A sintering endpoint prediction method based on dual adversarial graph domain adaptation

Abstract

The application discloses a sintering endpoint prediction method based on double adversarial graph domain adaptation, and belongs to the field of industrial process soft measurement modeling. First, a 3D adjacency matrix is constructed by using a difference coefficient, and a selective weighted aggregator is used to update a node feature representation. Then, a domain discriminator is used to align the feature distribution of a source domain and a target domain, so that common features between the domains are learned. Next, a domain confusion module is constructed, and a maximum information entropy method is used to confuse the joint features of the source domain and the target domain, so that double adversarial is formed with the domain discriminator, and domain-invariant features are promoted to be learned by the model. Finally, a trained 3D graph network feature extractor and a multi-step prediction model are used to predict test data. The method realizes multi-step prediction of the sintering endpoint under different working conditions. Compared with other models on real sintering data, the model of the application has high accuracy, and the multi-step prediction performance of the sintering endpoint is improved.

Description

Technical Field

[0001] This invention pertains to soft measurement methods for key performance indicators in the process industry, specifically involving a sintering endpoint prediction method based on adaptive dual adversarial graph domain. Background Technology

[0002] The sintering process of iron ore is one of the most important preliminary processes in blast furnace ironmaking and is key to improving the quality and efficiency of blast furnace ironmaking. Furthermore, the energy consumption of the sintering process accounts for more than 10% of the entire ironmaking process, making it one of the most energy-intensive stages. Therefore, research on the sintering process will help the steel industry improve production quality, increase output, and reduce energy consumption. Achieving intelligent sintering is one of the key aspects of the steel industry's transformation and upgrading.

[0003] The burn-through point (BTP) is a crucial indicator of the sintering state, representing the point at which the sinter is burned through on the sintering trolley. It is commonly used to determine whether the sintering process is operating normally. An advanced BTP indicates over-burning, meaning the sintering bellows are not fully utilized, resulting in resource waste and reduced output. Conversely, a delayed BTP indicates under-burning, leading to low yield, increased return rate, and decreased sinter quality. Therefore, a stable BTP ensures stable operation of sintering production, enabling efficient energy utilization while improving sinter output and quality. However, due to the harsh environment at the sintering site—high temperature, high humidity, and high dust levels—most sensors malfunction, preventing direct measurement of BTP. BTP is typically obtained through soft sensing, and predicting future BTP provides production guidance for the sintering process. Therefore, real-time and accurate prediction of the burn-through point is beneficial for maintaining stable sintering operation, significantly improving sinter output and quality, and reducing energy consumption.

[0004] Gao et al. first proposed a modified method for calculating the sintering endpoint based on the standard value of flue gas temperature and the classic bellows flue gas temperature fitting method. Then, considering the strong nonlinearity and large time delay characteristics of the sintering process, they proposed a nonlinear autoregressive moving average model (NARMAX) to predict the sintering endpoint. Wang et al. proposed a new time series prediction method for intelligent sensing of the sintering endpoint using wavelet analysis and Elman neural networks. Simulation results show that the proposed method improves prediction accuracy and has significant theoretical and engineering application value. Liu et al. developed a sintering endpoint prediction system using the gradient boosting decision tree model (GBDT) and decision rules. In fact, the sintering process involves multiple operating conditions, making it difficult for a single model to fit data with different distributions. To address this problem, Cao et al. first analyzed the influencing factors leading to multiple operating conditions and then constructed an improved Takagi-Sugeno (TS) fuzzy model to explain how different operating conditions change the system dynamics. Du et al., to reduce the impact of data distribution differences, used fuzzy mean clustering to divide different operating conditions and proposed a hybrid time series model for predicting the sintering endpoint.

