Dynamic Spatiotemporal Memory Graph Convolutional Network Thermal Error Model and Industrial Machine Learning Big Data Framework

Abstract

This invention discloses a thermal error model for dynamic spatiotemporal memory graph convolutional networks, characterized by comprising N DTSMGCN layers arranged in series, wherein the output h of the i-th DTSMGCN layer... i t The input to the (i+1)th DTSMGCN layer is used. The DTSMGCN layer includes DTSMGCN units, each containing edge units, joint units, and a hybrid adjacency matrix. Edge units mine the temporal features of each variable and transmit these features to the joint units. Joint units mine the spatiotemporal features between variables, and the extracted spatiotemporal features are tightly coupled and propagated within the recursive network. The hybrid adjacency matrix mines spatial features, including dynamic geographic adjacency matrices, semantic adjacency matrices, and motion adjacency matrices. This invention also discloses a machine learning big data framework for industry. The dynamic spatiotemporal memory graph convolutional network hot error model and the machine learning big data framework for industry presented in this invention can effectively improve prediction accuracy and solve the problem of limited bandwidth in cloud computing for industrial applications.

Description

Technical Field

[0001] This invention belongs to the field of thermal error prediction and control technology, specifically a dynamic spatiotemporal memory graph convolutional network thermal error model and a machine learning big data framework for industry. Background Technology

[0002] The machining accuracy of machine tools affects production efficiency and quality. Various error sources exist in actual machining processes, leading to reduced machining accuracy, with thermal error accounting for the largest proportion of total error. Robust and accurate predictive models are the core of thermal error control. Currently, there are two main methods for thermal error modeling: data-driven and simulation-driven methods. Simulation-driven methods numerically simulate the thermal behavior of machine tools and are widely used due to their strong interpretability. However, simulation-driven methods require building complex machine tool structures, and the resulting numerical simulation model of the thermal characteristics of a specific machine tool may not be applicable to other machine tools. That is, simulation-driven models have poor generalization ability; furthermore, mesh generation and computation are very time-consuming. Therefore, data-driven methods are widely used. Traditional data-driven methods cannot avoid collinearity among multiple input variables and cannot extract correlations from large amounts of thermal information data, resulting in poor prediction accuracy of thermal error models. To extract correlations from large amounts of data, machine learning techniques are used to construct data-driven thermal error models. Current thermal error modeling methods focus on mining the temporal characteristics of thermal errors, which may lead to ignoring the spatial characteristics of thermal error data and assuming that thermal error data is not limited by sensor networks. Capturing spatial features comprehensively is crucial for accurate thermal error prediction. On one hand, current thermal error prediction methods do not consider the spatial characteristics of thermal error information; on the other hand, existing GCN-based models cannot adequately account for the spatial characteristics of thermal error information, thus limiting their effectiveness in thermal error prediction. Furthermore, in addition to spatial features, fusing spatial and temporal information is essential for thermal error prediction because thermal errors exhibit spatiotemporal behavior, but currently, there is no effective method to fuse the temporal and spatial characteristics of thermal errors. Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide a dynamic spatiotemporal memory graph convolutional network hot error model and an industrial machine learning big data framework. The dynamic spatiotemporal memory graph convolutional network hot error model can capture the temporal features of variables and the spatiotemporal features between variables, and comprehensively capture the spatial features of variables, which can effectively improve prediction accuracy. The industrial machine learning big data framework can facilitate users to develop machine learning algorithms and solve the problem of limited industrial bandwidth in cloud computing.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] This invention first proposes a dynamic spatiotemporal memory graph convolutional network thermal error model, comprising N DTSMGCN layers arranged in series, where N≥1; and: when N≥2, the output h of the i-th DTSMGCN layer... i t This is the input to the (i+1)th layer of the DTSMGCN layer, where 1 ≤ i ≤ N-1;

[0006] The DTSMGCN layer includes DTSMGCN units, each containing edge units, joint units, and a hybrid adjacency matrix. The edge units are used to mine the temporal features of each variable and transmit these features to the joint units. The joint units are used to mine the spatiotemporal features between variables, and the extracted spatiotemporal features are tightly coupled and propagated in the recursive network. The hybrid adjacency matrix is ​​used to mine spatial features, which include dynamic geographic adjacency matrices, semantic adjacency matrices, and motion adjacency matrices.

[0007] Furthermore, the edge unit is used to extract time information from multidimensional variables: the input variables are divided into k groups, where the number of groups k is equal to the dimension of the variable; the principle of the edge unit is as follows:

[0008]

[0009]

[0010]

[0011]

[0012] Where, r t (k) This represents the reset gate for the k-th variable; This represents the update gate for the k-th variable; This represents the candidate hidden layer for the k-th variable; This represents the hidden layer representing the output of the k-th variable; and These represent the weights of the reset gate, update gate, and input variables in the candidate hidden layer for the k-th variable, respectively. and These represent the reset gate, update gate, and weights of the previous hidden layer in the candidate hidden layer, respectively; and These represent the reset gate, update gate, and bias of the candidate hidden layer for the k-th variable, respectively. denoted as the sequence of the k-th variable; σ(·) represents the sigmoid activation function; tanh(·) represents the tanh activation function; ⊙ represents the dot product, i.e., element-wise multiplication.

[0013] Furthermore, the principle of the joint unit is as follows:

[0014]

[0015] z t =σ(W z f(A g t A s t A m t ,X t )+U z h t-1 +b z )

[0016]

[0017] Among them, h t Indicates the output hidden layer of the joint unit; h t-1 This represents the output hidden layer of the joint unit at the previous time step; Represents the candidate hidden layer of the joint unit; This represents the hidden layer output by the k-th variable in the edge unit; z t Indicates the joint cell update gate; W z This indicates that the input state f(A) in the joint unit update gate is... g t A s t A m t ,X t The weight of U; z This indicates the weight of the hidden layer in the previous time step within the joint unit update gate; b represents the weights of the hidden layers in the candidate hidden layers of the joint unit; c b represents the bias of the candidate hidden layer of the joint unit; z Indicates the bias of the joint cell update gate; A g t Represents a dynamic geographic adjacency matrix; A s t Represents the semantic adjacency matrix; A m t Represents the motion adjacency matrix; X t represents all input variables; f(·) represents the GCN operation function; σ(·) represents sigmoid; tanh(·) represents tanh; ⊙ represents element-wise multiplication.

[0018] Furthermore, the dynamic geographic adjacency matrix is ​​as follows:

[0019]

[0020] Among them, A g i,j δ represents the geographic edge weights associated with the locations of nodes i and j; δ represents the control A g i,j The threshold of the distribution; d i,j This represents the distance between node i and node j.

