A blast furnace abnormal furnace condition root cause analysis method fusing expert knowledge and granger causality

Abstract

The application discloses a blast furnace abnormal furnace condition root cause analysis method fusing expert knowledge and Granger causality, which comprises the following steps: integrating furnace condition perception priori knowledge, determining a key variable set according to a current abnormal furnace condition type, and ensuring that the root cause analysis can capture a key target link; based on the Granger causality thought, learning a causality matrix among variables in a variable prediction process, and adopting an adaptive regularization strategy to dynamically adjust the causality matrix; in a time lag process among the variables, firstly performing fast positioning in a coarse granularity, then performing fine search, and further performing global optimization by means of a particle swarm optimization algorithm, and finally adjusting part of the time lag relations in combination with physical priori; constructing a link search and confidence evaluation process, performing propagation path search under the constraints of physical grouping priori, a causality matrix and a time lag matrix, and combining information such as process rules to construct a comprehensive link scoring index, and the application well makes up for the deficiencies of traditional methods in the aspect of blast furnace abnormal furnace condition root cause analysis.

Description

Technical Field

[0001] This invention relates to the field of blast furnace ironmaking technology, specifically to a root cause analysis method for abnormal blast furnace conditions that integrates expert knowledge and Granger causality. Background Technology

[0002] Blast furnace ironmaking is a crucial process in my country's steel manufacturing industry. The stable operation of the blast furnace directly affects the quality of molten iron, the efficiency of raw material and fuel utilization, and the level of on-site safety. In actual production, fluctuations in raw material and fuel quality and adjustments to process parameters can easily disrupt the smooth operation of the blast furnace, leading to frequent abnormal furnace conditions. Currently, handling abnormal furnace conditions largely relies on the subjective experience of operators to adjust operating parameters, lacking standardized systematic analysis methods and reliable quantitative assessment criteria, resulting in highly subjective and delayed control decisions. Therefore, conducting in-depth root cause analysis of abnormal blast furnace conditions can provide important engineering references for on-site analysis and control.

[0003] In recent years, with the development of sensor technology and industrial intelligence, data-driven machine learning and data mining methods have been widely applied in fault diagnosis and root cause analysis. Common methods include classification-based methods, clustering-based methods, association rule-based methods, and deep learning-based methods. However, these methods lack interpretability; the models struggle to learn explanations consistent with physical laws, and most do not fully utilize expert knowledge, resulting in poor generalization ability. Furthermore, causal inference methods, such as traditional Granger causality, structural equation modeling, and function-based causal models, are used to analyze causal relationships between variables to aid in root cause analysis. These methods identify causal transmission characteristics between variables by analyzing causal time-series dependencies. However, directly applying traditional causal discovery methods to root cause analysis of abnormal blast furnace conditions still has limitations. They struggle to analyze causal relationships with time lags of several hours, and fixed regularization parameters lead to over-pruning or under-pruning of the learned causal relationships. More importantly, most existing technologies remain at the stage of acquiring causal relationship graphs, without conducting transmission link analysis and confidence assessment, failing to provide appropriate root cause localization results and interpretive references for on-site operators.

[0004] Chinese invention patent CN121581207A discloses a time-series root cause analysis method and system based on dynamic causal inference. The method utilizes a dynamic causal topology discovery approach based on an improved DAG-GNN algorithm. It aggregates neighbor features using a graph convolutional network and combines this with a long short-term memory network for temporal feature aggregation, achieving joint extraction of spatiotemporal features. A multi-granularity root cause inference module is designed, and an adaptive weight fusion mechanism has been successfully applied to microservice systems such as Sockshop and Hipstershop, demonstrating good root cause localization performance. This method provides an effective technical solution for causal discovery in dynamic time-series systems.

[0005] However, the methods in the aforementioned patents are designed for microservice systems, whose service call topology differs fundamentally from the physical causal mechanisms of industrial processes, lacking the ability to model complex physical constraints in industrial processes; and their causal discovery process relies on data-driven approaches and does not integrate prior expert knowledge in the industrial field, which may lead to the inference of causal links that violate physical common sense when the data quality is poor or the sample is insufficient.

[0006] Chinese invention patent CN121010091A discloses a root cause analysis method for industrial processes based on graph neural networks and knowledge graphs. This method constructs a prior industrial knowledge graph, designs a time-series graph autoencoder to capture temporal dependencies and spatial correlations between variables, utilizes GCN for feature learning, calculates fault contribution based on reconstruction errors, and completes root cause reasoning and ranking using a ripple fault propagation algorithm. This method combines knowledge-driven and data-driven approaches, providing a new approach to root cause analysis of industrial processes.

[0007] However, the aforementioned patents do not explicitly consider the long time lag characteristics of causal relationships. Causal influences between variables in industrial processes often have long delays, and ignoring time lags may lead to inaccurate causal inferences. The calculation of fault contribution is entirely based on the reconstruction error of the time-series autoencoder, without establishing an explicit quantitative index of causal strength. This may lead to inaccurate causal discovery when there is significant data noise or unknown abnormal patterns. Summary of the Invention

[0008] This invention aims to propose a root cause analysis method for blast furnace anomalies that integrates expert knowledge and Granger causality. Addressing the lack of interpretability in blast furnace anomaly root cause analysis techniques, this invention effectively integrates expert knowledge and data-driven methods, constructing a multi-layered expert knowledge constraint system that systematically combines the physical mechanism knowledge, prior causal relationships, and operating condition characteristics of domain experts.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] A root cause analysis method for abnormal blast furnace conditions that integrates expert knowledge and Granger causality includes the following steps:

[0011] S1. Integrate prior knowledge of furnace condition perception, determine the set of key variables based on the current abnormal furnace condition type, and ensure that root cause analysis can capture key target links;

[0012] S2. Design an adaptive causal discovery module. Based on Granger causality, it learns the causal matrix between variables during the variable prediction process and uses an adaptive regularization strategy to dynamically adjust the causal matrix.

[0013] S3. Construct a hierarchical time lag estimation module that integrates time lag priors. First, perform rapid localization with coarse granularity, then perform fine search, and use particle swarm optimization algorithm for global optimization. Finally, combine physical priors to adjust the causal strength of some factors.

[0014] S4. Construct a link search and confidence assessment process, search for propagation paths under the constraints of physical group priors and causal matrix, and construct a comprehensive link scoring index by combining information such as process rules.

