An electric arc furnace state prediction method and system based on a graph convolution network

Abstract

This invention discloses a method and system for predicting the state of an electric arc furnace based on graph convolutional networks, comprising the following steps: collecting multi-source operating parameters during the electric arc furnace smelting process to generate irregularly sampled time-series data of multi-source operating parameters; constructing a continuous time axis based on timestamps to generate a continuous time-domain multivariate state observation sequence; constructing an electric arc furnace operating parameter graph based on the dynamic correlation between operating parameters and generating time-varying graph structure state features; using Bernstein polynomials to propagate spectral domain features of the time-varying graph structure state features to generate graph-spectral coupled state features; inputting the graph-spectral coupled state features into a neural controlled differential equation embedded with Bernstein polynomials to generate a continuous evolution trajectory of the hidden state of the electric arc furnace; generating a predicted furnace state value at the target prediction time based on the continuous evolution trajectory of the hidden state, and outputting the electric arc furnace state prediction result. This invention can achieve continuous dynamic prediction of the furnace state of an electric arc furnace.

Description

Technical Field

[0001] This invention relates to the field of intelligent control and industrial process prediction technology, and in particular to a method and system for predicting the state of an electric arc furnace based on graph convolutional networks. Background Technology

[0002] As a crucial smelting equipment in the metallurgical industry, the operation of electric arc furnaces involves multiple stages, including electrode adjustment, power input, charging control, and furnace temperature control. Due to the characteristics of electric arc furnace smelting processes, such as electrothermal coupling, drastic material changes, and frequent switching of operating conditions, strong nonlinear coupling relationships exist among operating parameters such as electrode current, electrode voltage, furnace temperature, flue gas composition, and oxygen flow rate. Furthermore, the rate of change in operating conditions varies significantly across different smelting stages, resulting in a continuous dynamic evolution of the electric arc furnace's condition. Therefore, accurately predicting the furnace condition has become an important research direction in the field of intelligent electric arc furnace control.

[0003] Existing technologies for predicting the condition of electric arc furnaces mainly include empirical rule-based methods, traditional statistical modeling methods, and deep learning-based discrete time series prediction methods. Empirical rule-based methods rely heavily on manually setting control logic and process parameter thresholds, making them ill-suited to complex operating conditions. Traditional statistical modeling methods typically employ linear or fixed-time-window models, which struggle to accurately represent the high-order nonlinear relationships between multiple operating parameters. While deep learning-based discrete time series prediction methods can improve prediction accuracy to some extent, they mostly model only regular sampled data, making them ill-suited to issues such as inconsistent sampling frequencies, missing data, and uneven time intervals present in electric arc furnace environments.

[0004] Furthermore, most existing graph convolutional network methods only extract features from the spatial relationships of the graph structure, lacking a description of the continuous-time dynamic evolution of the electric arc furnace. Existing continuous-time modeling methods typically ignore the graph correlation structure between different operating parameters, making it difficult for the model to simultaneously characterize the complex coupling relationships between operating parameters and the continuous evolution of furnace conditions. Especially during the switching between different smelting stages such as melting, oxidation, and reduction, existing technologies struggle to achieve continuous dynamic prediction of furnace conditions, thus affecting electric arc furnace process optimization, energy consumption control, and production stability.

[0005] Therefore, how to provide a method and system for predicting the state of electric arc furnaces based on graph convolutional networks is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] One objective of this invention is to propose a method and system for predicting the state of an electric arc furnace based on graph convolutional networks. This invention fully utilizes Bernstein polynomial spectral filtering, graph convolutional networks, and neural controlled differential equation techniques to describe in detail the graph correlation modeling and continuous-time state evolution prediction process of multi-source operating parameters of an electric arc furnace. It has the advantages of strong continuous dynamic prediction capability for complex furnace conditions, high adaptability to irregularly sampled industrial data, and high accuracy in predicting furnace conditions.

[0007] According to an embodiment of the present invention, a method and system for predicting the state of an electric arc furnace based on a graph convolutional network includes the following steps: Collect the original measured values ​​and corresponding timestamps of various operating parameters during the electric arc furnace smelting process, and generate irregularly sampled multi-source operating parameter time series data; A continuous time axis is constructed based on the timestamps in the time series data of irregularly sampled multi-source operating parameters, and the original measured values ​​are mapped to the continuous time axis to generate a continuous time domain multivariate state observation sequence. The dynamic correlation between different operating parameters is determined based on the continuous time domain multivariate state observation sequence. An electric arc furnace operating parameter map is constructed based on the dynamic correlation. The continuous time domain multivariate state observation sequence is embedded as a node feature into the electric arc furnace operating parameter map to generate time-varying graph structure state features. Bernstein polynomials are constructed based on the electric arc furnace operating parameter diagram, and the Bernstein polynomials are used to perform spectral domain feature propagation processing on the time-varying diagram structural state features to generate graph-spectral coupled state features. The continuous-time domain multivariate state observation sequence is constructed as a continuous-time control path, and the graph-coupled state features are used as state inputs. A neural controlled differential equation with Bernstein polynomials is constructed, and the state input is driven by the continuous-time control path to generate the continuous evolution trajectory of the hidden state of the electric arc furnace. The hidden state vector at the target prediction time is extracted based on the continuous evolution trajectory of the hidden state of the electric arc furnace, and the hidden state vector is input into the state prediction model to generate the furnace condition state prediction value at the target prediction time. The electric arc furnace status prediction result is generated based on the predicted furnace status value at the target prediction time.

[0008] Optionally, generating irregularly sampled multi-source runtime parameter time series data includes: Determine the categories of operating parameters to be collected during the electric arc furnace smelting process, and configure corresponding data acquisition channels for each category of operating parameters; The original measurement values ​​of the corresponding operating parameter categories are collected through each data acquisition channel, and the timestamps corresponding to the original measurement values ​​are recorded synchronously when collecting the original measurement values ​​to generate single-point operating parameter data with timestamps. The single-point operational parameter data with timestamps are aggregated according to the operational parameter category to generate single-parameter time-series data corresponding to each operational parameter category; Sort the single-parameter time series data corresponding to each category of operating parameters in chronological order to generate ordered single-parameter time series data; Channel identifiers are bound to the single-parameter ordered time-series data corresponding to each operational parameter category to generate a multi-source operational parameter data set with parameter category identifiers, original measurement values, and timestamps. Based on the timestamp distribution corresponding to different operational parameter categories in the multi-source operational parameter dataset, the sampling frequency differences and sampling time differences between different data acquisition channels are preserved to generate irregularly sampled multi-source operational parameter time series data.

[0009] Optionally, generating a continuous-time-domain multivariate state observation sequence includes: Read the timestamps corresponding to each category of operating parameter in the irregularly sampled multi-source operating parameter time series data, and summarize, deduplicate, and sort all timestamps in chronological order to generate a global timestamp sequence; The start and end range of the time axis is determined based on the first and last timestamps in the global timestamp sequence, and the start and end range of the time axis is divided according to a preset fixed time interval to generate a continuous time axis; Each time point in the continuous time axis is determined as the target mapping time, and adjacent timestamps are retrieved in the single-parameter ordered time series data corresponding to each running parameter category based on the target mapping time to generate time neighborhood data corresponding to each running parameter category. Based on the time neighborhood data corresponding to each running parameter category, the original measurement value corresponding to the target mapping time is extracted. When there is a timestamp in the time neighborhood data that is the same as the target mapping time, the original measurement value corresponding to the timestamp is determined as the mapping measurement value of the target mapping time. When there is no timestamp in the time neighborhood data that is the same as the target mapping time, time mapping is performed based on the original measurement values ​​in the time neighborhood data that are before and after the target mapping time to generate the mapped measurement value of the target mapping time; According to the category of operating parameters, the mapping measurement values ​​corresponding to each category of operating parameters at the same target mapping time are combined to generate a multivariate state observation vector corresponding to the target mapping time; According to the chronological order of the target mapping times in the continuous time axis, the multivariate state observation vectors corresponding to each target mapping time are arranged to generate a continuous time domain multivariate state observation sequence.

