Soft-sensing modeling method for multiphase batch processes based on improved geodesic flow core

Abstract

This invention discloses a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic manifold kernel. The method includes: collecting platform parameters from a cloud server; projecting source and target domain data onto a common manifold subspace using a geodesic manifold kernel method based on linear local tangent space arrangement to reduce the data distribution differences between the source and target domains; using a time-series-based fuzzy clustering method to divide the source domain data into phases, obtaining phase division points; and establishing sub-phase soft measurement models based on different phase characteristics using different modeling methods. For phases with slowly changing process characteristics, partial least squares regression is used to establish the soft measurement model; for phases with rapidly changing process characteristics, partial least squares regression based on real-time learning is used to establish the soft measurement model. This method establishes sub-phase soft measurement models for multiphase intermittent processes, enabling the estimation of difficult-to-measure variables and improving the performance of the soft measurement model under varying operating conditions.

Description

Technical Field

[0001] This invention relates to the field of soft measurement modeling of multiphase intermittent processes, and in particular to a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel. Background Technology

[0002] Batch processes are widely used in the production of high-value-added products such as pharmaceuticals, fine chemicals, and semiconductor materials. Accurately detecting and analyzing quality variables during batch processes can effectively improve product quality. However, due to constraints such as environmental factors and cost, it is difficult to directly monitor many key quality variables. Utilizing data from easily measurable variables in batch processes to establish soft sensor models, thereby obtaining estimates of these key variables, is an effective method to address the aforementioned problems.

[0003] During intermittent processes, the operational procedures constantly switch, and the collected data exhibits multi-stage characteristics, leading to poor predictive performance of global soft sensor models. Therefore, many researchers have established sub-phase soft sensor models based on phase partitioning to improve the prediction accuracy of quality variables. These soft sensor models require that the distribution of characteristics between the measured data and the modeling data be consistent. However, during intermittent processes, we cannot assume that the working conditions are identical for each batch; factors such as material replenishment and environmental changes can alter the operating conditions. Under different operating conditions, the characteristics of the process data are not necessarily the same, resulting in a decrease in the prediction accuracy of traditional soft sensor models.

[0004] As a novel machine learning paradigm, transfer learning can effectively reduce the distributional differences of data across different domains. Some researchers have used transfer learning methods to improve traditional soft measurement models, thereby enhancing their performance under varying operating conditions. Domain-adaptive extreme learning machines (DAX) expand the applicability of soft measurement models by utilizing useful information from different operating conditions; multi-source domain soft measurement based on joint distribution alignment and mapping structure preservation utilizes multi-view clustering to establish pseudo-labels and leverages dynamic distribution alignment to reduce data distribution differences across different operating conditions; and kernel partial least squares models with joint outputs use similar features from historical operating conditions to model new operating conditions. These transfer learning-based soft measurement methods effectively improve the performance of soft measurement models under varying operating conditions, but the difficulty in obtaining large amounts of training data in actual industrial production limits the application of these multi-source domain soft measurement methods.

[0005] Instance reweighting and feature transformation are two main transfer learning methods. Compared to instance reweighting, feature transformation can simultaneously consider marginal and conditional distribution differences, thus effectively handling data noise and dynamic factors. The geodesic manifold kernel is a classic feature transformation method that requires few parameters and does not require labeled target domain data. The first step of the geodesic manifold kernel algorithm is to project the source and target domain data onto a common manifold subspace and obtain the feature mapping matrix through principal component analysis (PCA). However, as a linear dimensionality reduction method, PCA cannot preserve the nonlinear characteristics of process data. Some nonlinear methods can effectively handle nonlinear data but cannot compute explicit mappings from the original space to the new space. Linear local tangent space permutations not only preserve the local nonlinear characteristics of the data but also explicitly compute the mapping matrix. Therefore, this invention proposes a soft-sensor modeling method for multiphase intermittent processes based on an improved geodesic manifold kernel. Summary of the Invention

[0006] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of this application to avoid obscuring the purpose of this section, the abstract and the title of the invention, and such simplifications or omissions should not be used to limit the scope of the present invention.

