Sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction

Abstract

The present application relates to the technical field of industrial big data processing, artificial intelligence and industrial process control, and particularly relates to a sintering state prediction method based on dynamic graph and topological perception hierarchical interaction, which comprises the following steps: S1, constructing an initial sample matrix based on original time series data of a sintering industrial site; S2, constructing a dynamic adjacency matrix in combination with a historical state feature matrix; S3, grouping the time feature and the dynamic graph adjacency matrix, and sequentially performing in-group convolution and inter-group interaction convolution to extract a current time granularity spatiotemporal representation; S4, predicting future parameters according to the spatiotemporal representation and a control instruction feature matrix. The method of the present application can respond to non-stationary working conditions such as raw material property changes and equipment state fluctuations in a timely manner, and effectively overcomes the problem of sudden drop in prediction performance of traditional static graph models when the working condition changes.

Description

Technical Field

[0001] This invention relates to the fields of industrial big data processing, artificial intelligence and industrial process control technology, and specifically to a sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction. Background Technology

[0002] Sintering, as a core upstream process in the iron and steel smelting process, plays a crucial role in processing raw materials such as iron ore powder into qualified sintered ore. Its process exhibits significant complexity, including strong coupling of multiple variables, large time lags, strong nonlinearity, and hierarchical process topology. Driven by increasingly stringent environmental standards and the persistently urgent need for cost reduction and efficiency improvement in steel enterprises, achieving precise and forward-looking prediction of key process states such as sintering endpoint temperature and waste gas composition has become a core prerequisite and key breakthrough for overcoming the limitations of traditional control models and realizing intelligent optimization control of the sintering process.

[0003] However, current technologies for predicting critical states in sintering still suffer from unavoidable systemic defects, failing to meet the high-precision and real-time requirements of actual industrial production. Traditional mechanistic models, such as computational fluid dynamics (CFD) models, while able to align with the physicochemical nature of sintering to some extent, suffer from high computational complexity and weak real-time response capabilities, making it difficult to support the dynamic prediction needs of continuous sintering production. Early data-driven methods, such as ARIMA and SVM, and current mainstream deep learning models, such as RNN, CNN, and Transformer, while significantly improving prediction efficiency compared to mechanistic models, neglect the inherent hierarchical topological characteristics of the sintering process, resulting in weak modeling capabilities for the spatiotemporal coupling relationships during sintering, and prediction accuracy and generalization capabilities that are insufficient to meet the requirements of actual production.

[0004] In recent years, Spatiotemporal Graph Neural Networks (STGNNs) have been gradually introduced into the field of complex industrial process modeling due to their powerful spatiotemporal correlation modeling capabilities. However, when applied to the prediction of critical states in sintering processes, they still face many key technical bottlenecks that urgently need to be overcome, as follows: The graph structure is static and rigid, lacking dynamic adaptability: Existing STGNN models all rely on fixed adjacency matrices to construct the graph structure. However, the dynamic evolution of working conditions during sintering, such as fluctuations in raw material composition, adjustments in operating parameters, and changes in equipment operating status, will cause the correlation between process nodes to change in real time. Fixed adjacency matrices cannot perceive the time-varying characteristics of such node relationships, resulting in inaccurate spatial correlation modeling and difficulty in adapting to the actual production with dynamic fluctuations in working conditions.

[0005] The models are detached from the actual process and violate physical logic: the sintering process has an inherent logical framework of "mixing-ignition-sintering-flue gas circulation", but existing models often ignore the actual process flow and physical relationships, causing the information propagation path to deviate from the physical reality of the process. This leads to problems such as feature extraction bias, model training instability, and decreased generalization ability. Insufficient capture of cross-regional influences and inadequate extraction of multi-scale interaction features: The sintering process exhibits significant characteristics of "local tight coupling" and "long-range cross-regional transmission," such as material transfer from the mixing section to the sintering section and flue gas flow from the die head to the tail section, all of which show obvious long-range cross-regional influences and local tight coupling effects. However, existing STGNN models lack a collaborative modeling mechanism for local neighborhood interactions and long-range cross-regional transmission, failing to fully extract multi-scale process interaction features. This limits the model's ability to dynamically represent complex sintering systems and makes it difficult to accurately capture the impact of cross-regional process correlations on critical states.

[0006] The ability to capture multi-scale dynamic characteristics is weak, making it difficult to adapt to long lag conditions: The sintering process has a typical long lag period, but the receptive field of existing related models is limited and cannot effectively cover this long lag period; at the same time, such models lack a fusion mechanism for shallow process detail features and deep long-term trend features, resulting in a weak ability to jointly represent the long-term and short-term dependencies in the sintering history, which ultimately makes the prediction results prone to trend deviation or detail distortion, and unable to accurately match the multi-scale dynamic evolution law of the sintering process.

[0007] Ignoring known operational commands and lacking forward-looking predictive capabilities: In actual sintering production, key operational commands such as fan speed, trolley speed, and ignition temperature are usually set in advance by the production scheduling plan and are predictable input information. However, all existing predictive models rely solely on historical sensor monitoring data to extrapolate future process states, completely ignoring such known key control commands as model inputs. This leads to problems such as predictive lag and amplified deviations during the operational adjustment phase, making it difficult to support forward-looking control decisions in the sintering process and failing to meet the actual needs of intelligent optimization control.