[0010] Optionally, the structural state features of the generated time-varying graph include: Read the continuous time domain multivariate state observation sequence, and extract the corresponding mapping measurement value sequence of each operating parameter according to the operating parameter category from the continuous time domain multivariate state observation sequence; Based on the mapping measurement value sequence corresponding to each operating parameter, the dynamic correlation value between any two operating parameters is calculated according to the preset sliding time window to generate dynamic correlation. Based on the dynamic correlation values, the graph connection relationships between different operating parameters are determined, and the corresponding dynamic correlation values ​​are determined as the edge weights of the graph connection relationships. The electric arc furnace operating parameter graph is constructed by using each operating parameter category as graph nodes, graph connection relationships as graph edges, and edge weights as graph edge attributes. Based on the target mapping time in the continuous time domain multivariate state observation sequence, extract the mapping measurement value at the same target mapping time from the mapping measurement value sequence corresponding to each operating parameter, and generate node feature data corresponding to the target mapping time; The node feature data corresponding to the target mapping time is embedded into the corresponding graph node in the electric arc furnace operating parameter graph according to the operating parameter category, thereby generating the graph structure state feature corresponding to the target mapping time. Arrange the graph structure state features corresponding to each target mapping time according to the chronological order of the target mapping time to generate time-varying graph structure state features.

[0011] Optionally, the generated map coupling state features include: Read the time-varying graph structure state features and extract the corresponding graph structure state features from the time-varying graph structure state features according to the target mapping time. Extract the electric arc furnace operating parameter graph, graph connectivity, edge weights, and node feature data from the graph structure state features corresponding to the target mapping time, and construct the weighted adjacency matrix corresponding to the target mapping time based on the graph connectivity and edge weights; The normalized graph Laplacian matrix is ​​calculated based on the weighted adjacency matrix, and the normalized graph Laplacian matrix is ​​determined as the spectral domain input object corresponding to the target mapping time. The spectral domain variables are determined based on the spectral domain input object, and Bernstein polynomial basis functions of each order are constructed based on the spectral domain variables and the preset polynomial order. The Bernstein polynomial basis functions of each order are combined in order of order to generate a set of Bernstein polynomial basis functions. Bernstein polynomials are generated by weighting and combining the Bernstein polynomial basis functions of each order and their corresponding trainable weights in the Bernstein polynomial basis function set. Input the node feature data corresponding to the target mapping time into the Bernstein polynomial, and use the Bernstein polynomial to propagate the spectral domain features of the node feature data according to the graph connection relationship and edge weight in the weighted adjacency matrix to generate the graph propagation features corresponding to the target mapping time. Arrange the spectral propagation features corresponding to each target mapping time according to the chronological order of the target mapping time to generate spectral coupling state features.

[0012] Optionally, constructing neurally controlled differential equations embedded with Bernstein polynomials includes: Read the continuous time domain multivariate state observation sequence, and according to the time sequence of each target mapping time in the continuous time axis, perform continuous path connection processing on the multivariate state observation vectors corresponding to each target mapping time to generate a continuous time control path; Read the graph coupling state features and extract the corresponding graph propagation features from the graph coupling state features according to the target mapping time. Input the graph propagation features corresponding to the target mapping time into the state mapping network, perform latent space mapping on the graph propagation features, generate the initial hidden state vector corresponding to the target mapping time, and determine the initial hidden state vector as the state input corresponding to the target mapping time. Read the Bernstein polynomial and input the initial hidden state vector corresponding to the target mapping time into the Bernstein polynomial. Perform spectral domain state propagation processing on the initial hidden state vector according to the spectral domain propagation relationship corresponding to the Bernstein polynomial to generate the spectral domain propagated hidden state corresponding to the target mapping time. The state input corresponding to the target mapping time, the hidden state propagated in the spectral domain, and the control input corresponding to the target mapping time in the continuous-time control path are all input into the state evolution network, and the hidden state derivative corresponding to the target mapping time is generated based on the correlation between the state input, the hidden state propagated in the spectral domain, and the control input. The state evolution function is constructed based on the latent state derivatives corresponding to the target mapping time, and the spectral domain propagation latent state corresponding to the target mapping time is determined as the spectral state evolution term in the state evolution function, thereby generating a state evolution function embedded with Bernstein polynomials. Neural controlled differential equations are constructed based on state evolution functions embedded with Bernstein polynomials. According to the temporal order of each target mapping moment in the continuous time axis, the control input of the corresponding target mapping moment in the continuous time control path drives the controlled differential equation of the neural network to perform continuous time state recursion. Based on the hidden state propagated in the spectral domain and the hidden state derivative corresponding to the previous target mapping moment, the hidden state of the electric arc furnace corresponding to the current target mapping moment is generated, thus obtaining the continuous evolution trajectory of the hidden state of the electric arc furnace.

[0013] Optionally, the predicted furnace condition values ​​for the target prediction time include: Read the continuous evolution trajectory of the hidden state of the electric arc furnace, and extract the hidden state of the electric arc furnace corresponding to each target mapping time according to the time sequence of each target mapping time in the continuous time axis. Based on the time position of the target prediction time in the continuous time axis, retrieve the hidden states of the electric arc furnace adjacent to the target prediction time from the hidden states of the electric arc furnace corresponding to each target mapping time, and generate the hidden state neighborhood data corresponding to the target prediction time. Extract the hidden state of the electric arc furnace corresponding to the target prediction time from the hidden state neighborhood data. When there is a target mapping time in the hidden state neighborhood data that is the same as the target prediction time, determine the hidden state of the electric arc furnace corresponding to the target mapping time as the hidden state vector of the target prediction time. When there is no target mapping time in the hidden state neighborhood data that is the same as the target prediction time, the hidden state mapping process is performed based on the hidden states of the electric arc furnace located before and after the target prediction time in the hidden state neighborhood data to generate the hidden state vector of the target prediction time. The hidden state vector at the target prediction time is determined as the input feature of the state prediction model, and the input feature is input into the feature mapping layer in the state prediction model to generate furnace condition discrimination features. The furnace condition discrimination features are input into the nonlinear activation layer of the state prediction model to generate state discrimination input features. The state discrimination input features are input into the state discrimination layer of the state prediction model to generate state discrimination values ​​corresponding to each furnace condition state category. The state discrimination value corresponding to each furnace condition state category is input into the output normalization layer in the state prediction model to generate the furnace condition state prediction value at the target prediction time.

