CN113268925A - Dynamic soft measurement method based on differential evolution algorithm time delay estimation - Google Patents

Dynamic soft measurement method based on differential evolution algorithm time delay estimation Download PDF

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CN113268925A
CN113268925A CN202110544959.1A CN202110544959A CN113268925A CN 113268925 A CN113268925 A CN 113268925A CN 202110544959 A CN202110544959 A CN 202110544959A CN 113268925 A CN113268925 A CN 113268925A
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刘瑞兰
郭储磊
韩仲鑫
左瑞雪
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Nanjing University of Posts and Telecommunications
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Abstract

The invention provides a dynamic soft measurement method based on differential evolution algorithm time delay estimation, which is used for predicting PTA average particle size in the PTA refining process, estimating time delay parameters through the differential evolution algorithm and obtaining optimal lag time tauiAnd dynamic data length diAnd then according to the obtained optimal lag time tauiAnd dynamic data length diSelecting corresponding input data sets and output data sets, establishing a PLS model, and predicting the PTA average particle size by the established PLS model. According to the method, dynamic characteristics in the industrial production process are introduced into the model, the prediction accuracy of the model is improved, and the effectiveness and the feasibility of the method are verified through a simulation result.

Description

Dynamic soft measurement method based on differential evolution algorithm time delay estimation
Technical Field
The invention relates to a dynamic soft measurement method based on differential evolution algorithm time delay estimation, which can be used in the field of chemical engineering.
Background
The soft measurement technique is a technique of building a regression model based on the relationship between a variable that is difficult to measure (output variable) and a variable that is easy to measure (process or input variable). Soft measurements play an important role in the monitoring of industrial processes, for example, they can be used to predict important variables that are difficult to measure online, and can also be used as a replacement for expensive hardware sensors. More importantly, because the hardware sensor needs to be maintained or replaced regularly, the hardware sensor is not always in a working state, and data can be backed up by using a soft measurement technology, so that data loss is prevented. However, in most engineering applications, the process is time-varying, multi-modal and non-linear, so these factors need to be considered when building a soft measurement model, otherwise the built model will not achieve the expected effect, affecting the final product quality.
Purified Terephthalic Acid (PTA) is an important raw material in the production of polyesters and chemical industry. In the PTA production process, the crystal grain size of the refining unit is a very important quality control index, and the PTA grain size is well controlled, thereby being beneficial to the stability of polyester production and improving the quality of polyester products.
In an actual industrial process, the establishment of the soft measurement model is not only influenced by process nonlinearity, but also great difficulty is brought to the establishment of the soft measurement model by process time delay. The time lag is ubiquitous in the system, for example, the accuracy of the soft measurement model is greatly affected by the volume delay caused by a storage unit, pure modeling brought by signal transmission and the like, so that it is necessary to accurately estimate the process delay for establishing the high-accuracy soft measurement model. Aiming at the problem, a soft measurement modeling method with time delay estimation is needed to estimate the PTA average grain diameter.
The above-mentioned problems are problems that should be considered and solved in the measurement of the PTA average particle size in the PTA refining process.
Disclosure of Invention
The invention aims to provide a dynamic soft measurement method based on differential evolution algorithm time delay estimation, which solves the problems of accurately estimating process time delay and improving the prediction precision of PTA average particle size in the PTA refining process so as to meet the control requirement in the prior art.
The technical solution of the invention is as follows:
a dynamic soft measurement method based on differential evolution algorithm time delay estimation is used for predicting PTA average particle size in the PTA refining process, estimating time delay parameters through a differential evolution algorithm and obtaining the optimal lag time tauiAnd dynamic data length diAnd then according to the obtained optimal lag time tauiAnd dynamic data length diSelecting corresponding input data sets and output data sets, establishing a PLS model, and predicting the PTA average particle size by the established PLS model, wherein the method comprises the following steps:
s1, initializing a population and parameters in the differential evolution algorithm, wherein the population comprises the time delay of an input variable, namely the lag time tauiAnd dynamic data length diThe parameters include maximum evolution algebra NGAnd the maximum error e allowed by the differential evolution algorithm model; acquiring a training data set, wherein the training data set comprises an input data set and an output data set which have corresponding relations, and constructing a fitness function J by a partial least square method;
s2, performing iteration including variation, intersection and selection on the population in the differential evolution algorithm, wherein the maximum error e is not more than the allowable fitness function J or the evolution algebra k is not less than the maximum evolution algebra NGTime-out, obtaining the lag time tau in the search range of the optimizationiAnd dynamic data length diThe global optimal solution of (a);
s3, obtaining the lag time tau according to the step S2iAnd dynamic data length d of input variableiSelecting a corresponding input data set and an output data set from the training data set, establishing a partial least square model (PLS) between the input data set and the output data set, and predicting the PTA average particle size through the PLS model.