[0015] As a preferred technical solution of the present invention, step S1 is specifically as follows:

[0016] S11. Identify abnormal furnace condition types:

[0017] When abnormal furnace conditions occur, the centralized control system at the smelting site uses an expert knowledge base or deep learning methods to identify the type of abnormal furnace condition.

[0018] S12. Furnace condition sensing mapping and data preprocessing:

[0019] Based on the operational experience and knowledge of on-site experts, the mapping relationship between abnormal furnace conditions and key outcome variables was determined, and data preprocessing was performed on the time-series process data.

[0020] S121. Determine the mapping relationship between abnormal furnace conditions and key outcome variables, as follows:

[0021] Under different abnormal furnace conditions, the key variables and abnormal propagation paths are different. First, it depends on the type of the current abnormal furnace condition. Determine the set of key variables by combining expert experience. :

[0022] ;

[0023] in, Indicates a mapping relationship;

[0024] S122. Preprocessing of time-series process data, as detailed below:

[0025] First, construct the original time series matrix: assuming the blast furnace ironmaking process includes... There are 1 process variable, and the sampling points are 1. , forming the original time series matrix ;

[0026] Then, data preprocessing is performed, including data cleaning, Z-score normalization, and sliding window sequence construction.

[0027] As a preferred technical solution of the present invention: in step S122, the data cleaning includes missing value, outlier value and noise processing, as follows:

[0028] Missing values ​​are handled using linear interpolation.

[0029] ;

[0030] in, Indicates the first The process variable at the th ... The value of each sampling point;

[0031] Outlier handling adopts The following criteria are used to exclude outliers: If a value meets the following condition, it is considered an outlier:

[0032] ;

[0033] in, and The first The mean and standard deviation of each variable;

[0034] Z-score standardization is performed on each variable to eliminate the influence of dimensions:

[0035] ;

[0036] in Indicates the normalized th Data for each variable;

[0037] Training samples are constructed using a sliding window sequence, with the sliding window length set to 1. Then the first The training samples are:

[0038] ;

[0039] For length is Historical time series;

[0040] This allows for the determination of target variables in data preparation and link analysis.

[0041] As a preferred technical solution of the present invention, step S2 is specifically as follows:

[0042] S21. Combining Granger causality with neural networks formed from prior expert knowledge:

[0043] For the blast furnace ironmaking process There are 10 variables, for each target variable. Train a prediction model that uses all source variables. Historical information to predict target variables Future value:

[0044] ;

[0045] in, For length is Historical time sequence, For the corresponding prediction network parameters, This is the predicted value of the variable for the next time step;

[0046] The hidden layer of the prediction model uses the ReLU activation function, so the forward propagation process is as follows:

[0047] ;

[0048] in, For the corresponding hidden intermediate state, and For the network parameters that need to be learned, and These are the weight and bias parameters corresponding to the output layer;

[0049] The loss function of the prediction model is:

[0050] ;

[0051] in For the corresponding variable in The true value of a moment Sample size during training

[0052] The above prediction model can capture the complex coupling relationships between blast furnace process variables;

[0053] S22, From source variable To target variable The strength of causal relationship is determined by connecting the weight matrix. To quantify, specifically Includes source variables All time steps to the target variable All hidden layer connection weights:

[0054] ;

[0055] in, , , , These are the weight matrices for each hidden layer;

[0056] definition The Group Lasso norm is:

[0057] ;

[0058] in Denotes the Frobenius norm;

[0059] S23. Introduce Group Lasso regularization to achieve automatic causal relationship selection, as follows:

[0060] If the source variable To target variable Connection weight matrix If the Frobenius norm is regularized to zero, it indicates that the source variable... For target variable There is no predictive contribution, meaning there is no Granger causality. The corresponding GroupLasso regularization term is:

[0061] ;

[0062] Introducing Rigde regularization loss:

[0063] ;

[0064] in This represents the connection weight matrix corresponding to the layer number;

[0065] The overall loss function is defined as:

[0066] ;

[0067] in is the Group Lasso regularization coefficient, used to control the sparsity of the causal graph.

[0068] S24. Construct a hybrid adaptive regularization coefficient adjustment strategy for dynamic adjustment of the causal graph during training:

[0069] Regularization coefficients are calculated based on causal density and causal strength. For dynamic adjustment, the graph density is first defined as:

[0070] ;

[0071] in For the first Original causal strength at epochs The edge strength threshold, Indicates the sparsity of the current causal graph;

[0072] The corresponding adaptive density basis is:

[0073] ;

[0074] in The initial regularization coefficients are... For the target graph density, This is the scaling factor;

[0075] The strength of causal relationships also affects the adjustment of regularization coefficients. The average strength of strong causal edges and the average strength of all edges are defined as follows:

[0076] ;

[0077] in For a set of strong causal edges, when the average strength of strong causal edges is higher than a preset threshold, it indicates that a preliminary causal relationship has been established. The regularization coefficient is then increased to further prune and remove false causal edges. Conversely, the regularization coefficient needs to be decreased. The corresponding dynamic adjustment method is as follows:

[0078] ;

[0079] Considering both causal density and intensity information:

[0080] ;

[0081] in These are weighting coefficients;

[0082] S24. Construct a set of prior causal edges to guide the learning of Granger causality:

[0083] For any edge in the prior causal edge set, a protection mechanism is applied:

[0084] ;

[0085] in The causal matrix obtained after training the neural network. The minimum protection strength threshold for the prior edge. This is the corrected causal matrix.

[0086] As a preferred technical solution of the present invention: in step S21, the prediction model adopts a three-layer fully connected structure with 128, 64 and 32 neurons respectively.

