Flash furnace fault prediction method based on graph fusion and multi-stage learning

Abstract

The invention relates to the technical field of fault prediction, and relates to a flash furnace fault prediction method based on graph fusion and multi-stage learning, which comprises the following steps: establishing a static graph and a dynamic graph, describing the influence intensity and dynamic change between sensor data according to the static graph and the dynamic graph, and obtaining spatial-temporal characteristics; inputting the spatial-temporal characteristics into a Transform coding model, and obtaining prediction data; the Transform coding model is trained by using a training set, and model parameters are adjusted by minimizing a prediction error to obtain the Transform coding model; the prediction data is coded, the coded data is stretched, translated and rotated, each data point is mapped to a high-dimensional space, the distribution position of abnormal points is obtained, the abnormal score of the data is calculated, the abnormal score is judged, and the fault result of the nickel flash furnace system is obtained. According to the method, the static relation and the dynamic relation can be mined and fused from various sensor data, so that fault prediction is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of fault prediction, and in particular to a flash furnace fault prediction method based on graph fusion and multi-stage learning. Background Art

[0002] In the nickel smelting process, flash smelting is the most representative nickel pyrometallurgical smelting method, with the advantages of high production capacity, low energy consumption and low pollution. In order to ensure the efficient operation of the nickel smelting process, the stable operation of the flash furnace system must be maintained, which is crucial to the production efficiency and economic benefits of the nickel smelter. During long-term operation, the complex production environment and variable operating conditions make it inevitable for the flash furnace system to suffer various failures. If not handled in time, it will lead to production interruptions and waste of resources, and even cause safety accidents. Although traditional post-maintenance can restore equipment functions, it is usually accompanied by high maintenance costs and long downtime, and it is difficult to completely avoid the adverse effects caused by equipment failures. Therefore, the need for the flash furnace system to accurately predict the operating status and accurately predict potential failures has become increasingly urgent.

[0003] With the development of industrial sensors and the Internet of Things (IoT) technology, sensors are playing an increasingly important role in nickel pyrometallurgy. Comprehensively collecting equipment operating status information provides a powerful foundation for subsequent predictive maintenance. Time series prediction, a crucial tool for studying the dynamics of data, can reveal patterns and trends in data over time, providing strong support for predicting equipment operating status and potential failures. Traditional time series prediction typically focuses solely on a single time series. Models such as recurrent neural networks (RNNs), long short-term memory networks (LSTMs), and gated recurrent units (GRUs) typically extract complex features from time series data and can handle high-dimensional time series data. However, RNNs and their variants can only be trained and predicted on complete time series and require processing input data incrementally over time. They lack parallel processing capabilities, resulting in high computational complexity and limited efficiency in large-scale tasks. Therefore, some researchers have attempted to combine traditional time series prediction models with techniques such as attention mechanisms, zero-shot learning, and transfer learning to improve their prediction accuracy and efficiency. Guan et al. proposed a time series prediction model based on a temporal attention mechanism and a bidirectional long short-term memory network. This model uses a bidirectional long short-term memory network to extract temporal features and enhances the saliency of temporal features through the temporal attention mechanism. Kamalov et al. proposed a NBEATS model based on zero-shot transfer learning, which significantly reduces power forecasting errors and is suitable for high-speed forecasting environments.

[0004] While traditional time series forecasting methods can perform in-depth analysis and accurate forecasting of single-variable time series data, modern industrial time series data exhibits complex spatiotemporal characteristics and spatiotemporal dependencies among multiple variables. Traditional time series forecasting methods are unable to capture these complex inter-variable correlations. Because the components of a flash furnace system inherently exhibit interrelated characteristics, including temporal and spatial correlations, fully exploiting and integrating these characteristics will be more beneficial for downstream tasks such as forecasting and classification. Existing methods have revealed that most multivariate time series analysis methods treat different variables as independent entities. This not only ignores inter-variable relationships but also undermines the integrity of the spatiotemporal model, impacting both the forecasting effectiveness and the efficiency of the model. To address these challenges, graph neural networks (GNNs) have attracted widespread attention due to their powerful correlation processing capabilities and key information extraction capabilities. By combining time series forecasting with GNNs, the temporal continuity and spatial correlation of data can be effectively integrated, better capturing both temporal and spatial characteristics, improving analysis reliability and forecasting accuracy.

[0005] Initially, graph neural network-based methods mostly explored dependencies between variables by constructing static graphs. Static graphs have a fixed topological structure and are primarily used to extract long-term stable features from spatiotemporal data. Tian et al. utilized stock price correlations to construct a stock relationship graph and proposed a hybrid attention-based graph neural network for predicting stock price trends. YTChou et al. proposed a graph neural network framework, StructGNN, which effectively captures stable and persistent relationships between variables while preserving the graph structure by introducing pseudo-nodes to optimize message passing. This allows for analysis and prediction of static structures. However, static graphs cannot effectively capture the dynamic patterns of relationship evolution and may overlook potential interactions that are critical for decision-making. Therefore, some researchers have proposed constructing dynamic graphs to model dynamic relationships in historical time series data. Dynamic graphs can adjust their topological structure over time and are significantly advantageous for capturing the evolving characteristics and dynamic dependencies of spatiotemporal data. Li et al. proposed a DSTGN model that leverages dynamic graph structures to effectively capture dynamic associations in data and perform data prediction based on the extraction of dynamic features from multivariate time series. Shao et al. designed a D2STGNN model for dynamic spatiotemporal graph neural networks, which can more accurately capture the dynamic characteristics and complex relationships of traffic data by decoupling data and dynamic graph learning.

[0006] Although static graphs and dynamic graphs can effectively complete the prediction tasks of spatiotemporal data in their respective fields, static and dynamic information often coexist in time series data. Relying solely on static graphs or dynamic graphs for modeling is difficult to cope with the data model changes of flash furnace systems under complex working conditions.

[0007] Therefore, to fully exploit the spatiotemporal characteristics of flash furnace system data for accurate prediction of equipment operating conditions and early detection of potential faults, a feasible approach is to fuse static and dynamic graphs to extract features from multivariate time series data. This deep fusion and complementarity of static and dynamic graphs allows for a more in-depth characterization of the operational characteristics of industrial equipment, which is crucial for timely detection of equipment anomalies and early warning of potential faults. However, this approach presents two challenges: first, how to construct a fusion mechanism for static and dynamic graph models to establish an optimal flash furnace system data model by weighing parameter contributions; and second, the complex parameter structure of the graph fusion model makes it difficult to obtain the globally optimal parameter combination through multi-parameter joint optimization. Therefore, a new learning mechanism should be developed to optimize the parameters. To more effectively address these issues, inspired by the concept of multi-stage learning, a feasible approach is to decompose the overall task after graph fusion into multiple simple subtasks. By setting different learning parameters and task objectives, the local solutions are gradually optimized to achieve the optimal solution for the overall task, thereby improving the prediction performance and robustness of the overall model. Summary of the Invention

[0008] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a flash furnace fault prediction method based on graph fusion and multi-stage learning, which mines and fuses static and dynamic relationships from multiple sensor data to achieve fault prediction. In order to optimize the graph fusion network model, a training process of a multi-stage learning strategy is designed to ensure that the parameter combination of the model reaches the global optimum, thereby ensuring the accuracy of the model fault prediction.

[0009] To achieve the above object, the present invention provides the following solutions:

[0010] A flash furnace fault prediction method based on graph fusion and multi-stage learning, including:

[0011] Establishing a static graph and a dynamic graph, describing the influence intensity and dynamic changes between sensor data based on the static graph and the dynamic graph, and obtaining spatiotemporal characteristics;

[0012] Inputting the spatiotemporal features into a Transformer coding model to obtain prediction data; the Transformer coding model is trained using a training set, and model parameters are adjusted to minimize prediction errors; the training set includes: original spatiotemporal features;

[0013] The predicted data is encoded, stretched, translated and rotated, each data point is mapped to a high-dimensional space, the distribution position of the abnormal point is obtained, and the abnormal score of the data is calculated. The abnormal score is judged to obtain the fault result of the nickel flash furnace system.

[0014] Optionally, describing the influence strength between the sensor data includes:

[0015] The relationship between the internal variables of the flash furnace system is described using a mechanism model to obtain the influence intensity between sensors;

[0016] The influence direction of the influence intensity is determined, and the influence level is divided to obtain the final influence intensity. The static adjacency matrix is constructed using the final influence intensity:

[0017] ;

[0018] ;

[0019] in, is the static adjacency matrix, To normalize each row of the matrix, To eliminate negative connections in the input, is the static weight matrix, is the static bias matrix, For sensors For sensors The bias part that affects the strength, is the total number of sensors;

[0020] The influence strength between the sensor data, ie, the static feature, is obtained according to the static graph combined with the static adjacency matrix.

[0021] Optionally, describing the dynamic changes between the sensor data includes:

[0022] Acquire the sensor data, and generate a first subspace based on the sensor data:

[0023] ;

[0024] in, and are learnable parameters, representing the subspaces and subspace The weight matrix, for Sensor data at each moment;

[0025] Based on the first subspace, construct the adjacency matrix:

[0026] ;

[0027] in, is the dynamic adjacency matrix, For subspace The transpose of

[0028] The weight matrix input is mapped to a subspace using a dynamic graph, and the adjacency matrix is dynamically adjusted to capture the dynamic changes between the sensor data, that is, dynamic features.