[0021] Furthermore, the semantic adjacency matrix is ​​as follows:

[0022]

[0023] Among them, A s i,j Represents semantic edge weights; X (i) and X (j) These represent the measured values ​​of the two measurement nodes, respectively.

[0024] Furthermore, the motion adjacency matrix is:

[0025]

[0026] Among them, A m i,j The elements represent the elements of the motion adjacency matrix, where i and j represent the positions of the elements in the matrix; cov(·) calculates the covariance; var(·) calculates the variance.

[0027] Furthermore, the spatial characteristics of thermal errors are captured using the GCN network, and are expressed as follows:

[0028] f(A g t A s t A m t ,X t )=σ(A m t Relu(σ(A s t X t W s )⊙tanh(A g t X t W g ))W m )

[0029] Among them, W s W represents the weights of the semantic adjacency matrix. g W represents the weights of the geographic adjacency matrix. mrepresents the weights of the motion adjacency matrix; Relu represents the ReLU activation function; σ(·) represents sigmoid; tanh(·) represents tanh; ⊙ represents element-wise multiplication.

[0030] This invention also proposes an industrial-oriented machine learning big data framework, including a cloud computing layer and an edge computing layer;

[0031] The edge computing layer includes a data production layer and a data transmission layer;

[0032] The data generation layer is used to control the processing and collect thermal information data, including structured, semi-structured, and unstructured data, generated during the manufacturing process. The collected thermal information data is uploaded to the corresponding MySQL database. The data transmission layer consists of Kafka and Flume to realize data transmission between the MySQL database and HDFS.

[0033] The cloud computing layer includes a data storage layer, a data computing layer, and a data analysis layer;

[0034] The data storage layer includes HDFS and HBase databases. HBase data is stored on HDFS, and HDFS provides underlying storage support for the HBase database. The hot information data temporarily stored in the MySQL database is imported into the HBase database to ensure real-time decision-making for the machine learning model. The data computation layer consists of Spark and is used to train the dynamic spatiotemporal memory graph convolutional network hot error model as described above. The data analysis layer is used to coordinate the operations of multiple distributed applications.

[0035] The PC within the edge computing layer develops the dynamic spatiotemporal memory graph convolutional network thermal error model based on the industrial scenario and transmits it to the data analysis layer. The data computing layer uses stored historical thermal information data to train the dynamic spatiotemporal memory graph convolutional network thermal error model, and downloads the trained dynamic spatiotemporal memory graph convolutional network thermal error model to the PC to update the dynamic spatiotemporal memory graph convolutional network thermal error model stored in the edge computer. The real-time thermal information data collected by the data generation layer is transmitted to the PC to perform prediction using the dynamic spatiotemporal memory graph convolutional network thermal error model stored in the PC.

[0036] The beneficial effects of this invention are as follows:

[0037] This invention presents a dynamic spatiotemporal memory graph convolutional network thermal error model, consisting of N cascaded DTSMGCN layers, each containing DTSMGCN units. Within each DTSMGCN unit, edge units are used to mine the temporal features of each variable itself; unique correspondences clarify the temporal features of the variables themselves, and important temporal features are transmitted to joint units. Joint units are used to mine the spatiotemporal features between variables, and the extracted spatiotemporal features are tightly coupled and propagated in the recursive network. A hybrid adjacency matrix is ​​used to comprehensively mine spatial features, including a dynamic geographic adjacency matrix, a semantic adjacency matrix, and a motion adjacency matrix. The DTSMGCN units can capture the temporal features of variables and the spatiotemporal features between variables, and comprehensively capture the spatial features of variables, effectively improving prediction accuracy. Attached Figure Description

[0038] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0039] Figure 1 This is a schematic diagram of an embodiment of the machine learning big data framework for industry-oriented applications of the present invention.

[0040] Figure 2 A schematic diagram illustrating the principles of data and model training;

[0041] Figure 3 This is a physical hardware diagram of the edge computing layer;

[0042] Figure 4 This is a schematic diagram of the data generation layer.

[0043] Figure 5 This is a schematic diagram of the data transmission layer.

[0044] Figure 6 A flowchart of Spark's workflow;

[0045] Figure 7 A schematic diagram illustrating the formation mechanism of thermal error in the feed drive system;

[0046] Figure 8 A simplified schematic diagram of the helical shaft model;

[0047] Figure 9 This is a dynamic spatiotemporal (TS) diagram of the temperature field;

[0048] Figure 10 This is a structural diagram of the thermal error model of the dynamic spatiotemporal memory graph convolutional network of the present invention;

[0049] Figure 11 Here is a structural diagram of the DTSMGCN unit;

[0050] Figure 12A framework diagram for predicting the spatiotemporal (TS) thermal error;

[0051] Figure 13 This is a diagram of a sensor network structure.

[0052] Figure 14 It is a dynamic geographic adjacency matrix;

[0053] Figure 15 Temperature field and thermal elongation at 1400 mm / min; (a) measured temperature; (b) thermal error;

[0054] Figure 16 Temperature field and thermal elongation at 1600 mm / min; (a) measured temperature; (b) thermal error;

[0055] Figure 17 For comparison of the prediction performance of different models: (a) thermal error at 1600 m / min; (b) temperature error at 1400 m / min; (c) thermal error residual at 1600 m / min; (d) temperature error residual at 1400 m / min;

[0056] Figure 18 For positional deviation comparison: (a): t = 0; (b): t = 1 / 6h; (c): t = 1 / 2h; (d): t = 1h; (e): t = 2h; (f): t = 3h; (g): t = 4h.

[0057] Name Explanation

[0058] Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0060] 1. An industrial-grade machine learning big data framework (IOMLBDF)

[0061] like Figure 1As shown, this embodiment of the industrial machine learning big data framework includes a cloud computing layer and an edge computing layer. The edge computing layer comprises a data production layer and a data transmission layer. The data production layer controls the processing and collects heat information data, including structured and unstructured data generated during manufacturing. The collected heat information data is uploaded to the corresponding MySQL database. The data transmission layer consists of Kafka and Flume to achieve data transmission between the MySQL database and HDFS. The cloud computing layer includes a data storage layer, a data computation layer, and a data analysis layer. The data storage layer includes HDFS and HBase databases. HBase data is stored on HDFS, and HDFS provides underlying storage support for the HBase database. Heat information data temporarily stored in the MySQL database is imported into the HBase database to ensure real-time decision-making for the machine learning model. The data computation layer consists of Spark and is used to train the Dynamic Spatiotemporal Memory Graph Convolutional Network Thermal Error Model (DTSMGCN). The data analysis layer coordinates the operations of multiple distributed applications.