[0087] As a preferred technical solution of the present invention, step S3 is as follows:

[0088] S31. Perform coarse-grained time delay estimation to quickly locate the time delay range:

[0089] First, for the original time series Perform downsampling and define the downsampling step size as... The downsampled sequence is as follows:

[0090] ;

[0091] in, Indicated by Sequences obtained by sampling at equal intervals;

[0092] Then, the target variable is calculated on the downsampled sequence. and source variables The cross-correlation function, and at the coarse-grained maximum hysteresis Search for the point where the absolute value of the cross-correlation function reaches its maximum value within the range;

[0093] Finally, the coarse-grained estimates are converted back to the original time scale:

[0094] ;

[0095] in, Representing variables and variables Cross-correlation calculation, This is a preliminary estimate of the time lag value;

[0096] S32. Based on the coarse-grained time delay estimation, perform a fine-grained search:

[0097] First, with coarse-grained estimates Define the search window centered on the search window:

[0098] ;

[0099] in The search radius is in the search window. Within, a fine search step size is employed. Calculate the cross-correlation coefficient ;

[0100] Then, search for the point where the absolute value of the cross-correlation is maximized:

[0101] ;

[0102] Finally, A point-by-point search is performed in the vicinity to find an accurate time delay estimate:

[0103] ;

[0104] S33. Integrate the results of the fine-grained search with prior physical time delay knowledge:

[0105] First, obtain the physical prior time delay. This value was provided by on-site experts based on the physical mechanism of blast furnace smelting;

[0106] Then, the difference between the data-driven estimate and the physical prior is calculated:

[0107] ;

[0108] Next, set the difference threshold. Different fusion strategies are adopted based on the magnitude of the differences:

[0109] ;

[0110] After incorporating prior lag knowledge, the time delay matrix is ​​obtained: ,in Represents source variable To target variable The final time delay estimate;

[0111] S34. Using particle swarm optimization for global time-delay optimization:

[0112] First, the particle swarm initialization is performed using the aforementioned time delay matrix. Based on this, for each particle and each pair of variables In the estimated value Disturbances generated nearby:

[0113] ;

[0114] in To obtain from a uniform distribution Random perturbations in the mid-sample;

[0115] Then, the initial speed is Define the fitness function:

[0116] ;

[0117] in The term represents the causal strength, indicating that it is based on the time delay matrix. The sum of causal strengths corresponding to the trained causal discovery model. Represents the prior lag set among known variables. for The elements in the text represent variables. Compared to variables Lagging time step, For the corresponding prior lag time step, For physical consistency items, For scale parameters, For smoothness, For variance, For scaling parameters, This represents the corresponding weighting coefficient;

[0118] Then, perform PSO iterations for the th... In the next iteration, the particle The velocity and position update formulas are:

[0119] ;

[0120] in, For inertial weights, , As a learning factor, , for Random numbers between, For particles exist The speed of time, For particles exist The speed of time, and Particles exist Time and The time delay matrix at time t, For particles The best historical position The globally optimal position;

[0121] Finally, set a convergence condition when the number of iterations reaches the maximum number of iterations. or continuous The improvement in the global optimal fitness in the next iteration is less than the threshold. At that time, the optimized time delay matrix is ​​output. The corresponding time delay matrix is ​​the optimized time delay matrix. .

[0122] As a preferred technical solution of the present invention, step S4 is specifically as follows:

[0123] S41. First, according to the causal strength matrix and time delay matrix Construct a weighted directed causal graph Node set express A process variable, edge set , Construct a threshold for the graph, edges The weight is The time delay attribute is ;

[0124] Then, exclude self-loops and set the diagonal elements to zero. ;

[0125] Finally, an adjacency list representation is constructed for each node. Stores the set of its parent nodes:

[0126] ;

[0127] S42. Introducing the beam search algorithm in directed causal graphs. In the process of path search, the bundle search retains only the optimal path at each step. Find the candidate path while ensuring efficiency. The path is as follows:

[0128] Initialize the beam search set: the set of key target variables obtained from the preceding steps. Target variable in The endpoint of the causal path, with a bundle width of The maximum depth is Initialize the bundle set: Each element is a triple. , respectively representing the current node, from arrive The reverse path and cumulative intensity;

[0129] For depth arrive All of them require initializing the bundle set. Then for the bundle Each element All nodes were found The parent node p, for each parent node Calculate the new cumulative intensity and construct a new path:

[0130] ;

[0131] in From parent node p to node The strength of the causal relationship;

[0132] Then Join ,from Choose the one with the highest cumulative strength Each element is used as a new bundle. From the final bundle The one with the highest cumulative strength Given a set of elements, return the corresponding path.

[0133] S43. By using short path search and long path search, paths of different scales are fully obtained, among which:

[0134] Shortest path search: Set maximum depth Then, by executing the above bundle search algorithm, the set of shortest paths can be obtained. ;

[0135] Long path search: Set minimum depth and maximum depth Then, by executing the bundle search algorithm, the set of long paths can be obtained. ;

[0136] S44. Conduct a comprehensive evaluation of each causal path and provide a basis for root cause ranking and screening, as detailed below:

[0137] Causal path ,in For path length, For the first on the path For each path with nodes, the overall score is defined as follows:

[0138] ;

[0139] in These are the weight coefficients for the corresponding items. Indicates the overall strength of the path. This refers to the path length and time delay consistency. Measuring the time-scale stationarity of causal relationships along a path:

[0140] ;

[0141] in Represents path variables Medium variables arrive The time lag between For scale parameters;

[0142] Abnormal correlation This indicates the degree of correlation between variables on the path and abnormal states:

[0143] ;

[0144] in, These are predefined anomaly indicators used to reflect the fluctuation range or slope of change of anomalous variables. For variables Time series, and These are the corresponding means;

[0145] For the final set of short paths and long path set According to the comprehensive scoring index Keep the shortest path and long path Then merge the two path sets:

[0146] ;

[0147] Ultimately based on the overall score Reorder to get the final result. The ranking of causal paths and their comprehensive scores provide on-site personnel with valuable insights into the root causes of abnormal furnace conditions.

[0148] To address the lack of interpretability in blast furnace anomaly root cause analysis techniques, this invention effectively integrates expert knowledge and data-driven methods, constructing a multi-layered expert knowledge constraint system that systematically combines the physical mechanism knowledge, prior causal relationships, and operating condition characteristics of domain experts. To achieve dynamic and adaptive causal discovery, an adaptive GroupLasso regularization strategy is proposed. This strategy dynamically adjusts the regularization coefficient based on the graph density and causal strength distribution during training, and applies a protection mechanism to strong causal edges to prevent over-pruning, thus resolving the over-pruning or under-pruning problems caused by fixed regularization parameters. To achieve long-term lag estimation between variables during blast furnace ironmaking, a hierarchical lag estimation method is proposed. This method first performs coarse-grained rapid localization, followed by fine-grained searching, and employs a particle swarm optimization algorithm for global optimization. Simultaneously, the fine-grained search results are integrated with prior physical time-lag knowledge to ensure a certain degree of interpretability. For the complete link analysis and confidence assessment of abnormal furnace conditions, a complete root cause analysis workflow is constructed, including multi-scale path search and comprehensive scoring confidence analysis, providing on-site production personnel with accurate, reliable, and confidence-based root cause localization reference results.

