A method for predicting penicillin concentration based on local migration modeling

Abstract

The present invention discloses a method for predicting penicillin concentration based on local migration modeling, belonging to the field of soft sensor modeling and application for industrial fermentation production processes. The method divides source and target domain data into subdomains for the penicillin fermentation process. A partial least squares model is used to identify the sub-source domain with the highest correlation with each sub-target domain. A refined migration between subdomains is constructed based on migration component analysis, minimizing the loss of local data information during the migration process. Finally, a prediction model is established within each subdomain, and the target domain data is used to predict penicillin concentration using the established model, thereby improving prediction accuracy.

Description

Technical Field

[0001] The invention relates to a penicillin concentration prediction method based on local migration modeling, and belongs to the field of soft measurement modeling and application of industrial fermentation production processes. Background Art

[0002] Penicillin is a class of antimicrobial drugs that attacks a wide range of bacteria. Penicillin is typically prepared using a liquid culture medium in a fixed container, ventilated with sterile air, for fermentation. During penicillin fermentation, penicillin concentration is a crucial process variable, and accurate measurement is crucial for optimizing control and increasing production. However, penicillin concentration sensors are expensive to measure, and offline analysis is time-consuming, making them unsuitable for practical production. Therefore, soft sensing technology offers an effective solution.

[0003] Soft sensing technology uses a key variable in an industrial process that is difficult or temporarily unmeasurable (such as the penicillin concentration in the aforementioned penicillin fermentation process) as the dominant variable. It then selects other easily measurable variables (such as aeration volume, cooling water flow rate, carbon dioxide levels, dissolved oxygen levels, and pH values, which are easily detected during the fermentation process) as auxiliary variables. By establishing a mathematical relationship between the two variables, the dominant variable can be inferred or estimated through the auxiliary variables. Commonly used soft sensing modeling methods in recent years include the partial least squares method (PLS), support vector machine (SVM), and artificial neural network (ANN). PLS, among others, maps historical process data from a high-dimensional data space to a corresponding low-dimensional data space, obtains mutually orthogonal eigenvectors for the independent and dependent variables, and then establishes a linear regression relationship between the eigenvectors of the independent and dependent variables to predict penicillin concentration. This method is a simple, yet highly accurate, basic soft sensing method. However, these soft sensor modeling methods usually require that the characteristic distribution of the test data is consistent with that of the modeling data, that is, the auxiliary variable of the penicillin concentration to be measured is consistent with the data distribution of the auxiliary variable used for training the model. However, in the penicillin fermentation process, it cannot be simply assumed that each fermentation is under the same operating conditions. Factors such as feeding and environmental changes will cause the operating conditions to change. The distribution of process data obtained under different operating conditions is not necessarily the same. This means that when a soft sensor model is established under known operating conditions using auxiliary variables and their corresponding dominant variables, if the operating conditions change during prediction, there will be a difference in the distribution of the auxiliary variables under the new operating conditions and the auxiliary variables used for modeling. This distribution difference will reduce the prediction accuracy of the existing soft sensor model.

[0004] In addition, due to its multi-stage nature, the data has its own local structure. That is, at different stages of the penicillin fermentation process, the relationship between the process data and the data to be measured is not the same. Therefore, in the process of transfer learning and aligning the distribution of the entire modeling data set, local information is easily ignored and the original data structure cannot be maintained. The soft measurement model established on this basis is underfitting, which leads to room for improvement in the prediction accuracy of penicillin. Summary of the Invention

[0005] In order to further improve the prediction accuracy of penicillin concentration in the penicillin fermentation process, the present invention provides a penicillin concentration prediction method based on local migration modeling. This method uses K-means clustering to divide the source domain data into sub-source domains, uses Euclidean distance to identify the sub-source domain with the greatest correlation with the auxiliary variable data of the target domain, and constructs refined migration between sub-domains based on geodesic streaming kernels to reduce the loss of local data information during the migration process. Finally, a prediction model is established in each sub-domain, and the target domain data is used to predict the penicillin concentration using the established model.

