Pressure compensation-based dynamic sizing control method for welded pipe

Abstract

This invention provides a dynamic adjustment control method for welded pipe sizing based on pressure compensation. The method includes collecting historical production data of welded pipes, using kernel density estimation to identify high-density regions of process parameters and calculating the covariance matrix, training prediction models for each region to construct an initial model pool; during real-time production, selecting candidate models based on the matching relationship between current process parameters and each high-density region, generating a disturbance vector set based on the covariance matrix of the most relevant region, and calculating the local prediction sensitivity of the candidate models; combining historical prediction accuracy, operating condition relevance, and local prediction sensitivity to select an active model subset, and dynamically weighting and integrating them to obtain the predicted outer diameter value; outputting the sizing frame adjustment control quantity based on the deviation between the predicted outer diameter value and the target value, and triggering online fine-tuning of the model when the error evaluation meets the preset fine-tuning trigger condition.

Description

Technical Field

[0001] This application belongs to the field of pressure compensation, and in particular relates to a dynamic adjustment and control method for welded pipe sizing based on pressure compensation. Background Technology

[0002] In the welded pipe production process, the sizing process plays a crucial role in controlling the outer diameter of the finished product and correcting deviations from previous forming processes. Current sizing adjustments largely rely on manual intervention based on operator experience, making it difficult to consistently guarantee adjustment efficiency and dimensional consistency. With the development of data-driven control technology, some methods have begun to collect production process parameters and build predictive models to assist in decision-making regarding the adjustment process of the sizing stand. However, the welded pipe production process is characterized by multivariate coupling and nonlinear changes. Actual operating conditions are easily affected by factors such as batch differences in raw materials, fluctuations in the forming unit's status, and changes in ambient temperature, causing process data to exhibit local clustering, dynamic drift, and distributional differences.

[0003] Existing sizing prediction and control methods typically employ a single global model or a static model ensemble strategy, which struggles to fully characterize the differentiated data patterns under various local operating conditions. When production conditions change or fluctuate, the generalization ability of the global model tends to decline. Traditional static ensemble methods often allocate weights based on historical overall errors, failing to adequately consider the model's compatibility with current real-time conditions and its local sensitivity to minor parameter disturbances. This results in prediction results and control variables failing to adapt promptly to changes in production status, increasing the risk of pipe outer diameter deviations. Therefore, how to integrate local operating condition characteristics to achieve dynamic optimization and adaptive weighted ensemble of the prediction model, thereby improving the stability of welded pipe outer diameter prediction and the adaptability of sizing regulation control, is a technical problem that needs to be solved in the field of intelligent control for welded pipe manufacturing. Summary of the Invention

[0004] To address the problems in existing welded pipe sizing prediction models, such as difficulty in adapting to local operating condition drift, insufficient accuracy of static weight allocation, and lag in adjustment and control leading to fluctuations in outer diameter, this invention proposes, in a first aspect, a pressure-compensated dynamic adjustment and control method for welded pipe sizing, comprising:

[0005] We acquire historical production data of welded pipes containing process parameters and outer diameter sizing results, use kernel density estimation to identify parameter density peak regions and calculate the corresponding covariance matrix, and build an initial model pool for training domain-specific prediction models for each region. The real-time process parameters of the welded pipe to be adjusted are obtained, the distance between the real-time process parameters and the center of the peak density region of each parameter is calculated to obtain the working condition correlation, K candidate models are selected based on the working condition correlation, and a perturbation vector set is generated based on the covariance matrix of the peak density region of the parameter with the highest working condition correlation. The real-time process parameters and the perturbation parameters in the perturbation vector set are input into the candidate models respectively, and the local prediction sensitivity is calculated. The historical prediction accuracy of the candidate models is obtained. Based on the historical prediction accuracy, working condition relevance and local prediction sensitivity, the comprehensive score is calculated. Based on the comprehensive score, M models are selected to form an active model subset. Based on the active model subset, the static integration benchmark weight is calculated. Based on the local prediction sensitivity, the static integration benchmark weight is corrected and normalized to obtain the dynamic integration weight. The predicted outer diameter is obtained by weighting and summing the output of the active model subset using dynamic integrated weights. The adjustment control quantity of the sizing frame is output based on the deviation between the predicted outer diameter and the preset target value. The actual outer diameter detection value of the continuously produced welded pipe is obtained. The error evaluation is performed on the predicted outer diameter and the output of the active model subset based on the actual outer diameter detection value. When the error evaluation result meets the preset fine-tuning trigger condition, the model that meets the preset model fine-tuning condition is fine-tuned online.

[0006] On the other hand, the present invention also proposes a pressure-compensated welded pipe sizing dynamic adjustment control system, comprising: The module is used to acquire historical production data of welded pipes containing process parameters and outer diameter sizing results, use kernel density estimation to identify parameter density peak regions and calculate the corresponding covariance matrix, and build an initial model pool for training domain-specific prediction models for each region. The calculation module is used to obtain the real-time process parameters of the welded pipe to be adjusted, calculate the distance between the real-time process parameters and the center of the peak region of each parameter density to obtain the working condition correlation, screen K candidate models based on the working condition correlation, generate a perturbation vector set based on the covariance matrix of the peak region of the parameter density with the highest working condition correlation, and input the real-time process parameters and the perturbation parameters in the perturbation vector set into the candidate models respectively to calculate the local prediction sensitivity. The transformation module is used to obtain the historical prediction accuracy of candidate models, calculate the comprehensive score based on the historical prediction accuracy, working condition relevance and local prediction sensitivity, select M models to form an active model subset based on the comprehensive score, calculate the static integration benchmark weight based on the active model subset, and correct and normalize the static integration benchmark weight based on the local prediction sensitivity to obtain the dynamic integration weight. The fine-tuning module is used to obtain the predicted outer diameter value by weighted summation of the output of the active model subset using dynamic integrated weights, output the adjustment control amount of the sizing frame based on the deviation between the predicted outer diameter value and the preset target value, obtain the actual outer diameter detection value of the continuously produced welded pipe, evaluate the error between the predicted outer diameter value and the output of the active model subset based on the actual outer diameter detection value, and perform online fine-tuning on the model that meets the preset model fine-tuning conditions when the error evaluation result meets the preset fine-tuning trigger conditions.