Further, in step S1, the fitness function constructed by the partial least squares method is:
Figure BDA0003071952840000021
wherein, y (t)k) Is tkOutput value of time course, yPLS(tk) For the model estimate, N is the number of individuals in the population.
Further, in step S2, performing variation, intersection and selection on the population in the differential evolution algorithm, specifically:
s21, carrying out variation operation on the initialized population; for the kth generation of population, randomly selecting 3 individuals from the population
Figure BDA0003071952840000022
Wherein p is1,p2，p3Is [1, N ]]And with individuals
Figure BDA0003071952840000023
Is not equal, each individual in the population is treated with the following formula
Figure BDA0003071952840000024
Performing mutation to generate variant individuals Vi k：
Figure BDA0003071952840000025
Wherein, F is the mutation probability;
s22, performing cross operation on the population, increasing the diversity of interference vectors, and specifically, performing cross operation on individuals
Figure BDA0003071952840000026
And step S21 of generating variant individuals Vi kThe following formula is operated by randomly generating a [0,1 ]]Random decimal between rand is compared with the cross probability CR, or [1, n ] is randomly generated]Random integer rand [1, n ] between]And J, J ∈ [1, n ]]Comparing to ensure that at least one component of the new individual is Vi kProvided thereby to generate a test subject
Figure BDA0003071952840000031
Wherein, among others,
Figure BDA0003071952840000032
Vi kis a matrix of N x N, and the matrix is a matrix of N x N,
Figure BDA0003071952840000033
is XkThe jth variable of the ith individual in (b),
Figure BDA0003071952840000034
is a VkThe jth variable of the ith individual in (b),
Figure BDA0003071952840000035
is UkJ variable of the ith individual:
Figure BDA0003071952840000036
s23, selecting operation is carried out, and
Figure BDA0003071952840000037
and
Figure BDA0003071952840000038
comparing the objective function values of (a) to determine the next generation members, only
Figure BDA0003071952840000039
Fitness ratio of
Figure BDA00030719528400000310
When the fitness of (2) is better, the user will
Figure BDA00030719528400000311
As a child, otherwise will
Figure BDA00030719528400000312
As next generation individuals, for each individual,
Figure BDA00030719528400000313
to be better than or equal to
Figure BDA00030719528400000314
Figure BDA00030719528400000315
Wherein f (-) is a fitness function
Figure BDA00030719528400000316
In the formula, yPLS(tk) Is an estimated value of the model;
s24, in the fitness function J not more than e or the evolution algebra k not less than NGThen, the differential evolution algorithm is iteratively terminated to obtain an optimal individual comprising a lag time τ as a global optimal solutioniAnd dynamic data length di(ii) a Otherwise, return to step S21 to continue the iteration.
Further, in step S3, selecting a corresponding input data set and output data set from the training data set, specifically: according to the obtained lag time tauiAnd dynamic data length diSelecting a lag time τ from the sampled data setiPreviously, the length is the dynamic data length diAs input variables of the PLS model:
si(t)＝[si(t-τi),si(t-τi-1),…,si(t-τi-di)]T
further, an input data set s (t) is determined based on each input variable determined by the above equation:
S(t)＝[s1(t),s2(t),…,si(t),…sm(t)]
wherein t is the sampling time, i is 1,2, …, m is the number of input variables;
by the input data set s (t), the output data set having the correspondence relationship.