[0006] A method for predicting penicillin concentration based on local migration modeling, the method comprising:

[0007] Step 1: Collect data from two working conditions during penicillin fermentation and define them as source domains D and D respectively. s ={X s , Y s} and target domain D t ={X t}; where source domain D s ={X s , Y s}Including auxiliary variable data X in the penicillin fermentation process s and the corresponding dominant variable data y s , where y s As the source domain label, the target domain data D t ={X t Only the auxiliary variable data X in the penicillin fermentation process are included t ; Of the two working conditions, one is a known fermentation process, and the other is a fermentation process to be predicted;

[0008] Step 2: Use K-means clustering to classify the source domain D s ={X s , Y s} perform clustering and obtain three sub-source domains D sj ={X sj ,Y sj}, j = 1, 2, 3;

[0009] Step 3: Determine the auxiliary variable data x for each target domainti The most relevant sub-source domain D sj ;

[0010] Step 4: Use geodesic flow kernel to perform feature mapping on the auxiliary variable data of the target domain and the auxiliary variable data of the most relevant sub-source domain:

[0011] (X' sj ,x' ti )=GFK(X sj ,x ti )

[0012] where X' sj 、x' ti They are the auxiliary variable data of the new sub-source domain and the auxiliary variable data of the new target domain after migration;

[0013] Step 5: Using partial least squares regression, the auxiliary variable data of the new sub-source domain after migration and its penicillin concentration (X' sj ,Y sj ) to establish a soft measurement model, and x' ti Bring it into the soft measurement model established in the sub-source domain with the highest correlation to obtain the final prediction result Y t .

[0014] Optionally, the auxiliary variable data X in step 1 s Including aeration volume, cooling water flow rate, carbon dioxide volume, dissolved oxygen volume and pH value; the dominant variable data y s is the corresponding penicillin concentration.

[0015] Optionally, step 2 includes:

[0016] Step 2.1: The source domain D s ={X s , Y s Auxiliary variable data X in the data s Pre-divided into 3 groups: X s ={X s1 ,X s2 ,X s3}, randomly select 3 sample data as the initial cluster centers {c1, c2, c3}, calculate the distance between each sample and each cluster center, and assign the sample to the cluster center closest to it, then recalculate the cluster center according to the sample data in the existing class until the cluster center no longer changes, and get the final three subclasses X s1 、X s2 、X s3 , the cluster centers of the final three subclasses are recorded as c j ;

[0017] Step 2.2, the three subclasses Xs1 、X s2 、X s3 The corresponding penicillin concentration Y s1 、Y s2 、Y s3 They are composed of sub-source domains D sj ={X sj ,Y sj}, j=1,2,3.

[0018] Optionally, step 3 includes:

[0019] Step 3.1, calculate the auxiliary variable data x for each target domain ti The distance d from the cluster centers of the three subclasses of the auxiliary variable data in the source domain data j ;

[0020] Step 3.2, d j The sub-source domain corresponding to the minimum value of the sub-class is used as the auxiliary variable data x of the target domain ti The sub-source domain with the highest correlation.

[0021] Optionally, the distance between each sample and each cluster center is calculated in step 2.1 and the auxiliary variable data x of each target domain is calculated in step 3.1. ti When the distances are calculated from the cluster centers of the three subclasses of the auxiliary variable data in the source domain data, the distances are of the same type, including Euclidean distance, Mahalanobis distance, bulldozer distance, Manhattan distance, Chebyshev distance, or Minkowski distance.

[0022] Optionally, step 4 includes:

[0023] Step 4.1: Source Domain X sj With the target domain x ti Obtain two groups of basis P respectively through PCA S , and P S Orthogonal complement satisfy

[0024] Step 4.2: Generalized Singular Value Decomposition Simultaneous Decomposition

[0025]

[0026]

[0027] The diagonal elements of U1, U2, Γ, Σ, Γ and Σ are recorded as cosθ respectively. i and sinθ i , i=1,2,...d,θ i For the protagonist,

[0028] The elements in Γ(t) and Σ(t) are expressed as cos(tθ i ) and sin(tθ i );

[0029] Step 4.3: Compute the positive semidefinite matrix The specific form is as follows:

[0030]

[0031] Where Λ1, Λ2, and Λ3 are diagonal matrices, and their diagonal elements are:

[0032]

[0033] Step 4.4: Let L be the square root of G, L T L=G, substitute get That is, the mapped data is obtained by z = Lx;

[0034] After obtaining L, substitute the following formula to obtain the new sub-source domain auxiliary variable data and the new target domain auxiliary variable data X' after migration: sj 、x' ti :

[0035] X' sj =LX sj ,x' ti =Lx ti .