[0007] This invention identifies parameter density peak regions in historical process data through kernel density estimation and constructs domain-specific prediction models for different operating conditions. During real-time sizing adjustment, candidate models are evaluated by combining operating condition correlation and local prediction sensitivity. The stability of the model's response near the current parameters is analyzed using a disturbance vector set generated based on the covariance matrix, thereby selecting a subset of active models that better suits the current production state. Furthermore, historical prediction accuracy, error covariance, and dynamic confidence information are integrated to adaptively weight and integrate the active model subset, obtaining the predicted outer diameter value and outputting the sizing stand adjustment control quantity. Simultaneously, error evaluation is performed based on the actual outer diameter detection value, and online fine-tuning of relevant models is conducted when preset fine-tuning conditions are met, which helps improve the prediction stability and control adaptability of welded pipe sizing. Attached Figure Description

[0008] Figure 1 The flowchart shows a dynamic adjustment control method for welded pipe sizing based on pressure compensation. Figure 2 This is a schematic diagram of clustering based on operating conditions. Figure 3 This is a schematic diagram of the historical error sequence; Figure 4 This is a schematic diagram of the ablation experiment results. Detailed Implementation

[0009] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0010] One or more embodiments of the present invention provide a dynamic adjustment and control method for welded pipe sizing based on pressure compensation, such as... Figure 1 As shown, the method includes: S1. Obtain historical production data of welded pipes containing process parameters and outer diameter sizing results. Use kernel density estimation to identify parameter density peak regions and calculate the corresponding covariance matrix to build an initial model pool for training domain-specific prediction models in each region.

[0011] The process parameters of strip wall thickness, strip width, forming roll reduction, and welding speed from the historical production process are read from the programmable logic controller via industrial Ethernet and aligned with the finished product outer diameter sizing results recorded by the laser diameter measuring instrument to obtain the historical sample set.

[0012] A kernel density estimation model was constructed, a Gaussian kernel function was set, and the optimal bandwidth parameter was determined using a grid search cross-validation algorithm. Density fitting was then performed on the multidimensional space of process parameters from a historical sample set. Based on the fitted continuous density field, a local extremum search algorithm was used to identify the coordinates of multiple local maxima points, which served as the centers of the parameter density peak regions. For each peak region, a Euclidean distance threshold was defined to extract a local data subset, and the covariance matrix of the feature dimension of this data subset was calculated.

[0013] Using subsets of data from each peak region as the training set, multiple regression models based on extreme gradient boosting trees are instantiated using the xgboost library for training. Mean squared error is used as the loss function, and the tree structure and leaf weights are updated based on the first and second gradient statistics of the loss function. All converged models are serialized, saved, and loaded into an in-memory database to form the initial model pool. Optionally, a multilayer perceptron network can also be used as the model.

[0014] In an optional embodiment, the step of acquiring historical welded pipe production data including process parameters and outer diameter sizing results, identifying parameter density peak regions using kernel density estimation and calculating the corresponding covariance matrix, and constructing an initial model pool for training domain-specific prediction models for each region includes: A multidimensional probability density function is constructed based on the multidimensional process parameters of the historical welded pipe production data. The mean-shift algorithm is used to iteratively optimize on the multidimensional probability density surface. The coordinates of the sample points and the probability density gradient vector are transformed into a dimensionless parameter space. The position of the sample points is updated along the upward direction of the probability density gradient in the dimensionless parameter space, and the magnitude of the dimensionless gradient vector is calculated until the magnitude is less than a preset convergence threshold. The convergence point in the dimensionless parameter space is inversely transformed to the original process parameter space and used as the center of the parameter density peak region. The sample points that converge to the center of the same parameter density peak region are clustered into an independent operating condition region, and the covariance matrix of the multidimensional process parameters of all sample points in the independent operating condition region is calculated. Based on the sample data in each independent working condition area, a corresponding domain-specific prediction model is trained, and an initial model pool is constructed from each domain-specific prediction model.

[0015] Four key process parameters were extracted from the historical data of welded pipe production: wall thickness (optimized range of 4.0 to 12.0 mm), strip width (e.g., 300 to 800 mm), forming roll reduction (e.g., 2.0 to 8.0 mm), and welding speed (e.g., 10 to 30 meters per minute). These parameters were then used to form a 4-dimensional feature vector space.

[0016] A Gaussian kernel function is used, and a basic kernel bandwidth parameter matrix is ​​set. For example, the bandwidth of the wall thickness dimension in the diagonal matrix is ​​set to 0.2 mm, and the speed is set to 1.5 meters per minute. After calculating the initial probability density surface, all data points in the historical data are selected as starting sample points. In the optimization phase, the mean-shift algorithm is used to calculate the probability density gradient vector at the current position of each starting sample point, and the coordinates of the sample point and the components of each dimension of the gradient vector are transformed to a dimensionless parameter space.

[0017] The Euclidean norm of the dimensionless gradient vector is calculated, and the sample points are guided to update their positions along the gradient ascent direction in the dimensionless parameter space with a preset step size. This iterative process continues until the calculated Euclidean norm is less than a preset convergence threshold, preferably 5 × 10⁻⁶. -5 At this point, the sample point stops moving, and its stationary position in the dimensionless parameter space is inversely transformed to the original process parameter space to obtain the center of the parameter density peak region.

[0018] Iterate through the coordinates of all converged sample points. If the dimensionless Euclidean distance between any two converged points is less than the clustering merging threshold (e.g., 0.01), they are identified as the center of the same parameter density peak region. Initial historical sample points belonging to the same convergence center are divided into an independent working condition region. Taking the two-dimensional parameter plane composed of the two core process parameters of wall thickness and welding speed as an example, the distribution of working condition regions obtained by mean-shift clustering is as follows: Figure 2 As shown.

[0019] The number of samples included in the independent operating condition region is counted, such as 2400 samples. The 4×4 covariance matrix of the multidimensional process parameters in the independent region is calculated using the standard sample covariance formula, which represents the joint distribution and fluctuation characteristics of different physical parameter variables under the specific operating condition.

[0020] Each domain-specific prediction model is trained using sample data from each independent working condition region. The domain-specific prediction model is a machine learning regression model, specifically one or more of the following: XGBoost regression model, support vector regression model, or multilayer perceptron regression model. The trained domain-specific prediction models are collected and saved to form an initial model pool.

[0021] S2. Obtain the real-time process parameters of the welded pipe to be adjusted, calculate the distance between the real-time process parameters and the center of the peak density region of each parameter to obtain the working condition correlation, select K candidate models based on the working condition correlation, generate a perturbation vector set based on the covariance matrix of the peak density region of the parameter with the highest working condition correlation, input the real-time process parameters and the perturbation parameters in the perturbation vector set into the candidate models respectively, and calculate the local prediction sensitivity.