Further, in step S1, the input variables in the input data set include 10 input variables of total water inflow of the slurry tank, liquid level adjustment of the first crystallizer, liquid levels of the first to fourth crystallizers, and pressures of the second to fifth crystallizers in the PTA refining process, and the average PTA particle size is used as an output variable of the model.
Further, in step S2, the lag time τ in the differential evolution algorithmiThe search range of (1) is set to [70,180min]Length of dynamic data diIs set to [0,120min ]]。
The invention has the beneficial effects that: according to the dynamic soft measurement method based on the differential evolution algorithm time delay estimation, the global optimal solution of the lag time and the dynamic data length is searched through the differential evolution algorithm, the corresponding input and output data set is selected according to the obtained lag time and the obtained dynamic data length, a dynamic soft measurement model is established, and the prediction precision of the model is improved by introducing the dynamic characteristics in the industrial production process into the model. The effectiveness and feasibility of the method are verified through simulation results.
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Fig. 1 is a flowchart illustration of a dynamic soft measurement method based on differential evolution algorithm delay estimation according to an embodiment of the present invention.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Examples
A dynamic soft measurement method based on differential evolution algorithm time delay estimation is used for predicting PTA average particle size in the PTA refining process, estimating time delay parameters through a differential evolution algorithm and obtaining the optimal lag time tauiAnd dynamic data length diAnd then according to the obtained optimal lag time tauiAnd dynamic data length diSelecting corresponding input data sets and output data sets, establishing a PLS model, and predicting the PTA average particle size by the established PLS model. As shown in fig. 1, specifically includes the following steps,
s1, initializing a population and parameters in the differential evolution algorithm, wherein the population comprises the time delay of an input variable, namely the lag time tauiAnd dynamic dataLength diThe parameters include maximum evolution algebra NGAnd the maximum error e allowed by the differential evolution algorithm model; and acquiring a training data set of the soft measurement model, wherein the training data set comprises an input data set and an output data set which have corresponding relations, and constructing a fitness function J by a partial least square method.
In one embodiment, the number of input variables of the input data set is preferably 10, and 10 input variables of the total water inflow of the slurry tank, the liquid level regulation of the first crystallizer, the liquid levels of the first to fourth crystallizers and the pressures of the second to fifth crystallizers in the PTA refining process are used as input variables in the input data set of the dynamic soft measurement model, and the PTA average particle size is used as an output variable of the model. Maximum evolution algebra NGThe population size is preferably 100, i.e., N is 100.
Time delay of input variable, i.e. lag time tauiAnd dynamic data length diInitialization is performed, specifically, N individuals are initialized randomly in a solution space, each individual consisting of an N-dimensional vector:
Figure BDA0003071952840000051
wherein
Figure BDA0003071952840000052
And each one of
Figure BDA0003071952840000053
Representing a solution to the problem. I.e. the initialization lag time tauiAnd dynamic data length diGenerating an initialization population of lag time and dynamic data length, each individual of the two populations
Figure BDA0003071952840000054
A set of lag times and dynamic data lengths are indicated.
In step S1, the fitness function constructed by the partial least squares method is:
Figure BDA0003071952840000055
wherein, y (t)k) Is tkOutput value of time course, yPLS(tk) Is tkThe output value of the time partial least squares model, N, is the size of the initialized population (i.e., the number of individuals in the population) in step S1.
S2, performing iteration including variation, intersection and selection on the population in the differential evolution algorithm, wherein the maximum error e is not more than the allowable fitness function J or the evolution algebra k is not less than the maximum evolution algebra NGTime-out, obtaining the lag time tau in the search range of the optimizationiAnd dynamic data length diThe global optimum solution of (2).
