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CN109376337B - A Distributed Soft Sensing Method Based on Girvan-Newman Algorithm - Google Patents

A Distributed Soft Sensing Method Based on Girvan-Newman Algorithm Download PDF

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CN109376337B
CN109376337B CN201811213322.9A CN201811213322A CN109376337B CN 109376337 B CN109376337 B CN 109376337B CN 201811213322 A CN201811213322 A CN 201811213322A CN 109376337 B CN109376337 B CN 109376337B
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宋励嘉
童楚东
俞海珍
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Dragon Totem Technology Hefei Co ltd
Hangzhou Woyi Digital Technology Co ltd
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Ningbo University
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Abstract

本发明公开一种基于Girvan‑Newman算法的集散软测量方法，旨在解决如何从数据角度对大规模生产过程实施过程分解，以建立分散式的软测量模型，以及如何集成利用分散式的软测量结果来得到产品质量数据估计值的问题。本发明发法首次利用Girvan‑Newman算法实现了过程对象的分解，从而为建立分散式软测量模型奠定了前期基础。其次，本发明方法利用偏最小二乘算法集成分散式软测量结果，完成了由分散式建模到集成软测量的实施过程。可以说，本发明方法是一种新颖的集散软测量方法，能适应于大规模生产过程对象产品质量指标的软测量。

Figure 201811213322

The invention discloses a distributed soft measurement method based on the Girvan-Newman algorithm, aiming at solving how to implement process decomposition for a large-scale production process from a data perspective to establish a distributed soft measurement model, and how to integrate and utilize the distributed soft measurement. results to the problem of obtaining estimates of product quality data. The method of the present invention realizes the decomposition of the process object by using the Girvan-Newman algorithm for the first time, thereby laying a preliminary foundation for establishing a decentralized soft measurement model. Secondly, the method of the present invention utilizes the partial least squares algorithm to integrate the distributed soft measurement results, and completes the implementation process from distributed modeling to integrated soft measurement. It can be said that the method of the present invention is a novel distributed soft measurement method, which can be adapted to the soft measurement of the quality index of the object product in the mass production process.

Figure 201811213322

Description

Distributed soft measurement method based on Girvan-Newman algorithm
Technical Field
The invention relates to an industrial process soft measurement method, in particular to a distributed soft measurement method based on a Girvan-Newman algorithm.
Background
In modern industrial processes, measurement techniques and equipment play an important role in the overall production system, and corresponding measurement data can provide a solid data base for production planning scheduling, process monitoring and other industrial "big data" applications. Although. Advanced meter technology is rapidly developed in recent years, information such as flow, liquid level, pressure, temperature and the like can be easily measured in an industrial process, and information of direct or indirect reaction product quality can also be measured by an instrument to obtain real-time data. However, the equipment for analyzing the product quality information on line in real time is generally expensive and expensive to maintain, compared to the flow or temperature meters. If an offline analysis means is adopted, a certain time delay exists in the acquisition of the product quality data, so that an operator cannot know the product quality data timely and accurately. However, quality monitoring is not isolated from these data information, which reflect product quality. In recent decades, with the widespread use of data-driven methods, soft-measurement techniques have come into play. The method realizes real-time estimation of quality data by establishing a regression model between data which is easy to measure in the production process and product quality data. In recent years, research on soft measurement technique has received more and more attention from the industry and academia.
The core of soft measurement techniques is to establish a regression model between input data (typically information that is easily measured in an industrial process, such as pressure, temperature, flow, etc.) and output data (typically measurement indicators that directly or indirectly reflect quality information, such as concentration). In the existing literature and patent documents, the methods commonly used for establishing the regression model include: statistical regression, neural networks, support vector machines, and the like. In addition, as modern industrial processes, in particular the process industry, are increasingly scaled up, a plurality of production units are linked in a staggered manner. If a single soft measurement model is directly established, the soft measurement accuracy which can be achieved is always poor. In recent years, decentralized soft measurement models have gained importance, since the generalization performance of multiple models is generally superior to that of a single model. Generally speaking, implementing multi-model modeling first requires decomposing the process objects. However, due to the complex interleaving of production cells and control system feedback relationships, implementing an effective process decomposition requires relying on sufficient process mechanism knowledge and a priori knowledge of the operator.
