Industrial Process Soft Sensing Modeling Methods and Systems for Incomplete Data

Abstract

This invention relates to the field of online measurement technology, and more particularly to a method and system for soft measurement modeling of industrial processes for incomplete data. The steps include: acquiring historical sample data containing missing values ​​in the industrial process and constructing a BGPLVM model; extracting sample features based on the historical sample data and using them as prior constraints to initialize the hyperparameters of the BGPLVM model; acquiring query sample data and obtaining the latent variable variational distribution of the query sample data based on the BGPLVM model; extracting historical sample data most similar to the latent variable variational distribution to construct a local sample dataset; constructing a Gaussian process regression model and determining the parameters of the Gaussian process regression model by maximizing the log-likelihood; and substituting the latent variable variational distribution of the query sample data into the Gaussian process regression model to predict the output variable corresponding to the query sample data.

Description

Technical Field

[0001] This invention relates to the field of online measurement technology, and in particular to a method and system for soft measurement modeling of industrial processes with incomplete data. Background Technology

[0002] Industrial processes typically involve complex multivariate coupling relationships. During the sampling process, production systems are affected by factors such as equipment aging, communication interruptions, and sensor drift, resulting in widespread data gaps in process data. Incomplete data not only disrupts the correlation between input variables but also weakens the sensitivity of soft sensor models to changes in process states, thereby affecting the modeling accuracy and stability of soft sensor models in high-dimensional nonlinear scenarios.

[0003] Traditional soft measurement modeling methods mostly rely on the assumption of data integrity, and repair missing samples through linear interpolation, mean imputation or multiple imputation. However, such methods ignore the temporal characteristics of missing data and the structural relationship between variables, making it difficult to effectively maintain the dynamic characteristics of the real process.

[0004] In soft measurement modeling research addressing incomplete data, the Bayesian Gaussian Process Latent Variable Model (BGPLVM) has attracted attention due to its excellent nonlinear mapping capabilities. It can achieve low-dimensional probabilistic embedding of high-dimensional data in the latent space through variational inference, thus adapting to the modeling needs of missing data. However, existing methods still have the following shortcomings when dealing with complex industrial scenarios: (1) The lack of prior constraints on the features of historical samples during the model initialization stage leads to high randomness in the latent space distribution and poor model convergence; (2) The lack of sufficient consideration of data missing patterns, dynamic time delay characteristics, and spatial correlation of data measurement points results in insufficient generalization performance of the modeling results under conditions of working condition switching and multi-measurement point coupling.

[0005] To address the aforementioned problems, this invention proposes a method and system for soft measurement modeling of industrial processes with incomplete data. Summary of the Invention

[0006] To overcome the defects and shortcomings of existing technologies, this invention provides a method and system for soft measurement modeling of industrial processes with incomplete data. By introducing multi-dimensional feature prior constraints based on historical sample data in the model initialization stage, the interpretability and stability of the soft measurement model are effectively improved.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a method for soft sensing modeling of industrial processes oriented towards incomplete data, including:

[0009] Acquire historical sample data containing missing values ​​from industrial processes and construct a BGPLVM model;

[0010] Based on historical sample data, sample features are extracted and used as prior constraints to initialize the hyperparameters of the BGPLVM model, thereby obtaining the latent variable variational distribution of the historical sample data and the optimal values ​​of the model hyperparameters.

[0011] Obtain query sample data and perform probability modeling based on the trained BGPLVM model to obtain the latent variable variational distribution of the query sample data;

[0012] By using SKL divergence measurement on the latent variable variational distribution of historical sample data and query sample data, a local sample dataset is constructed by extracting historical sample data that is most similar to the latent variable variational distribution.

[0013] A Gaussian process regression model is constructed and the nonlinear features between latent variables and output variables in a local sample dataset are extracted. The parameters of the Gaussian process regression model are determined by maximizing the log-likelihood.

[0014] Substitute the latent variational distribution of the query sample data into the Gaussian process regression model to predict the output variable corresponding to the query sample data.

[0015] Furthermore, the extraction of sample features based on historical sample data includes:

[0016] Based on historical sample data, multi-dimensional sample features are extracted and multi-dimensional sample feature vectors are constructed. The multi-dimensional sample feature vectors include the sample's missing feature vector, time delay feature vector, measurement point spatial feature vector, and working condition label feature vector.

[0017] The missing feature vector, time delay feature vector, measurement point spatial feature vector, and working condition label feature vector are concatenated to generate a sample feature description matrix;

[0018] The sample feature description matrix is ​​used as a prior constraint input to the BGPLVM model to adjust the kernel function hyperparameters during the model initialization phase.

