A soft sensing method for polypropylene melt index based on SFA-RBFNN model

Abstract

The present invention discloses a polypropylene melt index soft measurement method based on the SFA-RBFNN model, which combines SFA and RBFNN to solve the polypropylene melt index soft measurement problem, and simultaneously considers the optimization problem of the center point vector of the hidden layer neurons of the RBFNN, so that the soft measurement accuracy of the polypropylene melt index based on the SFA-RBFNN model is effectively guaranteed. Specifically, the method of the present invention first extracts the slowly changing features in the input variables of the polypropylene process through SFA, and then uses the extracted slowly changing features as the input of the RBFNN model, so as to use the essential features that can reflect the slow changes of the data to soft measure the polypropylene melt index. At the same time, the differential evolution algorithm is used to optimize and solve the center point vector of the hidden layer neurons of the RBFNN, and the soft measurement of the polypropylene process melt index is implemented from the perspective of minimizing the estimation error.

Description

Technical Field

[0001] The invention relates to a soft measurement technology, in particular to a polypropylene melt index soft measurement method based on a SFA-RBFNN model. Background Art

[0002] With the development of industrial modernization, the demand for chemical products is increasing day by day, and higher requirements are put forward for the chemical industry. Polypropylene, as a kind of non-polar plastic, has a wide range of uses, from high-tech fields such as aerospace to people's daily necessities. In the production process of polypropylene, the melt index (Melt Index, abbreviated as: MI) is an important indicator reflecting the fluidity of the plastic melt and an important parameter to measure whether the quality of polypropylene products meets the standards. The melt index is often used in industry to distinguish different grades of thermoplastic resins. It can not only be used for product valuation, but also to determine the different uses of products. Therefore, in the production process of polypropylene, real-time measurement of the melt index is very important!

[0003] The measurement methods of polypropylene melt index are generally divided into two categories, namely direct measurement and indirect measurement. Direct measurement can also be called instrumental measurement of melt index, that is, using hardware facilities to directly measure polypropylene products. Although direct instrument measurement can obtain more accurate MI data, when measuring polypropylene melts of different grades, there will be residues in the measuring instrument during the switching process, resulting in a low measurement frequency of the melt index, which makes the melt index have great limitations when measured by hardware. Fortunately, soft measurement technology does not need to consider the problem of brand switching, and there are different research methods for soft measurement of polypropylene melt index.

[0004] In existing scientific research literature and patent documents, the Radial Basis Function Neural Network (RBFNN) has been proven to have application value in soft measurement of polypropylene melt index. Researchers have proposed different improvement and optimization strategies for data modeling and soft measurement application research based on RBFNN. However, an overlooked problem is that RBF neural networks are prone to overfitting. The so-called overfitting is to use irrelevant input features to estimate output variables, and these irrelevant features play an important role in model training. In addition, the center point vectors of the hidden layer neurons of the RBF neural network are generally given by clustering algorithms, and the center point vectors of the hidden layer neurons are not determined from the perspective of minimizing the estimation error.

[0005] In recent years, in the field of statistical learning, slow feature analysis (SFA) can be used to analyze and extract slowly changing features in data, thereby discovering the essential driving factors of data changes. This is mainly because fast-changing features usually represent noise, and slowly changing features can better reflect the essential information hidden in the data. Therefore, SFA has an irreplaceable effect in eliminating the interference of measurement data. However, there has been no precedent for the application of SFA in the research of polypropylene melt index soft measurement technology. Summary of the invention

[0006] The main technical problem to be solved by the present invention is: how to use SFA and RBFNN in combination to solve the soft measurement problem of polypropylene melt index, and at the same time consider the optimization problem of the center point vector of the hidden layer neurons of RBFNN, so that the soft measurement accuracy of polypropylene melt index based on SFA-RBFNN model is effectively guaranteed. Specifically, the method of the present invention first extracts the slowly changing features in the input variables of the polypropylene process through SFA, and then uses the extracted slowly changing features as the input of the RBFNN model, and at the same time uses the differential evolution algorithm to optimize and solve the center point vector of the hidden layer neurons of RBFNN, so as to implement the soft measurement of the melt index of the polypropylene process from the perspective of minimizing the estimation error.