[0149] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0150] This invention constructs a multi-layered expert knowledge constraint system, systematically integrating physical mechanism knowledge, prior causal relationships, and operational condition perception characteristics. Expert knowledge is injected into the causal discovery method, ensuring that root cause analysis results conform to physical laws and possess interpretability. An adaptive Group Lasso regularization strategy is designed, dynamically adjusting the regularization coefficient based on the training state and protecting strong causal edges, avoiding over-pruning or under-pruning caused by fixed parameters. A hierarchical lag estimation method is proposed, first using coarse-grained rapid localization followed by fine-grained search, and integrating with physical priors to solve the problem of difficult long lag estimation. Multi-scale path search avoids the limitations of single-scale search, improving the model's root cause path discovery capability. A comprehensive index is proposed to solve the confidence assessment problem of causal paths. This provides a large amount of root cause analysis results for blast furnace field operations, possessing certain regulatory reference value. Attached Figure Description

[0151] Figure 1 This is the overall flowchart of the present invention.

[0152] Figure 2 It is a causal intensity matrix diagram of process time series variables under the condition of a collapsing furnace.

[0153] Figure 3 It is a time lag estimation plot between various variables.

[0154] Figure 4 This is an example diagram of the Top 5 root cause analysis path. Detailed Implementation

[0155] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0156] like Figure 1 As shown, the present invention proposes a root cause analysis method for abnormal blast furnace conditions that integrates expert knowledge and Granger causality, comprising the following steps:

[0157] S1. Integrate prior knowledge of furnace condition perception, determine the set of key variables based on the current abnormal furnace condition type, and ensure that root cause analysis can capture key target links;

[0158] S2. Design an adaptive causal discovery module. Based on Granger causality, it learns the causal matrix between variables during the variable prediction process and uses an adaptive regularization strategy to dynamically adjust the causal matrix.

[0159] S3. Construct a hierarchical time lag estimation module that integrates time lag priors. First, perform rapid localization with coarse granularity, then perform fine search, and use particle swarm optimization algorithm for global optimization. Finally, combine physical priors to adjust the causal strength of some factors.

[0160] S4. Construct a link search and confidence assessment process, search for propagation paths under the constraints of physical group priors and causal matrix, and construct a comprehensive link scoring index by combining information such as process rules.

[0161] The specific implementation plan is as follows:

[0162] S1. Integrate prior knowledge of furnace condition perception, determine the set of key variables based on the current abnormal furnace condition type, and ensure that root cause analysis can capture key target links, as detailed below:

[0163] When abnormal furnace conditions occur, the centralized control system at the smelting site usually uses an expert knowledge base or deep learning methods to identify the type of abnormal furnace condition.

[0164] To present root cause analysis as a transmission path, target outcome variables need to be identified based on abnormal furnace conditions. This invention first determines the mapping relationship between abnormal furnace conditions and key outcome variables based on the operational experience and knowledge of on-site experts. Simultaneously, it performs data cleaning, standardization, and sliding window sequence construction on the time-series process data.

[0165] Under different abnormal furnace conditions, the key variables and abnormal propagation paths are different. First, it depends on the type of the current abnormal furnace condition. Determine the set of key variables by combining expert experience. :

[0166] ;

[0167] in, This indicates a mapping relationship.

[0168] For the blast furnace smelting process, under normal furnace conditions, the key variables are top pressure, gas utilization rate, total pressure difference, and permeability index. When a pipeline furnace condition occurs, the local edge of the burden surface experiences excessive airflow, and the top temperature rises sharply. Therefore, the key variables are top pressure, gas utilization rate, and top temperature. Abnormal furnace conditions such as suspended burden, sliding burden, and collapse are essentially due to inconsistent speeds of burden descent. Therefore, the key variables for suspended burden, sliding burden, and collapse all include total pressure difference, upper pressure difference, lower pressure difference, permeability index, and probe data. Collapse, due to the rapid collapse of the burden, also significantly causes changes in top pressure.

[0169] Simultaneously with the above-mentioned abnormal furnace condition-key variable mapping is the preprocessing of time-series process data.

[0170] Assume the blast furnace ironmaking process includes Several process variables, including key parameters such as top temperature, top pressure, permeability index, furnace static pressure, and blast kinetic energy, were sampled at the following points: , forming the original time series matrix .

[0171] Data preprocessing mainly consists of three parts: data cleaning, Z-score normalization, and sliding window sequence construction. In the data cleaning part, missing values, outliers, and noise are handled. Missing values ​​are represented using linear interpolation.

[0172] ;

[0173] in, Indicates the first The process variable at the th ... The values ​​of each sampling point. For outliers, use... The following criteria are used to eliminate outliers: If a value meets the following formula, it is considered an outlier:

[0174] ;

[0175] in, and The first The mean and standard deviation of each variable.

[0176] Next, Z-score standardization is performed on each variable to eliminate the influence of dimensions:

[0177] ;

[0178] in Indicates the normalized th Data for each variable.

[0179] Then, a sliding window sequence is used to construct training samples. Let the length of the sliding window be... Then the first The training samples are:

[0180] ;

[0181] For length is Historical time series;

[0182] This achieves the determination of target variables for data preparation and link analysis.

[0183] S2. Design an adaptive causal discovery module. Based on Granger causality, it learns the causal matrix between variables during variable prediction and uses an adaptive regularization strategy to dynamically adjust the causal matrix, as detailed below:

[0184] To characterize the relationships between various process variables in blast furnace smelting, this invention combines Granger causality prediction with expert prior knowledge. Multivariate Granger causality is predicted using multiple MLPs to capture causal relationships. Then, an adaptive Group Lasso sparsity strategy and expert prior knowledge are proposed to correct the causal relationships.

[0185] Granger causality is a prediction-based definition of causality. Its core idea is that if variables are used... Historical information can significantly improve the understanding of variables The accuracy of the prediction is called the variable's accuracy. It is a variable Granger's reason.

[0186] This invention combines Granger causality with neural networks formed from expert prior knowledge. For the blast furnace ironmaking process... There are 10 variables, for each target variable. Train a prediction model that uses all source variables. Historical information is used to predict the future value of the target variable.

[0187] ;

[0188] in, For length is Historical time sequence, For the corresponding prediction network parameters, This is the predicted value of the variable for the next time step.