[0022] The OPC unified architecture protocol is used to collect real-time process parameters such as strip wall thickness, strip width, forming roll reduction, and welding speed of the current production batch from the equipment control bus, and combine them into a feature vector of the current working condition.

[0023] Combining the inverses of the covariance matrices obtained in the first step, calculate the Mahalanobis distance between the current operating condition feature vector and the center vectors of all parameter density peak regions. After negativening the Mahalanobis distance, perform an exponential mapping to obtain the operating condition correlation with values ​​within a preset range.

[0024] Run the quicksort algorithm to sort the parameters in descending order of relevance to the working conditions, and select the top K parameter density peak regions and their corresponding regressors as K candidate models.

[0025] For the parameter density peak region with the highest correlation to the operating conditions, after dimensionless processing of its covariance matrix, matrix decomposition is performed to obtain a one-dimensional array of eigenvalues ​​and a two-dimensional matrix of orthogonal eigenvectors.

[0026] In the dimensionless parameter space, along each eigenvector direction, a spatial perturbation step is generated by multiplying the corresponding eigenvalue square root by a preset scaling factor. After transforming the current operating condition eigenvector to the dimensionless parameter space, a vector addition operation is performed with each spatial perturbation step, and the perturbed parameters are inversely transformed back to the original process parameter space to generate a perturbation vector set containing multiple test samples.

[0027] The current operating condition feature vector and each disturbance parameter vector in the disturbance vector set are input one by one into K candidate models for forward inference to obtain the baseline outer diameter prediction value and the disturbance outer diameter prediction value.

[0028] The partial derivative matrix of the prediction difference relative to the perturbation step size is calculated using the central finite difference numerical differential algorithm, and the L2 norm of this partial derivative matrix is ​​calculated. This L2 norm scalar value is used as the local prediction sensitivity to measure the degree to which each candidate model responds drastically to small changes in the current operating condition input.

[0029] In an optional embodiment, calculating the distance between the real-time process parameters and the center of each parameter density peak region to obtain the operating condition correlation includes: The Mahalanobis distance between the real-time process parameters and the center of the density peak regions of each parameter is calculated using the inverse matrix of the covariance matrix corresponding to the peak regions of each parameter density. The negative Mahalanobis distance is used as the independent variable of the exponential function to calculate the corresponding working condition correlation. The smaller the Mahalanobis distance, the higher the output working condition correlation.

[0030] When the real-time process parameters of the welded pipe to be adjusted, such as an input vector containing 4-dimensional features, wall thickness of 6.5mm, strip width of 500mm, forming roll reduction of 4.2mm, and welding speed of 20 meters per minute, are collected in real time, the center vectors of the peak density regions of each parameter obtained from historical clustering and the corresponding multi-dimensional process parameter covariance matrices are retrieved respectively. The inverse matrix of the covariance matrix of each region is obtained through matrix inversion.

[0031] The Mahalanobis distance between the eigenvector of the current real-time process parameter and the center vector of the k-th parameter density peak region is calculated one by one using the standard formula. For example, when the current real-time process parameter is close to the center of a certain historical normal operating condition, the Mahalanobis distance calculated by the quadratic form of the eigenvector and the inverse covariance matrix may be 1.25.

[0032] After obtaining the Mahalanobis distances corresponding to each peak region, to convert the distance values ​​in the range of zero to positive infinity into a nonlinear probabilistic metric between 0 and 1, the Mahalanobis distance is negatively represented as the independent variable of the natural exponential function. A distance decay adjustment coefficient, preferably set between 0.5 and 2.0 (1.0 in this example), is used within the exponential function and multiplied by the negative Mahalanobis distance. For the Mahalanobis distance of 1.25 calculated above, the operating condition correlation calculated by the exponential function is... ≈0.2865.

[0033] Through this monotonically decreasing exponential mapping mechanism, it can be ensured that when the real-time process parameters match a certain historical operating condition center more closely and the Mahalanobis distance is closer to 0, the operating condition correlation output by the model approaches the highest value of 1.

[0034] In an optional embodiment, generating a perturbation vector set based on the covariance matrix of the parameter density peak region with the highest correlation to operating conditions includes: After dimensionless processing, the covariance matrix of the parameter density peak region with the highest correlation to the real-time process parameters is decomposed to obtain multiple eigenvectors and corresponding eigenvalues. Each eigenvector is used as a parameter perturbation direction, and the square root of the corresponding eigenvalue is multiplied by a preset scaling factor to obtain the dimensionless perturbation amplitude in the direction. After the real-time process parameters are dimensionless, the dimensionless disturbance amplitude is increased and decreased along the disturbance direction of each parameter, and then inverse dimensionless processing is performed to generate a disturbance vector set composed of multiple disturbance parameters.

[0035] Select the independent operating condition region that has the highest operating condition correlation with the current real-time process parameters, for example, the calculated correlation is 0.85, and extract its corresponding original process parameter covariance matrix of size 4×4.

[0036] Extract the standard deviation of each parameter within the operating condition region to construct a diagonal variance matrix. Then, perform pre- and post-matrix multiplication on the original covariance matrix to complete the dimensionless standardization process.

[0037] Eigenvalue decomposition is performed on the generated standard correlation coefficient matrix to extract four mutually orthogonal eigenvectors and their corresponding four eigenvalues. These four orthogonal eigenvectors are then defined as four independent parameter perturbation directions. The square root of the eigenvalue for each direction is calculated and multiplied by a preset scaling factor, preferably between 0.01 and 0.10; here, 0.05 can be used. For example, if the square root of a principal eigenvalue is 2.0, multiplying it by 0.05 sets the dimensionless perturbation amplitude for that direction to 0.1. This process preserves the fluctuation proportions of historical operating data, allowing highly volatile parameter directions to obtain larger perturbation step sizes.

[0038] The current real-time process parameters are retrieved synchronously and subjected to dimensionless processing using the same mean and standard deviation. Based on this, the previously calculated dimensionless perturbation amplitudes are accumulated in the positive direction and subtracted in the negative direction along the four feature vectors obtained above, thereby generating a total of 8 sets of edge perturbation samples in the dimensionless high-dimensional space.

[0039] The eight groups of dimensionless samples were uniformly subjected to inverse dimensionless processing, that is, multiplied by the standard deviation corresponding to each feature and the mean was added in turn to restore the data to the engineering operation space with actual units such as millimeters or meters per minute, and a perturbation vector set containing eight bias process states was constructed.

