CN108388218B - Correction self-adaptive batch process optimization method based on latent variable process migration model - Google Patents

Correction self-adaptive batch process optimization method based on latent variable process migration model Download PDF

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CN108388218B
CN108388218B CN201810126743.1A CN201810126743A CN108388218B CN 108388218 B CN108388218 B CN 108388218B CN 201810126743 A CN201810126743 A CN 201810126743A CN 108388218 B CN108388218 B CN 108388218B
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褚菲
沈建
王洁
程相
张道明
常俊林
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China University of Mining and Technology CUMT
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Abstract

The invention discloses a correction self-adaptive batch process optimization method based on a latent variable process migration model, which comprises the following steps: acquiring input data and output data of an old batch process and a new batch process; establishing a latent variable process migration model according to input and output data of the old batch process and the new batch process; when a new batch process is used for production, acquiring the predicted output data of the current batch according to the latent variable process migration model and the optimal input data of the current batch, and acquiring the optimal input data of the next batch according to the latent variable process migration model and the input data of the current batch; updating the latent variable process migration model according to the optimal input data and the actual output data of the current batch; judging whether the stability of the new batch process meets the requirement or not according to the predicted output data and the actual output data of a plurality of batches in the new batch process; and if the stability of the new batch process meets the requirement, removing partial data from the input data and the output data of the old batch process.

Description

Correction self-adaptive batch process optimization method based on latent variable process migration model
Technical Field
The invention relates to the technical field of batch process optimization control in an industrial production process, in particular to a correction self-adaptive batch process optimization method based on a latent variable process migration model.
Background
In industrial production, batch process is also called batch production process, and is widely applied to production and manufacturing of products such as food, chemical industry, medicines and the like, and plays a very important role in national economy. With the development of society, the requirements of people on product quality, production cost, environmental protection and the like are continuously improved, and the quality control and optimization of batch processes play more and more important roles in the aspects of product production, environmental protection and the like. Therefore, it is necessary to research and provide an advanced batch process quality optimization method to improve the comprehensive economic benefit of enterprises.
Taking the production of cobalt oxalate crystals as an example, cobalt oxalate is an important intermediate product in the production process of metal cobalt, the quality of cobalt oxalate directly affects the crystal size of metal cobalt powder, and the problems of filter screen blockage, slow drying time, low production efficiency and the like can be caused by too small crystal size of cobalt oxalate. Therefore, in the production process of cobalt oxalate crystallization, the method has important practical significance for improving the production efficiency by optimizing the crystal size of the cobalt oxalate crystallization.
In the optimization of batch process, the optimization method based on mechanism model is an important research direction, and the method can use the prior knowledge in the control and optimization strategy. However, in many cases, it takes a lot of time and effort to establish a mechanism model of the production process, which in turn leads to an increase in production costs. In addition, there are some assumptions in the mechanistic model that may degrade or even exceed the normal level of optimization performance if the assumed mechanistic relationships are invalid. To reduce the requirements for mechanistic models, some researchers have focused on hybrid models, which consist of simplified mechanistic models and data-driven models. However, these hybrid model-based methods are still only applicable to processes for which the mathematical mechanism model is known, and it remains a challenge to use these methods for completely unknown or new production processes. Data-driven modeling and optimization control methods have attracted worldwide attention over the past few decades and have been successfully applied to a variety of complex industrial processes. Latent variable techniques have been widely used, particularly in the fields of modeling and control optimization. However, the existing data-driven method needs to accumulate enough process data, and the data of one process can only be used on the corresponding object, even if two similar processes are used, the data cannot be mixed. When the data volume of a brand-new batch process is insufficient, data can only be accumulated by repeating a large number of experiments, so that the modeling and control optimization efficiency is low, and the product quality of the batch process which is newly put into production can not be ensured to meet the requirement.
Disclosure of Invention
The invention aims to solve the technical problem that quality optimization cannot be implemented due to the fact that a Process Model cannot be accurately established due to less data in a new batch Process at least to a certain extent, and therefore the invention aims to provide a modified adaptive batch Process optimization method based on a Latent Variable Process Transfer Model (LV-PTM), which can quickly establish a new batch Process Model, effectively implement quality optimization, and has high quality optimization effect and efficiency, thereby improving the comprehensive economic benefit of enterprises.
In order to achieve the above object, an embodiment of the present invention provides a modified adaptive batch process optimization method based on a latent variable process migration model, including the following steps: acquiring input data and output data of an old batch process, and acquiring input data and output data of a new batch process; establishing a latent variable process migration model according to the input data and the output data of the old batch process and the input data and the output data of the new batch process; when the new batch process is used for production, acquiring the predicted output data of the current batch according to the latent variable process migration model and the optimal input data of the current batch, and acquiring the optimal input data of the next batch according to the latent variable process migration model and the input data of the current batch; updating the latent variable process migration model according to the optimal input data and the actual output data of the current batch; judging whether the stability of the new batch process meets the requirement or not according to the predicted output data and the actual output data of a plurality of batches in the new batch process; and if the stability of the new batch process meets the requirement, removing partial data from the input data and the output data of the old batch process.
