A top-blown furnace tin smelting multi-target endpoint prediction method based on enhanced time sequence fusion

Abstract

The application discloses a top-blown furnace tin smelting multi-target endpoint prediction method based on enhanced time sequence fusion, and belongs to the technical field of intelligent control of non-ferrous metal smelting process. In order to solve the problem that the tin content in slag, the iron content in stannum and the antimony content in stannum in the reduction smelting process of the oxygen-enriched top-blown furnace are difficult to be accurately predicted simultaneously, the application takes a furnace cycle as a unit, and fuses static characteristics of a furnace condition and variable-length process time sequence data to jointly model; the core is to replace linear transformation in a gating residual network in a time sequence fusion Tansformer main body with a Fourier-KAN layer, so as to construct a model main body with strong non-linear fitting capability and interpretability; a variable selection network, static enrichment, LSTM and an interpretable multi-head attention are cooperated to complete variable-length time sequence modeling; and the three endpoint indexes are jointly optimized by using a weighted Huber loss. The application significantly improves the prediction accuracy and stability of the top-blown furnace tin smelting endpoint indexes, and provides a reliable decision basis for process parameter optimization and closed-loop control.

Description

Technical Field

[0001] This invention relates to the field of intelligent control technology for non-ferrous metal smelting processes, specifically to a multi-objective endpoint prediction method for top-blown furnace tin smelting based on enhanced temporal fusion. Background Technology

[0002] In the top-blown furnace tin refining process, the residual tin content in the slag directly reflects the recovery effect of reduction smelting on metallic tin and is a core indicator for judging whether the furnace condition has reached its endpoint. Meanwhile, the iron and antimony content in the tin-alkaline product jointly determine the quality grade of crude tin and the load of subsequent refining processes, making them critical quality indicators that must be monitored simultaneously. However, these endpoint indicators are usually only obtained through sampling and chemical analysis after the furnace cycle, resulting in a significant feedback lag and making timely intervention difficult. Any deviation can lead to increased defect rates, exacerbated metal loss, and energy waste. If endpoint indicators could be predicted early based on observed process data during the furnace cycle, valuable response time could be provided for process control.

[0003] However, due to the complex smelting reaction mechanism of top-blown furnaces, the coexistence of solid, liquid, and gas phases within the furnace, and the severe coupling between parameters, existing methods for predicting smelting endpoints have the following shortcomings: Traditional mechanistic models rely on detailed thermodynamic and kinetic parameters, making numerous simplified assumptions about the metallurgical reaction, making it difficult to characterize the complex nonlinear characteristics caused by raw material fluctuations, furnace condition drift, lance status changes, and differences in human operation; shallow machine learning methods (such as multiple linear regression, random forest, support vector regression, and XGBoost) often only utilize statistical features or manually summarized features at a few fixed time points, ignoring the temporal structure and stages of the entire furnace process data, making it difficult to fully explore the differential impact of different process stages such as melting and reduction on endpoint indicators; conventional deep time series models (such as naive LSTM, GRU, or pure Transformer regressors) can model long-sequence dependencies, but their ability to capture the widespread diurnal and process cycle, stage-specific abrupt changes, and nonlinear coupling between variables in top-blown furnace processes is limited, and they lack effective variable selection mechanisms and interpretability, making it difficult for process engineers to identify key process influencing factors.

[0004] In existing technologies, the Temporal Fusion Transformer (TFT) combines a variable selection network, a gated residual network (GRN), an LSTM local encoder, and a multi-head attention module to provide a backbone structure with good interpretability for multivariate time series prediction. However, its GRN uses conventional linear layers as feature transformation units, which has limited expressive power and is difficult to fit the strong nonlinearity, segmentation, and strong periodicity of process variables in the top-blown tin refining process. In addition, the original design of TFT is geared towards single-objective or multi-quantile prediction. When jointly modeling multiple endpoint quality indicators with significant differences in dimensions, magnitudes, and fluctuations, it is easy to be dominated by the target with larger values ​​or greater fluctuations if reasonable loss weighting is not applied, affecting the convergence and generalization of other key indicators. Furthermore, in industrial applications, it is often desirable to make early predictions based on observed partial process data before the furnace cycle is completed. This requires the model to be able to robustly handle variable-length sequence inputs with different furnace lengths and different prefix lengths.