[0040] In an optional embodiment, the step of inputting real-time process parameters and perturbation parameters from the perturbation vector set into the candidate model respectively, and calculating the local prediction sensitivity, includes: The real-time process parameters and the corresponding disturbance parameters in the disturbance vector set are input into K candidate models respectively, and the baseline outer diameter prediction value and the disturbance outer diameter prediction value output by each candidate model are obtained. Calculate the difference between the predicted outer diameter of each disturbance and the predicted outer diameter of the reference. Perform dimensionless processing on the difference and the corresponding disturbance amplitude. Divide the dimensionless difference by the corresponding dimensionless disturbance amplitude to obtain the dimensionless directional derivative. Calculate the square root of the sum of squares of the dimensionless directional derivatives to obtain the gradient norm of each candidate model under the current real-time process parameters, and use the gradient norm as the local prediction sensitivity of each candidate model.

[0041] The disturbance vector set generated by the above process, for example, includes 8 sets of parameter feature sets after biasing the current real-time operating conditions, and the unperturbed baseline real-time process parameters, respectively, which are then input into the K candidate prediction models initially selected.

[0042] When the candidate prediction model employs a multilayer perceptron network (MLPF), the MPF adopts a feedforward network architecture, comprising an input layer, multiple hidden layers, and an output layer. The input layer of the MPF receives real-time process parameters or perturbation parameters with 4-dimensional features as input data, including wall thickness, strip width, forming roll reduction, and welding speed. The hidden layers of the MPF contain several neurons, and feature extraction and nonlinear mapping are achieved through a combination of linear transformations and activation functions. The forward propagation process is represented as follows: ,in This represents the output matrix of the i-th hidden layer. This represents the output or input data of the previous hidden layer. This represents the connection weight matrix of the i-th hidden layer. denoted by , where f represents the corresponding bias parameter term, and f represents the nonlinear activation function.

[0043] The output layer of the multilayer perceptron network consists of a single linear neuron, used to perform regression and combination calculations on the high-order features output from the last hidden layer. When the input is an unperturbed real-time process parameter, the output is a baseline outer diameter prediction; when the input is a perturbed parameter, the output is a perturbed outer diameter prediction. The inference process for each candidate model will output one baseline outer diameter prediction. Assuming that the baseline outer diameter output of a certain model is 219.00 mm and the corresponding eight perturbed outer diameter predictions for the aforementioned perturbed vector set, for example, the output outer diameter prediction value under a positive perturbation of a certain feature vector is 219.05 mm.

[0044] For any candidate model among the K models, iterate through and calculate the absolute deviation between each predicted outer diameter value of the disturbance and the predicted outer diameter value of the baseline. For example, calculate the difference between 219.05 mm and 219.00 mm, which is 0.05 mm. Use the pre-calibrated outer diameter process tolerance range to perform dimensionless processing on this outer diameter prediction difference, and extract the dimensionless disturbance amplitude corresponding to the generation of this disturbance sample, such as the 0.1 set in the previous step.

[0045] Divide the dimensionless output prediction difference by the corresponding dimensionless input perturbation amplitude to obtain the dimensionless directional derivative of the candidate model in the perturbation direction. This derivative quantifies the model's response rate to input changes.

[0046] After calculating the dimensionless directional derivatives of the candidate model in all perturbation directions, the L2 norm is solved by summing the squares of all directional derivatives generated by the model and taking the square root. The calculated norm result is then confirmed as the gradient norm of the candidate model under the current real-time process parameters.

[0047] The gradient norm is used as the local prediction sensitivity of the model. For example, the gradient norm of a candidate model is calculated to be 1.85. The larger the value, the stronger the sensitivity of the candidate model to small input disturbances at the current operating point, and the lower the stability of the prediction output.

[0048] S3. Obtain the historical prediction accuracy of the candidate models. Calculate the comprehensive score based on the historical prediction accuracy, working condition relevance, and local prediction sensitivity. Select M models to form an active model subset based on the comprehensive score. Calculate the static integration benchmark weights based on the active model subsets. Correct and normalize the static integration benchmark weights according to the local prediction sensitivity to obtain the dynamic integration weights.

[0049] Retrieve the absolute percentage error data sequences of K candidate models within the past two-hour time window from the time series database, and map them to the historical prediction accuracy scalar by taking the reciprocal.

[0050] Set preset weight coefficients for historical prediction accuracy, operating condition correlation, and local prediction sensitivity. After normalizing the historical prediction accuracy, operating condition correlation, and local prediction sensitivity, multiply the historical prediction accuracy and operating condition correlation by their respective weight coefficients and add them together. Subtract the product of local prediction sensitivity and the penalty coefficient to calculate the comprehensive score of each candidate model.

[0051] The quicksort algorithm is run again on the overall score, and the top M highest-scoring model instances are selected to form a subset of active models.

[0052] Extract the prediction residual time series of M models on the recent validation dataset, calculate the error covariance matrix among these M models, and use mathematical statistics methods to calculate the root mean square error of the residuals of each model.

[0053] Based on this error covariance matrix, we solve the Lagrange multiplier method quadratic programming optimization problem with a sum-to-one constraint, thereby obtaining the static integrated benchmark weight vector that minimizes the overall integrated prediction variance theory.

[0054] The static ensemble baseline weights are corrected and normalized based on the local prediction sensitivity to obtain the dynamic ensemble weights. Specifically, the calculated local prediction sensitivity is input into a negative exponential decay activation function with the natural constant as the base, transforming it into a dynamic confidence factor that is inversely proportional to the sensitivity. The static ensemble baseline weights of each model are then multiplied element-wise by the corresponding dynamic confidence factor, and normalized by summation and division to obtain a one-dimensional array of dynamic ensemble weights.

[0055] In an optional embodiment, the calculation of static ensemble baseline weights based on a subset of the active model includes: Calculate the prediction error sequence of M models in the active model subset on the recent historical validation set to obtain the root mean square error of prediction for each model; Calculate the covariance between each pair of the prediction error sequences of the M models, and construct an error covariance matrix of size M×M; For any model in the subset of active models, the reciprocal of the root mean square error of prediction is calculated as the first evaluation factor. The sum of the error covariances of the model and all other models is calculated. The sum of the error covariances is dimensionless. The negative value of the dimensionless result is used as the independent variable of the exponential function to calculate the second evaluation factor. After multiplying the first evaluation factor and the second evaluation factor, the results of all models in the active model subset are normalized to obtain the static integrated benchmark weights of each model.