According to the correcting self-adaptive batch process optimization method based on the latent variable process migration model, the latent variable process migration model is established by using the data of the new and old batch processes, the problem that quality optimization cannot be implemented due to the fact that the process model cannot be accurately established because of less data in the new batch process is effectively solved, and the purposes of quickly establishing the new batch process model and effectively implementing the quality optimization are achieved; by means of data elimination of the old batch process and continuous updating of the model, the quality optimization effect of the new batch process is continuously improved, the efficiency of quality optimization of modeling of the new batch process with insufficient data is greatly improved, and the comprehensive economic benefit of an enterprise is improved.
In addition, the modified adaptive batch process optimization method based on the latent variable process migration model according to the above embodiment of the present invention may further have the following additional technical features:
further, establishing a latent variable process migration model according to the input data and the output data of the old batch process and the input data and the output data of the new batch process, specifically comprising: obtaining input data matrix X obtained by expanding the input data of the old batch process and the input data of the new batch process according to the batch directiona、XbAnd obtaining the corresponding output data matrix Y of the old batch process and the new batch processa、YbWherein X isa、XbThe element in (1) is an operation variable, Ya、YbWherein the element is a product quality variable, Xa∈RM×i、Xb∈RN×j、Ya∈RM×m、Yb∈RN×mM, N is the number of samples of the old batch process and the new batch process respectively, i and j are the number of operation variables of the old batch process and the new batch process respectively, and m is the number of quality variables; for the input data matrix Xa、XbAnd said output data matrix Ya、YbAnd carrying out standardization processing to establish the latent variable process migration model.
Further, for the input data matrix Xa、XbAnd said output data matrix Ya、YbPerforming a normalization process to establish the latent variable process migration model, including:
a) respectively adding Ya、YbIs assigned to ua、ubWherein u isa、ubRespectively representing the score vector of the output data matrix of the old batch process and the score vector of the output data matrix of the new batch process;
b) mixing Xa、XbReturn to ua、ubTo calculate the regression coefficient wa、wbNamely:
wa＝Xa Tua(ua Tua)-1,wb＝Xb Tub(ub Tub)-1；
c) normalizing said regression coefficient wa、wbNamely:
Figure GDA0002467143210000041
d) will unite the output matrices
Figure GDA0002467143210000042
Regression to the Joint score vector tJTo obtain YJIs given by the joint load vector qJNamely:
qJ＝YJ TtJ(tJ TtJ)-1；
e) will Ya、YbReturn to qJTo recalculate ua、ubAnd through and ua、ubAre compared to determine ua、ubIf not, using the recalculated ua、ubAnd returning to step b;
f) if it converges, then X is calculateda、XbLoad vector p ofa、pb：
pa＝Xa Tta(ta Tta)-1、pb＝Xb Ttb(tb Ttb)-1，
Wherein, ta、tbThe output data matrix X of the current old batch process and the output data matrix X of the new batch process are respectivelya、XbA score vector of (a);
g) according to Xa＝Xa-tapa T、Xb＝Xb-tbpb TTo Xa、XbUpdating, then returning to the step a to extract the next principal component, and repeating the steps until the principal components with the preset number are extracted;
h) obtaining an input data matrix X for the new batch processbCorresponding load matrix Pb＝[pb1，…，pbA]A regression coefficient matrix Wb＝[wb1,...,wbA]And a joint output matrix YJCorresponding load matrix QJ＝[qJ1,...,qJA]；
i) Obtaining the latent variable process migration model:
Figure GDA0002467143210000051
wherein the content of the first and second substances,
Figure GDA0002467143210000052
for predicting the output data, xnewIs new input data.
Further, acquiring the optimal input data of the next batch according to the latent variable process migration model and the input data of the current batch, specifically comprising:
according to the formula
Figure GDA0002467143210000053
And formula
Figure GDA0002467143210000054
Calculating a gradient of the predicted output data of the current batch and the actual output data of the current batch, wherein σyAs standard deviation of the mass variable, σuIs the standard deviation of the input variables and,
Figure GDA0002467143210000055
is a matrix of regression coefficients, Δ is the incremental sign, x(k)For the optimal input data of the current batch, x(k-1)The optimal input data of the previous batch is obtained; solving correction-based latent variable process migrationThe optimization problem of the model prediction value is obtained by the following formula, and the optimal input data x of the next batch is obtained(k+1)，
Figure GDA0002467143210000056
Wherein the content of the first and second substances,
Figure GDA0002467143210000057
for normalized input data of the current batch, T is a joint score matrix, cpfThe threshold, which is the input data, is a constant calculated from historical data,
Figure GDA0002467143210000058
for the linearly corrected predicted output data of the current lot,
Figure GDA0002467143210000059
in order to be an index of the performance of the object,
Figure GDA00024671432100000510
for constraints containing input variables and output variables,
Figure GDA0002467143210000061
a regression coefficient vector for the kth batch predictor; judging whether the norm of the difference between the input data of the current batch and the obtained optimal input data of the next batch is smaller than a preset threshold value or not; if the current batch of input data is smaller than the preset threshold, taking the current batch of input data as the optimal input data of the next batch; if not less than the preset threshold, according to the formula x(k+1)＝(I-K)x(k)+Kx(k+1)+g·ρ(k+1)Generate new next lot of optimal input data x(k+1)And taking the new next batch of optimal input data as the next batch of optimal input data, wherein I is an N-order identity matrix
Figure GDA0002467143210000062
Is a diagonal gain matrix, p(k+1)For the excitation signal, g is an amplitude selected according to the magnitude of the input data matrix elements.