[0005] In existing technologies, Kolmogorov-Arnold Networks (KANs) offer a novel network paradigm that replaces fixed activation functions with learnable univariate functions. Their Fourier-based variant (Fourier-KAN) uses a set of sine and cosine basis functions as learnable units, possessing inherent periodic modeling capabilities, strong nonlinear fitting abilities, and relatively smooth optimization characteristics. It is well-suited for characterizing periodic and piecewise nonlinear process variables such as furnace temperature, lance flow rate, oxygen enrichment ratio, fuel quantity, and feed rhythm during top-blown tin refining. However, there are currently no publicly available reports of embedding Fourier-KANs within the GRN of a TFT backbone and systematically applying them to predict endpoint indicators in oxygen-enriched top-blown furnace reduction melting. Summary of the Invention

[0006] To overcome the above-mentioned technical problems, the present invention provides a multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion.

[0007] To achieve the above technology, the specific method is as follows: Using the unique identifier of each furnace as the primary key, the static characteristic table, the process time sequence characteristic table, and the endpoint target table are aligned by an inner join. The endpoint target table includes three indicators: slag tin content, tin-iron content, and tin-antimony content. Next, preprocessing operations are performed on the aligned data and the dataset is divided according to a preset ratio; Construct a Fourier-KAN-enhanced temporal fusion Transformer model; The Fourier-KAN-enhanced temporal fusion Transformer model is trained using the training set, and the model training is performed using the weighted Huber loss function to obtain the optimal model weights. Using the trained model for prediction, a closed-loop design was completed for a multi-objective endpoint prediction method for top-blown furnace tin refining based on Fourier-KAN enhanced temporal fusion Transformer.

[0008] Furthermore, the Fourier-KAN enhanced temporal fusion Transformer model includes: a static encoder, a temporal variable selection network, a temporal projection layer, an LSTM local encoder, a post-LSTM gated residual normalization module, a static enrichment module, a position-by-position gated residual network, an interpretable multi-head attention module, a shared fusion linear projection layer, and multiple independent target output heads; wherein, the linear transformation layers in the gated residual networks within the static encoder, temporal variable selection network, static enrichment module, position-by-position gated residual network, and interpretable multi-head attention module are all replaced with Fourier-KAN units.

[0009] Furthermore, the operation process of the Fourier-KAN unit is as follows: In the formula, LayerNorm(·) is layer normalization; Dropout is random deactivation operation; GLU(·) is gated linear unit; For the second layer Fourier-KAN pair The transformed result is used as the input to the GLU; This is the intermediate result of adding the first layer Fourier-KAN and the context projection, followed by ELU activation; P ( x ELU(·) is the residual shape-fitting linear mapping when the dimensions of the input feature vector and the output vector are equal; ELU(·) is the exponential linear activation function. , and These are three independent Fourier-KAN layers obtained by replacing the first fully connected layer, the context projection layer, and the second fully connected layer in the original GRN; where, when there is no context vector input, This item is not enabled.

[0010] Furthermore, the Fourier-KAN layer operation process is as follows: In the formula, For the input vector of the th One portion, The first of the output vectors One portion, , Indicates the dimension of the output feature vector; and These are the learnable cosine and sine coefficients, respectively. Frequency number; The total number of frequencies; The dimension of the input feature vector.

[0011] Furthermore, the static feature table includes: raw material ratio, furnace condition history, shift, spray gun condition, and raw material batch attributes; The timing characteristic table includes: step number, relative start time, original timestamp, original clock, process stage, as well as furnace temperature, molten pool temperature, top-blown oxygen-enriched flow rate, fuel flow rate, air flow rate, feeding rate, and flue gas temperature.

[0012] Furthermore, the preprocessing operation includes the following methods: For the timing feature table, the step numbers and relative start times are sorted in ascending order; the original timestamp column and the original clock are expanded into day-night cycle features using sin / cos transformation, and then the original columns are deleted; the process stages are encoded into integers for embedded lookup. Remove quality control remarks columns that are irrelevant to quality analysis; First, perform a forward filling operation within the furnace. If the filling is complete, the operation is finished; otherwise, calculate the statistics on the training set and perform a global fallback filling operation.