[0056] For the M models selected and included in the active model subset by the preliminary evaluation process (e.g., M equals 3 high-performance prediction models), retrieve their historical prediction output sequences generated from the most recent historical validation set, such as records of 500 welded pipes with real outer diameter measurement labels produced recently. Subtract the model prediction sequence from the real label sequence to obtain the residual, and use this to calculate the root mean square error (RMSE) of each model. For example, the RMSEs of these three models are 0.12 mm, 0.15 mm, and 0.18 mm, respectively. The prediction residual change sequences of the three candidate models within the sample interval are shown below. Figure 3 As shown.

[0057] The 500 discrete prediction residuals of each model are treated as a one-dimensional error vector sequence. Covariance is calculated for each pair of models to construct a 3×3 error covariance matrix, quantifying the correlation and redundancy of prediction errors among the candidate models. For each model in the active model subset (taking the first model as an example), the reciprocal of its root mean square error (RMSE), 8.33, is extracted and designated as the primary evaluation factor for measuring the model's basic accuracy.

[0058] Simultaneously, from the aforementioned 3×3 error covariance matrix, the cross-covariances of this model and the other two models are extracted and summed (i.e., the row summation of off-diagonal elements). This summation of covariances is then divided by the absolute value of the sum of all cross-covariances in the matrix to render it dimensionless. The dimensionless value is then negative and used as the independent variable of the natural exponential function for calculation. For example, the equation is: The coefficient γ is preferably set to 1.0 here, and the second evaluation factor representing the independence of the model is calculated to be, for example, 0.65. The higher this independence evaluation factor, the lower the probability that the model will commit the common source error in cluster decision-making.

[0059] Multiply the first evaluation factor by the second evaluation factor, resulting in 5.41. Calculate the product scores for the other two candidate models using the same procedure. Aggregate the product results of all M models, using their absolute sum as the denominator and the product of each model as the numerator. Perform a normalization operation to limit the sum of the weights of all models to 1.0.

[0060] The normalized set of proportional coefficients, such as the constant sequence calculated and distributed as 0.45, 0.35 and 0.20, serves as the static integrated baseline weights assigned by the system to these M activity models.

[0061] In an optional embodiment, obtaining the historical prediction accuracy of the candidate model and calculating a comprehensive score based on the historical prediction accuracy, working condition correlation, and local prediction sensitivity includes: Obtain the root mean square error of each candidate model's predictions on the recent historical validation set, and take the reciprocal as the historical prediction accuracy. The historical prediction accuracy, working condition correlation, and local prediction sensitivity are normalized and mapped to the same dimensionless interval. A positive weighting coefficient is assigned to the normalized historical prediction accuracy and the correlation with operating conditions, and a negative weighting coefficient is assigned to the normalized local prediction sensitivity. The normalized indicators are multiplied by their corresponding weight coefficients and summed to obtain the overall performance score of each candidate model.

[0062] In the comprehensive performance evaluation phase of candidate models, the root mean square error (RMSE) of predictions for the K candidate models generated in the previous screening is extracted on the most recent historical sample set, for example, a sample set covering 1000 samples with ground truth labels. The reciprocal of this RMSE is calculated as the historical prediction accuracy of the candidate model; for example, the reciprocal of the accuracy of a candidate model is 8.5. Subsequently, the historical prediction accuracy (e.g., 8.5), the operational correlation (e.g., 0.82) obtained in the Mahalanobis distance calculation phase, and the local prediction sensitivity norm (e.g., 1.45) calculated via the directional derivative are retrieved. Normalization is applied to map these three indicators to a dimensionless interval of 0 to 1, ensuring that the data can be calculated on the same scale.

[0063] A pre-defined scoring weighting system is used, in which normalized historical prediction accuracy and normalized chemical condition correlation are assigned positive weight coefficients, with their preferred range typically between 0.30 and 0.50. For example, in this case, they can be set to 0.40 and 0.40. Normalized local prediction sensitivity is assigned a negative weight coefficient, with its preferred range concentrated between -0.10 and -0.30. In this example, it is set to -0.20.

[0064] For each candidate model, multiply the normalized historical prediction accuracy by 0.40, the normalized condition correlation by 0.40, and the normalized local prediction sensitivity by -0.20. Sum the products of these three indicators to obtain the overall score of the candidate model. This overall score will be used to rank the models in the database.

[0065] S4. The outer diameter prediction value is obtained by weighted summation of the output of the active model subset using dynamic integrated weights. The adjustment control amount of the sizing frame is output based on the deviation between the outer diameter prediction value and the preset target value. The actual outer diameter detection value of the continuously produced welded pipe is obtained. The error evaluation is performed on the outer diameter prediction value and the output of the active model subset based on the actual outer diameter detection value. When the error evaluation result meets the preset fine-tuning trigger condition, the model that meets the preset model fine-tuning condition is fine-tuned online.

[0066] Extract floating-point tensors from the forward inference outputs of M models in the active model subset, based on the feature vectors of the current operating condition. Perform a vector inner product algebra operation between the model output tensors and the aforementioned dynamically integrated weight one-dimensional array to obtain the predicted outer diameter of the pipe being produced. Subtract this predicted outer diameter from the preset target value of the outer diameter required by the production process issued by the manufacturing execution system to calculate the feedforward control deviation. The positive and negative directions of the feedforward control deviation are determined according to the calibration relationship of the sizing frame actuator.

[0067] The feedforward control deviation is input into the incremental proportional-integral-derivative (PID) control algorithm module. Combined with preset proportional and integral coefficients, the incremental control command for adjusting the speed of the sizing frame servo motor is calculated and sent to the underlying frequency converter drive mechanism via the industrial field control bus to execute the mechanical pressing action. The adjustment control quantity of the sizing frame is used to adjust the sizing pressing amount or equivalent pressing pressure to form pressure compensation control for the deviation of the welded pipe's outer diameter.

[0068] A monitoring daemon runs in the background of the edge computing gateway, continuously calculating the average absolute error between the predicted outer diameter of the latest fifty consecutive welded pipes and the actual feedback measurement value from the laser diameter gauge. Simultaneously, it calculates the individual prediction error between the output value of each model in the active model subset and the actual feedback measurement value from the laser diameter gauge. When the individual prediction error of any model exceeds a preset individual error threshold, that model is identified as a model to be fine-tuned. The preset individual error threshold is determined based on the statistical distribution of individual prediction errors on a recent historical validation set, for example, by taking the sum of the mean of the individual average absolute errors and 1 to 3 times the standard deviation.