In order to facilitate the popularization and application of the soft measurement technology, how to implement decomposition on the whole production process object on the premise of not needing process mechanism knowledge is the first difficult problem in implementing the distributed soft measurement technical scheme. In addition, even if the process object can be successfully decomposed, how to integrate these distributed soft measurement models to obtain the final estimation value of the product quality is the second problem faced by the technology of implementing the distributed soft measurement method. The concept of clustering as presented here is, above all, that the soft measurement models have to be scattered, but the estimation or prediction of the product quality gives only one result, i.e. the results of a plurality of soft measurement models are to be integrated.
Disclosure of Invention
The invention aims to solve the main technical problems that: how to decompose the large-scale production process from the data perspective to build a decentralized soft measurement model, and how to integrate and use decentralized soft measurement result integration to obtain the estimated value of the product quality data.
The technical scheme adopted by the invention for solving the technical problems is as follows: a distributed soft measurement method based on a Girvan-Newman algorithm comprises the following steps:
(1): finding out data corresponding to index capable of reflecting product quality from historical database of production process object to form output matrix Y belonging to Rn×fThe sampled data corresponding to the output Y form an input matrix X ∈ Rn×mWherein n is the number of training samples, m is the number of process measurement variables, f is the number of quality indicators, R is the set of real numbers, R is the number of training samplesn×mRepresenting a matrix of real numbers in dimension n x m.
(2): calculating the mean value mu of each column vector in the output matrix Y1，μ2，…，μfAnd standard deviation delta1，δ2，…，δfThen according to the formula
Figure BSA0000172239770000021
Standardizing each row vector in Y to obtain a standardized output matrix
Figure BSA0000172239770000022
Wherein the row vector y is equal to
Figure BSA0000172239770000023
Respectively represent matrices Y and
Figure BSA0000172239770000024
is given as a mean value vector mu [ mu ] of any one of the row vectors1，μ2，…，μf]Output standard deviation diagonal matrix
Figure BSA0000172239770000025
The element on the middle diagonal is δ1，δ2，…，δf。
(3): carrying out standardization processing on the matrix X to obtain a standardNormalized input matrix
Figure BSA0000172239770000026
(4): according to the formula
Figure BSA0000172239770000027
After the correlation coefficient matrix C is calculated, the number of neighbors is set to C and j is initialized to 1.
(5): the largest C elements of the jth row vector in matrix C are all set to 1, while the remaining elements are set to 0.
(6): judging whether the conditions are met: j < m? If yes, returning to the step (5) after j is set to j + 1; and if not, obtaining the updated correlation coefficient matrix C.
(7): according to the formula xi ═ max { C, CTXi, calculating to obtain a matrix xi, wherein max { C, CTDenotes taking the matrix C and the matrix CTThe maximum value of the same position element in the network is marked with a reference number T to represent the transpose of a matrix or a vector, the matrix xi can be regarded as a connecting network matrix among m variables, each variable can be used as a node in the network, the element 1 represents that a connecting edge exists between two nodes, and the element 0 represents that no connecting edge exists between the two nodes.
(8) Hierarchical clustering is carried out on m variables by utilizing a Girvan-Newman algorithm, and the specific implementation process is as follows:
calculating the edge betweenness of all connecting edges in the m node connecting networks.
Finding the connecting edge with the highest edge betweenness and removing the connecting edge from the network, namely setting 0 to the corresponding element in the connecting network matrix xi.
And thirdly, recalculating the edge betweenness of the residual connecting edges in the network.
And fourthly, repeating the steps of the second step and the third step to guide all connecting edges in the connecting network to be removed, namely the matrix xi becomes a zero matrix.
The edge betweenness of a certain connecting edge in the step (i) is defined as: and repeating the same calculation for all the nodes starting from a certain node and reaching the shortest path number of other nodes through the connecting road edge, and adding the obtained edge betweenness relative to different nodes to obtain the edge betweenness of the connecting edge.
(9): according to the hierarchical clustering result in the step (8), m variables can be divided into D blocks, and correspondingly, an input matrix can be divided into D blocks
Figure BSA0000172239770000031
Division into D matrices:
Figure BSA0000172239770000032
the step (8) and the step (9) complete the decomposition of the process object through the Girvan-Newman algorithm, and the process measurement variable is decomposed into D sub-blocks on the basis of depending on the correlation among the variables, so that the first step of the establishment of the distributed soft measurement model is completed.