[0007] In view of the above-mentioned problems, the present invention is proposed.

[0008] Therefore, the technical problem solved by this invention is: to perform soft measurement modeling of multiphase intermittent processes based on improved geodesic flow verification, which effectively reduces the data distribution differences under different operating conditions and improves the performance of the soft measurement model under varying operating conditions.

[0009] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0010] This invention provides a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel, comprising:

[0011] Source domain data and target domain data are collected and calculated using the geodesic stream kernel method based on linear local tangent space arrangement;

[0012] A time-series-based fuzzy clustering method is used to perform phase partitioning on the source domain data to obtain phase partitioning points;

[0013] A sub-phase soft measurement model is established based on the phase division points.

[0014] As a preferred embodiment of the multiphase intermittent process soft measurement modeling method based on the improved geodesic stream kernel described in this invention, wherein: the geodesic stream kernel method based on linear local tangent space arrangement includes:

[0015] Use PCA to analyze the source domain data X s and target domain data X t Projecting each component into the principal component subspace, we obtain the eigenmap matrix A. PCA1 and A PCA2 ;

[0016] Calculate geodesics, geodesic streaming kernels, and mapped source and target domain data.

[0017] As a preferred embodiment of the multiphase intermittent process soft measurement modeling method based on the improved geodesic stream cytometer kernel described in this invention, the calculation of geodesics, geodesic stream cytometer kernels, and mapped source and target domain data includes:

[0018] The problem of calculating the generalized eigenvalues ​​as shown in the formula:

[0019] XH N BH N X T α=λXH N X T α

[0020] Where B = SWW T S T S = [S1, ..., S2] N ], S i It is a 0-1 selection matrix, W = dia g (W1, ..., W) N ), W i =H k (IV i V i T V i It is corresponding to X i H k A matrix consisting of d right singular vectors with d maximum singular values. α1, α2, ..., α d It constitutes the feature mapping matrix A LLTSA ;

[0021] For the source domain and the target domain, their feature mapping matrices are A and B, respectively. LLTSA1 and A LLTSA2 The final feature mapping matrix is ​​P. S =A PCA1 A LLTSA1 , P T =A PCA2 A LLTSA2 ;

[0022] The formula for calculating geodesics is:

[0023] Φ(t)=P SU1Γ(t)-R S U2Σ(t)

[0024] Among them, R S It is P S The orthogonal complements of U1 and U2 are orthogonal matrices obtained by singular value decomposition:

[0025]

[0026] Here, Γ and Σ are diagonal matrices, and their diagonal elements are cosθ. i and sinθ i θ i It is P S and P T The main characters between;

[0027] The formula for calculating the geodesic flow kernel is:

[0028]

[0029] Among them, Λ1, Λ2, and Λ3 are diagonal matrices, and their diagonal elements are represented as follows:

[0030]

[0031] The formula for calculating the mapped source and target domain data is:

[0032]

[0033] As a preferred embodiment of the multiphase intermittent process soft measurement modeling method based on the improved geodesic stream kernel described in this invention, the time-series-based fuzzy clustering method includes:

[0034] Construct a time-series dataset, assuming all training data belong to the same class, with cluster centers v, but their membership degrees u. i Different; let U = [u1, ... u] n ] is the membership matrix, u i This indicates the probability that each data point xi belongs to that class;

[0035] Calculate its membership matrix;

[0036] Determine the membership degree of the sample at the current moment.

[0037] As a preferred embodiment of the multiphase intermittent process soft measurement modeling method based on the improved geodesic flow kernel described in this invention, wherein: the calculation of its membership matrix includes:

[0038] Membership degree u i The iterative update formula for cluster centers v is expressed as:

[0039]

[0040]

[0041] Where η is the clustering scale, τ is the splitting factor, and they determine the number of clusters; m is the fuzzy factor.