[0007] The technical solution adopted by the method of the present invention to solve the above problem is: a polypropylene melt index soft measurement method based on the SFA-RBFNN model, comprising the following steps:

[0008] Step (1): first determine 28 measurement variables of four reactors in the polypropylene process as input variables of the soft sensor model, and then determine the polypropylene melt index at the product outlet as the output variable of the soft sensor model; wherein the polypropylene process is specifically composed of four reactors connected in series, the first reactor and the second reactor are liquid phase continuous stirring reactors, the third reactor and the fourth reactor are gas phase fluidized bed reactors, and each reactor is correspondingly equipped with 7 measuring instruments to collect data of 7 measurement variables in real time, which are respectively: reactor temperature, reactor pressure, reactor liquid level, hydrogen feed flow rate, propylene feed flow rate, catalyst feed flow rate and reflux flow rate.

[0009] Step (2): After continuously collecting sample data at n sampling moments according to the determined input variables and output variables, the sample data corresponding to the 28 input variables are stored as an n×28-dimensional data matrix X, and the data corresponding to the output variables are stored as an n×1-dimensional data vector y.

[0010] Step (3): According to the following formula, the column vector z in X is 1 , z 2 , …, z28 Standardization is performed separately, and 28 column vectors are obtained accordingly And the column vector Merge into input matrix

[0011]

[0012] Among them, μ i With δ i Represents the column vector z i The mean and standard deviation of all elements in , i∈{1, 2, …, 28}.

[0013] Step (4): Use the SFA algorithm to solve the transformation matrix P∈R 28×K Then, the matrix Transformed into input feature matrix The specific implementation process is shown in steps (4.1) to (4.4); where R 28×K represents a 28×K-dimensional real matrix, and R represents a real number set.

[0014] Step (4.1): The covariance matrix of Implement singular value decomposition, that is, C = UΛU T ; Among them, U∈R 28×28 The unitary matrix representing the singular value decomposition, the diagonal matrix Λ∈R 28×28 The elements on the diagonal are singular values.

[0015] Step (4.2): According to the formula After calculating the whitening matrix Z, according to the formula Compute the first-order difference matrix Among them, the inverse matrix of Λ -1 =Λ -1 / 2 Λ -1 / 2 , Z 2 Represents the matrix composed of row vectors from the 2nd row to the nth row in the whitening matrix Z, Z 1 Represents the matrix composed of row vectors from row 1 to row n-1 in the whitening matrix Z, R (n -1)×m Represents a (n-1)×m-dimensional real matrix.

[0016] Step (4.3): Calculate the matrix Then solve the eigenvalue problem The 28 eigenvalues ​​λ 1 ≤λ 2 ≤…≤λ 28 The corresponding eigenvector v 1 , v 2 , …, v 28; where i∈{1, 2,…, 28}.

[0017] Step (4.4): Take the smallest K eigenvalues ​​λ 1 ,λ 2 , …, λ K The corresponding eigenvector v 1 , v 2 , …, v K The matrix V = [v 1 , v 2 , …, v K ], and then calculate the transformation matrix P = UΛ -1 / 2 V.

[0018] Step (5): According to the following formula, the K column vectors s in the input feature matrix S are 1 ,s 2 ,…,s K And the data vector y are normalized respectively, and the corresponding column vector is obtained And the output vector

[0019]

[0020] Among them, γ∈{1, 2, …, K}, s γ (min) and s γ (max) respectively represent the γth column vector s γ y(min) and y(max) represent the minimum and maximum values ​​in the data vector y, respectively.

[0021] Step (6): Construct the input feature matrix Finally, build an RBFNN model consisting of an input layer, a hidden layer, and an output layer; the number of neurons in the input layer is equal to K, the number of neurons in the hidden layer is equal to H, the number of neurons in the output layer is equal to 1, and determine the center point vector c of the hidden layer neurons. 1 , c 2 , …, c H , smoothing factor β best , and the output layer weight vector θ best The specific implementation process is shown in steps (6.1) to (6.5).