[0062] like Figure 2 As shown, the PC in the edge computing layer develops a dynamic spatiotemporal memory graph convolutional network model based on the industrial scenario and transmits it to the data analysis layer. The data computing layer uses the stored historical thermal information data to train the dynamic spatiotemporal memory graph convolutional network thermal error model, and downloads the trained dynamic spatiotemporal memory graph convolutional network thermal error model to the PC to update the dynamic spatiotemporal memory graph convolutional network thermal error model stored in the edge computer. The real-time thermal information data collected by the data generation layer is transmitted to the PC to make predictions using the dynamic spatiotemporal memory graph convolutional network thermal error model stored in the PC.

[0063] 1.1 Edge Computing Layer (EC)

[0064] The Edge Computing (EC) layer is considered a potential solution to the latency problem in Industrial Internet of Things (IIoT) applications (CC). Time-sensitive data is well-suited for EC processing because it is located close to the data source. In the context of thermal error prediction and control, the EC layer comprises a data generation layer and a data transmission layer. Edge layer hardware such as... Figure 3As shown, the edge layer hardware is deployed on the machine terminal. Data acquisition, transmission, and thermal error prediction are then implemented. The edge layer hardware works as follows: On one hand, temperature and thermal error are collected by the acquisition system. The collected data is then transmitted to a database in MySQL. Kafka is combined with Flume to leverage Flume's existing HDFS writing capabilities. On the other hand, the current data is transmitted to a local PC instead of a cloud server to predict thermal errors and calculate compensation values. The edge layer hardware communicates with the human-machine interface (HMI) of the computer numerical control (CNC) system via a serial port, and the compensation components are sent to the programmable logic controller (PLC) in the CNC system. That is, the compensation components are used as inputs to the edge layer hardware. A trained thermal error model is deployed on the edge layer hardware. The parameters of the trained model are transmitted from the cloud to the edge layer hardware. When the deployed DTSMGCN model degrades, it causes a decrease in prediction accuracy. The cloud server will then begin retraining the DTSMGCN model with historical data and newly uploaded data as input.

[0065] 1.1.1 Data Generation Layer

[0066] The data generation layer controls the manufacturing process and collects data generated during manufacturing, including structured and unstructured data. Structured data includes machine temperature, thermal error, and rotational speed. Unstructured data includes photographs taken by infrared thermal imagers and industrial cameras. The collection of structured data will be used as an example. The data generation layer process is as follows: Figure 4 As shown. For data acquisition, the left side shows the measurement program, and the right side shows the acquisition system. Temperature and displacement sensors collect thermal information data. The data is transmitted to the NI-CRIO9045 acquisition system and measurement program. The acquired historical thermal information data of the machine tool is uploaded to MySQL. For the application, multiple MySQL databases are used to store a large amount of historical data generated by the machine tool, and then the data is transmitted to a cloud server through a data transmission layer for training the machine learning model. The trained machine learning model is downloaded from the cloud server to the local PC, and real-time data is sent to the local PC for classification, real-time prediction, and control. Then, the compensation value of the compensation axis is determined based on the prediction value of the local PC and input into FB3 in the control system to adjust the speed and position of the servo motor, thereby controlling the actual position of the axis. For thermal error control, the task only involves real-time prediction and control. For other manufacturing processes, including weld point identification, the task involves real-time classification and control.

[0067] 1.1.2 Data Transmission Layer

[0068] The data transmission layer consists of Kafka and Flume, used for data transfer between MySQL and HDFS. The machine learning model uses historical data for training and real-time data for prediction. Kafka and Flume can flexibly handle activity stream data and are used to import machine tool thermal information data temporarily stored in the MySQL database into the HBase database, ensuring real-time decision-making for the machine learning model. Kafka is a distributed message queue. For machine tool data, the upstream connection mainly connects to the machine tool's MySQL database for data upload, and the downstream connection connects to Flume, such as... Figure 5 As shown. The Kafka framework is based on a publish / subscribe model. The Producer within Kafka is used to send messages to the broker server; in this study, the Producer is MySQL. The Consumer within Kafka is used to receive messages sent by the Producer to the broker. Both publishing and subscribing to data are topic-oriented transmissions. A topic has multiple partitions, and this multi-partition strategy significantly improves Kafka's efficiency. Researchers can decide based on their working conditions. The sink mainly consists of three parts: the source, the tank, and the channel. The source is mainly used to connect upstream data to the tank. In this study, it relates to upstream data in Kafka. Therefore, the chosen source is the Kafka source. The channel is the pipeline for data transmission. The Sink is used to connect downstream data to the tank; the downstream connection is HDFS. Therefore, the sink used is the HDFS sink.

[0069] 1.2 Cloud Computing Layer

[0070] Machine learning models mine potential relationships from massive amounts of data, and the training process is time-consuming. Big data frameworks provide machine learning models with a wealth of data, while CC can improve the training efficiency of machine learning models, making them suitable for industrial development scenarios. The CC layer includes a data storage layer, a data computation layer, and a data analysis layer.

[0071] 1.2.1 Data storage layer

[0072] The data storage layer primarily comprises HDFS and HBase to ensure the stable storage of historical data for the machine tool group. HBase data is typically stored on HDFS. HDFS provides the underlying storage support for HBase and can be understood as a Hadoop database. HDFS has nodes such as NameNode and DataNode. The NameNode manages the entire HDFS, while the DataNodes are responsible for reading and writing data. The data in the data storage layer contains a large amount of historical data, daily new data, and intermediate data. Furthermore, a large amount of intermediate data is generated through computational analysis. The data storage layer is hosted on cloud servers, providing instant data access support for the data processing layer. Additionally, the machine learning models in the data processing layer require a large amount of reliable historical data. Cloud servers offer data security. Even if local hardware fails, data is backed up to the cloud server. Therefore, the enterprise will not suffer losses.

[0073] 1.2.2 Data Computation Layer

[0074] The data computation layer, composed of Spark, is used to train various machine learning models. The data storage layer provides the structured and unstructured data required by these models. Leveraging the superior computing power of cloud servers and Spark's unique distributed computing architecture, the training speed of machine learning models can be further improved. Spark is used to achieve rapid computation on large datasets, providing computational support for the data analysis layer.