[0069] When the mean absolute error is determined to be greater than the preset error threshold and a model to be fine-tuned exists, the fifty most recently collected real feature input and target output data pairs are used as incremental training sample sets. An incremental training interface matching the type of the model to be fine-tuned is called to perform online incremental updates of the prediction parameters of the model to be fine-tuned. The preset error threshold is determined based on the allowable tolerance of the welded pipe outer diameter and the distribution of outer diameter prediction errors on the recent historical verification set. For example, the mean of the historical mean absolute error is taken as the sum of 1 to 3 times the standard deviation, and the amplitude is limited in combination with the allowable tolerance of the outer diameter.

[0070] The ablation experiment was conducted based on 2000 continuously collected historical production data points for welded pipes. Input features included wall thickness of 4.0 to 12.0 mm, strip width of 300 to 800 mm, forming roll reduction of 2.0 to 8.0 mm, and welding speed of 10 to 30 meters per minute. 1500 data points were randomly allocated as the training and validation set, and the remaining 500 data points as the test set. Three conditions were set for the comparison scheme: the baseline scheme only used the recent root mean square error of the model to assign static weights; some ablation schemes used operating condition correlation for evaluation and weighted the accuracy and correlation; the complete scheme combined positive historical prediction accuracy, positive operating condition correlation, and negative local prediction sensitivity to calculate a comprehensive performance score and performed weighted ensemble accordingly.

[0071] Accuracy metrics were recorded in the outer diameter prediction of 500 test samples. The baseline scheme had a root mean square error (RMSE) of 0.185 mm, a mean absolute error (MAE) of 0.142 mm, and a maximum absolute deviation of 0.410 mm. Some ablation schemes, by incorporating model matching that closely approximates historical similar operating conditions, reduced the RMSE to 0.152 mm, the MAE to 0.125 mm, and the maximum absolute deviation to 0.335 mm. The complete scheme, by constructing a set of orthogonally characteristic perturbation vectors to evaluate the output response of each model at real-time operating points and penalizing high-risk sensitive models, reduced the RMSE to 0.118 mm, the MAE to 0.096 mm, and the maximum absolute deviation to within 0.245 mm. The error comparison results of the three schemes on the three core evaluation metrics are as follows: Figure 4 As shown.

[0072] Compared to the baseline scheme that relies solely on historical static errors, utilizing Mahalanobis distance correlation reduces the root mean square error by 17.8%, demonstrating the environmental adaptability brought by spatial matching characteristics. After superimposing local prediction gradient norm constraints, the complete scheme further reduces the root mean square error by 22.4% compared to the partial ablation scheme, and the maximum absolute deviation is also reduced. This improvement indicates that sensitivity verification based on dimensionless perturbation amplitude can identify potential output oscillations, reduce the weight of models susceptible to minor process fluctuations in integrated predictions, and improve the overall prediction stability and anti-interference capability of the model cluster in actual production processes.

[0073] One or more embodiments of the present invention also provide a pressure-compensated welded pipe sizing dynamic adjustment control system, the system comprising: The module is used to acquire historical production data of welded pipes containing process parameters and outer diameter sizing results, use kernel density estimation to identify parameter density peak regions and calculate the corresponding covariance matrix, and build an initial model pool for training domain-specific prediction models for each region. The calculation module is used to obtain the real-time process parameters of the welded pipe to be adjusted, calculate the distance between the real-time process parameters and the center of the peak region of each parameter density to obtain the working condition correlation, screen K candidate models based on the working condition correlation, generate a perturbation vector set based on the covariance matrix of the peak region of the parameter density with the highest working condition correlation, and input the real-time process parameters and the perturbation parameters in the perturbation vector set into the candidate models respectively to calculate the local prediction sensitivity. The transformation module is used to obtain the historical prediction accuracy of candidate models, calculate the comprehensive score based on the historical prediction accuracy, working condition relevance and local prediction sensitivity, select M models to form an active model subset based on the comprehensive score, calculate the static integration benchmark weight based on the active model subset, and correct and normalize the static integration benchmark weight based on the local prediction sensitivity to obtain the dynamic integration weight. The fine-tuning module is used to obtain the predicted outer diameter value by weighted summation of the output of the active model subset using dynamic integrated weights, output the adjustment control amount of the sizing frame based on the deviation between the predicted outer diameter value and the preset target value, obtain the actual outer diameter detection value of the continuously produced welded pipe, evaluate the error between the predicted outer diameter value and the output of the active model subset based on the actual outer diameter detection value, and perform online fine-tuning on the model that meets the preset model fine-tuning conditions when the error evaluation result meets the preset fine-tuning trigger conditions.

[0074] In an optional embodiment, the step of acquiring historical welded pipe production data including process parameters and outer diameter sizing results, identifying parameter density peak regions using kernel density estimation and calculating the corresponding covariance matrix, and constructing an initial model pool for training domain-specific prediction models for each region includes: A multidimensional probability density function is constructed based on the multidimensional process parameters of the historical welded pipe production data. The mean-shift algorithm is used to iteratively optimize on the multidimensional probability density surface. The coordinates of the sample points and the probability density gradient vector are transformed into a dimensionless parameter space. The position of the sample points is updated along the upward direction of the probability density gradient in the dimensionless parameter space, and the magnitude of the dimensionless gradient vector is calculated until the magnitude is less than a preset convergence threshold. The convergence point in the dimensionless parameter space is inversely transformed to the original process parameter space and used as the center of the parameter density peak region. The sample points that converge to the center of the same parameter density peak region are clustered into an independent operating condition region, and the covariance matrix of the multidimensional process parameters of all sample points in the independent operating condition region is calculated. Based on the sample data in each independent working condition area, a corresponding domain-specific prediction model is trained, and an initial model pool is constructed from each domain-specific prediction model.

[0075] In an optional embodiment, calculating the distance between the real-time process parameters and the center of each parameter density peak region to obtain the operating condition correlation includes: The Mahalanobis distance between the real-time process parameters and the center of the density peak regions of each parameter is calculated using the inverse matrix of the covariance matrix corresponding to the peak regions of each parameter density. The negative Mahalanobis distance is used as the independent variable of the exponential function to calculate the corresponding working condition correlation. The smaller the Mahalanobis distance, the higher the output working condition correlation.