Further, updating the latent variable process migration model according to the optimal input data and the actual output data of the current batch, specifically comprising: according to the optimal input data and the actual output data x of the current batch(k)、y(k)Updating the input data matrix and the output data matrix X of the new batch processb、Yb：
Figure GDA0002467143210000063
According to the updated data Xb(k)、Yb(k)And establishing a new latent variable process migration model.
The method comprises the steps of obtaining predicted output data and actual output data of H batches, selecting a preset confidence level to calculate a confidence interval, calculating the number of batches with prediction errors in the confidence interval, and judging that the stability of the new batch process meets requirements if M continuous batches are in the confidence interval, wherein H is the window width, and M is not more than H.
Preferably, M/H > 2/3.
Further, the removing of partial data from the input data and the output data of the old batch process specifically includes: acquiring the similarity between the input data of the new batch process and the input data of the old batch process; and sorting the batches in the old batch process according to the sequence of the similarity from small to large, and removing the batches in the old batch process according to the sorting.
Further, the similarity is calculated by the following formula:
Figure GDA0002467143210000071
Figure GDA0002467143210000072
wherein | | represents the euclidean distance,
Figure GDA0002467143210000073
is the average of the input data for the new batch process,
Figure GDA0002467143210000074
the euclidean distance between the input data for the old batch process and the input data for the new batch process,
Figure GDA0002467143210000075
is the similarity.
Drawings
FIG. 1 is a flow diagram of a modified adaptive batch process optimization method based on a latent variable process migration model according to an embodiment of the present invention;
FIG. 2 is a flow diagram of a modified adaptive batch process optimization method based on latent variable process migration models, according to an embodiment of the present invention;
FIG. 3 is a schematic view of a production apparatus and a production process of cobalt oxalate crystals according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating a comparison of latent variable process migration model predicted values and partial least squares method predicted values according to one embodiment of the present invention;
FIG. 5 is a diagram of the relative error between the latent variable process migration model predicted value and the partial least squares method predicted value, according to one embodiment of the present invention;
FIG. 6 is a diagram illustrating the quality optimization results of a latent variable process migration model and a partial least squares method without eliminating data according to an embodiment of the present invention;
FIG. 7 is a diagram illustrating the quality optimization results of a latent variable process migration model when data is culled, according to an embodiment of the invention;
FIG. 8 is a T of an optimal trajectory according to one embodiment of the present invention2A schematic of the statistics;
FIG. 9 is a graph of the trend of the residual between actual measured and predicted values as a function of batch run, according to one embodiment of the present invention;
FIG. 10 is a diagram of optimizing trajectory changes according to one embodiment of the present invention;
fig. 11 is a schematic diagram illustrating a variation of the ammonium oxalate supply according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The following describes a modified adaptive batch process optimization method based on a latent variable process migration model according to an embodiment of the present invention with reference to the accompanying drawings.
The invention provides a correcting self-adaptive batch process optimization method based on a latent variable process migration model, which is used for optimizing the product quality of a batch process, and particularly relates to a correcting self-adaptive batch process quality optimization method based on a latent variable process migration model.
FIG. 1 is a flow chart of a modified adaptive batch process optimization method based on a latent variable process migration model according to an embodiment of the present invention.
As shown in fig. 1, the modified adaptive batch process optimization method based on latent variable process migration model according to the embodiment of the present invention includes the following steps:
s1, the input data and the output data of the old batch process are acquired, and the input data and the output data of the new batch process are acquired.
In the actual production process, there are some batch production processes, although their production sites, production parameters or production scales are different, they produce the same or the same products belonging to a series, and although there are differences in the production processes, the physicochemical principles utilized in the production are the same, and the process equipment and operation management schemes are also the same.
The old batch process and the new batch process of the embodiment of the invention have the differences in the aspects of the production site, the production parameters or the production scale, and the like, but the produced products are the same or belong to a series, the physical and chemical principles utilized in production are the same, and the process equipment and the operation management scheme are also the same.
In a batch production process, there is some process data, i.e., input data, which may be manipulated variables or manipulated trajectories, and output data, which may be product quality variables corresponding to the input data. The new batch process is a brand-new batch process and is in an initial running state, and only a small amount of input and output data can be acquired; the old batch process is a batch process with a long production time and has a large amount of input and output data.
And S2, establishing a latent variable process migration model according to the input data and the output data of the old batch process and the input data and the output data of the new batch process.
In an embodiment of the present invention, an input data matrix X obtained by expanding input data of an old batch process and input data of a new batch process according to a batch direction may be obtaineda、XbAnd obtaining the output data matrix Y of the corresponding old batch process and new batch processa、YbWherein X isa、XbThe element in (1) is an operation variable, Ya、YbWherein the element is a product quality variable, Xa∈RM×i、Xb∈RN×j、Ya∈RM×m、Yb∈RN×mWherein M, N is the number of samples of the old batch process and the new batch process, i and j are the number of operation variables of the old batch process and the new batch process, and m is the number of quality variables.
Then, for the input data matrix Xa、XbAnd the output data matrix Ya、YbA normalization process is performed to build a latent variable process migration model.
In one embodiment of the invention, the structure of the latent variable process migration model may include:
Figure GDA0002467143210000101
Figure GDA0002467143210000102
Figure GDA0002467143210000103
Figure GDA0002467143210000104
Figure GDA0002467143210000105
wherein, Ta、TbIs Xa、XbCorresponding score matrix, Pa、PbIs Xa、XbLoad matrix of Ea、Eb、EJYAre each Xa、Xb、YJCorresponding residual error, YJFor joint output matrix, YJ＝[YaYb]T，
Figure GDA0002467143210000106
Is Xa、XbThe projection matrix of (2). QJAnd the load matrix corresponding to the joint output matrix.