[0022] Step (6.1): Initialize the number of iterations m=1, and set the parameters of the differential evolution algorithm, including: population number N, scaling factor zf, crossover probability cp, and maximum number of iterations M.

[0023] Step (6.2): ​​Randomly generate N H×K dimensional population matrices U 1 , U2 , …, U N , each element in the population matrix is ​​randomly selected in the interval [0, 1].

[0024] Step (6.3): Calculate the population matrix U separately 1 , U 2 , …, U N The corresponding fitness value L 1 , L 2 , …, L N ; Among them, calculate the kth population matrix U k The corresponding fitness value L k The specific implementation process is shown in steps (6.3-1) to (6.3-3).

[0025] Step (6.3-1): Input feature matrix The n row vectors s in 1 ,s 2 ,…,s n As the input vector, the hidden layer output vector v is calculated according to the following formula 1 , v 2 , …, v n :

[0026]

[0027] Among them, exp() represents the exponential function with the natural constant e as the base, v j (h) indicates v j ∈R H×1 The hth element in U k (h) indicates U k The row vector of the hth row in ||s j -U k (h)|| 2 =[s j -U k (h)][s j -U k (h)] T , the superscript T represents the transpose of a matrix or vector, h∈{1,2,…,H}, k∈{1,2,…,N}, j∈{1,2,…,n}, R H×1 represents a real vector of H×1, β k is the matrix U corresponding to the kth population k The smoothness factor.

[0028] Smoothing factor β k The determination method of is as follows: First, according to the formula D(h, d) = || U k (h)-U k(d)|| 2 Calculate the population matrix U k After calculating the square distance D(h, d) between the row vectors of the hth row and the dth row in the distance matrix D∈R H×H The largest value in is recorded as D max ; Secondly, according to the formula β k =D max / H Calculate the smoothing factor β k ; Among them, the element in the hth row and dth column in D is equal to D(h, d), d∈{1, 2,…, H}.

[0029] Step (6.3-2): The hidden layer output vector v 1 , v 2 , …, v n Merge into a matrix V k =[v 1 , v 2 , …, v n ] T , and then according to the formula Calculate the output layer weight vector θ of the RBF neural network k ∈R H×1 Then calculate the output layer estimation vector of RBFNN

[0030] Step (6.3-3): According to the formula Calculate the fitness value L corresponding to the kth population matrix k .

[0031] Step (6.4): L 1 , L 2 , …, L N The population matrix, smoothing factor, and output layer weight vector corresponding to the minimum value in are recorded as U best , β best , and θ best Then, perform the population update operation of the differential evolution algorithm according to the following steps (6.4-1) to (6.4-4) to obtain the updated N population vectors U 1 , U 2 , …, U N .

[0032] Step (6.4-1): According to the following formula, the population matrix U is 1 , U 2 , …, U N Generate a corresponding mutation matrix M 1 , M 2 , …, M N :

[0033] Mk =U k +zf×(U best -U k )+zf×(U a -U b ) ④

[0034] In the above formula, k∈{1, 2, …, N}, subscripts a and b are two different integers randomly generated from the interval [1, N];

[0035] Step (6.4-2): According to the following formula, the variation matrix M k Modify each element in:

[0036]

[0037] Among them, M k (h, γ) represents the mutation matrix M k ∈R H×K The element in the hth row and γth column of R, γ∈{1, 2, …, K}, H×K represents a real matrix of dimension H×K;

[0038] Step (6.4-3): Generate N trial matrices W according to the formula shown below 1 , W 2 , …, W N :

[0039]

[0040] Among them, W k (h, γ) and U k (h, γ) represent W k ∈R H×K with U k ∈R H×K A(h,γ) represents the element of the h-th row and the γ-th column in the random number matrix A. The elements in the random number matrix A are all random numbers between 0 and 1.

[0041] Step (6.4-4): Update the population matrix U according to the following formula: 1 , U 2 , …, U N :

[0042]

[0043] In the above formula, Indicates that W k After the population matrix is ​​formed, execute steps (6.3-1) to (6.3-3) to calculate the fitness value.