In the examples, the lag time τ in the Differential Evolution (DE) algorithmiThe search range for the optimization is preferably set to [70,180min ]]Length of dynamic data diThe search range for the optimization is preferably set to [0,120min]。
S21, carrying out mutation operation on the initialized population, assuming that the current generation is the kth generation population, and randomly selecting 3 individuals from the population
Figure BDA0003071952840000056
Wherein p is1,p2,p3Is [1, N ]]And with individuals
Figure BDA0003071952840000057
I in are not equal. For each individual in the population using the formula
Figure BDA0003071952840000058
Performing mutation to generate variant individuals Vi k，
Figure BDA0003071952840000059
Wherein F is the mutation probability. Preferably, the variation probability F is 0.1,
s22, performing cross operation on the population to increase the diversity of interference vectorsThe specific steps are to the individual
Figure BDA0003071952840000061
Vi kThe following formula is performed to randomly generate a [0,1 ] by rand]The random fraction therebetween is compared with the crossover probability CR (preferably CR ═ 0.3), or by rand [1, n ═ c]To produce [1, n]A random integer of (d) and j (j ∈ [1, n)]N-10 in the example) so as to ensure that at least one component of the new individual is represented by Vi kProvided thereby to generate a test subject
Figure BDA0003071952840000062
Wherein,
Figure BDA0003071952840000063
Vi kis a matrix of N x N, and the matrix is a matrix of N x N,
Figure BDA0003071952840000064
is XkThe jth variable of the ith individual in (b),
Figure BDA0003071952840000065
is a VkThe jth variable of the ith individual in (b),
Figure BDA0003071952840000066
is UkThe jth variable of the ith individual.
Figure BDA0003071952840000067
S23, selecting operation is carried out, and
Figure BDA0003071952840000068
and
Figure BDA0003071952840000069
and comparing the objective function values to determine the next generation member. Only is provided with
Figure BDA00030719528400000610
Fitness ratio of
Figure BDA00030719528400000611
When the fitness of (2) is better, the user will
Figure BDA00030719528400000612
As a child, otherwise will
Figure BDA00030719528400000613
As a next generation individual. For each of the individuals, the individual is presented with,
Figure BDA00030719528400000614
to be better than or equal to
Figure BDA00030719528400000615
Figure BDA00030719528400000616
Wherein f (-) is a fitness function
Figure BDA00030719528400000617
y(tk) Is tkOutput value of time course, yPLS(tk) Is tkAnd (4) output values of the time partial least square model.
S24, in the fitness function J not more than e or the evolution algebra k not less than NGThen, the differential evolution algorithm is iteratively terminated to obtain an optimal individual comprising a lag time τ as a global optimal solutioniAnd dynamic data length di(ii) a Otherwise, return to step S21 to continue the iteration. New solutions are generated through mutation, crossover and selection.
S3, obtaining the lag time tau according to the step S2iAnd dynamic data length d of input variableiSelecting corresponding input data set and output data set from training data set, and establishing the relationship between input data set and output data setThe partial least squares model (PLS) of (2) is used to predict the average particle size of PTA.
In step S3, a corresponding input data set and output data set are selected from the training data set, specifically,
according to the obtained lag time tauiAnd dynamic data length diSelecting a lag time τ from the sampled data setiPreviously, the length is the dynamic data length diAs input variables of the PLS model:
si(t)＝[si(t-τi),si(t-τi-1),…,si(t-τi-di)]T
further, an input data set s (t) is determined based on each input variable determined by the above equation:
S(t)＝[s1(t),s2(t),…,si(t),…sm(t)]
where t is the sampling time, i is 1,2, …, and m is the number of input variables.
The dynamic soft measurement modeling method based on the differential evolution algorithm time delay estimation uses a time series data block related to measurable variables in the PTA refining process as the input of a model, introduces the dynamic characteristics of the variables in the production process into the model, selects the optimal lag time and the optimal dynamic data length according to the differential evolution algorithm, selects a corresponding input and output data set according to the lag time and the optimal dynamic data length, establishes a dynamic soft measurement model, and predicts the PTA average particle size in the PTA refining process.
Compared with the dynamic soft measurement modeling method based on the differential evolution algorithm time delay estimation, the dynamic soft measurement modeling method based on the differential evolution algorithm time delay estimation adopts the differential evolution algorithm to estimate the time delay and converts the time delay estimation problem into the multidimensional nonlinear optimization problem, the differential evolution algorithm with the global search capability is used for solving to obtain the optimal time delay and the optimal dynamic data length, the problem of time delay in the actual industrial process is solved, and the prediction accuracy of the soft measurement model is further improved.