[0013] Furthermore, in the Fourier-KAN enhanced temporal fusion Transformer model, sequence encoding is performed first, specifically as follows: The static feature data from the preprocessed data is input into the static encoder to obtain the static context vector, static enrichment vector, and the initial hidden state and initial cell state of LSTM. The time-series numerical and categorical features from the preprocessed data are input into a time-series variable selection network. Based on the static context vector, the network expands step-by-step to obtain the weighted fusion feature at each time step. The calculation method is as follows: In the formula, For scoring gated residual networks; For the first Embedding vectors of variables; The total number of variables; For the first The selection weights of each variable; For the first Transform-gated residual networks with independent variables; The weighted fusion features of each time step in the temporal variable selection network are projected onto a preset dimension through a temporal projection layer, where the temporal projection layer is a standard linear projection layer. The hidden states and memory units in the LSTM local encoder are initialized with the initial hidden states and initial cell states of the LSTM, replacing the conventional all-zero initialization; then, according to the effective row mask, the sequence is compressed using a packing operation to remove padding time steps and improve computational efficiency; the LSTM processes the compressed sequence step by step, updating the hidden states and cell states at each step; the output of the LSTM is restored to a fixed-shape temporal tensor using an unpacking operation. The fixed-shape temporal tensor and the projected temporal features are gated and normalized using the post-LSTM gated residual normalization module. The static enrichment module expands the static enrichment vector by copying it to each effective time step to align with the output sequence features of the LSTM-gated residual normalization module. Then, the expanded feature sequence is concatenated with the last dimension of the sequence features output by the aligned LSTM-gated residual normalization module along the channel. The concatenated vector is then input into the gated residual network whose internal linear layer is replaced by a Fourier-KAN layer, and the output is an enriched temporal feature sequence injected with global context information. The location-gated residual network receives the enriched temporal feature sequence, and the input of each time step into the internal linear layer is replaced by a gated residual network with a Fourier-KAN layer. The result is a refined temporal hidden state sequence after the gated residual representation is passed again and the invalid positions are masked and zeroed out.

[0014] Furthermore, the Fourier-KAN-enhanced temporal fusion Transformer model also performs an interpretable multi-head attention aggregation operation, specifically as follows: Extract the last hidden vector from the temporal hidden state sequence and concatenate it with the static context vector. After GRN transformation, it is used as the query vector for the attention mechanism. The entire temporal hidden state is then used as the key and value. If the effective temporal length of a sample is greater than 1, then the last effective temporal step is set to invisible in the attention mask; The application uses an interpretable multi-head attention module, where each head independently computes the query vector and key vector, all heads share the value projection, and the final attention context vector is obtained by averaging the values ​​of all heads. The final attention context vector, static context vector, and hidden vector of the last valid time step are concatenated along the channel dimension and linearly mapped through a shared fusion linear projection layer to obtain a shared hidden representation containing all input information. The shared fusion linear projection layer is a standard linear projection layer.

[0015] Furthermore, the Fourier-KAN enhanced temporal fusion Transformer model uses multiple independent target output heads, each corresponding to the tin content in slag, the iron content in tin-methane, and the antimony content in tin-methane, respectively. Each output head takes a shared hidden representation as input and linearly maps the quantile prediction value of the corresponding target. The result with a quantile of 0.5 is the point prediction.

[0016] Furthermore, in the weighted Huber loss function, the target weight of tin content in slag is set to be greater than the target weights of iron content in tin oxide and antimony content in tin oxide, in order to suppress the risk that this key indicator will be dominated by other targets.

[0017] Beneficial effects of the present invention This invention significantly enhances the model's ability to express periodic and nonlinear process laws in smelting by embedding the Fourier-KAN layer into the gated residual network of the temporal fusion Transformer, breaking through the fitting bottleneck of conventional linear GRN. By combining the variable selection network with interpretable multi-head attention, it can output process variables and time steps that contribute significantly to the prediction in a weighted manner, which helps process engineers understand and utilize the model's decision-making basis and has good interpretability.

[0018] This invention proposes a weighted Huber loss for three tin smelting endpoint indicators, which effectively alleviates the convergence imbalance caused by differences in dimensions, magnitudes, and fluctuations among multiple objectives and improves the prediction stability of small-weight objectives.

[0019] This invention, by strictly dividing the process into batches and combining it with prefix sample expansion and validity masking, enables the model to make early predictions based on partially observed process data before the end of a batch, providing more sufficient response time for process control.

[0020] This invention can directly connect to industrial data pipelines through an end-to-end training and export process, which is convenient for deployment and secondary development, and has good engineering practicality and broad application prospects. Attached Figure Description

[0021] Figure 1 This is a logical concept diagram of the present invention; Figure 2 This is a diagram illustrating the results of an embodiment of the present invention; wherein, Figure 2 (a) indicates the predicted tin content in the slag; Figure 2 (b) A graph showing the predicted iron content of tin; Figure 2 (c) shows the predicted results of the antimony content in tin methyl ester. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to specific embodiments.

[0023] Tin is an important strategic non-ferrous metal, widely used in solders, plating, alloys, and next-generation electronics manufacturing. Large domestic tin smelting enterprises, represented by Yunnan Tin Group, primarily employ an oxygen-enriched top-blown furnace smelting process: using tin concentrate as the main raw material, supplemented with reducing coal, limestone, quartz, and other auxiliary materials, the smelting process involves drying, batching, and feeding the smelting into a top-blown furnace. Oxygen-enriched air and fuel are injected into the molten pool using a top-blown lance, sequentially completing the drying, melting, and reduction reactions to produce crude tin and tin-rich slag. The tin-rich slag is then fed hot into a fuming furnace for further smelting to recover metallic tin. The entire tin smelting chain mainly includes four stages: tin concentrate pre-treatment, top-blown reduction smelting, fuming furnace smelting, and crude tin refining. Among these, the top-blown furnace reduction smelting is the key stage determining the final metal recovery rate, product purity, and energy consumption level.

