CN111797540A - Timely online Gaussian process regression model method for crystal size distribution in crystallization process - Google Patents

Timely online Gaussian process regression model method for crystal size distribution in crystallization process Download PDF

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CN111797540A
CN111797540A CN202010692708.3A CN202010692708A CN111797540A CN 111797540 A CN111797540 A CN 111797540A CN 202010692708 A CN202010692708 A CN 202010692708A CN 111797540 A CN111797540 A CN 111797540A
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杨克允
肖凡
娄维尧
马正阳
沈伟健
林韩波
赵世超
蔡姚杰
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Abstract

A timely online Gaussian process regression model method for crystal size distribution in a crystallization process belongs to the technical field of industrial distributed product prediction. It comprises the following steps: 1. extracting characteristics of a typical batch crystallization process, wherein the extracted characteristic parameters comprise time, temperature and seed length; 2. and establishing a local online Gaussian process regression model for the extracted features for training and evaluation, and analyzing and predicting the data by adopting a GPR (general purpose algorithm) and JIT (just in time) strategy set. The method extracts features from simulation data, establishes a local online Gaussian process regression model, evaluates the training model, integrates a JIT (just-in-time) strategy on the basis of the Gaussian process regression model, enables the result to better accord with an actual label value, and finally can be applied to the crystal size distribution prediction process of the industrial crystallization process to provide certain guiding significance.

Description

Timely online Gaussian process regression model method for crystal size distribution in crystallization process
Technical Field
The invention belongs to the technical field of industrial distributed product prediction, and particularly relates to a timely online Gaussian process regression model method for crystal size distribution in a crystallization process.
Background
Currently, due to the competitive market in the chemical industry, the demand for product diversification is growing, requiring shorter product life cycles and more stringent performance specifications, and furthermore, in certain chemical processes, the output product of interest has a distributed nature rather than a single value. In the crystallization process, the Crystal Size Distribution (CSD) is critical in producing high quality products and determining the efficiency of downstream operations such as filtration and washing.
In order to model product quality in those chemical processes with distributed output, many previous studies have focused on a single collective value of distributed quality variables. For example, melt index is generally considered to be the product quality in a polymerization process, but recent studies have shown that economic benefits can be further improved by adjusting the distributed output, as it can significantly affect product quality and process efficiency. Typically, such chemical processes are non-gaussian and may also exhibit strong non-linearity, in which case the output is a probabilistic behavior that adequately characterizes the random output of the process. Instead, the goal of the controller design should be to track the output of the profile for the desired profile shape, so obtaining reliable and accurate distributed output information (i.e., product quality) online is critical to further develop a good control scheme.
However, on-line CSD measurement in crystallization processes remains unsolved, and it is often difficult to build a comprehensive first principles model for these complex processes with distributed outputs despite the tremendous efforts of many researchers. Furthermore, a set of partial differential equations for distributed output is valid only for white noise inputs. Thus, the implementation of distributed output control for these complex processes remains challenging.
Currently, data-driven modeling methods have become a useful alternative to predicting product quality online in time in chemical processes when there is no online analyzer. B-splines and other Neural Networks (NN) are currently popular methods for processing distributed output approximations. However, for a given modeling task, the determination of the network topology and the generalization capability of the NN remain unresolved, and the NN approach typically requires a large number of training examples.
Currently, Gaussian Process Regression (GPR) and other nuclear learning (KL) methods have been increasingly used in chemical process modeling. The results obtained show that GPR is a promising alternative for non-linear process modeling, especially in cases where training data is limited. One major advantage of GPR over B-splines and NN-based models is that it can derive its uncertainty (i.e. give a variance interpretation) for generalized errors.
However, since the gaussian process regression model is a global prediction for data, the global nonlinear model is difficult to work well in the entire complex distributed process, and especially under different conditions, there will not be enough data to train the model in the entire input space. Thus, instead of constructing a globally distributed model, the local modeling approach may divide the process area into small multiple regions and provide better prediction performance in certain operating regions.