[0008] In summary, existing sintering critical state prediction technologies have significant shortcomings in terms of dynamic adaptability to operating conditions, process logic fit, cross-scale correlation capture capability, and utilization efficiency of known control commands. As a result, when faced with common operating condition changes in sintering production, such as raw material fluctuations and operational adjustments, they generally suffer from inaccurate predictions and slow response. This makes it difficult to meet the core requirements of steel enterprises for high precision, strong robustness, and practical control guidance in sintering production, thus hindering the improvement of intelligent optimization control of the sintering process. There is an urgent need to develop a sintering critical state prediction technology that can overcome the above-mentioned technical bottlenecks. Summary of the Invention

[0009] To address the shortcomings of existing technologies in terms of dynamic adaptability, process logic fit, cross-scale correlation capture, and utilization of control commands, the present invention aims to provide a sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction, so as to effectively improve the accuracy, adaptability, and foresight of prediction and meet the needs of industrial real-time optimization control.

[0010] Specifically, the present invention provides a sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction, which includes the following steps: S1. Construct an initial sample matrix based on the original time-series data of the pre-processed sintering industrial site; the initial sample matrix includes a historical state feature matrix, a control command feature matrix, and a truth matrix; S2. Extract time features based on the historical state feature matrix and construct a dynamic graph adjacency matrix; S3. Based on the process topology, the temporal features and the adjacency matrix of the dynamic graph are grouped, and intra-group convolution and inter-group cross-convolution are performed sequentially to extract spatiotemporal representations: S31. Generate a hierarchical partitioning tree based on the sintering process; S32. Based on the hierarchical partitioning tree, group the temporal features and the adjacency matrix of the dynamic graph to obtain the local temporal features and the local dynamic graph adjacency matrix: ; ; in, As a time feature, These are local time features, This indicates that all elements in the matrix are in the real number field, B is the number of samples, and N is the number of samples. g1 N g2 Here, DA represents the number of nodes for the local temporal feature, D represents the feature dimension, and DA represents the number of nodes for the local temporal feature. (l) For a dynamic graph adjacency matrix, A 11 A 12 A 21 A 22 These are the adjacency matrices of the local dynamic graph. , The number of nodes in the adjacency matrix of the local dynamic graph; S33. Intra-group convolution: Perform graph convolution operations on the local temporal features and the local dynamic graph adjacency matrix within the group respectively to capture the local spatial dependencies within each process region. S34, Inter-group interactive convolution: Construct a learnable cross-regional adjacency matrix and perform inter-group graph convolution to generate spatiotemporal representations; S4. Predict future parameters based on the spatiotemporal representation and control command feature matrix. The steps include: S41. Based on the historical state feature matrices at different time granularities, generate multiple sets of spatiotemporal representations at the current time granularity, fuse and convolve them, and generate a preliminary prediction sequence based on the historical state feature matrices. ; in, For preliminary sequence prediction, It is an activation function. As a spatiotemporal representation, and For two convolution kernels Convolution operations; S42. Output the final prediction sequence: Combine gating and bias to perform weighted modulation on the preliminary prediction sequence and output the final prediction sequence of the sintering state.

[0011] Preferably, the method for constructing the cross-regional adjacency matrix that can be learned in S34 is as follows: S3411. Constructing a cross-regional adjacency matrix: Through graph propagation, the predefined adjacency matrix... Symmetric singular value decomposition is performed to generate two learnable node embeddings, E3 and E4. The latent associations between nodes are extracted by calculating the transpose dot product of E3 and E4. Subsequently, a ReLU activation function is introduced to filter noise and achieve matrix sparsity. Row normalization is then performed using the Softmax function, ultimately generating an adaptive cross-regional adjacency matrix that captures implicit long-range dependencies. : ; Where Softmax(·) is the normalization function, ReLU(·) is the activation function, and E3 and E4 are the learnable node embeddings, respectively. S3412. Group the cross-regional adjacency matrix according to the hierarchical partitioning tree to generate a local cross-regional adjacency matrix; ; Among them, S 11 S 12 S 21 S 22 These are local cross-regional adjacency matrices.

[0012] Preferably, the inter-group graph convolution in S34 specifically includes: S3421. The local temporal features, local dynamic graph adjacency matrix and local cross-region adjacency matrix after grouping are matched one by one, and a learnable linear weighted fusion is performed. The fusion result is normalized row by row to generate a cross-region sub-adjacency matrix. ; in, , These are the cross-regional sub-adjacency matrices, and Softmax(·) is the normalization function. Each parameter is a learnable parameter, and the fusion ratio of the cross-region matrix is ​​learned through model training; S3422. Guided by the cross-regional sub-adjacency matrix, perform inter-group interactive convolution between the local spatial dependency and the cross-regional sub-adjacency matrix to obtain the cross-regional propagation feature matrix. ; in, , These are the cross-regional propagation feature matrices; S3423. Introducing a gating mechanism, a nonlinear mapping is performed between the local spatial dependency obtained in S33 and the cross-regional propagation feature matrix generated in S3422 to obtain a gating vector that controls the flow of information. The fused hierarchical grouped spatiotemporal feature matrix is ​​then output using complementary weighting. : ; ; ; ; in, , , and For linear mapping weights; It is the sigmoid activation function; S3424, Generating Spatiotemporal Representations: Concatenate the hierarchical grouped spatiotemporal feature matrices from S3423, and generate spatiotemporal representations using the original node order as indices. ; in, For the first Input to the layered spatiotemporal block, This is the spatiotemporal representation of the output of this layer. Concat() is the concatenation operation.