(10): establishing using partial least squares algorithm
Figure BSA0000172239770000033
And output matrix
Figure BSA0000172239770000034
Soft measurement model in between:
Figure BSA0000172239770000035
wherein D is 1, 2, …, D, BdAs a matrix of regression coefficients, EdIs an error matrix.
It is to be emphasized that although the soft measurement model is established by using the partial least square algorithm in step (10), the method of the present invention may also use a neural network, support vector regression, or kernel partial least square algorithm to establish the soft measurement model.
(11): repeating the step (10) until D soft measurement models are obtained, and utilizing a regression coefficient matrix B1，B2，…，BDAccording to the formula
Figure BSA0000172239770000036
Calculating output estimation values corresponding to the soft measurement models
Figure BSA0000172239770000037
(12): will output the estimated value
Figure BSA0000172239770000038
Are combined into a matrix
Figure BSA0000172239770000039
Establishing using partial least squares algorithm
Figure BSA00001722397700000310
And output
Figure BSA00001722397700000311
Soft measurement model in between:
Figure BSA00001722397700000312
wherein
Figure BSA00001722397700000313
In the form of a matrix of regression coefficients,
Figure BSA00001722397700000314
is an error matrix.
The above steps (1) to (12) are the off-line modeling stages of the method of the present invention, wherein step (11) establishes the distributed D soft measurement models, and step (12) integrates the distributed soft measurement results. The steps (13) to (18) shown below are the on-line soft measurement implementation process of the method of the present invention.
(13): acquiring sample data z epsilon R of new time process object1×mAnd subjecting it to the same normalization process as the matrix X to obtain a vector
Figure BSA00001722397700000315
(14): according to the hierarchical clustering result in the step (8), vectors are subjected to hierarchical clustering
Figure BSA00001722397700000323
Divided into D rowsVector quantity:
Figure BSA00001722397700000316
and initializes d to 1.
(15): according to the formula
Figure BSA00001722397700000317
Calculating to obtain an output estimation value y corresponding to the d-th soft measurement modeld。
(16): judging whether the conditions are met: d < D? If yes, returning to the step (15) after d is set to d + 1; if not, combining the output estimated values of the D soft measurement models into a vector
Figure BSA00001722397700000318
(17): according to the formula
Figure BSA00001722397700000319
Integrating to obtain final estimation value of distributed soft measurement model to output
Figure BSA00001722397700000320
Then the estimate of the quality indicator at the current sampling instant is
Figure BSA00001722397700000321
Wherein μ and
Figure BSA00001722397700000322
and (3) obtaining a mean vector and a standard deviation diagonal matrix in the step (2).
(18): and returning to the step (13) to continue to carry out soft measurement on the quality index at the new sampling moment.
Compared with the prior art, the method has the advantages that:
the Girvan-Newman algorithm can be said to be used for blocking processing of variables in the method of the invention for the first time, without any process mechanism knowledge and prior operation experience. The method of the invention utilizes the Girvan-Newman algorithm to complete the process decomposition task of the monitored object, and lays a cushion for establishing a distributed soft measurement model. In addition, although the method of the present invention uses partial least squares algorithm to build the soft measurement model in step (10), the method of the present invention is not limited to use of partial least squares algorithm, and other methods such as neural network, support vector machine, kernel partial least squares algorithm, etc. can be used to build the soft measurement model. In addition, in order to integrate the distributed soft measurement results, the method completes the integration of the soft measurement results by using the partial least square algorithm again. The method is a novel distributed soft measurement method, and can be suitable for soft measurement of the quality index of the target product in the large-scale production process.
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FIG. 1 is a flow chart of an embodiment of the method of the present invention.
FIG. 2 is a flow chart of an implementation of the Girvan-Newman algorithm.
