A tundish erosion prediction method based on a hierarchical hybrid expert framework

Abstract

The application relates to the technical field of industrial process prediction, in particular to a tundish erosion prediction method based on a hierarchical hybrid expert framework. The method comprises the following steps: collecting tundish time series physical field data, screening features and constructing a unified feature space; shunting the feature space to obtain time series features and statistical aggregation features; training a classifier using the statistical aggregation features to generate calibrated posterior probability and construct a gating network; generating an initial mode subset based on the posterior probability and training a corresponding expert model; for the to-be-tested data, obtaining the confidence thereof from the gating network, and selecting a single expert model for prediction or fusing multiple expert models for weighted prediction through an adaptive strategy according to whether the confidence exceeds a threshold; and finally inversely transforming and reconstructing the prediction value into an absolute value of the erosion thickness. The application effectively improves the accuracy and adaptability of tundish erosion prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of industrial process prediction, in particular to a tundish erosion prediction method based on a hierarchical hybrid expert framework. BACKGROUND

[0002] In the steel continuous casting process, the tundish is a key equipment for distribution and buffering of molten steel, and the erosion degree of its refractory lining directly affects the production safety, molten steel cleanliness and equipment life. The erosion process is essentially a complex nonlinear time series dynamics problem under the combined action of high-temperature molten steel, multiphase turbulent scouring and chemical erosion, which is affected by multiple variables such as pulling speed, temperature, flow field structure, and the dominant physical mechanism will undergo discontinuous switching with the working condition, for example, from "flow field scouring dominant" to "thermal fatigue dominant".

[0003] In the prior art, tundish erosion prediction mainly relies on time series modeling methods based on a single global model. This kind of method tries to fit all working conditions with a set of fixed parameters, and when facing mechanism switching or data distribution drift, the "generalization cliff" phenomenon often occurs, and the prediction accuracy decreases sharply. In addition, the traditional sliding window model lags in response when the working condition changes step by step because it relies on historical window information, and cannot meet the requirements of real-time monitoring and rapid adjustment. At the same time, the existing hybrid model generally lacks an evaluation mechanism for model cognitive uncertainty, and when encountering an out-of-distribution abnormal working condition, it is easy to output false predictions instead of timely warnings, which poses a potential safety hazard in industry.

[0004] Therefore, it becomes a technical problem to be solved in the field to provide a tundish erosion prediction method that can accurately identify physical patterns, quickly respond to working condition changes, and has a safety warning mechanism. SUMMARY

[0005] The present application provides a tundish erosion prediction method based on a hierarchical hybrid expert framework to improve the accuracy and adaptability of tundish erosion prediction.

[0006] In a first aspect, the present application provides a tundish erosion prediction method based on a hierarchical hybrid expert framework, the method comprising:

[0007] S1, collecting time series physical field data of the tundish under multiple working conditions, and screening out feature variables related to erosion prediction by combining a causal analysis method to construct a unified feature space;

[0008] S2, performing shunt processing on the unified feature space to obtain time series features and statistical aggregation features;

[0009] S3, training a pattern recognition classifier using the statistical aggregation features to generate calibrated posterior probabilities and construct a gating network model;

[0010] S4, generating an initial mode subset based on the calibrated posterior probability, and training an expert model corresponding to each mode subset;

[0011] S5, inputting the to-be-tested time-series physical field data into the gating network model to obtain a to-be-tested data confidence probability, and judging whether the to-be-tested data confidence probability is greater than a preset confidence threshold; if yes, selecting a single expert model to perform prediction to obtain a prediction value; and if no, selecting multiple expert models to perform weighted fusion prediction through an adaptive strategy to obtain a prediction value;

[0012] S6, converting the prediction value into an actual erosion thickness absolute value as a final prediction result by using an inverse transformation reconstruction method.

[0013] Optionally, time-series physical field data of the intermediate package under multiple working conditions are collected, the time-series physical field data including flow velocity, turbulence intensity and temperature; a causal analysis method is used to filter out pressure-related features that may cause future information leakage, to obtain feature variables related to erosion prediction; a linear discriminant analysis method is used to reduce the dimension of the feature variables to obtain a unified feature space.

[0014] Optionally, time-series data that have not been compressed in the time domain are extracted from the unified feature space; an aggregation operator is calculated along the time dimension and channel by channel in the unified feature space, and the aggregation operator is spliced to obtain statistical aggregation features, the aggregation operator including mean, standard deviation and end time value.

[0015] Optionally, the statistical aggregation features are taken as training samples, a gradient boosting decision tree is used to construct an initial classifier to obtain original output scores of each sample corresponding to each physical mode; the original output scores are paired with real mode labels to form a calibration training set; an order-preserving regression algorithm is used to obtain a mapping relationship between the scores and the accuracy of the calibration training set, and a probability calibration model is constructed based on the mapping relationship; the original output scores are post-processed by using the probability calibration model to generate calibrated posterior probability; and the calibrated posterior probability is written into an output layer of the gating network model to obtain a gating network that can output real confidence.

[0016] Optionally, based on the calibrated posterior probability, each time sequence physical field sample is classified into a physical mode with the maximum probability to form an initial mode subset; based on the initial mode subset, the corresponding original time sequence features are divided into K independent training data; an expert network containing a bidirectional LSTM and a Transformer self-attention unit is constructed for each training data, and the expert network is independently trained on the respective mode subset to obtain K candidate expert models; the K candidate expert models are used to calculate sample-level prediction errors on a historical validation set to generate an expert performance matrix, and based on the expert performance matrix, the samples are remapped in combination with minimizing global errors to obtain an optimized final mode subset; the expert network is independently trained again on the final mode subset, and the corresponding expert model of each mode subset is obtained after the parameters are fixed.