[0019] Furthermore, the construction of the multi-dimensional sample feature vector includes:

[0020] By performing missing data analysis on each input variable in historical sample data, the missing rate and missing distribution pattern of each input variable are determined; a sliding time window is used to calculate the curve of the missing rate of each variable changing over time and the missing time autocorrelation coefficient is extracted; a missing feature vector of historical sample data is constructed based on the missing rate, missing distribution pattern and missing time autocorrelation coefficient.

[0021] By performing cross-correlation analysis on each input variable and the target output variable in historical sample data, the correlation coefficient distribution curves of each input variable and the output variable under different time lags are obtained; by searching for the peak position of the correlation coefficient distribution curve, the optimal lag time of each input variable relative to the output variable is determined and a time delay feature vector is constructed.

[0022] Based on the physical spatial distance between data measurement points, construct the spatial adjacency matrix of measurement points and calculate the cross-correlation matrix among all input variables; merge the adjacency matrix and cross-correlation matrix to generate the spatial correlation matrix of measurement points and use the main feature vector in the spatial correlation matrix of measurement points as the spatial correlation feature vector of the sample;

[0023] Based on the load changes of industrial processes and the clustering algorithm, discrete operating condition labels are labeled for historical sample data. The operating condition labels are then one-hot encoded to construct the operating condition label feature vector of the sample.

[0024] Furthermore, obtaining the latent variable variational distribution and the optimal values ​​of the model hyperparameters from the historical sample data includes:

[0025] A joint probability distribution of a Bayesian Gaussian process latent variable model is established for historical sample data containing missing values. By introducing sparse induced variables, a mapping relationship between the observation space and the latent space is constructed and a variational distribution is defined.

[0026] The covariance matrix between samples is calculated by using an automatic correlation method to determine the squared exponential kernel function, and a variational lower bound function is established based on the data in the non-missing dimensions.

[0027] Using the variational lower bound function as the objective function, the variational inference algorithm is used to initialize the model hyperparameters, including kernel function hyperparameters, noise variance, and the location of induced variables.

[0028] The optimal solution is obtained by iteratively solving the quantized conjugate gradient algorithm, which yields the mean and covariance of the latent variable variational distribution corresponding to the historical samples, as well as the optimal values ​​of the hyperparameters of the BGPLVM model.

[0029] Furthermore, obtaining the latent variable variational distribution of the query sample data includes:

[0030] Obtain query sample data and identify missing input dimensions in the query sample. Calculate the Mahalanobis distance between the non-missing dimensions of the query sample and the corresponding dimensions of the historical samples. Select the latent variable variational distribution of the historical sample with the smallest distance as the initial latent variable distribution of the query sample.

[0031] Under the condition that the BGPLVM model structure and hyperparameters are fixed, the query samples are added to the model's observation set and their non-missing dimensions are used as constraints to establish a variational lower bound function containing the query samples.

[0032] By maximizing the variational lower bound and iteratively optimizing the mean and covariance of the latent variable distribution of the query sample, the optimal latent variable variational distribution corresponding to the query sample is obtained, which is used to characterize the probability distribution of the query sample in the latent space.

[0033] Furthermore, the step of extracting historical sample data most similar to the latent variable variational distribution to construct a local sample dataset includes:

[0034] Obtain the latent variable variational distribution parameters corresponding to historical sample data and query sample data. The latent variable variational distribution parameters include the mean vector and the covariance matrix.

[0035] SKL divergence is used as a distribution similarity metric to calculate the distribution difference between the query sample data and each historical sample data.

[0036] Arrange the SKL divergence values ​​in ascending order to obtain the distribution similarity ranking results between each historical sample data and the query sample data.

[0037] A local sample dataset is constructed by selecting the top N historical sample data from the distribution similarity ranking results. The value of N is determined based on the stable interval of the variance distribution of the latent variables of the historical samples.

[0038] Secondly, the present invention provides an industrial process soft measurement modeling system for incomplete data, comprising:

[0039] The latent variable model building module is used to obtain historical sample data containing missing values ​​in industrial processes and build a BGPLVM model.

[0040] The latent variable model initialization module is used to extract sample features based on historical sample data and use them as prior constraints to initialize the hyperparameters of the BGPLVM model, thereby obtaining the latent variable variational distribution of the historical sample data and the optimal values ​​of the model hyperparameters.

[0041] The query sample probability modeling module is used to obtain query sample data and perform probability modeling based on the trained BGPLVM model to obtain the latent variable variational distribution of the query sample data.

[0042] The SKL divergence measurement module is used to measure the SKL divergence by analyzing the latent variable variational distribution of historical sample data and query sample data, and to extract the historical sample data that is most similar to the latent variable variational distribution to construct a local sample dataset.

[0043] The regression model building module is used to construct a Gaussian process regression model and extract the nonlinear features between latent variables and output variables in a local sample dataset. The parameters of the Gaussian process regression model are determined by maximizing the log-likelihood.