[0042] As a preferred embodiment of the multiphase intermittent process soft measurement modeling method based on the improved geodesic flow kernel described in this invention, the determination of the membership degree of the sample at the current moment includes:

[0043] Determine if the membership degree of the sample at the current time is less than τ. If true, add the samples at the next time and the two times after that to the time series dataset. Further determine if its membership degree is less than τ. If true, construct a new time series dataset after this split point. If false, add the sample at the next time to the time series dataset. All data can be divided into several phases, and then sub-phase soft measurement models can be constructed for each phase.

[0044] As a preferred embodiment of the multiphase intermittent process soft measurement modeling method based on the improved geodesic flow kernel described in this invention, wherein: the establishment of the sub-phase soft measurement model includes:

[0045] In phases where process characteristics change slowly, partial least squares regression is used to establish a soft measurement model; in phases where process characteristics change rapidly, partial least squares regression based on real-time learning is used to establish a soft measurement model.

[0046] As a preferred embodiment of the soft measurement modeling method for multiphase intermittent processes based on the improved geodesic flow kernel described in this invention, wherein: the partial least squares regression based on instantaneous learning includes:

[0047] Set the source domain data to X s ={x1, x2, ..., x e-1 x e}, construct the time-series dataset L of the source domain data q , means as follows:

[0048]

[0049] Where 'a' determines the width of the time series dataset, and 'x' represents the sample size. k and test data x test The time is t;

[0050] Calculate and filter similar samples from the test data, construct a similar dataset from the test data, and use partial least squares regression to construct a local model of the similar dataset L;

[0051] Predict the test data x using the established local model. test The value is then discarded.

[0052] As a preferred embodiment of the multiphase intermittent process soft measurement modeling method based on the improved geodesic flow kernel described in this invention, wherein: the calculation and screening of samples to construct test data and datasets includes:

[0053] Calculate test data x test and time series dataset L q The Euclidean distance d between each data point in the dataset i The smaller the distance, the higher the similarity between the two samples.

[0054] Select N pairs of data that are related to the test data x. test Find the most similar sample and construct test data x test A similar dataset L.

[0055] As a preferred embodiment of the multiphase intermittent process soft measurement modeling method based on the improved geodesic flow kernel described in this invention, wherein: the method of predicting test data x using the established local model... test The value is then discarded from the current model, including:

[0056] For the new test data x test+1 The time series dataset L q Updated to:

[0057]

[0058] At this time, sample x k+1 and test data x test+1 The time is t.

[0059] The beneficial effects of this invention are as follows: The multiphase intermittent process soft measurement modeling method based on the improved geodesic manifold kernel provided by this invention utilizes the geodesic manifold kernel method based on linear local tangent space arrangement to project source domain data and target domain data onto a common manifold subspace, reducing the data distribution difference between the source domain and the target domain; it uses a time-series-based fuzzy clustering method to perform phase division of the source domain data, obtaining phase division points; and it adopts different modeling methods according to the characteristics of different phases to establish a subphase soft measurement model of the multiphase intermittent process. Attached Figure Description

[0060] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0061] Figure 1 This is an overall flowchart of a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel, as described in one embodiment of the present invention.

[0062] Figure 2 This is a schematic diagram of a geodesic streamer kernel based on a linear local tangent space arrangement in a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic streamer kernel according to an embodiment of the present invention.

[0063] Figure 3 This is a flowchart of the geodesic stream kernel based on linear local tangent space arrangement in a multiphase intermittent process soft measurement modeling method based on an improved geodesic stream kernel according to an embodiment of the present invention;

[0064] Figure 4 This is a schematic diagram of time-based phase partitioning in a multiphase intermittent process soft measurement modeling method based on an improved geodesic flow kernel according to an embodiment of the present invention;

[0065] Figure 5 This is a phase partitioning effect diagram for operating condition 1 of a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel, as described in an embodiment of the present invention.

[0066] Figure 6 The image shows the characteristic distribution effect before and after migration for operating conditions 1 and 2, respectively, according to an embodiment of the present invention, of a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel.

[0067] Figure 7 This is a diagram illustrating the penicillin concentration prediction effect of a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel, as described in one embodiment of the present invention.