[0029] Optionally, obtaining the spatiotemporal features includes:

[0030] A graph neural network is constructed by fusing the static graph and the dynamic graph to describe the influence intensity and dynamic changes between sensor data, obtain static features and dynamic features, generate a second subspace based on the static features and the dynamic features, extract steady-state spatial coupling features and time-varying spatial coupling features from the time series data in the second subspace, balance the steady-state spatial coupling features and the time-varying spatial coupling features using a proportion coefficient, and perform feature fusion to obtain a comprehensive spatial feature;

[0031] The integrated spatial features are input into a multi-layer TCN model, where each layer of TCN further abstracts and refines features based on the output of the previous layer to obtain the spatiotemporal features; the multi-layer TCN model is trained using a training set; the training set includes: the original integrated spatial features; wherein the multi-layer TCN model obtains the temporal features by introducing dilated convolution;

[0032] During the training process of the Transformer encoding model, the graph neural network and the multi-layer TCN model, a multi-stage learning strategy is adopted to initialize the model, use the training set to train the model's bias matrix, weight coefficient, and proportion coefficient to obtain the target proportion coefficient, train the model's bias matrix and weight coefficient again to obtain the target bias matrix, and finally train the model's weight coefficient to obtain the target weight coefficient.

[0033] Optionally, acquiring the static feature and the dynamic feature includes:

[0034] ;

[0035] ;

[0036] in, is the steady-state spatial coupling characteristic, is the static adjacency matrix, is a subspace, is the time-varying spatial coupling feature, is a dynamic adjacency matrix.

[0037] Optionally, obtaining the comprehensive spatial features includes:

[0038] ;

[0039] in, For comprehensive spatial characteristics, and All are proportion coefficients.

[0040] Optionally, encoding the prediction data includes:

[0041] By minimizing the reconstruction error, determining that the distribution of normal data in the predicted data in space is close to the standard normal distribution, and mapping the predicted data to a low-dimensional latent space;

[0042] The distribution of the normal data in space is close to the standard normal distribution and is expressed as:

[0043] ;

[0044] in, is the latent space dimension, and are the mean and variance of the latent space data, and Respectively The actual value and predicted value at the moment, is the gap between the spatial distribution and the standard normal distribution.

[0045] Optionally, obtaining the distribution positions of the outliers includes:

[0046] Stretch, translate, and rotate the encoded data, map each data point to a high-dimensional space, and construct a hypersphere:

[0047] ;

[0048] in, is the center point of the hypersphere, is the radius of the hypersphere, is a positive coefficient, For the data points, for The corresponding slack variable, is the mapping function, is a set of positive integers, is the total number of data points, is a constraint condition;

[0049] The distance from the mapping point of the encoded data to the center of the hypersphere can be expressed as:

[0050] ;

[0051] in, is the distance from the mapping point of the encoded data to the center of the hypersphere, is the center of the hypersphere, is the mapping point.

[0052] Optionally, calculating an anomaly score for the data includes:

[0053] ;

[0054] in, is an abnormal point, is the mapping point set, is the radius of the hypersphere, is the distance from the outlier point to the center of the hypersphere, is the anomaly score of the data.

[0055] Optionally, obtaining a fault result of the nickel flash furnace system includes:

[0056] A target threshold is set, and the abnormality score is judged according to the target threshold. If the abnormality score exceeds zero, it is determined to be fault data. If the abnormality score exceeds the target threshold, it is determined to have a potential fault. Otherwise, it is determined to be operating normally.

[0057] The beneficial effects of the present invention are:

[0058] This paper adopts the idea of graph attention network, integrates mechanism model and expert knowledge, and constructs static graph and dynamic graph respectively to reflect the stable correlation and fluctuating correlation between variables.

[0059] The present invention adopts the method of fusing static graphs and dynamic graphs to construct a graph neural network, and balances the influence of the two graph structures by adaptively adjusting the proportion coefficient to improve the adaptability of the model.

[0060] The present invention adopts a multi-stage learning strategy and focuses on recent data changes through a fixed-length sliding window, which can avoid the influence of early data on the prediction results and improve the execution efficiency and prediction accuracy of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0062] Figure 1 This is a framework diagram of a flash furnace fault prediction method based on graph fusion and multi-stage learning according to an embodiment of the present invention;

[0063] Figure 2 Schematic diagram of a two-layer TCN according to an embodiment of the present invention;

[0064] Figure 3 Schematic diagram of a Transformer according to an embodiment of the present invention;

[0065] Figure 4 A schematic diagram of a process flow of a nickel flash furnace system according to an embodiment of the present invention;

[0066] Figure 5 A flow chart of a multi-stage learning strategy according to an embodiment of the present invention;

[0067] Figure 6 This is a schematic diagram of the mean absolute error of data prediction evaluation indicators according to an embodiment of the present invention;

[0068] Figure 7 This is a schematic diagram of the mean square error of the data prediction evaluation indicator according to an embodiment of the present invention;

[0069] Figure 8 Schematic diagram of the root mean square error of the data prediction evaluation indicator according to an embodiment of the present invention;

[0070] Figure 9 Schematic diagram of the determination coefficient of the data prediction evaluation index according to an embodiment of the present invention;

[0071] Figure 10 is a fault prediction confusion matrix of an embodiment of the present invention; (a) is the prediction confusion matrix of the AE method under three working conditions, (b) is the prediction confusion matrix of the VAE method under three working conditions, and (c) is the prediction confusion matrix of the VAE-Deep SVDD method under three working conditions. DETAILED DESCRIPTION

[0072] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0073] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0074] Hardware Overview: The multi-source perception platform consists of three parts: hardware, server, and host computer. It mainly implements functions such as data collection, edge feature extraction, and data visualization.

[0075] The hardware, comprised of sensors, display screens, and communication modules, is used to monitor the operating status of industrial equipment in real time and extract key data features. This data and feature information can then be uploaded to a server to build a massive data repository, providing a solid foundation for subsequent data analysis.

[0076] The server includes a database, a listener, and intelligent algorithms for data storage and analysis. The listener receives uploaded data and stores it in the database. The intelligent algorithm accesses the database data and performs prediction, classification, and diagnosis operations to meet complex and ever-changing business needs.

[0077] The host computer serves as a tool for human interaction, allowing for data access and visualization, and can remotely execute server programs. Furthermore, through a permissions management mechanism, the host computer enables multi-level user operations, ensuring data security and privacy.

[0078] Hardware development: The hardware part consists of acquisition module and transmission module, and the overall network mode is "star".

[0079] The single module uses an STM32 microcontroller as the main control chip and adopts a "core board + baseboard" design model. The core board, as the control part of the module, integrates the minimum system and function keys of the microcontroller; the baseboard, as the functional part of the module, provides a rich interface for peripherals.

[0080] Acquisition module: The acquisition module integrates temperature and humidity sensors, vibration sensors, sound sensors, inertial measurement units (IMUs), OLED displays, and LoRa modules.

[0081] The acquisition module enables accurate data collection and stable transmission. It performs diversified testing of industrial equipment, structures the test data, and displays it in real time. It also uses fast Fourier transforms to extract data features in the time, frequency, and time-frequency domains. Furthermore, it receives and responds to commands from the transmission module.

[0082] Transmission module: The transmission module integrates RGBTFT display, LoRa module and ESP8266 module.

[0083] The transmission module implements a loop for issuing commands and uploading data. On the one hand, the transmission module sequentially issues acquisition and upload commands to multiple acquisition modules and waits for the acquisition modules to transmit data. Furthermore, to ensure stable data transmission, the module issues commands repeatedly until data is successfully received. On the other hand, the transmission module consolidates data from all acquisition modules and uploads it to the server.

[0084] Data features: To effectively reduce the data computing pressure on the server, feature extraction is implemented in edge devices to provide data support for subsequent analysis and decision-making. The data features extracted by edge devices include time domain features and frequency domain features.

[0085] Time-domain features primarily focus on how data changes over time, reflecting the dynamic characteristics of data in the temporal dimension. They are suitable for tasks such as anomaly detection and real-time monitoring. Frequency-domain features focus on the performance of data in the frequency domain, revealing the distribution and energy of data across frequency components. They are suitable for tasks such as noise suppression and signal recognition. The two complement each other and together provide a comprehensive description of the signal.

[0086] Hardware optimization: During hardware development, limitations such as storage space and computing power can significantly impact the implementation of hardware functionality. This is especially true for data storage and feature extraction, where the following three key issues need to be addressed:

[0087] (1) Storage space: The internal space of the main control chip is limited, with a capacity of only a few hundred KB. It can support basic program logic and real-time operations, but cannot process or store large amounts of data.

[0088] (2) Time series data: The collected data is time series data, which has the characteristics of continuity. In actual work, it is necessary to collect data infinitely for dynamic analysis and decision-making, but data cannot be stored infinitely.

[0089] (3) Operational efficiency: During the feature extraction process, discrete Fourier transform is required to convert time domain data into frequency domain data and extract frequency domain features from it. However, discrete Fourier transform is complex and cannot be directly implemented in edge devices.

[0090] Storage space: The static data memory within the main control chip has limited storage space, with a capacity of only 256KB, which cannot store large amounts of data. Therefore, appropriate strategies must be adopted to overcome resource limitations.

[0091] On the one hand, a dynamic data memory is connected to the outside of the main control chip to provide 32MB of non-volatile storage space for storing data and features.

[0092] On the other hand, efficient drivers and interface functions are written to enable the main control chip to access and manage the dynamic data storage, ensuring the stability and reliability of data transmission.

[0093] Memory Management:

[0094] In practical applications, industrial equipment collects data over long periods of time, generating massive amounts of data while facing the challenge of limited storage space. Since it's impossible to store all the data, an effective data forgetting mechanism is needed to ensure continuous and stable system operation while retaining the data most valuable for analysis.