[0044] The output variable prediction module is used to substitute the latent variational distribution of the query sample data into the Gaussian process regression model to predict the output variable corresponding to the query sample data.

[0045] Thirdly, the present invention provides an electronic device, comprising: a processor and a memory, wherein the memory stores a computer program that can be called by the processor, and the processor executes an industrial process soft measurement modeling method for incomplete data by calling the computer program stored in the memory.

[0046] Fourthly, the present invention provides a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform a soft measurement modeling method for industrial processes oriented towards incomplete data.

[0047] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0048] (1) By introducing multi-dimensional feature prior constraints based on historical sample data in the initialization stage of the BGPLVM model, this invention comprehensively considers the missing features, time delay features, measurement point spatial features and working condition label features of the samples, which significantly enhances the model's ability to understand the internal structure of industrial process data and effectively improves the interpretability and stability of the model.

[0049] (2) In the feature extraction stage, the present invention introduces spatial feature modeling of measurement points. By fusing the physical space adjacency matrix and the cross-correlation matrix between variables, a spatial correlation matrix of measurement points is generated and used as a spatial consistency constraint input into the BGPLVM model. This enables spatially similar measurement points to maintain a small distance in the latent space, thereby realizing spatial correlation modeling consistent with the actual physical topology and improving the prediction consistency of the model in multi-measurement point coupling scenarios.

[0050] (3) This invention combines the multi-condition operation characteristics of industrial processes and introduces condition label feature vectors as discrete prior terms to realize adaptive clustering and distribution separation of latent variable distribution under different conditions. This enables the model to maintain stable prediction performance under complex operating conditions such as multiple loads and mode switching, and significantly improves the cross-condition generalization ability of the soft measurement model. Attached Figure Description

[0051] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0052] Figure 1 This is a flowchart illustrating the industrial process soft measurement modeling method for incomplete data provided in an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram of the soft measurement modeling process provided in an embodiment of the present invention;

[0054] Figure 3 This is a schematic diagram of the structure of the industrial process soft measurement modeling system for incomplete data provided in an embodiment of the present invention;

[0055] Figure 4 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0056] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0057] Please see Figure 1 , Figure 1 This is a schematic diagram of the overall process of the industrial process soft measurement modeling method for incomplete data provided in this embodiment of the invention, which specifically includes the following steps:

[0058] S100. Obtain historical sample data containing missing values ​​in the industrial process and construct a BGPLVM model. The Bayesian Gaussian Process Latent Variable Model (BGPLVM) is a Bayesian extension of the Gaussian Process Latent Variable Model (GPLVM), which can effectively handle the problem of missing data and mine the hidden low-dimensional features of the process. After further considering the random noise of the process, the latent variables of each data sample all follow a Gaussian distribution.

[0059] S200. Extract sample features based on historical sample data and use them as prior constraints to initialize the hyperparameters of the BGPLVM model, thereby obtaining the latent variable variational distribution of the historical sample data and the optimal value of the model hyperparameters.

[0060] Based on the correlation between easily measurable process variables and the output variables to be measured, and by appropriately selecting some auxiliary variables as input variables for the mathematical model, the fundamental principle of soft sensor modeling is to estimate key quality variables that are difficult to measure directly in real time. Please refer to [link to relevant documentation]. Figure 2 , Figure 2This is a flowchart illustrating the soft measurement modeling process provided in this embodiment of the invention. The basic steps of soft measurement modeling include: auxiliary variable selection, data preprocessing, soft measurement modeling based on historical data, online correction based on analyzed data, and finally outputting the dominant variable. In actual production scenarios of industrial processes, the collected process data often exhibits characteristics such as frequent missing values, inconsistent sampling delays, complex coupling between measurement points, and significant disturbances under multiple operating conditions. Therefore, by extracting sample features from historical sample data, the aim is to establish a priori understanding of the input features from the data source by systematically analyzing and quantifying the multidimensional feature information of historical samples before model training. This provides a more physically meaningful and statistically regular initialization basis for the hyperparameters of the kernel function of the BGPLVM model, thereby realizing an adaptive modeling mechanism based on process features. The sample feature extraction based on historical sample data includes:

[0061] Based on historical sample data, multi-dimensional sample features are extracted and multi-dimensional sample feature vectors are constructed. The multi-dimensional sample feature vectors include the sample's missing feature vector, time delay feature vector, measurement point spatial feature vector, and working condition label feature vector.

[0062] The missing feature vector, time delay feature vector, measurement point spatial feature vector, and working condition label feature vector are concatenated to generate a sample feature description matrix;

[0063] The sample feature description matrix is ​​used as a prior constraint input to the BGPLVM model to adjust the kernel function hyperparameters during the model initialization phase.