[0005] Analysis of the multi-step prediction problem of the sintering endpoint reveals two main challenges: (1) Due to fluctuations in raw materials and changes in operating parameters, the sintering process exhibits multiple operating conditions, resulting in significant differences in data distribution under each condition. These differences violate the independent and identically distributed assumption, meaning that conventional deep learning models, once trained under one condition, often fail to perform well under another. (2) The number of effective samples in the sintering process is scarce, preventing the training data from covering all conditions. Consequently, the model exhibits poor generalization under different conditions, necessitating cross-condition domain adaptive research. Summary of the Invention

[0006] This invention addresses the problem of poor generalization performance in predicting the sintering endpoint across different operating conditions during sintering. It proposes a multi-step prediction method for the sintering endpoint based on dual adversarial graph domain adaptation. The goal of this method is to reduce distribution differences between different operating conditions and learn common features across these conditions. The method mainly includes the following four steps: First, a 3D graph network is constructed to extract features from the source and target domains respectively. Then, a domain discriminator is established using fully connected layers to distinguish whether sample features originate from the source or target domain. Subsequently, a domain confusion module is proposed, which further confuses the source and target domain features by maximizing the information entropy through the calculation of the dynamic information encoding entropy of the joint features. Finally, the binary cross-entropy function of the domain discriminator and the information entropy function of the domain confusion module are embedded into the loss function, enabling the network to learn common features of the source and target domains. A predictor is constructed using a long short-term memory network, and the source domain features are input into the predictor to achieve multi-step prediction of the sintering endpoint. The invented method has been validated using real data from an actual sintering plant, and the results show that this method has higher accuracy than other methods.

[0007] This invention is achieved using the following technical solution:

[0008] 1) Select two historical data sets under different operating conditions, determine the auxiliary variables related to the sintering endpoint, and construct the source domain dataset and the target domain dataset using the sliding window method;

[0009] 2) Construct a 3D adjacency matrix using the temporal difference method, and use a selective weighted aggregator to build a 3D graph neural network to extract features from the source and target domains respectively;

[0010] 3) Construct a neighborhood discriminator using the cross-entropy loss function to determine whether the extracted features come from the source domain or the target domain, thereby achieving the goal of aligning feature distributions;

[0011] 4) Construct a domain obfuscation module and use the method of maximizing dynamic information entropy to obfuscate the features of the source domain and the target domain. The domain obfuscation module and the domain discriminator form a dual adversarial relationship to fully learn the common features under different working conditions.

[0012] 5) Construct a predictor using a long short-term memory network and input source domain features into the predictor to achieve multi-step prediction of the sintering endpoint; construct a joint loss function; a dual adversarial graph domain adaptive model is composed of a 3D graph neural network, a domain discriminator, a domain confusion module, and the predictor, and the model is trained using historical data;

[0013] 6) Deploy the trained dual adversarial graph domain adaptive model to the actual sintering site to perform multi-step prediction of the sintering endpoint.

[0014] The beneficial effects of this invention are as follows:

[0015] 1. This invention utilizes an adversarial domain adaptive strategy to construct a multi-step prediction model for sintering endpoints across various working conditions. Previous multi-step prediction models for sintering endpoints assumed that the training and test sets came from the same working condition and followed the independent and identically distributed assumption. However, in actual sintering processes, multiple working conditions often exist, leading to significant differences in the distribution of the dataset and reducing the model's predictive performance. This invention combines graph neural networks and adversarial domain adaptive learning methods, proposing a dual adversarial graph domain adaptive method to achieve multi-step prediction of sintering endpoints across various working conditions. This model exhibits better generalization ability in actual sintering processes.

[0016] 2. This invention uses a 3D graph neural network to extract the coupling between variables across time scales during the sintering process. Previous studies only considered the coupling between variables at the same moment, neglecting the coupling between variables at different moments. This invention uses a 3D graph network to fully consider the spatial characteristics across time during the sintering process, and uses a 3D adjacency matrix to represent the interrelationship of variables at different moments, which can realistically capture the strong dynamics of the sintering process.