[0095] Multi-source perception platforms rely on the latest sensor data to achieve short-term data prediction and anomaly diagnosis. Therefore, a sliding window mechanism can be implemented, using a linked list queue to store the latest multiple data items. This not only effectively alleviates hardware storage pressure but also simplifies data addition and deletion operations, improving data storage flexibility.

[0096] Algorithm optimization: Before extracting frequency domain features, Fourier transform (FT) is required to convert time domain data into frequency domain data. However, due to various reasons, Fourier transform cannot be directly used on hardware.

[0097] Although device data changes continuously, the hardware will discretize the data, so the discrete Fourier transform (DFT) is used. However, the fast Fourier transform (FFT) can be performed based on the periodicity of the conversion factors in the discrete Fourier transform to significantly reduce the time complexity of the calculation.

[0098] When writing an FFT program, you can use either recursion or in-situ update. However, because the recursion level of FFT can be very deep, it consumes a lot of hardware computing resources and may not be complete. Therefore, you need to use in-situ update to write the program.

[0099] Furthermore, considering that the hardware uses a moving window mechanism to store data, only the latest data is stored. Accordingly, the short-time Fourier transform (STFT) is used to process only the latest data, which can provide the time-frequency distribution information of the data, reflecting the frequency components of the data at different time points.

[0100] Server deployment: The server is used for data storage and analysis. It can monitor the data uploaded by the hardware in real time and store it in the database, and then analyze and make decisions based on the data.

[0101] Database: MySQL database is used on the server to store relevant data, including user accounts and passwords, collected raw data and feature information.

[0102] Python's PyMySQL library provides MySQL-related functions, allowing you to connect to MySQL from your local computer and perform operations at the database, table, and data levels. Based on this, you can write a MySQL driver on the server to facilitate subsequent database access and management.

[0103] User data table: The user data table is used to store user account information and password information.

[0104] Feature data table: The feature data table is divided into a time domain feature table and a frequency domain feature table, and is used to store the characteristics of device data as well as the device name and date and time. The characteristics include the maximum value, mean, skewness, and kurtosis.

[0105] Data monitoring: The server and the hardware module use the Message Queuing Telemetry Transport Protocol (MQTT) for data transmission. MQTT is a lightweight communication protocol based on the "publish / subscribe" model and is widely used in the field of the Internet of Things. MQTT allows different system components to communicate in a decoupled manner. That is, the publisher does not need to know the specific information of the subscriber. It only needs to publish data to a specific topic, and the subscriber can listen to this specific topic to receive data. In the present invention, the hardware module acts as a publisher, which can realize the encapsulation and publication of collected data and data features. The server acts as a subscriber, which can realize data monitoring, disassemble the data using the subscriber's callback function, and store it in the database.

[0106] Data analysis: After completing real-time data collection, stable transmission, and efficient storage, it is necessary to write an analysis program on the server to analyze the collected data and extracted features to achieve prediction of equipment operating status and abnormal diagnosis.

[0107] On the one hand, the operating status of equipment changes over time and often contains a wealth of valuable information. Time series analysis can capture dynamic changes, revealing evolving trends, periodicity, and abnormal patterns in equipment status. By modeling time series data, it is possible to predict the future operating status of equipment, enabling proactive maintenance or adjustments to prevent potential equipment failures.

[0108] On the other hand, devices are composed of complex network structures, where components are interconnected and influence each other. Graph neural networks can effectively process this network structure data, capturing the dependencies between nodes and the propagation paths of information. Through graph neural networks, we can explore the potential relationships between device components, understand how devices work together, and how faults propagate within the network.

[0109] Combining time series analysis and graph neural networks can fully leverage the advantages of both to conduct a comprehensive and in-depth analysis of the device's operating status. The specific steps are as follows:

[0110] Step 1: Build a network model of the device, where nodes represent devices and edges represent the connection relationships between devices.

[0111] Step 2: Collect time series data for each device, which reflects the operating status of the device at different time points.

[0112] Step 3: Input the time series data as node features into the graph neural network, and use the learning process of the graph neural network to mine the dependency relationships between nodes and the patterns of state changes.

[0113] Step 4: Use the trained graph neural network model to perform prediction or classification tasks.

[0114] Host computer design: Host computer design plays a central role in automation and control systems, placing particular emphasis on user-friendly experience. Its intuitive and user-friendly interface allows users to easily master the system with simple operations. The system provides a clear overview of equipment operating status, significantly improving work efficiency. Furthermore, the host computer features data visualization, presenting complex data in an intuitive manner. This helps users better understand the underlying meaning of the data and provides strong support for decision-making.

[0115] User management: The user management function in the host computer not only includes basic operations such as registration, login, password modification, and account cancellation, but also implements permission management to ensure data security.

[0116] When registering, in addition to filling in basic information, the system also assigns initial permissions to the user based on pre-set rules. These permissions determine the user's scope of operations and data access level within the system. After successful registration, the user logs into the host system using their personal account and performs operations based on the permissions assigned.

[0117] When logging in, users are not only required to enter their correct username and password, but also have different functional modules opened up based on their level of authority. Users with advanced authority can access more core data and perform more advanced operations, while ordinary users can only access and operate content within their authority scope.

[0118] When changing your password, the system will verify it based on the user's current permissions to ensure that only legitimate users can successfully change their passwords. In addition, when a user's permissions change, the system will prompt the user to update their password to further enhance account security.

[0119] The account cancellation function deletes all user permissions in the system when canceling a user's account. This ensures that when a user decides to abandon their account, the relevant permissions are properly handled, preventing potential security risks. The account information and management interface allows users to view account information, change passwords, cancel accounts, and log out.

[0120] Permission management allows system administrators to dynamically adjust user permissions based on actual needs. Administrators can assign or adjust permissions based on user job responsibilities, roles, or needs, ensuring that each user can maximize their contribution to the system while remaining within their intended scope of operation. The permissions management interface allows users to query relevant personnel, departments, or positions.

[0121] In summary, the user management function in the host computer provides users with a comprehensive, secure, and efficient user management experience. It not only meets users' basic needs but also improves the overall security and stability of the system, laying a solid foundation for the long-term development of industrial enterprises.

[0122] Data query: The data query function of the host computer plays a vital role in equipment management and analysis. It allows users to efficiently retrieve, browse, and analyze various types of data stored in the database, achieving comprehensive monitoring of the equipment.

[0123] The host computer's data query function allows users to query the latest data records for a specified device number, displaying the latest 20 relevant data items in real time, ensuring users are always aware of the device's latest status. This function also supports real-time refresh, ensuring data timeliness and accuracy, providing users with an efficient way to fully understand the current status of the device.

[0124] In addition to querying the latest data, the host computer also supports querying data for a specific time period based on the device ID. Users simply specify the start and end times, and the system automatically retrieves and displays relevant data for the device within that time period. This feature also supports data export, allowing users to easily save query results to local files for subsequent data processing and analysis. This provides users with greater flexibility and allows them to process and analyze data according to their needs.

[0125] In summary, querying the latest data or time interval data for a device based on its device ID is an important application scenario for the host computer's data query function. It provides users with powerful data retrieval and processing capabilities, helping them better understand device status, optimize device performance, and improve production efficiency.

[0126] Data visualization: The data visualization function of the host computer can intuitively display data such as fault classification results and fault types, providing users with powerful data analysis and troubleshooting capabilities.

[0127] Through data visualization, users can clearly understand the distribution, frequency, and changing trends of various fault types. Different fault types are distinguished by different colors, shapes, or symbols, making fault data clear at a glance. This helps users quickly locate fault points and analyze the causes and patterns of faults, providing strong support for fault prediction and resolution. Furthermore, data visualization can combine fault data with other equipment operation data for comprehensive analysis. For example, users can correlate fault data with equipment operating time, temperature, humidity, and other parameters to identify the relationship between faults and certain parameters, providing data support for equipment optimization and maintenance.

[0128] In summary, the data visualization function of the host computer plays an important role in fault classification and fault type data analysis. It can provide users with intuitive and accurate data display, helping users to better understand and solve equipment failure problems.

[0129] like Figure 1 As shown, this embodiment discloses a flash furnace fault prediction method based on graph fusion and multi-stage learning, including: establishing a static graph and a dynamic graph, describing the influence intensity and dynamic changes between sensor data according to the static graph and the dynamic graph, and obtaining spatiotemporal features; inputting the spatiotemporal features into the Transformer encoding model to obtain predicted data; the Transformer encoding model is trained using a training set, and the model parameters are adjusted to minimize the prediction error; the training set includes: original spatiotemporal features; encoding the predicted data, stretching, translating and rotating the encoded data, mapping each data point to a high-dimensional space, obtaining the distribution position of the abnormal points, and calculating the abnormal score of the data, judging the abnormal score, and obtaining the fault result of the nickel flash furnace system. Specifically, the flash furnace system can be regarded as a graph structure composed of multiple sensor measurement points, defined as Among them, sensor data , Represents the total number of sensors, connection matrix Indicates that there are mutual influences between different sensors, elements Indicates sensor For sensors If there is an impact, the element Defined as:

[0130] ;

[0131] in, and Representing the The sensor and sensors.

[0132] Adjacency Matrix Indicates the intensity of the mutual influence between different sensors, elements Indicates sensor For sensors Influential, defined as:

[0133] ;

[0134] in, represents the static part of the weight, Represents the dynamic part, and is the proportion coefficient, and satisfies . Adjacency Matrix and connection matrix If ,but ,otherwise .