[0014] Optionally, an electric arc furnace state prediction system based on graph convolutional networks includes the following modules: The data acquisition module is used to collect the original measured values ​​and corresponding timestamps of various operating parameters during the electric arc furnace smelting process, and generate irregularly sampled multi-source operating parameter time series data; The continuous time series generation module is used to construct a continuous time axis based on the timestamps in the irregularly sampled multi-source operating parameter time series data, and to map the original measured values ​​to the continuous time axis to generate a continuous time domain multivariate state observation sequence. The time-varying graph structure construction module is used to determine the dynamic correlation between different operating parameters based on the continuous time domain multivariate state observation sequence, construct the electric arc furnace operating parameter graph based on the dynamic correlation, and generate the time-varying graph structure state features. The graph coupling feature generation module is used to construct Bernstein polynomials based on the electric arc furnace operating parameter graph, and to use Bernstein polynomials to perform spectral domain feature propagation processing on the time-varying graph structure state features to generate graph coupling state features. The state evolution construction module is used to construct a continuous-time control path from the continuous-time domain multivariate state observation sequence, and to use the graph-coupled state features as the state input to construct a neural controlled differential equation embedded with Bernstein polynomials. The state input is driven by the continuous-time control path to perform state evolution and generate the continuous evolution trajectory of the hidden state of the electric arc furnace. The state prediction module is used to extract the hidden state vector at the target prediction time based on the continuous evolution trajectory of the hidden state of the electric arc furnace, and input the hidden state vector into the state prediction model to generate the furnace condition state prediction value at the target prediction time. The results output module is used to generate electric arc furnace status prediction results based on the predicted furnace status values ​​at the target prediction time.

[0015] The beneficial effects of this invention are: This invention combines Bernstein polynomial spectral filtering, graph convolutional networks, and neural controlled differential equations to achieve joint modeling of the complex nonlinear coupling relationships and continuous-time dynamic evolution processes among multiple operating parameters of electric arc furnaces. This enables the system to simultaneously characterize the spectral correlation features and continuous changes in furnace condition among electrode current, voltage, power, furnace temperature, feed rate, and flue gas parameters, thereby improving the accuracy and stability of electric arc furnace condition prediction under complex operating conditions.

[0016] This invention constructs an electric arc furnace operating parameter diagram and uses Bernstein polynomials to propagate the spectral domain features of the time-varying diagram structure state features. This enables adaptive propagation and aggregation of high-order correlation information between multiple operating parameters, allowing the system to adjust the spectral feature propagation mode according to the dynamic correlation between operating parameters under different smelting stages, thereby improving the ability to identify different furnace conditions such as melting, oxidation, and reduction periods.

[0017] This invention constructs a neural controlled differential equation embedded with Bernstein polynomials to convert irregularly sampled industrial time-series data into a continuous-time control path. By using the continuous-time control path to drive the continuous evolution of hidden states, it achieves continuous-time dynamic prediction of the furnace condition of electric arc furnaces. This enables the system to adapt to situations such as inconsistent sampling frequencies, missing data, and drastic fluctuations in operating conditions in industrial settings, thereby improving the model's adaptability to actual industrial data.

[0018] This invention predicts the state of the furnace at the target prediction time by performing state prediction on the continuous evolution trajectory of the hidden state of the electric arc furnace. This enables the system to provide state prediction basis for electrode adjustment, power distribution, feeding control and energy consumption optimization, thereby improving the operational stability, production efficiency and energy consumption control capability of the electric arc furnace smelting process. Attached Figure Description

[0019] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of an electric arc furnace state prediction method based on graph convolutional networks proposed in this invention; Figure 2 This is a flowchart of a neural controlled differential equation construction method that embeds Bernstein polynomials, as proposed in this invention. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0021] refer to Figures 1-2 A method for predicting the state of an electric arc furnace based on graph convolutional networks includes the following steps: Collect the original measured values ​​and corresponding timestamps of various operating parameters during the electric arc furnace smelting process, and generate irregularly sampled multi-source operating parameter time series data; A continuous time axis is constructed based on the timestamps in the time series data of irregularly sampled multi-source operating parameters, and the original measured values ​​are mapped to the continuous time axis to generate a continuous time domain multivariate state observation sequence. The dynamic correlation between different operating parameters is determined based on the continuous time domain multivariate state observation sequence. An electric arc furnace operating parameter map is constructed based on the dynamic correlation. The continuous time domain multivariate state observation sequence is embedded as a node feature into the electric arc furnace operating parameter map to generate time-varying graph structure state features. Bernstein polynomials are constructed based on the electric arc furnace operating parameter diagram, and the Bernstein polynomials are used to perform spectral domain feature propagation processing on the time-varying diagram structural state features to generate graph-spectral coupled state features. The continuous-time domain multivariate state observation sequence is constructed as a continuous-time control path, and the graph-coupled state features are used as state inputs. A neural controlled differential equation with Bernstein polynomials is constructed, and the state input is driven by the continuous-time control path to generate the continuous evolution trajectory of the hidden state of the electric arc furnace. The hidden state vector at the target prediction time is extracted based on the continuous evolution trajectory of the hidden state of the electric arc furnace, and the hidden state vector is input into the state prediction model to generate the furnace condition state prediction value at the target prediction time. The electric arc furnace status prediction result is generated based on the predicted furnace status value at the target prediction time.

[0022] In this embodiment, generating irregularly sampled multi-source operating parameter time series data includes: Determine the categories of operating parameters to be collected during the electric arc furnace smelting process, and configure corresponding data acquisition channels for each category of operating parameters; The original measurement values ​​of the corresponding operating parameter categories are collected through each data acquisition channel, and the timestamps corresponding to the original measurement values ​​are recorded synchronously when collecting the original measurement values ​​to generate single-point operating parameter data with timestamps. The single-point operational parameter data with timestamps are aggregated according to the operational parameter category to generate single-parameter time-series data corresponding to each operational parameter category; Sort the single-parameter time series data corresponding to each category of operating parameters in chronological order to generate ordered single-parameter time series data; Channel identifiers are bound to the single-parameter ordered time-series data corresponding to each operational parameter category to generate a multi-source operational parameter data set with parameter category identifiers, original measurement values, and timestamps. Based on the timestamp distribution of different operational parameter categories in the multi-source operational parameter dataset, the sampling frequency differences and sampling time differences between different data acquisition channels are preserved to generate irregularly sampled multi-source operational parameter time series data. Based on the timestamps corresponding to each category of operating parameters in the multi-source operating parameter dataset, the data records of each operating parameter are directly retained in the original acquisition order. No time alignment or resampling processing is performed between different operating parameters, so that each operating parameter still maintains its own independent sampling time interval and sampling time distribution, thus forming a time-series data structure with an inconsistent time axis.

[0023] In this embodiment, generating a continuous-time-domain multivariate state observation sequence includes: Read the timestamps corresponding to each category of operating parameter in the irregularly sampled multi-source operating parameter time series data, and summarize, deduplicate, and sort all timestamps in chronological order to generate a global timestamp sequence; Specifically, the timestamps corresponding to each category of operating parameters are collected in a unified manner to form a timestamp set; duplicate timestamps in the timestamp set are deleted so that each time point is retained only once; and the deduplicated timestamps are arranged in ascending order of time to generate a global timestamp sequence that increases in chronological order. The start and end range of the time axis is determined based on the first and last timestamps in the global timestamp sequence, and the start and end range of the time axis is divided according to a preset fixed time interval to generate a continuous time axis; Specifically, the preset fixed time interval is a uniform time step selected based on the sampling characteristics of the electric arc furnace operating parameters. This time step is taken as the least common multiple of the sampling interval of each operating parameter or set as an integer multiple of the system acquisition cycle. It is used to divide time points in an equally spaced manner within the start and end range of the time axis so that the time difference between adjacent time points remains consistent. Each time point in the continuous time axis is determined as the target mapping time, and adjacent timestamps are retrieved in the single-parameter ordered time series data corresponding to each running parameter category based on the target mapping time to generate time neighborhood data corresponding to each running parameter category. Based on the time neighborhood data corresponding to each running parameter category, the original measurement value corresponding to the target mapping time is extracted. When there is a timestamp in the time neighborhood data that is the same as the target mapping time, the original measurement value corresponding to the timestamp is determined as the mapping measurement value of the target mapping time. When there is no timestamp in the time neighborhood data that is the same as the target mapping time, time mapping is performed based on the original measurement values ​​in the time neighborhood data that are before and after the target mapping time to generate the mapped measurement value of the target mapping time; Specifically, in the time neighborhood data, the original measurement values ​​and their corresponding timestamps before the target mapping time and the original measurement values ​​and their corresponding timestamps after the target mapping time are selected. Based on the relative position of the target mapping time between the two timestamps, the ratio of the original measurement values ​​before and after is calculated to generate the mapping measurement value corresponding to the target mapping time. According to the category of operating parameters, the mapping measurement values ​​corresponding to each category of operating parameters at the same target mapping time are combined to generate a multivariate state observation vector corresponding to the target mapping time; According to the chronological order of the target mapping times in the continuous time axis, the multivariate state observation vectors corresponding to each target mapping time are arranged to generate a continuous time domain multivariate state observation sequence.