[0017] 3. The dual-adversarial mechanism proposed in this invention can fully extract general features under different operating conditions. Previous studies often used a single-domain discriminator to distinguish whether sample features came from the source domain or the target domain, which could not effectively extract domain-invariant features. This invention, from the perspective of information entropy, utilizes a dynamic information entropy encoding loss function to further obfuscate the joint features of the source and target domains, forming a dual-adversarial relationship with the discriminator. This enables the model to solve the data drift problem across operating conditions and improves the prediction accuracy of the sintering endpoint. This method can provide a multi-step prediction approach for key indicators in other industrial processes under different operating conditions, thereby improving industrial production efficiency. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of a multi-step prediction method for sintering endpoint based on adaptive dual adversarial graph domain.

[0019] Figure 2 A diagram comparing the prediction results of different models;

[0020] Figure 3 Schematic diagram of the probability density distribution of prediction errors for different models;

[0021] Figure 4 Schematic diagram of the original feature distribution and the feature distribution after migration;

[0022] Figure 5 A diagram showing the comparison of model prediction performance under different input and output step sizes. Detailed Implementation

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not limit it in any way.

[0024] Some of the terms or terms that appear in the description of the embodiments of this application shall be interpreted as follows:

[0025] Different operating conditions: These refer to the different operating conditions of the sintering process caused by changes in raw material composition and operating parameters. For example, a sintering plant typically changes its raw materials weekly, resulting in a change in the sintering raw materials and thus altering the operating conditions.

[0026] Sliding window: refers to the operation of using a time window of length T to slide across the original time series to form a series of time segments.

[0027] 3D Graph Neural Network: refers to a graph neural network whose adjacency matrix contains three dimensions, mainly used to extract the relationship between variables at different times.

[0028] Figure 1 The steps of a multi-step prediction method for sintering endpoint based on dual adversarial graph domain adaptation are provided, specifically including:

[0029] 1) Select two different operating conditions, determine the auxiliary variables related to the sintering endpoint, and construct time segments using the sliding window method. Each time segment is treated as a sample, and all samples from one operating condition constitute the source domain dataset X. s The dataset X consists of all samples from another operating condition. t ;

[0030] The auxiliary variables selected in this invention are process parameters related to the sintering process, specifically including five categories: raw material parameters, operating parameters, equipment parameters, state parameters, and index parameters. Preferably, in this embodiment, 12 auxiliary variables are selected, namely: neutralized ore-fuel ratio, quicklime ratio, blended ore ratio, lightly calcined ore ratio, return ore ratio, trolley speed, material layer thickness, ignition temperature, main flue negative pressure, main exhaust air volume, annular cooler temperature, and BRP (Burn Rising Point, the position where the preheating layer temperature rises the fastest).

[0031] 2) The auxiliary variables are used as nodes in the 3D graph neural network (in this embodiment, 12 auxiliary variables correspond to 12 nodes, each node forms a vector in a continuous time period, and the 12 nodes are combined to form the input features of the model, which are used to calculate the adjacency matrix). Then, the 3D adjacency matrix is ​​constructed using the temporal difference method, and a selective weighted aggregator is used to build a 3D graph neural network to extract features from the source domain and the target domain respectively.

[0032] The 3D adjacency matrix is ​​constructed as follows: Assume v i,t-k v represents the feature representation of the i-th node at time tk. j,k Let A represent the feature representation of the j-th node at time t, and k represent the time difference coefficients. Then, the 3D adjacency matrix A... i,j,k The calculation formula is as follows:

[0033]

[0034] Among them, dist(v i,t-k -v j,k ) 2 Represents different times v i,t-k and v j,k The Euclidean distance between them, δ is a hyperparameter, exp is the exponential function, softmax is the normalization function, ReLU is the activation function, and E i , Let represent the learnable weight matrices of the i-th node and the j-th node, respectively;

[0035] The steps for constructing a 3D graph neural network using a selective weighted aggregator to extract features from the source and target domains are as follows: assuming This represents the feature representation of the neighboring node w of node v in the l-th layer of a 3D graph neural network. Let v represent the message received by node v at layer (l+1). Let AGG represent the message aggregation function, and MLP represent the feedforward neural network (a submodule of a graph neural network) used to aggregate information from different neighboring nodes. This represents the set of neighboring nodes of node v.