[0135] Assume that the historical sensor data is ,in The spatiotemporal feature module extracts the spatiotemporal features of historical data to predict future sensor data. ,in Then, the health status of the flash furnace system is predicted by analyzing the historical data and predicted data of the flash furnace system under normal conditions.

[0136] To achieve the goal of flash furnace fault prediction, two key issues need to be addressed during model training: first, the adjacency matrix and the proportion coefficient influence each other, causing the model to fall into a local optimal solution, making it difficult to find the globally optimal parameter combination; second, the characteristic boundary between normal data and fault data is not obvious, which may lead to false alarms or omissions of faults.

[0137] Furthermore, describing the influence intensity between sensor data includes: using a mechanism model to describe the relationship between the internal variables of the flash furnace system to obtain the influence intensity between sensors; determining the influence direction of the influence intensity and dividing the influence level to obtain the final influence intensity; using the final influence intensity to construct a static adjacency matrix; combining the static adjacency matrix with the static graph to obtain the influence intensity between sensor data, that is, the static feature.

[0138] Specifically, the static image It is used to describe the stability of the influence between variables. First, a static weight matrix is constructed based on the mechanism model and expert knowledge. , where the element Indicates sensor For sensors The impact strength, is the connection matrix, is a static adjacency matrix.

[0139] Mechanism models are mathematical models based on physical principles or chemical reactions, used to describe the relationships between variables within a system. Mechanism models can be used to derive the influence strength between sensors. In flash furnace systems, mechanism models can be developed from multiple perspectives, such as material balance, energy balance, and compound analysis, to reflect the changing relationships between various physical quantities. For example, the temperature relationships between the reaction tower, sedimentation tank, depletion zone, and riser in a nickel flash furnace system can be established using heat balance equations and energy calculation formulas.

[0140] ;

[0141] in, is the sensible heat of the first part, For the second part, is the heat of reaction, For the heat of combustion, To dissipate heat, is the heat of vaporization, is the heat loss, For heat, and are the mass and specific heat capacity of the reactants or products, respectively, is the temperature of the substance at time t, measured by the sensor, is the temperature of the substance at time t-1, recorded by the acquisition system.

[0142] For the reaction tower, the heat input includes the sensible heat of the reaction tower material ( ), reaction heat of reaction tower charge ( ), reaction tower fuel heat ( ) and inlet air sensible heat ( ), thermal expenditure includes the sensible heat of nickel matte produced by the reaction tower ( ), slag sensible heat ( ), sensible heat of soot production ( ), flue gas sensible heat ( ), reaction tower heat dissipation ( ), heat of evaporation of water in the reaction tower ( ). Equipped with various temperature sensors The state vector composed of the moment measurement values is:

[0143] ;

[0144] in, is transposed.

[0145] Since the temperature of the material at time t It is obtained by actual measurement of the sensor, so the current state of the reaction sensor can be directly used. Combined with formula (3), the relationship equation between the states of each sensor in the reaction tower can be obtained as follows:

[0146] ;

[0147] in, is the coefficient vector, is the state vector composed of the measurement values of multiple temperature sensors at time t, The state vector is composed of the measurement values of multiple temperature sensors at time t-1. There is a thermodynamic coupling effect between the temperature sensors, which is mainly achieved through processes such as heat conduction and chemical reaction. In order to quantify the influence strength between sensors, the coupling coefficient is introduced. , its physical meaning is that the sensor changes under unit temperature For sensors The impact strength is defined as follows:

[0148] ;

[0149] in, is the symbol of partial derivative, For sensors The temperature at time t, For sensors The temperature at time t.

[0150] Expert knowledge is a qualitative cognition formed based on the experience and judgment of domain experts. When the mechanism model leads to significant deviations or fails to fully describe the system behavior due to idealized assumptions or simplified processing, the model can be modified by integrating expert knowledge. In specific applications, expert knowledge mainly describes the relationship between variables through two dimensions: one is to qualitatively determine the direction of influence (changes in the same direction are positive, and changes in the opposite direction are negative); the other is to use fuzzy quantification methods to divide the influence intensity into three levels: strong (0.8), medium (0.5), and weak (0.3), and finally obtain the influence intensity. , indicating the sensor For sensors While maintaining the theoretical integrity of the mechanism model, the introduction of expert knowledge significantly improves the model's adaptability to complex real-world operating conditions. In flash furnace systems, the relationships between some physical quantities are difficult to fully summarize using clear physical equations or chemical expressions and require description through expert knowledge.

[0151] For example, in a waste heat boiler (HRSG), when the boiler liquid level is too low, steam may accumulate, causing the boiler pressure to increase. When the boiler liquid level is too high, the steam space is restricted, potentially causing the boiler pressure to decrease. This indicates a negative impact between the boiler liquid level and boiler pressure. Based on expert experience, the impact is moderate, so the mutual impact intensity between the boiler liquid level and boiler pressure can be quantified as -0.5.

[0152] Similarly, for the flash furnace system, several relevant mechanism models and expert knowledge can be listed to more accurately reflect the relationship between the system variables and construct a static weight matrix , where the element If determined by the mechanism model, it is the static part of the weight , determined by expert knowledge, is the impact intensity .

[0153] Then, considering that the mechanism model is usually a description of the ideal state of the system, and expert knowledge may have subjective deviations, in order to bridge the numerical gap between the ideal state and the actual state, a data-driven approach is combined to construct a static bias matrix through model training. . Then the static adjacency matrix It can be expressed as:

[0154] ;

[0155] Among them, the function Used to eliminate negative connections in the input and enhance the sparsity of the adjacency matrix. Normalize each row of the matrix to preserve the relative size relationship between the data.

[0156] Ultimately, under the guidance of mechanism models and expert knowledge, and combined with model training, static graphs can quickly find stable influence relationships between variables in the system, providing strong support for subsequent tasks.

[0157] Furthermore, describing the dynamic changes between sensor data includes: acquiring sensor data, generating a first subspace based on the sensor data, and constructing an adjacency matrix based on the subspace; using a dynamic graph to map the weight matrix input to the subspace, and dynamically adjusting the adjacency matrix to capture the dynamic changes between sensor data, namely dynamic features.

[0158] Specifically, static graphs are primarily used to describe fixed relationships between variables and their stable influence strength, but they cannot capture temporal dependencies or dynamic changes between variables. To overcome this limitation, dynamic graphs are introduced to characterize dynamic dependencies in time series data, thereby more comprehensively describing the evolution of the system.

[0159] dynamic image It is used to capture the complexity and dynamic characteristics of the system over time and continuously adjust the weights between variables according to dynamic inputs. First, based on sensor data Generate two subspaces and :

[0160] ;

[0161] in, and are learnable parameters, representing the and The weight matrix of . Then the dynamic adjacency matrix It can be expressed as:

[0162] ;

[0163] in, and The role of is to spontaneously find the spatial dependence between variables through weighted processing. For subspace The transpose of . Function To eliminate negative connections in the input, the function Normalize the dependencies and Scale the input to prevent the calculation results from diverging, Indicates the total number of sensors.

[0164] The dynamic graph maps dynamic inputs to subspaces through weight matrices and dynamically adjusts the adjacency matrix. It can capture the dynamic dependencies between variables in time series data, thereby more comprehensively describing the evolution of the system.

[0165] Furthermore, obtaining spatiotemporal features includes: constructing a graph neural network by fusing the static graph and the dynamic graph to describe the influence intensity and dynamic changes between sensor data, obtaining static features and dynamic features, generating a second subspace based on the static features and the dynamic features, extracting steady-state spatial coupling features and time-varying spatial coupling features from the time series data in the second subspace, using a proportion coefficient to balance the steady-state spatial coupling features and the time-varying spatial coupling features, and performing feature fusion to obtain comprehensive spatial features; inputting the comprehensive spatial features into a multi-layer TCN model, and each layer of TCN further abstracts based on the output of the previous layer and refine features to obtain the spatiotemporal features; the multi-layer TCN model is obtained by training using a training set; the training set includes: original comprehensive spatial features; wherein, the multi-layer TCN model obtains temporal features by introducing dilated convolution; during the training of the Transformer encoding model, the graph neural network and the multi-layer TCN model, a multi-stage learning strategy is adopted to initialize the model, and the bias matrix, weight coefficient and proportion coefficient of the model are trained using the training set to obtain the target proportion coefficient, and the bias matrix and weight coefficient of the model are trained again to obtain the target bias matrix, and finally the weight coefficient of the model is trained to obtain the target weight coefficient.

[0166] Specifically, the nickel flash smelting furnace system, as a typical complex industrial process system, exhibits a unique dual nature in its operation. While adhering to fundamental physical and chemical laws such as thermodynamic equilibrium equations and the law of conservation of mass, the system is also subject to time-varying factors such as material fluctuations and equipment aging. This dual nature makes it difficult for a single graph structure to fully represent the system's state. Therefore, a graph fusion module is employed to deeply fuse the static and dynamic features extracted in the graph construction module, thereby obtaining more comprehensive and practical features from time series data.

[0167] For graph learning models used for time series prediction, the future state of each node in the graph is influenced not only by its immediate neighbors but also by the historical features of each neighboring node. Therefore, when designing the feature fusion strategy for the graph fusion module, it is important to ensure that each node can obtain more and more critical features from its more influential neighbors. This means that the fusion mechanism needs to be able to identify and weight important neighboring nodes in order to more effectively integrate these features, thereby improving the accuracy and reliability of time series prediction.

