Pipe production line speed and cutting precision collaborative optimization method and system

Abstract

The application provides a pipe production line speed and cutting precision collaborative optimization method and system, the method comprises collecting historical operation data containing process parameters, production line speed and cutting precision, and constructing a decision tree twin support vector regression model; during training, the dimensionless composite index of cutting precision variance and speed interval width is used to optimize the split point, and a tilted split hyperplane is generated in combination with kernel principal component analysis; based on the condition number threshold value of the Hessian matrix, node splitting is controlled, a twin support vector regression model with insensitive loss and upper and lower bound cross penalty constraint is introduced in the leaf node training, and the upper and lower bounds of the speed prediction interval are output; the to-be-optimized process parameters are addressed to the corresponding leaf node, the risk preference coefficient is generated according to the node condition number, and the production line setting speed is obtained by weighting the interval boundary.

Description

Technical Field

[0001] This application belongs to the field of pipe production lines, and in particular relates to a method and system for synergistic optimization of speed and cutting accuracy in pipe production lines. Background Technology

[0002] In modern pipe manufacturing, production line efficiency and product quality are crucial indicators of a company's production capacity and market competitiveness. Production line speed directly impacts pipe output and manufacturing cycle time, while cutting accuracy affects pipe dimensional consistency, end-face quality, and subsequent splicing and assembly performance. In actual production, production line speed and cutting accuracy are often mutually restrictive. Simply increasing production line speed to pursue higher output can easily lead to increased equipment vibration, delayed response of the cutting mechanism, and increased synchronization control errors, resulting in uneven pipe cut ends and increased length deviations. Conversely, maintaining an overly conservative low-speed operating mode to ensure cutting accuracy reduces production efficiency, leads to insufficient equipment utilization, and increases unit product manufacturing costs. Therefore, how to reasonably increase production line speed while meeting cutting accuracy requirements, achieving synergistic optimization between production efficiency and cutting quality, is a critical technical problem that needs to be solved in the pipe processing and manufacturing field.

[0003] Because the pipe manufacturing process involves multivariate coupling, strong correlation, and nonlinear dynamic changes, cutting accuracy is easily affected by factors such as pipe material properties, geometric dimensions, traction conditions, cooling conditions, cutting response characteristics, and real-time process parameters. Currently, some pipe production lines still rely heavily on the experience and repeated adjustments of on-site operators for speed setting. This method is highly dependent on personnel experience and struggles to obtain optimal speed settings in a timely manner when operating conditions change frequently. Meanwhile, faced with a large amount of historical operating data, conventional control strategies or single data-driven prediction models often fail to fully characterize the distribution differences in the high-dimensional process parameter space, nor can they accurately depict the complex nonlinear mapping relationship between process parameters, production line speed, and cutting accuracy. Under different process conditions, the impact of speed changes on cutting quality and the potential risk of runaway vary. Existing methods still do not adequately characterize the uncertainty of prediction results and decision-making risks, making it difficult to adaptively balance increasing speed and ensuring accuracy based on the current risk level. Therefore, there is an urgent need for a method for the collaborative optimization of pipe production line speed and cutting accuracy that can utilize historical operating data and take into account both speed prediction uncertainty and risk control. Summary of the Invention

[0004] To address the problems of existing pipe production line speed settings relying on manual experience, difficulty in balancing cutting accuracy, and insufficient adaptive adjustment capabilities to address prediction uncertainties and operational risks, this invention proposes a method and system for the coordinated optimization of pipe production line speed and cutting accuracy.

[0005] In a first aspect, the present invention proposes a method for synergistic optimization of speed and cutting accuracy in a pipe production line, comprising the following steps: Acquire historical operating data of the pipe production line, including process parameters, production line speed and corresponding cutting accuracy; Based on the historical operating data, a decision tree twin support vector regression model is constructed. The training process of this model includes: calculating the statistical variance of the candidate child node data cutting accuracy and the composite index of the velocity interval width predicted by the temporary twin support vector regression model after dimensionless processing; selecting the split point that minimizes the composite index; performing kernel principal component analysis on the current node process parameters; generating a tilted splitting hyperplane to partition the data based on the first principal component vector and the split point; stopping the split when the ratio of the Hessian matrix condition number of the quadratic programming problem solved by the temporary model of the candidate child node to the condition number of the parent node exceeds a threshold determined based on the sample size; training a twin support vector regression model with an insensitive loss function and upper and lower bound cross-penalty constraints at the leaf nodes to generate two non-parallel velocity prediction hyperplanes. The process parameters to be optimized are input into the model, and the leaf node is located along the inclined split hyperplane path. The upper and lower bounds of the production line speed prediction interval are calculated using the twin support vector regression model at the leaf node. The risk preference coefficient is generated based on the Hessian matrix condition number mapping of the leaf node. The target speed setpoint is calculated by weighted averaging the upper and lower bounds using the risk preference coefficient and then output.