Further, establishing the latent variable process migration model can comprise the following steps a-i:
a) respectively adding Ya、YbIs assigned to ua、ubWherein u isa、ubThe score vector of the output data matrix of the old batch process and the score vector of the output data matrix of the new batch process are respectively.
b) Mixing Xa、XbReturn to ua、ubTo calculate the regression coefficient wa、wbNamely:
wa＝Xa Tua(ua Tua)-1,wb＝Xb Tub(ub Tub)-1；
c) normalized regression coefficient wa、wbNamely:
Figure GDA0002467143210000107
d) will unite the output matrices
Figure GDA0002467143210000108
Regression to the Joint score vector tJTo obtain YJIs given by the joint load vector qJNamely:
qJ＝YJ TtJ(tJ TtJ)-1。
e) will Ya、YbReturn to qJTo recalculate ua、ubAnd through and ua、ubAre compared to determine ua、ubIf not, using the recalculated ua、ubAnd returning to the step b.
f) If it converges, then X is calculateda、XbLoad vector p ofa、pb：
pa＝Xa Tta(ta Tta)-1、pb＝Xb Ttb(tb Ttb)-1，
Wherein, ta、tbOutput data matrix X of current old batch process and new batch process respectivelya、XbThe score vector of (2).
g) According to Xa＝Xa-tapa T、Xb＝Xb-tbpb TTo Xa、XbAnd (c) updating, then returning to the step (a) to extract the next principal component, and repeating the steps until a preset number of principal components are extracted. Wherein the predetermined number may be determined by a cross-validation method.
h) Obtaining input data matrix X for a new batch processbCorresponding load matrix Pb＝[pb1，…，pbA]A regression coefficient matrix Wb＝[wb1,...,wbA]And a joint output matrix YJCorresponding load matrix QJ＝[qJ1,...,qJA]。
i) Obtaining a latent variable process migration model:
Figure GDA0002467143210000111
wherein the content of the first and second substances,
Figure GDA0002467143210000112
for predicting the output data, xnewIs new input data.
S3, when the new batch process is used for production, the predicted output data of the current batch is obtained according to the latent variable process migration model and the optimal input data of the current batch, and the optimal input data of the next batch is obtained according to the latent variable process migration model and the input data of the current batch.
In an embodiment of the present invention, the current batch is denoted as the kth batch, and the optimal input data of the current batch can be obtained according to the input and output data of the last batch, i.e. the kth-1 batch.
And substituting the optimal input data of the current batch into the latent variable process migration model to obtain the predicted output data of the current batch.
For the optimal input data of the next batch, the formula can be firstly used
Figure GDA0002467143210000121
And formula
Figure GDA0002467143210000122
When calculatingGradient of predicted output data of previous batch and actual output data of current batch, wherein σyIs the standard deviation, σ, of the mass variableuIs the standard deviation of the input variables and,
Figure GDA0002467143210000123
is a matrix of regression coefficients, Δ is the incremental sign, x(k)For the optimal input data of the current batch, x(k-1)The optimal input data for the last batch.
Then, the optimization problem of the predicted value of the latent variable process migration model based on the correction is solved to obtain the following formula, and the optimal input data x of the next batch is obtained(k+1)，
Figure GDA0002467143210000124
Wherein the content of the first and second substances,
Figure GDA0002467143210000125
for normalized input data of the current batch, T is a joint score matrix, cpfThe threshold, which is the input data, is a constant calculated from historical data,
Figure GDA0002467143210000126
for the linearly corrected predicted output data of the current lot,
Figure GDA0002467143210000127
in order to be an index of the performance of the object,
Figure GDA0002467143210000128
for constraints containing input variables and output variables,
Figure GDA0002467143210000129
the regression coefficient vector is the predicted value of the kth batch.
Wherein the content of the first and second substances,
Figure GDA00024671432100001210
wherein σuFor the standard deviation of the input data for the new batch process,
Figure GDA00024671432100001211
and
Figure GDA00024671432100001212
the prediction error and the gradient of the prediction error, which are based on the latent variable process migration model, for the current batch, respectively, can be calculated by the following formulas:
Figure GDA00024671432100001213
Figure GDA00024671432100001214
wherein, yp(x(k)) In order to actually output the data,
Figure GDA00024671432100001215
the data is output for prediction.
Then, whether the norm of the difference between the input data of the current batch and the obtained optimal input data of the next batch is smaller than a preset threshold value or not is judged, namely whether | x exists or not is judged(k+1)-x(k)||≤θ。
And if the input data is smaller than the preset threshold, taking the input data of the current batch as the optimal input data of the next batch.
If not less than the preset threshold, according to the formula x(k+1)＝(I-K)x(k)+Kx(k+1)+g·ρ(k+1)Generate new next lot of optimal input data x(k+1)And using the new next batch of optimal input data as the next batch of optimal input data. It should be understood that using the input data of the current batch as the optimal input data of the next batch is a simple adaptive strategy, however, if the actual data is different from the optimal solution greatly, it may cause an overcorrection problem and it may be very sensitive to measurement noise. Therefore, the temperature of the molten metal is controlled,in an embodiment of the invention, the filtering is performed with a first order filter, i.e. according to the formula x(k+1)＝(I-K)x(k)+Kx(k+1)+g·ρ(k+1)Generate new next lot of optimal input data x(k+1). Wherein I is an N-order identity matrix
Figure GDA0002467143210000131
Is a diagonal gain matrix, p(k+1)For the excitation signal, g is an amplitude selected according to the magnitude of the input data matrix elements.