[0168] When extracting spatial features from spatial data at a certain moment in history, based on sensor data Generate a subspace :

[0169] ;

[0170] in, is a learnable parameter, representing the subspace The weight matrix of . Then the steady-state spatial coupling features extracted from the time series data are and time-varying spatial coupling characteristics It can be expressed as:

[0171] ;

[0172] ;

[0173] in, is the static adjacency matrix, is a dynamic adjacency matrix.

[0174] The adjacency matrix of the static graph is constant and does not change over time, providing the inherent physical constraints and stable topology of the flash furnace system. The adjacency matrix of the dynamic graph will be updated in real time with dynamic input, and through the adaptive learning mechanism, it can capture the dynamic correlation between variables caused by operating condition fluctuations in real time. Therefore, the features extracted by the two have different focuses. In order to enhance the comprehensive expression ability of the features extracted by the two graph structures, the proportion coefficient is used. and Balance the steady-state spatial coupling characteristics and the time-varying spatial coupling characteristics, and perform feature fusion to obtain comprehensive spatial characteristics :

[0175] ;

[0176] Among them, the proportion coefficient Determines the embedding strength of prior knowledge in the system space characteristics, the proportion coefficient The synergistic optimization of the two enables the system to adaptively adjust feature representations while maintaining structural stability, thereby more accurately characterizing the evolving behavior of complex systems. This fusion strategy demonstrates strong generalization capabilities in dynamic modeling tasks and is particularly suitable for analyzing complex systems with time-varying characteristics.

[0177] In the sliding window The same operation is used to gradually extract the spatial features of each moment and construct a spatial feature sequence where p is the length of the historical time series. A multi-layer TCN is then used to extract temporal features from the feature time series. This approach not only considers the spatial characteristics of graph data but also fully accounts for temporal dependencies, thereby improving the accuracy of model predictions.

[0178] TCN is a network model that extracts features of data of limited time length. Unlike traditional recurrent neural networks (RNNs) and long short-term memory networks (LSTMs), TCN captures the long-term dependencies of time series data through convolution operations.

[0179] To capture data features over longer time periods using a single-layer TCN, the time span of the input data is generally increased. By expanding the temporal range of the input data, TCN can capture dependencies over longer time spans. However, increasing the time span increases computational cost, especially when processing large datasets, where a trade-off between computational resources and model performance is necessary. Therefore, dilated convolutions are introduced in a single-layer TCN to expand the network's receptive field and help capture long-range dependencies.

[0180] Spatial feature sequence Perform dilated convolution to obtain temporal features for:

[0181] ;

[0182] in, is the convolution kernel size, is the expansion coefficient, the convolution kernel size and expansion coefficient It is a hyperparameter that needs to be adjusted, which will limit the receptive field of TCN. is a positive coefficient, i.e., an ergodic variable. and Improper configuration may result in a limited receptive field, failing to fully cover long time series and making it difficult to capture long-range dependencies. At the same time, dilated convolutions may skip too much input data, causing discontinuities in the receptive field. This increases the difficulty for the model to capture subtle changes or short-term dependencies in time series.

[0183] Therefore, a single-layer TCN may not capture all important information, which can affect the model's predictive performance. It is necessary to build a deeper network structure through multiple layers of TCN to gradually extract and integrate important information from time series data, thereby enhancing the model's ability to learn complex features. When increasing the number of TCN layers, network parameters must be carefully adjusted to ensure model stability and avoid problems such as overfitting, vanishing gradients, and exploding gradients that may occur in deep networks.

[0184] Multi-layer TCN will gradually extract and integrate features. Each layer of TCN further abstracts and refines the features based on the output of the previous layer, and finally obtains the spatiotemporal features. , which can reflect the more complex and deep spatiotemporal correlations in the input data. The middle layer and the output layer are both designed based on TCN. Different expansion coefficient d parameters are used to configure each layer differently, forming a hierarchical feature learning system. The network data flow starts from the input layer, which is the bottom layer of the network. As the data entry of the model, the horizontal arrow indicates that the order of the time series is passed to the middle layer TCN (d=1), which is the first layer of the middle layer. The local features of the time series data are extracted, the basic change patterns in the time series data are identified, and the features are initially abstracted. The vertical arrow indicates the feature transfer between layers, and the original data is converted into a low-level feature representation. The second layer: TCN (d=2) is the second layer of the middle layer. At this time, the temporal receptive field is expanded by dilated convolution, and deeper feature extraction is performed on the basis of the first layer. The slash connection indicates the jump connection of the dilated convolution, which integrates multiple local patterns into global features and passes them to the top layer of the network, the output layer, to generate the final prediction result, such as Figure 2 shown.

[0185] The fault prediction module captures the dynamic laws of the flash furnace system's operation by predicting the basic changing trends of the flash furnace system's future operating status, and comprehensively analyzes whether the flash furnace system may fail in the future based on historical data and predicted data.

[0186] Data prediction: Data prediction tasks require considering both the temporal and spatial attributes of spatiotemporal features to achieve node sequence prediction for flash furnace data. Accurately predicting future trends in industrial data can provide a reliable data basis for subsequent fault prediction.

[0187] Given the advantages of multi-head self-attention and parallel computing, Transformer can process complex time series data. Therefore, the Transformer structure is improved for spatiotemporal sequence prediction tasks to predict the future operating status of the flash furnace system. The model structure is as follows Figure 3 As shown, the spatiotemporal characteristics As input, after multiple layers of encoders and decoders, the predicted data of the flash furnace system can be obtained.

[0188] Since Transformer does not have a recursive structure for processing the order of sequences, it is necessary to generate a learnable position encoding vector and add it to the input time series data so that the model can distinguish the order relationship of each element in the time series data. The encoder and decoder of Transformer are composed of multiple multi-head self-attention layers and feedforward neural network layers. The multi-head self-attention layer consists of multiple independent self-attention layers, which are used to query the matrix and bond matrix and value matrix The output of each layer is optimized through residual connections and layer normalization operations, which can prevent gradients from disappearing or exploding, and improve the training effect and performance of the model.

[0189] Figure 3 This paper presents a spatiotemporal sequence prediction model based on the Transformer architecture, which is primarily used to process historical data and predict future spatiotemporal sequences. The historical data sequence is input, and "spatiotemporal features" are first extracted. Then, combined with positional encoding, the temporal or spatial position information is injected into the model via sine / cosine encoding or learnable parameters to compensate for the Transformer's lack of temporal awareness. The encoder consists of multiple stacked encoding layers, each of which contains the following sublayers: a multi-head attention mechanism calculates the dependencies between different temporal / spatial positions in the historical sequence to capture long-range patterns; layer normalization normalizes the attention output to stabilize the training process; the feedforward layer performs nonlinear transformations on the features through a fully connected network; and residual links, typically with each sublayer, prevent gradient vanishing. The decoder gradually generates a future prediction sequence through multiple decoding layers. Its structure includes: the decoder pays attention to the output of the encoder through a multi-head attention mechanism, uses historical information to guide prediction, and the self-attention layer inside the decoder processes the generated part of the future sequence to ensure the consistency of the prediction. The feedforward layer and normalization are similar to the encoder, including feedforward networks and normalization operations. Position encoding adds position information to the input of the decoder (such as the initial embedding of the target sequence or the prediction of the previous moment), and outputs feature data, which refers to the high-level features extracted by the decoder, or is spliced with other auxiliary features (such as external variables). Linear layer: maps the high-dimensional features output by the decoder to the dimensions of the target spatiotemporal sequence to generate the final prediction results.

[0190] The mean square error (MSE) is used to measure the accuracy of data prediction. The formula is as follows:

[0191] (15);

[0192] in, and Respectively The actual value and predicted value at the moment, is the length of the forecast period, The result is measured as mean squared error. By minimizing the mean squared error, the model is optimized using gradient descent to improve the accuracy of data prediction.

[0193] Furthermore, encoding the predicted data includes: determining that the distribution of normal data in the predicted data in space is close to a standard normal distribution by minimizing the reconstruction error, and mapping the predicted data to a low-dimensional latent space;

[0194] Obtaining the distribution position of the abnormal points includes: stretching, translating and rotating the encoded data, mapping each data point to a high-dimensional space, constructing a hypersphere, and obtaining the distance from the mapping point of the encoded data to the center of the hypersphere.

[0195] Obtaining the fault results of the nickel flash furnace system includes: setting a target threshold, judging the abnormality score according to the target threshold, if the abnormality score exceeds zero, it is determined to be fault data, if the abnormality score exceeds the target threshold, it is determined to have a potential fault, otherwise it is determined to be operating normally.

[0196] Specifically, in flash furnace systems, equipment data suffers from data imbalance, with normal data comprising the majority and faulty data being relatively scarce. This unbalanced distribution makes it difficult for traditional classification methods to effectively define the boundary between normal and faulty data, resulting in a low model sensitivity to faulty data, which in turn affects the accuracy and reliability of fault prediction. Specifically, data imbalance can cause models to overfit to the majority class (normal data) and neglect the minority class (faulty data) during training, leading to insufficient prediction capabilities. Effectively processing unbalanced data and extracting effective features from it poses a significant challenge in fault prediction systems. To mitigate the impact of data imbalance on prediction, this paper combines a variational autoencoder with Deep SVDD to improve fault prediction accuracy. The variational autoencoder extracts data features, specifically potential features that are more conducive to distinguishing normal from faulty data. Deep SVDD constructs a compact boundary that maximizes the inclusion of normal data features within the boundary while excluding faulty data features. By combining these two methods, the model's sensitivity to faulty data can be effectively enhanced, thereby improving the accuracy and reliability of fault prediction.