[0076] In an optional embodiment, generating a perturbation vector set based on the covariance matrix of the parameter density peak region with the highest correlation to operating conditions includes: After dimensionless processing, the covariance matrix of the parameter density peak region with the highest correlation to the real-time process parameters is decomposed to obtain multiple eigenvectors and corresponding eigenvalues. Each eigenvector is used as a parameter perturbation direction, and the square root of the corresponding eigenvalue is multiplied by a preset scaling factor to obtain the dimensionless perturbation amplitude in the direction. After the real-time process parameters are dimensionless, the dimensionless disturbance amplitude is increased and decreased along the disturbance direction of each parameter, and then inverse dimensionless processing is performed to generate a disturbance vector set composed of multiple disturbance parameters.

[0077] In an optional embodiment, the step of inputting real-time process parameters and perturbation parameters from the perturbation vector set into the candidate model respectively, and calculating the local prediction sensitivity, includes: The real-time process parameters and the corresponding disturbance parameters in the disturbance vector set are input into K candidate models respectively, and the baseline outer diameter prediction value and the disturbance outer diameter prediction value output by each candidate model are obtained. Calculate the difference between the predicted outer diameter of each disturbance and the predicted outer diameter of the reference. Perform dimensionless processing on the difference and the corresponding disturbance amplitude. Divide the dimensionless difference by the corresponding dimensionless disturbance amplitude to obtain the dimensionless directional derivative. Calculate the square root of the sum of squares of the dimensionless directional derivatives to obtain the gradient norm of each candidate model under the current real-time process parameters, and use the gradient norm as the local prediction sensitivity of each candidate model.

[0078] In an optional embodiment, the calculation of static ensemble baseline weights based on a subset of the active model includes: Calculate the prediction error sequence of M models in the active model subset on the recent historical validation set to obtain the root mean square error of prediction for each model; Calculate the covariance between each pair of the prediction error sequences of the M models, and construct an error covariance matrix of size M×M; For any model in the subset of active models, the reciprocal of the root mean square error of prediction is calculated as the first evaluation factor. The sum of the error covariances of the model and all other models is calculated. The sum of the error covariances is dimensionless. The negative value of the dimensionless result is used as the independent variable of the exponential function to calculate the second evaluation factor. After multiplying the first evaluation factor and the second evaluation factor, the results of all models in the active model subset are normalized to obtain the static integrated benchmark weights of each model.

[0079] In an optional embodiment, obtaining the historical prediction accuracy of the candidate model and calculating a comprehensive score based on the historical prediction accuracy, working condition correlation, and local prediction sensitivity includes: Obtain the root mean square error of each candidate model's predictions on the recent historical validation set, and take the reciprocal as the historical prediction accuracy. The historical prediction accuracy, working condition correlation, and local prediction sensitivity are normalized and mapped to the same dimensionless interval. A positive weighting coefficient is assigned to the normalized historical prediction accuracy and the correlation with operating conditions, and a negative weighting coefficient is assigned to the normalized local prediction sensitivity. The normalized indicators are multiplied by their corresponding weight coefficients and summed to obtain the overall performance score of each candidate model.

[0080] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0081] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A dynamic adjustment and control method for welded pipe sizing based on pressure compensation, characterized in that, include: We acquire historical production data of welded pipes containing process parameters and outer diameter sizing results, use kernel density estimation to identify parameter density peak regions and calculate the corresponding covariance matrix, and build an initial model pool for training domain-specific prediction models for each region. The real-time process parameters of the welded pipe to be adjusted are obtained, the distance between the real-time process parameters and the center of the peak density region of each parameter is calculated to obtain the working condition correlation, K candidate models are selected based on the working condition correlation, and a perturbation vector set is generated based on the covariance matrix of the peak density region of the parameter with the highest working condition correlation. The real-time process parameters and the perturbation parameters in the perturbation vector set are input into the candidate models respectively, and the local prediction sensitivity is calculated. The historical prediction accuracy of the candidate models is obtained. Based on the historical prediction accuracy, working condition relevance and local prediction sensitivity, the comprehensive score is calculated. Based on the comprehensive score, M models are selected to form an active model subset. Based on the active model subset, the static integration benchmark weight is calculated. Based on the local prediction sensitivity, the static integration benchmark weight is corrected and normalized to obtain the dynamic integration weight. The predicted outer diameter is obtained by weighting and summing the output of the active model subset using dynamic integrated weights. The adjustment control quantity of the sizing frame is output based on the deviation between the predicted outer diameter and the preset target value. The actual outer diameter detection value of the continuously produced welded pipe is obtained. The error evaluation is performed on the predicted outer diameter and the output of the active model subset based on the actual outer diameter detection value. When the error evaluation result meets the preset fine-tuning trigger condition, the model that meets the preset model fine-tuning condition is fine-tuned online.

2. The method according to claim 1, characterized in that, The process involves acquiring historical welded pipe production data including process parameters and outer diameter sizing results, identifying parameter density peak regions using kernel density estimation, calculating the corresponding covariance matrix, and constructing an initial model pool for training domain-specific prediction models in each region, including: A multidimensional probability density function is constructed based on the multidimensional process parameters of the historical welded pipe production data. The mean-shift algorithm is used to iteratively optimize on the multidimensional probability density surface. The coordinates of the sample points and the probability density gradient vector are transformed into a dimensionless parameter space. The position of the sample points is updated along the upward direction of the probability density gradient in the dimensionless parameter space, and the magnitude of the dimensionless gradient vector is calculated until the magnitude is less than a preset convergence threshold. The convergence point in the dimensionless parameter space is inversely transformed to the original process parameter space and used as the center of the parameter density peak region. The sample points that converge to the center of the same parameter density peak region are clustered into an independent operating condition region, and the covariance matrix of the multidimensional process parameters of all sample points in the independent operating condition region is calculated. Based on the sample data in each independent working condition area, a corresponding domain-specific prediction model is trained, and an initial model pool is constructed from each domain-specific prediction model.

3. The method according to claim 2, characterized in that, The correlation between the calculated real-time process parameters and the center of the peak density region of each parameter is used to derive the operating condition correlation, including: The Mahalanobis distance between the real-time process parameters and the center of the density peak regions of each parameter is calculated using the inverse matrix of the covariance matrix corresponding to the peak regions of each parameter density. The negative Mahalanobis distance is used as the independent variable of the exponential function to calculate the corresponding working condition correlation. The smaller the Mahalanobis distance, the higher the output working condition correlation.