Disclosure of Invention
In view of the above problems in the prior art, the present invention provides a local online gaussian process regression model and a prediction method for crystal size distribution in a crystallization process, which extract relevant features from the crystal size distribution in the crystallization process to realize accurate prediction of CSD.
The invention provides the following technical scheme: the timely online Gaussian process regression model method for the crystal size distribution in the crystallization process is characterized by comprising the following specific steps of:
1) extracting characteristics of a typical batch crystallization process, and specifically comprising the following steps:
1.1) obtaining related parameter data in the crystallization process, and repeatedly generating N groups of data;
1.2), the time interval in each group of data is within the range of 0-10000s, N1 time points are taken at equal intervals, N1 temperature data are taken in each group of data, and N2 points are taken at equal intervals in the range of 0-0.0015m for the length of the crystal seeds in each group of data;
2) establishing a local online Gaussian process regression model for the extracted features for training and evaluation, namely analyzing and predicting data by adopting a GPR (general purpose algorithm) and JIT (just in time) strategy set and inquiring the distribution shape
Figure BDA0002589864180000031
Wherein x isq,iDenotes the ith query sample, T denotes the transpose of the matrix, yiA label representing the ith query sample,
Figure BDA0002589864180000032
representing the input of the ith query sample, NqRepresenting the total number of query samples; establishing an online prediction model, which comprises the following specific steps:
2.1), based on similarity criteria, selecting relevant input samples to build a similarity set S in a database Sqi；
2.2), using the relevant dataset SqiConstructing a timely online Gaussian process regression model fJGPR(xqi)；
2.3) obtaining a predicted value fJGPR(xqi) Then discarding the in-time online Gaussian process regression model fJGPR(xqi) To save memory.
The timely online Gaussian process regression model method for the crystal size distribution in the crystallization process is characterized in that in the step 1.2, the time point data is selected according to the following formula:
batch_time＝160*60*(1+0.001*randn)
tt＝linspace(0.001，batch_time，N1)
where, batch _ time represents the maximum value of the reaction time, randn represents the normal distribution noise generated randomly, line represents the interval range [0.001, batch _ time ] and is equally divided into N1 parts, and tt represents the generated time point data.
The timely online Gaussian process regression model method for crystal size distribution in the crystallization process is characterized in that in the step 1.2, temperature data are selected according to the following formula:
TT＝32-tt/batch_time*(32-22)*(1+0.001*randn)
where TT represents the N1 temperature data generated.
The timely online Gaussian process regression model method for crystal size distribution in the crystallization process is characterized in that in the step 1.2, length points of 0.0007m are selected and removed from the length of the crystallization seeds.
The method for on-line Gaussian process regression model of crystal size distribution in crystallization process is characterized in that in the step 2.2, a relevant data set S is usedqiThe similarity S between the data sets is evaluated by adopting an evaluation index of a similarity distance based on Euclidean distanceqiPerforming descending arrangement, thereby obtaining the required training set again; similarity between data sets
Figure BDA0002589864180000041
The following is defined between the data sets:
Figure BDA0002589864180000042
wherein
Figure BDA0002589864180000043
Is dataSet xq,iAnd xk,jThe similarity of the distance between the two groups,
Figure BDA0002589864180000044
is between 0 and 1, and when
Figure BDA0002589864180000045
The smaller the Euclidean distance, i.e. x, when approaching 1q,iThe closer to xk,jThen S isqiThe higher the priority of, then to all
Figure BDA0002589864180000046
Performing descending order to obtain required training set, modeling the training set with Gaussian process regression model, and constructing timely online Gaussian process regression model fJGPR(xqi)。
The method for the timely online Gaussian process regression model of the crystal size distribution in the crystallization process is characterized in that in the step 2.3, x is usedq,iInputting the model trained in the step 2.2 to obtain a predicted value fJGPR(xqi)。
By adopting the technology, compared with the prior art, the invention has the following beneficial effects:
the method extracts features from simulation data, establishes a local online Gaussian process regression model, evaluates the training model, integrates a JIT (just-in-time) strategy on the basis of the Gaussian process regression model, enables the result to better accord with an actual label value, and finally can be applied to the crystal size distribution prediction process of the industrial crystallization process to provide certain guiding significance.
