CN-118964839-B - Data complement method and system for depth matrix decomposition considering dynamic constraint

CN118964839BCN 118964839 BCN118964839 BCN 118964839BCN-118964839-B

Abstract

The invention relates to a depth matrix decomposition method and a system considering dynamic constraint, wherein the method comprises the steps of obtaining an original complete data set, and carrying out data deletion processing on the original complete data set to obtain a deletion processing data set; the method comprises the steps of carrying out standardized pretreatment on a missing processing data set, training to obtain a depth matrix decomposition model considering dynamic constraint by using the missing processing data set subjected to standardized pretreatment, and carrying out data complementation on the current data set through the depth matrix decomposition model considering dynamic constraint when the current data set of missing data is received. The data change rate is used as a dynamic constraint condition to improve the data complement capability of the model, the change condition of the data along with time is considered, the dynamic characteristics of the data are emphasized instead of the static numerical values, and the depth matrix decomposition model considering dynamic constraint is guided to understand the dynamic change rule of the data by constraining the data change rate, so that the data complement precision is improved.

Inventors

LI YONGGANG
HE JINGXIU
JI ZHIYI
YANG CHUNHUA
LI DONG

Assignees

中南大学

Dates

Publication Date: 20260508
Application Date: 20240719

Claims (6)

1. A method of data completion for depth matrix factorization with consideration of dynamic constraints, comprising: acquiring an original complete data set from a BSM1 sewage treatment simulation platform, and performing data deletion treatment on the original complete data set to obtain a deletion treatment data set; carrying out standardized pretreatment on the missing processing data set; according to the original sparse matrix after standardized pretreatment Obtaining an expression of the original sparse matrix: ; the original sparse matrix is a missing processing data set, the m represents a row, the n represents a column, the U and the V are obtained by decomposing the original sparse matrix Y, and the method comprises the steps of The said The following steps Representing a non-linear mapping and applying to the Is executed by each column of the system Representing an activation function, wherein W is a weight matrix in an artificial neural network, and B is a bias vector in the artificial neural network; the numerical value of the original sparse matrix is changed along with time to obtain a new sparse matrix Modeling to obtain the expression of the new sparse matrix is as follows: ; Calculating the data transformation rate of each data point in the new sparse matrix through differential operation; converting the data rate As dynamic constraint conditions, an initial model expression is constructed: ; Wherein the said Is to the said Penalty term of (1); said Is a regularization parameter, the Is to the said Regularization parameters of penalty of (c) said Representing the Hadamard product, the For presetting a mask matrix, when M ij =1, the data corresponding to the position in the original sparse matrix is not missing, when M ij =0, the data corresponding to the position in the original sparse matrix is missing, the method comprises the steps of Is an adjustable super parameter; the initial model expression is expressed by the method Performing approximation processing by using an artificial neural network to obtain a first model expression approximating the initial model expression: ; Wherein the said Representing a weight matrix of Representing a bias vector, said Representing the said Is the first of (2) Columns of the Representing the said Is the first of (2) Columns of the Representing the said Is the first of (2) Columns of the Is a weight decay parameter; and carrying out deep upgrade on the single-layer artificial neural network of the first model expression to obtain a second model expression: ; Wherein the said The said , The said The number of layers is hidden; Taking the second model expression as an expression of a depth matrix decomposition model taking dynamic constraint into consideration; And when the current data set of the missing data is received, carrying out data complementation on the current data set through the depth matrix decomposition model considering dynamic constraint.
2. The method for data complement of depth matrix factorization with dynamic constraint according to claim 1, wherein said obtaining an original complete data set, performing data deletion processing on said original complete data set to obtain a deletion processed data set, comprises: Acquiring an original complete data set; Obtaining an original complete matrix according to the original complete data set; and performing dot multiplication operation on the original complete matrix through a preset mask matrix to obtain an original sparse matrix, wherein the preset mask matrix is preset according to the data missing condition.
3. The data complement method of depth matrix factorization with consideration of dynamic constraints of claim 2 wherein the preset mask matrix comprises a first mask matrix and a second mask matrix, the first mask matrix being set according to a regular data loss condition, the second mask matrix being set according to a large fragment data loss condition.
4. The method of data complement for depth matrix factorization with dynamic constraints of claim 2 wherein said normalizing the missing processed data set comprises: And carrying out standardized pretreatment on the original sparse matrix by adopting a standard Score Z-Score.
5. The method of data completion for depth matrix factorization with consideration of dynamic constraints of claim 1, wherein said calculating the data transformation rate for each data point in said new sparse matrix by differential operation comprises: the data points of the observation part in the new sparse matrix are ; For the 1 st initial data point And nth end data point The ith intermediate data point outside Estimating the using a center difference method The derivative of (2) is: ; for the initial data point Calculating corresponding time using forward difference method The derivative at this point is: ; for the end data point Calculating corresponding time using backward differencing The derivative at this point is: ; the derivative of each data point is taken as the data rate of the corresponding data point.
6. A data completion system for depth matrix factorization that accounts for dynamic constraints, comprising: The deletion processing module is used for acquiring an original complete data set from the BSM1 sewage treatment simulation platform, and carrying out data deletion processing on the original complete data set to obtain a deletion processing data set; the standardized processing module is used for carrying out standardized preprocessing on the missing processing data set; The model training module is used for carrying out standardized preprocessing on the original sparse matrix Obtaining an expression of the original sparse matrix: ; the original sparse matrix is a missing processing data set, the m represents a row, the n represents a column, the U and the V are obtained by decomposing the original sparse matrix Y, and the method comprises the steps of The said The following steps Representing a non-linear mapping and applying to the Is executed by each column of the system Representing an activation function, wherein W is a weight matrix in an artificial neural network, and B is a bias vector in the artificial neural network; the numerical value of the original sparse matrix is changed along with time to obtain a new sparse matrix Modeling to obtain the expression of the new sparse matrix is as follows: ; Calculating the data transformation rate of each data point in the new sparse matrix through differential operation; converting the data rate As dynamic constraint conditions, an initial model expression is constructed: ; Wherein the said Is to the said Penalty term of (1); said Is a regularization parameter, the Is to the said Regularization parameters of penalty of (c) said Representing the Hadamard product, the For presetting a mask matrix, when M ij =1, the data corresponding to the position in the original sparse matrix is not missing, when M ij =0, the data corresponding to the position in the original sparse matrix is missing, the method comprises the steps of Is an adjustable super parameter; the initial model expression is expressed by the method Performing approximation processing by using an artificial neural network to obtain a first model expression approximating the initial model expression: ; Wherein the said Representing a weight matrix of Representing a bias vector, said Representing the said Is the first of (2) Columns of the Representing the said Is the first of (2) Columns of the Representing the said Is the first of (2) Columns of the Is a weight decay parameter; and carrying out deep upgrade on the single-layer artificial neural network of the first model expression to obtain a second model expression: ; Wherein the said The said , The said The number of layers is hidden; Taking the second model expression as an expression of a depth matrix decomposition model taking dynamic constraint into consideration; and the data complement module is used for carrying out data complement on the current data set through the depth matrix decomposition model considering dynamic constraint when the current data set of the missing data is received.