[0036]

[0037]

[0038] Where A[v,:,:] represents the adjacency matrix of node v, C represents the set of random Bernoulli variables, and c k w represents the probability of the k-th time difference coefficient. k The weights are learnable, k = 1, 2, ..., K, where K is the maximum order of the time difference coefficients, and Bernoulli represents the Bernoulli distribution.

[0039] The features of node v in layer (l+1) are calculated as follows:

[0040]

[0041] Where UPDATE represents the update function, σ represents the sigmoid activation function, and W u and b uThis represents the learnable weight matrix. Generally, a 3D graph neural network only needs two layers; the 3D graph neural network in this embodiment also uses two layers. As a supplementary explanation, this invention uses the source domain dataset X... s and target domain dataset X t The feature extraction process is exactly the same; that is, the method of this invention can be understood as containing two identical 3D graph neural networks, one of which is used for the source domain branch (the input is the source domain dataset X). s The features extracted from the (l+1)th layer node v are the source domain features, and another feature is used for the target domain branch (the input is the target domain dataset X). t The features of the (l+1)th layer node v extracted are the features of the target domain.

[0042] 3) Construct a neighborhood discriminator using the cross-entropy loss function to determine whether the extracted features originate from the source or target domain, thereby aligning feature distributions. Assume F... s and F t These represent 3D graph neural networks in the source and target domains, respectively. The function of these 3D graph neural networks is feature extraction. and Let L represent the features extracted from the source and target domains, respectively. The domain discriminator consists of two fully connected layers and its purpose is to distinguish whether sample features come from the source or target domain. Correspondingly, the discriminator's output is either 0 or 1, making it a binary classification problem. Therefore, the cross-entropy loss function is used as the domain adversarial loss L. ADV :

[0043]

[0044] in, and Let i represent the samples in the source and target domains, respectively. Let i be the sample number, log represent the logarithmic function, N represent the number of samples, and D represent the neighborhood discriminator.

[0045] 4) Construct a domain obfuscation module and use the method of maximizing dynamic information entropy to obfuscate the features of the source domain and the target domain. The domain obfuscation module and the domain discriminator form a dual adversarial relationship to fully learn the common features under different working conditions.

[0046] The process of obfuscating the features of the source and target domains using the method of maximizing dynamic information entropy is as follows:

[0047] Assume Z s and Z t Representing source and target domain features respectively, a fully connected network is used to project the original features into a 2D space, obtaining new feature representations. and and To capture dynamic information, this invention designs a time encoding function ψ(u) to construct dynamic features, where:

[0048] ψ(u)=[cos(u1θ1),sin(u2θ2),...,cos(u m-1 θ m-1 ),sin(u m θ m (6)

[0049] Where u i and θ i Let u and u represent the i-th feature representation and its corresponding learnable parameters, respectively. u is the independent variable of the temporal encoding function, which is determined by a series of u1, u2, ..., u... m The set formed by i = 1, 2, ..., m, where m is the number of nodes, i.e., the number of auxiliary variables; then, the dynamic characteristics and It can be written as:

[0050]

[0051] in, and ψ represents the dynamic characteristics of the source and target domains, respectively. s (u s ) and ψ t (u t ) represent the time coding functions of the source domain and the target domain, respectively, u s and u t Let u represent the sets of the source domain and the target domain, respectively. Then, the dynamic information encoding entropy L that maximizes the features of the source and target domains is... DMEC for:

[0052]

[0053] Where det represents the determinant, I N Let represent the identity matrix, and ∈ be a hyperparameter. To reduce computational complexity, the above equation can be simplified using a Taylor expansion:

[0054]

[0055] Where, trace represents the trace of the matrix. P L represents the order of the Taylor expansion, where P is the maximum order of the Taylor expansion. DCM This represents the domain confusion loss function.