Drawings
FIG. 1 is a graph showing true values of raw data of a regression model of a Gaussian process;
FIG. 2 is a graph showing the predicted values of a regression model for a Gaussian process;
FIG. 3 is a graph showing the true values of the raw data in the local online Gaussian process;
FIG. 4 is a graph showing the predicted values of the local online Gaussian process regression model.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
On the contrary, the invention is intended to cover alternatives, modifications, equivalents and alternatives which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. It will be apparent to one skilled in the art that the present invention may be practiced without these specific details.
Example 1:
1. the method comprises the following specific steps of extracting characteristics of a typical batch crystallization process:
1.1, obtaining related parameter data in the crystallization process, and repeatedly generating N groups of data;
1.2, the time interval in each group of data is within the range of 0-10000s, N1 time points are taken at equal intervals, N1 temperature data are taken in each group of data, and N2 points are taken at equal intervals from the range of 0-0.0015m (0.0007 m length points are removed) for the length of the crystal seeds in each group of data.
The time point data is selected by adopting the following formula:
batch_time＝160*60*(1+0.001*randn)
tt＝linspace(0.001，batch_time，N1)
wherein, batch _ time represents the maximum value of the reaction time, randn represents the normal distribution noise generated randomly, line represents the interval range [0.001, batch _ time ] and is equally divided into N1 parts, and tt represents the generated time point data;
the temperature data was selected using the following formula:
TT＝32-tt/batch_time*(32-22)*(1+0.001*randn)
where TT represents the N1 temperature data generated.
2. Establishing a local online Gaussian process regression model for the extracted features for training and evaluation, analyzing and predicting data by adopting a Gaussian Process Regression (GPR) and just-in-time (JIT) strategy set, and inquiring the distribution shape
Figure BDA0002589864180000061
Wherein x isq,iDenotes the ith query sample, T denotes the transpose of the matrix, yiA label representing the ith query sample,
Figure BDA0002589864180000062
representing the input of the ith query sample, NqRepresenting the total number of query samples; the three main steps for establishing an online prediction model are as follows:
2.1 selecting related samples to build a similarity set S in a database S based on similarity criteriaqi；
2.2 use of the relevant dataset SqiThe similarity S between the data sets is evaluated by adopting an evaluation index of a similarity distance based on Euclidean distanceqiPerforming descending arrangement, thereby obtaining the required training set again; similarity between datasets (SF)
Figure BDA0002589864180000063
The following is defined between the data sets:
Figure BDA0002589864180000064
wherein
Figure BDA0002589864180000065
Is a data set xq,iAnd xk,jThe similarity of the distance between the two groups,
Figure BDA0002589864180000066
is between 0 and 1, and when
Figure BDA0002589864180000067
Near 1 hour, Europe and NeiThe smaller the distance, i.e. xq,iThe closer to xk,jThen S isqiThe higher the priority of (A), to all
Figure BDA0002589864180000068
Performing descending order to obtain the required training set, modeling the training set by using a Gaussian Process Regression (GPR) model, and constructing a timely online Gaussian process regression (JGPR) model fJGPR(xqi)；
2.3, mixing xq,iInputting the model trained in the step 2.2 to obtain a predicted value fJGPR(xqi) Then discard the just-in-time online Gaussian process regression (JGPR) model fJGPR(xqi) To save memory.
Example 2:
the characteristic extraction step for the typical batch crystallization process in the embodiment 1 is repeated, the selected characteristics are used as input, the crystal growth length under three conditions is used as output, a local online Gaussian Process Regression (GPR) model is established and trained, the model performance is evaluated by adopting relative root prediction standard deviation (RPV), and the smaller the value is, the smaller the uncertainty of the model is.