[0064] By normalizing and concatenating missing features, time delay features, spatial features, and operating condition label features to form a sample feature description matrix, and using this matrix as a prior constraint input to the BGPLVM model, the kernel function hyperparameters and latent variable distribution can be adaptively adjusted during the model initialization phase. This makes the model's latent space more consistent with the real data structure characteristics of industrial processes, thereby achieving efficient and robust soft measurement modeling under incomplete data conditions. Specifically, by statistically analyzing and modeling the missing rate, missing distribution pattern, and temporal autocorrelation of each input variable in historical sample data to form a missing feature vector, the missing pattern and temporal dependence of different variables can be effectively revealed. Furthermore, by extracting input variables... By establishing dynamic time delay feature vectors between output variables, the model can identify time lag patterns in industrial processes and capture the time differences in the response of different input variables to the output. By constructing spatial adjacency matrices and cross-correlation matrices between measurement points, and fusing them to generate a spatial correlation matrix of measurement points and extracting its principal feature vectors, the model can quantify the coordinated change trends of spatially adjacent measurement points, achieving consistency constraints on the actual physical topology. By combining historical operating loads and cluster analysis to extract operating condition label feature vectors, the model can automatically distinguish the sample distribution under different operating conditions during the latent variable learning phase, achieving adaptive clustering under operating conditions and robust cross-operating condition modeling, constructing multi-dimensional sample feature vectors, including:

[0065] By performing missing data analysis on each input variable in historical sample data, the missing rate and missing distribution pattern of each input variable are determined; a sliding time window is used to calculate the curve of the missing rate of each variable changing over time and the missing time autocorrelation coefficient is extracted; a missing feature vector of historical sample data is constructed based on the missing rate, missing distribution pattern and missing time autocorrelation coefficient.

[0066] By performing cross-correlation analysis on each input variable and the target output variable in historical sample data, the correlation coefficient distribution curves of each input variable and the output variable under different time lags are obtained; by searching for the peak position of the correlation coefficient distribution curve, the optimal lag time of each input variable relative to the output variable is determined and a time delay feature vector is constructed.

[0067] Based on the physical spatial distance between data measurement points, construct the spatial adjacency matrix of measurement points and calculate the cross-correlation matrix among all input variables; merge the adjacency matrix and cross-correlation matrix to generate the spatial correlation matrix of measurement points and use the main feature vector in the spatial correlation matrix of measurement points as the spatial correlation feature vector of the sample;

[0068] Based on the load changes of industrial processes, a clustering algorithm is used to label historical sample data with discrete operating condition labels. The operating condition labels are then one-hot encoded to construct the sample's operating condition label feature vector.

[0069] In soft measurement modeling of industrial processes, historical sample data often suffers from high dimensionality, strong nonlinearity, and missing dimensions. Traditional linear modeling or mean imputation methods struggle to accurately describe the implicit dependencies between variables. Bayesian Gaussian process latent variable models provide a unified framework for nonlinear dimensionality reduction and probabilistic modeling. Their core idea is to establish a nonlinear mapping between input data and output features in a latent low-dimensional space. However, ensuring the interpretability and generalization ability of the model in the latent space under incomplete data conditions hinges on the optimization and inference process of latent variable distributions and hyperparameters. Therefore, establishing a joint probability distribution for historical sample data containing missing values ​​and introducing sparse induced variables to construct a mapping between the observation space and the latent space can effectively reduce the computational complexity of large-scale industrial data while preserving key statistical features. Establishing a variational lower bound function based on data with non-missing dimensions further ensures the convergence and robustness of model training under incomplete data conditions. By jointly optimizing the solution using variational inference and the quantized conjugate gradient algorithm, the optimal solutions for the latent variable distribution and kernel function hyperparameters can be obtained efficiently. This provides a reliable statistical basis for subsequent probabilistic inference and local modeling of query samples, yielding the latent variable variational distribution and optimal values ​​of model hyperparameters from historical sample data, including:

[0070] A joint probability distribution of a Bayesian Gaussian process latent variable model is established for historical sample data containing missing values. By introducing sparse induced variables, a mapping relationship between the observation space and the latent space is constructed and a variational distribution is defined.

[0071] The covariance matrix between samples is calculated by using an automatic correlation method to determine the squared exponential kernel function, and a variational lower bound function is established based on the data in the non-missing dimensions.

[0072] Using the variational lower bound function as the objective function, the variational inference algorithm is used to initialize the model hyperparameters, including kernel function hyperparameters, noise variance, and the location of induced variables.

[0073] The optimal solution is obtained by iteratively solving the quantized conjugate gradient algorithm, which yields the mean and covariance of the latent variable variational distribution corresponding to the historical samples, as well as the optimal values ​​of the hyperparameters of the BGPLVM model.

[0074] S300. Obtain the query sample data and perform probability modeling based on the trained BGPLVM model to obtain the latent variable variational distribution of the query sample data.