[0044] Step (6.5): Determine whether the condition m>M is satisfied; if not, set m=m+1 and return to step (6.3); if yes, obtain the smoothing factor β best and the output layer weight vector θ best , and U best Each row vector in is recorded as the center point vector c 1 , c 2 , …, c H .

[0045] Step (7): At the latest sampling time t, collect the sample data u corresponding to the 28 input variables described in step (1) 1 (t),u 2 (t),…,u 28 (t), and standardize them according to the following formula to obtain the standardized data

[0046]

[0047] In the above formula, i∈{1, 2,…, 28}.

[0048] Step (8): Composed input data vector Then calculate the input feature vector s t =x t P.

[0049] Step (9): Calculate s according to the following formula: t Normalize each element in to get the normalized input feature vector

[0050]

[0051] Among them, s t (γ) and Respectively represent s t and The γth element in .

[0052] Step (10): Calculate the soft measurement value y(t) of the polypropylene melt index according to steps (10.1) to (10.2) as shown below.

[0053] Step (10.1): Calculate the hidden layer output vector u∈R of RBFNN according to the following formula: H×1 :

[0054]

[0055] In the above formula, u(h) represents the hth element in u,

[0056] Step (10.2): According to the formula Calculate the output estimate Then, the soft measurement value of polypropylene melt index is calculated.

[0057] Step (11): Return to step (7) to continue to implement soft measurement of the polypropylene melt index at the latest sampling moment.

[0058] Through the above-described implementation steps, the advantages of the method of the present invention are introduced as follows.

[0059] When the method of the present invention establishes a soft measurement model of polypropylene melt index, the SFA algorithm is first used to convert the data corresponding to the original input variables into representative input features, so as to use the essential features that can reflect the slow changes of the data to soft measure the polypropylene melt index; secondly, the method of the present invention uses the differential evolution algorithm to optimize and solve the center point vector of the hidden layer neurons of the RBFNN, the photochemical factor and the output layer weight vector, which can improve the soft measurement accuracy from the perspective of minimizing the estimation error. In the following specific implementation case, the effectiveness of the method of the present invention in the soft measurement of polypropylene melt index is verified by comparing the experimental results. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a schematic diagram of the implementation process of the method of the present invention.

[0061] Figure 2 Schematic diagram of the production process of polypropylene DETAILED DESCRIPTION

[0062] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] like Figure 1 As shown, the present invention discloses a polypropylene melt index soft sensing method based on the SFA-RBFNN model. The specific implementation of the method of the present invention is described below in conjunction with a specific application example.

[0064] like Figure 2 As shown in the figure, the production process of the polypropylene process object includes four main reaction links, the first two are continuous stirred reactors, and the last two are gas phase fluidized bed reactors. The product coming out of the last equipment reactor is the polypropylene product powder.

[0065] Step (1): first determine the 28 measurement variables of the four reactors in the polypropylene process as the input variables of the soft sensor model, and then determine the polypropylene melt index at the product outlet as the output variable of the soft sensor model; wherein the 7 measurement variables belonging to each reactor in the polypropylene process are: reactor temperature, reactor pressure, reactor liquid level, hydrogen feed flow rate, propylene feed flow rate, catalyst feed flow rate and reflux flow rate.

[0066] Step (2): After continuously collecting sample data at n sampling moments according to the determined input variables and output variables, the sample data corresponding to the 28 input variables are stored as an n×28-dimensional data matrix X, and the data corresponding to the output variables are stored as an n×1-dimensional data vector y.

[0067] Step (3): According to the above formula ①, the column vector z in X is 1 , z 2 , …, z 28 Standardization is performed separately, and 28 column vectors are obtained accordingly And the column vector Merge into input matrix

[0068] Step (4): Use the SFA algorithm to solve the transformation matrix P∈R 28×K Then, the matrix Transformed into input feature matrix The specific implementation process is shown in the above steps (4.1) to (4.4).