[0017] Optionally, the time sequence physical field data to be measured is input into the gating network model to obtain the posterior probability of the to-be-measured data; the information entropy of the posterior probability of the to-be-measured data is calculated, and the preset confidence threshold is adjusted according to the information entropy; it is judged whether the posterior probability of the to-be-measured data is greater than the adjusted preset confidence threshold; if yes, a single expert model is selected for prediction to directly obtain a prediction value; if not, multiple expert networks are selected for weighted fusion prediction through an adaptive strategy to obtain a prediction value.

[0018] Optionally, an inverse transformation reconstruction method is used to load the inverse transformation parameter set saved in the training stage; the inverse standardization and the inverse logarithmization are sequentially performed according to the inverse transformation parameter set to obtain the instantaneous erosion thickness with a physical dimension; the instantaneous erosion thickness is converted into the actual erosion thickness absolute value of the tundish wall surface at the current time to obtain the final prediction result.

[0019] Optionally, in the weighted fusion prediction process, the variance of the prediction result of the activated expert model is calculated synchronously, and if the variance exceeds a preset safety limit, it is determined that the current working condition is an out-of-distribution anomaly, and an uncertainty warning signal is immediately output and switched to a fault safety prediction mode.

[0020] Optionally, the division of the initial mode subset is first pre-classified based on the physical parameter experience interval, and then iteratively optimized based on the expert performance matrix to remap the transition working condition with a fuzzy physical boundary to a mode with the minimum prediction error, so that the data-driven subset refinement is realized.

[0021] Optionally, the end time value is calculated in real time by using a sliding window single-step updating method, and when the working condition changes in steps, the gating network completes mode switching within 1-3 sampling periods to eliminate the recognition lag caused by the traditional sliding window.

[0022] Compared with the prior art, the beneficial effects of the present application are at least as follows:

[0023] The intermediate package erosion prediction method based on the hierarchical hybrid expert framework can significantly improve the accuracy and adaptability of intermediate package erosion prediction. By collecting time series physical field data under multiple working conditions and combining causal analysis to filter out feature variables related to erosion prediction, the problem of being unable to handle complex working condition changes in traditional methods is overcome. In addition, the present application can dynamically adjust the prediction model, switch the physical mode in real time when the working condition changes step by step, and fuse multiple expert models through an adaptive strategy, thereby avoiding the response lag problem of the traditional sliding window model. By introducing a gating network and weighted fusion of expert models, the prediction confidence under different working conditions can be accurately evaluated, and uncertainty warning can be provided when facing out-of-distribution anomalies, thereby ensuring the safety of the industrial process. These measures make the method have significant advantages in the field of intermediate package erosion prediction, especially in handling complex and nonlinear time series data and dynamically changing working conditions, and can provide more accurate and reliable prediction results. BRIEF DESCRIPTION OF DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor based on these drawings.

[0025] Figure 1 A flowchart of a method for predicting intermediate package erosion based on a hierarchical hybrid expert framework according to the present application;

[0026] Figure 2 A flowchart of a hybrid expert model decision-making method based on uncertainty perception according to the present application. DETAILED DESCRIPTION

[0027] The embodiment of the present application provides a method for predicting intermediate package erosion based on a hierarchical hybrid expert framework. The terms "first", "second", "third", "fourth" and the like (if any) in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily mean a specific order or sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the term "comprising" or "having" and any variation thereof is intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units does not necessarily limit to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0028] For the sake of understanding, the specific process of the embodiments of the present application will be described below. Please refer toFigure 1 One embodiment of a tundish erosion prediction method based on a hierarchical hybrid expert framework in the embodiments of the present application includes:

[0029] Step S1, sampling time series physical field data of the tundish under multiple working conditions, screening out characteristic variables related to erosion prediction combined with causal analysis method, and constructing a unified feature space.

[0030] In a specific embodiment, the process of performing step S1 can specifically include the following steps:

[0031] Sampling time series physical field data of the tundish under multiple working conditions, the time series physical field data including flow rate, turbulence intensity and temperature;

[0032] Using a causal analysis method to screen the time series physical field data, eliminating pressure-related features that may cause future information leakage, and obtaining characteristic variables related to erosion prediction;

[0033] Using a linear discriminant analysis method to reduce the dimension of the characteristic variables and obtain a unified feature space.

[0034] Specifically, sampling time series physical field data of the tundish under multiple working conditions, the data including physical quantities such as flow rate, turbulence intensity and temperature, the sampling frequency being 1 Hz, and the time window length being 30 seconds, thus forming an original time series matrix with a dimension of 30 x D, where D represents the total number of physical field variables.

[0035] The feature variables are screened by using a causality analysis method based on transfer entropy. The transfer entropy is an information theory-based metric for quantifying the causal influence of a candidate feature variable on the target variable, i.e., the erosion thickness. In implementation, the target variable of erosion thickness and each candidate feature variable, such as flow rate, turbulence intensity, temperature, and pressure, are respectively arranged into corresponding time series. Then, for each candidate feature variable, the transfer entropy value from the candidate feature variable to the target variable of erosion thickness is calculated. The core of the calculation is to evaluate how much the uncertainty of predicting the future value of the erosion thickness can be reduced by introducing the historical information of the candidate feature variable under the premise of knowing the historical information of the erosion thickness itself. This reduced uncertainty is the transfer entropy, and the value is in bits. Two key parameters, the historical embedding length, are required to be set during the calculation process, which are used to define the size of the erosion thickness historical window and the size of the candidate variable historical window. Then, by performing statistics on all time steps, the corresponding joint probability and conditional probability are estimated, and the calculation is completed according to the definition formula of the transfer entropy. In order to make a screening decision, a causal significance threshold, for example, 0.05 bits, needs to be set in advance. The calculated transfer entropy value of each candidate variable is compared with the threshold. If the transfer entropy value of a variable is lower than the threshold, it is considered that the variable lacks significant causal driving effect on the erosion thickness and should be excluded. In particular, analysis shows that the transfer entropy value of the pressure variable is usually lower than the threshold, and the future operation information may be hidden in its historical data, which will lead to future information leakage. Therefore, according to the causality analysis result, the pressure variable is excluded from the feature set. Finally, the variables whose transfer entropy values reach or exceed the threshold form the erosion prediction-related feature variable set.