[0075] Newly collected query samples often have missing input variables or incomplete measurement point information. Directly inputting them into a soft sensing model can lead to uncertainty in the mapping relationship between the input space and the latent space, thus affecting the reliability of the output prediction. By calculating the Mahalanobis distance between the non-missing dimensions of the query sample and historical samples, the distribution of the most similar historical sample latent variables is selected as the initial estimate to ensure that the initial position of the query sample in the latent space is consistent with its corresponding historical pattern. Subsequently, with the BGPLVM model structure and hyperparameters fixed, a variational lower bound function incorporating the query sample is constructed to achieve probabilistic constraints and optimization of the latent variable distribution. Finally, by maximizing the variational lower bound, the optimal mean and covariance of the query sample latent variable distribution are obtained, enabling the model to accurately infer the position of the sample in the latent space under incomplete input conditions. This achieves adaptive probabilistic modeling under missing information conditions, yielding the variational distribution of the latent variables of the query sample data, including:

[0076] Obtain query sample data and identify missing input dimensions in the query sample. Calculate the Mahalanobis distance between the non-missing dimensions of the query sample and the corresponding dimensions of the historical samples. Select the latent variable variational distribution of the historical sample with the smallest distance as the initial latent variable distribution of the query sample.

[0077] Under the condition that the BGPLVM model structure and hyperparameters are fixed, the query samples are added to the model's observation set and their non-missing dimensions are used as constraints to establish a variational lower bound function containing the query samples.

[0078] By maximizing the variational lower bound and iteratively optimizing the mean and covariance of the latent variable distribution of the query sample, the optimal latent variable variational distribution corresponding to the query sample is obtained, which is used to characterize the probability distribution of the query sample in the latent space.

[0079] S400. By performing SKL divergence measurement on the latent variable variational distribution of historical sample data and query sample data, extract the historical sample data that is most similar to the latent variable variational distribution to construct a local sample dataset.

[0080] Query samples often correspond to the process state at a specific moment or under a specific working condition, and their latent space distribution may differ significantly from the global sample distribution. Directly predicting based on all historical samples would not only introduce a large amount of irrelevant or low-relevance data but also increase the computational complexity of modeling and reduce prediction accuracy. Therefore, it is necessary to identify the subset of historical samples most similar to the query sample in the latent space based on its probability distribution, in order to construct a more targeted local modeling sample set. By extracting the latent variable variational distribution parameters corresponding to the historical samples and the query sample, and using Symmetric Kullback-Leibler (SKL) divergence as a distribution similarity metric, distribution alignment and similarity quantification at the latent space level are achieved. By calculating the SKL divergence between the query sample and each historical sample and sorting them in ascending order, the sample group most closely related to the query sample can be selected from a probability distribution perspective. The local sample dataset is constructed by extracting the historical sample data most similar to the latent variable variational distribution, including:

[0081] Obtain the latent variable variational distribution parameters corresponding to historical sample data and query sample data. The latent variable variational distribution parameters include the mean vector and the covariance matrix.

[0082] SKL divergence is used as a distribution similarity metric to calculate the distribution difference between the query sample data and each historical sample data.

[0083] Arrange the SKL divergence values ​​in ascending order to obtain the distribution similarity ranking results between each historical sample data and the query sample data.

[0084] A local sample dataset is constructed by selecting the top N historical sample data from the distribution similarity ranking results. The value of N is determined based on the stable interval of the variance distribution of the latent variables of the historical samples.

[0085] S500. Construct a Gaussian process regression model and extract the nonlinear features between latent variables and output variables in the local sample dataset. Determine the parameters of the Gaussian process regression model by maximizing the log-likelihood. The Gaussian process regression (GPR) model can extract the hidden detailed features and highly nonlinear features in the process data, overcoming the shortcomings of traditional deep learning methods that only utilize the information of the highest-level latent variables and cannot fully explore the features of the process object.

[0086] S600. Substitute the latent variational distribution of the query sample data into the Gaussian process regression model to predict the output variable corresponding to the query sample data.

[0087] Please see Figure 3 , Figure 3This is a schematic diagram of the structure of an industrial process soft measurement modeling system for incomplete data provided in an embodiment of the present invention, including:

[0088] Latent variable model building module 210 is used to obtain historical sample data containing missing values ​​in industrial processes and build a BGPLVM model.

[0089] The latent variable model initialization module 220 is used to extract sample features based on historical sample data and use them as prior constraints to initialize the hyperparameters of the BGPLVM model, thereby obtaining the latent variable variational distribution of the historical sample data and the optimal values ​​of the model hyperparameters.

[0090] The query sample probability modeling module 230 is used to acquire query sample data and perform probability modeling based on the trained BGPLVM model to obtain the latent variable variational distribution of the query sample data.

[0091] The SKL divergence measurement module 240 is used to measure the SKL divergence by analyzing the latent variable variational distribution of historical sample data and query sample data, and to extract the historical sample data that is most similar to the latent variable variational distribution to construct a local sample dataset.