[0068] Figure 8 This image shows the penicillin concentration prediction effect of a hybrid modeling method based on a linear locally tangent space arrangement of geodesic stream kernels, as described in an embodiment of the present invention, for a multiphase intermittent process soft measurement modeling method based on an improved geodesic stream kernel. Detailed Implementation

[0069] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0070] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0071] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0072] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0073] In the description of the present invention, it should be noted that the terms "upper, lower, inner, and outer" and other references to orientations or positional relationships are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first, second, or third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0074] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0075] Example 1

[0076] Reference Figure 1 As an embodiment of the present invention, a soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel is provided, comprising:

[0077] S1. Project the source and target domain data onto a common manifold subspace using the geodesic manifold kernel method based on linear local tangent space arrangement to reduce the data distribution difference between the source and target domains;

[0078] Furthermore, the geodesic stream kernel method based on linear local tangent space arrangement includes: using PCA to process the source domain data X s and target domain data X t Projecting each component into the principal component subspace, we obtain the eigenmap matrix A. PCA1 and A PCA2 ;

[0079] Furthermore, consider the following generalized eigenvalue problem:

[0080] XH N BH N X T α=λXH N X T α

[0081] Where B = SWW T S T S = [S1, ..., S2] N ], S i It is a 0-1 selection matrix, W = dia g (W1, ..., W) N ), W i =H k (IV i V i T V i It is corresponding to X i H k A matrix consisting of d right singular vectors with d maximum singular values; α1, α2, ..., α d It constitutes the feature mapping matrix A LLTSA ;

[0082] For the source domain and the target domain, their feature mapping matrices are A and B, respectively. LLTSA1 and A LLTSA2 Then the final feature mapping matrix P S =A PCA1 A LLTSA1 , P T =A PCA2 A LLTSA2 ;

[0083] It should be noted that traditional PCA cannot preserve the nonlinear characteristics of process data, while linear local tangent space permutation can preserve local nonlinear characteristics in small neighborhoods; therefore, compared with traditional geodesic stream kernel, geodesic stream kernel based on linear local tangent space permutation can find a more suitable mapping matrix.

[0084] Furthermore, the formula for calculating geodesics is:

[0085] Φ(t)=PS U1Γ(t)-R S U2Σ(t)

[0086] Among them, R S It is P S The orthogonal complements of U1 and U2 are orthogonal matrices obtained by singular value decomposition:

[0087]

[0088] Here, Γ and Σ are diagonal matrices, and their diagonal elements are cosθ. i and sinθ i θ i It is P S and P T The main characters between;

[0089] Furthermore, the calculation formulas for the mapped source and target domain data are expressed as follows:

[0090]

[0091] It should be noted that during intermittent processes, we cannot set identical working conditions for each batch; material replenishment and environmental changes will alter the operating conditions. Under different operating conditions, the characteristics of the process data may not be the same. The geodesic manifold kernel, based on a linear local tangent space arrangement, projects the source and target domain data onto a common manifold subspace, effectively reducing the data distribution differences between different operating conditions. For example... Figure 2 and Figure 3 As shown;

[0092] S2. Use a time-series-based fuzzy clustering method to perform phase partitioning on the source domain data to obtain phase partitioning points;

[0093] Furthermore, the time-series-based fuzzy clustering method includes:

[0094] Assume all training data belong to the same class, their cluster centers are v, but their membership degrees are u. i Different; let U = [u1, ... u] n ] is the membership matrix, u i Represents each data x i The possibility of belonging to this category;

[0095] Furthermore, membership degree u i The iterative update formula for cluster centers v is expressed as:

[0096]

[0097]

[0098] Where η is the clustering scale, τ is the partitioning factor, and they determine the number of clusters; m is the fuzzy factor.