[0069] Step (5): According to the above formula ②, the K column vectors s in the input feature matrix S 1 ,s 2 ,…,s K And the data vector y are normalized respectively, and the corresponding column vector is obtained And the output vector

[0070] Step (6): Construct the input feature matrix Finally, build an RBFNN model consisting of an input layer, a hidden layer, and an output layer; the number of neurons in the input layer is equal to K, the number of neurons in the hidden layer is equal to H, the number of neurons in the output layer is equal to 1, and determine the center point vector c of the hidden layer neurons. 1 , c 2 , …, c H , smoothing factor β best , and the output layer weight vector θ best The specific implementation process is shown in the above steps (6.1) to (6.5).

[0071] Step (7): At the latest sampling time t, collect the data u corresponding to the 28 input variables described in step (1) 1 (t),u 2 (t),…,u 28 (t), and standardize them according to the above formula ⑧ to obtain the standardized data

[0072] Step (8): Composed input data vector Then calculate the input feature vector s t =x t P;

[0073] Step (9): According to the above formula ⑨, s t Normalize each element in to get the normalized input feature vector

[0074] Step (10): Calculate the soft measurement value y(t) of the polypropylene melt index according to the above steps (10.1) to (10.2).

[0075] Step (11): Return to step (7) to continue to implement soft measurement of the polypropylene melt index at the latest sampling moment.