Figure BDA0002589864180000071
Wherein sigmayiExpressed as a function of the predicted variance(s),
Figure BDA0002589864180000072
is a predicted value.
The attached figures 1 and 2 are comparison graphs of a GPR model predicted value and an original data real value, the figures 3 and 4 are comparison graphs of a JGPR model predicted value and an original data real value, and the table 1 is performance evaluation of a JGPR model established by the characteristics.
TABLE 1 model prediction Performance evaluation
Figure BDA0002589864180000073
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (6)

1. The timely online Gaussian process regression model method for the crystal size distribution in the crystallization process is characterized by comprising the following specific steps of:
1) extracting characteristics of a typical batch crystallization process, and specifically comprising the following steps:
1.1) obtaining related parameter data in the crystallization process, and repeatedly generating N groups of data;
1.2), the time interval in each group of data is within the range of 0-10000s, N1 time points are taken at equal intervals, N1 temperature data are taken in each group of data, and N2 points are taken at equal intervals in the range of 0-0.0015m for the length of the crystal seeds in each group of data;
2) establishing a local online Gaussian process regression model for the extracted features for training and evaluation, namely analyzing and predicting data by adopting a GPR (general purpose algorithm) and JIT (just in time) strategy set and inquiring the distribution shape
Figure FDA0002589864170000011
Wherein x isq,iDenotes the ith query sample, T denotes the transpose of the matrix, yiA label representing the ith query sample,
Figure FDA0002589864170000012
representing the input of the ith query sample, NqRepresenting the total number of query samples; establishing an online prediction model, which comprises the following specific steps:
2.1), based on similarity criteria, selecting relevant input samples to build a similarity set S in a database Sqi；
2.2), using the relevant dataset SqiConstructing a timely online Gaussian process regression model fJGPR(xqi)；
2.3) obtainingObtaining a predicted value fJGPR(xqi) Then discarding the in-time online Gaussian process regression model fJGPR(xqi) To save memory.
2. The method of claim 1, wherein in step 1.2, the time point data is selected according to the following formula:
batch_time＝160*60*(1+0.001*randn)
tt＝linspace(0.001，batch_time，N1)
where, batch _ time represents the maximum value of the reaction time, randn represents the normal distribution noise generated randomly, line represents the interval range [0.001, batch _ time ] and is equally divided into N1 parts, and tt represents the generated time point data.
3. The method of claim 1, wherein in step 1.2, the temperature data is selected according to the following formula:
TT＝32-tt/batch_time*(32-22)*(1+0.001*randn)
where TT represents the N1 temperature data generated.
4. The method of claim 1, wherein in step 1.2, the length of the seed is selected to exclude the length points of 0.0007 m.
5. The method of claim 1, wherein in step 2.2, the correlation data set S is usedqiThe similarity S between the data sets is evaluated by adopting an evaluation index of a similarity distance based on Euclidean distanceqiPerforming descending arrangement, thereby obtaining the required training set again; similarity between data sets
Figure FDA0002589864170000021
The following is defined between the data sets:
Figure FDA0002589864170000022
wherein
Figure FDA0002589864170000023
Is a data set xq,iAnd xk,jThe similarity of the distance between the two groups,
Figure FDA0002589864170000024
is between 0 and 1, and when
Figure FDA0002589864170000025
The smaller the Euclidean distance, i.e. x, when approaching 1q,iThe closer to xk,jThen S isqiThe higher the priority of, then to all
Figure FDA0002589864170000026
Performing descending order to obtain required training set, modeling the training set with Gaussian process regression model, and constructing timely online Gaussian process regression model fJGPR(xqi)。
6. The method of claim 1, wherein in step 2.3, x is calculated by using a time-in-time gaussian process regression model of crystal size distribution during crystallizationq,iInputting the model trained in the step 2.2 to obtain a predicted value fJGPR(xqi)。
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