[0189] The prediction network employs a three-layer fully connected structure with 128, 64, and 32 neurons respectively. The hidden layers use the ReLU activation function, and the forward propagation process is as follows:

[0190] ;

[0191] in, For the corresponding hidden intermediate state, and For the network parameters that need to be learned, and These are the weight and bias parameters corresponding to the output layer.

[0192] The loss function for the prediction model is:

[0193] ;

[0194] This nonlinear prediction model can capture the complex coupling relationships between blast furnace process variables.

[0195] From source variable To target variable The strength of causal relationship is determined by connecting the weight matrix. To quantify. Specifically, Includes source variables All time steps to the target variable All hidden layer connection weights:

[0196] ;

[0197] in , , , These are the weight matrices for each hidden layer.

[0198] definition The Group Lasso norm is:

[0199] ;

[0200] in This represents the Frobenius norm.

[0201] In the Granger causality framework, traditional methods adjust Granger relationships through significance tests, but these are easily limited by hypothesis testing and sample size. Therefore, this invention introduces a Group Lasso regularization term to achieve automatic causal relationship selection.

[0202] If the source variable To target variable Connection weight matrix If the Frobenius norm is regularized to zero, it indicates that the source variable... For target variable There is no predictive contribution, meaning there is no Granger causality. The corresponding GroupLasso regularization term is:

[0203] ;

[0204] Furthermore, to prevent overfitting and improve the model's generalization ability, this invention introduces Rigde regularization loss:

[0205] ;

[0206] in This represents the connection weight matrix corresponding to the layer number;

[0207] The overall loss function is defined as:

[0208] ;

[0209] in is the Group Lasso regularization coefficient, used to control the sparsity of the causal graph.

[0210] Fixed regularization coefficients can easily lead to over-pruning or under-pruning. In order to dynamically adjust the causal graph during training, this invention constructs a hybrid adaptive regularization coefficient adjustment strategy.

[0211] Regularization coefficients are calculated based on causal density and causal strength. Dynamic adjustment. First, define the graph density as:

[0212] ;

[0213] in For the first Original causal strength at epochs The edge strength threshold, This indicates the sparsity of the current causal graph.

[0214] The corresponding adaptive density basis is:

[0215] ;

[0216] in The initial regularization coefficients are... For the target graph density, This is the scaling factor.

[0217] The strength of causal relationships also affects the adjustment of regularization coefficients. The average strength of strong causal edges and the average strength of all edges are defined as follows:

[0218] ;

[0219] in This represents the set of strong causal edges. When the average strength of strong causal edges is relatively high, it indicates the existence of a preliminary causal relationship, and the regularization coefficient can be appropriately increased for further pruning to remove false causal edges. Conversely, it needs to be decreased. The corresponding dynamic adjustment method is as follows:

[0220] ;

[0221] For a more robust and stable scenario, this invention considers both causal density and strength information:

[0222] ;

[0223] in These are weighting coefficients;

[0224] Furthermore, based on the operational experience and knowledge of on-site foremen and experts in blast furnace smelting, it is necessary to construct a set of prior causal edges to guide the learning of Granger causality and prevent the loss or fabrication of some causal relationships. Typical prior causal edges include: (blast parameters, pressure difference), (pressure difference, furnace top parameters), (permeability, pressure difference), (blast parameters, furnace condition), etc.

[0225] For any edge in the prior causal edge set, a protection mechanism is applied:

[0226] ;

[0227] in This is the minimum protection threshold for prior edges, ensuring that causal relationships known to experts are not over-pruned.

[0228] S3. Construct a hierarchical time lag estimation module that integrates time lag priors. First, perform coarse-grained fast localization, then fine-grained search, and use particle swarm optimization algorithm for global optimization. Finally, combine physical priors to adjust the partial causal strength, as detailed below:

[0229] In the blast furnace ironmaking process, there are significant time lags between different variables, determined by the movement of the furnace charge and its physicochemical reactions. Specifically, coke and raw materials move downwards from the top of the blast furnace, while gas continuously rises, undergoing combustion, heat exchange, and other processes. The overall smelting cycle from a batch of charge to the production of molten iron is 4-6 hours. This process involves a large amount of sampled data, and directly calculating the cross-correlation is extremely complex. This invention employs a two-layer search strategy, integrating physical priors and particle swarm optimization algorithms to achieve time lag estimation.

[0230] First, coarse-grained time delay estimation is performed to quickly determine the approximate range of the time delay. For the original time series... Perform downsampling. Define the downsampling step size as... The downsampled sequence is as follows:

[0231] ;

[0232] in, Indicated by Sequences obtained by sampling at equal intervals;

[0233] Then calculate the variable on the downsampled sequence. and variables The cross-correlation function, and at the coarse-grained maximum hysteresis The maximum value of the absolute value of the cross-correlation function is searched within the range, and then the coarse-grained estimate is converted back to the original time scale:

[0234] ;

[0235] in, Representing variables and variables Cross-correlation calculation, This is a preliminary estimate of the time lag value.

[0236] The fine-grained search is performed based on the coarse-grained time delay estimation. First, the coarse-grained estimate is used... Define the search window centered on the search window:

[0237] ;

[0238] in The search radius is in the search window. Within, a fine search step size is employed. Calculate the cross-correlation coefficient Then search for the point where the absolute value of the cross-correlation is maximized:

[0239] ;

[0240] exist A point-by-point search is performed in the vicinity to find an accurate time delay estimate:

[0241] ;

[0242] Purely data-driven time delay estimation may conflict with prior physical knowledge. To prevent unreasonable time delay estimation from affecting subsequent root cause analysis, this invention integrates refined search results with prior physical time delay knowledge.

[0243] Obtaining physical prior time delay This value, provided by on-site experts based on the physical mechanisms of blast furnace smelting, describes the approximate time lag range between the quantitative variables. The difference between the data-driven estimate and the physical prior is then calculated:

[0244] ;

[0245] Next, set the difference threshold. Different fusion strategies are adopted based on the magnitude of the differences:

[0246] ;

[0247] After incorporating prior lag knowledge, the time delay matrix is ​​obtained. ,in Represents source variable To target variable The final time delay estimate.

[0248] Time lag provides a crucial reference in subsequent causal link searches. To further improve the accuracy of time lag estimation, this invention utilizes particle swarm optimization (PSO) for global time lag optimization.