[0056] 5) A predictor is constructed using a Long Short-Term Memory (LSTM) network, and source domain features are input into the predictor to achieve multi-step prediction of the sintering endpoint. A joint loss function is constructed based on the prediction loss function, cross-entropy loss function, and maximum entropy loss function. A dual adversarial graph domain adaptive network model is formed by combining a 3D graph neural network, a domain discriminator, a domain confusion module, and the predictor, and historical data is used to train the dual adversarial graph domain adaptive model. Joint Loss Function It consists of three parts: the prediction loss function L MSE Domain confrontation loss L ADV Domain confusion loss function L DCM First, a predictor is constructed using a Long Short-Term Memory network and a fully connected layer. Features from the source domain are then input into the predictor to obtain predicted values ​​for the source domain. The mean squared error is used to calculate the predicted value and the true value y. t The difference is used to obtain the prediction loss function L. MSE :

[0057]

[0058] Among them, T f This indicates the predicted output step size. Joint loss function. The calculation is as follows:

[0059]

[0060] Here, λ1 and λ2 are two balancing factors. Finally, stochastic gradient descent is used to optimize and update the parameters of the entire model.

[0061] 6) Deploy the trained dual adversarial graph domain adaptive model to the actual sintering site to perform multi-step prediction of the sintering endpoint.

[0062] In this embodiment, to verify the accuracy of the method, the constructed dual adversarial graph domain adaptive network model was trained using real data from a sintering plant, and the trained model was deployed to the actual industrial site for multi-step prediction of the sintering endpoint.

[0063] The present invention will be further explained below with reference to specific examples.

[0064] (1) Determination of auxiliary variables and calculation of sintering endpoint

[0065] The sintering process can be summarized as follows: iron ore is mixed with quicklime, coke powder, coal powder, and recycled ore in a certain proportion, and then heated at high temperature in a sintering machine. The powder is melted into blocks, and after cooling, it is transformed into a blocky solid, ultimately forming sinter that meets the requirements of raw materials for blast furnace. In this process, the iron ore undergoes complex physicochemical reactions, roughly including six steps: batching, mixing, feeding, ignition, screening, and cooling. The process parameters generated during sintering include five categories: raw material parameters, operating parameters, equipment parameters, state parameters, and index parameters. In this embodiment, based on the experience of on-site workers, mechanism analysis, and experimental tests, 12 auxiliary variables related to determining the sintering endpoint were selected. These auxiliary variables form a 12-dimensional vector as the input parameters of the prediction model constructed in this invention, as shown in Table 1. The 12 auxiliary variables are: neutralized ore to fuel ratio, quicklime ratio, mixed ore ratio, lightly burned ore ratio, recycled ore ratio, trolley speed, bed thickness, ignition temperature, main flue negative pressure, main exhaust air volume, annular cooler temperature, and BRP. BRP refers to the position where the temperature rises fastest in the preheating layer. BTP is the sintering endpoint, calculated using the exhaust gas temperature fitting method.

[0066]

[0067] (2) Multi-condition analysis of sintering process

[0068] The sintering process relies heavily on worker operation, and the raw material composition and operating parameters are constantly changing, resulting in dynamic operating conditions. For example, sintering plants typically change raw materials weekly. Changes in raw materials alter the physicochemical reactions, leading to variations in the sintering endpoint. The changing day and night shifts of workers also affect operating parameters, such as trolley speed, thus altering the sintering endpoint. Similarly, the distribution of auxiliary variables changes under different operating conditions, resulting in data distribution drift. Traditional deep learning requires the assumption of identically distributed (ISD) data, meaning the training and test sets have the same data distribution. However, with changes in operating conditions, the training and test sets often come from different environments, leading to data distribution discrepancies that violate the ISD assumption and significantly reduce the model's predictive performance. Domain adaptation is an important research method in transfer learning, addressing the impact of data distribution differences under different operating conditions. Therefore, this invention utilizes domain adaptation to predict the sintering endpoint under different operating conditions, employing an adversarial mechanism to align the data distributions of the source and target domains and learning domain-invariant features.