[0013] Preferably, S2 includes: S21. Construct a static adjacency matrix, and determine the weights of the static adjacency matrix. The effective process distance is calculated by combining the equivalent process distance with the Gaussian kernel function; whereby the equivalent process distance is obtained by weighted fusion of the spatial distance between sintering nodes and the process lag time; the weights are... The calculation formula is: ; Where exp(·) is the Gaussian kernel function, For node i, For node j, Represents a node and The equivalent process distance between them; h is the attenuation coefficient, and k is the maximum cutoff distance.

[0014] S22. Extract time features from the historical state feature matrix, perform graph structure learning on the time features, and construct a primary dynamic adjacency matrix. S23. Weighted merge the primary dynamic adjacency matrix and the static adjacency matrix to output the dynamic graph adjacency matrix DA at the current time step. (l) : ; in, This is a primary dynamic adjacency matrix; It is a static adjacency matrix. The weights are adaptive for the model.

[0015] Preferably, S22 includes the following steps: S221. Extracting temporal features: First, map the features of historical nodes into high-dimensional hidden states, and then input the high-dimensional hidden states into a gated temporal causal convolutional network to extract temporal features. ; ; in, This is a high-dimensional hidden state. Let be the historical state feature matrix, and Linear(·) be a linear mapping. For the first Output features of layer-gated dilated causal convolution. The hyperbolic tangent activation function is used. The learnable convolution kernel weights are used for filter branches. The bias of the bias filter branch can be learned for the convolution kernel bias. The collision rate of dilated causal convolution is d. This indicates element-wise multiplication; It is the Sigmoid activation function. , These are the parameters for the gated branch; S222, Generating Dynamic Filters: Temporal features are input through two independent hypernetworks to generate dynamic filters for modulating source node representations. The target node represents a dynamic filter. ; ; in, Represents graph convolution. Represents the parameters that can be learned; S223. Generate static embeddings: Through graph propagation, on a predefined adjacency matrix Perform symmetric singular value decomposition to generate static source node embeddings respectively. Embedded with static target nodes : ; Where l is the dimension of node embedding. The left singular vector matrix of the first d largest singular values ​​of the predefined adjacency matrix; The right singular vector matrix of the first d largest singular values ​​of the predefined adjacency matrix; For the predefined adjacency matrix A diagonal matrix composed of the largest singular values; S224. Generate dynamic embedding: ... , respectively with Element-wise multiplication yields the modulated dynamic embedding. ; ; S225. The dynamically embedded function adjusted in S224 is processed by activation function, and combined with ReLU activation function for nonlinear mapping and denoising to obtain the primary dynamic adjacency matrix. ; .

[0016] Preferably, S41 includes: S411. Extract hierarchical features generated by each spatiotemporal coding layer in the encoder through skip connections; adopt an end alignment strategy, using the time dimension of the current deep features as a benchmark, and truncate the shallow accumulated features by the same length, thereby aligning the features of each level in the time dimension; subsequently, accumulate the aligned hierarchical features element-wise to fuse multi-scale temporal information and spatial topological features under different receptive fields, generating a global spatiotemporal representation that aggregates historical inertial features. ; S412. Based on the global spatiotemporal feature matrix tensor, spatiotemporal convolution operation is performed through a two-level cascaded convolutional neural network to output a preliminary prediction sequence based on the features of historical state nodes.

[0017] Preferably, the historical state feature matrix, control command feature matrix, and truth matrix in S1 are constructed as follows: Historical state feature matrix: time interval extraction All variables within the system characterize the historical dynamic inertia of the system; Control command feature matrix: extracting future intervals The control variable data within the model are used as known external intervention conditions for the model; Truth matrix: extracting the same future interval The state variable data within the model are used as the true values ​​for model training. Where P and Q represent the historical review window length and the future prediction step size, respectively; the state variable is the current operating state data of the system in the original time series data, and the control variable is the predictable human operation or system-set intervention action data in the original time series data.

[0018] Preferably, the final predicted sequence generation method in S42 is as follows: BiLSTM is used to extract features from the control command feature matrix to generate the future control context feature matrix. And then The input is linearly projected and activated by the Sigmoid function to generate an adjustment gate. The final prediction sequence is output by weighting and modulating the initial prediction sequence of S41. ; ; ; in, Represents element-wise product; , The weights are for the linear projection.

[0019] Preferably, the preprocessing in S1 refers to cleaning and standardizing the original time-series data from the sintering industrial site; in S4, a loss function is constructed by calculating the error between the final predicted sequence output by the model and the true value matrix, and the model parameters are optimized by backpropagation algorithm.

[0020] Preferably, in step S33, graph convolution operations are performed on the local temporal features and the local dynamic graph adjacency matrix within the group respectively to capture the local spatial dependencies within each process region: .

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The method of the present invention enhances the spatiotemporal correlation expression through dynamic graph modeling. By constructing an adaptive dynamic graph adjacency matrix, it captures the connection relationship between nodes and its intensity changes in real time, which significantly improves the ability to characterize the spatial-temporal coupling correlation in industrial processes, thereby improving the modeling accuracy and prediction accuracy of graph diffusion processes.

[0022] (2) The method of the present invention locks the process logic skeleton through topology-aware hierarchical partitioning, making the hierarchical propagation consistent with the real topology. This makes the model more in line with industrial reality and exhibits stronger robustness and generalization performance when facing different production lines or operating conditions.