[0024] In this embodiment, the structural state features of the generated time-varying graph include: Read the continuous time domain multivariate state observation sequence, and extract the corresponding mapping measurement value sequence of each operating parameter according to the operating parameter category from the continuous time domain multivariate state observation sequence; Based on the mapping measurement value sequence corresponding to each operating parameter, the dynamic correlation value between any two operating parameters is calculated according to the preset sliding time window to generate dynamic correlation. Specifically, according to the preset sliding time window, the corresponding time range of the mapped measurement value sequence is extracted sequentially from the continuous time domain multivariate state observation sequence, and the correlation between the two is calculated based on the changing trend of the mapped measurement values ​​corresponding to any two operating parameters within the same sliding time window, and the corresponding dynamic correlation value is generated. Based on the dynamic correlation values, the graph connection relationships between different operating parameters are determined, and the corresponding dynamic correlation values ​​are determined as the edge weights of the graph connection relationships. Specifically, two operating parameters whose dynamic correlation values ​​are greater than a preset correlation threshold are identified as having a graph connection relationship, and graph edges are established between the graph nodes of the corresponding two operating parameters; the corresponding dynamic correlation values ​​are assigned to the established graph edges as edge weights representing the degree of correlation between the two operating parameters. The electric arc furnace operating parameter graph is constructed by using each operating parameter category as graph nodes, graph connection relationships as graph edges, and edge weights as graph edge attributes. Based on the target mapping time in the continuous time domain multivariate state observation sequence, extract the mapping measurement value at the same target mapping time from the mapping measurement value sequence corresponding to each operating parameter, and generate node feature data corresponding to the target mapping time; The node feature data corresponding to the target mapping time is embedded into the corresponding graph node in the electric arc furnace operating parameter graph according to the operating parameter category, thereby generating the graph structure state feature corresponding to the target mapping time. Specifically, a correspondence between operating parameter categories and graph nodes is established according to the operating parameter categories, and the mapping measurement values ​​corresponding to each operating parameter category are extracted from the node feature data corresponding to the target mapping time. The mapping measurement values ​​corresponding to each operating parameter category are assigned to the corresponding graph nodes in the electric arc furnace operating parameter graph as the node feature data of the corresponding graph nodes at the target mapping time. Arrange the graph structure state features corresponding to each target mapping time according to the chronological order of the target mapping time to generate time-varying graph structure state features.

[0025] In this embodiment, the generated spectrum coupling state features include: Read the time-varying graph structure state features and extract the corresponding graph structure state features from the time-varying graph structure state features according to the target mapping time. Extract the electric arc furnace operating parameter graph, graph connectivity, edge weights, and node feature data from the graph structure state features corresponding to the target mapping time, and construct the weighted adjacency matrix corresponding to the target mapping time based on the graph connectivity and edge weights; The normalized graph Laplacian matrix is ​​calculated based on the weighted adjacency matrix, and the normalized graph Laplacian matrix is ​​determined as the spectral domain input object corresponding to the target mapping time. Specifically, the node degree matrix is ​​calculated based on the edge weights between each graph node in the weighted adjacency matrix, and the weighted adjacency matrix is ​​normalized based on the node degree matrix to generate a normalized graph Laplace matrix that simultaneously represents the graph node connection relationship and edge weight distribution. The spectral domain variables are determined based on the spectral domain input object, and Bernstein polynomial basis functions of each order are constructed based on the spectral domain variables and the preset polynomial order. Specifically, the preset polynomial order is the pre-defined Bernstein polynomial expansion order, which is used to determine the number of Bernstein polynomial basis functions and the order range of spectral domain feature propagation; different orders correspond to different levels of graph node feature propagation depth, and are used to control the range of neighborhood information aggregation between graph nodes during spectral domain feature propagation. The Bernstein polynomial basis functions of each order are combined in order of their orders to generate a set of Bernstein polynomial basis functions, where each order of Bernstein polynomial basis function is represented as follows: ; in, Denotes the basis functions of the k-th order Bernstein polynomial. Indicates the predefined polynomial order. Represents spectral domain variables, Represents the combination coefficients; Specifically, the formula originates from the Bernstein basis polynomial in mathematical approximation theory. Its original form is used to construct polynomial approximation functions on the interval [0,1]. This application replaces the independent variable with a spectral domain variable determined by the normalized graphical Laplace matrix, instead of a regular continuous variable. This allows the Bernstein basis polynomial to act on the spectral space of the electric arc furnace operating parameter diagram; a preset polynomial order K is used to limit the spectral propagation order, and the k-th order basis function... It is used to characterize the propagation components of the spectrum at the corresponding order, and to form the Bernstein spectrum filtering operator by combining the basis functions of each order with the trainable weights. The Bernstein polynomial is derived from the function approximation form into a spectrum domain filtering structure suitable for the propagation of node features of the electric arc furnace operation parameter graph. Bernstein polynomials are generated by weighting and combining the Bernstein polynomial basis functions of each order and their corresponding trainable weights in the Bernstein polynomial basis function set. Specifically, the basis functions of each order of Bernstein polynomial are multiplied with the corresponding trainable weights, and the product results are accumulated to generate a Bernstein spectral filtering operator for spectral domain feature propagation. Each trainable weight is used to adjust the propagation intensity of the feature information of the corresponding order of the node in the figure below. Input the node feature data corresponding to the target mapping time into the Bernstein polynomial, and use the Bernstein polynomial to propagate the spectral domain features of the node feature data according to the graph connection relationship and edge weight in the weighted adjacency matrix to generate the graph propagation features corresponding to the target mapping time. Specifically, the node feature data is input into the Bernstein spectral filtering operator, and the propagation path of the node feature information is determined based on the graph connection relationship in the weighted adjacency matrix. During the node feature propagation process, the node feature information transmitted by adjacent graph nodes is weighted according to the edge weights corresponding to each graph edge, and the multi-order neighborhood node feature information is aggregated according to the different orders corresponding to the Bernstein polynomial to generate the spectral domain propagation features corresponding to each graph node. Arrange the spectral propagation features corresponding to each target mapping time according to the chronological order of the target mapping time to generate spectral coupling state features.