[0197] First, a variational autoencoder is used to encode the sensor's predicted data. As an unsupervised learning method, it can fully learn the latent space distribution of normal data. The variational autoencoder maps the original data into a low-dimensional latent space by minimizing the reconstruction error and ensuring that the distribution of the latent space is close to a standard normal distribution. The reconstruction error is represented by the mean squared error loss function, and the difference in the latent space data distribution is represented by the KL divergence. The overall loss function is:

[0198] (16);

[0199] in, is the latent space dimension, and are the mean and variance of the latent space data, and Respectively The actual value and predicted value at the moment, is the gap between the spatial distribution and the standard normal distribution.

[0200] The encoded data is then stretched, translated, and rotated through Deep SVDD, and a kernel function is used to map each data point to a higher-dimensional space and construct a hypersphere.

[0201] (17);

[0202] The center point of the hypersphere is , the radius of the hypersphere is , is a positive coefficient used to control the trade-off between maximizing the radius of the hypersphere and minimizing the sum of the distances from the data points to the center of the hypersphere during the optimization process. For the data points, for The corresponding slack variable allows some data points to be outside the sphere, is the total number of data points, is the constraint condition, is a mapping function, which means that the data points are mapped to a high-dimensional feature space.

[0203] If the mapping point of the encoded data is , then the mapping point To the center of the hypersphere The distance can be expressed as:

[0204] ;

[0205] like , then the mapping point is considered a normal point, otherwise the mapping point Considered an outlier.

[0206] Finally, the anomaly score of the data is calculated based on the distribution of the anomaly points to quantify the degree of anomaly of the data, which is defined as:

[0207] (18);

[0208] in, is an abnormal point, is the mapping point set, is the radius of the hypersphere, is the distance from the outlier point to the center of the hypersphere, is the anomaly score of the data.

[0209] Since there may be isolated points among normal points and some data are tolerated to be outside the hypersphere, the abnormal score of normal data may be slightly greater than zero. Some normal data points may be misjudged as abnormal due to noise, fluctuation or boundary effects. Therefore, data with a score greater than zero cannot be simply judged as faulty data. In order to avoid such misjudgment, a threshold is introduced. Fault prediction is optimized and adjusted based on data distribution, ensuring that only data with a score significantly above zero is considered faulty, thereby balancing the false positive and false negative rates of fault prediction. If the anomaly score exceeds the threshold, the device is considered to have a potential fault; otherwise, the device is considered to be operating normally.

[0210] Multi-stage learning strategy: In the proposed model, determining the graph weight coefficient is a prerequisite for constructing the fusion graph. Only when the fusion graph is constructed with the optimal weight coefficient can it fully mine and extract the most accurate data features. During model training, the weight coefficient is trained simultaneously with the weight coefficients of the two graph structures, ultimately adjusting each parameter by minimizing the prediction error. However, the joint optimization of multiple parameters may cause the model to fall into a local optimum, thus affecting the final performance and preventing the global optimal parameter combination from being found.

[0211] Therefore, in order to ensure that each parameter learns the optimal effect under the best conditions and avoid the mutual influence of different parameters during training, a multi-stage learning strategy is adopted:

[0212] 1. Initialize the model. 2. Train the bias matrix, weight coefficient, and proportion coefficient to keep the proportion coefficient constant. 3. Train the bias matrix and weight coefficient to keep the bias matrix constant. 4. Train the weight coefficient.

[0213] The model training is carried out step by step in a stage-by-stage sequence to ensure that each part can be fully trained under optimal conditions, thereby improving the accuracy of data prediction and fault prediction.

[0214] When predicting future data, the key is to extract effective spatiotemporal features. This requires not only accurately capturing the temporal changes in the data but also fully reflecting the evolution of the data's spatial structure, providing good information for downstream tasks and improving data prediction. Because the effectiveness of data prediction inhibits learning during feature extraction, and because the adjacency matrix and the proportion coefficients are mutually constrained, if one part performs well in training, the training of other parts will be too slow. Therefore, it is important to ensure that all parts of the data prediction phase are coordinated to achieve optimal data prediction results. See Algorithm 1 for pseudocode.

[0215] Algorithm 1: Training feature extraction model

[0216]

[0217] The key to predicting potential failures lies in effectively learning the characteristics and distribution of normal data, identifying the clear distinction between normal and abnormal data, and thereby determining whether the equipment is at risk of future potential failures. Because the boundary between normal and faulty data is often fuzzy, it is difficult to define a clear demarcation point directly from the raw data. Therefore, a VAE model is used to encode and process normal data, learning its inherent patterns. A Deep SVDD model is then used to construct a hypersphere to represent the distribution range of normal data. This allows the model to effectively learn behavioral patterns under normal conditions and provide clear criteria for determining abnormal data.

[0218] First, a VAE is trained on normal data, mapping the raw data into a latent space to capture the data's inherent structure and patterns, providing a foundation for subsequent tasks. Next, Deep SVDD is used to construct an optimal hypersphere in the latent space, minimizing its radius while ensuring that it covers the majority of normal data points. Finally, an anomaly score is calculated to quantify the degree of data anomaly and a threshold is set. When determining a fault, if the anomaly score of a data point exceeds the threshold, the device is considered to have a potential for future failure. See Algorithm 2 for pseudocode.

[0219] Algorithm 2: Fault Prediction

[0220]

[0221] Through a multi-stage step-by-step optimization approach, the model effectively reduces the mutual influence between its components, can fully extract the steady-state and dynamic characteristics of the data, improves the prediction accuracy of the system state, and improves the accuracy of potential fault prediction, thereby providing more reliable fault warning and prevention capabilities in practical applications.

[0222] The data used in this example are from a nickel flash furnace system in a nickel smelter. This system processes nickel concentrate through a flash furnace, produces low-nickel matte, and discharges nickel smelting slag. The data used in this example are from a nickel flash furnace system in a nickel smelter. This system processes nickel concentrate through a flash furnace, produces low-nickel matte, and discharges nickel smelting slag. The process flow of the nickel flash furnace system is as follows: Figure 4The diagram shows the main steps and material flows, as follows: 1. Raw Material Preparation: Steam Drying: Pulverized coal and solvent are pre-treated through steam drying to remove moisture. Blended Concentrate: Domestic concentrate, purchased concentrate, dried pulverized coal, and solvent are mixed to form the smelting raw material. 2. Smelting Stage: Electric Furnace: The blended concentrate is smelted in an electric furnace, producing slag, high-nickel matte (an intermediate product with a high nickel content), and flue gas. Converter: The high-nickel matte is further blown in the converter to purify it into a higher-grade nickel product, generating slag and flue gas. 3. Flue Gas Treatment: Process Flue Gas: Flue gas from the electric furnace and converter is recycled through a waste heat boiler and then passes through an electrostatic precipitator to remove particulate matter. Environmental Flue Gas: A portion of the flue gas is fed into a flue gas desulfurization system to reduce sulfur emissions. Acid Production: The desulfurized flue gas is used in sulfuric acid production, achieving resource utilization. 4. By-Products and Emissions: Slag: Slag generated during the smelting process can be treated as a by-product or further utilized. Low-nickel matte: It may be an intermediate product of smelting and requires further processing. Industrial flue gas: After dust removal and desulfurization, it is discharged through a smoke exhaust fan or enters the acid production process. To address the problem of sensor data prediction and fault prediction in the flash furnace system, this embodiment selects 14 representative sensors under three working conditions for simulation verification, covering key parameters such as temperature, pressure, sound, and vibration. Among them, each working condition contains 10 sets of data: 1 set of normal data (120,000 data) and 9 sets of fault data (1,280 data per set). All data are randomly stratified and split, 80% for training and 20% for testing. The selected sensors and their detailed information are shown in Table 1.

[0223] The precise placement and functional configuration of sensors is crucial. They not only enable comprehensive monitoring of key areas of the flash furnace system but also lay the foundation for data collection and analysis. The data captured by these sensors enables in-depth analysis of the equipment's operating status and the prediction of potential failures.

[0224] Therefore, based on data from various sensors, it is possible to effectively analyze and determine whether a flash furnace is likely to fail in the future. This is crucial for improving equipment efficiency and ensuring safety. Table 2 lists common failure types that occur during long-term operation of a flash furnace.

[0225] Table 1 Sensor location description

[0226]

[0227] Table 2 Common fault types of flash furnace

[0228]

[0229] Data preprocessing and model building: Since the collected nickel flash furnace data has problems such as inconsistent magnitude, inconsistent collection frequency, and timestamp deviation, it is necessary to perform corresponding preprocessing operations on the collected data.

[0230] First, the data is divided into intervals, with each interval being one minute. Within each interval, the original data is replaced with the average value of the data within that interval. If there are intervals with no data, they are filled in using time interpolation. The data is then normalized to ensure that different data have the same magnitude. This not only aligns data timestamps but also reduces the impact of frequent fluctuations and magnitude differences on subsequent data analysis.

[0231] When building the model, in order to explore the numerical connections between different data at different scales, the variational mode decomposition (VMD) method is used to decompose the data into multiple modal components (IMFs) of different frequencies to represent the trends, fluctuations and errors of the data. The graphical structure of the model is then constructed for the modal components of all the data.

[0232] For length Time series , the energy can be expressed as:

[0233] ;

[0234] The original sequence can be decomposed into modal components, Represents the zth modal component, the energy of the zth modal component sequence The expression is similar to formula (19), and the corresponding energy ratio can be expressed as:

[0235] ;

[0236] in, For time series energy, For the modal component sequence, is the energy ratio.