[0075] Spark is a fast, general-purpose computing platform for processing large volumes of data. It supports both offline massive data processing and real-time data streaming. Therefore, it is suitable for running machine learning algorithms. Spark clusters use a master-slave architecture. The master is the controller of the entire cluster and is responsible for its normal operation. Slave nodes are nodes in the cluster that contain worker processes. The Spark cluster architecture consists of a cluster manager, worker nodes, executors, drivers, and other components. Its basic architecture is as follows: Figure 6 As shown. The cluster manager is responsible for allocating and managing resources across the entire cluster. Depending on the deployment mode, it is categorized as Hadoop YARN, Mesos, and Standalone. In this study, the standalone mode is used to reduce computational overhead. Worker nodes are used to execute submitted tasks. One or more executor processes run on the nodes to further allocate resources and tasks to the executors.

[0076] 1.2.3 Data Analysis Layer

[0077] To coordinate the operation of multiple distributed applications, Spark's machine learning libraries or Python libraries, combined with PySpark, are used to build models based on historical data from a large number of machine tool factories. Each user can have one Spark Master and multiple Spark Worker nodes on the Beikun cloud server. Each Worker is also an HDFS data node, allowing direct access to the data. Jupyter notebooks provide a web-based Python editor, allowing edge PC users to develop suitable machine learning models based on industrial scenarios. Parallel execution of machine learning models and optimization of computing resources are handled by Spark. Thanks to this work, a convenient, fast, and efficient environment is automatically generated on the cloud server within the combined framework of Jupyter notebooks and PySpark. For machine learning users, Jupyter notebooks are launched directly on the Spark Master and accessed using a public IP address. The Jupyter user interface (UI) is available in a browser. Both the Jupyter UI and Spark UI are password protected, and users can also configure their own port numbers.

[0078] 2. Thermal error model based on dynamic TS (temporal-spatial) behavior

[0079] Under the combined influence of impact, vibration, heavy load, and thermal load, the machining accuracy of machine tools decreases. Under normal operating conditions, the machining accuracy of machine tools is mainly affected by ambient temperature and localized heating. Axial thermal elongation of the lead screw shaft leads to an increase in the lead screw pitch due to increased ambient temperature or heat generated by friction components during actual machining. The increased pitch leads to an increase in the linear travel distance between the nut and the worktable at the same revolutions, thus affecting the positioning accuracy ΔX. Figure 7 As shown. That is, the thermal expansion Δ of the lead screw shaft leads to the positioning accuracy ΔX.

[0080] 2.1 Dynamic Spatiotemporal (TS) Behavior

[0081] Simplify the machine tool's feed axis to a one-dimensional axis, such as... Figure 8 As shown, heat flux is continuously conducted from the fixed end to the free end. The thermal elongation process of the lead screw shaft includes two dynamic processes: the temperature field reaching equilibrium and the thermal deformation reaching a steady state. Therefore, thermal deformation lags behind temperature rise. Taking the micro-element Δx of the lead screw shaft as an example, Δl is the thermal elongation of the micro-element Δx.

[0082] Δl(x,t)=α(T(x,t))·T(x,t)·Δx

[0083] Where α(T(x,t)) is the linear expansion coefficient, reflecting the thermal deformation process reaching a steady state; T(x,t) is the temperature, reflecting the temperature rise process reaching equilibrium. Then, the total thermal elongation ΔE is obtained by superimposing the micro-elongations of each micro-element.

[0084]

[0085] Temperature is a key variable affecting thermal expansion. Previous thermal error models used the critical temperature as input but neglected the dynamic behavior of temperature, resulting in unsatisfactory prediction accuracy. Therefore, this embodiment discusses the heat transfer process from a new perspective. The partial differential equation for heat conduction is:

[0086]

[0087] Where ρ is density; k is thermal conductivity; and c is specific heat capacity; It is the Laplace operator.

[0088] The Laplace transform is used to solve the heat conduction equation. The Laplace transform is:

[0089]

[0090] get:

[0091]

[0092] Through the Laplace transform, T(x,t) becomes T(x,p), and is updated as follows:

[0093]

[0094] In other words, the Laplace transform method is understood as replacing the time dimension t with the frequency p of temperature change. The frequency p of temperature change is directly affected by the motor speed, which is reflected in the feed speed of the moving nut. Therefore, the frequency of the nut's reciprocating motion can reflect the frequency p of temperature change. If the temperature variable is used as input, the dynamic characteristics of the moving nut need to be considered in the error modeling process. Having demonstrated the memory behavior of thermal errors, this embodiment discusses the spatiotemporal (TS) characteristics of the temperature variable, revealing that temperature measurements only reflect time behavior and cannot fully reflect the spatiotemporal (TS) characteristics of temperature. To reflect the TS characteristics, the dynamic characteristics of the moving nut should be considered.

[0095] To further understand the spatiotemporal (TS) characteristics of thermal error, the heat conduction model is discretized into n nodes and constructed on a spatiotemporal (TS) graph. The expression for heat conduction is:

[0096]

[0097] Where T = [T1, T2, T3, ..., T] n ] T L is the Laplace matrix, L = DA, where D is the degree matrix and A is the adjacency matrix. In existing technologies, the adjacency matrix is ​​fixed because the measurement nodes are fixed in current studies. However, the nut is an important measurement node, and the nut is moving. Therefore, the dynamic spatiotemporal (TS) characteristics of the measurement node should be considered. Considering that the feed motion is reciprocating, a dynamic spatiotemporal (TS) diagram is then obtained, as shown... Figure 9 As shown. Figure 9 The term "dynamic spatiotemporal (TS) plot" arises because the feature sequences collected by the sensor nodes and the positions of the measurement nodes change over time; specifically, the position of the nut (indicated by the yellow dot) changes with runtime. Therefore, previous spatiotemporal (TS) modeling methods based on static plots are no longer applicable, necessitating a dynamic spatiotemporal (TS) modeling method that reflects the dynamic characteristics of the moving nut. When the nut moves to the same position at different runtimes, the temperature rise of the ball screw becomes more pronounced; the higher the temperature, the brighter the image. In other words, the machine tool's temperature exhibits spatiotemporal (TS) characteristics, and so does its thermal error.

[0098] 3. Dynamic Spatiotemporal Memory Graph Convolutional Network Thermal Error Model

[0099] To capture the spatiotemporal (TS) dependencies of sensor networks, this embodiment proposes a DTSMGCN model (Dynamic Spatiotemporal Memory Graph Convolutional Network Thermal Error Model) and uses stacked DTSMGCN layers to construct the network. The spatiotemporal (TS) prediction process of the DTSMGCN model is as follows: Figure 10 As shown. Specifically, the dynamic spatiotemporal memory graph convolutional network thermal error model in this embodiment includes N DTSMGCN layers arranged in series, where N≥1; and: when N≥2, the output h of the i-th DTSMGCN layer... i t This is the input to the (i+1)th DTSMGCN layer, where 1 ≤ i ≤ N-1.