[0026] In this embodiment, constructing a neurally controlled differential equation embedded with Bernstein polynomials includes: Read the continuous time domain multivariate state observation sequence, and according to the time sequence of each target mapping time in the continuous time axis, perform continuous path connection processing on the multivariate state observation vectors corresponding to each target mapping time to generate a continuous time control path; Specifically, according to the temporal order of each target mapping moment in the continuous time axis, the multivariate state observation vectors corresponding to adjacent target mapping moments are sequentially correlated in time, and a continuous state change relationship is established based on the time interval between adjacent target mapping moments, thereby generating a continuous time control path that changes continuously with the continuous time axis. Read the graph coupling state features and extract the corresponding graph propagation features from the graph coupling state features according to the target mapping time. Input the graph propagation features corresponding to the target mapping time into the state mapping network, perform latent space mapping on the graph propagation features, generate the initial hidden state vector corresponding to the target mapping time, and determine the initial hidden state vector as the state input corresponding to the target mapping time. Specifically, the state mapping network is a neural network structure used to transform the graph propagation features corresponding to the target mapping time into the hidden state space. Its input is the graph propagation features, and its output is the initial hidden state vector. The state mapping network performs dimensional transformation and feature transformation on the graph propagation features through linear mapping layers and nonlinear activation layers. The graph propagation features are input into the state mapping network, and the feature dimension of the graph propagation features is transformed through the linear mapping layer in the state mapping network. Then, the transformed features are processed by nonlinear mapping through the nonlinear activation layer to generate an initial hidden state vector that represents the evolution features of the current state. Read the Bernstein polynomial and input the initial hidden state vector corresponding to the target mapping time into the Bernstein polynomial. Perform spectral domain state propagation processing on the initial hidden state vector according to the spectral domain propagation relationship corresponding to the Bernstein polynomial to generate the spectral domain propagated hidden state corresponding to the target mapping time. Specifically, the initial hidden state vector is input into the Bernstein polynomial, and the propagation path of the hidden state information is determined according to the graph connectivity relationship corresponding to the normalized graph Laplacian matrix. According to the different orders corresponding to the Bernstein polynomial, the hidden state information corresponding to the multi-order neighboring graph nodes that have a connection relationship with the current graph node is weighted, propagated and aggregated to generate the corresponding spectral domain propagated hidden state. The state input corresponding to the target mapping time, the hidden state propagated in the spectral domain, and the control input corresponding to the target mapping time in the continuous-time control path are all input into the state evolution network, and the hidden state derivative corresponding to the target mapping time is generated based on the correlation between the state input, the hidden state propagated in the spectral domain, and the control input. Specifically, the state evolution network is a neural network structure used to generate hidden state derivatives. Its inputs are state inputs, spectral domain propagated hidden states, and control inputs, and its output is the corresponding hidden state derivatives. The state evolution network performs joint mapping processing on the correlation features between the state inputs, spectral domain propagated hidden states, and control inputs through multiple linear mapping layers and nonlinear activation layers. The state input, the spectral domain propagated hidden state, and the control input are concatenated according to the corresponding target mapping time to form a joint state feature. The joint state feature is then mapped through a state evolution network so that the current hidden state, the hidden state information after the spectral propagation, and the control changes in the continuous-time control path all participate in the generation of the hidden state derivative. The state evolution function is constructed based on the latent state derivatives corresponding to the target mapping time, and the spectral domain propagation latent state corresponding to the target mapping time is determined as the spectral state evolution term in the state evolution function, thereby generating a state evolution function embedded with Bernstein polynomials. Specifically, the state evolution function is a function in the neural controlled differential equation used to characterize the rate of change of the hidden state. Its inputs are the current hidden state, the spectral domain propagated hidden state, and the control input, and its output is the hidden state derivative. The state evolution function is determined by the state evolution network, and the spectral domain propagated hidden state is used as a graph state evolution term in the calculation of the hidden state derivative. A neurally controlled differential equation is constructed based on a state evolution function embedded with Bernstein polynomials. The neurally controlled differential equation is expressed as follows: ; in, Indicates time The corresponding hidden state of the electric arc furnace, This represents a state evolution function embedded with Bernstein polynomials. This represents the spectral domain propagated hidden state generated after propagating the current hidden state using Bernstein polynomials. Represents the normalized graph Laplacian matrix. Indicates a continuous-time control path; Specifically, this formula originates from the standard continuous-time state equation in neural controlled differential equations, and its original form is a differential relationship of hidden state changes driven by the control path; based on this original form, this application further develops the hidden state of the electric arc furnace. As a state variable, the continuous-time control path X(t) is used as the driving term, and further, the Bernstein polynomial is applied to the normalized graphical Laplace matrix L to influence the current hidden state. Obtained by spectral domain propagation , so that the state evolution function Simultaneously receiving the current hidden state and the spectral domain propagated hidden state, the neural controlled differential equation is deduced into a continuous evolution equation of the hidden state of the electric arc furnace that includes the spectral state propagation term. According to the temporal order of each target mapping moment in the continuous time axis, the control input of the corresponding target mapping moment in the continuous time control path drives the controlled differential equation of the neural network to perform continuous time state recursion. Based on the hidden state propagated in the spectral domain and the derivative of the hidden state corresponding to the previous target mapping moment, the hidden state of the electric arc furnace corresponding to the current target mapping moment is generated, and the continuous evolution trajectory of the hidden state of the electric arc furnace is obtained. Specifically, according to the time sequence of the continuous time axis, the control input corresponding to the target mapping time of the continuous time control path is read, and the control input is applied to the state evolution function of the neural controlled differential equation, so that the state evolution function generates the hidden state derivative based on the current hidden state and the hidden state propagated in the spectral domain, and then updates the hidden state at the next target mapping time based on the hidden state derivative.

[0027] In this embodiment, the predicted furnace condition value for the target prediction time includes: Read the continuous evolution trajectory of the hidden state of the electric arc furnace, and extract the hidden state of the electric arc furnace corresponding to each target mapping time according to the time sequence of each target mapping time in the continuous time axis. Based on the time position of the target prediction time in the continuous time axis, retrieve the hidden states of the electric arc furnace adjacent to the target prediction time from the hidden states of the electric arc furnace corresponding to each target mapping time, and generate the hidden state neighborhood data corresponding to the target prediction time. Extract the hidden state of the electric arc furnace corresponding to the target prediction time from the hidden state neighborhood data. When there is a target mapping time in the hidden state neighborhood data that is the same as the target prediction time, determine the hidden state of the electric arc furnace corresponding to the target mapping time as the hidden state vector of the target prediction time. When there is no target mapping time in the hidden state neighborhood data that is the same as the target prediction time, the hidden state mapping process is performed based on the hidden states of the electric arc furnace located before and after the target prediction time in the hidden state neighborhood data to generate the hidden state vector of the target prediction time. Specifically, the hidden states of electric arc furnaces located before and after the target prediction time are extracted from the hidden state neighborhood data. Based on the time position of the target prediction time between the adjacent target mapping times, the hidden states of electric arc furnaces are time-related mapped to generate the hidden state vector corresponding to the target prediction time. The hidden state vector at the target prediction time is determined as the input feature of the state prediction model, and the input feature is input into the feature mapping layer in the state prediction model to generate furnace condition discrimination features. Specifically, the state prediction model includes a feature mapping layer, a nonlinear activation layer, a state discrimination layer, and an output normalization layer connected in sequence. The feature mapping layer receives the hidden state vector at the target prediction time and generates furnace condition discrimination features. The nonlinear activation layer generates state discrimination input features. The state discrimination layer generates state discrimination values ​​for each furnace condition state category. The output normalization layer generates furnace condition state prediction values. The furnace condition discrimination features are input into the nonlinear activation layer of the state prediction model to generate state discrimination input features. The state discrimination input features are input into the state discrimination layer of the state prediction model to generate state discrimination values ​​corresponding to each furnace condition state category. The state discrimination value corresponding to each furnace condition state category is input into the output normalization layer in the state prediction model to generate the furnace condition state prediction value at the target prediction time.