[0036] Optionally, the three sub-source domains D in step 2 sj They correspond to the three stages of penicillin fermentation: bacterial growth period, penicillin secretion period and bacterial autolysis period.

[0037] Optionally, the soft measurement model established using partial least squares regression in step 5 is a trained soft measurement model. During the training process, data under two known working conditions are used to form a data set, which is divided into a training set and a test set. The root mean square error and mean absolute error between the predicted value and the true value of the penicillin concentration are used to characterize the model prediction accuracy.

[0038] The present application also provides application of the above method in a fermentation process.

[0039] The beneficial effects of the present invention are:

[0040] Through the Grassmann manifold, a subspace mapping with similar distribution between the source domain and the target domain is found, the similarity between the source domain and the target domain is found, and the similarity is used to apply the knowledge learned in the source domain to the target domain. In this way, when realizing the prediction of penicillin concentration, the problem of inaccurate prediction results caused by changes in data structure due to changes in working conditions and the multi-stage nature of the fermentation process is solved. The method of this application can effectively adapt to changes in working conditions and still maintain good penicillin concentration prediction accuracy under variable working conditions; it also reduces the loss of local data information during the migration process and improves the prediction accuracy of the transfer learning soft measurement model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0042] Figure 1 It is a geodesic diagram;

[0043] Figure 2 It is a schematic diagram of overall migration and local migration;

[0044] Figure 3 This is a schematic diagram of the soft sensor modeling framework based on local migration modeling;

[0045] Figure 4A This is a simulation result diagram of the predicted value and true value of penicillin obtained by the conventional method PLS;

[0046] Figure 4B This is the simulation result diagram of the predicted value and true value of penicillin obtained by LWPLS;

[0047] Figure 4C This is a simulation result diagram of the predicted value and true value of penicillin obtained by the LTL-PLS method of this application;

[0048] Figure 5A This is the simulation result diagram of the predicted value and true value of penicillin obtained by the overall migration GFK-PLS;

[0049] Figure 5B This is a simulation result diagram of the predicted value and true value of penicillin obtained by introducing the local migration method LTL-PLS in this application. DETAILED DESCRIPTION

[0050] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0051] Introduction to basic theory:

[0052] 1. K-means clustering:

[0053] As a basic clustering method, the k-means (k-means clustering algorithm, k-means) algorithm has been widely used in many fields related to industrial processes.

[0054] K-means divides the data into k groups through iterative solution: C = {C1, C2, ... C k}, randomly select k sample data as the initial cluster centers {c1,c2,...,c k}, calculate the Euclidean distance between each sample p and each cluster center, and assign the sample to the cluster center closest to it, and then recalculate the cluster center based on the sample data in the existing class until the cluster center no longer changes.

[0055] The performance of the k-means algorithm is highly dependent on the initial number of clusters k. The optimal number of clusters k can be determined using the elbow rule. The sum of squared errors (SSE) after clustering is calculated for different values ​​of k using the following formula: Computing the sum of squares of each point and its cluster center, the SSE decreases rapidly as the value of k increases. Once k reaches the actual number of clusters, the SSE decreases only slowly. A graph of the SSE vs. k value resembles an elbow, with the optimal k value being at the "elbow joint."

[0056] 2. Geodesic Stream Kernel:

[0057] The geodesic flow kernel (GFK) is a feature-map-based transfer learning method. Its goal is to find a subspace on the Grassmann manifold where the source and target domains have similar distributions. GFK is based on the theory of manifold learning, which posits that observable data is actually mapped from a low-dimensional manifold into a high-dimensional space. This manifold allows for better feature analysis, data processing, and distance measurement.

[0058] Manifolds have special structures and properties. The Grassmann manifold used by GFK can be defined as follows: Let G be a D-dimensional vector space, and the set G(d,D) consisting of all d-dimensional subspaces in G. That is, G(d,D) represents a Grassmann manifold, which is composed of all d-dimensional vectors in the D-dimensional vector space. In general distance metric spaces, the shortest path length between two points is a straight line, but in manifolds, geodesics are often used to represent the shortest distance between two points. Figure 1Taking a sphere as an example, A and B are two points on the surface of the sphere. The shortest distance between points AB is the arc AB, that is, the geodesic between the two points is the shortest.