[0024] Yunnan Tin Industry introduced Ausmelt top-blown smelting technology around 2001. In 2007, it upgraded the original air top-blown technology to oxygen-enriched top-blown technology. In recent years, it has independently developed a high-efficiency molten pool smelting technology for dry powder materials in top-blown furnaces and its core spray gun device. This has enabled the top-blown furnace to achieve a fully enclosed circulation of self-generated flue gas back into the molten pool, significantly reducing overall energy consumption, increasing smelting efficiency by about 5%, and significantly improving the direct tin recovery rate. At the same time, the tin smelting branch has integrated more than 20,000 real-time operation point data from more than 500 production units, from material acceptance, batching, roughing, refining to by-product recovery and flue gas treatment, providing a rich data foundation for data-driven intelligent modeling.

[0025] Taking the reduction smelting process of an oxygen-enriched top-blown furnace (Ausmelt type) at Yunnan Tin Industry as an example, a multi-objective endpoint prediction experiment was conducted. This smelting process is equipped with one oxygen-enriched top-blown furnace, which uses a top-blown nozzle to inject oxygen-enriched air and fuel into the molten pool to complete reactions such as drying, melting, and reduction, producing crude tin and tin-rich slag. The process data acquisition system has integrated more than 20,000 real-time operation data points from over 500 production units, achieving comprehensive digital management from material acceptance, batching, roughing, refining to by-product recovery and flue gas treatment.

[0026] See Figure 1 A multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion includes the following steps: S1. Multi-source data alignment and intra-furnace sorting; Collect three data tables for N historical furnaces, using the furnace_id as the primary key, and perform inner joins to align the furnace static feature table furnace_static_input, the process time series feature table furnace_ts_input_trainable, and the endpoint target table furnace_target_trainable, retaining only the furnaces that appear in all three tables. The static feature table `furnace_static_input` has one line per furnace, recording static variables such as raw material ratio, furnace condition history, shift, spray gun condition, and raw material batch attributes. The time series feature table `furnace_ts_input_trainable` contains several rows for each furnace, recording the step number `step_idx`, the relative start time `minutes_from_start`, the original timestamp `ts_datetime`, the original clock `ts_clock`, the process stage `phase`, and key process variables of the top-blown furnace such as furnace temperature, molten pool temperature, top-blown oxygen enrichment flow rate, fuel flow rate, air flow rate, charging rate, and flue gas temperature. The endpoint target table `furnace_target_trainable` records three indicators for each furnace run: tin content in the slag (`target_fuslag_sn`), iron content in tin (`target_jiaxi_fe`), and antimony content in tin (`target_jiaxi_sb`).

[0027] S2. Based on the sorted data from S1, perform time-series feature preprocessing. The specific steps are as follows: Feature engineering and cleaning: For the time-series feature table `furnace_ts_input_trainable`, the step number `step_idx` and the relative start time `minutes_from_start` are sorted in ascending order to ensure a stable time sequence for the process data of each furnace. The original timestamp column `ts_datetime` and the clock column `ts_clock` are expanded into diurnal cycle features using sin / cos transformations, and then the original columns are deleted. The process stage `phase` is integer-encoded for embedding lookup. Outlier removal: Remove the row_invalid_reason column of quality control notes that is irrelevant to the quality analysis; Missing value handling: First, perform forward filling within the furnace. Then, if there are still missing values, perform global fallback filling using statistics from the training set (such as mean and median).

[0028] S3. Based on the preprocessed data from S2, perform dataset partitioning, standardization, and sample expansion. The specific steps are as follows: Grouping and slicing: Using furnace_id as the unit, the dataset is divided into three parts for training, validation and testing in a ratio of 70% / 15% / 15%; Fitting and Transformation: Use a standardizer (such as Z-score) that fits the numerical features only on the training set, and then apply the fitted standardizer to the validation and test sets to ensure strict group isolation; Prefix sample expansion: Based on the configured truncation ratio, the complete time series of a furnace is expanded into a preset number of prefix sequence samples of different lengths to support early prediction and data augmentation for furnaces that have not yet ended; for example, a 100-step furnace can generate multiple prediction samples for step 10, step 20... up to the end of step 100.