[0092] The regression model building module 250 is used to build a Gaussian process regression model and extract the nonlinear features between latent variables and output variables in a local sample dataset. The parameters of the Gaussian process regression model are determined by maximizing the log-likelihood.

[0093] The output variable prediction module 260 is used to substitute the latent variable variational distribution of the query sample data into the Gaussian process regression model to predict the output variable corresponding to the query sample data.

[0094] In this embodiment of the invention, the latent variable model initialization module 220 is used to extract sample features based on historical sample data and use them as prior constraints to initialize the hyperparameters of the BGPLVM model, thereby obtaining the latent variable variational distribution of the historical sample data and the optimal values ​​of the model hyperparameters. The extraction of sample features based on historical sample data includes:

[0095] Based on historical sample data, multi-dimensional sample features are extracted and multi-dimensional sample feature vectors are constructed. The multi-dimensional sample feature vectors include the sample's missing feature vector, time delay feature vector, measurement point spatial feature vector, and working condition label feature vector.

[0096] The missing feature vector, time delay feature vector, measurement point spatial feature vector, and working condition label feature vector are concatenated to generate a sample feature description matrix;

[0097] The sample feature description matrix is ​​used as a prior constraint input to the BGPLVM model to adjust the kernel function hyperparameters during the model initialization phase.

[0098] The construction of multi-dimensional sample feature vectors includes:

[0099] By performing missing data analysis on each input variable in historical sample data, the missing rate and missing distribution pattern of each input variable are determined; a sliding time window is used to calculate the curve of the missing rate of each variable changing over time and the missing time autocorrelation coefficient is extracted; a missing feature vector of historical sample data is constructed based on the missing rate, missing distribution pattern and missing time autocorrelation coefficient.

[0100] By performing cross-correlation analysis on each input variable and the target output variable in historical sample data, the correlation coefficient distribution curves of each input variable and the output variable under different time lags are obtained; by searching for the peak position of the correlation coefficient distribution curve, the optimal lag time of each input variable relative to the output variable is determined and a time delay feature vector is constructed.

[0101] Based on the physical spatial distance between data measurement points, construct the spatial adjacency matrix of measurement points and calculate the cross-correlation matrix among all input variables; merge the adjacency matrix and cross-correlation matrix to generate the spatial correlation matrix of measurement points and use the main feature vector in the spatial correlation matrix of measurement points as the spatial correlation feature vector of the sample;

[0102] Based on the load changes of industrial processes, a clustering algorithm is used to label historical sample data with discrete operating condition labels. The operating condition labels are then one-hot encoded to construct the sample's operating condition label feature vector.

[0103] This includes obtaining the latent variable variational distribution and the optimal values ​​of the model hyperparameters from the historical sample data, including:

[0104] A joint probability distribution of a Bayesian Gaussian process latent variable model is established for historical sample data containing missing values. By introducing sparse induced variables, a mapping relationship between the observation space and the latent space is constructed and a variational distribution is defined.

[0105] The covariance matrix between samples is calculated by using an automatic correlation method to determine the squared exponential kernel function, and a variational lower bound function is established based on the data in the non-missing dimensions.

[0106] Using the variational lower bound function as the objective function, the variational inference algorithm is used to initialize the model hyperparameters, including kernel function hyperparameters, noise variance, and the location of induced variables.

[0107] The optimal solution is obtained by iteratively solving the quantized conjugate gradient algorithm, which yields the mean and covariance of the latent variable variational distribution corresponding to the historical samples, as well as the optimal values ​​of the hyperparameters of the BGPLVM model.

[0108] In this embodiment of the invention, the query sample probability modeling module 230 is used to acquire query sample data and perform probability modeling based on the trained BGPLVM model to obtain the latent variable variational distribution of the query sample data, including:

[0109] Obtain query sample data and identify missing input dimensions in the query sample. Calculate the Mahalanobis distance between the non-missing dimensions of the query sample and the corresponding dimensions of the historical samples. Select the latent variable variational distribution of the historical sample with the smallest distance as the initial latent variable distribution of the query sample.

[0110] Under the condition that the BGPLVM model structure and hyperparameters are fixed, the query samples are added to the model's observation set and their non-missing dimensions are used as constraints to establish a variational lower bound function containing the query samples.

[0111] By maximizing the variational lower bound and iteratively optimizing the mean and covariance of the latent variable distribution of the query sample, the optimal latent variable variational distribution corresponding to the query sample is obtained, which is used to characterize the probability distribution of the query sample in the latent space.

[0112] In this embodiment of the invention, the SKL divergence measurement module 240 is used to perform SKL divergence measurement on the latent variable variational distribution of historical sample data and query sample data, and extract the historical sample data most similar to the latent variable variational distribution to construct a local sample dataset, including:

[0113] Obtain the latent variable variational distribution parameters corresponding to historical sample data and query sample data. The latent variable variational distribution parameters include the mean vector and the covariance matrix.