[0059] GFK transforms the source domain and target domain into Grassmann manifold space, and then finds a geodesic line from the source domain to the target domain in this manifold space to perform the best feature mapping. Assume that the source domain sample dataset is The target domain sample dataset is Where s, t are the number of samples in the source domain and the target domain respectively, and D is the dimension of each sample. The source domain and the target domain are respectively obtained by PCA to obtain two sets of basis P S , P S The orthogonal complement of Assume P S With P T After being mapped by the geodesic mapping function φ(t), it is located at two extreme points, 0 and 1, that is, φ(0) = P S ,φ(1)=P T φ(t) is the geodesic mapping function of the Grassmann manifold space G(d,D), which can map data to the Grassmann manifold. When t∈(0,1), φ(t) can be expressed as follows:

[0060]

[0061] In the formula, U1, U2, Γ(t), and Σ(t) are simultaneously decomposed by generalized singular value decomposition The specific expression is shown in (2):

[0062]

[0063] and are matrices whose column vectors are mutually orthogonal, and is a diagonal matrix, since the product of two matrices is decomposed by the singular value Therefore, each element of the diagonal matrix can be used as the principal angle to represent the similarity between the two matrices. The diagonal elements are denoted as cosθ i and sinθ i (i=1,2,...d),θ i For the protagonist, Therefore, the elements in Γ(t) and Σ(t) can be expressed as cos(tθ i ) and sin(tθ i ).

[0064] The geodesic flow between the two extreme points of the source domain φ(0) and the target domain φ(1) can be calculated by integration, assuming that the original sample point in the source domain is x i , the original sample point of the target domain is x j , after being mapped to G(d,D) by φ(t), it is z i 、z j , define their inner product:

[0065]

[0066] Here is a semi-positive definite matrix with the following form:

[0067]

[0068] Where Λ1, Λ2, and Λ3 are diagonal matrices, and their diagonal elements are:

[0069]

[0070] In order to obtain the mapped source and target domain data, we assume that L is the square root of G, that is, L T L=G, formula (3) can be changed to That is, the mapped data is obtained by z=Lx.

[0071] Example 1:

[0072] This embodiment provides a method for predicting penicillin concentration based on local migration modeling, comprising:

[0073] Step 1: Collect data from two working conditions during penicillin fermentation and define them as source domains D and D respectively. s ={X s , Y s} and target domain D t ={X t}; where source domain D s ={X s , Y s}Including auxiliary variable data X in the penicillin fermentation process s and the corresponding dominant variable data y s , where y s As the source domain label, the target domain data D t ={X t Only the auxiliary variable data X in the penicillin fermentation process are included t ; Of the two working conditions, one is a known fermentation process, and the other is a fermentation process to be predicted;

[0074] Step 2: Use K-means clustering to classify the source domain D s ={X s, Y s} perform clustering and obtain three sub-source domains D sj ={X sj ,Y sj}, j = 1, 2, 3;

[0075] Step 3: Determine the auxiliary variable data x for each target domain ti The most relevant sub-source domain D sj ;

[0076] Step 4: Use geodesic flow kernel to perform feature mapping on the auxiliary variable data of the target domain and the auxiliary variable data of the most relevant sub-source domain:

[0077] (X' sj ,x' ti )=GFK(X sj ,x ti )

[0078] where X' sj 、x' ti They are the auxiliary variable data of the new sub-source domain and the auxiliary variable data of the new target domain after migration;

[0079] Step 5: Using partial least squares regression, the auxiliary variable data of the new sub-source domain after migration and its penicillin concentration (X' sj ,Y sj ) to establish a soft measurement model, and x' ti Bring it into the soft measurement model established in the sub-source domain with the highest correlation to obtain the final prediction result Y t .

[0080] Example 1:

[0081] This embodiment provides a method for predicting penicillin concentration based on local migration modeling, see Figure 3 The method assumes that the source domain and target domain data of penicillin fermentation process are D s ={X s , Y s} and D t ={X t The source domain data and the target domain data are respectively for the fermentation process under known working conditions and the fermentation process under the working conditions to be predicted.

