim(ii) a If yes, the quality of the polypropylene product at the current sampling moment is not abnormal, and the step (8) is returned; if not, executing step (13) to decide whether to trigger an abnormal alarm.

Step (13): returning to the step (8) to continue to carry out the quality abnormity detection of the polypropylene product at the latest sampling time, if the abnormity detection indexes of the continuous 6 latest sampling times are all larger than D_limTriggering an abnormal alarm of the quality of the polypropylene product; otherwise, no exception alarm is triggered.

Claims (1)

1. A polypropylene production process abnormity detection method based on multi-block related component analysis is characterized by comprising the following steps:

step (1): determining measurement variables of the polypropylene production process, specifically comprising 28 measurement variables of four reaction kettles; wherein, every reation kettle all relates to 7 measured variables, is in proper order: reactor temperature, reactor pressure, reactor liquid level, hydrogen feed flow, propylene feed flow, catalyst feed flow, and reflux flow;

step (2): continuously collecting sample data of N sampling moments according to the determined measurement variables, and storing the sample data corresponding to the measurement variables into an Nx 28-dimensional data matrix X e R^N×28Then, the column vectors z in X are respectively aligned according to the following formula₁，z₂，…，z₂₈Performing a normalization process to obtainTo the data matrix

Wherein R is^N×28Representing a matrix of real numbers of dimension Nx 28, R representing a set of real numbers, mu_kAnd delta_kRespectively representing column vectors z_k∈R^N×1The mean and standard deviation of all elements in (k) e {1, 2, …, 28},

representing a matrix of data

A column vector of the kth column;

and (3): according to the measured variable related to each reaction kettle, correspondingly combining the data matrix

Divided into four sub-block matrices X₁，X₂，X₃，X₄(ii) a Wherein, X_b∈R^N×7Is a subblock matrix R corresponding to the b-th reaction kettle in the production process of polypropylene^N×7Representing a real number matrix of dimension Nx 7, b ∈ {1, 2, 3, 4 };

and (4): four subblock matrices X according to steps (4.1) to (4.6) as shown below₁，X₂，X₃，X₄Carrying out multi-block correlation component analysis to obtain a correlation transformation matrix W corresponding to each sub-block matrix_bThe load matrix P_bCorrelation component matrix S_bAnd residual matrix E_b；

Step (4.1): after the threshold value sigma is set, initializing d to be 1;

step (4.2): randomly initializing four transformation vectors w₁∈R^7×1，w₂∈R^7×1，w₃∈R^7×1And w₄∈R^7×1Then, setting b to be 1;

step (4.3): solving generalized eigenvalue problem

Medium maximum eigenvalue lambda_bCorresponding feature vector v_bThen according to the formula

Updating a transformation vector w_b(ii) a Wherein the upper symbol T represents the transpose of a matrix or vector, and the matrix theta_bThe calculation of (c) is as follows:

in the above formula, c is formed by {1, 2, 3, 4}, and when b is not equal to c, H is formed_b，cWhen b is c, H_b，c＝0；

Step (4.4): judging whether b is less than 4; if yes, after b is set to b +1, returning to the step (4.3); if not, obtaining the updated transformation vector w₁，w₂，w₃，w₄And then executing the step (4.5);

step (4.5): judging four transformation vectors w₁，w₂，w₃，w₄Whether both converge; if not, setting b to be 1 and then returning to the step (4.3); if yes, the correlation coefficient J ═ λ is calculated₁+λ₂+λ₃+λ₄) After/4, performing step (4.6);

step (4.6): judging whether the correlation coefficient J is larger than a threshold value sigma; if yes, the formula s is firstly and respectively determined according to_b＝X_bw_bAnd

calculating a correlation component vector s_bAnd a load vector p_bThen according to the formula

Updating subblock matrix X₁，X₂，X₃，X₄And setting a correlation transformation matrix W₁，W₂，W₃，W₄The column vectors of the d-th column in the column are respectively equal to w₁，w₂，w₃，w₄Setting a load matrix P₁，P₂，P₃，P₄The column vectors of the d-th column in (A) are respectively equal to p₁，p₂，p₃，p₄Setting a correlation component matrix S₁，S₂，S₃，S₄The column vectors of the d-th column in (A) are respectively equal to s₁，s₂，s₃，s₄Then, after d is set to d +1, the step (4.2) is returned; if not, obtaining a related transformation matrix W corresponding to the four subblock matrixes₁，W₂，W₃，W₄The load matrix P₁，P₂，P₃，P₄And a correlation component matrix S₁，S₂，S₃，S₄And by setting E_b＝X_bA residual matrix E can be obtained₁，E₂，E₃，E₄；

And (5): according to

Respectively for residual error matrix E₁，E₂，E₃，E₄Performing singular value decomposition with retention of decomposition matrix

Where b is ∈ {1, 2, 3, 4}, diagonal matrix Λ_bThe elements on the diagonal being composed of non-zero singular values, U_bAnd V_bAre two unitary matrices of a singular value decomposition,

is represented by_bInverse moment ofArraying;

and (6): according to the formula respectively

And

calculating an anomaly detection index vector psi_bAnd Q_bThen respectively transferring psi_bAnd Q_bThe maximum value of the element in (1) is recorded as

And

wherein diag () represents an operation of converting elements of matrix diagonal in parentheses into vectors;

and (7): calculating an abnormal comprehensive detection index vector D according to a formula shown in the specification, and recording the maximum value in the D as the D_lim：

And (8): at the latest sampling time t, sample data x corresponding to the measured variable is collected_t(1)，x_t(2)，…，x_t(28) And respectively normalizing them according to the following formula to obtain data vectors

Where k ∈ {1, 2, …, 28},

representing input vectors

The kth element in (1);

and (9): according to the measured variable related to each reaction kettle, correspondingly calculating the data vector

Division into four sub-block vectors

Then, again according to

And

respectively calculating related feature vectors

And residual vector e_b；

Step (10): according to

And

respectively calculating abnormality detection indexes

And q is_bThen, the abnormal comprehensive detection index D corresponding to the latest sampling time t is calculated according to the formula shown in the specification_t：

Step (11): judging whether the conditions are met: d_t≤D_lim(ii) a If yes, the polypropylene production process at the current sampling moment is not abnormal, and the step (8) is returned to continue to carry out the abnormal detection of the latest sampling moment; if not, executing the step (12) to decide whether to trigger an abnormal alarm;

step (12): returning to the step (8) to continue to carry out the abnormal detection of the latest sampling time until the abnormal comprehensive detection indexes of the continuous 6 latest sampling times are obtained, and then judging whether the 6 abnormal comprehensive detection indexes are all larger than D_lim(ii) a If yes, triggering an abnormal alarm; if not, the abnormal alarm is not triggered, and the step (8) is returned to continue to detect the abnormality of the latest sampling time.

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