[0023] (3) The method of the present invention achieves adaptive collaborative learning of local dependencies and long-range cross-regional dependencies through a learnable cross-regional adjacency matrix and a gating fusion mechanism. This is particularly suitable for complex industrial systems such as sintering, which involve multivariate coupling and significant effect transmission, thereby comprehensively improving the ability to capture key states represented by the sintering endpoint.

[0024] (4) The method of the present invention uses a gated temporal causal convolutional network (Gated TCN) to fuse the encoder-decoder and skip connections, synchronously capture the short-term fluctuations and long-term trends of the sintering process, deeply fuse multi-scale features, and effectively suppress trend shifts and detail distortions in multi-step prediction.

[0025] (5) The method of the present invention projects and fuses the feature matrix of the known future operation instructions by BiLSTM, so that the model can predict the impact of the operation instructions, significantly reducing the prediction lag of the traditional method when adjusting the working condition, and realizing accurate multi-step prediction with foresight. Attached Figure Description

[0026] Figure 1 This is a flowchart of the data preprocessing and dynamic graph adjacency matrix generation process of the present invention; Figure 2 This is a flowchart of the spatiotemporal interaction of the present invention; Figure 3 This is a flowchart illustrating the prediction process of the present invention; Figure 4 The sintering process grouping of the present invention; Figure 5 This is a structural diagram of the model of the present invention; Figure 6 This is a spatiotemporal interaction structure diagram of the present invention. Detailed Implementation

[0027] This invention provides a sintering process state prediction method based on dynamic graph construction and topology-aware hierarchical interaction. Its core lies in employing a spatio-temporal dynamic graph network with feature interaction and bidirectional long short-term memory (ST-DGFI) hybrid model for sintering process state prediction. This model consists of stacked spatio-temporal coding layers and decoders.

[0028] First, the raw time-series data from the sintering industrial site are grouped into different time granularities to obtain historical state feature matrices, control command feature matrices, and corresponding truth matrices at different time granularities. Then, the grouped historical state feature matrices are input into different spatiotemporal coding layers to obtain spatiotemporal representations at different time granularities. Next, the spatiotemporal representations at different time granularities and the control command feature matrices are input into a decoder to obtain the final predicted sequence. Finally, a loss function is constructed by calculating the error between the final predicted sequence output by the model and the truth matrix, and the model is continuously optimized using a backpropagation algorithm.

[0029] Specifically, this invention provides a method for predicting the state of a sintering process based on dynamic graph construction and topology-aware hierarchical interaction, comprising the following steps: S1. Construct an initial sample matrix based on the original time-series data from the pre-processed sintering industrial site; the initial sample matrix includes a historical state feature matrix, a control command feature matrix, and a truth matrix. For example... Figure 1 As shown, this step includes: S11. Data Acquisition and Preprocessing: Collect raw time-series data from the sintering industrial site, and clean, fill in, and normalize the raw time-series data.

[0030] Data cleaning and imputation: Abnormal data from the CO monitoring sensor restart calibration and backflushing stages are removed; for missing data, a forward imputation strategy is adopted to maintain the temporal continuity of industrial data.

[0031] Independent Z-Score Normalization: To eliminate dimensional differences between different sensors, such as the difference between temperature (°C) and pressure (kPa), and to accelerate model convergence, Z-Score normalization is performed independently for each variable. ; in, To find the mean of this variable in the training set, The standard deviation of this variable in the training set, For values ​​that need to be standardized, This is the standardized value.

[0032] S12. Constructing the initial sample matrix: Select a fixed time granularity, and based on the observation data at each time step within that granularity, use a sliding window strategy to group the original time series data to construct the initial sample matrix; wherein, the initial sample matrix includes: historical state feature matrix. Control command feature matrix and truth matrix .

[0033] ; in, This indicates that all elements in the matrix are in the real number field. C represents the number of historical state nodes, and C represents the number of channels. This is the control instruction feature matrix.

[0034] Specifically, the initial sample matrix is ​​constructed using a short-time, multi-step prediction task: by sliding a sliding window along the time axis, a training sample consisting of three parts is generated for any time t: Historical state feature matrix: time interval extraction All variables within the system (including state variables and control variables) are used to characterize the historical dynamic inertia of the system.

[0035] Control command feature matrix: extracting future intervals The control variable data within the model are used as known external intervention conditions.

[0036] Truth matrix: extracting the same future interval The state variable data within the model are used as the ground truth for model training.

[0037] Where P and Q represent the historical review window length and the future prediction step size, respectively. The state variable is the current operating state data of the system in the original time series data, and the control variable is the predictable human operation or system-set intervention action data in the original time series data.

[0038] S2. Extract time features based on the historical state feature matrix and construct a dynamic graph adjacency matrix, such as Figure 5 As shown, the steps include: S21. Construct a static adjacency matrix. The connection weights of the static adjacency matrix are calculated by combining the equivalent process distance with the Gaussian kernel function. The equivalent process distance is obtained by weighted fusion of the spatial distance between sintering nodes and the process lag time.

[0039] The construction of the equivalent process distance aims to reflect the nonlinear decay of node influence with time and distance during sintering. Specifically, the equivalent process distance is calculated by weighting the spatial distance between nodes and the process lag time. Its specific value is empirically calibrated based on the measured time delay and approximate physical position relationship between each node in the sintering process.

[0040] A predefined static adjacency matrix is ​​calculated by combining equivalent process distance and a Gaussian kernel function. The weights, their weights The calculation formula is as follows: ; Where exp(·) is the Gaussian kernel function, For node i, For node j, Represents a node and The equivalent process distance between them, h is the attenuation coefficient, and k is the maximum cutoff distance.