[0082] where X s is the auxiliary variable data of the source domain, namely, aeration volume, cooling water flow rate, carbon dioxide volume, dissolved oxygen volume and pH value, y s is the source domain label dataset, i.e., penicillin concentration;

[0083] X tFor the auxiliary variable data of the target domain (aeration volume, cooling water flow rate, carbon dioxide content, dissolved oxygen content and pH value), the soft sensor modeling steps based on local migration modeling are as follows:

[0084] (1) For source domain data D s ={X s , Y s} Perform clustering;

[0085] Combining the elbow rule with the three-stage mechanism of penicillin fermentation process, K-means clustering is used to cluster the auxiliary variable data in the source domain data, and three subclasses X are obtained. s1 、X s2 、X s3 , associate the three subclasses with their corresponding penicillin concentrations Y s1 、Y s2 、Y s3 They are divided into three sub-source domains. sj They correspond to the three stages of penicillin fermentation: bacterial growth period, penicillin secretion period and bacterial autolysis period.

[0086] Specifically, k-means pre-divides the auxiliary variable data in the source domain data into three groups through iterative solution: X s ={X s1 ,X s2 ,X s3}, randomly select one sample data from each of the three groups of data as the initial cluster center {c1, c2, c3}, calculate the Euclidean distance between each sample p and each cluster center, and assign the sample to the cluster center closest to it, then recalculate the cluster center based on the sample data in the existing class until the cluster center no longer changes, and obtain the final three subclasses X s1 、X s2 、X s3 , the cluster centers of the final three subclasses are recorded as c j ;.

[0087] (2) Determine the auxiliary variable data x for each target domain ti The most relevant sub-source domain X sj ;

[0088] The higher the correlation between the auxiliary variable of the target domain and the sub-source domain, the smaller the distance between it and the sub-source domain cluster center. Therefore, the Euclidean distance is used to judge the distance between the auxiliary variable and each target domain test sample x. ti The most relevant sub-source domain X sj ;

[0089] The Euclidean distance calculation formula is as follows:

[0090]

[0091] According to the above formula, we can calculate the auxiliary variable data x of the target domain respectively. ti The distance from the three cluster centers is determined by the size of the Euclidean distance to each target domain test sample x ti The most relevant sub-source domain X sj .

[0092] In practical applications, the Euclidean distance between each sample p and each cluster center is calculated, and the auxiliary variable data x of each target domain is calculated. ti The distance from the cluster centers of the three subclasses of the auxiliary variable data in the source domain data can also be Mahalanobis distance, Bulldozer distance, Manhattan distance, Chebyshev distance, or Minkowski distance.

[0093] (3) Use geodesic flow kernel to perform feature mapping between target domain auxiliary variable data and its most relevant sub-source domain data: (X' sj ,x' ti )=GFK(X sj ,x ti ), where X' sj 、x' ti They are the auxiliary variable data of the new sub-source domain and the auxiliary variable data of the new target domain after migration;

[0094] Step 4.1: Source Domain X sj With the target domain x ti Obtain two groups of basis P respectively through PCA S , and P S Orthogonal complement satisfy

[0095] Step 4.2: Generalized Singular Value Decomposition Simultaneous Decomposition

[0096]

[0097]

[0098] The diagonal elements of U1, U2, Γ, Σ, Γ and Σ are recorded as cosθ respectively. i and sinθ i , i=1,2,...d,θ i For the protagonist,

[0099] The elements in Γ(t) and Σ(t) are expressed as cos(tθ i ) and sin(tθ i );

[0100] Step 4.3: Compute the positive semidefinite matrix The specific form is as follows:

[0101]

[0102] Where Λ1, Λ2, and Λ3 are diagonal matrices, and their diagonal elements are:

[0103]

[0104] Step 4.4: Let L be the square root of G, L T L=G, substitute get That is, the mapped data is obtained by z = Lx;

[0105] After obtaining L, substitute the following formula to obtain the new sub-source domain auxiliary variable data and the new target domain auxiliary variable data X' after migration: sj 、x' ti :

[0106] X' sj =LX sj ,x' ti =Lx ti .

[0107] (4) Using partial least squares regression, the most relevant sub-source domain and its penicillin concentration (X' sj ,Y sj ) to establish a soft measurement model, and x' ti Bring it into the soft measurement model established in the sub-source domain with the highest correlation to obtain the final prediction result Y t .

[0108] To verify the accuracy of the prediction results of the present method, this example verifies the present method through experiments. Specifically, experimental data for the penicillin fermentation process was obtained using the Pensim simulation platform. (The Pensim simulation platform, based on the Birol mechanism model, considers a variety of variables related to the actual penicillin fermentation process and has been widely used in the field of process modeling and detection.) In the present method, auxiliary variables are selected from the aeration rate, cooling water flow rate, carbon dioxide level, dissolved oxygen level, and pH value, which are easy to detect in the actual production process; the dominant variable is the penicillin concentration, which is difficult to measure online.