[0036] It should be noted that the above causality analysis based on transfer entropy is only an example and is not the only limitation of the 'causality analysis method' in the present application. In other embodiments of the present application, the causality analysis method can also include but is not limited to: a method based on Granger causality test, a method based on convergent cross mapping, a causality discovery method based on conditional independence test (such as PC algorithm), or a method based on time-lag mutual information / correlation coefficient, etc. These methods can all quantify or infer the causal driving relationship between the feature variables and the target variable of erosion thickness from different angles, so as to achieve the common technical purpose of screening features with real causal correlation and avoiding the introduction of future information or pseudo-correlation features. Those skilled in the art can select a suitable causality analysis method according to the data characteristics and computing resources to achieve the purpose.

[0037] The screened feature variables are processed by using a linear discriminant analysis method (Linear Discriminant Analysis, LDA) to reduce the dimensionality, improve the class separability of the feature space, and reduce redundancy. Specifically, assuming that there are C physical mode categories, LDA finds the optimal projection direction W by solving a generalized eigenvalue problem: wherein, is the inter-class scatter matrix, is the intra-class scatter matrix, is the eigenvalue. By selecting the eigenvectors corresponding to the top k largest eigenvalues, a projection matrix is obtained. is the original high-dimensional feature , where n is the number of samples and m is the number of features. The original high-dimensional feature is projected into a low-dimensional subspace: , thereby obtaining a unified feature space , where k is much smaller than m. For example, in a specific implementation, the feature dimension can be reduced from the original 120 to 15, thereby obtaining a unified feature space, which not only retains most of the discriminative information, but also effectively suppresses noise and multicollinearity.

[0038] Taking the production data of one casting of a continuous caster as an example, the mean value of flow rate, the standard deviation of turbulence intensity, and the first-order lag value of temperature are identified as strong causal features with a transfer entropy value significantly higher than the threshold value, and each order statistic of the pressure variable is excluded. Subsequently, linear discriminant analysis is used to reduce the dimension of the 10 strong causal features selected, and the two-dimensional feature space after projection is visualized to show that the three physical mode categories corresponding to different casting speed intervals are clearly separated, the overlap between categories is significantly reduced, and the unified feature space constructed has good mode separability, laying a foundation for accurate identification of the subsequent gating network.

[0039] Step S2, performing shunt processing on the unified feature space to obtain time series features and statistical aggregation features.

[0040] In a specific embodiment, the process of performing step S2 can specifically include the following steps:

[0041] Extracting time series data that has not been compressed in the time domain from the unified feature space;

[0042] Calculating an aggregation operator along the time dimension for each channel of the unified feature space and concatenating the aggregation operators to obtain statistical aggregation features, the aggregation operator including the mean, standard deviation, and end time value.

[0043] Specifically, time series data that has not been compressed in the time domain is extracted from the unified feature space, which retains the original time dimension information, assuming that the dimension is , where is the time step, which is 30,The number of features after causal screening and dimension reduction is 2. This part of time series data is used as time series features and directly input into the subsequent expert network to retain the complete time series evolution details. For the unified feature space, an aggregation operator is calculated for each feature channel along the time dimension. For each feature channel, a set of predefined aggregation statistics is calculated along its time dimension independently. The aggregation operator at least includes: mean, used to capture the overall level of the feature within the time window; standard deviation, used to measure the fluctuation degree of the feature within the time window; and the last time value, which is the instantaneous value of the feature at the last sampling time of the time window. The introduction of the last time value gives the gating network the ability to quickly respond to step changes in working conditions.

[0044] In the specific calculation process, for a specific feature channel , the time series data of which is The calculation formula of the mean is:

[0045]

[0046] After the calculation is completed, the multiple aggregation operator results corresponding to each feature channel are spliced into a one-dimensional vector in the order of the features. This vector is the statistical aggregation feature, and the dimension of the statistical aggregation feature is , wherein is the number of aggregation operators calculated for each channel. For example, when and 3 operators (mean, standard deviation, and last time value) are calculated for each channel, the dimension of the statistical aggregation feature is 6. The statistical aggregation feature will be used as the input of the gating network.

[0047] In a specific implementation case, for the feature channel representing the flow rate, the mean reflects the average scouring intensity within the time window, the standard deviation reflects the pulsation of the flow rate, and the last time value can immediately capture the step change of the flow rate from 1.0 m / min to 1.4 m / min. Experiments show that after introducing the last time value, the gating network does not need to wait for the update of the entire 30-step window, but only needs the latest 1 to 3 data points to identify the trend change, realizes the response of the mode switching in seconds, and eliminates the identification lag caused by the traditional sliding window method.

[0048] Step S3, training a pattern recognition classifier using the statistical aggregation feature to generate a calibrated posterior probability and constructing a gating network model.