[0029] S4. Based on the sample morphology constructed in S3, a Fourier-KAN enhanced temporal fusion Transformer model is constructed, including: a static encoder (StaticEncoder), a temporal variable selection network (VariableSelectionNetwork), a temporal projection layer, an LSTM local encoder, a post-LSTM gated residual normalization module (GateAddNorm), a static enrichment module, a location-by-location gated residual network, an interpretable multi-head attention module (TemporalAttentionBlock), a shared fusion linear projection layer, and multiple independent target output heads. Among them, the linear transformation layers in the gated residual networks of the static encoder (StaticEncoder), the temporal variable selection network (VariableSelectionNetwork), the static enrichment module, the location-by-location gated residual network, and the interpretable multi-head attention module (TemporalAttentionBlock) are all replaced with Fourier-KAN units. The Fourier-KAN layer uses a set of learnable cosine and sine coefficient tensors as core parameters. It calculates the cosine and sine responses after multiplying the input signal by the frequency vector, and then obtains the output features by summing all frequency components with the input dimension. The expression for the Fourier-KAN unit operation process is as follows: In the formula, , and These are three independent Fourier-KAN layers obtained by replacing the first fully connected layer, the context projection layer, and the second fully connected layer in the original GRN; ELU(·) is the exponential linear activation function, GLU(·) is the gated linear unit, and LayerNorm(·) is the layer normalization function. GLU(·) and LayerNorm(·) maintain the linear gating and layer normalization structure unchanged. Dropout only applies to branches after GLU. P ( x () means that the dimensions of the input feature vector and the output vector are equal. The residual shape is adapted to a linear mapping when ( ), otherwise P ( x ) is an identity mapping; when there is no context vector c as input, The item has been blocked.

[0030] Optionally, the Fourier-KAN layer can be supplemented with linear residual branches and bias terms to the input, giving it both nonlinear expressive power and a robust baseline.

[0031] Therefore, while retaining the original GRN gate-residual-normalization skeleton, FKAN-GRN replaces all conventional linear transformations in the original GRN that would destroy periodicity and strong nonlinearity with Fourier-KAN layers. This significantly enhances the model's ability to express the periodic and piecewise nonlinear features in the top-blown furnace tin refining process variables while maintaining training stability. This is the core improvement of this invention compared to traditional TFT.

[0032] The calculation formula for the gated linear unit (GLU) is as follows: In the formula, W1 and W2 are the weight matrices of the linear mapping and the gated mapping, respectively, and is the sigmoid activation function. For element-wise multiplication, x For input features.

[0033] In this invention, the hidden dimension is set to hidden_size=64, the static hidden dimension is set to static_hidden_size=64, the temporal variable is set to the network hidden dimension to temporal_hidden_size=64, the number of attention heads is set to attention_heads=4, dropout is set to 0.2, the number of LSTM layers is set to lstm_layers=3, the number of targets is set to target_dim=3, the quantile list is set to quantiles=[0.5], and the output head consists of 3 independent linear output heads indexed by target name.

[0034] In this invention, Fourier-KAN uses num_frequencies=8 frequencies as the learnable base, and enables use_bias=true, smooth_initialization=true, input_scale=1.0, and use_linear_residual=false.

[0035] The forward calculation formula for the Fourier-KAN layer is: In the formula, For the input vector of the th One portion, The first of the output vectors One portion, and These are the learnable cosine and sine coefficients, respectively. For frequency serial number, =8 represents the total number of frequencies.

[0036] During initialization, a normal distribution is initialized with the following standard deviation: Then smooth the signal according to the frequency sequence: This results in smaller initial amplitudes for high-frequency components and more stable training.

[0037] S5. Based on the model built in S4, sequence encoding is performed to transform static and time-series data into deep features. Specific operations include: Specifically, the static feature vectors (quantities that do not change over time, such as raw material ratios) from the samples constructed by S3 are input into the static encoder to obtain the static context, the static enrichment vector, and the initial hidden state of the LSTM. Compared with the initial cell state .

[0038] The temporal numeric features (continuous variables such as furnace temperature, flow rate, and feeding rate at each time step) and the temporal categorical features (such as integer encodings of process phases, converted into dense vectors by an embedding layer) are input into the temporal variable selection network. Guided by expanding the context step by step, the network outputs the fused features for each time step. The fused features are linearly projected onto the hidden_size dimension, and then packaged using a validity mask (pack_padded_sequence). An LSTM encoder is used to complete variable-length temporal encoding under the influence of the initial hidden state. Subsequently, the data is unpacked and restored to a fixed-length temporal tensor, as detailed below: Guided by the static context, the weights of each variable at each time step are calculated and the fused features are output. The selection weights and output features of the time-series variable selection network are calculated according to the following formulas: In the formula, For the first Embedding vectors of variables, For scoring gated residual networks, For the first Transform-gated residual networks with independent variables For the first The selection weights of each variable This represents the total number of variables.