4. The method according to claim 1, characterized in that, The perturbation vector set generated based on the covariance matrix of the parameter density peak region with the highest correlation to operating conditions includes: After dimensionless processing, the covariance matrix of the parameter density peak region with the highest correlation to the real-time process parameters is decomposed to obtain multiple eigenvectors and corresponding eigenvalues. Each eigenvector is used as a parameter perturbation direction, and the square root of the corresponding eigenvalue is multiplied by a preset scaling factor to obtain the dimensionless perturbation amplitude in the direction. After the real-time process parameters are dimensionless, the dimensionless disturbance amplitude is increased and decreased along the disturbance direction of each parameter, and then inverse dimensionless processing is performed to generate a disturbance vector set composed of multiple disturbance parameters.

5. The method according to claim 1, characterized in that, The step of inputting real-time process parameters and perturbation parameters from the perturbation vector set into the candidate model to calculate local prediction sensitivity includes: The real-time process parameters and the corresponding disturbance parameters in the disturbance vector set are input into K candidate models respectively, and the baseline outer diameter prediction value and the disturbance outer diameter prediction value output by each candidate model are obtained. Calculate the difference between the predicted outer diameter of each disturbance and the predicted outer diameter of the reference. Perform dimensionless processing on the difference and the corresponding disturbance amplitude. Divide the dimensionless difference by the corresponding dimensionless disturbance amplitude to obtain the dimensionless directional derivative. Calculate the square root of the sum of squares of the dimensionless directional derivatives to obtain the gradient norm of each candidate model under the current real-time process parameters, and use the gradient norm as the local prediction sensitivity of each candidate model.

6. The method according to claim 1, characterized in that, The calculation of static integrated baseline weights based on a subset of the active model includes: Calculate the prediction error sequence of M models in the active model subset on the recent historical validation set to obtain the root mean square error of prediction for each model; Calculate the covariance between each pair of the prediction error sequences of the M models, and construct an error covariance matrix of size M×M; For any model in the subset of active models, the reciprocal of the root mean square error of prediction is calculated as the first evaluation factor. The sum of the error covariances of the model and all other models is calculated. The sum of the error covariances is dimensionless. The negative value of the dimensionless result is used as the independent variable of the exponential function to calculate the second evaluation factor. After multiplying the first evaluation factor and the second evaluation factor, the results of all models in the active model subset are normalized to obtain the static integrated benchmark weights of each model.

7. The method according to claim 6, characterized in that, The process of obtaining the historical prediction accuracy of candidate models and calculating a comprehensive score based on historical prediction accuracy, operational condition relevance, and local prediction sensitivity includes: Obtain the root mean square error of each candidate model's predictions on the recent historical validation set, and take the reciprocal as the historical prediction accuracy. The historical prediction accuracy, working condition correlation, and local prediction sensitivity are normalized and mapped to the same dimensionless interval. A positive weighting coefficient is assigned to the normalized historical prediction accuracy and the correlation with operating conditions, and a negative weighting coefficient is assigned to the normalized local prediction sensitivity. The normalized indicators are multiplied by their corresponding weight coefficients and summed to obtain the overall performance score of each candidate model.

8. A pressure-compensated dynamic adjustment and control system for welded pipe sizing, characterized in that, include: The module is used to acquire historical production data of welded pipes containing process parameters and outer diameter sizing results, use kernel density estimation to identify parameter density peak regions and calculate the corresponding covariance matrix, and build an initial model pool for training domain-specific prediction models for each region. The calculation module is used to obtain the real-time process parameters of the welded pipe to be adjusted, calculate the distance between the real-time process parameters and the center of the peak region of each parameter density to obtain the working condition correlation, screen K candidate models based on the working condition correlation, generate a perturbation vector set based on the covariance matrix of the peak region of the parameter density with the highest working condition correlation, and input the real-time process parameters and the perturbation parameters in the perturbation vector set into the candidate models respectively to calculate the local prediction sensitivity. The transformation module is used to obtain the historical prediction accuracy of candidate models, calculate the comprehensive score based on the historical prediction accuracy, working condition relevance and local prediction sensitivity, select M models to form an active model subset based on the comprehensive score, calculate the static integration benchmark weight based on the active model subset, and correct and normalize the static integration benchmark weight based on the local prediction sensitivity to obtain the dynamic integration weight. The fine-tuning module is used to obtain the predicted outer diameter value by weighted summation of the output of the active model subset using dynamic integrated weights, output the adjustment control amount of the sizing frame based on the deviation between the predicted outer diameter value and the preset target value, obtain the actual outer diameter detection value of the continuously produced welded pipe, evaluate the error between the predicted outer diameter value and the output of the active model subset based on the actual outer diameter detection value, and perform online fine-tuning on the model that meets the preset model fine-tuning conditions when the error evaluation result meets the preset fine-tuning trigger conditions.

9. The system according to claim 8, characterized in that, The process involves acquiring historical welded pipe production data including process parameters and outer diameter sizing results, identifying parameter density peak regions using kernel density estimation, calculating the corresponding covariance matrix, and constructing an initial model pool for training domain-specific prediction models in each region, including: A multidimensional probability density function is constructed based on the multidimensional process parameters of the historical welded pipe production data. The mean-shift algorithm is used to iteratively optimize on the multidimensional probability density surface. The coordinates of the sample points and the probability density gradient vector are transformed into a dimensionless parameter space. The position of the sample points is updated along the upward direction of the probability density gradient in the dimensionless parameter space, and the magnitude of the dimensionless gradient vector is calculated until the magnitude is less than a preset convergence threshold. The convergence point in the dimensionless parameter space is inversely transformed to the original process parameter space and used as the center of the parameter density peak region. The sample points that converge to the center of the same parameter density peak region are clustered into an independent operating condition region, and the covariance matrix of the multidimensional process parameters of all sample points in the independent operating condition region is calculated. Based on the sample data in each independent working condition area, a corresponding domain-specific prediction model is trained, and an initial model pool is constructed from each domain-specific prediction model.

10. The system according to claim 8, characterized in that, The correlation between the calculated real-time process parameters and the center of the peak density region of each parameter is used to derive the operating condition correlation, including: The Mahalanobis distance between the real-time process parameters and the center of the density peak regions of each parameter is calculated using the inverse matrix of the covariance matrix corresponding to the peak regions of each parameter density. The negative Mahalanobis distance is used as the independent variable of the exponential function to calculate the corresponding working condition correlation. The smaller the Mahalanobis distance, the higher the output working condition correlation.

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