[0249] The first step is particle swarm initialization, using the aforementioned time delay matrix. Based on this, for each particle and each pair of variables In the estimated value Disturbances generated nearby:

[0250] ;

[0251] in To obtain from a uniform distribution Random perturbations in the mid-sample;

[0252] Initialization speed Then, a fitness function is defined, which comprehensively considers causal strength, consistency with physical priors, and time delay smoothness:

[0253] ;

[0254] in The term represents the causal strength, indicating that it is based on the time delay matrix. The sum of causal strengths corresponding to the trained causal discovery model. Represents the prior lag set among known variables. for The elements in the text represent variables. Compared to variables Lagging time step, For the corresponding prior lag time step, For physical consistency items, For scale parameters, For smoothness, For variance, For scaling parameters, This represents the corresponding weighting coefficient.

[0255] Then proceed with the PSO iteration. For the ... In the next iteration, the particle The velocity and position update formulas are:

[0256] ;

[0257] in, For inertial weights, , As a learning factor, , for Random numbers between, For particles exist The speed of time, For particles exist The speed of time, and Particles exist Time and The time delay matrix at time t, For particles The best historical position This is the globally optimal position.

[0258] Finally, set the convergence condition. The convergence occurs when the number of iterations reaches the maximum number of iterations. or continuous The improvement in the global optimal fitness in the next iteration is less than the threshold. At that time, the optimized time delay matrix is ​​output. The corresponding time delay matrix is ​​the optimized time delay matrix. .

[0259] S4. Construct a link search and confidence assessment process. Under the constraints of physical group prior and causal matrix, conduct propagation path search, and construct a comprehensive link scoring index by combining information such as process rules, as detailed below:

[0260] Obtain the causal strength matrix and time delay matrix Subsequently, this invention designs a multi-scale path search strategy, integrates physical structure knowledge for path mining, and comprehensively analyzes root cause paths to obtain path confidence scores.

[0261] According to the causality strength matrix and time delay matrix Construct a weighted directed causal graph Node set express A process variable, edge set , Construct a threshold for the graph, edges The weight is The time delay attribute is .

[0262] Next, exclude self-loops and set the diagonal elements to zero. This ensures that variables do not have a causal effect on themselves. Then, an adjacency list representation is constructed for fast path search. For each node... Stores the set of its parent nodes:

[0263] ;

[0264] Next, in the directed causal graph The present invention introduces a beam search algorithm, which retains only the optimal path at each step. Find the candidate path while ensuring efficiency. The path is as follows:

[0265] Initialize the beam search set. The set of key target variables obtained from the preceding steps. Target variable in The endpoint of the causal path, with a bundle width of The maximum depth is Initialize the bundle set: Each element is a triple. , respectively representing the current node, from arrive The reverse path and cumulative intensity.

[0266] For depth arrive All of them require initializing the bundle set. Then for the bundle Each element All nodes were found The parent node p, for each parent node Calculate the new cumulative intensity and construct a new path:

[0267] ;

[0268] in From parent node p to node The strength of the causal relationship;

[0269] Then Join ,from Choose the one with the highest cumulative strength Each element is used as a new bundle. From the final bundle The one with the highest cumulative strength Given a set of elements, return the corresponding path.

[0270] In addition, in order to fully obtain paths of different scales, this invention designs two path search methods: short path search and long path search.

[0271] Shortest path search, set maximum depth By executing the above beam search algorithm, the set of shortest paths is obtained. Short paths are used to reflect fast causal chains, typically corresponding to direct causal relationships in real-world scenarios. Long path search sets a minimum depth. and maximum depth Then, the bundle search algorithm is executed to obtain the set of long paths. Long paths often reflect complex indirect causal relationships, involving multiple physicochemical reaction stages.

[0272] For each causal path, in order to provide on-site personnel with a certain confidence reference, this invention comprehensively evaluates the causal path strength, length, time delay consistency, and abnormal correlation, and provides a basis for root cause ranking and screening.

[0273] Causal path ,in For path length, For the first on the path For each path with nodes, the overall score is defined as follows:

[0274] ;

[0275] in These are the weight coefficients for the corresponding items. Indicates the overall strength of the path. This refers to the path length and time delay consistency. Measuring the time-scale stationarity of causal relationships along a path:

[0276] ;

[0277] in Represents path variables Medium variables arrive The time lag between For scale parameters;

[0278] Abnormal correlation This indicates the degree of correlation between variables on the path and abnormal states:

[0279] ;

[0280] in, These are predefined anomaly indicators used to reflect the fluctuation range or slope of change of anomalous variables. For variables Time series, and These are the corresponding means.

[0281] For the final set of short paths and long path set According to the comprehensive scoring index Keep the shortest path and long path Then merge the two path sets:

[0282] ;

[0283] Ultimately based on the overall score Reorder to get the final result. The system ranks causal paths and assigns comprehensive scores to them. This provides on-site personnel with valuable root cause analysis results for abnormal furnace conditions.

[0284] The present invention will be further described below with reference to specific embodiments.

[0285] This embodiment is based on a 2650 iron smelting plant in China. The blast furnace was deployed, and the data samples used included process time-series data such as top pressure, gas utilization rate, and cold blast flow rate, as well as the corresponding blast furnace conditions. The sampling interval for the process time-series data was 10 seconds, the process time-series data dimension was 19, the total number of samples was 43201, and the data shape was (43201, 19). The blast furnace condition data shape was (43201, 1), representing the blast furnace condition at the corresponding time. The process time-series data and blast furnace condition data were input into the proposed root cause analysis method for abnormal blast furnace conditions, and an abnormal blast furnace condition root cause analysis experiment was carried out.

[0286] Figure 2 The model demonstrates its performance in causal relationship analysis, describing the causal relationships between time-series variables in various processes under the condition of a collapsing furnace, and effectively integrating data and prior knowledge.

[0287] Figure 3 This demonstrates the time lag between variables obtained by the two-stage hierarchical time delay estimation module proposed in this invention.

[0288] Figure 4 The study demonstrates the Top 5 root cause paths and overall confidence scores identified by the proposed method under abnormal blast furnace conditions, including a collapse of the blast furnace charge. The propagation paths, to some extent, align with the experience of on-site personnel. In summary, the experimental results effectively validate the effectiveness of the proposed method in root cause analysis of abnormal blast furnace conditions, providing a valuable reference for on-site blast furnace personnel in their operational analysis.