[0099] Furthermore, a time-series dataset is constructed, its membership matrix is ​​calculated, and it is determined whether the membership degree of the sample at the current time step is less than τ. If it is true, the samples at the next time step and the two time steps after that are added to the time-series dataset. The membership degree is then further determined to be less than τ. If it is true, a new time-series dataset is constructed after this split point. If it is false, the samples at the next time step are added to the time-series dataset. All data can be divided into several phases, and then sub-phase soft measurement models are constructed for each phase.

[0100] It should be noted that the time-series-based phase partitioning method takes into account the temporal characteristics of intermittent process data, and can more accurately partition intermittent processes, providing a foundation for establishing sub-phase soft measurement models; such as Figure 4 As shown;

[0101] S3. Based on the characteristics of different phases, different modeling methods are used to establish sub-phase soft measurement models. For phases where process characteristics change slowly, partial least squares regression is used to establish soft measurement models. For phases where process characteristics change rapidly, partial least squares regression based on real-time learning is used to establish soft measurement models.

[0102] Furthermore, the partial least squares regression based on instant learning includes:

[0103] Set the source domain data to X s ={x1, x2, ..., x e-1 x e}, construct the time-series dataset L of the source domain data q , represented as:

[0104]

[0105] Where 'a' determines the width of the time series dataset, and 'x' is set as the number of samples. k and test data x test The time is t;

[0106] Furthermore, calculate the test data x test and time series dataset L q The Euclidean distance d between each data point in the dataset i The smaller the distance, the higher the similarity between the two samples; select N samples that are similar to the test data x. test Find the most similar sample and construct test data x test Find a similar dataset L; construct a local model of the similar dataset L using partial least squares regression; use the constructed local model to predict the test data x. test The value is then determined, and the current model is discarded.

[0107] It should be noted that when we determine the test data x test When given a similar dataset L, select the time series data x that is closest to the test data. test A portion of the sample set, to improve computational efficiency and avoid global search;

[0108] Furthermore, regarding the new test data x test+1 The time series dataset L q Updated to, represented as:

[0109]

[0110] At this time, sample x k+1 and test data x test+1 The time is t.

[0111] Example 2

[0112] Pensim v2.0 is a soft sensor and fault diagnosis model widely used for testing batch processes, based on the actual penicillin fermentation process. The penicillin fermentation process is a multi-phase batch process, which can be divided into four phases: preparation phase, logarithmic growth phase, stationary phase, and extinction phase. During the preparation phase, rapid bacterial growth consumes oxygen. When the dissolved oxygen concentration drops to a certain level, the bacteria produce intermediate metabolites and begin producing penicillin. After the stationary phase, the hyphae gradually hydrolyze. During the logarithmic growth phase, penicillin is produced in large quantities. At this time, the process characteristics change significantly; therefore, this phase can be considered an unstable phase. All other phases in this scheme are considered stable phases.

[0113] Table 1 shows the 11 process variables used for modeling; process variables 1 to 10 are auxiliary variables, and the 11th process variable, penicillin concentration, is the dominant variable; the six phase-sensitive variables numbered 3 to 8 are used for phase division.

[0114] Table 1. Process variables in the penicillin fermentation process

[0115]

[0116] Each batch fermentation time was 400 hours, with a sampling interval of 0.5 hours; the training and test datasets contained 800 samples; the matrix concentration was varied, and other initial conditions were defined as default values ​​to simulate differences between various working conditions; three different sets of data were generated when the initial matrix concentrations were 5, 10, and 15; these were named Condition 1, Condition 2, and Condition 3, respectively; the clustering scale η was set to 0.1; during the preparation phase, the penicillin concentration was approximately 0, then increased rapidly; the process characteristics of the preparation phase were significantly different from other phases; to accurately distinguish between different phases, two different allocation factors τ1 and τ2 were set; τ1 was used to find the first phase split point, and τ2 was used to find other phase split points; τ1 and τ2 were equal to 0.005 and 0.0028, respectively; the time series dataset L was determined. q The length N is set to 48;

[0117] The prediction accuracy of various methods is evaluated using root mean square error and coefficient of determination, and their calculation formulas are as follows:

[0118]

[0119]

[0120] Where RMSE represents the root mean square error, R 2 The coefficient of determination is represented by the coefficient of determination. Represents the predicted value, y i Indicates the actual value. This represents the average of the actual values, and n represents the number of test data.