[0069] (3) Dataset construction and experimental setup

[0070] To verify the predictive performance of this method, real data was obtained from a bag sintering machine in a sintering plant in South China. Data from October 10th to October 20th, 2023 was selected as the training set (source domain), and data from October 20th to October 30th, 2023 was selected as the test set (target domain). After data preprocessing and sliding window partitioning, the source domain had 5000 data samples, and the target domain had 1500 samples. The model results were evaluated using the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 These three evaluation indicators are used to measure, among which, Represents the predicted value, y (i) This represents the true value; the evaluation metric for all models is the average of 10 results.

[0071]

[0072] (4) Offline model building and comparison

[0073] To compare the superiority of the dual adversarial graph domain adaptation method (DAGDA) proposed in this invention, three typical deep learning methods and five domain adaptation methods were selected for comparison, including: Long Short-Term Memory Network (LSTM)[1], Sequence to Sequence Model (Seq2Seq)[2], Denoising Spatiotemporal Coding and Decoding Network (DSTED)[3] and Correlation Alignment Adaptation Method (Coral-LSTM)[4], Transfer Component Analysis Method (TCA-LSTM)[5] and Deep Adaptive Domain Adaptation Method (DANN-LSTM)[6], Adaptive Domain Adaptation Method (ADARUL)[7] and Contrastive Adversarial Domain Adaptation (CADA)[8]. The corresponding references for each method are as follows:

[0074] [1]S.Hochreiter and J.Schmidhuber, "Long short-term memory," NeuralComputation, vol.9, no.8, pp.1735–1780, 1997.

[0075] [2] J.Chung, C.Gulcehre, K.Cho, and Y.Bengio, "Empirical evaluation of gated recurrent neural networks on sequence modeling," in NIPS2014Workshop onDeep Learning, December 2014, 2014.

[0076] [3]F.Yan,C.Yang,and X.Zhang,“DSTED:Adenoising spatial–temporalencoder–decoder framework for multistep prediction of burn-through point insintering process,”IEEE Transactions on Industrial Electronics,vol.69,no.10,pp.10 735–10744,2022

[0077] [4]W.Mao,J.He,and M.J.Zuo,“Predicting remaining useful life ofrolling bearings based on deep feature representation and transfer learning,”IEEE Transactions on Instrumentation and Measurement,vol.69,no.4,pp.1594–1608,2019

[0078] [5]B.Sun and K.Saenko,“Deep coral:Correlation alignment for deepdomain adaptation,”in Computer Vision–ECCV 2016Workshops:Amsterdam,TheNetherlands,October 8-10and 15-16,2016,Proceedings,Part III 14.Springer,2016,pp.443–450.

[0079] [6]P.R.d.O.da Costa,A.Akc,ay,Y.Zhang,and U.Kaymak,“Remaining usefullifetime prediction via deep domain adaptation,”Reliability Engineering&System Safety,vol.195,p.106682,2020.

[0080] [7] M.Ragab, Z.Chen, M.Wu, CKKwoh, and X.Li, "Adversarial transferlearning for machine remaining useful life prediction," in 2020IEEEInternational Conference on Prognostics and Health Management (ICPHM). IEEE, 2020, pp.1–7.