Description

Data complement method and system for depth matrix decomposition considering dynamic constraint Technical Field The invention belongs to the technical field of industrial informatization, and particularly relates to a data complement method and system for depth matrix decomposition considering dynamic constraint. Background With the advancement of industrial informatization, large amounts of data are collected and used for monitoring, optimization and prediction of production processes. However, due to equipment failure, sensor anomalies, etc., there are often deletions in the data that severely affect the accuracy of data analysis and model training. The traditional missing data complement method mainly comprises constant value filling, regression filling, multiple interpolation and the like. These methods, while simple and portable to operate, often only consider simple relationships between data, fail to effectively capture the complex structure of the data, and when processing large-scale data sets, the computational complexity and time overhead are large, resulting in limited applications. Aiming at the defects of the traditional missing data complement method, a learner puts forward the concept of sparse matrix complement. Common sparse matrix completion methods include matrix decomposition, optimization algorithms, machine learning methods, and the like. These matrix completion methods all belong to the linear completion method and when highly non-linear data is encountered, it is difficult to provide accurate results because they are limited to low rank hypotheses. To better complement highly non-linear data. The method comprises the steps of processing a situation that missing values exist in a plurality of related data sets or modes by utilizing non-negative matrix factorization, capturing and modeling complex nonlinear relations in multi-view data through multi-manifold regularization and non-negative matrix factorization, processing a data recovery problem with nonlinear inequality constraint in a manufacturing process based on collaborative filtering, ensuring that the recovered data meets specified nonlinear constraint by utilizing correlation among sensor data, and the third method is a kernel sparse Bayesian matrix factorization method, capturing and modeling the nonlinear relations in the data by introducing a kernel function, and effectively processing the missing values and noise. However, none of these three approaches take into account the highly incomplete data matrix, e.g., data loss rates up to 80%. Therefore, if there are a large number of deletions in the nonlinear data, the high-precision data complement result cannot be ensured. Depth matrix factorization (Deep Matrix Factorization Model, DMF) provides the possibility to efficiently process highly incomplete data, and DMF models combine matrix factorization with depth neural networks, implemented using different artificial neural networks (ARTIFICIAL NEURAL NETWORK, ANN), such as multi-layer perceptrons (Multilayer Perceptron, MLP), convolutional neural networks (Convolutional Neural Networks, CNN), and recurrent neural networks. DMF is based on a nonlinear latent variable model, can recover a data matrix with nonlinear characteristics in a structure, can effectively process highly missing data, and is successfully applied to the fields of recommendation systems, image processing and the like. However, when the missing data block is just located at the data mutation position, the data complement effect cannot be guaranteed. In the process industry, sample data is severely changed, and the critical data points of the data mutation positions are missing, so that the completion accuracy cannot be ensured when the completion is carried out. Disclosure of Invention In order to make up the defects of the prior art, the invention provides a data complement method and a system for depth matrix decomposition considering dynamic constraint. In order to solve the technical problems, the invention adopts the following technical scheme: in a first aspect, a data complement method for depth matrix decomposition taking dynamic constraints into account is provided, including: Acquiring an original complete data set, and carrying out data deletion processing on the original complete data set to obtain a deletion processing data set; Carrying out standardized pretreatment on the missing processing data set; Training to obtain a depth matrix decomposition model considering dynamic constraint by using the standardized pre-processed missing processing data set; When the current data set of the missing data is received, the current data set is data-complemented by a depth matrix decomposition model taking into account dynamic constraints. Further, acquiring an original complete data set, performing data deletion processing on the original complete data set to obtain a deletion processing data set, including: Acquiring an original complete data set; Ob