[0041] S22. Extract time features from the historical state feature matrix, perform graph structure learning on the time features, and construct a primary dynamic adjacency matrix. The steps include: S221. Extracting temporal features: First, map the features of historical nodes into high-dimensional hidden states, and then input the high-dimensional hidden states into a gated temporal causal convolutional network to extract temporal features. Specifically, this invention employs an encoder and decoder architecture to process the historical state feature matrix. Mapping to a high-dimensional feature matrix space yields a high-dimensional hidden state. Then the higher-dimensional hidden state Input-gated dilated causal convolution is used to expand the temporal receptive field and extract temporal features from it. .

[0042] ; ; in, This is a high-dimensional hidden state. Let be the historical state feature matrix, and Linear(·) be a linear mapping. For the first Output features of layer-gated dilated causal convolution. The hyperbolic tangent activation function is used. The learnable convolution kernel weights are used for filter branches. The bias of the bias filter branch can be learned for the convolution kernel bias. The collision rate of dilated causal convolution is d. This indicates element-wise multiplication; It is the Sigmoid activation function. , These are the parameters for the gated branch.

[0043] Preferably, and Responsible for extracting temporal content features; and Used to calculate the retention ratio of information flow.

[0044] S222, Generating Dynamic Filters: Temporal features are input through two independent hypernetworks to generate dynamic filters for modulating source node representations. The target node represents a dynamic filter. ; ; in, , For dynamic filters, Represents graph convolution. This represents the parameters that can be learned.

[0045] S223. Generate static embeddings: Through graph propagation, on a predefined adjacency matrix Perform symmetric singular value decomposition to generate static source node embeddings respectively. Embedded with static target nodes .

[0046] ; Where l is the dimension of node embedding. The left singular vector matrix of the first d largest singular values ​​of the predefined adjacency matrix; The right singular vector matrix of the first d largest singular values ​​of the predefined adjacency matrix; For the predefined adjacency matrix A diagonal matrix consisting of the largest singular values.

[0047] Preferably, , The principal component features of the graph structure in the row space and column space were captured respectively; It contains the top d largest singular values, which represent the importance weights of the corresponding feature vectors when reconstructing the graph structure.

[0048] S224. Generate dynamic embedding: ... , respectively with Element-wise multiplication yields the modulated dynamic embedding. : ; S225. The dynamically embedded function adjusted in S224 is processed by activation function, and combined with ReLU activation function for nonlinear mapping and denoising to obtain the primary dynamic adjacency matrix. ; ; ReLU(·) is the activation function.

[0049] S23. Construct a dynamic graph adjacency matrix: Weight and fuse the initial dynamic adjacency matrix with the static adjacency matrix to output the dynamic graph adjacency matrix at the current time step. This enables the model to adaptively perceive changes in the connection relationships and strength between nodes based on real-time input.

[0050] ; in, In order to learn parameters.

[0051] Specifically, It is a learnable parameter that is automatically optimized through model training, rather than a preset fixed hyperparameter. It acts as a regulating valve for static and dynamic information flow, and can automatically quantify the relative importance of physical priors and real-time feature matrices in prediction based on the backpropagation signal of the loss function through model training.

[0052] S3. Based on the process topology, the temporal features and the adjacency matrix of the dynamic graph are grouped, and intra-group convolution and inter-group cross-convolution are performed sequentially to extract spatiotemporal representations; such as Figure 2 as well as Figure 6 As shown, the steps include: S31. Generate a hierarchical partitioning tree based on the sintering process.

[0053] To avoid the disruption of the actual process topology caused by simple data index partitioning, this invention employs an offline preprocessing method to generate a hierarchical partitioning tree, which is then solidified into a guidance file for use during training and inference. Specifically, this method constructs a partitioning tree based on a graph structure feature matrix. In a preferred embodiment, sensor nodes are first pre-grouped according to the process logic of "mixing-ignition-sintering-flue gas circulation"; then, the node adjacency matrix is ​​traversed, and the connection weights between different groups are calculated to form a "group-to-group" adjacency matrix; finally, recursive spectral clustering is performed on this matrix, ensuring that nodes within the same process group are assigned to the same leaf node as an indivisible whole, thereby ensuring that the hierarchical structure is strictly consistent with the actual process flow. Preferably, for the sintering process, this invention uses a single-layer partitioning tree, degenerating into two groups, and extracting spatiotemporal interaction features between the two groups.

[0054] S32. Based on the hierarchical tree, divide the time features... Adjacency Matrix of Dynamic Graph Grouping is performed to obtain the local temporal features and the adjacency matrix of the local dynamic graph.

[0055] like Figure 4 As shown, in this preferred embodiment, the process is divided into two groups according to the sintering process.

[0056] ; ; in, , The number of nodes in the two groups. These are local time features, A 11 A 12 A 21、 A 22 These are the adjacency matrices of the local dynamic graph.

[0057] S33. Intra-group convolution: For local temporal features within a group. Adjacency matrix A of the local dynamic graph 11 A 22 Perform graph convolution operations separately to capture the local spatial dependencies within each process region.

[0058] ; in, , These represent local spatial dependencies, and GCN(·) is the convolution function.