[0049] In a specific embodiment, the process of performing step S3 can specifically include the following steps:

[0050] The statistical aggregation feature is used as a training sample, and a gradient boosting decision tree is used to construct an initial classifier to obtain the original output score of each sample corresponding to each physical mode.

[0051] pair the original output scores with the true pattern labels to form a calibration training set;

[0052] obtain a mapping relationship between the scores and the accuracy of the calibration training set by using the monotonic regression algorithm, and construct a probability calibration model based on the mapping relationship;

[0053] perform post-processing on the original output scores by using the probability calibration model to generate calibrated posterior probabilities;

[0054] write the calibrated posterior probabilities into the output layer of the gating network model to obtain a gating network that can output true confidence.

[0055] Specifically, the statistical aggregation features are taken as training samples and input into an initial classifier constructed by gradient boosting decision trees for training. The training process adopts a supervised learning manner, and each training sample is composed of its statistical aggregation feature vector and the corresponding true physical pattern label. For example, in a dataset containing 1000 historical working condition samples, the statistical aggregation features of each sample are 6-dimensional vectors, and the label is a discrete value representing the physical mode to which it belongs (for example, 0 represents a low-speed scouring dominant mode, 1 represents a transition mixed mode, and 2 represents a high-speed thermal fatigue dominant mode). The gradient boosting decision tree model approximates the target function by iteratively constructing a series of weak learners (i.e., decision trees). Specifically, in each iteration m (m = 1, 2,..., M), the model calculates the negative gradient of the loss function (for classification tasks, the log-likelihood loss is commonly used) based on the integrated results of all the constructed trees, and takes the negative gradient as the pseudo-residuals to be fitted in the current round. Then, a new decision tree is trained to fit these pseudo-residuals, and the optimal weight of the tree is determined through linear search to minimize the loss function. Finally, the prediction results of all the trees are weighted and summed to obtain the original output scores of the sample belonging to each category. For a K-class classification problem (K = 3), the model outputs K scores, each of which is normalized by the Softmax function and the sum is 1, which can be used as the preliminary class confidence. Each training sample output by the classifier corresponds to the original output scores of each physical mode. These scores numerically reflect the preliminary confidence ranking of the model in attributing the sample to a certain mode, but due to the influence of model structure, optimization target and data distribution, their numerical size does not strictly equal the true posterior probability of the sample belonging to the mode. Then, the initial classifier is predicted on an independent validation set (for example, 200 samples not involved in training) to obtain the original output scores of the output, and these scores are paired with the true pattern labels of the samples in the validation set to form a calibration training set.

[0056] The ordination-preserving regression algorithm is used to obtain the mapping relationship between the scores and accuracy of the calibration training set. Ordination-preserving regression is a non-parametric probabilistic calibration model whose core is to find a monotonically increasing function that maps the raw output scores of the classifier to the true probability space. This mapping process is achieved by solving the following optimization problem:

[0057]

[0058] in, Representing the The original output scores of each sample It is the true pattern indicator variable corresponding to the sample (usually 0 or 1 in binary classification calibration, and can be handled by a one-to-many strategy in multi-class classification). The desired calibration function is a monotonically increasing function. The optimization objective is to minimize the squared error between the calibrated output and the true label while maintaining the monotonicity of the function. By solving this optimization problem, a mapping relationship from the original output score to the calibrated probability is obtained. A probabilistic calibration model is constructed based on this mapping relationship. Subsequently, the original output score is post-processed using this probabilistic calibration model. For any sample, its original output score is... Input calibration function To obtain the calibrated posterior probability This probability value truly reflects the likelihood that a sample belongs to the corresponding pattern. Finally, the overall computational framework integrating the initial gradient boosting decision tree classifier and the subsequent order-preserving regression calibration module is defined as a gated network model. In the actual deployment of this model, the calibrated posterior probability is written into the output layer of the gated network model; that is, the final interface provided by the model directly outputs the calibrated probability value, thus replacing the uncalibrated score output by the original classifier. Therefore, the constructed gated network becomes an integrated system capable of receiving statistically aggregated feature inputs and directly outputting the true confidence posterior probability.

[0059] In one specific embodiment, 1000 historical working condition samples collected from the production site were used for training and calibration. Before calibration, the gating network output a raw score of 0.65 for a certain transitional mode sample, but the actual belonging probability of this sample, verified by an independent test set, was only 0.42, indicating a significant overestimation. After applying the above-mentioned ordinal-preserving regression calibration, the calibrated probability output for this sample was adjusted to 0.45, which highly matches its actual probability. After this calibration, the pattern recognition accuracy of the gating network on the entire test set improved from 92.1% before calibration to 98.7%, significantly solving the problem of inaccurate classifier confidence and providing a reliable probabilistic basis for subsequent adaptive routing.

[0060] Step S4: Based on the calibrated posterior probabilities, generate an initial subset of patterns and train an expert model corresponding to each subset of patterns.

[0061] In a specific embodiment, the process of performing step S4 can specifically include the following steps:

[0062] Based on the calibrated posterior probability, each time series physical field sample is classified into the physical mode with the maximum probability to form an initial mode subset;

[0063] Based on the initial mode subset, the corresponding original time series features are divided into K independent training data;

[0064] For each training data, an expert network containing bidirectional LSTM and Transformer self-attention unit is constructed, and independent training is performed on the respective mode subset to obtain K candidate expert models;

[0065] The K candidate expert models are used to calculate the sample-level prediction error on the historical validation set to generate an expert performance matrix, and based on the expert performance matrix, the samples are remapped in combination with minimizing the global error to obtain an optimized final mode subset;

[0066] The expert network is independently trained again on the final mode subset, and the corresponding expert model of each mode subset is obtained after the parameters are fixed.