Detailed Description
The method of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in FIG. 1, the invention provides a distributed soft measurement method based on Girvan-Newman algorithm, and the specific implementation mode of the method is as follows:
step (1): finding out data corresponding to index capable of reflecting product quality from historical database of production process object to form output matrix Y belonging to Rn×fThe sampled data corresponding to the output Y form an input matrix X ∈ Rn×mWherein n is the number of training samples, m is the number of process measurement variables, f is the number of quality indicators, R is the set of real numbers, R is the number of training samplesn×mA real number matrix representing dimensions n × m;
step (2): calculating the mean value mu of each column vector in the output matrix Y1，μ2，…，μfAnd standard deviation delta1，δ2，…，δfThen according to the formula
Figure BSA0000172239770000041
Standardizing each row vector in Y to obtain a standardized output matrix
Figure BSA0000172239770000042
Wherein the row vector y is equal to
Figure BSA0000172239770000043
Respectively represent matrices Y and
Figure BSA0000172239770000044
is given as a mean value vector mu [ mu ] of any one of the row vectors1，μ2，…，μf]Output standard deviation diagonal matrix
Figure BSA0000172239770000045
The element on the middle diagonal is δ1，δ2，…，δf；
And (3): standardizing the matrix X to obtain a standardized input matrix
Figure BSA0000172239770000046
And (4): according to the formula
Figure BSA0000172239770000047
After the correlation coefficient matrix C is calculated, a neighbor parameter C is set and j is initialized to 1.
And (5): the largest C elements of the jth row vector in matrix C are all set to 1, while the remaining elements are set to 0.
And (6): judging whether the conditions are met: j < m? If yes, returning to the step (5) after j is set to j + 1; if not, obtaining an updated correlation coefficient matrix C;
and (7): according to the formula xi ═ max { C, CTXi, calculating to obtain a matrix xi, wherein max { C, CTDenotes taking the matrix C and the matrix CTThe maximum value of the elements at the same position is marked with a number T to represent the transpose of a matrix or a vector, the matrix xi can be regarded as a connecting network matrix among m variables, each variable can be used as a node in the network, the element 1 represents that a connecting edge exists between two nodes, and the element 0 represents that no connecting edge exists between the two nodes;
and (8): and (3) performing hierarchical clustering on the m variables by using a Girvan-Newman algorithm, wherein the implementation flow of the Girvan-Newman algorithm is shown in a figure 2, and the specific implementation mode comprises the following steps (8.1) to (8.4).
Step (8.1): calculating the edge betweenness of all connecting edges in the m node connecting networks;
step (8.2): finding the connecting edge with the highest edge betweenness and removing the connecting edge from the network, namely setting 0 to the corresponding element of the connecting network matrix xi;
step (8.3): recalculating edge betweenness of the residual connecting edges in the network;
step (8.4): repeating the second step and the third step, and guiding all connecting edges in the connecting network to be removed, namely the matrix xi becomes a zero matrix;
and (9): according to the hierarchical clustering result in the step (8), m variables can be divided into D blocks, and correspondingly, an input matrix can be divided into D blocks
Figure BSA0000172239770000051
Division into D matrices:
Figure BSA0000172239770000052
step (10): establishing using partial least squares algorithm
Figure BSA0000172239770000053
And output matrix
Figure BSA0000172239770000054
Soft measurement model in between:
Figure BSA0000172239770000055
the specific embodiment is as follows:
initializing h to 1, setting the matrix
Figure BSA0000172239770000056
And matrix
Figure BSA0000172239770000057
And initializes the vector uIs a matrix Y0The first column of (2).
② according to formula wh＝ZTu/(uTu) calculating an input weight vector whAnd using formula wh＝wh/||wh| | unitized vector wh。
Thirdly according to formula sh＝Zwh/(wh Twh) Calculating a score vector sh。
Fourthly, according to a formula gh＝Y0 Tsh/(sh Tsh) Calculating an output weight vector gh。
According to the formula u-Y0ghThe vector u is updated.
Sixthly, repeating from (1) to (v) until shConvergence, the criterion being the vector shWherein the elements do not change.
Keeping the input weight vector whAnd the output weight ghAnd according to the formula ph＝Xi Tsh/(sh Tsh) Calculating a projection vector ph。
Updating input matrix Z and matrix Y according to the following two formulas0：
Z＝Z-shph T (7)
Y0＝Y0-shgh (8)
Ninthly, judging whether the conditions are met: h is less than MdIs there a Wherein M isdIs a matrix
Figure BSA0000172239770000058
If yes, setting h as h +1, and returning to the step two; if not, all the obtained input weight vectors form a matrix W0＝[w1，w2，…，wh]All the output weight vectors form a matrix G0＝[g1，g2，…，gh]And all projection vectors form a matrix P0＝[p1，p2，…，ph]。
Method for determining number k of projection vectors reserved in partial least square model in R (zero) by using cross validation methoddThen the soft measurement model established by the partial least squares algorithm can be expressed as:
Figure BSA0000172239770000059
wherein the regression coefficient matrix Bd＝W(PTW)-1GTThe matrices W, P, G are each formed by a matrix W0、P0And G01 st column to k th column ofdThe column vector of the column.