[0059] S34. Inter-group convolution: Constructing a learnable cross-regional adjacency matrix and performing inter-group graph convolution to generate spatiotemporal representations, the steps of which include: S341. Constructing a learnable cross-regional adjacency matrix to capture long-range process dependencies that are difficult to model locally convolutional features, the steps of which include: S3411. Construct the cross-regional adjacency matrix S: Through graph propagation, on the predefined adjacency matrix... Symmetric singular value decomposition is performed to generate two learnable node embeddings, E3 and E4. The latent associations between nodes are extracted by calculating the transpose dot product of E3 and E4. Subsequently, a ReLU activation function is introduced to filter noise and achieve matrix sparsity. Row normalization is then performed using the Softmax function, ultimately generating an adaptive cross-regional adjacency matrix that captures implicit long-range dependencies. .

[0060] ; Where Softmax(·) is the Softmax function, ReLU(·) is the ReLU activation function, and E3 and E4 are the learnable node embeddings, respectively.

[0061] S3412. Group the cross-regional adjacency matrix according to the hierarchical partitioning tree to generate a local cross-regional adjacency matrix.

[0062] ; Where S is the cross-region adjacency matrix, S 11 S 12 S 21 S 22 These are the local cross-regional adjacency matrices of S.

[0063] S342. Perform inter-group graph convolution to generate a spatiotemporal representation at the current temporal granularity; S3421. The local temporal features, local dynamic graph adjacency matrix and local cross-region adjacency matrix after grouping are matched one by one. The cross-region sub-adjacency matrix is ​​generated by learning linear weighted fusion and the fusion result is normalized row by row.

[0064] ; in, , These are the cross-regional sub-adjacency matrices, and Softmax(·) is the normalization function. Each parameter is a learnable parameter, and the fusion ratio of the cross-region matrix is ​​learned through model training.

[0065] S3422. Guided by the cross-regional sub-adjacency matrix, perform inter-group interactive convolution between the local spatial dependency and the cross-regional sub-adjacency matrix to obtain the cross-regional propagation feature matrix.

[0066] ; in, , These are the cross-regional propagation feature matrices, and GCN(·) is the convolution function.

[0067] S3423. Introducing a gating mechanism, a nonlinear mapping is performed between the local spatial dependency obtained in S33 and the cross-regional propagation feature matrix generated in S3422 to obtain a gating vector that controls the flow of information. The fused hierarchical grouped spatiotemporal feature matrix is ​​then output using complementary weighting. .

[0068] ; ; ; ; in, , , and For linear mapping weights; It is the sigmoid activation function; S3424, Generating Spatiotemporal Representations: Concatenate the hierarchical grouped spatiotemporal feature matrices from S3423, and generate spatiotemporal representations using the original node order as indices. ; in, For the first Input to the layered spatiotemporal block, This is the spatiotemporal representation of the output of this layer to the jump connection. Concat() is the concatenation operation.

[0069] S4. Predict future parameters based on the spatiotemporal representation and control command feature matrix, such as... Figure 3 As shown, the steps include: S41. Based on historical state feature matrices at different time granularities, generate multiple sets of spatiotemporal representations at the current time granularity, fuse and convolve them, and generate a preliminary prediction sequence based on the historical state feature matrices. The steps include: S411. Extract the hierarchical features generated by each spatiotemporal coding layer in the encoder through skip connections. Due to the difference in length of each layer's features on the time axis caused by different dilation rates, this step adopts an end alignment strategy. Using the time dimension of the current deep features as a benchmark, the shallow accumulated features are truncated to the same length, thereby aligning the features of each level in the time dimension. Subsequently, the aligned hierarchical features are accumulated element-wise to fuse multi-scale temporal information and spatial topological features under different receptive fields, generating a global spatiotemporal representation that aggregates historical inertial features. .

[0070] S412. Based on global spatiotemporal representation, spatiotemporal convolution operation is performed through a two-layer cascaded convolutional neural network to output a preliminary prediction sequence based on the historical state feature matrix.

[0071] First layer Convolution represents the global spatiotemporal structure. High-dimensional features are obtained by mapping to a high-dimensional hidden layer space and superimposing ReLU nonlinear activation, thereby enhancing the expressive power of complex nonlinear feature matrices.

[0072] Second floor Convolution projects the high-dimensional features obtained from the first layer onto the target prediction dimension, thereby transforming the extracted deep features into a preliminary prediction sequence based on historical states. .

[0073] ; in, For preliminary sequence prediction, It is an activation function, representing the spatiotemporal representation obtained from jump connections. Perform nonlinear activation. and For two convolution kernels The convolution operation is responsible for linear projection to produce the final output.

[0074] S42. Output the final prediction sequence: Combine gating and bias to perform weighted modulation on the preliminary prediction sequence and output the final prediction sequence of the sintering state.

[0075] Specifically, BiLSTM is used to extract features from the control command feature matrix to generate the future control context feature matrix. And then The input is linearly projected and activated by the Sigmoid function to generate an adjustment gate. By weighting and modulating the initial prediction sequence of S41, the final prediction sequence is output. .

[0076] ; ; in, Represents element-wise product; , The weights are for the linear projection.

[0077] In this preferred embodiment, the parameters of the final predicted sequence are shown in Table 1.

[0078] Table 1 Parameters of the final predicted sequence S43. Model Optimization: Construct a loss function by calculating the error between the final predicted sequence output by the model and the true value matrix, and optimize the model parameters using the backpropagation algorithm.

[0079] The encoder-decoder structure used in this model employs skip connections to fuse feature matrices from different network depths, thereby enriching the granularity of spatiotemporal representation and helping to alleviate the gradient vanishing problem during training.

[0080] S5. Model performance evaluation; The present invention uses mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and weighted percentage error (WAPE) to evaluate the performance of the model.