According to the dynamic soft measurement modeling method based on the differential evolution algorithm time delay estimation, a time series data block related to measurable variables in the PTA refining process is used as the input of a model, and the average particle size of the PTA is used as the output of the model. Firstly, initializing a population and each parameter in a differential evolution algorithm, constructing a proper fitness function by a partial least square method, carrying out variation, intersection and selection on the population, searching the time delay of an input variable and the global optimal solution of the dynamic data length of the input variable, selecting a corresponding input and output data set according to the obtained optimal solution, establishing a dynamic soft measurement model, and predicting the PTA average particle size. The invention introduces the dynamic characteristics in the industrial production process into the model, and improves the prediction precision of the model.
The effectiveness of the present invention was verified by establishing a PLS model for comparison by a comparative example method (dynamic data length does not exist), an example method (dynamic data length exists).
Table 1 comparison of the results of the example process with the prior art process model
Figure BDA0003071952840000071
Figure BDA0003071952840000081
Table 1 shows the average relative error (MRE) of the dynamic soft measurement model established for the comparative example method and the example method. It can be seen from table 1 that the training error of the comparative example method is 0.0329 and the testing error is 0.0407 due to the absence of dynamic data length. The dynamic data length of the embodiment method exists, the training error of the soft measurement model is 0.0150, and the testing error is 0.0273. Therefore, the prediction accuracy and generalization capability of the soft measurement model established by the embodiment method are better.
The invention has various embodiments, and all technical solutions formed by adopting equivalent transformation or equivalent transformation are within the protection scope of the invention.

Claims (6)

1. A dynamic soft measurement method based on differential evolution algorithm time delay estimation is used for predicting PTA average particle size in the PTA refining process, and is characterized in that: estimating time delay parameters through a differential evolution algorithm to obtain the optimal lag time tauiAnd dynamic data length diAnd then according to the obtained optimal lag time tauiAnd dynamic data length diSelecting corresponding input data sets and output data sets, establishing a PLS model, and predicting the PTA average particle size by the established PLS model, wherein the method comprises the following steps:
s1, initializing a population and parameters in the differential evolution algorithm, wherein the population comprises the time delay of an input variable, namely the lag time tauiAnd dynamic data length diThe parameters include maximum evolution algebra NGAnd the maximum error e allowed by the differential evolution algorithm model; acquiring a training data set, wherein the training data set comprises an input data set and an output data set which have corresponding relations, and constructing a fitness function J by a partial least square method;
s2, performing iteration including variation, intersection and selection on the population in the differential evolution algorithm, wherein the maximum error e is not more than the allowable fitness function J or the evolution algebra k is not less than the maximum evolution algebra NGTime-out, obtaining the lag time tau in the search range of the optimizationiAnd dynamic data length diThe global optimal solution of (a);
s3, obtaining the lag time tau according to the step S2iAnd dynamic data length d of input variableiSelecting a corresponding input data set and an output data set from the training data set, establishing a partial least square model (PLS) between the input data set and the output data set, and predicting the PTA average particle size through the PLS model.
2. The dynamic soft measurement method based on the differential evolution algorithm time delay estimation as claimed in claim 1, characterized in that: in step S1, the fitness function constructed by the partial least squares method is:
Figure FDA0003071952830000011
wherein, y (t)k) Is tkOutput value of time course, yPLS(tk) For the model estimate, N is the number of individuals in the population.