Therefore, the problem of correcting self-adaptive quality optimization is further established on the basis of establishing the latent variable process migration model, the quality of a new batch process is optimized, and the quality optimization efficiency is greatly improved. Under the condition of ensuring that the latent variable process migration model is within an effective range, the T2 statistic is directly used as a hard constraint term, and optimization performance can be improved.
And S4, updating the latent variable process migration model according to the optimal input data and the actual output data of the current batch.
As the production process proceeds, new batches of input and output data are continuously generated. Therefore, in the embodiment of the invention, after the current batch is completed, the latent variable process migration model can be updated according to the optimal input data and the actual output data of the current batch. Specifically, the optimal input data and the actual output data x of the current batch can be obtained(k)、y(k)Updating input data matrix and output data matrix X of new batch processb、Yb：
Figure GDA0002467143210000141
Then, the updated data X can be usedb(k)、Yb(k)A new latent variable process migration model is created in accordance with step S2 described above, and returns to step S3.
S5, according to the predicted output data and the actual output data of a plurality of batches in the new batch process, judging whether the stability of the new batch process meets the requirement.
And S6, if the stability of the new batch process meets the requirement, removing partial data from the input data and the output data of the old batch process.
It should be understood that as the production process continues to progress and the data of the new batch process continues to increase, the latent variable process migration model established mainly by the data of the old batch process gradually generates the problem of model mismatch, thereby affecting further improvement of quality optimization. Therefore, when the data of the new batch process is enough, namely the stability of the new batch process can meet the requirement, the data of the old batch process can be removed according to certain criteria.
The method comprises the steps of obtaining H batches of predicted output data and actual output data on the assumption that residual errors between the predicted output data and the actual output data based on a latent variable process migration model obey Gaussian distribution, selecting a preset confidence level, for example, 95% of the confidence level to calculate a confidence interval, calculating the number of batches with prediction errors in the confidence interval, and judging that the stability of a new batch process meets requirements if M continuous batches are in the confidence interval, wherein H is the window width, and M is less than or equal to H.
In a preferred embodiment of the invention, M/H > 2/3.
If the stability of the new batch process meets the requirement, the similarity between the input data of the new batch process and the input data of the old batch process can be acquired. Specifically, the similarity can be calculated by the following formula:
Figure GDA0002467143210000142
Figure GDA0002467143210000151
wherein | | represents the euclidean distance,
Figure GDA0002467143210000152
is the average of the input data for the new batch process,
Figure GDA0002467143210000153
the euclidean distance between the input data for the old batch process and the input data for the new batch process,
Figure GDA0002467143210000154
is the degree of similarity.
Then, the batches in the old batch process can be sorted according to the sequence of the similarity from small to large, and the batches in the old batch process can be removed in the order. That is, data of an old batch process which is largely different from data of a new batch process is preferentially culled.
After the data in the old batch process is removed, a new latent variable process migration model may be established according to step S2, i.e., after step S6 is executed, step S2 may be returned, and the process is cycled through such a cycle to continuously optimize the quality of the production process.
To summarize, referring to fig. 2, a modified adaptive batch process optimization method based on a latent variable process migration model according to an embodiment of the present invention includes:
s201, data of the old batch process is obtained.
S202, expanding the data according to batches.
S203, acquiring data of the new batch process.
And S204, expanding the data according to batches.
And S205, carrying out data standardization and establishing a latent variable process migration model.
And S206, carrying out gradient estimation and solving an optimal solution.
S207, judging whether | x exists or not(k+1)-x(k)And | | is less than or equal to theta. If yes, go to step S208; if not, step S209 is performed.
And S208, setting the optimal operation track of the next batch.
And S209, generating a new optimal operation track.
And S210, assigning the optimal operation track to the (k + 1) th batch. After which steps S211 and S212 are performed.
And S211, updating parameters in the latent variable process migration model and the optimization problem. After this step, the process returns to step S206.
And S212, outputting the process.
In summary, according to the correction adaptive batch process optimization method based on the latent variable process migration model provided by the embodiment of the invention, the latent variable process migration model is established by using the data of the new and old batch processes, so that the problem that quality optimization cannot be implemented due to the fact that the process model cannot be accurately established because of less data in the new batch process is effectively solved, and the purposes of rapidly establishing the new batch process model and effectively implementing the quality optimization are achieved; by means of data elimination of the old batch process and continuous updating of the model, the quality optimization effect of the new batch process is continuously improved, the efficiency of quality optimization of modeling of the new batch process with insufficient data is greatly improved, and the comprehensive economic benefit of an enterprise is improved.
The modified adaptive batch process optimization method based on latent variable process migration model according to the embodiment of the invention is further described in detail by taking the production of cobalt oxalate crystals as an example.