[0289] This invention constructs a multi-dimensional expert knowledge constraint mechanism, encompassing condition perception based on anomaly types, time-lag priors matching long-range blast furnace responses, physical grouping following the process system, and prior causal edges that solidify known mechanisms. This ensures that the discovered root cause transmission links strictly follow the physical laws of blast furnace smelting and possess high on-site interpretability.

[0290] This invention proposes a strategy based on adaptive adjustment of regularization coefficients using causal graph density and strength bases. The regularization coefficients are dynamically adjusted according to the graph density and causal strength distribution during the training process, and physical priors are used to protect strong causal edges and prevent over-pruning.

[0291] This invention constructs a two-stage hierarchical time delay estimation module to reduce computational complexity and uses particle swarm optimization for global optimization. At the same time, it intelligently integrates refined search results with physical prior time delay knowledge, solving the problem that existing technologies fail to fully consider the long-term lag effects between variables.

[0292] Therefore, the present invention proposes a root cause analysis method for blast furnace anomalies that integrates expert knowledge and Granger causality. This method realizes a complete process from data preprocessing, expert knowledge constraint fusion, adaptive causal discovery, hierarchical lag estimation, multi-scale path search to uncertainty quantification, providing a new reference method for root cause analysis of blast furnace anomalies.

[0293] It should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A root cause analysis method for abnormal blast furnace conditions that integrates expert knowledge and Granger causality, characterized in that, Includes the following steps: S1. Integrate prior knowledge of furnace condition perception, determine the set of key variables based on the current abnormal furnace condition type, and ensure that root cause analysis can capture key target links; S2. Design an adaptive causal discovery module. Based on Granger causality, it learns the causal matrix between variables during the variable prediction process and uses an adaptive regularization strategy to dynamically adjust the causal matrix. S3. Construct a hierarchical time lag estimation module that integrates time lag priors. First, perform rapid localization with coarse granularity, then perform fine search, and use particle swarm optimization algorithm for global optimization. Finally, combine physical priors to adjust the causal strength of some factors. S4. Construct a link search and confidence assessment process, search for propagation paths under the constraints of physical group priors and causal matrix, and construct a comprehensive link scoring index by combining information such as process rules.

2. The root cause analysis method for blast furnace abnormal conditions that integrates expert knowledge and Granger causality as described in claim 1, characterized in that, Step S1 is as follows: S11. Identify abnormal furnace condition types: When abnormal furnace conditions occur, the centralized control system at the smelting site uses an expert knowledge base or deep learning methods to identify the type of abnormal furnace condition. S12. Furnace condition sensing mapping and data preprocessing: Based on the operational experience and knowledge of on-site experts, the mapping relationship between abnormal furnace conditions and key outcome variables was determined, and data preprocessing was performed on the time-series process data. S121. Determine the mapping relationship between abnormal furnace conditions and key outcome variables, as follows: Under different abnormal furnace conditions, the key variables and abnormal propagation paths are different. First, it depends on the type of the current abnormal furnace condition. Determine the set of key variables by combining expert experience. : in, Indicates the mapping relationship; S122. Preprocessing of time-series process data, as detailed below: First, construct the original time series matrix: assuming the blast furnace ironmaking process includes... There are 1 process variable, and the sampling points are 1. , forming the original time series matrix ; Then, data preprocessing is performed, including data cleaning, Z-score normalization, and sliding window sequence construction.

3. The root cause analysis method for abnormal blast furnace conditions that integrates expert knowledge and Granger causality as described in claim 2, characterized in that, In step S122, the data cleaning includes handling missing values, outliers, and noise, as detailed below: Missing values ​​are handled using linear interpolation. ； in, Indicates the first The process variable at the th ... The value of each sampling point; Outlier handling adopts The following criteria are used to eliminate outliers: If a value meets the following condition, it is considered an outlier: ； in, and The first The mean and standard deviation of each variable; Z-score standardization is performed on each variable to eliminate the influence of dimensions: in Indicates the normalized th Data for each variable; Training samples are constructed using a sliding window sequence, with the sliding window length set to 1. Then the first The training samples are: ； For length is Historical time series; This allows for the determination of target variables in data preparation and link analysis.

4. The root cause analysis method for abnormal blast furnace conditions that integrates expert knowledge and Granger causality as described in claim 1, characterized in that, Step S2 is as follows: S21. Combining Granger causality with neural networks formed from prior expert knowledge: For the blast furnace ironmaking process There are 10 variables, for each target variable. Train a prediction model that uses all source variables. Historical information to predict target variables Future value: ； in, For length is Historical time sequence, For the corresponding prediction network parameters, This is the predicted value of the variable for the next time step; The hidden layer of the prediction model uses the ReLU activation function, so the forward propagation process is as follows: ； in, For the corresponding hidden intermediate state, and For the network parameters that need to be learned, and These are the weight and bias parameters for the output layer; The loss function of the prediction model is: ； in For the corresponding variable in The true value of a moment This refers to the sample size during training. The above prediction model can capture the complex coupling relationships between blast furnace process variables; S22, From source variable To target variable The strength of causal relationship is determined by connecting the weight matrix. To quantify, specifically Includes source variables All time steps to the target variable All hidden layer connection weights: ； in, , , , These are the weight matrices for each hidden layer; definition The Group Lasso norm is: ； in Denotes the Frobenius norm; S23. Introduce Group Lasso regularization to achieve automatic causal relationship selection, as follows: If the source variable To target variable Connection weight matrix If the Frobenius norm is regularized to zero, it indicates that the source variable... For target variable There is no predictive contribution, meaning there is no Granger causality. The corresponding Group Lasso regularization term is: ； Introduce Rigde regularization loss: ； in This represents the connection weight matrix corresponding to the layer number; The overall loss function is defined as: ； in is the Group Lasso regularization coefficient, used to control the sparsity of the causal graph; S24. Construct a hybrid adaptive regularization coefficient adjustment strategy for dynamic adjustment of the causal graph during training: Regularization coefficients are calculated based on causal density and causal strength. For dynamic adjustment, the graph density is first defined as: ； in For the first Original causal strength at epochs The edge strength threshold, Indicates the sparsity of the current causal graph; The corresponding adaptive density basis is: ； in The initial regularization coefficients are... For the target graph density, This is the scaling factor; The strength of causal relationships also affects the adjustment of regularization coefficients. The average strength of strong causal edges and the average strength of all edges are defined as follows: ； in For a set of strong causal edges, when the average strength of strong causal edges is higher than a preset threshold, it indicates that a preliminary causal relationship has been established. The regularization coefficient is then increased to further prune and remove false causal edges. Conversely, the regularization coefficient needs to be decreased. The corresponding dynamic adjustment method is as follows: ； Considering both causal density and intensity information: ； in These are weighting coefficients; S24. Construct a set of prior causal edges to guide the learning of Granger causality: For any edge in the prior causal edge set, a protection mechanism is applied: ； in The causal matrix obtained after training the neural network. The minimum protection strength threshold for the prior edge. This is the corrected causal matrix.