[0100]

[0101] Multidimensional data is acquired from sensors, but the dependencies between the data are complex. RNNs, similar to GRUs, can predict thermal errors by inputting multidimensional data. However, it is undesirable to indiscriminately input data from different nodes into a neural network, and it is unrealistic to expect the network itself to distinguish the complex dependencies between multidimensional data. Therefore, it is necessary to design a reasonable structure for the GRU to effectively mine the features of multidimensional data. Therefore, this embodiment proposes a DTSMGCN unit, such as... Figure 11As shown, the DTSMGCN layer comprises DTSMGCN units, each containing edge units, joint units, and a hybrid adjacency matrix. Edge units mine the temporal features of each variable and transmit these features to the joint units. Joint units mine the spatiotemporal features between variables, and the extracted spatiotemporal features are tightly coupled and propagated within the recursive network. The hybrid adjacency matrix mines spatial features, including dynamic geographic adjacency matrices, semantic adjacency matrices, and motion adjacency matrices. This DTSMGCN unit structure can effectively capture the spatiotemporal (TS) features of multidimensional data.

[0102] 3.1 Marginal unit

[0103] Temporal features are crucial for spatiotemporal (TS) prediction. However, mining the temporal features of multidimensional variables is challenging. RNNs can extract temporal features but cannot adequately consider the historical characteristics of each variable itself. Therefore, marginal units are designed to extract temporal information from multidimensional variables. Input variables are divided into k groups based on the marginal units. For optimal performance, the number of groups k is equal to the dimension of the variable. Figure 11 As shown in the red box, the time information of multidimensional variables has been extracted. This design reduces the difficulty of extracting time information from multidimensional variables. The most important historical information for each variable is stored in... In this context, spatiotemporal (TS) information is integrated into the joint unit. The principle of the edge unit is as follows:

[0104]

[0105]

[0106]

[0107]

[0108] Where, r t (k) This represents the reset gate for the k-th variable; This represents the update gate for the k-th variable; This represents the candidate hidden layer for the k-th variable; This represents the hidden layer representing the output of the k-th variable; and These represent the weights of the reset gate, update gate, and input variables in the candidate hidden layer for the k-th variable, respectively. and These represent the reset gate, update gate, and weights of the previous hidden layer in the candidate hidden layer, respectively; and These represent the reset gate, update gate, and bias of the candidate hidden layer for the k-th variable, respectively. denoted as the sequence of the k-th variable; σ(·) represents the sigmoid activation function; tanh(·) represents the tanh activation function; ⊙ represents the dot product, i.e., element-wise multiplication.

[0109] 3.2 Joint unit

[0110] Besides the temporal information of the variables themselves, the latent spatiotemporal (TS) correlations between variables are also important. To comprehensively explore these TS correlations, a joint unit was designed. Unlike previous studies, a unique hybrid adjacency matrix helps the joint unit fully uncover the spatial correlations between variables. The gating design preserves the necessary spatiotemporal (TS) information, such as... Figure 11 As shown in the blue box. The principle of the joint unit is:

[0111]

[0112] z t =σ(W z f(A g t A s t A m t ,X t )+U z h t-1 +b z )

[0113]

[0114] Among them, h t Indicates the output hidden layer of the joint unit; h t-1 This represents the output hidden layer of the joint unit at the previous time step; Represents the candidate hidden layer of the joint unit; This represents the hidden layer output by the k-th variable in the edge unit; z t Indicates the joint cell update gate; W z This indicates that the input state f(A) in the joint unit update gate is... g t A s t A m t ,X t The weight of U; z This indicates the weight of the hidden layer in the previous time step within the joint unit update gate; b represents the weights of the hidden layers in the candidate hidden layers of the joint unit; c b represents the bias of the candidate hidden layer of the joint unit; zIndicates the bias of the joint cell update gate; A g t Represents a dynamic geographic adjacency matrix; A s t Represents the semantic adjacency matrix; A m t Represents the motion adjacency matrix; X t represents all input variables; f(·) represents the GCN operation function; σ(·) represents sigmoid; tanh(·) represents tanh; ⊙ represents element-wise multiplication.

[0115] 3.3 Hybrid adjacency matrix

[0116] (1) Dynamic geographical adjacency matrix

[0117] The geographical location of measurement nodes can reflect local spatial characteristics. Nodes closer to heat sources are more susceptible to their influence. Based on the movement patterns of the measurement nodes, the dynamic geographical adjacency matrix is ​​as follows:

[0118]

[0119] Among them, A g i,j δ represents the geographic edge weights associated with the locations of nodes i and j; δ represents the control A g i,j The threshold of the distribution; d i,j This represents the distance between node i and node j.

[0120] (2) Semantic adjacency matrix

[0121] Potential dependencies may exist even between distant nodes, manifested in similar trends in the node measurement data. To consider global spatial information, it is necessary to mine the semantic relationships between different measurement nodes. In machine learning, features are typically represented as vectors. To analyze the similarity between two vectors, cosine similarity is often used. Therefore, the semantic adjacency matrix is:

[0122]

[0123] Among them, A s i,j Represents semantic edge weights; X (i) and X (j) These represent the measured values ​​of the two measurement nodes, respectively. Considering the dynamic nature of the data, in this embodiment, X... (i) and X(j) Updated every 20 minutes.

[0124] (3) Motion adjacency matrix

[0125] Nodes that are close to each other may exhibit similar trends in their measurements. For example, two adjacent nodes may show the same trend due to the influence of the same heat source. However, there is a hysteresis effect in heat conduction, so the trends of the two nodes may also differ. Therefore, it is necessary to explore the potential relationship between geography and semantics. The motion adjacency matrix is:

[0126]

[0127] Among them, A m i,j The elements represent the elements of the motion adjacency matrix, where i and j represent the positions of the elements in the matrix; cov(·) calculates the covariance; var(·) calculates the variance.

[0128] 3.4 GCN Network

[0129] Temporal behavior is insufficient for achieving high prediction accuracy and robustness, and spatial behavior should be characterized. GCN can capture the spatial behavior of thermal errors. The equation for GCN is:

[0130]

[0131] in, X is the feature sequence; W0 is the weight parameter of the first layer; σ is the activation function; Where I is the identity matrix.