[0121] Several clustering methods are compared, including Density Peak Clustering (DPC), Fuzzy C-means Clustering (FCM), Gaussian Mixture Model (GMM), k-means Clustering, and Time-Based Fuzzy Clustering (SBFC); such as Figure 5 The phase division results for condition 1 are shown. DPC, k-means, and FCM cannot accurately identify the extinction phase. Although GMM can identify each phase more accurately, there are still some differences between the phase division results and the actual phases. For example, the end time of the preparation phase obtained by GMM is relatively late. In fact, penicillin fermentation has already entered the logarithmic growth phase at this time. SBFC takes into account the temporal nature of the penicillin fermentation process, so the phase division points obtained are more consistent with the actual situation.

[0122] Figure 6The image shows the feature distribution before and after the migration for working conditions 1 and 2. All data were reduced in dimensionality by PCA and the first three dimensions were selected. The Geodesic Stream Kernel (GFK) algorithm reduced the distribution difference of data under different working conditions to a certain extent. The Geodesic Stream Kernel (LLTSA-GFK) algorithm based on linear locally tangent space arrangement further reduced the distribution difference.

[0123] Figure 7 The following methods are used to predict penicillin concentration using JITL-PLSR (Just-in-Time Learning-based Hybrid Modeling), GFK-JITL-PLSR (Geodesic Streamline Kernel-based Hybrid Modeling), LLTSA-GFK-PLSR (Geodesic Streamline Kernel-based Modeling), and LLTSA-GFK-JITL-PLSR (Geodesic Streamline Kernel-based Modeling), with Condition 1 as the source domain and Condition 2 as the target domain. Table 2 shows the root mean square error of penicillin concentration prediction for JITL-PLSR, GFK-JITL-PLSR, LLTSA-GFK-PLSR, and LLTSA-GFK-JITL-PLSR methods. Table 3 shows the root mean square error of penicillin concentration prediction for JITL-PLSR, GFK-JITL-PLSR, and LLTSA-GFK-JITL-PLSR methods. The GFK-PLSR and LLTSA-GFK-JITL-PLSR methods predict penicillin concentration using coefficients of determination. A smaller root mean square error corresponds to a larger coefficient of determination, indicating better prediction performance. Without transfer learning, the prediction of penicillin concentration is poor. Soft measurement based on GFK-JITL-PLSR improves model performance; however, the prediction error remains large when operating conditions differ significantly. Soft measurement based on LLTSA-GFK-JITL-PLSR considers the nonlinear characteristics of penicillin fermentation data and the distribution differences under different operating conditions, significantly reducing prediction error. Due to the use of a hybrid modeling strategy to address the dynamic and time-varying characteristics of penicillin fermentation data, soft measurement based on LLTSA-GFK-JITL-PLSR provides better prediction performance than soft measurement based on LLTSA-GFK-PLSR. Figure 7 The data and results shown in Tables 2 and 3 indicate that the LLTSA-GFK-JITL-PLSR method has the best prediction performance when the operating conditions change.

[0124] Table 2. Prediction results of four methods in the penicillin fermentation process.

[0125]

[0126] Table 3. Prediction results of four methods in the penicillin fermentation process.

[0127]

[0128] When the two different operating conditions are the source domain and the target domain, respectively, the prediction results of the LLTSA-GFK-JITL-PLSR method are as follows: Figure 8 As shown, the prediction error of the LLTSA-GFK-JITL-PLSR method increases when the difference between operating conditions increases; however, compared with the other methods listed in Table 2, the prediction error of the LLTSA-GFK-JITL-PLSR method is still the smallest; therefore, the above results show that the LLTSA-GFK-JITL-PLSR method is suitable for soft measurement modeling of multiphase intermittent processes.