3. The differential evolution algorithm-based dynamic soft measurement method for time delay estimation as claimed in claim 1, characterized in that: in step S2, performing variation, crossover and selection on the population in the differential evolution algorithm, specifically:
s21, carrying out variation operation on the initialized population; for the kth generation of population, randomly selecting 3 individuals from the population
Figure FDA0003071952830000012
Wherein p is1,p2,p3Is [1, N ]]And with individuals
Figure FDA0003071952830000013
Is not equal, each individual in the population is treated with the following formula
Figure FDA0003071952830000014
Performing mutation to generate variant individuals Vi k：
Figure FDA0003071952830000021
Wherein, F is the mutation probability;
s22, performing cross operation on the population, increasing the diversity of interference vectors, and specifically, performing cross operation on individuals
Figure FDA00030719528300000218
And step S21 of generating variant individuals Vi kThe following formula is operated by randomly generating a [0,1 ]]Random decimal betweenrand is compared with the cross probability CR, or randomly generated [1, n ]]Random integer rand [1, n ] between]And J, J ∈ [1, n ]]Comparing to ensure that at least one component of the new individual is Vi kProvided thereby to generate a test subject
Figure FDA0003071952830000022
Wherein,
Figure FDA0003071952830000023
Vi kis a matrix of N x N, and the matrix is a matrix of N x N,
Figure FDA0003071952830000024
is XkThe jth variable of the ith individual in (b),
Figure FDA0003071952830000025
is a VkThe jth variable of the ith individual in (b),
Figure FDA0003071952830000026
is UkJ variable of the ith individual:
Figure FDA0003071952830000027
s23, selecting operation is carried out, and
Figure FDA0003071952830000028
and
Figure FDA0003071952830000029
comparing the objective function values of (a) to determine the next generation members, only
Figure FDA00030719528300000210
Fitness ratio of
Figure FDA00030719528300000211
When the fitness of (2) is better, the user will
Figure FDA00030719528300000212
As a child, otherwise will
Figure FDA00030719528300000213
As next generation individuals, for each individual,
Figure FDA00030719528300000214
to be better than or equal to
Figure FDA00030719528300000215
Figure FDA00030719528300000216
Wherein f (-) is a fitness function
Figure FDA00030719528300000217
In the formula, yPLS(tk) Is an estimated value of the model;
s24, in the fitness function J not more than e or the evolution algebra k not less than NGThen, the differential evolution algorithm is iteratively terminated to obtain an optimal individual comprising a lag time τ as a global optimal solutioniAnd dynamic data length di(ii) a Otherwise, return to step S21 to continue the iteration.
4. The dynamic soft measurement method based on differential evolution algorithm time delay estimation according to any one of claims 1 to 3, characterized in that: in step S3, selecting a corresponding input data set and output data set from the training data set, specifically: according to the obtained lag time tauiAnd dynamic data length diSelecting a lag time τ from the sampled data setiPreviously, the length is the dynamic data length diAs an input to the PLS modelEntering variables:
si(t)＝[si(t-τi),si(t-τi-1),…,si(t-τi-di)]T
further, an input data set s (t) is determined based on each input variable determined by the above equation:
S(t)＝[s1(t),s2(t),…,si(t),…sm(t)]
wherein t is the sampling time, i is 1,2, …, m is the number of input variables;
by the input data set s (t), the output data set having the correspondence relationship.
5. The dynamic soft measurement method based on differential evolution algorithm time delay estimation according to any one of claims 1 to 3, characterized in that: in step S1, the input variables in the input data set include total water inflow of the slurry tank, liquid level adjustment of the first crystallizer, liquid levels of the first to fourth crystallizers, and pressures of the second to fifth crystallizers in the PTA refining process, and the PTA average particle size is used as the output variable of the output data set.
6. The dynamic soft measurement method based on differential evolution algorithm time delay estimation according to any one of claims 1 to 3, characterized in that: in step S2, the lag time τ in the differential evolution algorithmiThe search range of (1) is set to [70,180min]Length of dynamic data diIs set to [0,120min ]]。
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CN117740632A (en) * 2024-02-21 2024-03-22 江苏嘉通能源有限公司 PTA particle size dynamic soft measurement method based on differential evolution algorithm

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CN115796269A (en) * 2023-02-09 2023-03-14 中国人民解放军国防科技大学 Atom cooling parameter online optimization method and device based on artificial neural network
CN117740632A (en) * 2024-02-21 2024-03-22 江苏嘉通能源有限公司 PTA particle size dynamic soft measurement method based on differential evolution algorithm
CN117740632B (en) * 2024-02-21 2024-04-26 江苏嘉通能源有限公司 PTA particle size dynamic soft measurement method based on differential evolution algorithm

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