In the industrial production process of hard alloy, the requirement on the quality of cobalt powder is higher and higher, the crystal size of the cobalt powder is required to meet the standard, and the particle size distribution is required to be concentrated as much as possible. The cobalt oxalate is the main raw material for preparing the cobalt powder, and the granularity and the morphology of the cobalt powder are determined to a great extent. Therefore, the method has important practical significance for improving the production efficiency through the optimization of the crystal size of the cobalt oxalate. In order to optimize the crystal size of cobalt oxalate, the method of the present invention was applied to a fed-batch cobalt oxalate crystallization process.
In the hydrometallurgical industry of metal cobalt, the crystallization process of cobalt oxalate belongs to liquid phase reaction, and the main step is to generate cobalt oxalate and ammonium chloride by utilizing the reaction of cobalt chloride and ammonium oxalate. The production equipment and the reaction process are shown in figure 3, and the synthesis procedure consists of an ammonium oxalate dissolver and a reaction kettle. In the actual production, cobalt chloride solution with fixed concentration and volume is introduced into a reaction kettle, steam is used for heating to the appropriate reaction temperature, and then ammonium oxalate solution is introduced at a certain speed. The temperature in the reactor was kept constant by a heating jacket and a PI (Proportional Integral) controller, and the stirring rate of the reactor was also generally constant. Therefore, the only operational variables that can affect the final crystallite size of cobalt oxalate are the feed rate of the ammonium oxalate solution, and the production index, measured in terms of the crystallite size of cobalt oxalate, can be obtained off-line after the end of each batch.
1) Data generation and model correction
The embodiment of the invention further verifies the method by taking the cobalt oxalate crystallization process as a simulation object, analyzes the cobalt oxalate mechanism process, establishes a mechanism model, and provides reasonable modeling data for a data model by utilizing the cobalt oxalate synthesis process mechanism model to replace the actual production process. The parameter settings of the mechanism model are shown in table 1.
TABLE 1
Figure GDA0002467143210000171
Wherein KaNucleation Rate temperature index, KbGrowth rate temperature index, KnNucleation Rate coefficient, KgGrowth rate coefficient, KvShape factor, α nucleation rate supersaturation index, β growth rate supersaturation index, gamma stirring rate index.
In the process of producing the cobalt oxalate, the difference of the new batch process and the old batch process mainly comes from the concentration of raw materials and production process parameters, and is greatly influenced by the environment, geographical position and process. Table 2 shows the value ranges of the input variables of the new and old batch processes.
TABLE 2
Figure GDA0002467143210000181
As shown in Table 2, the manipulated variable to be optimized is the rate of supply of batch-wise ammonium oxalate (F)B) Each batch lasted 11min and was divided into 11 time segments. To obtain training data, the training data were obtained by adding a band of. + -. 0.0005m3The pseudo-random binary signal of/s is used for exciting the dynamic characteristic of the process to generate the batch-to-batch variation characteristic in the actual process; meanwhile, 0.5% white noise was added to the final cobalt oxalate crystal size measurement. According to the experimental measurementsAmount, prediction error converges to 5 × 10 when the number of transitions is 40-9And the prediction error of the later batch has small change. Therefore, the finalize models latent variable process migration with 40 batches of old process data and 5 batches of new process data.
2) Predictive error analysis of latent variable process migration model
Comparing the measured value of the cobalt oxalate crystal size with a latent variable process migration model predicted value and a Partial Least Squares (PLS) method predicted value, wherein the test result of 40 batches is shown in fig. 4, the latent variable process migration model can well predict the cobalt oxalate crystal size under the condition that the process data volume of a new batch is very small, a relative error graph is shown in fig. 5, and the calculation of the relative error is as follows:
Figure GDA0002467143210000182
wherein, ykIs the crystal size of the cobalt oxalate,
Figure GDA0002467143210000183
is the model prediction value, k 1.. 40 is the kth sample.
From fig. 5, it can be obtained that the prediction value accuracy of the latent variable process migration model under the condition of insufficient data is higher than that of the PLS which is not migrated, and the latent variable process migration model can effectively solve the problem of insufficient data.
3) Quality optimization analysis of cobalt oxalate crystallization process
To analyze the quality optimization process, the optimization results of the average particle size of cobalt oxalate based on PLS and latent variable process migration model are given, and fig. 6 shows the process optimization effect without old data culling. Both methods use the same optimization strategy and set the same initial conditions. As can be seen from FIG. 6, the modified adaptive optimization method based on latent variable process migration model can rapidly increase the crystal size of cobalt oxalate, and the two-step optimization effect in FIG. 6 is achieved in the 9 th batch, while the same optimization effect is achieved in the 26 th batch based on PLS optimization. The latent variable process migration model migrates old batch process information to assist the operation of the new process, so that the optimization effect of the new batch process can be accelerated. However, the crystal size of cobalt oxalate optimized based on these two methods after 30 batches was constantly crossed, stabilizing at 2.24 um. Mainly because the data is continuously abundant along with the accumulation of new batch process data, the optimization effect of PLS is improved. However, after 30 batches, the cobalt oxalate crystals optimized based on the latent variable process migration model were slightly degraded and deviated from the optimal trajectory calculated by the genetic algorithm (dotted line in fig. 6), mainly because the difference between the process data of the new and old batches prevented further improvement of the process quality optimization of the new batch. Aiming at the problem, the invention carries out the elimination step of the process data of the old batch and the updating of the process migration model of the latent variable.