Step (11): repeating the step (10) until D soft measurement models are obtained, and utilizing a regression coefficient matrix B1，B2，…，BDAccording to the formula
Figure BSA0000172239770000061
Calculating output estimation values corresponding to the soft measurement models
Figure BSA0000172239770000062
Step (12): will output the estimated value
Figure BSA0000172239770000063
Are combined into a matrix
Figure BSA0000172239770000064
Establishing using partial least squares algorithm
Figure BSA0000172239770000065
And output
Figure BSA0000172239770000066
Soft measurement model in between:
Figure BSA0000172239770000067
the embodiment is the same as in steps (r) to (r) above.
The steps (1) to (12) are off-line modeling stages implemented by the method of the present invention, and steps need to be reservedOutput mean vector mu and output standard deviation diagonal matrix in step (2)
Figure BSA0000172239770000068
And (3) performing hierarchical clustering on the result in the step (8), the regression coefficient matrixes in the step (11) and the regression coefficient matrixes in the step (12) for calling when online distributed soft measurement is performed.
Step (13): sample data z epsilon R of the latest sampling time of the acquisition process object1×mAnd subjecting it to the same normalization process as the matrix X to obtain a vector
Figure BSA0000172239770000069
Step (14): according to the hierarchical clustering result in the step (8), vectors are subjected to hierarchical clustering
Figure BSA00001722397700000610
Division into D row vectors:
Figure BSA00001722397700000611
and initializes d to 1.
Step (15): according to the formula
Figure BSA00001722397700000612
Calculating to obtain an output estimation value y corresponding to the d-th soft measurement modeld。
Step (16): judging whether the conditions are met: d < D? If yes, returning to the step (15) after d is set to d + 1; if not, combining the output estimated values of the D soft measurement models into a vector
Figure BSA00001722397700000613
Step (17): according to the formula
Figure BSA00001722397700000614
Integrating to obtain final estimation value of distributed soft measurement model to output
Figure BSA00001722397700000615
Then the estimate of the quality indicator at the current sampling instant is
Figure BSA00001722397700000616
Wherein μ and
Figure BSA00001722397700000617
and (3) obtaining a mean vector and a standard deviation diagonal matrix in the step (2).
Step (18): and (4) returning to the step (13) to continue to carry out soft measurement on the quality index at the new sampling moment.
The above-described embodiments are only preferred embodiments of the present invention, and any modifications and changes made to the present invention within the spirit of the present invention and the scope of the claims should not be excluded from the scope of the present invention.

Claims (2)

1. A distributed soft measurement method based on a Girvan-Newman algorithm is characterized by comprising the following steps:
firstly, the off-line modeling stage comprises the following steps (1) to (12);
step (1): finding out data corresponding to index capable of reflecting product quality from historical database of production process object to form output matrix Y belonging to Rn×fThe sampled data corresponding to the output matrix Y form an input matrix X ∈ Rn×mWherein n is the number of training samples, m is the number of process measurement variables, f is the number of quality indicators, R is the set of real numbers, R is the number of training samplesn×mA real number matrix representing dimensions n × m;
step (2): calculating the mean value mu of each column vector in the output matrix Y1，μ2，…，μfAnd standard deviation delta1，δ2，…，δfThen according to the formula
Figure FSB0000195370850000011
Standardizing each row vector in Y to obtain a standardized output matrix
Figure FSB0000195370850000012
Wherein the row vector y is equal to
Figure FSB0000195370850000013
Respectively represent Y and
Figure FSB0000195370850000014
is given as a mean value vector mu [ mu ] of any one of the row vectors1，μ2，…，μf]Output standard deviation diagonal matrix
Figure FSB0000195370850000015
The element on the middle diagonal is δ1，δ2，…，δf；
And (3): standardizing the input matrix X to obtain a standardized input matrix
Figure FSB0000195370850000016
And (4): according to the formula
Figure FSB0000195370850000017
After a correlation coefficient matrix C is calculated, setting the number of neighbors as C and initializing j to be 1;
and (5): setting all maximum C elements of j-th row vectors in a correlation coefficient matrix C to be 1, and setting the rest elements to be 0;