[0028] In this embodiment, an electric arc furnace state prediction system based on graph convolutional networks includes the following modules: The data acquisition module is used to collect the original measured values ​​and corresponding timestamps of various operating parameters during the electric arc furnace smelting process, and generate irregularly sampled multi-source operating parameter time series data; The continuous time series generation module is used to construct a continuous time axis based on the timestamps in the irregularly sampled multi-source operating parameter time series data, and to map the original measured values ​​to the continuous time axis to generate a continuous time domain multivariate state observation sequence. The time-varying graph structure construction module is used to determine the dynamic correlation between different operating parameters based on the continuous time domain multivariate state observation sequence, construct the electric arc furnace operating parameter graph based on the dynamic correlation, and generate the time-varying graph structure state features. The graph coupling feature generation module is used to construct Bernstein polynomials based on the electric arc furnace operating parameter graph, and to use Bernstein polynomials to perform spectral domain feature propagation processing on the time-varying graph structure state features to generate graph coupling state features. The state evolution construction module is used to construct a continuous-time control path from the continuous-time domain multivariate state observation sequence, and to use the graph-coupled state features as the state input to construct a neural controlled differential equation embedded with Bernstein polynomials. The state input is driven by the continuous-time control path to perform state evolution and generate the continuous evolution trajectory of the hidden state of the electric arc furnace. The state prediction module is used to extract the hidden state vector at the target prediction time based on the continuous evolution trajectory of the hidden state of the electric arc furnace, and input the hidden state vector into the state prediction model to generate the furnace condition state prediction value at the target prediction time. The results output module is used to generate electric arc furnace status prediction results based on the predicted furnace status values ​​at the target prediction time.

[0029] Example 1:

[0030] To verify the feasibility of this invention in practice, it was applied to a steel company's scrap steel smelting process using an ultra-high power AC electric arc furnace. During the smelting process, real-time monitoring of operating parameters such as electrode current, electrode voltage, active power, reactive power, furnace temperature, oxygen flow rate, feed rate, flue gas temperature, carbon monoxide concentration in the flue gas, and dust removal duct pressure is required. Due to the frequent switching between the melting, oxidation, and reduction phases of the electric arc furnace, and the differences in sampling frequencies among different devices, the data collected on-site exhibits significant irregular sampling characteristics. For example, the sampling period for electrode current and electrode voltage is 0.1 seconds, the furnace temperature data sampling period is 2 seconds, the flue gas composition sampling period is 5 seconds, and the dust removal duct pressure sampling period is 1 second. In actual operation, some sensors also experience intermittent data loss and sampling delays due to the high-temperature dust environment, making it difficult for traditional prediction methods based on regular time series to accurately reflect the changes in furnace conditions.

[0031] In traditional operation, furnace conditions are primarily assessed based on fixed thresholds and manual experience. Operators determine the current smelting stage by observing current fluctuations, power changes, and furnace temperature trends, and manually adjust electrode lifting speed and power input. When the electric arc furnace enters the oxidation phase, significant fluctuations in oxygen lance flow cause noticeable oscillations in the electrode current, making it difficult for traditional methods to promptly identify furnace anomalies. Statistical data shows that under traditional predictive methods, the accuracy rate for identifying electric arc furnace conditions is only 82.6%, with an average early warning time for abnormal conditions of less than 18 seconds. This leads to frequent power fluctuations, molten pool instability, and localized overheating during smelting, resulting in an average smelting time of 56 minutes per furnace and an average power consumption of 412 kWh per ton of steel.

[0032] In this embodiment, the original measured values ​​and corresponding timestamps of various operating parameters are collected through the electric arc furnace on-site data acquisition system, and irregularly sampled multi-source time-series data of operating parameters are generated. The acquisition system accesses 27 types of operating parameter channels, of which high-frequency electrical parameter data accounts for approximately 63% of the total data volume. Approximately 126 million data entries were collected over 30 days of continuous operation, of which approximately 4.8% were missing data and approximately 6.3% were data with irregular time intervals.

[0033] A continuous time axis is constructed based on the timestamps corresponding to each operating parameter, and the original measurements are mapped to the continuous time axis to generate a continuous time-domain multivariate state observation sequence. During the construction of the continuous time axis, a uniform time step of 0.5 seconds is set, and continuous time mapping processing is performed on data with different sampling frequencies. After processing, the original irregular sampling data is uniformly converted into a continuous time-domain state sequence, enabling correlation analysis of different operating parameters within a unified time dimension. The processed continuous time-domain multivariate state observation sequence contains a total of 27 state variables, including electrode current, voltage, power, furnace temperature, and flue gas parameters.

[0034] The system constructs an electric arc furnace operating parameter map based on continuous-time domain multivariate state observation sequences. The system establishes graph connectivity relationships according to the dynamic correlations between operating parameters, with the dynamic correlation coefficients between electrode current and active power reaching 0.91, furnace temperature and flue gas temperature reaching 0.88, and oxygen flow rate and carbon monoxide concentration reaching 0.79. The system establishes a weighted adjacency matrix based on these dynamic correlations and constructs the electric arc furnace operating parameter map. The continuous-time domain multivariate state observation sequences are embedded as node features into the operating parameter map, forming a time-varying graph structure with state features.

[0035] In the process of generating graph coupling state features, the system constructs Bernstein polynomials based on the normalized graph Laplacian matrix and uses Bernstein polynomials to propagate spectral domain features of the graph structure state features. During implementation, the pre-set polynomial order is set to 5, and the propagation and aggregation of associated features between different neighboring graph nodes are achieved through the spectral domain propagation range corresponding to different orders. Experimental data show that after adopting Bernstein polynomials, the model's ability to identify high-order coupling relationships between operating parameters is significantly improved. Specifically, the feature recognition accuracy for the strong current fluctuation state during the melting period increased from 87.4% of the original graph convolution model to 94.2%; and the recognition accuracy for the flue gas fluctuation state during the oxidation period increased from 85.1% to 92.7%.

[0036] In the continuous evolution modeling of hidden states, graph-coupled state features are input into the state mapping network to generate corresponding initial hidden state vectors. Bernstein polynomials are used to propagate the initial hidden state vectors in the spectral domain, and the generated spectral-domain propagated hidden states, along with the continuous-time control path, are input into the neural controlled differential equation to achieve continuous-time state recursion. In implementation, the state evolution network employs a four-layer neural network structure, with each layer containing 128 hidden nodes. The model training data uses 20 consecutive days of production data, resulting in approximately 2.4 million continuous-time training samples.

[0037] After training, online prediction tests were conducted using the remaining 10 days of data. Test results show that this invention can continuously and dynamically predict the furnace condition status within the next 30 seconds. During the melting phase, the furnace condition prediction accuracy reached 96.1%; during the oxidation phase, it reached 95.4%; during the reduction phase, it reached 94.8%; and the overall furnace condition prediction accuracy reached 95.6%. Compared to the 88.3% prediction accuracy of the traditional Long Short-Term Memory (LSTM) network model and the 90.7% prediction accuracy of the traditional graph convolutional network model, this invention significantly improves the ability to predict furnace conditions under complex operating conditions.