An adaptive batch process optimization based on latent variable process migration model modification with old data culling is shown in fig. 7, which utilizes a 100 batch process for production process simulation experiments. To compare the optimization effects presented, the optimization effects of the two-step method and the genetic optimization algorithm were used for comparison. As shown in FIG. 7, the crystal size of cobalt oxalate corrected and adaptively optimized based on latent variable process migration model in the first 10 batches reaches 2.17um, which is very close to the two-step optimization result commonly used in industrial process, mainly because the optimization track is controlled at T2Within the statistics, the optimization effect is poorer than the two-step method in the initial optimization stage. T of the optimal trajectory2The values of the statistics are shown in fig. 8.
After 10 batches, the correction self-adaptive optimization effect based on the latent variable process migration model is higher than that of two-step optimization, mainly the correction self-adaptive algorithm utilizes online measured information to make up the problem of mismatching between the latent variable process migration model and the new batch process, and the optimization effect is continuously improved. Fig. 9 shows a trend graph of the variation of the residual between the actual measured value and the predicted value with the batch operation, the variation range of the residual is large at the initial stage of the batch operation, and the data of the new batch process and the old batch process at the initial stage of the migration are mostly not matched, so that the initial stage is unstable. And starting from the 40 th batch, operating the residual error within a confidence interval, determining that the migration process is in a stable period at the moment, and starting the online latent variable process migration model correction and data elimination. In fig. 7, the slightly decreased crystal size of cobalt oxalate from the 40 th batch is mainly because the elimination of the old data causes instability of the model, so that the optimization quality is decreased, but after 80 batches, the old data is completely eliminated, the optimization quality is close to the optimization value of the genetic algorithm, and the elimination of the old data increases the optimization value of the cobalt oxalate crystal.
The variation of the optimized trajectory part is shown in fig. 10. The optimized track change graphs of the initial run stage, the old data removing stage and the data replacement finishing stage of the batches can be selected, and the 1 st batch, the 50 th batch and the 80 th batch are respectively selected. Fig. 11 shows the ammonium oxalate supply for each batch, which was gradually reduced to the constraint value before the 40 th iteration. But the supply increases between 40 and 50 iterations due to interference from old data. During the substitution (from 40 to 80 batches) it was found that the total amount of ammonium oxalate added to the crystalliser gradually approached the constraint. After the 80 th iteration, there was no longer a significant reduction in supply.
According to the production simulation example of the cobalt oxalate crystal, the latent variable process migration model is established by using the process data of the new batch and the old batch, a large amount of data in the process of the old batch is migrated and applied to the process of the new batch, and the problem that quality optimization cannot be implemented due to the fact that the process model cannot be accurately established due to the fact that the data in the process of the new batch is few can be effectively solved. Because the difference exists between the new batch process and the old batch process, the problem of mismatching of the latent variable process migration model and the object is caused, the method of the embodiment of the invention utilizes correction self-adaptive optimization, and updates the latent variable process migration model by utilizing the new data obtained on line after each batch is finished, thereby further improving the prediction precision of the latent variable process migration model and realizing the optimization of the batch process. After enough new process data are obtained, the data with low similarity in the process of the old batch are removed one by one so as to eliminate the influence caused by the self deviation of the old data. In order to improve the optimization performance, T is used for ensuring that the latent variable process migration model is within an effective range2The statistics act directly as hard constraints.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and are not to be considered limiting of the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "over," and "above" a second feature may be directly or diagonally above the second feature, or may simply indicate that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (5)

1. A correction self-adaptive batch process optimization method based on a latent variable process migration model is characterized by comprising the following steps:
acquiring input data and output data of an old batch process, and acquiring input data and output data of a new batch process;
establishing a latent variable process migration model according to the input data and the output data of the old batch process and the input data and the output data of the new batch process;
when the new batch process is used for production, acquiring the predicted output data of the current batch according to the latent variable process migration model and the optimal input data of the current batch, and acquiring the optimal input data of the next batch according to the latent variable process migration model and the input data of the current batch;
updating the latent variable process migration model according to the optimal input data and the actual output data of the current batch;
judging whether the stability of the new batch process meets the requirement or not according to the predicted output data and the actual output data of a plurality of batches in the new batch process;
if the stability of the new batch process meets the requirement, removing partial data from the input data and the output data of the old batch process,
establishing a latent variable process migration model according to the input data and the output data of the old batch process and the input data and the output data of the new batch process, which specifically comprises the following steps:
obtaining input data matrix X obtained by expanding the input data of the old batch process and the input data of the new batch process according to the batch directiona、XbAnd obtaining the corresponding output data matrix Y of the old batch process and the new batch processa、YbWherein X isa、XbThe element in (1) is an operation variable, Ya、YbWherein the element is a product quality variable, Xa∈RM×i、Xb∈RN×j、Ya∈RM×m、Yb∈RN×mM, N is the number of samples of the old batch process and the new batch process respectively, i and j are the number of operation variables of the old batch process and the new batch process respectively, and m is the number of quality variables;