[0081] [8]M.Ragab,Z.Chen,M.Wu,CSFoo,CKKwoh,R.Yan,and

[0082] Table 2 compares the results of different prediction models, with the bolded version representing the performance of the proposed DAGDA method. As can be seen from Table 2, the proposed DAGDA method achieves the highest accuracy and lowest error, with RMSE, MAE, and R0 being the lowest. 2The values ​​are 0.8800, 0.6743, and 81.12%, respectively. Overall, it can be seen that the three conventional deep learning methods perform worse than the domain-adaptive methods because the former cannot address the problem of data distribution differences and lacks good generalization performance. The table shows that the Seq2Seq method performs better than the LSTM method because LSTM cannot capture long-term dependencies, while the Seq2Seq model is better at long-term prediction. However, industrial data generally contains random noise, and the DSTED model uses a noise reduction gate to mitigate noise interference, greatly improving the model's robustness. Among the domain-adaptive methods, TCA-LSTM achieves better results than Coral-LSTM because the TCA method reduces the distance between the source and target domains through the maximum mean difference. The maximum mean difference is a method for measuring the distance between two distributions, based on a mapping function in the reproducing Hilbert space. The Coral-LSTM method mainly uses second-order statistics to measure distribution differences. For regression prediction problems, the maximum mean difference better characterizes the distribution distance, thus TCA achieves ideal results. However, both of these methods are shallow distribution adaptations and do not align deep features. DANN-LSTM uses deep network feature alignment, improving the transfer learning effect. The other two adversarial domain adaptation methods, ADARUL and CADA, do not employ a dual adversarial mechanism, resulting in lower prediction performance than DAGDA. To intuitively reflect the fitting between predicted and true values, Figure 2 The top four best-performing models are visualized, showing that the proposed DAGDA model achieves the best fit. To compare the prediction errors of the four models, Figure 3 The probability distribution of their prediction errors is provided, and it can be seen that the prediction errors of the proposed DAGDA method are mostly concentrated between -1 and 1, which also proves the effectiveness and feasibility of the proposed method.

[0083] The DAGDA proposed in this invention utilizes a dual adversarial mechanism to extract common features from both the source and target domains, thereby improving the model's predictive performance. Therefore, the DAGDA proposed in this invention surpasses all other comparative models, significantly improving the accuracy of drum intensity. To enhance the interpretability of the DAGDA model, this invention visualizes the feature distribution before and after the transfer, such as... Figure 4 As shown, comparing the original feature distribution and the transferred feature distribution reveals a significant difference in feature distribution between the original and transferred features. This difference is significantly reduced after the transfer, indicating that the adversarial mechanism narrows the distribution distance between the source and target domains, validating the model's good transfer performance. Furthermore, Figure 5 (a) and (b) in the paper discuss the changes in model prediction performance with different input and output step sizes, respectively. Figure 5As shown in (a), the model's accuracy initially increases and then decreases with increasing input step size. This is because increasing the input step size provides more historical information, but excessive input information can also negatively impact the model. Through repeated experiments, it was found that the model's prediction error is lowest when the input step size is 40. Figure 5 As can be seen from (b) in the figure, the performance of the model gradually decreases as the output step size increases, because an excessively long output step size will bring more randomness and reduce the predictive performance of the model.

[0084] Table 2 Comparison of Model Prediction Results

[0085]

[0086]

[0087] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A sintering endpoint prediction method based on dual adversarial graph domain adaptation, characterized in that, Includes the following steps: 1) Select two historical data sets under different operating conditions, determine the auxiliary variables related to the sintering endpoint, and construct the source domain dataset and the target domain dataset using the sliding window method; Auxiliary variables include: neutralized ore fuel ratio, quicklime ratio, blended ore ratio, lightly burned ore ratio, return ore ratio, bogie speed, bed thickness, ignition temperature, main flue negative pressure, main exhaust volume, annular cooler temperature, and BRP; 2) Construct a 3D adjacency matrix using the temporal difference method, and use a selective weighted aggregator to build a 3D graph neural network to extract features from the source and target domains respectively; The auxiliary variables are used as nodes in a 3D graph neural network, and a 3D adjacency matrix is ​​constructed using a temporal difference method, as detailed below: Assumption Representing the The node at the th The characteristics of time, Representing the The node at the th The characteristics of time, Representing the time difference coefficients, the 3D adjacency matrix... The calculation formula is as follows: （1） in, Indicates different times and The Euclidean distance between them It's a hyperparameter. It is an exponential function. It is a normalization function. It is an activation function. They represent the first The node and the first 3) Construct a domain discriminant using the cross-entropy loss function to determine whether the extracted features come from the source domain or the target domain, thereby achieving the purpose of aligning feature distributions. 4) Construct a domain obfuscation module and use the method of maximizing dynamic information entropy to obfuscate the features of the source domain and the target domain. The domain obfuscation module and the domain discriminator form a dual adversarial relationship to fully learn the common features under different working conditions. The method of maximizing dynamic information entropy to confuse the features of the source and target domains includes the following steps: Assumption and Representing the source and target domain features respectively, a fully connected network layer is used to project the original features into a 2D space to obtain new feature representations. and ; and To capture dynamic information from static features, a time encoding function was designed. To construct dynamic features: （6） in and Distribution representation of the first Each feature representation and its corresponding learnable parameters Refer to , ,…, Given a set consisting of m nodes, then the dynamic characteristics of the source and target domains are... and Written as: （7） and These represent the time coding functions for the source and target domains, respectively. and The sets representing the source domain and the target domain, respectively. ; Therefore, the dynamic information encoding entropy that maximizes the features of the source and target domains is obtained. for: （8） in, Represents a determinant. Represents the identity matrix. These are hyperparameters; simplifying the above equation using Taylor expansion, we get: （9） Where, trace represents the trace of the matrix. P represents the order of the Taylor expansion, where P is the maximum order of the Taylor expansion. Indicates the domain confusion loss function; 5) Construct a predictor using a long short-term memory network and input source domain features into the predictor to achieve multi-step prediction of the sintering endpoint; construct a joint loss function; a dual adversarial graph domain adaptive model is composed of a 3D graph neural network, a domain discriminator, a domain confusion module, and the predictor, and the model is trained using historical data; 6) Deploy the trained dual adversarial graph domain adaptive model to the actual sintering site to perform multi-step prediction of the sintering endpoint.