[0067] Specifically, based on the calibrated posterior probability, each time series physical field sample is classified into the physical mode with the maximum posterior probability to form an initial mode subset. For example, for fluid temperature field time series monitoring data, each sample is composed of temperature and flow rate sequences in the past 24 hours, and the calibrated posterior probability output is a vector , respectively corresponding to the three physical modes of "laminar flow", "transition flow" and "turbulent flow". If the of a certain sample is 0.83, it is classified into the "turbulent flow" mode subset corresponding to the probability value 0.83. After forming the initial mode subset, the time series physical field samples in the subset are divided into K independent training data subsets according to their belonging physical modes. For example, assuming that after initial division, the three mode subsets ("laminar flow", "transition flow" and "turbulent flow") (K=3) contain 1200, 800 and 1500 samples respectively, then the corresponding original multi-dimensional time series feature data (such as temperature, pressure, flow rate and other multi-sensor synchronous sequences) are also divided into three independent training data subsets.

[0068] For each subset of training data, an expert network is constructed, comprising a Bi-LSTM network and Transformer self-attention units. This network is then trained independently on the corresponding subset, yielding K candidate expert models. Taking the expert network corresponding to the "turbulence" mode as an example, its input layer receives the original temporal features of 1500 samples from this mode. The network captures the forward and backward dependencies of the sequence through the Bi-LSTM network, and its hidden state output... The calculation formula is:

[0069]

[0070] in, This represents the original temporal feature tensor of the input. and These represent the forward and backward LSTM units, respectively. and For its corresponding network parameters, This indicates a splicing operation along the feature dimension. The input is then fed into the Transformer's self-attention unit, which focuses on key time steps by calculating attention weights. Its core attention score matrix... The calculation formula is:

[0071]

[0072] in, Representative query, Representative key, It is a matrix transpose operation; both are performed by... The matrix obtained through linear transformation This is the dimension of the key vector; the Softmax function is used to normalize it to obtain the attention weights. The output of this unit... ( The value matrix is ​​then processed by a feedforward network to serve as the final feature representation of the expert network, used for subsequent regression or classification tasks. Each expert network is trained on its own independent subset of data, without interference. Forward prediction is performed on the historical validation set using the K candidate expert models, calculating the sample-level prediction error, and generating an expert performance matrix based on the sample-level prediction error. The historical validation set contains 300 labeled independent samples covering all patterns. Let the... The expert model for the first The prediction error of the validation samples is (For example, mean squared error). Then the expert performance matrix... It is a matrix with K rows and 300 columns, whose elements The matrix quantifies the performance of each expert model in handling any validation sample.

[0073] Based on the expert performance matrix, the time-series physical field samples are remapped and divided into subsets to obtain an optimized final pattern subset, with the goal of minimizing the global prediction error. This is achieved by solving an optimization problem: for each validation sample reassign an expert model with the goal of minimizing the total prediction error of all validation samples The optimization process can be achieved by the Hungarian algorithm and other methods. According to the optimization results, the samples in the training set are remapped and divided according to their most suitable expert model, thereby obtaining the optimized final pattern subset. This process may change the sample composition and quantity of each subset.

[0074] On the final pattern subset, the expert network is independently trained again, and after the parameters are fixed, the expert model corresponding to each pattern subset is obtained. After obtaining the final stable pattern subset division, the data of these subsets are used to train each expert network from scratch. After training, all parameters of the network are fixed to obtain a series of fixed expert models specialized in specific physical patterns.

[0075] Step S5, input the time-series physical field data to be measured into the gating network model, obtain the confidence probability of the data to be measured, and determine whether the confidence probability of the data to be measured is greater than the preset confidence threshold. If yes, select a single expert model for prediction to obtain a prediction value. If no, select multiple expert models for weighted fusion prediction through an adaptive strategy to obtain a prediction value.

[0076] In a specific embodiment, the process of performing step S5 can specifically include the following steps:

[0077] Input the time-series physical field data to be measured into the gating network model to obtain the posterior probability of the data to be measured;

[0078] Calculate the information entropy of the posterior probability of the data to be measured, and adjust the preset confidence threshold according to the information entropy;

[0079] Determine whether the posterior probability of the data to be measured is greater than the adjusted preset confidence threshold;

[0080] If yes, select a single expert model for prediction to directly obtain a prediction value;

[0081] If no, select multiple expert networks for weighted fusion prediction through an adaptive strategy to obtain a prediction value.

[0082] Specifically, the time series physical field data to be tested is input into the gating network model to obtain the posterior probability of the data to be tested. The data to be tested refers to the newly collected time series signal of the physical field that needs to be predicted or classified. Taking the temperature field of multiphase flow in a reactor in industrial process monitoring as an example, the data to be tested is the temperature time series collected from five temperature measuring points arranged at different heights of the reactor, with a length of 256 time steps (sampling interval of 1 second, about 4.27 minutes), forming an input tensor of [5, 256]. The gating network model is a pre-trained lightweight classifier (for example, a neural network with two fully connected layers, the input dimension is a fixed length vector after feature extraction, and the output dimension is K=4, corresponding to four operating modes of “steady operation”, “slight disturbance”, “moderate heat transfer unevenness”, and “serious abnormality”). The data to be tested is input into the gating network model, and the model outputs a K-dimensional posterior probability vector , wherein , represents the predicted probability that the data to be tested belongs to the kth mode. For example, the output of a certain test is . The information entropy of the posterior probability of the data to be tested is calculated, and the pre-set confidence threshold is adjusted according to the information entropy. The information entropy is used to quantify the uncertainty of the probability distribution , and the calculation formula is:

[0083]

[0084] wherein, is the posterior probability of the kth mode in , and the entropy value ranges between . For the above example , the calculation result is 7 (bits). The pre-set confidence threshold is initially set to 0.85. The adjustment mechanism is to dynamically adjust the pre-set confidence threshold according to the information entropy . The specific adaptive adjustment formula is:

[0085]

[0086] wherein, is an adjustment coefficient, which is a pre-defined positive number hyperparameter, for example, . The formula means that when the uncertainty of the posterior probability distribution is high (the entropy value is large), the confidence threshold is reduced, so that the system tends to adopt the fusion prediction; otherwise, the threshold is maintained or closer to a higher threshold. The calculation result of is obtained by substituting the formula. It is judged whether the posterior probability of the data to be tested is greater than the adjusted pre-set confidence threshold. The specific judgment method is to take the maximum probability value in . . For , . Compare and . Since , the judgment condition is yes.

[0087] If the judgment is yes, i.e., the maximum posterior probability of the to-be-tested data is greater than the adjusted threshold, a single expert model is selected for prediction, and the prediction value is directly obtained. According to the corresponding mode index (in the above example, the third mode, "moderate heat transfer unevenness"), a single expert model (denoted as ) specially trained and solidified for this mode is selected. The original to-be-tested time-series physical field data ([5, 256] temperature sequence) are directly input into the expert model . Based on its internal complex feature extraction and mapping (which may include time-series convolution, attention mechanism, etc.), the final prediction value is output. The prediction value can be a specific classification label, a continuous health index score, or a regression quantity. For example, the output prediction value is "heat transfer coefficient decline rate estimate = 0.15". This result is the final prediction value.

[0088] If the judgment is no, i.e., the maximum posterior probability of the to-be-tested data is not greater than the adjusted threshold, multiple expert networks are selected for weighted fusion prediction through an adaptive strategy, and the prediction value is obtained. Suppose another to-be-tested data has , and , , , so the fusion prediction path is triggered. The adaptive strategy is as follows:

[0089] Select multiple expert models: according to the size of the mode probability in , select the expert models corresponding to the top L modes with the highest probability, or select all expert models with a probability exceeding a certain small threshold (such as 0.1). In the above example, the top 2 models with the highest probability ( ) can be selected, or all models with a probability greater than 0.1 ( ) can be selected.

[0090] Weighted fusion prediction: input the to-be-tested data into each selected expert model to obtain the respective preliminary prediction values . Then, the posterior probabilities of the modes corresponding to these models are used as weights to perform weighted averaging to obtain the fusion prediction value :

[0091]

[0092] wherein, for the ensemble of expert models, for the preliminary prediction value, i is the index of the selected expert model, represents the posterior probability of the prediction result corresponding to the i-th expert model, represents the posterior probability of the prediction result corresponding to the j-th expert model, j represents a loop variable, and represents each model index when summing up in the selected expert model set.

[0093] For example, select , whose original probability is [0.30, 0.35, 0.25], and the normalized weight is about [0.333, 0.389, 0.278]. Assuming their prediction outputs are , the calculation is as the final prediction value. Referring to Figure 2 , the figure shows the flow chart of the mixed expert model decision-making based on uncertainty perception.

[0094] Step S6, using the inverse transform reconstruction method, converts the prediction value into the actual erosion thickness absolute value as the final prediction result.

[0095] In a specific embodiment, the process of performing step S6 can specifically include the following steps:

[0096] Using the inverse transform reconstruction method, load the inverse transform parameter set saved in the training phase;

[0097] According to the inverse transform parameter set, sequentially perform inverse normalization and inverse logarithm to obtain the instantaneous erosion thickness with physical dimension;

[0098] Convert the instantaneous erosion thickness into the actual erosion thickness absolute value of the tundish wall surface at the current time to obtain the final prediction result.

[0099] Specifically, in order to stabilize numerical calculation and improve model convergence, the original erosion thickness time series data is preprocessed and transformed. The preprocessing usually includes at least two steps: normalization and logarithm. The corresponding transformation parameters are calculated and saved in the training phase to form an inverse transform parameter set. In this embodiment, it is assumed that the parameter set includes:

[0100] Normalization parameters: mean value of erosion thickness sequence in training data set and standard deviation .

[0101] Logarithm parameters: a small offset constant , used to process zero or very small values before logarithm to ensure numerical stability. The training phase performs operation.

[0102] Examples of parameters saved in the training phase are: , , .

[0103] According to the inverse transformation parameter set, inverse normalization and inverse logarithmization are performed in sequence to obtain the instantaneous erosion thickness with physical dimension. Since the original erosion thickness data The normalization transformation formula executed during training is:

[0104]

[0105] The inverse transformation formula is:

[0106]

[0107] where, is the direct output value of the model, and are the loaded normalization parameters. The purpose of this step is to convert the model output from the standard normal distribution space back to the approximate scale of the original data. For example, if the model output , then the calculation is = 19.47 mm.

[0108] Since the logarithmization operation was performed before normalization, the inverse transformation formula is:

[0109]

[0110] where, is the loaded logarithmization offset constant. The purpose of this step is to undo the logarithmic transformation and restore the original linear scale and magnitude of the data. Continuing the example above, if = 2.5, then the calculation is After inverse normalization and inverse logarithmization are performed, the obtained is the instantaneous erosion thickness prediction value with physical dimension, whose unit is determined by the training data, such as millimeters.