[0039] The initial cell state is used to encode the fused variable-length temporal features using LSTM; The temporal projection layer receives the fused features and unifies the dimensions through a standard linear projection layer (nn.Linear, without Fourier-KAN replacement); The LSTM local encoder receives the projected temporal features and passes them through multiple LSTM layers. The hidden state sequence (dimension = hidden_size) is obtained for each time step of the LSTM. The LSTM gated residual normalization module receives the LSTM hidden state sequence and the projected temporal features (as skip connections), and obtains the temporal feature sequence after gating, residual connection and layer normalization through gated linear units and residual connections. The static enrichment module receives the normalized temporal feature sequence, extends the vector to each effective time step, concatenates it with the temporal features, and then feeds it into an FKAN-GRN for transformation to obtain an enriched temporal feature sequence injected with global context information. The location-gated residual network receives the enriched temporal feature sequence, applies an FKAN-GRN independently to each time step, refines the feature representation again through the gated residual structure, and masks invalid positions to zero again to obtain a refined temporal hidden state sequence.

[0040] S6. Based on the temporal hidden state sequence generated in S5, perform an interpretable multi-head attention aggregation operation, specifically including: Extract the hidden vector of the last valid time step from the temporal hidden state sequence, concatenate this vector with the static context vector c generated in step S5, and after GRN transformation, use it as the query vector of the attention mechanism. Then use the entire temporal hidden state as the key and value. If the effective time sequence length of the sample is greater than 1, the last effective time step is made invisible in the attention mask to force the attention mechanism to focus on the historical time step information. The application employs an interpretable multi-head attention module, where each head independently computes the query and key vectors, projects them, and performs attention computation. All heads share the value projection. The final attention context vector is calculated by averaging the attention and output of each head, using the following formula: In the formula, For querying the matrix, The key matrix, For value matrices, Dimensions for each attention head.

[0041] The outputs of each head are averaged to form the final attention context, and the attention weights of each head are averaged to support interpretability analysis.

[0042] The attention context, static context, and hidden vector of the last valid time step are concatenated and linearly mapped through a shared fusion projection layer to obtain a shared hidden representation that condenses all input information. The shared projection layer is a standard linear projection layer (nn.Linear).

[0043] S7. Based on the shared hidden representation generated by S6, independently predict the three endpoint indicators; For the three endpoint quality indicators of slag tin content target_fuslag_sn, tin-iron content target_jiaxi_fe and tin-antimony content target_jiaxi_sb, three independent linear output heads are constructed respectively. Each output head takes the shared hidden representation of S6 as input and linearly maps the quantile prediction value of the corresponding target. The result with a quantile of 0.5 is the point prediction.

[0044] S8. Based on the predicted and actual values ​​from S7, construct a weighted Huber loss function; To address the convergence imbalance caused by differences in dimensions and magnitudes among multiple objectives, a weighted Huber loss is used for joint optimization of multiple objectives. The calculation logic is as follows: Calculate the prediction matrix With the truth matrix Target residual r, , Represents the true value. Indicates the predicted value; For each target, calculate its weighted Huber loss based on its configured Huber inflection point parameters, as shown in the following expression: In the formula, Here are the Huber inflection point parameters; r is the prediction residual. , Represents the true value. Indicates the predicted value; The Huber loss of all targets is weighted and summed according to the preset normalized weights to obtain the final loss, as shown in the following expression: In the formula, Represents the total sample. Index representing the total sample; Indicates the first The normalized weights of the user configuration for each objective are expressed as follows: In the formula, For the first User configuration weights for each target; Indicates the first User configuration weights for each target This represents the sum of all target weights; among them, the target weight of tin content in slag is greater than the target weights of iron content in tin and antimony content in tin, in order to suppress the risk of this key indicator being dominated by other targets; In this invention, target_fuslag_sn has a delta of 1.0 and a weight w1 of 2.0, target_jiaxi_fe has a delta of 0.5 and a weight w2 of 1.0, and target_jiaxi_sb has a delta of 0.5 and a weight w3 of 1.0. After normalization... 1 = 0.5 2 = 0.25 3 = 0.25.

[0045] S9. Based on the loss function defined in S8, implement model training and early stopping strategies. Specific operations include: using the AdamW optimizer to update parameters, combined with gradient pruning to prevent gradient explosion, and using the ReduceLROnPlateau learning rate scheduler to decay the learning rate when performance stagnates; using the root mean square error (RMSE) of the validation set weighted by the target weights as a monitoring metric. If this metric no longer decreases within several consecutive epochs, early stopping is triggered, and the model weights that perform best on the validation set are saved.