for the input data matrix Xa、XbAnd said output data matrix Ya、YbA normalization process is performed to build the latent variable process migration model,
for the input data matrix Xa、XbAnd said output data matrix Ya、YbPerforming a normalization process to establish the latent variable process migration model, including:
a) respectively adding Ya、YbIs assigned to ua、ubWherein u isa、ubRespectively representing the score vector of the output data matrix of the old batch process and the score vector of the output data matrix of the new batch process;
b) mixing Xa、XbReturn to ua、ubTo calculate the regression coefficient wa、wbNamely:
wa＝Xa Tua(ua Tua)-1,wb＝Xb Tub(ub Tub)-1；
c) normalizing said regression coefficient wa、wbNamely:
Figure FDA0002467143200000021
d) will unite the output matrices
Figure FDA0002467143200000022
Regression to the Joint score vector tJTo obtain YJIs given by the joint load vector qJNamely:
qJ＝YJ TtJ(tJ TtJ)-1；
e) will Ya、YbReturn to qJTo recalculate ua、ubAnd through and ua、ubAre compared to determine ua、ubIf not, using the recalculated ua、ubAnd returning to step b;
f) if it converges, then X is calculateda、XbLoad vector p ofa、pb：
pa＝Xa Tta(ta Tta)-1、pb＝Xb Ttb(tb Ttb)-1，
Wherein, ta、tbThe output data matrix X of the current old batch process and the output data matrix X of the new batch process are respectivelya、XbA score vector of (a);
g) according to Xa＝Xa-tapa T、Xb＝Xb-tbpb TTo Xa、XbUpdating, then returning to the step a to extract the next principal component, and repeating the steps until the principal components with the preset number are extracted;
h) obtaining an input data matrix X for the new batch processbCorresponding load matrix Pb＝[pb1，…，pbA]A regression coefficient matrix Wb＝[wb1,...,wbA]And a joint output matrix YJCorresponding load matrix QJ＝[qJ1,...,qJA]；
i) Obtaining the latent variable process migration model:
Figure FDA0002467143200000031
wherein the content of the first and second substances,
Figure FDA0002467143200000032
for predicting the output data, xnewIn order for the new input data to be available,
acquiring the optimal input data of the next batch according to the latent variable process migration model and the input data of the current batch, wherein the optimal input data of the next batch specifically comprises the following steps:
according to the formula
Figure FDA0002467143200000033
And formula
Figure FDA0002467143200000034
Calculating predicted output data of current batch and actual output data of current batchGradient, where σyAs standard deviation of the mass variable, σuIs the standard deviation of the input variables and,
Figure FDA0002467143200000036
is a matrix of regression coefficients, Δ is the incremental sign, x(k)For the optimal input data of the current batch, x(k-1)The optimal input data of the previous batch is obtained;
solving the optimization problem of the predicted value of the latent variable process migration model based on the correction to obtain the following formula, and obtaining the optimal input data x of the next batch(k+1)，
Figure FDA0002467143200000035
Wherein the content of the first and second substances,
Figure FDA0002467143200000042
for normalized input data of the current batch, T is a joint score matrix, cpfThe threshold, which is the input data, is a constant calculated from historical data,
Figure FDA0002467143200000043
for the linearly corrected predicted output data of the current lot,
Figure FDA0002467143200000044
in order to be an index of the performance of the object,
Figure FDA0002467143200000045
for constraints containing input variables and output variables,
Figure FDA0002467143200000046
a regression coefficient vector for the kth batch predictor;
judging whether the norm of the difference between the input data of the current batch and the obtained optimal input data of the next batch is smaller than a preset threshold value or not;
if the current batch of input data is smaller than the preset threshold, taking the current batch of input data as the optimal input data of the next batch;
if not less than the preset threshold, according to the formula x(k+1)＝(I-K)x(k)+Kx(k+1)+g·ρ(k+1)Generate new next lot of optimal input data x(k+1)And taking the new next batch of optimal input data as the next batch of optimal input data, wherein I is an N-order identity matrix
Figure FDA0002467143200000047
Figure FDA0002467143200000048
Is a diagonal gain matrix, p(k+1)G is an amplitude selected according to the magnitude of the input data matrix elements,
updating the latent variable process migration model according to the optimal input data and the actual output data of the current batch, and specifically comprises the following steps:
according to the optimal input data and the actual output data x of the current batch(k)、y(k)Updating the input data matrix and the output data matrix X of the new batch processb、Yb：
Figure FDA0002467143200000041
According to the updated data Xb(k)、Yb(k)And establishing a new latent variable process migration model.
2. The method for optimizing the modified adaptive batch process based on the latent variable process migration model according to claim 1, wherein predicted output data and actual output data of H batches are obtained, a preset confidence level is selected to calculate a confidence interval, the number of batches with prediction errors in the confidence interval is calculated, and if M batches are continuously in the confidence interval, the stability of the new batch process is judged to meet the requirement, wherein H is a window width, and M is less than or equal to H.
3. The method for modified adaptive batch process optimization based on latent variable process migration model according to claim 2, wherein M/H > 2/3.
4. The method for optimizing the modified adaptive batch process based on the latent variable process migration model according to claim 3, wherein the step of removing partial data from the input data and the output data of the old batch process specifically comprises:
acquiring the similarity between the input data of the new batch process and the input data of the old batch process;
and sorting the batches in the old batch process according to the sequence of the similarity from small to large, and removing the batches in the old batch process according to the sorting.
5. The method of claim 4, wherein the similarity is calculated by the following formula:
Figure FDA0002467143200000051
Figure FDA0002467143200000052
wherein | | represents the euclidean distance,
Figure FDA0002467143200000053
is the average of the input data for the new batch process,
Figure FDA0002467143200000054
the input data of the old batch process and the input number of the new batch processAccording to the Euclidean distance between the two,
Figure FDA0002467143200000055
is the similarity.
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