[0237] Based on the proposed component energy proportions, we expect that the energy proportions of different components of the same data will vary significantly, while the energy proportions of corresponding components of different data will vary slightly. Therefore, the nickel flash furnace data is decomposed into four modal components. When constructing the graph, we assume that there are correlations between different components of the same data and between corresponding components of different data, while no correlations exist between the remaining components.

[0238] Weight coefficients: Use a dual optimizer to update the model parameters. Set the learning rate to 0.005 for the weight coefficients and 0.001 for the other parameters. Update curve for the weight coefficients.

[0239] To ensure that weight coefficient updates are not affected by the initial values, training is performed by setting multiple initial values. In a single round of training, the weight coefficient updates undergo a process of first convergence and then increase. When the weight coefficients converge to a certain level, they are constrained by the updates of other parameters and the weight coefficients are not stopped. The weight coefficients will continue to increase without constraints. Although each round will not completely converge to a single value, the convergence error range will become smaller and smaller, eventually converging to a smaller error range.

[0240] The update curve of the static image ratio is as follows Figure 5 As shown. In the process of updating the static image proportion coefficient, in order to ensure that the update of the static image proportion coefficient is not affected by the initial value, training is performed with initial values of 0.1-0.9, with a total of 9 update curves. The training of the static image proportion coefficient went through three rounds, with the width ranges of range1, range2 and range3 respectively. In a single round of training, the update of the static image proportion coefficient first converges and then rises. When the proportion coefficient converges to a certain optimal point, it is constrained by the update of other parameters and the proportion coefficient is not stopped. The proportion coefficient will continue to rise without constraints. The optimal points in the three rounds of training are represented by point1, point2 and point3 respectively. Although each round will not completely converge to a value, the convergence error range is getting smaller and smaller, and finally converges to a smaller error range. The error ranges of the three rounds of training are the height ranges of range1, range2 and range3 respectively.

[0241] The point before the final rise is the optimal point for the current round of updates, and the average of all curve values corresponding to this point is used as the optimal selection value for the proportion coefficient. The optimal selection results are shown in Table 3, setting the proportion coefficient of the static graph to 0.4966.

[0242] Table 3 Weight coefficient update data

[0243]

[0244] Ablation experiment:

[0245] To clearly demonstrate the advantages of fusing static and dynamic images, the following three sets of experiments are designed to highlight the superiority of fused images by comparing models with different configurations.

[0246] a) Baseline group: fusion graph, which combines static and dynamic graphs; b) Control group 1: dynamic graphs are deleted and static graphs are retained; c) Control group 2: static graphs are deleted and dynamic graphs are retained.

[0247] The comparison was based on a single-step prediction experiment, and the following evaluation indicators were selected to compare and analyze the three groups of results: mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and coefficient of determination (R²). MAE is the average of the absolute deviations between the predicted value and the actual value, which intuitively reflects the average magnitude of the error. MSE is the average of the squares of the differences between the predicted value and the actual value, giving higher weights to larger errors, thereby highlighting their impact. RMSE is the square root of MSE and retains the original unit of the error, which helps to intuitively understand the error magnitude. R² is used to measure the degree of fit between the predicted value and the actual value, and the value range is between 0 and 1. The formulas for the above evaluation indicators are as follows:

[0248] Mean absolute error:

[0249] ;

[0250] Mean Squared Error:

[0251] ;

[0252] Root mean square error:

[0253] (twenty three);

[0254] Coefficient of determination:

[0255] (twenty four);

[0256] in, It is True value, It is predicted values, It is The mean of the true values, is the number of samples. MAE, MSE, and RMSE measure the error between the predicted value and the true value from different perspectives. Smaller values indicate better predictions. R² measures the goodness of fit between the predicted value and the true value, indicating the model's ability to explain the data. Values closer to 1 indicate better predictions.

[0257] Three groups of comparative experiments were conducted using the normal data of nickel flash furnace under three working conditions. The experimental results are as follows: Figure 6-9 shown. Figure 6-9 The performance of three spatial methods (static graph, dynamic graph, and fusion graph) under different working conditions is shown. The vertical axis of each graph represents different evaluation indicators, namely: Figure 6 The mean absolute error (MAE) Figure 7The mean square error (MSE) Figure 8 The root mean square error (RMSE) and Figure 9 The coefficient of determination (R 2 ). In working condition 1, the MAE, MSE and RMSE of the dynamic graph are higher than those of the other two methods, while the MAE and MSE of the static graph are higher than those of the fusion graph, but the RMSE is slightly higher than that of the fusion graph, and lower than that of the dynamic graph. In working condition 2, the MAE, MSE and RMSE of the fusion graph are the lowest, followed by the dynamic graph, while the static graph is the highest under all three indicators. In working condition 3, the performance is roughly similar to that of working condition 1. The MAE, MSE and RMSE of the three methods are also the highest in the dynamic graph, followed by the static graph, and finally the fusion graph. 2 In terms of the dynamic graph, the R value is the lowest in working conditions 1 and 3, while the determination coefficients of the dynamic graph and the fusion graph are similar and high. The R value of the fusion graph in working condition 1 is higher than that of the static graph, and the R value of the fusion graph in working condition 3 is slightly higher than that of the static graph. In working condition 2, the static graph, dynamic graph, and fusion graph have the lowest R value. Figure 3 The R values of the three methods increase gradually and are relatively stable. In summary, the fusion graph generally performs better in terms of MAE, MSE and RMSE indicators, especially in working conditions 1 and 3. The dynamic graph generally performs slightly better than the other two methods in terms of MAE, MSE and RMSE indicators in all working conditions, but 2 The fusion graph performs relatively stably in all working conditions, especially in R 2 These charts show that the fusion graph approach is likely the best choice when considering all evaluation metrics, as it maintains high accuracy across all conditions and performs well on the error metrics. The static graph performs well on the error metrics but falls slightly short on accuracy. The dynamic graph performs well on accuracy but slightly higher on the error metrics.

[0258] Experimental results demonstrate that the prediction model based on the fusion graph structure demonstrates significant advantages over static and dynamic graph models under three different operating conditions. Specifically, the model achieves not only lower prediction errors but also a higher coefficient of determination, demonstrating robust and consistent prediction performance. This finding confirms the significant application value of the fusion graph structure in complex operating conditions, effectively improving the reliability and accuracy of prediction models.

[0259] Comparative Experiments: Fusion graphs demonstrate superior performance compared to static and dynamic graphs in single-step prediction tasks, better capturing complex relationships between data and providing more accurate prediction results. However, the advantages of fusion graphs may be limited in multi-step predictions. Therefore, we set the prediction duration for different time periods, analyzed the prediction results of the last step, and used RMSE and MAE as evaluation metrics to compare the prediction performance of the models at different time periods, as shown in Table 4.

[0260] Table 4 TCN multi-step prediction results

[0261]

[0262] The model uses TCN to capture the temporal dependence of data. For short-term forecasts of one hour, the forecast results are relatively accurate. As the forecast time increases, the error gradually increases within the range [1, 12], but subsequently decreases. Overall, the model performs well for shorter forecasts, while the error increases for longer forecasts. However, the reduction in error for longer forecasts also indicates that the model has a certain degree of stability and, in some cases, can better adapt to long-term trends and provide relatively stable forecast results.

[0263] The model uses TCN as its temporal module and has achieved initial good results in multi-step forecasting. To further verify the impact of TCN on the model's forecasting performance, we introduced LSTM, GRU, Informer, and Autoformer for comparative experiments. These four networks are widely used in time series data processing and have achieved significant results. A comparison of their forecasting performance is shown in Tables 5-8.

[0264] Table 5 LSTM multi-step prediction effect

[0265]

[0266] Table 6 GRU multi-step prediction results

[0267]

[0268] Table 7 Informer multi-step prediction results

[0269]

[0270] Table 8 Autoformer multi-step prediction results

[0271]

[0272] Comparing the experimental results in Tables 4-8, TCN performs best among the five networks. Its convolutional structure and parallel computing capabilities enable it to demonstrate significant advantages in accuracy and stability in long-term time series forecasting, effectively capturing the characteristics of industrial time series data and avoiding error accumulation. In contrast, GRU and LSTM perform relatively poorly in this area due to the limitations of recursive computation. While GRU slightly outperforms LSTM, it still lags significantly behind TCN. Although Informer and Autoformer are theoretically more suitable for long-term sequence modeling based on their self-attention mechanism, their actual performance does not surpass TCN. This is primarily due to the high computational complexity of the global attention mechanism and its limited adaptability to the characteristics of industrial data. Overall, TCN, with its combined advantages in computational efficiency, long-term dependency modeling, and noise robustness, has become the most practical choice for industrial time series forecasting.

[0273] Fault prediction: Based on historical data and predicted data, combined with effective predictions of future data, we determine whether the equipment is likely to fail. The following classification performance indicators are used to evaluate the prediction effect of the proposed method.

[0274] Accuracy:

[0275] ;

[0276] Accuracy:

[0277] ;

[0278] Recall:

[0279] ;

[0280] F1 score:

[0281] ;

[0282] Where TP represents the number of samples correctly predicted as positive by the model. TN represents the number of samples correctly predicted as negative by the model. FP represents the number of samples incorrectly predicted as positive by the model. FN represents the number of samples incorrectly predicted as negative by the model.

[0283] Three methods were used to predict the 24-hour equipment operating status. The classification evaluation indicators are shown in Table 7, and the classification confusion matrix is shown in Figure 10(a)-(c). The confusion matrix shows the probability of correct or incorrect prediction for different types of faults (including normal and faults 1 to 9) under three operating conditions.