2. The sintering endpoint prediction method based on dual adversarial graph domain adaptation according to claim 1, characterized in that, In step 1), one segment of historical data from operating conditions is constructed as the source domain dataset, and the other segment of historical data from operating conditions is constructed as the target domain dataset.

3. The sintering endpoint prediction method based on dual adversarial graph domain adaptation according to claim 1, characterized in that, In step 2), the step of using a selective weighted aggregator to build a 3D graph neural network to extract features from the source and target domains is as follows: Assumption Represents the 3D graph neural network's first... Layer nodes Adjacent nodes Feature representation, Indicates the first Layer nodes The received message indicates that, Represents message aggregation functions, This represents a feedforward neural network. Represents a node The set of neighboring nodes （2） （3） in, Represents a node The adjacency matrix, The set representing random Bernoulli variables, Representing the The probability of the time difference coefficients. Let k represent the learnable weights, k = 1, 2, ..., K, where K is the maximum order of the time difference coefficients. Indicates the Bernoulli distribution; Nodes in layer l+1 of a 3D graph neural network The features are calculated as follows: （4） in, Represents the update function. Represents the sigmoid activation function. and This represents the learnable weight matrix.

4. The sintering endpoint prediction method based on dual adversarial graph domain adaptation according to claim 1, characterized in that, Step 3) is as follows: Assumption and Represent the 3D graph networks of the source and target domains, respectively. and Let represent the features extracted from the source domain and the target domain, respectively. The domain discriminator consists of two fully connected layers and aims to distinguish whether sample features come from the source domain or the target domain. The output of the domain discriminator is either 0 or 1, making it a binary classification problem. Therefore, the cross-entropy loss function is used as the domain adversarial loss. : （5） in, and Let these represent samples from the source and target domains, respectively. Represents the logarithmic function. This represents the number of samples, and D represents the neighborhood discriminator.

5. The sintering endpoint prediction method based on dual adversarial graph domain adaptation according to claim 1, characterized in that, In step 5), the joint loss function It consists of three parts: prediction loss function Domain confrontation losses Domain confusion loss function First, the features of the source domain are input into the predictor to obtain the predicted values ​​of the source domain. The mean squared error is used to calculate the predicted value and the true value. The difference is used to obtain the prediction loss function. : （10） in, Indicates the output step size of the prediction; Joint loss function The calculation is as follows: （11） in, and These are two balancing factors; finally, the parameters of the adaptive model for the entire dual adversarial graph domain are optimized and updated using stochastic gradient descent.

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