[0114] SKL divergence is used as a distribution similarity metric to calculate the distribution difference between the query sample data and each historical sample data.

[0115] Arrange the SKL divergence values ​​in ascending order to obtain the distribution similarity ranking results between each historical sample data and the query sample data.

[0116] A local sample dataset is constructed by selecting the top N historical sample data from the distribution similarity ranking results. The value of N is determined based on the stable interval of the variance distribution of the latent variables of the historical samples.

[0117] The steps for implementing the corresponding functions of each parameter and each unit module in the industrial process soft measurement modeling system for incomplete data of the present invention can be referred to the parameters and steps in the embodiments of the industrial process soft measurement modeling method for incomplete data described above, and will not be repeated here.

[0118] Please refer to Figure 4Embodiments of the present invention also provide an electronic device 300, including a memory 310, a processor 320, and a communication bus 330; the memory 310 and the processor 320 are connected via the communication bus 330. The memory 310 stores an industrial process soft measurement modeling method for incomplete data, which can be loaded and executed by the processor 320, as provided in the above embodiments.

[0119] The memory 310 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 310 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system, instructions for at least one function, and instructions for implementing the industrial process soft measurement modeling method for incomplete data provided in the above embodiments. The data storage area may store data involved in the industrial process soft measurement modeling method for incomplete data provided in the above embodiments.

[0120] Processor 320 may include one or more processing cores. Processor 320 executes instructions, programs, code sets, or instruction sets stored in memory 310, and calls data stored in memory 310 to perform various functions and process data according to the present invention. Processor 320 may be at least one of the following: Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), Central Processing Unit (CPU), Controller, Microcontroller, and Microprocessor. It is understood that, for different devices, the electronic devices used to implement the functions of processor 320 may also be other types, and the embodiments of the present invention do not specifically limit this.

[0121] The communication bus 330 may include a path for transmitting information between the aforementioned components. The communication bus 330 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. The communication bus 330 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 4The symbol is represented by a single double arrow, but this does not mean that there is only one bus or one type of bus.

[0122] This invention provides a computer-readable storage medium storing a computer program that can be loaded by a processor and executed as described in the above embodiments, which is a soft measurement modeling method for industrial processes with incomplete data.

[0123] In this embodiment of the invention, the computer-readable storage medium can be a tangible device that holds and stores instructions used by an instruction execution device. The computer-readable storage medium can be, but is not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof. Specifically, the computer-readable storage medium can be a portable computer disk, a hard disk, a USB flash drive, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), lectern random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory stick, floppy disk, optical disk, magnetic disk, mechanical encoding device, or any combination thereof.

[0124] The terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0125] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of this application is not limited to the technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the foregoing concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions claimed in this invention.

Claims

1. A method for soft-sensing modeling of industrial processes with incomplete data, characterized in that, The application relates to a method for predicting industrial process output variables. The method comprises the following steps: acquiring historical sample data containing missing values in an industrial process and constructing a BGPLVM model; extracting sample features based on the historical sample data and initializing BGPLVM model hyperparameters as prior constraints to obtain the latent variable variational distribution of the historical sample data and the optimal value of the model hyperparameters; acquiring query sample data and performing probabilistic modeling based on the trained BGPLVM model to obtain the latent variable variational distribution of the query sample data; extracting the most similar historical sample data to the latent variable variational distribution by performing SKL divergence measurement on the latent variable variational distribution of the historical sample data and the query sample data to construct a local sample data set; constructing a Gaussian process regression model and extracting the nonlinear features between the latent variables and the output variables in the local sample data set to determine the Gaussian process regression model parameters by maximizing the log-likelihood; substituting the latent variable variational distribution of the query sample data into the Gaussian process regression model to predict the output variable corresponding to the query sample data. The method comprises the following steps: extracting multi-dimensional sample features based on the historical sample data and constructing a multi-dimensional sample feature vector, wherein the multi-dimensional sample feature vector comprises a missing feature vector, a time delay feature vector, a measurement point space feature vector and a working condition label feature vector of the sample; splicing the missing feature vector, the time delay feature vector, the measurement point space feature vector and the working condition label feature vector to generate a sample feature description matrix; inputting the sample feature description matrix as prior constraints into the BGPLVM model to adjust the kernel function hyperparameters in the model initialization stage; The method comprises the following steps: determining the missing rate and the missing distribution mode of each input variable by performing missing statistics on the input variables in the historical sample data; calculating the missing time autocorrelation coefficient by adopting a sliding time window; and constructing a missing feature vector of the historical sample data based on the missing rate, the missing distribution mode and the missing time autocorrelation coefficient; performing cross-correlation analysis on each input variable and the target output variable in the historical sample data to obtain the correlation coefficient distribution curve of each input variable and the output variable at different time lags; determining the optimal lag time of each input variable compared with the output variable by searching the peak position of the correlation coefficient distribution curve and constructing a time delay feature vector; constructing a measurement point space adjacency matrix based on the physical space distance between data measurement points and calculating the cross-correlation matrix among all input variables; generating a measurement point space correlation matrix by fusing the adjacency matrix and the cross-correlation matrix and taking the principal feature vector in the measurement point space correlation matrix as the spatial correlation feature vector of the sample; 2. The industrial process soft sensor modeling method for imperfect data according to claim 1, characterized in that, labeling discrete working condition labels for the historical sample data based on the load change of the industrial process and combining a clustering algorithm; and constructing a working condition label feature vector of the sample by one-hot encoding the working condition labels. The method comprises the following steps: The joint probability distribution of the Bayesian Gaussian process latent variable model is established for historical sample data containing missing values, a sparse inducing variable is introduced to construct a mapping relationship between the observation space and the latent space and define a variational distribution; An automatic correlation is used to determine a square exponential kernel function to calculate the covariance matrix between samples, and a variational lower bound function is established based on the data of the non-missing dimensions; A variational inference algorithm is used to initialize the model hyperparameters including the kernel function hyperparameters, noise variance and inducing variable position, taking the variational lower bound function as the objective function; A quantized conjugate gradient algorithm is used to iteratively solve the optimal solution to obtain the mean and covariance of the latent variable variational distribution corresponding to the historical samples and the optimal value of the BGPLVM model hyperparameters.