[0132] The spatiotemporal (TS) prediction model for thermal errors needs to consider spatiotemporal (TS) characteristics. Spatial characteristics are reflected by the graph G generated by the sensor network, and temporal characteristics are reflected by the signal sequence from the displacement sensor. Therefore, the spatiotemporal (TS) prediction problem for thermal errors is represented by the graph G and the feature sequence X. t The problem is to learn the mapping relationship f between them, and the predicted value at the next time T is represented as:

[0133] [X t+1 ,…,X t+T ] = f(G; (X) t-n ,…,X t-1 ,X t ))

[0134] Where (X) t-n ,…,X t-1 ,X t) represents a series of historical data from runtime tn to t, which are used as input to the designed DTSMGCN model; n is the length of the historical data; [X t+1 ,…,X t+T ] represents the predicted number of future steps, where X t+1 It is the predicted thermal error at runtime t+1, X t+T It is the predicted thermal error during runtime t+T. That is, the predicted thermal error for the next T steps.

[0135] This embodiment utilizes the GCN network to capture the spatial characteristics of thermal errors, as follows:

[0136] f(A g t A s t A m t ,X t )=σ(A m t Relu(σ(A s t X t W s )⊙tanh(A g t X t W g ))W m )

[0137] Among them, W s W represents the weights of the semantic adjacency matrix. g W represents the weights of the geographic adjacency matrix. m represents the weights of the motion adjacency matrix; Relu represents the ReLU activation function; σ(·) represents sigmoid; tanh(·) represents tanh; ⊙ represents element-wise multiplication.

[0138] 4. Thermal error modeling

[0139] The spatiotemporal (TS) prediction framework for thermal errors is as follows: Figure 12 As shown, it is divided into four steps: sensor network construction, dynamic spatiotemporal (TS) graph dataset construction, DTSMGCN model parameter construction, and thermal error prediction.

[0140] 4.1 Sensor Network Construction

[0141] Typically, temperature sensors are placed on the main heat source. However, the placement of temperature sensors relies on expert experience. Unlike previous methods that relied on expert experience for sensor placement, infrared thermal imagers are used to provide orientation for the placement of measurement nodes. The collected thermal images are shown below. Figure 13As shown, the brighter the image, the higher the temperature of the machine parts. These bright spots represent measurement nodes, where temperature sensors should be placed. Note that the brightest part in the lower left corner is the coolant motor, which is not connected to the machine tool. Thus, eight temperature measurement nodes and two displacement measurement nodes are obtained on the machine tool. The sensors are then connected to form a sensor network, as shown... Figure 13 As shown, U and L represent two displacement sensors, placed at the radial support ends of the upper and lower lead screw shafts, respectively. Table 1 lists the names of the measurement nodes. The above eight temperature measurement nodes can reflect the temperature field distribution of the upper and lower lead screw shafts, and the dependence of the thermal error obtained by the displacement sensors on the above temperatures collected from the eight temperature detection nodes should be explored. Spatiotemporal (TS) prediction can be competent for the task of exploring the correlation.

[0142] Table 1 Measurement Nodes and Nodes

[0143]

[0144] 4.2 Construction of Dynamic Spatiotemporal (TS) Graph Dataset

[0145] The locations and historical signals of adjacent sensors are necessary for generating a spatiotemporal (TS) map. The total length of the leadscrew is 1800m, and the feed rate is 1600mm / min. The distance between two measurement nodes is then obtained. The dynamic geographic adjacency matrix is ​​as follows: Figure 14 As shown, the horizontal axis represents the sensor label, and the vertical axis represents the number of adjacency matrices. Therefore, a matrix of dimension (1088×9)×9 is generated for 1088 rows of time-series data. It can be seen that the weights of the geographic adjacency matrix vary with the distance between sensor nodes. Therefore, it is necessary to construct a dynamic geographic adjacency matrix.

[0146] Figure 15 This was achieved at a feed rate of 1400 mm / min, with a running time of approximately 550 minutes. Figure 15 The data was obtained at a feed rate of 1600 mm / min and a runtime of approximately 550 minutes. The collected data was used to calculate the semantic adjacency matrix and generate the motion adjacency matrix. Furthermore, Figure 15 The data collection time shown is compared to Figure 16 The times shown are two days later. The machine tool's condition changed because the experiments were not conducted on the same day. However, the mechanism of thermal error generation remains unchanged. That is, the dynamic spatiotemporal (TS) dependence of thermal error remains unchanged. The results of these two experiments demonstrate the time characteristics.

[0147] 4.3DTSMGCN Model Construction

[0148] The prediction performance and robustness were then compared to validate the proposed DTSMGCN model. The PyTorch machine learning library was used for programming. To highlight the effectiveness of the proposed model, multiple linear regression (MLR), long short-term memory (LSTM), gated recurrent units (GRU), temporal convolutional networks (TCN), convolutional neural networks with long short-term memory, temporal convolutional graph convolutional networks (T-GCN), and dynamic temporal-spatial memory graph convolutional networks were compared. To avoid ambiguity in the prediction results in the figures, representative models were selected from the prediction result figures. MLR represents the traditional data-driven method, GRU represents the temporal prediction method, CNN-LSTM represents the concatenation of a CNN and a temporal model, T-GCN represents the concatenation of a graph convolutional network and a temporal model, and DTSMGCN is the model proposed in this embodiment. In this embodiment, the DTSMGCN model has a value of 2 for N, meaning two DTSMGCN layers are stacked. The first layer's DTSMGCN unit contains 64 hidden neurons, and the second layer's DTCMGCN unit contains 32 hidden neurons. The learning rate is 0.01, the batch size is 128, the epoch size is 100, and the loss is RMSE. Since different sensor nodes have different signal levels, the model is trained by normalizing the feature sequences, and then inverse normalization is performed to obtain the prediction results. Early stopping is used to avoid overfitting.

[0149] 5. Prediction Results and Experimental Verification

[0150] 5.1 Prediction Results

[0151] Predicted thermal error of upper and lower lead screw shafts, such as Figure 17 As shown. The machine tool has a cooling system, so the thermal error of the upper and lower leadscrews exhibits fluctuating characteristics. Different models have different performance; these models, which consider the generation mechanism of thermal error, perform much better than those that do not. Therefore, models that can capture the spatiotemporal (TS) characteristics of thermal error have higher predictive performance than other models. The vertical coordinate shows the predicted thermal error, not the residual, as... Figure 17 As shown in (a) and 17(b), the residual is the difference between the predicted and measured thermal errors, as... Figure 17 As shown in (c) and 17(d), the vertical coordinates represent the residuals between the prediction and measurement thermal errors. The residuals of DTSMGCN were found to be lower than those of the MLR, TCN, GRU, LSTM, CNN-LSTM, and T-GCN models. Therefore, DTSMGCN exhibits the best prediction performance among the MLR, TCN, GRU, LSTM, CNN-LSTM, T-GCN, and DTSMGCN models.