[0284] Figures 10(a)-(c) show the prediction accuracy and false positive rates of nine different fault types for the AE, VAE, and VAE-Deep SVDD methods, respectively, under three different operating conditions. The horizontal axis represents the fault type, and the vertical axis represents the prediction accuracy under different operating conditions. It can be seen that VAE-Deep SVDD achieves high accuracy for all nine fault types under all three operating conditions, demonstrating the robustness and accuracy of the method. The AE method's overall prediction accuracy is less than 70%, with particularly poor performance for faults 1, 2, 3, 6, 7, and 9, where the difference between the accuracy and false positive rates is generally less than 35%, indicating its limited ability to distinguish complex fault patterns. In contrast, the performance of the VAE method further deteriorates, with an average accuracy rate below 65%. The classification stability for the same fault type is insufficient, and the false positive rate is significantly increased. The VAE-Deep SVDD method, however, demonstrates excellent performance under all operating conditions, significantly outperforming both the AE and VAE methods in fault prediction accuracy. Under operating condition 1, this method maintained a false positive rate below 3% for almost all faults, with most falling below 1.6%. Under operating conditions 2 and 3, this method also maintained an extremely low false positive rate, demonstrating excellent robustness and generalization capabilities. Overall, the VAE-Deep SVDD method achieved stable and accurate predictions across a wide range of operating conditions and fault types, significantly outperforming both AE and VAE methods overall, making it the optimal choice for equipment fault prediction.

[0285] Table 7 Fault prediction evaluation indicators

[0286]

[0287] This experiment used three unsupervised learning models: automatic autoencoder (AE), variable autoencoder (VAE), and the proposed VAE-Deep SVDD. All models focus on extracting features from normal operating data and perform fault detection by analyzing reconstruction errors and the distribution differences between normal and faulty samples. However, all three methods face the challenge of determining the boundary between normal and faulty points, necessitating a trade-off between false positive and false negative rates. The setup for this task allows for a moderate reduction in the accuracy of the judgment of normal data to improve fault detection capabilities.

[0288] A comparative analysis of the performance of the three fault prediction models shows that the traditional autoencoder method achieves an accuracy of 92.08% for detecting fault 4, while the variational autoencoder method achieves 90.18%. However, there is significant fluctuation in overall performance, with the accuracy rates for detecting fault 6 being only 50.98% and 51.81%, respectively. More seriously, the two methods have misclassification rates for normal samples as high as 63.99% and 53.52%, respectively, severely impacting their practical application value.

[0289] In contrast, the method based on combining variational autoencoders with deep support vector data descriptions demonstrates significant advantages. Experimental data shows that this method maintains a stable detection accuracy of over 95% for all fault types, while keeping the false alarm rate below 4.5% and the missed alarm rate below 3.2%. This outstanding performance stems from its innovative model architecture, which achieves a dual improvement in detection sensitivity and stability through the synergy of latent space modeling and boundary optimization techniques. It is worth noting that this method still has room for improvement in the identification of normal samples, which points the way for subsequent research. Overall, VAE-Deep SVDD, with its stable and high performance, better meets the actual needs of industrial scenarios for fault prediction systems.

[0290] This embodiment proposes a SDGFN model for the fault prediction problem of the nickel flash furnace system. This model constructs a spatiotemporal graph neural network by combining static and dynamic graphs to deeply explore the stability and fluctuation characteristics of the system. In model training, a multi-stage learning strategy is introduced to gradually optimize the parameters, thereby significantly improving the prediction effect of the model. At the same time, the VAE-Deep SVDD method is used to achieve efficient fault prediction, which not only greatly improves the overall performance, but also effectively reduces the false alarm rate and missed alarm rate of faults. It can relatively accurately and stably predict whether a fault will occur, but it is still unable to accurately identify the type of fault.

[0291] The SDGFN model effectively captures the complex dynamic characteristics of industrial systems, offering potential application in similar industrial scenarios such as petrochemicals, power systems, and manufacturing production lines. These industrial scenarios are often characterized by large data volumes and complex system dynamics, challenges that this model addresses. However, it is important to note that the model's performance is closely related to the data quality of the target system. Predictions may be affected by insufficient data samples or significant noise. Furthermore, due to significant differences between different industrial systems, targeted parameter tuning and model adaptation may be required for actual deployment.

[0292] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A flash furnace fault prediction method based on graph fusion and multi-stage learning, characterized in that: include: Establishing a static graph and a dynamic graph, describing the influence intensity and dynamic changes between sensor data based on the static graph and the dynamic graph, and obtaining spatiotemporal characteristics; Inputting the spatiotemporal features into a Transformer encoding model to obtain prediction data; The Transformer encoding model is trained using a training set and the model parameters are adjusted to minimize the prediction error; the training set includes: original spatiotemporal features; The predicted data is encoded, stretched, translated and rotated, each data point is mapped to a high-dimensional space, the distribution position of the abnormal point is obtained, and the abnormal score of the data is calculated. The abnormal score is judged to obtain the fault result of the nickel flash furnace system.

2. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 1 is characterized in that: Describing the influence strength between the sensor data includes: The relationship between the internal variables of the flash furnace system is described using a mechanism model to obtain the influence intensity between sensors; The influence direction of the influence intensity is determined, and the influence level is divided to obtain the final influence intensity. The static adjacency matrix is constructed using the final influence intensity: ； ； in, is the static adjacency matrix, To normalize each row of the matrix, To eliminate negative connections in the input, is the static weight matrix, is the static bias matrix, For sensors For sensors The bias part that affects the strength, is the total number of sensors; The influence strength between the sensor data, ie, the static feature, is obtained according to the static graph combined with the static adjacency matrix.

3. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 1 is characterized in that: Describing the dynamic changes between the sensor data includes: Acquire the sensor data, and generate a first subspace based on the sensor data: ； in, and are learnable parameters, representing the subspaces and subspace The weight matrix, for Sensor data at each moment; Based on the first subspace, construct the adjacency matrix: ； in, is the dynamic adjacency matrix, For subspace The transpose of The weight matrix input is mapped to a subspace using a dynamic graph, and the adjacency matrix is dynamically adjusted to capture the dynamic changes between the sensor data, that is, dynamic features.

4. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 1 is characterized in that: Acquiring the spatiotemporal features includes: A graph neural network is constructed by fusing the static graph and the dynamic graph to describe the influence intensity and dynamic changes between sensor data, obtain static features and dynamic features, generate a second subspace based on the static features and the dynamic features, extract steady-state spatial coupling features and time-varying spatial coupling features from the time series data in the second subspace, balance the steady-state spatial coupling features and the time-varying spatial coupling features using a proportion coefficient, and perform feature fusion to obtain a comprehensive spatial feature; The integrated spatial features are input into a multi-layer TCN model, where each layer of TCN further abstracts and refines features based on the output of the previous layer to obtain the spatiotemporal features; the multi-layer TCN model is trained using a training set; the training set includes: the original integrated spatial features; wherein the multi-layer TCN model obtains the temporal features by introducing dilated convolution; During the training process of the Transformer encoding model, the graph neural network and the multi-layer TCN model, a multi-stage learning strategy is adopted to initialize the model, use the training set to train the model's bias matrix, weight coefficient, and proportion coefficient to obtain the target proportion coefficient, train the model's bias matrix and weight coefficient again to obtain the target bias matrix, and finally train the model's weight coefficient to obtain the target weight coefficient.

5. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 4 is characterized in that: Acquiring the static features and the dynamic features includes: ； ； in, is the steady-state spatial coupling characteristic, is the static adjacency matrix, is a subspace, is the time-varying spatial coupling feature, is a dynamic adjacency matrix.

6. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 4 is characterized in that: Obtaining the comprehensive spatial features includes: ； in, For comprehensive spatial characteristics, and All are proportion coefficients.

7. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 1 is characterized in that: Encoding the prediction data includes: By minimizing the reconstruction error, determining that the distribution of normal data in the predicted data in space is close to the standard normal distribution, and mapping the predicted data to a low-dimensional latent space; The distribution of the normal data in space is close to the standard normal distribution and is expressed as: ； in, is the latent space dimension, and are the mean and variance of the latent space data, and Respectively The actual value and predicted value at the moment, is the gap between the spatial distribution and the standard normal distribution.

8. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 1 is characterized in that: Obtaining the distribution position of the abnormal point includes: Stretch, translate, and rotate the encoded data, map each data point to a high-dimensional space, and construct a hypersphere: ； in, is the center point of the hypersphere, is the radius of the hypersphere, is a positive coefficient, For the data points, for The corresponding slack variable, is the mapping function, is a set of positive integers, is the total number of data points, is a constraint condition; The distance from the mapping point of the encoded data to the center of the hypersphere can be expressed as: ； in, is the distance from the mapping point of the encoded data to the center of the hypersphere, is the center of the hypersphere, is the mapping point.

9. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 1 is characterized in that: Calculating the anomaly score of the data involves: ； in, is an abnormal point, is the mapping point set, is the radius of the hypersphere, is the distance from the outlier point to the center of the hypersphere, is the anomaly score of the data.

10. The flash furnace fault prediction method based on graph fusion and multi-stage learning according to claim 1 is characterized in that: Obtaining the fault result of the nickel flash furnace system includes: A target threshold is set, and the abnormality score is judged according to the target threshold. If the abnormality score exceeds zero, it is determined to be fault data. If the abnormality score exceeds the target threshold, it is determined to have a potential fault. Otherwise, it is determined to be operating normally.

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