[0081] Table 2 shows the mean and variance of the performance indicators of the ST-DGFI model provided in this invention in five repeated experiments. The model achieved low errors on the test set (MAE: 134.091, RMSE: 952.791, MAPE: 9.568%, WAPE: 2.669%), and the standard deviations of each indicator were small (MAE standard deviation 0.103, MAPE standard deviation 0.045), indicating that it has stable predictive performance and strong robustness, verifying that the proposed dynamic graph construction and spatial interaction mechanism can effectively reduce the sensitivity to random factors.

[0082] Table 2. Repeated experimental results of the spatiotemporal dynamic graph feature interaction-bidirectional long short-term memory hybrid model As shown in Table 3, the ST-DGFI provided by this invention achieves optimal or near-optimal results in MAE, RMSE, and MAPE, significantly outperforming traditional models such as GCN, LSTM, and Transformer. Compared with graph structure models AGCRN, DGCRN, and GWNet, its error index is also the lowest among all models. This indicates that its dynamic graph construction and hierarchical spatial interaction mechanism can more accurately characterize the dynamic relationships and cross-regional dependencies between nodes, thereby improving prediction accuracy. Although it is slightly lower than LSTM in WAPE, it still has significant advantages in other key indicators, and its overall performance is more robust.

[0083] Table 3 Comparative experimental results of the spatiotemporal dynamic graph feature interaction-bidirectional long short-term memory hybrid model The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction, characterized in that: It includes: S1. Construct an initial sample matrix based on the original time-series data from the pre-processed sintering industrial site; The initial sample matrix includes the historical state feature matrix, the control command feature matrix, and the truth matrix; S2. Extract time features based on the historical state feature matrix and construct a dynamic graph adjacency matrix; S3. Based on the process topology, the temporal features and the adjacency matrix of the dynamic graph are grouped, and intra-group convolution and inter-group cross-convolution are performed sequentially to extract spatiotemporal representations: S31. Generate a hierarchical partitioning tree based on the sintering process; S32. Based on the hierarchical partitioning tree, group the temporal features and the adjacency matrix of the dynamic graph to obtain the local temporal features and the local dynamic graph adjacency matrix: ； ； in, As a time feature, These are local time features, This indicates that all elements in the matrix are in the real number field, B is the number of samples, and N is the number of samples. g1 N g2 Here, DA represents the number of nodes for the local temporal feature, D represents the feature dimension, and DA represents the number of nodes for the local temporal feature. (l) For a dynamic graph adjacency matrix, A 11 A 12 A 21 A 22 These are the adjacency matrices of the local dynamic graph. , The number of nodes in the adjacency matrix of the local dynamic graph; S33. Intra-group convolution: Perform graph convolution operations on the local temporal features and the local dynamic graph adjacency matrix within the group respectively to capture the local spatial dependencies within each process region. S34, Inter-group interactive convolution: Construct a learnable cross-regional adjacency matrix and perform inter-group graph convolution to generate spatiotemporal representations; S4. Predict future parameters based on the spatiotemporal representation and control command feature matrix. The steps include: S41. Based on the historical state feature matrices at different time granularities, generate multiple sets of spatiotemporal representations at the current time granularity, fuse and convolve them, and generate a preliminary prediction sequence based on the historical state feature matrices. ； in, For preliminary sequence prediction, It is an activation function. As a spatiotemporal representation, and For two convolution kernels Convolution operations; S42. Output the final prediction sequence: Combine gating and bias to perform weighted modulation on the preliminary prediction sequence and output the final prediction sequence of the sintering state.

2. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 1, characterized in that: The cross-region adjacency matrix that can be learned in S34 is constructed as follows: S3411. Constructing a cross-regional adjacency matrix: Through graph propagation, the predefined adjacency matrix... Perform symmetric singular value decomposition to generate two learnable node embeddings E3 and E4; extract the latent associations between nodes by calculating the transpose dot product of the two embeddings. Subsequently, the ReLU activation function is introduced to filter out noise and achieve matrix sparsity. Row normalization is then performed using the Softmax function, ultimately generating an adaptive cross-regional adjacency matrix that captures implicit long-range dependencies. : ； Where Softmax(·) is the normalization function, ReLU(·) is the activation function, and E3 and E4 are the learnable node embeddings, respectively. S3412. Group the cross-regional adjacency matrix according to the hierarchical partitioning tree to generate a local cross-regional adjacency matrix; ； Among them, S 11 S 12 S 21 S 22 These are local cross-regional adjacency matrices.

3. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 2, characterized in that: The inter-group graph convolution in S34 specifically includes: S3421. The local temporal features, local dynamic graph adjacency matrix and local cross-region adjacency matrix after grouping are matched one by one, and a learnable linear weighted fusion is performed. The fusion result is normalized row by row to generate a cross-region sub-adjacency matrix. ； in, , These are the cross-regional sub-adjacency matrices, and Softmax(·) is the normalization function. Each parameter is a learnable parameter, and the fusion ratio of the cross-region matrix is ​​learned through model training; S3422. Guided by the cross-regional sub-adjacency matrix, perform inter-group interactive convolution between the local spatial dependency and the cross-regional sub-adjacency matrix to obtain the cross-regional propagation feature matrix. ； in, , These are the cross-regional propagation feature matrices, , These represent local spatial dependencies, and GCN(·) is the convolution function; S3423. Introducing a gating mechanism, a nonlinear mapping is performed between the local spatial dependency obtained in S33 and the cross-regional propagation feature matrix generated in S3422 to obtain a gating vector that controls the flow of information. The fused hierarchical grouped spatiotemporal feature matrix is ​​then output using complementary weighting. : ； ； ； in, , , and For linear mapping weights; It is the sigmoid activation function; S3424, Generating Spatiotemporal Representations: Concatenate the hierarchical grouped spatiotemporal feature matrices from S3423, and generate spatiotemporal representations using the original node order as indices. ； in, For the first Input to the layered spatiotemporal block, This is the spatiotemporal representation of the output of this layer. Concat() is the concatenation operation.

4. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 1, characterized in that: S2 includes: S21. Construct a static adjacency matrix, and determine the weights of the static adjacency matrix. The effective process distance is calculated by combining the equivalent process distance with the Gaussian kernel function; whereby the equivalent process distance is obtained by weighted fusion of the spatial distance between sintering nodes and the process lag time; the weights are... The calculation formula is: ； Where exp(·) is the Gaussian kernel function, For node i, For node j, Represents a node and The equivalent process distance between them; h is the attenuation coefficient, k is the maximum cutoff distance; S22. Extract time features from the historical state feature matrix, perform graph structure learning on the time features, and construct a primary dynamic adjacency matrix. S23. Weighted merge the primary dynamic adjacency matrix and the static adjacency matrix to output the dynamic graph adjacency matrix DA at the current time step. (l) : ； in, This is a primary dynamic adjacency matrix; It is a static adjacency matrix. The weights are adaptive for the model.

5. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 4, characterized in that: S22 includes the following steps: S221. Extracting temporal features: First, map the features of historical nodes into high-dimensional hidden states, and then input the high-dimensional hidden states into a gated temporal causal convolutional network to extract temporal features. ； ； in, This is a high-dimensional hidden state. Let be the historical state feature matrix, and Linear(·) be a linear mapping. For the first Output features of layer-gated dilated causal convolution. The hyperbolic tangent activation function is used. The learnable convolution kernel weights are used for filter branches. The bias of the bias filter branch can be learned for the convolution kernel bias. The collision rate of dilated causal convolution is d. This indicates element-wise multiplication; It is the Sigmoid activation function. , These are the parameters for the gated branch; S222, Generating Dynamic Filters: Temporal features are input through two independent hypernetworks to generate dynamic filters for modulating source node representations. The target node represents a dynamic filter. ; ； in, Represents graph convolution. Represents the parameters that can be learned; S223. Generate static embeddings: Through graph propagation, on a predefined adjacency matrix Perform symmetric singular value decomposition to generate static source node embeddings respectively. Embedded with static target nodes : ； Where l is the dimension of node embedding. The left singular vector matrix of the first d largest singular values ​​of the predefined adjacency matrix; The right singular vector matrix of the first d largest singular values ​​of the predefined adjacency matrix; For the predefined adjacency matrix A diagonal matrix composed of the largest singular values; S224. Generate dynamic embedding: ... , respectively with Element-wise multiplication yields the modulated dynamic embedding. ; ； S225. The dynamically embedded function adjusted in S224 is processed by activation function, and combined with ReLU activation function for nonlinear mapping and denoising to obtain the primary dynamic adjacency matrix. ; ； Where T represents the transpose operation.

6. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 1, characterized in that: S41 includes: S411. Extract hierarchical features generated by each spatiotemporal coding layer in the encoder through skip connections; adopt an end alignment strategy, using the time dimension of the current deep features as a benchmark, and truncate the shallow accumulated features by the same length, thereby aligning the features of each level in the time dimension; subsequently, accumulate the aligned hierarchical features element-wise to fuse multi-scale temporal information and spatial topological features under different receptive fields, generating a global spatiotemporal representation that aggregates historical inertial features. ; S412. Based on the global spatiotemporal feature matrix tensor, spatiotemporal convolution operation is performed through a two-level cascaded convolutional neural network to output a preliminary prediction sequence based on the features of historical state nodes.

7. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 1, characterized in that: The final predicted sequence in S42 is generated by using BiLSTM to extract features from the control command feature matrix to generate the future control context feature matrix. And then The input is linearly projected and activated by the Sigmoid function to generate an adjustment gate. The final prediction sequence is output by weighting and modulating the initial prediction sequence of S41. ; ； ； in, Represents element-wise product; , The weights are for the linear projection.

8. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 1, characterized in that: The historical state feature matrix, control command feature matrix, and truth matrix in S1 are constructed as follows: Historical state feature matrix: time interval extraction All variables within the system characterize the historical dynamic inertia of the system; Control command feature matrix: extracting future intervals The control variable data within the model are used as known external intervention conditions for the model; Truth matrix: extracting the same future interval The state variable data within the model are used as the true values ​​for model training. Where P and Q represent the historical review window length and the future prediction step size, respectively; the state variable is the current operating state data of the system in the original time series data, and the control variable is the predictable human operation or system-set intervention action data in the original time series data.

9. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 1, characterized in that: Preprocessing in S1 refers to cleaning and standardizing the raw time-series data from the sintering industrial site. In S4, a loss function is constructed by calculating the error between the final predicted sequence output by the model and the true value matrix, and the model parameters are optimized by the backpropagation algorithm.

10. The sintering state prediction method based on dynamic graph and topology-aware hierarchical interaction according to claim 1, characterized in that: In step S33, graph convolution operations are performed on the local temporal features and the local dynamic graph adjacency matrix within the group to capture the local spatial dependencies within each process region: 。

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