[0076] The above implementation cases are only used to explain the specific implementation of the present invention, rather than to limit the present invention. Any modification made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A soft measurement method for polypropylene melt index based on SFA-RBFNN model, characterized in that: The following steps are involved: Step (1): firstly, 28 measurement variables of four reactors in the polypropylene process are determined as input variables of the soft sensor model, and then the polypropylene melt index at the product outlet is determined as the output variable of the soft sensor model; wherein, the seven measurement variables belonging to each reactor in the polypropylene process are: reactor temperature, reactor pressure, reactor liquid level, hydrogen feed flow rate, propylene feed flow rate, catalyst feed flow rate and reflux flow rate; Step (2): after continuously collecting sample data at n sampling moments according to the determined input variables and output variables, the sample data corresponding to the 28 input variables are stored as an n×28-dimensional data matrix X, and the data corresponding to the output variables are stored as an n×1-dimensional data vector y; Step (3): According to the following formula, the column vectors z1, z2, ..., z in X are respectively 28 Standardization is performed separately, and 28 column vectors are obtained accordingly And the column vector Merge into input matrix Among them, μ i With δ i Represents the column vector z i The mean and standard deviation of all elements in , i∈{1, 2, …, 28}; Step (4): Use the SFA algorithm to solve the transformation matrix P∈R 28×K Then, the matrix Transformed into input feature matrix The specific implementation process is shown in steps (4.1) to (4.4); where R 28×K represents a 28×K-dimensional real matrix, and R represents a real number set; Step (4.1): The covariance matrix of Implement singular value decomposition, that is, C = UΛU T ; Among them, U∈R 28×28 The unitary matrix representing the singular value decomposition, the diagonal matrix Λ∈R 28×28 The elements on the diagonal are singular values; Step (4.2): According to the formula After calculating the whitening matrix Z, according to the formula Compute the first-order difference matrix Among them, Z2 represents the matrix composed of row vectors from the 2nd row to the nth row in the whitening matrix Z, Z1 represents the matrix composed of row vectors from the 1st row to the n-1th row in the whitening matrix Z, and R (n-1)×m represents a real matrix of (n-1)×m dimensions; Step (4.3): Calculate the matrix Then solve the eigenvalue problem The 28 eigenvalues ​​λ1≤λ2≤…≤λ 28 The corresponding eigenvectors v1, v2, …, v 28 ; Where i∈{1, 2, …, 28}; Step (4.4): Take the smallest K eigenvalues ​​λ1, λ2, …, λ K The corresponding eigenvectors v1, v2, …, v K The matrix V = [v1, v2, ..., v K ], and then calculate the transformation matrix P = UΛ -1 / 2 V; Step (5): According to the following formula, the K column vectors s1, s2, ..., s in the input feature matrix S are K And the data vector y are normalized respectively, and the corresponding column vector is obtained And the output vector Among them, γ∈{1, 2, …, K}, s γ (min) and s γ (max) respectively represent the γth column vector s γ y(min) and y(max) represent the minimum and maximum values ​​in the data vector y, respectively; Step (6): Construct the input feature matrix Finally, build an RBFNN model consisting of an input layer, a hidden layer, and an output layer; the number of neurons in the input layer is equal to K, the number of neurons in the hidden layer is equal to H, the number of neurons in the output layer is equal to 1, and determine the center point vectors c1, c2, ..., c H , smoothing factor β best , and the output layer weight vector θ best The specific implementation process is shown in steps (6.1) to (6.5); Step (6.1): Initialize the number of iterations m = 1, and set the population size N and the maximum number of iterations M of the differential evolution algorithm; Step (6.2): ​​Randomly generate N H×K dimensional population matrices U1, U2, …, U N , each element in the population matrix is ​​randomly selected in the interval [0, 1]; Step (6.3): Calculate the population matrices U1, U2, ..., U N The corresponding fitness values ​​are L1, L2, ..., L N ; Among them, calculate the kth population matrix U k The corresponding fitness value L k The specific implementation process is shown in step (6.3-1) to step (6.3-3); Step (6.3-1): Input feature matrix The n row vectors s1, s2, …, s n As the input vector, the hidden layer output vector v1, v2, ..., v is calculated according to the following formula n : Among them, exp() represents the exponential function with the natural constant e as the base, v j (h) indicates v j ∈R H×1 The hth element in U k (h) indicates U k The row vector of the hth row in ||s j -U k (h)|| 2 =[s j -U k (h)][s j -U k (h)] T , the superscript T represents the transpose of a matrix or vector, h∈{1,2,…,H}, k∈{1,2,…,N}, j∈{1,2,…,n}, R H×1 represents a real vector of H×1, β k is the matrix U corresponding to the kth population k The smoothing factor determines β k The specific process is shown in step (A) to step (B); Step (A): According to the formula D(h, d) = || U k (h)-U k (d)|| 2 Calculate the population matrix U k The square distance D(h, d) between the row vectors of the hth row and the dth row in , and D(h, d) is set as the distance matrix D∈R H×H The element in the hth row and dth column of , where d∈{1, 2, …, H}; Step (B): Distance matrix D∈R H×H The maximum value of the elements in is recorded as D max , then β k =D max / H; Step (6.3-2): Substitute the hidden layer output vectors v1, v2, ..., v n Merge into a matrix V k =[v1, v2, …, v n ] T , and then according to the formula Calculate the output layer weight vector θ of the RBF neural network k ∈R H×1 Then calculate the output layer estimation vector of RBFNN Step (6.3-3): According to the formula Calculate the fitness value L corresponding to the kth population matrix k ; Step (6.4): Replace L1, L2, ..., L N The population matrix, smoothing factor, and output layer weight vector corresponding to the minimum value in are recorded as U best , β best , and θ best After that, the population update operation of the differential evolution algorithm is performed to obtain the updated N population vectors U1, U2, ..., U N ; Step (6.5): Determine whether the condition m>M is satisfied; if not, set m=m+1 and return to step (6.3); if yes, obtain the smoothing factor β best and the output layer weight vector θ best , and U best The row vectors in are recorded as center point vectors c1, c2, ..., c H ; Step (7): At the latest sampling time t, collect the data u1(t), u2(t), ..., u corresponding to the 28 input variables in step (1). 28 (t), and standardize them according to the following formula to obtain the standardized data Step (8): Composed input data vector Then calculate the input feature vector s t =x t P; Step (9): Calculate s according to the following formula: t Each element in is normalized to obtain the normalized input feature vector Among them, s t (γ) and Respectively represent s t and The γth element in ; Step (10): Calculate the soft measurement value y(t) of the polypropylene melt index according to steps (10.1) to (10.2) as shown below; Step (10.1): Calculate the hidden layer output vector u∈R of RBFNN according to the following formula: H×1 : In the above formula, u(h) represents the hth element in u, Step (10.2): According to the formula Calculate the output estimate Then, the soft measurement value of polypropylene melt index is calculated. Step (11): Return to step (7) to continue to implement soft measurement of the polypropylene melt index at the latest sampling moment.

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