[0152] Predictive power is used to evaluate the predictive accuracy of the established model, and it is calculated as follows:

[0153]

[0154] Among them, y i and y represents the measured value and the predicted value, respectively. i This represents the average of the measured values, and n represents the number of data points.

[0155] The prediction results were evaluated, as shown in Table 2-3. In this embodiment, the average values ​​of the evaluation metrics for ten experiments were calculated for the MLR, TCN, GRU, LSTM, CNN-LSTM, T-GCN, and DTSMGCN models. The RMSE values ​​for the MLR, TCN, GRU, LSTM, CNN-LSTMN, T-GCN, and DTSMGCN models were 5.3981, 3.4093, 2.3369, 1.1170, 1.8810, 0.5115, and 0.3366, respectively. DTSMGCN's unique structure gives it superiority: First, its graph structure includes a dynamic geographic map, a dynamic semantic map, and a motion map. The geographic map, built based on the movement of heat sources, directly influences the temperature field distribution, thus affecting thermal errors. The geographic map captures the local spatial features of thermal errors, while the semantic map, constructed based on the correlation between every two measurement nodes (which changes significantly over time), reflects the abrupt changes in the correlation between thermal errors and temperature, capturing the global spatial features of thermal errors. The motion map, built based on the correlation between the geographic and semantic maps, integrates the local and global spatial features of thermal errors. Furthermore, semantic spatial features are used to filter geographic spatial features to capture the long-term spatial features of thermal errors. Thermal error data is divided into long-term trends and short-term abrupt changes. To capture long-term trends, DTSMGCN's edge units vertically capture the long-term historical features of variables, avoiding confusion caused by long-term trends. Key temporal information from edge units flows into joint units and is fused with spatial information. Joint units horizontally capture the spatiotemporal (TS) features between variables, effectively reflecting short-term abrupt changes in thermal errors. DTSMGCN can capture the dynamic spatiotemporal (TS) features of thermal error, making its prediction accuracy higher than T-GCN. Although T-GCN is a concatenation of GCN and a temporal model, GCN is better suited for processing unstructured data than CNN, therefore T-GCN has higher prediction accuracy than CNN-LSTMN. Thermal error is a function of the temperature change frequency p, which is determined by the spatiotemporal (TS) features of the heat source. Figure 17It can also reflect the dependence of thermal errors on spatiotemporal (TS) features. Therefore, it can be concluded that thermal errors are a type of spatiotemporal (TS) data, and time series prediction cannot meet the requirements. DTSMGCN, T-GCN, and CNN-LSTM models all outperform time prediction models such as LSTM, GRU, and TCN. The prediction performance of LSTM, GRU, and TCN models is similar and superior to traditional MLR. MLR cannot capture the temporal correlation of variables, resulting in poor prediction performance.

[0156] Table 2 shows the predictive performance of different models for screw thermal error.

[0157]

[0158]

[0159] Table 3. Predictive performance of different models on the thermal error of the lower lead screw.

[0160]

[0161] 5.2 Ablation Experiment

[0162] Ablation experiments were introduced to explore the effectiveness of each part of the DTSMGCN model. The results of the ablation experiments are listed in Table 4. DTSMGCN1 is the DTSMGCN without the hybrid adjacency matrix, DTSMGCN2 is the DTSMGCN without edge units, and DTSMGCN3 is the DTSMGCN without joint units. The RMSE of DTSMGCN, DTSMGCN1, DTSMGCN2, and DTSMGCN3 are 0.3366, 0.4999, 0.5826, and 1.6395, respectively. The results show that DTSMGCN has higher prediction accuracy than DTSMGCN1. The hybrid adjacency matrix can fully reflect the spatial characteristics of spatiotemporal (TS) data, enabling the DTSMGCN network to have better performance than DTSMGCN1. The prediction accuracy of DTSMGCN2 is higher than that of DTSMGCN1. Edge units can vertically capture the temporal characteristics of each variable, and the absence of edge units will weaken the ability of the DTSMGCN model to capture temporal characteristics. The joint unit can capture the spatiotemporal (TS) features between variables laterally and is also responsible for integrating important information uploaded by edge units. Without the joint unit, the DTSMGCN model would become a traditional temporal machine learning model, resulting in reduced prediction accuracy.

[0163] Table 4 shows the predictive performance of different models for ball screw thermal error.

[0164]

[0165] 5.3 IOMLBDF Architecture and Control Experiment

[0166] In this embodiment, the virtual machine is VMware Workstation 16, the Linux operating system is Centoos 7, the Java version is 1.8.0_241, the Python version is 3.8.8, the Hadoop version is 3.3.0, the Spark version is 3.2.0, the HBase version is 2.1.0, the Zookeeper version is 3.4.6, and the Hive version is 3.1.2. Spark is written in the Scala programming language. The libraries required for the machine learning model are based on the Python language, and the PySpark tool is used, which allows Spark to support the Python language. To test the effectiveness of the designed IOMLBDF, the speedup ratio of different numbers of virtual machine nodes was compared, and the results are listed in Table 5. The results show that the proposed IOMLBDF can effectively help machine learning models be applied to industrial scenarios.

[0167] Table 5. Proposed acceleration on IOMLBDF for different numbers of virtual machine nodes.

[0168]

[0169] The DTSMGCN model is embedded in IOMLBDF. Figure 18 As axial elongation decreases, the positioning error decreases. To verify the effectiveness of the DTSMGCN model, a series of experiments were conducted on the feed drive system. Before implementing IOMLBDF, the feed drive system operated under no-load conditions. The nut moved within the range of [0, 500 mm] for four hours, and the positional deviation with and without IOMLBDF implementation was measured. Figure 18 As shown, the position deviations at different axial positions and times were compared with those without IOMLBDF. The results show that the position deviation is significantly reduced when IOMLBDF is implemented, validating the effectiveness of the DTSMGCN model and IOMLBDF. Notably, the thermal effect is reduced during the thermal equilibrium process, indicating that the proposed IOMLBDF and DTSMGCN models are effective throughout the entire thermal equilibrium process of the feed drive system.