[0109] The fermentation time was set to 400 hours, the sampling interval was 0.2 hours, and 1000 sets were used for both the training and test sets. To simulate variations in operating conditions, other initial conditions were fixed to their default values. Two different sets of process data, defined as Operating Condition 1 and Operating Condition 2, were generated with initial substrate concentrations of 5 and 15 (the initial substrate concentration refers to the initial nutrient concentration for Penicillium cultivation). The initial substrate concentration was expressed in g / L.

[0110] To quantify the prediction accuracy, this application uses two indicators, Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), for comparison. The calculation formula is:

[0111]

[0112] (1) In order to illustrate that the proposed scheme can effectively solve the problem of deterioration of soft sensor model performance caused by data distribution differences under variable working conditions, the conventional method PLS (refer to the introduction in "Wang Z, He Q, Wang J. Comparison of Variable Selection Methods for PLS-based Soft Sensor Modeling[J]. Journal of Process Control(S0959-1524), 2015, 26: 56-72.") and LWPLS (local weighted partial least squares, refer to the introduction in "Xue Mingchen, Xiong Weili, Xu Baoguo. Online multi-model modeling based on local weighted partial least squares[J]. Computer Application Research, 2015, 32(10): 2981-2984+2995.") are selected for comparison with the method of this application LTL-PLC.

[0113] All methods use working condition 1 as the source domain and working condition 2 as the target domain. The number of clusters set by the mixed Gaussian model is determined to be 3, which is consistent with the process mechanism that penicillin fermentation is divided into three stages: bacterial growth stage, penicillin secretion stage, and bacterial autolysis stage.

[0114] The calculation results of the three indicators are shown in Table 1, and the prediction results are shown in Appendix Figure 4A 、 Figure 4B and Figure 4C shown.

[0115] Table 1 Penicillin prediction results

[0116]

[0117] It can be seen from Table 1 that compared with the basic soft sensing method PLS and the locally weighted LWPLS, the LTL-PLS method of the present application reduces the difference in the distribution of auxiliary variables under new working conditions and the auxiliary variables used for modeling due to the introduction of transfer learning ideas, so the prediction error is smaller, indicating that the method of the present application can effectively solve the problem of data differences reducing the accuracy of the soft sensing model.

[0118] (2) In order to illustrate that the method of this application can reduce the loss of overall migration data information and further improve the prediction accuracy of penicillin concentration, this scheme uses the local migration modeling in the specific implementation method in a targeted manner and selects GFK-PLS that introduces the overall transfer learning method for comparison (the overall migration and local migration methods are shown in the figure below) Figure 2 As shown in the figure), this application solution specifically selects the migration component analysis in the implementation method. Simulation comparison is carried out under different working conditions. Figure 5A and Figure 5B The experimental results of two soft sensing methods are given respectively when working condition 1 is used as the source domain modeling data and working condition 2 is used as the target domain to predict the concentration of penicillin.

[0119] Table 2 shows the calculation results of the predicted indicators.

[0120] Table 2 Penicillin prediction results

[0121]

[0122] The same transfer learning strategy was introduced. The prediction results of penicillin concentration by the LTL-PLS method in this application have smaller RMSE and MAE values ​​than those by the GFK-PLS method. This shows that the method of this application first captures the local features of the data, performs refined migration of sub-domains, and then establishes a soft measurement model. This method can improve the data information loss of the overall migration and improve the prediction performance and generalization ability of the soft measurement model.

[0123] Some steps in the embodiments of the present invention may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as a CD or a hard disk.