and (6): judging whether the conditions are met: j is less than m; if yes, returning to the step (5) after j is set to j + 1; if not, obtaining a correlation coefficient matrix C;
and (7): according to the formula xi ═ max { C, CTXi, calculating to obtain a matrix xi, wherein max { C, CTMeans take C and CTThe maximum value of the element at the same position is marked with a number T which represents the transpose of a matrix or a vector, the matrix xi can be regarded as a connecting network matrix among m variables, each variable can be used as a node in the network, the element 1 represents that a connecting edge exists between two nodes, and the element 0 represents that no connecting edge exists between the two nodes;
and (8): hierarchical clustering is carried out on m variables by utilizing a Girvan-Newman algorithm, and the specific implementation process is as follows:
step (8.1): calculating the edge betweenness of all connecting edges in the m node connecting networks;
step (8.2): finding the connecting edge with the highest edge betweenness and removing the connecting edge from the network, namely setting 0 to the corresponding element of the connecting network matrix xi;
step (8.3): recalculating edge betweenness of the residual connecting edges in the network;
step (8.4): repeating the step (8.2) -and the step (8.3) until all connecting edges in the connecting network are removed, i.e. the matrix xi becomes a zero matrix;
and (9): according to the hierarchical clustering result in the step (8), m variables can be divided into D blocks, and correspondingly, an input matrix can be divided into D blocks
Figure FSB0000195370850000018
Division into D matrices:
Figure FSB0000195370850000019
step (10): establishing using partial least squares algorithm
Figure FSB00001953708500000110
And output matrix
Figure FSB00001953708500000111
Soft measurement model in between:
Figure FSB00001953708500000112
wherein D is 1, 2, …, D, BdAs a matrix of regression coefficients, EdIs an error matrix;
step (11): repeating the step (10) until D soft measurement models are obtained, and utilizing a regression coefficient matrix B1，B2，…，BDAccording to the formula
Figure FSB00001953708500000113
Calculating output estimation values corresponding to the soft measurement models
Figure FSB00001953708500000114
Step (12): will output the estimated value
Figure FSB0000195370850000021
Are combined into a matrix
Figure FSB0000195370850000022
Establishing using partial least squares algorithm
Figure FSB0000195370850000023
And output
Figure FSB0000195370850000024
Soft measurement model in between:
Figure FSB0000195370850000025
wherein
Figure FSB0000195370850000026
In the form of a matrix of regression coefficients,
Figure FSB0000195370850000027
is an error matrix; secondly, after the off-line modeling stage is finished, implementing on-line soft measurement, comprising the following steps (13) to (18);
step (13): sample data z epsilon R of the latest sampling time of the acquisition process object1×mAnd subjecting it to the same normalization process as the matrix X to obtain a vector
Figure FSB0000195370850000028
Step (14): according to the hierarchical clustering result in the step (8), vectors are subjected to hierarchical clustering
Figure FSB0000195370850000029
Division into D row vectors:
Figure FSB00001953708500000210
and initializing d ═ 1;
step (15): according to the formula
Figure FSB00001953708500000211
Calculating to obtain an output estimation value y corresponding to the d-th soft measurement modeld；
Step (16): judging whether the conditions are met: d is less than D; if yes, returning to the step (15) after d is set to d + 1; if not, combining the output estimated values of the D soft measurement models into a vector
Figure FSB00001953708500000212
Step (17): according to the formula
Figure FSB00001953708500000213
Integrating to obtain final estimation value of distributed soft measurement model to output
Figure FSB00001953708500000214
Then the estimate of the quality indicator at the current sampling instant is
Figure FSB00001953708500000215
Wherein μ and
Figure FSB00001953708500000216
the mean vector and the output standard deviation diagonal matrix in the step (2) are obtained;
step (18): and (4) returning to the step (13) to continue to carry out soft measurement on the quality index at the new sampling moment.
2. The distributed soft measurement method based on Girvan-Newman algorithm according to claim 1, wherein the soft measurement model is established by partial least squares algorithm in the step (10), but the method can also adopt neural network, support vector regression, and kernel partial least squares algorithm to establish the soft measurement model.
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