5. The root cause analysis method for abnormal blast furnace conditions that integrates expert knowledge and Granger causality as described in claim 4, characterized in that, In step S21, the prediction model adopts a three-layer fully connected structure with 128, 64 and 32 neurons respectively.

6. The root cause analysis method for blast furnace abnormal conditions that integrates expert knowledge and Granger causality as described in claim 1, characterized in that, Step S3 is as follows: S31. Perform coarse-grained time delay estimation to quickly locate the time delay range: First, for the original time series Perform downsampling and define the downsampling step size as... The downsampled sequence is as follows: ； in, Indicates Sequences obtained by sampling at equal intervals; Then, the target variable is calculated on the downsampled sequence. and source variables The cross-correlation function, and at the coarse-grained maximum hysteresis Search for the point where the absolute value of the cross-correlation function reaches its maximum value within the range; Finally, the coarse-grained estimates are converted back to the original time scale: ； in, Representing variables and variables Cross-correlation calculation, This is a preliminary estimate of the time lag value; S32. Based on the coarse-grained time delay estimation, perform a fine-grained search: First, with coarse-grained estimates Define the search window centered on the search window: ； in The search radius is in the search window. Within, a fine search step size is employed. Calculate the cross-correlation coefficient ; Then, search for the point where the absolute value of the cross-correlation is maximized: ； Finally, A point-by-point search is performed in the vicinity to find an accurate time delay estimate: ； S33. Integrate the results of the fine-grained search with prior physical time delay knowledge: First, obtain the physical prior time delay. This value was provided by on-site experts based on the physical mechanism of blast furnace smelting; Then, the difference between the data-driven estimate and the physical prior is calculated: ； Next, set the difference threshold. Different fusion strategies are adopted based on the magnitude of the differences: ； After incorporating prior lag knowledge, the time delay matrix is ​​obtained: ,in Represents source variable To target variable The final time delay estimate, The weights corresponding to the physical prior time delay; S34. Using particle swarm optimization for global time-delay optimization: First, the particle swarm initialization is performed using the aforementioned time delay matrix. Based on this, for each particle and each pair of variables In the estimated value Disturbances generated nearby: ； in To obtain from a uniform distribution Random perturbations in the mid-sample; Then, the initial speed is Define the fitness function: ； in The term represents the causal strength, indicating that it is based on the time delay matrix. The sum of causal strengths corresponding to the trained causal discovery model. Represents the prior lag set among known variables. for The elements in the text represent variables. Compared to variables Lagging time step, For the corresponding prior lag time step, For physical consistency items, For scale parameters, For smoothness, For variance, For scaling parameters, This represents the corresponding weighting coefficient; Then, perform PSO iterations for the th... In the next iteration, the particle The velocity and position update formulas are: ； in, For inertial weights, , As a learning factor, , for Random numbers between, For particles exist The speed of time For particles exist The speed of time and Particles exist Time and The time delay matrix at time t, For particles The best historical position The globally optimal position; Finally, set a convergence condition when the number of iterations reaches the maximum number of iterations. or continuous The improvement in the global optimal fitness in the next iteration is less than the threshold. At that time, the optimized time delay matrix is ​​output. The corresponding time delay matrix is ​​the optimized time delay matrix. .

7. The root cause analysis method for abnormal blast furnace conditions that integrates expert knowledge and Granger causality as described in claim 1, characterized in that, Step S4 is as follows: S41. First, according to the causal strength matrix and time delay matrix Construct a weighted directed causal graph Node set express A process variable, edge set , Construct a threshold for the graph, edges The weight is The time delay attribute is ; Then, exclude self-loops and set the diagonal elements to zero. ; Finally, an adjacency list representation is constructed for each node. Stores the set of its parent nodes: ； S42. Introducing the beam search algorithm in directed causal graphs. In this process, a path search is performed, and the bundle search retains only the optimal path at each step. Find the candidate path while ensuring efficiency. The path is as follows: Initialize the beam search set: the set of key target variables obtained from the preceding steps. Target variable in The endpoint of the causal path, with a bundle width of The maximum depth is Initialize the bundle set: Each element is a triple. , respectively representing the current node, from arrive The reverse path and cumulative intensity; For depth arrive All of them require initializing the bundle set. Then for the bundle Each element All nodes were found The parent node p, for each parent node Calculate the new cumulative intensity and construct a new path: ； in From parent node p to node The strength of the causal relationship; Then Join ,from Choose the one with the highest cumulative strength Each element is used as a new bundle. From the final bundle The one that achieved the highest cumulative strength Given a set of elements, return the corresponding path. S43. By using short path search and long path search, paths of different scales are fully obtained, among which: Shortest path search: Set maximum depth Then, by executing the above bundle search algorithm, the set of shortest paths can be obtained. ; Long path search: Set minimum depth and maximum depth Then, by executing the bundle search algorithm, the set of long paths can be obtained. ; S44. Conduct a comprehensive evaluation of each causal path and provide a basis for root cause ranking and screening, as detailed below: Causal path ,in For path length, For the first on the path For each path with nodes, the overall score is defined as follows: ； in These are the weight coefficients for the corresponding items. Indicates the overall strength of the path. This refers to the path length and time delay consistency. Measuring the time-scale stationarity of causal relationships along a path: ； in Represents path variables Medium variables arrive The time lag between For scale parameters; Abnormal correlation This indicates the degree of correlation between variables on the path and abnormal states: ； in, These are predefined anomaly indicators used to reflect the fluctuation range or slope of change of anomalous variables. For variables Time series, and These are the corresponding means; For the final set of short paths and long path set According to the comprehensive scoring index Keep the shortest path and long path Then merge the two path sets: ； Ultimately based on the overall score Reorder to get the final result. The ranking of causal paths and their comprehensive scores provide on-site personnel with valuable insights into the root causes of abnormal furnace conditions.

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