[0111] Convert the instantaneous erosion thickness to the actual erosion thickness absolute value of the tundish wall surface at the current time to obtain the final prediction result. If the model predicts the instantaneous erosion increment or the change relative to a certain initial thickness, it needs to be converted to the absolute erosion thickness of the wall surface. Assuming that the original thickness of the tundish wall surface at the initial time (or after the last maintenance) is , then the actual erosion thickness absolute value of the current time is:

[0112]

[0113] For example, the initial design thickness of the tundish wall facing refractory material is known The instantaneous cumulative erosion thickness prediction value obtained after inverse transformation The absolute value of the actual thickness of the wall remaining at the current time is This value is the final prediction result, representing the quantitative assessment of the system on the erosion state of the tundish wall at the current time, which can be directly used for life prediction, maintenance decision, and other downstream tasks.

[0114] If the model predicts the instantaneous erosion rate or other related quantities, the conversion formula needs to be adjusted accordingly. However, the core principle remains the same: by loading the inverse transformation parameter set saved during training, all mathematical transformations during preprocessing are performed in reverse, and the abstract numerical values output by the model are restored to actual engineering parameters with clear physical meaning and units.

[0115] Further, during the execution of the weighted fusion prediction, the system simultaneously starts the prediction reliability monitoring mechanism. Specifically, when the system activates multiple expert models for fusion prediction due to insufficient confidence, it simultaneously calculates the statistical variance between the preliminary prediction results output by all activated expert models while calculating the final fusion prediction value. This variance value is used to measure the consistency of different expert models in predicting the same data. The system presets a variance safety threshold. This threshold is determined based on the statistical characteristics of the variance of the prediction results of each expert model during fusion prediction under normal historical operating conditions. After obtaining the variance of the current prediction task, it is immediately compared with the safety threshold.

[0116] If the calculated variance does not exceed the safety threshold, it indicates that the prediction results of each expert model are consistent, and the system's understanding of the current operating condition is relatively unified. At this time, the fusion prediction value is normally output as the final result.

[0117] If the calculated variance exceeds the safety threshold, it indicates that the activated multiple expert models have significant differences in predicting the current data. This high inconsistency strongly suggests that the operating condition represented by the input time-series physical field data may be outside the data distribution range learned by all expert models during the training phase, i.e., it belongs to an out-of-distribution abnormal operating condition.

[0118] Once it is determined to be out-of-distribution, the system will immediately execute a two-level response:

[0119] (1) Output an uncertainty warning signal. The system generates and sends an explicit uncertainty warning signal to the upper monitoring system. This signal at least contains the warning level, timestamp, and variance value exceeding the safety threshold, prompting the operator to pay attention to the abnormality of the current state and the unreliability of the prediction result.

[0120] (2) Switch to a fail-safe prediction mode. The system automatically switches from the current fusion prediction mode to a pre-defined, conservative fail-safe prediction mode. This mode does not rely on the outputs of the aforementioned expert models, but instead adopts a pre-defined safety strategy to generate the prediction results, such as directly outputting a specific identifier value representing "high uncertainty" or "human intervention required", or invoking a backup prediction module based on simple physical models or historical worst-case estimates, to ensure that the system's output behavior is deterministic and safe when facing unknown abnormalities, avoiding making incorrect decisions based on highly divergent fusion results.

[0121] Further, the division of the initial mode subset is first pre-classified by the physical parameter empirical interval, and then iteratively optimized according to the expert performance matrix, so that the transition working conditions with fuzzy physical boundaries are remapped to the mode with the minimum prediction error, and the data-driven subset refinement is realized. The first stage is pre-classification based on the physical parameter empirical interval. Before generating the initial mode subset, first, according to the domain knowledge or historical experience, one or more typical value ranges or empirical intervals of key physical parameters are defined for each target physical mode. For example, in the state monitoring of fluid machinery, the "vortex frequency main band" and "inlet and outlet pressure difference stability coefficient" can be used as key parameters. The system will first preliminarily classify the time series physical field samples into the physical mode categories represented by the corresponding empirical intervals according to the values of these key physical parameters calculated by the samples to be divided, forming a pre-classified mode subset. This ensures that the initial division has a solid physical basis and avoids the unreasonable mixing of modes in the physical sense that may be caused by pure data-driven methods. The second stage is iterative optimization and remapping based on the expert performance matrix. After obtaining the initial subset through pre-classification and training the first batch of candidate expert models, the system uses the expert performance matrix to start an iterative optimization process. The core of this process is to identify samples located near the boundaries of different physical mode empirical intervals, or samples processed by multiple expert models with similar errors. These samples usually correspond to transition working conditions with fuzzy physical boundaries. For these fuzzy samples, the system does not force to retain their initial labels in the pre-classification stage, but checks their prediction errors when processed by different candidate expert models according to the expert performance matrix. Then, the system reassigns each such fuzzy sample to the mode subset corresponding to the expert model with the minimum prediction error.

[0122] Further, the end time value is calculated in real time by using a sliding window single-step update method. When the working condition changes in steps, the gating network completes mode switching within 1-3 sampling periods, eliminating the recognition lag caused by the traditional sliding window. For scenes where the working condition changes in steps (for example, sudden increase in device load, jump in key process setting value), the advantage of this mechanism is particularly obvious. Since the new window contains end time data representing the latest state change, the gating network model can quickly re-evaluate the state representation of the entire sequence based on this latest information, thereby completing the identification and switching of the dominant physical mode within one to three sampling periods. For example, if the sampling period is 1 second, the system can complete the switching judgment from the "steady-state operation" mode to the "transient overload" mode within 1-3 seconds, and immediately call the corresponding expert model for prediction. This completely eliminates the recognition lag caused by the traditional sliding window method, which needs to wait for a complete window to be slowly filled with new data, and realizes near-real-time tracking and adaptive prediction of step changes in working conditions.