[0046] In this invention, the learning rate is 1e -3 Weight decay 1e -2 The gradient pruning threshold is 1.0; the learning rate scheduler uses ReduceLROnPlateau with the following modes: min, decay factor 0.5, patience for 5 epochs, and minimum learning rate 1e. -6Early stopping and optimal model saving are performed using the target weighted validation RMSE as a monitoring metric. The patience is 20 epochs, and the maximum training time is 200 epochs. Here, patience refers to a configuration parameter of the ReduceLROnPlateau learning rate scheduler.

[0047] S10: Based on the best model trained in S9, perform inference and result export. The specific operation is as follows: Load the best model weights saved in S9, perform forward inference once on the test set, predict three endpoint indicators for each prefix sample of each furnace ID, and export the prediction results (including point prediction and quantile prediction) along with furnace ID, prefix truncation ratio and other information to a CSV file for use in process optimization and closed-loop control systems. Interpretability analysis can also be performed based on the output attention weights and variable selection weights.

[0048] See Figure 2 middle Figure 2 (a) Figure 2 (b) and Figure 2 (c) shows the prediction results for three indicators: tin content in slag, iron content in tin-methane, and antimony content in tin-methane. The horizontal axis represents the actual values ​​obtained from laboratory analysis, and the vertical axis represents the predicted values ​​output by the model. Each scatter point represents a sample from a test furnace. Overall, the scatter points in the three subplots are closely distributed, indicating good consistency between the model's predicted and actual values ​​for the three indicators. The scatter points for tin content in slag are the most concentrated, which aligns with the design of assigning the highest weight (0.50) to this indicator in the weighted Huber loss, prioritizing its prediction accuracy. As the furnace process progresses and more time-series data is observed, the predicted points gradually converge towards the diagonal, verifying the model's effective early prediction capability—even in the pre-heat phase before the furnace is finished, it can provide prediction results consistent with the final laboratory value trend, buying valuable adjustment and response time for process engineers.

[0049] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Those skilled in the art can make various modifications and variations to the above embodiments based on the technical concept of the present invention, including but not limited to adjusting the frequency and number of Fourier KAN layers, the hidden dimension, the number of LSTM layers, the number of attention heads, the loss weights and delta parameters, and changing the number and name of targets. All such modifications and variations should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion, characterized in that: Using the unique identifier of each furnace as the primary key, the static characteristic table, the process time sequence characteristic table, and the endpoint target table are aligned by an inner join. The endpoint target table includes three indicators: slag tin content, tin-iron content, and tin-antimony content. Next, preprocessing operations are performed on the aligned data and the dataset is divided according to a preset ratio; Construct a Fourier-KAN-enhanced temporal fusion Transformer model; The Fourier-KAN-enhanced temporal fusion Transformer model is trained using the training set, and the model training is performed using the weighted Huber loss function to obtain the optimal model weights. The trained model is used for prediction to complete the closed-loop design of a multi-objective endpoint prediction method for top-blown furnace tin refining based on Fourier-KAN enhanced temporal fusion Transformer. The Fourier-KAN-enhanced temporal fusion Transformer model includes: a static encoder, a temporal variable selection network, a temporal projection layer, an LSTM local encoder, a post-LSTM gated residual normalization module, a static enrichment module, a position-by-position gated residual network, an interpretable multi-head attention module, a shared fusion linear projection layer, and multiple independent target output heads; wherein, the linear transformation layers in the static encoder, the temporal variable selection network, the static enrichment module, the position-by-position gated residual network, and the gated residual network within the interpretable multi-head attention module are all replaced with Fourier-KAN units; The operation process of the Fourier-KAN unit is as follows: In the formula, LayerNorm(·) is layer normalization; Dropout is random deactivation operation; GLU(·) is gated linear unit; For the second layer Fourier-KAN pair The transformed result is used as the input to the GLU; This is the intermediate result of adding the first layer Fourier-KAN and the context projection, followed by ELU activation; P ( x ELU(·) is the residual shape-fitting linear mapping when the dimensions of the input feature vector and the output vector are equal; ELU(·) is the exponential linear activation function. , and These are three independent Fourier-KAN layers obtained by replacing the first fully connected layer, the context projection layer, and the second fully connected layer in the original GRN, respectively, when there is no context vector. When inputting, Item not enabled; The Fourier-KAN layer operation process is as follows: In the formula, For the input vector of the th One portion, The first of the output vectors One portion, , Indicates the dimension of the output feature vector; and These are the learnable cosine and sine coefficients, respectively. Frequency number; The total number of frequencies; The dimension of the input feature vector.