[0038] In terms of predicting abnormal operating conditions, this invention can identify abnormal states such as abnormal current fluctuations, electrode misalignment, and molten pool instability in advance. Specifically, the average advance warning time for abnormal electrode current fluctuations reaches 52 seconds, for molten pool instability reaches 47 seconds, and for abnormal oxygen flow reaches 39 seconds. Compared to the average warning time of 18 seconds for traditional systems, this invention significantly improves the ability to identify abnormal operating conditions in advance.

[0039] During production, the system feeds back the predicted furnace conditions to the electrode adjustment and power control systems in real time. When the system predicts that the furnace condition is about to enter a high-fluctuation state, it automatically reduces the power fluctuation amplitude and adjusts the electrode lifting and lowering speed; when the system predicts that the oxidation reaction is too strong, it automatically adjusts the oxygen lance flow rate and charging speed. After continuous operation testing, the average smelting time per furnace was reduced from 56 minutes to 49 minutes, a reduction of 7 minutes; the average power consumption per ton of steel was reduced from 412 kWh to 379 kWh, a reduction of approximately 8.0%; electrode consumption was reduced from 2.21 kg per ton of steel to 1.94 kg; and the number of furnace shutdowns due to abnormal conditions was reduced from an average of 17 times per month to 6 times.

[0040] Even in scenarios with missing data and irregular sampling, this invention maintains high prediction stability. When the on-site data missing rate reaches 10%, the accuracy of the furnace condition prediction remains above 92.8%, while the prediction accuracy of the traditional discrete time series model drops to 81.5%. When the sampling frequency of operating parameters fluctuates by 30%, the fluctuation range of the prediction results of this invention remains within ±2.7%, which is significantly better than the ±9.4% fluctuation range of the traditional model.

[0041] In summary, this embodiment combines Bernstein polynomial spectral filtering with neural controlled differential equations to achieve joint modeling of the correlation between multiple operating parameters of an electric arc furnace and its continuous-time dynamic evolution process. This enables it to adapt to the furnace condition prediction requirements under complex operating conditions, irregular sampling, and strongly coupled operating environments, thereby improving the state identification capability, anomaly early warning capability, and process control capability of the electric arc furnace smelting process.

[0042] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the state of an electric arc furnace based on graph convolutional networks, characterized in that, include: Collect the original measured values ​​and corresponding timestamps of various operating parameters during the electric arc furnace smelting process, and generate irregularly sampled multi-source operating parameter time series data; A continuous time axis is constructed based on the timestamps in the time series data of irregularly sampled multi-source operating parameters, and the original measured values ​​are mapped to the continuous time axis to generate a continuous time domain multivariate state observation sequence. The dynamic correlation between different operating parameters is determined based on the continuous time domain multivariate state observation sequence. An electric arc furnace operating parameter map is constructed based on the dynamic correlation. The continuous time domain multivariate state observation sequence is embedded as a node feature into the electric arc furnace operating parameter map to generate time-varying graph structure state features. Bernstein polynomials are constructed based on the electric arc furnace operating parameter diagram, and the Bernstein polynomials are used to perform spectral domain feature propagation processing on the time-varying diagram structural state features to generate graph-spectral coupled state features. The continuous-time domain multivariate state observation sequence is constructed as a continuous-time control path, and the graph-coupled state features are used as state inputs. A neural controlled differential equation with Bernstein polynomials is constructed, and the state input is driven by the continuous-time control path to generate the continuous evolution trajectory of the hidden state of the electric arc furnace. The hidden state vector at the target prediction time is extracted based on the continuous evolution trajectory of the hidden state of the electric arc furnace, and the hidden state vector is input into the state prediction model to generate the furnace condition state prediction value at the target prediction time. The electric arc furnace status prediction result is generated based on the predicted furnace status value at the target prediction time.

2. The method for predicting the state of an electric arc furnace based on a graph convolutional network according to claim 1, characterized in that, The generation of irregularly sampled multi-source runtime parameter time series data includes: Determine the categories of operating parameters to be collected during the electric arc furnace smelting process, and configure corresponding data acquisition channels for each category of operating parameters; The original measurement values ​​of the corresponding operating parameter categories are collected through each data acquisition channel, and the timestamps corresponding to the original measurement values ​​are recorded synchronously when collecting the original measurement values ​​to generate single-point operating parameter data with timestamps. The single-point operational parameter data with timestamps are aggregated according to the operational parameter category to generate single-parameter time-series data corresponding to each operational parameter category; Sort the single-parameter time series data corresponding to each category of operating parameters in chronological order to generate ordered single-parameter time series data; Channel identifiers are bound to the single-parameter ordered time-series data corresponding to each operational parameter category to generate a multi-source operational parameter data set with parameter category identifiers, original measurement values, and timestamps. Based on the timestamp distribution corresponding to different operational parameter categories in the multi-source operational parameter dataset, the sampling frequency differences and sampling time differences between different data acquisition channels are preserved to generate irregularly sampled multi-source operational parameter time series data.

3. The method for predicting the state of an electric arc furnace based on a graph convolutional network according to claim 1, characterized in that, Generating continuous-time domain multivariate state observation sequences includes: Read the timestamps corresponding to each category of operating parameter in the irregularly sampled multi-source operating parameter time series data, and summarize, deduplicate, and sort all timestamps in chronological order to generate a global timestamp sequence; The start and end range of the time axis is determined based on the first and last timestamps in the global timestamp sequence, and the start and end range of the time axis is divided according to a preset fixed time interval to generate a continuous time axis; Each time point in the continuous time axis is determined as the target mapping time, and adjacent timestamps are retrieved in the single-parameter ordered time series data corresponding to each running parameter category based on the target mapping time to generate time neighborhood data corresponding to each running parameter category. Based on the time neighborhood data corresponding to each running parameter category, the original measurement value corresponding to the target mapping time is extracted. When there is a timestamp in the time neighborhood data that is the same as the target mapping time, the original measurement value corresponding to the timestamp is determined as the mapping measurement value of the target mapping time. When there is no timestamp in the time neighborhood data that is the same as the target mapping time, time mapping is performed based on the original measurement values ​​in the time neighborhood data that are before and after the target mapping time to generate the mapped measurement value of the target mapping time; According to the category of operating parameters, the mapping measurement values ​​corresponding to each category of operating parameters at the same target mapping time are combined to generate a multivariate state observation vector corresponding to the target mapping time; According to the chronological order of the target mapping times in the continuous time axis, the multivariate state observation vectors corresponding to each target mapping time are arranged to generate a continuous time domain multivariate state observation sequence.

4. The method for predicting the state of an electric arc furnace based on a graph convolutional network according to claim 1, characterized in that, The structural state features of the generated time-varying graph include: Read the continuous time domain multivariate state observation sequence, and extract the corresponding mapping measurement value sequence of each operating parameter according to the operating parameter category from the continuous time domain multivariate state observation sequence; Based on the mapping measurement value sequence corresponding to each operating parameter, the dynamic correlation value between any two operating parameters is calculated according to the preset sliding time window to generate dynamic correlation. Based on the dynamic correlation values, the graph connection relationships between different operating parameters are determined, and the corresponding dynamic correlation values ​​are determined as the edge weights of the graph connection relationships. The electric arc furnace operating parameter graph is constructed by using each operating parameter category as graph nodes, graph connection relationships as graph edges, and edge weights as graph edge attributes. Based on the target mapping time in the continuous time domain multivariate state observation sequence, extract the mapping measurement value at the same target mapping time from the mapping measurement value sequence corresponding to each operating parameter, and generate node feature data corresponding to the target mapping time; The node feature data corresponding to the target mapping time is embedded into the corresponding graph node in the electric arc furnace operating parameter graph according to the operating parameter category, thereby generating the graph structure state feature corresponding to the target mapping time. Arrange the graph structure state features corresponding to each target mapping time according to the chronological order of the target mapping time to generate time-varying graph structure state features.