[0129] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A soft-sensor modeling method for multiphase intermittent processes based on an improved geodesic flow kernel, characterized in that, include: Data from different operating conditions during penicillin fermentation were collected and divided into source domain data and target domain data. The geodesic manifold kernel method based on linear local tangent space arrangement was used to calculate the geodesics, geodesic manifold kernels, and mapped source and target domain data. A time-based fuzzy clustering method is used to perform phase partitioning on the mapped source domain data during the penicillin fermentation process to obtain phase partitioning points. Specifically, two different allocation factors τ1 and τ2 are set; τ1 is used to find the first phase partitioning point, and τ2 is used to find other phase partitioning points. Based on the phase division point, a sub-phase soft measurement model was established to address the characteristics of different stages in the penicillin fermentation process.

2. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 1, characterized in that, The geodesic stream kernel method based on linear local tangent space arrangement includes: Principal component analysis was used to analyze the source domain data X. s and target domain data X t Projecting each component into the principal component subspace, we obtain the eigenmap matrix A. PCA1 and A PCA2 ; Calculate geodesics, geodesic streaming kernels, and mapped source and target domain data.

3. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 1 or 2, characterized in that, Calculate geodesics, geodesic streaming kernels, and mapped source and target domain data, including: The formula for calculating geodesics is: Φ(t)=P S U1Γ(t)-R S U2∑(t) Among them, R S It is P S The orthogonal complements of U1 and U2 are orthogonal matrices obtained by singular value decomposition: Here, Γ and ∑ are diagonal matrices, and their diagonal elements are cosθ. i and sinθ i θ i It's P S and P T The main characters between; The formula for calculating the geodesic flow kernel is: Among them, Λ1, Λ2, and Λ3 are diagonal matrices, and their diagonal elements are represented as follows: The formula for calculating the mapped source and target domain data is:

4. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 3, characterized in that, Time-based fuzzy clustering methods include: Construct a time-series dataset, assuming all training data belong to the same class, with cluster centers v, but their membership degrees u. i Different; let U = [u1, ..., u n ] is the membership matrix, u i Represents each data x i The possibility of belonging to this category; Calculate its membership matrix; Determine the membership degree of the sample at the current moment.

5. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 4, characterized in that, The calculation of its membership matrix includes: The cluster center is v and the membership degree is u. i The iterative update formula is expressed as: Where η is the clustering scale, τ is the splitting factor, and they determine the number of clusters; m is the fuzzy factor.

6. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 5, characterized in that, Determining the membership degree of a sample at the current time includes: Determine if the membership degree of the sample at the current time is less than τ. If true, add the samples at the next time and the two times after that to the time series dataset. Further determine if its membership degree is less than τ. If true, construct a new time series dataset after this split point. If false, add the sample at the next time to the time series dataset. All data can be divided into several phases, and then sub-phase soft measurement models can be constructed for each phase.

7. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 6, characterized in that, The establishment of the sub-phase soft measurement model includes: In phases where process characteristics change slowly, partial least squares regression is used to establish a soft measurement model; in phases where process characteristics change rapidly, partial least squares regression based on real-time learning is used to establish a soft measurement model.

8. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 7, characterized in that, The partial least squares regression based on instant learning includes: Define the source domain data and construct a time-series dataset of the source domain data; Calculate and filter similar samples from the test data, construct a similar dataset from the test data, and use partial least squares regression to construct a local model of the similar dataset L; Predict the test data x using the established local model. test The value is then discarded.

9. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 8, characterized in that, The calculation and selection of samples to construct test data and datasets includes: Calculate test data x test and time series dataset L q The Euclidean distance d between each data point in the dataset i The smaller the distance, the higher the similarity between the two samples. Select N pairs of data that are related to the test data x. test Find the most similar sample and construct test data x test A similar dataset L.

10. The soft measurement modeling method for multiphase intermittent processes based on an improved geodesic flow kernel as described in claim 9, characterized in that, Predict the test data x using the established local model. test The value is then discarded from the current model, including: For the new test data x test+1 The time series dataset L q Updated to: At this time, sample x k+1 and test data x test+1 The time period is t; a determines the width of the time series dataset.

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