[0124] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting penicillin concentration based on local migration modeling, characterized in that: The method comprises: Step 1: Collect data from two working conditions during penicillin fermentation and define them as source domains D and D respectively. s ={X s , Y s } and target domain D t ={X t }; where source domain D s ={X s , Y s }Including auxiliary variable data X in the penicillin fermentation process s and the corresponding dominant variable data y s , where y s As the source domain label, the target domain data D t ={X t Only the auxiliary variable data X in the penicillin fermentation process are included t ; Of the two working conditions, one is a known fermentation process, and the other is a fermentation process to be predicted; Step 2: Use K-means clustering to classify the source domain D s ={X s , Y s } perform clustering and obtain three sub-source domains D sj ={X sj ,Y sj }, j = 1, 2, 3; Step 3: Determine the auxiliary variable data x for each target domain ti The most relevant sub-source domain D sj ; Step 4: Use geodesic flow kernel to perform feature mapping on the auxiliary variable data of the target domain and the auxiliary variable data of the most relevant sub-source domain: (X′ sj ,x′ ti )=GFK(X sj ,x ti ) where X′ sj , x′ ti They are the auxiliary variable data of the new sub-source domain and the auxiliary variable data of the new target domain after migration; Step 5: Use partial least squares regression to calculate the auxiliary variable data of the new sub-source domain and its penicillin concentration (X′ sj ,Y sj ) to establish a soft measurement model, and x′ ti Bring it into the soft measurement model established in the sub-source domain with the highest correlation to obtain the final prediction result Y t .

2. The method according to claim 1, characterized in that The auxiliary variable data X in step 1 s Including aeration volume, cooling water flow rate, carbon dioxide volume, dissolved oxygen volume and pH value; the dominant variable data y s is the corresponding penicillin concentration.

3. The method according to claim 2, characterized in that The step 2 includes: Step 2.1: The source domain D s ={X s , Y s Auxiliary variable data X in the data s Pre-divided into 3 groups: X s ={X s1 ,X s2 ,X s3 }, randomly select 3 sample data as the initial cluster centers {c1, c2, c3}, calculate the distance between each sample and each cluster center, and assign the sample to the cluster center closest to it, then recalculate the cluster center according to the sample data in the existing class until the cluster center no longer changes, and get the final three subclasses X s1 、X s2 、X s3 , the cluster centers of the final three subclasses are recorded as c j ; Step 2.2, the three subclasses X s1 、X s2 、X s3 The corresponding penicillin concentration Y s1 、Y s2 、Y s3 They are composed of sub-source domains D sj ={X sj ,Y sj }, j=1,2,3.

4. The method according to claim 3, characterized in that The step 3 includes: Step 3.1, calculate the auxiliary variable data x for each target domain ti The distance d from the cluster centers of the three subclasses of the auxiliary variable data in the source domain data j ; Step 3.2, d j The sub-source domain corresponding to the minimum value of the sub-class is used as the auxiliary variable data x of the target domain ti The sub-source domain with the highest correlation.

5. The method according to claim 4, characterized in that The distance between each sample and each cluster center is calculated in step 2.1, and the auxiliary variable data x of each target domain is calculated in step 3.

1. ti When the distances are calculated from the cluster centers of the three subclasses of the auxiliary variable data in the source domain data, the distances are of the same type, including Euclidean distance, Mahalanobis distance, bulldozer distance, Manhattan distance, Chebyshev distance, or Minkowski distance.

6. The method according to claim 5, characterized in that The step 4 comprises: Step 4.1: Source Domain X sj With the target domain x ti Obtain two groups of basis P respectively through PCA S , and P S Orthogonal complement satisfy Step 4.2: Generalized Singular Value Decomposition Simultaneous Decomposition The diagonal elements of U1, U2, Γ, Σ, Γ and Σ are recorded as cosθ respectively. i and sinθ i , i=1,2,d,θ i For the protagonist, The elements in Γ(t) and Σ(t) are expressed as cos(tθ i ) and sin(tθ i ); Step 4.3: Compute the positive semidefinite matrix The specific form is as follows: Where Λ1, Λ2, and Λ3 are diagonal matrices, and their diagonal elements are: Step 4.4: Let L be the square root of G, L T L=G, substitute get That is, the mapped data is obtained by z = Lx; After obtaining L, the following formula is used to obtain the new sub-source domain auxiliary variable data and the new target domain auxiliary variable data X′ after migration: sj , x′ ti : X′ sj =LX sj ,x′ ti =Lx ti 。 7. The method according to claim 6, characterized in that The three sub-source domains D in step 2 sj They correspond to the three stages of penicillin fermentation: bacterial growth period, penicillin secretion period and bacterial autolysis period.

8. The method according to claim 7, characterized in that The soft sensor model established using partial least squares regression in step 5 is a trained soft sensor model. During the training process, data under two known working conditions are used to form a data set, which is divided into a training set and a test set. The root mean square error and mean absolute error between the predicted value and the true value of penicillin concentration are used to characterize the model prediction accuracy.

9. Use of any one of the methods of claims 1-8 in a fermentation process.

Images