5. The method for predicting the state of an electric arc furnace based on a graph convolutional network according to claim 1, characterized in that, The generated spectrum coupling state features include: Read the time-varying graph structure state features and extract the corresponding graph structure state features from the time-varying graph structure state features according to the target mapping time. Extract the electric arc furnace operating parameter graph, graph connectivity, edge weights, and node feature data from the graph structure state features corresponding to the target mapping time, and construct the weighted adjacency matrix corresponding to the target mapping time based on the graph connectivity and edge weights; The normalized graph Laplacian matrix is ​​calculated based on the weighted adjacency matrix, and the normalized graph Laplacian matrix is ​​determined as the spectral domain input object corresponding to the target mapping time. The spectral domain variables are determined based on the spectral domain input object, and Bernstein polynomial basis functions of each order are constructed based on the spectral domain variables and the preset polynomial order. The Bernstein polynomial basis functions of each order are combined in order of order to generate a set of Bernstein polynomial basis functions. Bernstein polynomials are generated by weighting and combining the Bernstein polynomial basis functions of each order and their corresponding trainable weights in the Bernstein polynomial basis function set. Input the node feature data corresponding to the target mapping time into the Bernstein polynomial, and use the Bernstein polynomial to propagate the spectral domain features of the node feature data according to the graph connection relationship and edge weight in the weighted adjacency matrix to generate the graph propagation features corresponding to the target mapping time. Arrange the spectral propagation features corresponding to each target mapping time according to the chronological order of the target mapping time to generate spectral coupling state features.

6. The method for predicting the state of an electric arc furnace based on a graph convolutional network according to claim 1, characterized in that, Constructing neurally controlled differential equations embedded with Bernstein polynomials includes: Read the continuous time domain multivariate state observation sequence, and according to the time sequence of each target mapping time in the continuous time axis, perform continuous path connection processing on the multivariate state observation vectors corresponding to each target mapping time to generate a continuous time control path; Read the graph coupling state features and extract the corresponding graph propagation features from the graph coupling state features according to the target mapping time. Input the graph propagation features corresponding to the target mapping time into the state mapping network, perform latent space mapping on the graph propagation features, generate the initial hidden state vector corresponding to the target mapping time, and determine the initial hidden state vector as the state input corresponding to the target mapping time. Read the Bernstein polynomial and input the initial hidden state vector corresponding to the target mapping time into the Bernstein polynomial. Perform spectral domain state propagation processing on the initial hidden state vector according to the spectral domain propagation relationship corresponding to the Bernstein polynomial to generate the spectral domain propagated hidden state corresponding to the target mapping time. The state input corresponding to the target mapping time, the hidden state propagated in the spectral domain, and the control input corresponding to the target mapping time in the continuous-time control path are all input into the state evolution network, and the hidden state derivative corresponding to the target mapping time is generated based on the correlation between the state input, the hidden state propagated in the spectral domain, and the control input. The state evolution function is constructed based on the latent state derivatives corresponding to the target mapping time, and the spectral domain propagation latent state corresponding to the target mapping time is determined as the spectral state evolution term in the state evolution function, thereby generating a state evolution function embedded with Bernstein polynomials. Neural controlled differential equations are constructed based on state evolution functions embedded with Bernstein polynomials. According to the temporal order of each target mapping moment in the continuous time axis, the control input of the corresponding target mapping moment in the continuous time control path drives the controlled differential equation of the neural network to perform continuous time state recursion. Based on the hidden state propagated in the spectral domain and the hidden state derivative corresponding to the previous target mapping moment, the hidden state of the electric arc furnace corresponding to the current target mapping moment is generated, thus obtaining the continuous evolution trajectory of the hidden state of the electric arc furnace.

7. The method for predicting the state of an electric arc furnace based on a graph convolutional network according to claim 1, characterized in that, The predicted furnace condition values ​​at the target prediction time include: Read the continuous evolution trajectory of the hidden state of the electric arc furnace, and extract the hidden state of the electric arc furnace corresponding to each target mapping time according to the time sequence of each target mapping time in the continuous time axis. Based on the time position of the target prediction time in the continuous time axis, retrieve the hidden states of the electric arc furnace adjacent to the target prediction time from the hidden states of the electric arc furnace corresponding to each target mapping time, and generate the hidden state neighborhood data corresponding to the target prediction time. Extract the hidden state of the electric arc furnace corresponding to the target prediction time from the hidden state neighborhood data. When there is a target mapping time in the hidden state neighborhood data that is the same as the target prediction time, determine the hidden state of the electric arc furnace corresponding to the target mapping time as the hidden state vector of the target prediction time. When there is no target mapping time in the hidden state neighborhood data that is the same as the target prediction time, the hidden state mapping process is performed based on the hidden states of the electric arc furnace located before and after the target prediction time in the hidden state neighborhood data to generate the hidden state vector of the target prediction time. The hidden state vector at the target prediction time is determined as the input feature of the state prediction model, and the input feature is input into the feature mapping layer in the state prediction model to generate furnace condition discrimination features. The furnace condition discrimination features are input into the nonlinear activation layer of the state prediction model to generate state discrimination input features. The state discrimination input features are input into the state discrimination layer of the state prediction model to generate state discrimination values ​​corresponding to each furnace condition state category. The state discrimination value corresponding to each furnace condition state category is input into the output normalization layer in the state prediction model to generate the furnace condition state prediction value at the target prediction time.

8. A graph convolutional network-based electric arc furnace state prediction system, comprising the graph convolutional network-based electric arc furnace state prediction method according to any one of claims 1-7, characterized in that, Includes the following modules: The data acquisition module is used to collect the original measured values ​​and corresponding timestamps of various operating parameters during the electric arc furnace smelting process, and generate irregularly sampled multi-source operating parameter time series data; The continuous time series generation module is used to construct a continuous time axis based on the timestamps in the irregularly sampled multi-source operating parameter time series data, and to map the original measured values ​​to the continuous time axis to generate a continuous time domain multivariate state observation sequence. The time-varying graph structure construction module is used to determine the dynamic correlation between different operating parameters based on the continuous time domain multivariate state observation sequence, construct the electric arc furnace operating parameter graph based on the dynamic correlation, and generate the time-varying graph structure state features. The graph coupling feature generation module is used to construct Bernstein polynomials based on the electric arc furnace operating parameter graph, and to use Bernstein polynomials to perform spectral domain feature propagation processing on the time-varying graph structure state features to generate graph coupling state features. The state evolution construction module is used to construct a continuous-time control path from the continuous-time domain multivariate state observation sequence, and to use the graph-coupled state features as the state input to construct a neural controlled differential equation embedded with Bernstein polynomials. The state input is driven by the continuous-time control path to perform state evolution and generate the continuous evolution trajectory of the hidden state of the electric arc furnace. The state prediction module is used to extract the hidden state vector at the target prediction time based on the continuous evolution trajectory of the hidden state of the electric arc furnace, and input the hidden state vector into the state prediction model to generate the furnace condition state prediction value at the target prediction time. The results output module is used to generate electric arc furnace status prediction results based on the predicted furnace status values ​​at the target prediction time.

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