2. The multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion according to claim 1, characterized in that: The static feature table includes: raw material ratio, furnace condition history, shift, spray gun condition, and raw material batch attributes. The timing characteristic table includes: step number, relative start time, original timestamp, original clock, process stage, as well as furnace temperature, molten pool temperature, top-blown oxygen-enriched flow rate, fuel flow rate, air flow rate, feeding rate, and flue gas temperature.

3. The multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion according to claim 2, characterized in that: The preprocessing operations include the following methods: For the timing feature table, the step numbers and relative start times are sorted in ascending order; the original timestamp column and the original clock are expanded into day-night cycle features using sin / cos transformation, and then the original columns are deleted; the process stages are encoded into integers for embedded lookup. Remove quality control remarks columns that are irrelevant to quality analysis; First, perform a forward filling operation within the furnace. If the filling is complete, the operation is finished; otherwise, calculate the statistics on the training set and perform a global fallback filling operation.

4. The multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion according to claim 3, characterized in that: In the Fourier-KAN enhanced temporal fusion Transformer model, sequence encoding is performed first, specifically as follows: The static feature data from the preprocessed data is input into the static encoder to obtain the static context vector, static enrichment vector, and the initial hidden state and initial cell state of LSTM. The time-series numerical and categorical features from the preprocessed data are input into a time-series variable selection network. Based on the static context vector, the network expands step-by-step to obtain the weighted fusion feature at each time step. The calculation method is as follows: In the formula, For scoring gated residual networks; For the first Embedding vectors of variables; The total number of variables; For the first The selection weights of each variable; For the first Transform-gated residual networks with independent variables; The weighted fusion features of each time step in the temporal variable selection network are projected onto a preset dimension through a temporal projection layer, where the temporal projection layer is a standard linear projection layer. The hidden states and memory units in the LSTM local encoder are initialized with the initial hidden states and initial cell states of the LSTM, replacing the conventional all-zero initialization; then, according to the effective row mask, the sequence is compressed using a packing operation to remove padding time steps and improve computational efficiency; the LSTM processes the compressed sequence step by step, updating the hidden states and cell states at each step; the output of the LSTM is restored to a fixed-shape temporal tensor using an unpacking operation. The fixed-shape temporal tensor and the projected temporal features are gated and normalized using the post-LSTM gated residual normalization module. The static enrichment module expands the output sequence features of the LSTM-gated residual normalization module by copying the static enrichment vector to each effective time step. The expanded feature sequence is then concatenated along the channel with the last dimension of the sequence features output by the aligned LSTM gated residual normalization module; the concatenated vector is then input into the gated residual network whose internal linear layer is replaced by a Fourier-KAN layer, and the output is an enriched temporal feature sequence injected with global context information. The location-gated residual network receives the enriched temporal feature sequence, and the input of each time step into the internal linear layer is replaced by a gated residual network with a Fourier-KAN layer. The result is a refined temporal hidden state sequence after the gated residual representation is passed again and the invalid positions are masked and zeroed out.

5. The multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion according to claim 4, characterized in that: The Fourier-KAN-enhanced temporal fusion Transformer model also performs an interpretable multi-head attention aggregation operation, specifically as follows: Extract the last hidden vector from the temporal hidden state sequence and concatenate it with the static context vector. After GRN transformation, it is used as the query vector for the attention mechanism. The entire temporal hidden state is then used as the key and value. If the effective temporal length of a sample is greater than 1, then the last effective temporal step is set to invisible in the attention mask; The application uses an interpretable multi-head attention module, where each head independently computes the query vector and key vector, all heads share the value projection, and the final attention context vector is obtained by averaging the values ​​of all heads. The final attention context vector, static context vector, and hidden vector of the last valid time step are concatenated along the channel dimension and linearly mapped through a shared fusion linear projection layer to obtain a shared hidden representation containing all input information. The shared fusion linear projection layer is a standard linear projection layer.

6. The multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion according to claim 5, characterized in that: The Fourier-KAN enhanced temporal fusion Transformer model uses multiple independent target output heads, each corresponding to the tin content in slag, the iron content in tin-methane, and the antimony content in tin-methane, respectively. Each output head takes a shared hidden representation as input and linearly maps the quantile prediction value of the corresponding target. The result with a quantile of 0.5 is the point prediction.

7. The multi-objective endpoint prediction method for top-blown furnace tin refining based on enhanced temporal fusion according to claim 6, characterized in that: In the weighted Huber loss function, the target weight of tin content in slag is set to be greater than the target weights of iron content in tin and antimony content in tin, in order to suppress the risk that this key indicator will be dominated by other targets.

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