[0123] It can be understood that the execution subject of the present application can be a kind of intermediate package erosion prediction system based on hierarchical hybrid expert framework, also can be terminal or server, specific here is not limited.

[0124] The above-described and the above embodiments are only used to illustrate the technical solutions of the present application, but not limited thereto; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for predicting intermediate package erosion based on a hierarchical hybrid expert framework, characterized in that, The method includes: S1. Collect time-series physical field data of intermediate packages under multiple working conditions, combine causal analysis methods to screen out characteristic variables related to erosion prediction, and construct a unified feature space; S2. Perform splitting processing on the unified feature space to obtain temporal features and statistical aggregated features; S3. Use the statistical aggregation features to train a pattern recognition classifier, and use the order-preserving regression algorithm to calibrate the original score output by the classifier to generate a calibrated posterior probability. Use the calibrated posterior probability as the output of the gated network model to construct the gated network model. S4. Based on the calibrated posterior probabilities, generate an initial subset of patterns and train an expert model corresponding to each subset of patterns. S5. Input the time series physical field data to be tested into the gated network model, obtain the confidence probability of the data to be tested, and determine whether the confidence probability of the data to be tested is greater than the preset confidence threshold. If so, select a single expert model for prediction and obtain the predicted value. If not, select multiple expert models for weighted fusion prediction through an adaptive strategy and obtain the predicted value. S6. Using the inverse transformation reconstruction method, the predicted value is converted into the actual absolute value of the erosion thickness, which is used as the final prediction result. S2 includes: extracting time-series data that has not been compressed in the time domain from the unified feature space; calculating aggregation operators for each channel along the time dimension of the unified feature space, and concatenating the aggregation operators to obtain statistical aggregation features, wherein the aggregation operators include the mean, standard deviation and the final time value; S4 includes: based on the calibrated posterior probability, classifying each temporal physical field sample into the physical mode with the highest probability to form an initial mode subset; based on the initial mode subset, dividing the corresponding original temporal features into K independent training data; constructing an expert network containing bidirectional LSTM and Transformer self-attention units for each training data, and training it independently on their respective mode subsets to obtain K candidate expert models; using the K candidate expert models to calculate the sample-level prediction error on the historical validation set to generate an expert performance matrix; based on the expert performance matrix, remapping the samples by minimizing the global error to obtain the optimized final mode subset; training the expert network independently again on the final mode subset, and solidifying the parameters to obtain the expert model corresponding to each mode subset.

2. The method according to claim 1, characterized in that, S1 includes: Collect time-series physical field data of the intermediate package under multiple operating conditions, including flow velocity, turbulence intensity and temperature; The time-series physical field data were screened using causal analysis to remove pressure-related features that could lead to future information leakage, thus obtaining feature variables related to erosion prediction. The feature variables are reduced in dimensionality using linear discriminant analysis to obtain a unified feature space.

3. The method according to claim 1, characterized in that, S3 includes: Using statistical aggregated features as training samples, an initial classifier is constructed using gradient boosting decision trees to obtain the original output scores for each sample corresponding to each physical mode. The original output scores are paired with the real pattern labels to form a calibration training set; The mapping relationship between the scores and accuracy of the calibration training set is obtained by using the ordinal-preserving regression algorithm, and a probabilistic calibration model is constructed based on the mapping relationship. The original output score is post-processed using the probability calibration model to generate a calibrated posterior probability. The calibrated posterior probability is written into the output layer of the gated network model to obtain a gated network that can output the true confidence level.

4. The method according to claim 1, characterized in that, S5 includes: The time-series physical field data to be tested is input into the gated network model to obtain the posterior probability of the data to be tested. Calculate the information entropy of the posterior probability of the test data, and adjust the preset confidence threshold according to the information entropy; Determine whether the posterior probability of the test data is greater than the adjusted preset reliability threshold; If so, select a single expert model for prediction and directly obtain the predicted value; If not, an adaptive strategy is used to select multiple expert networks for weighted fusion prediction to obtain the predicted value.

5. The method according to claim 1, characterized in that, S6 includes: The inverse transform reconstruction method is adopted, and the inverse transform parameter set saved during the training phase is loaded; Based on the inverse transformation parameter set, inverse normalization and inverse logarithmic transformation are performed sequentially to obtain the instantaneous erosion thickness with physical dimensions; The instantaneous erosion thickness is converted into the absolute value of the actual erosion thickness of the tundish wall at the current moment to obtain the final prediction result.

6. The method according to claim 1, characterized in that, During the weighted fusion prediction process, the variance of the prediction results of the activated expert model is calculated simultaneously. If the variance exceeds the preset safety limit, the current operating condition is determined to be an out-of-distribution anomaly, and an uncertainty warning signal is immediately output and the system switches to the fault safety prediction mode.

7. The method according to claim 1, characterized in that, The initial mode subset is first pre-classified using empirical ranges of physical parameters, and then iteratively optimized based on the expert performance matrix to remap the transitional working conditions with ambiguous physical boundaries to the mode with the smallest prediction error, thereby achieving data-driven subset refinement.

8. The method according to claim 1, characterized in that, The final time value is calculated in real time using a sliding window single-step update method. When the operating conditions change abruptly, the gating network completes the mode switching within 1 to 3 sampling periods, eliminating the recognition lag caused by the traditional sliding window.

Images