[0170] 6. Conclusion

[0171] Based on the generation mechanism of thermal errors, this embodiment proposes a Dynamic Spatiotemporal Memory Graph Convolutional Network Thermal Error Model (DTSMGCN model) to capture the spatiotemporal features of thermal errors. A hybrid adjacency matrix, edge units, and joint units are designed for the DTSMGCN units to capture the temporal features of the variables themselves and the spatiotemporal (TS) features between variables. The hybrid adjacency matrix fully reflects the local and global spatial features of thermal errors. To address the deployment problem of machine learning models and alleviate the bandwidth pressure of cloud computing, this embodiment proposes an Industrial Machine Learning Big Data Framework (IOMLBDF) and embeds the DTSMGCN model into IOMLBDF. Prediction results show that the proposed DTSMGCN model outperforms other machine learning models, and the efficiency of the proposed IOMLBDF increases with the number of computing nodes.

[0172] The advantages of this embodiment are as follows: (1) The proposed IOMLBDF can accelerate the model training process and realize real-time control; (2) The proposed DTSMGCN based on the error mechanism has higher prediction accuracy than other models; (3) The sensor is deployed based on infrared thermal images, avoiding the disadvantage of relying on expert experience.

[0173] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. An industry-oriented machine learning big data framework, characterized in that: The cloud computing layer and the edge computing layer are included; The edge computing layer includes a data generation layer and a data transmission layer; The data generation layer is used for controlling a machining process and collecting thermal information data including structured, semi-structured and unstructured data generated in a manufacturing process, and the collected thermal information data is uploaded into a corresponding MySQL database; the data transmission layer is composed of Kafka and Flume to realize data transmission between the MySQL database and HDFS; The cloud computing layer includes a data storage layer, a data computing layer and a data analysis layer; The data storage layer includes HDFS and an Hbase database, the HBase data is stored on the HDFS, and the HDFS provides underlying storage support for the HBase database; the thermal information data temporarily stored in the MySQL database is imported into the Hbase database to provide guarantee for real-time decision of a machine learning model; the data computing layer is composed of Spark and is used for training a dynamic spatio-temporal memory graph convolution network thermal error model; and the data analysis layer is used for coordinating operations of multiple distributed application programs; The PC in the edge computing layer develops the dynamic spatio-temporal memory graph convolution network thermal error model according to an industrial scene and transmits the model to the data analysis layer, the data computing layer trains the dynamic spatio-temporal memory graph convolution network thermal error model by using stored historical thermal information data, downloads the trained dynamic spatio-temporal memory graph convolution network thermal error model to the PC to update the dynamic spatio-temporal memory graph convolution network thermal error model stored in the edge computer, and the data generation layer transmits real-time thermal information data collected to the PC to perform prediction by using the dynamic spatio-temporal memory graph convolution network thermal error model stored in the PC. The dynamic spatio-temporal memory graph convolution network thermal error model includes N layers of DTSMGCN layers arranged in series, where N≥1; and: the output of the DTSM GCN layer of the i-th layer when N ≥ 2 is the input of the DTSM GCN layer of the i+1-th layer, 1 ≤ i ≤ N-1; The DTSMGCN layer includes a DTSMGCN unit, the DTSMGCN unit is provided with an edge unit, a joint unit and a hybrid adjacency matrix; the edge unit is used for mining time features of each variable and transmitting the time features to the joint unit; the joint unit is used for mining spatio-temporal features between variables, and the extracted spatio-temporal features are tightly coupled and propagated in a recursive network; and the hybrid adjacency matrix is used for mining spatial features, and the spatial features include a dynamic geographical adjacency matrix, a semantic adjacency matrix and a motion adjacency matrix. 2.The industrial-oriented machine learning big data framework of claim 1, wherein: The edge unit is used for extracting time information of multi-dimensional variables: input variables are divided into k groups, and the number k of groups is equal to the dimension of the variables; and the principle of the edge unit is as follows: where, represents the reset gate of the k-th variable; represents the update gate of the k-th variable; represents the candidate hidden layer of the k-th variable; represents the hidden layer of the k-th variable output; , and represent the weights of the input variables in the reset gate, the update gate and the candidate hidden layer of the k-th variable, respectively; , and represent the weights of the hidden layer of the previous time in the reset gate, the update gate and the candidate hidden layer of the k-th variable, respectively; , and represent the biases of the reset gate, the update gate and the candidate hidden layer of the k-th variable, respectively; represents the sequence of the k-th variable; represents the sigmoid activation function; represents the tanh activation function; represents the dot product, i.e., the multiplication of the corresponding elements. 3.The industrial-oriented machine learning big data framework of claim 1, wherein: The principle of the joint unit is as follows: in, Indicates the output hidden layer of the joint unit; This represents the output hidden layer of the joint unit at the previous time step; Represents the candidate hidden layer of the joint unit; This represents the hidden layer where the k-th variable is output in the edge unit; Indicates the joint unit update gate; Indicates the input state in the joint unit update gate. The weights; This indicates the weight of the hidden layer in the previous time step within the joint unit update gate; This represents the weights of the hidden layers within the candidate hidden layers of the joint unit; Indicates the bias of the candidate hidden layer of the joint unit; This indicates the bias of the joint cell update gate; Represents a dynamic geographic adjacency matrix; Represents a semantic adjacency matrix; Represents the motion adjacency matrix; This represents all input variables; Represents the operational functions of GCN; It represents sigmoid; Indicates tanh; This indicates element-wise multiplication. 4.The industrial-oriented machine learning big data framework of claim 3, wherein: The dynamic geographical adjacency matrix is as follows: wherein, denotes a geographical edge weight related to the position of a node and a node ; denotes a threshold value controlling the distribution of ; denotes a distance between a node and a node .

5. The industry-oriented machine learning big data framework of claim 3, wherein: The semantic adjacency matrix is as follows: wherein, denotes a semantic edge weight; and denote the measurements of the two measurement nodes, respectively. 6.The industrial-oriented machine learning big data framework of claim 3, wherein: The motion adjacency matrix is as follows: wherein, represents an element of the motion adjacency matrix, i, j represents the position of the element in the matrix; represents computing the covariance; represents computing the variance. 7.The industrial-oriented machine learning big data framework of claim 3, wherein: The spatial features of the thermal error are captured by using a GCN network, and are expressed as follows: wherein, denotes the weight of the semantic adjacency matrix; denotes the weight of the geographical adjacency matrix; denotes the weight of the motion adjacency matrix; denotes the RELU activation function; denotes sigmoid; denotes tanh; denotes element-wise multiplication.

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