3. The industrial process soft sensor modeling method for imperfect data according to claim 1, wherein, The latent variable variational distribution of the query sample data is obtained, including: The query sample data is obtained and the input dimensions with missing values in the record query sample are identified, the Mahalanobis distance between the non-missing dimensions of the query sample and the corresponding dimensions of the historical samples is calculated, and the latent variable variational distribution of the historical sample with the smallest distance is selected as the initial latent variable distribution of the query sample; Under the condition that the BGPLVM model structure and hyperparameters are fixed, the query sample is added to the observation set of the model and the non-missing dimensions thereof are used as constraint terms to establish a variational lower bound function including the query sample; The mean and covariance of the query sample latent variable distribution are iteratively optimized by maximizing the variational lower bound to obtain the optimal latent variable variational distribution corresponding to the query sample, which is used to represent the probability distribution of the query sample in the latent space.

4. The industrial process soft sensor modeling method for imperfect data according to claim 1, wherein, The local sample data set is constructed by extracting the historical sample data most similar to the latent variable variational distribution, including: The latent variable variational distribution parameters corresponding to the historical sample data and the query sample data are obtained, including the mean vector and the covariance matrix; The SKL divergence is used as a distribution similarity measurement index to calculate the distribution difference between the query sample data and each historical sample data; The SKL divergence values are arranged in ascending order to obtain the distribution similarity sorting results of each historical sample data and the query sample data; The top N historical sample data in the distribution similarity sorting results are selected to construct a local sample data set, and the value of N is determined according to the stable interval of the historical sample latent variable variance distribution.

5. An industrial process soft-sensing modeling system for incomplete data, for implementing the industrial process soft-sensing modeling method for incomplete data according to any one of claims 1 to 4, characterized in that, The system comprises: A latent variable model construction module for obtaining historical sample data containing missing values in an industrial process and constructing a BGPLVM model; A latent variable model initialization module for performing sample feature extraction based on the historical sample data and initializing the BGPLVM model hyperparameters as a prior constraint to obtain the latent variable variational distribution of the historical sample data and the optimal value of the model hyperparameters; A query sample probability modeling module for obtaining query sample data and performing probability modeling based on the trained BGPLVM model to obtain the latent variable variational distribution of the query sample data; An SKL divergence measurement module for measuring the SKL divergence of the latent variable variational distribution of the historical sample data and the query sample data to extract the historical sample data most similar to the latent variable variational distribution and construct a local sample data set; The regression model construction module is configured to construct a Gaussian process regression model and extract nonlinear features between the latent variables and the output variables in the local sample data set, and determine parameters of the Gaussian process regression model by maximizing a log-likelihood. The output variable prediction module is configured to input a latent variable variational distribution of a query sample data into the Gaussian process regression model to predict an output variable corresponding to the query sample data.

6. An electronic device comprising: A processor and a memory, wherein the memory stores a computer program that can be invoked by the processor; characterized in that the processor invokes the computer program stored in the memory to perform the industrial process soft-sensing modeling method for incomplete data according to any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, An instruction is stored, and when the instruction runs on a computer, the computer executes the industrial process soft-sensing modeling method for incomplete data according to any one of claims 1-4.

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