[0006] Optionally, the composite index, after dimensionless processing of the statistical variance of the candidate child node data cutting accuracy and the velocity interval width predicted by the temporary twin support vector regression model, includes: Calculate the mean of the cutting accuracy within the candidate child nodes, and obtain the statistical variance by summing the squares of the differences between the accuracy of each sample and the mean, and dividing by the total number of samples. A temporary twin support vector regression model is constructed, and the average difference between the upper and lower bounds of the predicted velocity interval for all samples of the node is calculated to obtain the velocity interval width. The composite index is obtained by multiplying the statistical variance and the speed interval width by a preset precision weighting coefficient and speed weighting coefficient, respectively, after performing dimensionless processing.

[0007] Optionally, the step of performing kernel principal component analysis on the current node process parameters and generating tilted splitting hyperplane partitioning data based on the first principal component vector and the splitting points includes: Calculate the kernel matrix of the process parameter set within the current node using the Gaussian kernel function; The kernel matrix is ​​decomposed into eigenvalues, and the eigenvector corresponding to the largest eigenvalue is extracted to obtain the first principal component vector; The kernel matrix column vectors corresponding to the process parameters are projected onto the first principal component vector, and the projection value of the first principal component corresponding to the split point is used as a threshold to construct an inclined splitting hyperplane for data partitioning.

[0008] Optionally, stopping the splitting when the ratio of the Hessian matrix condition number to the parent node condition number in the quadratic programming problem solved by the temporary model of the candidate child node exceeds a threshold determined based on the sample size includes: Calculate the ratio of the largest eigenvalue to the smallest non-zero eigenvalue of the Hessian matrix corresponding to the temporary model and the parent node model respectively as their condition numbers; Calculate the ratio of the number of temporary model conditions for the left and right candidate child nodes to the number of conditions for the parent node, respectively; Set the stability threshold T = α + β·N / (N + N0), where α, β and N0 are positive empirical constants, and N is the number of candidate child node data samples; When the ratio corresponding to any candidate child node is greater than its corresponding stability threshold T, the node splitting termination condition is triggered, and the splitting stops.

[0009] Optionally, the step of training a twin support vector regression model at the leaf nodes, incorporating an insensitive loss function and upper / lower bound cross-penalty constraints, to generate two non-parallel velocity prediction hyperplanes includes: We construct two dual quadratic programming problems with upper and lower bound cross-penalty constraints, and set different penalty parameters and asymmetric tolerance hyperparameters for the upper and lower bound prediction hyperplanes. By solving the two quadratic programming problems, the first weight vector and the first bias are used to construct the upper bound prediction hyperplane of the velocity interval, and the second weight vector and the second bias are used to construct the lower bound prediction hyperplane of the velocity interval.

[0010] Optionally, the step of generating risk preference coefficients based on the condition number mapping of the leaf node Hessian matrix, and using the risk preference coefficients to calculate and output the target speed setpoint by weighted averaging of the upper and lower bounds, includes: Obtain the Hessian matrix condition number saved during the training phase for the currently arrived leaf node, and generate a risk preference coefficient using a negative exponential mapping relationship with the condition number as the independent variable. The risk preference coefficient decreases as the Hessian matrix condition number increases, and its value range is greater than 0 and less than or equal to 1. The upper and lower bounds of the speed range output by the leaf nodes are weighted and averaged, with the risk preference coefficient as the weight of the upper bound of the speed range and the difference between 1 and the risk preference coefficient as the weight of the lower bound of the speed range. The target speed setpoint is calculated and output.

[0011] On the other hand, the present invention also proposes a system for the coordinated optimization of speed and cutting accuracy in a pipe production line, comprising the following modules: The acquisition module is used to acquire historical operating data of the pipe production line, including process parameters, production line speed and corresponding cutting accuracy. The calculation module is used to construct a decision tree twin support vector regression model based on the historical operating data. The training process of this model includes: calculating the statistical variance of the candidate child node data cutting accuracy and the composite index of the velocity interval width predicted by the temporary twin support vector regression model after dimensionless processing; selecting the split point that minimizes the composite index; performing kernel principal component analysis on the process parameters of the current node; generating a tilted splitting hyperplane to divide the data based on the first principal component vector and the split point; stopping the splitting when the ratio of the Hessian matrix condition number of the quadratic programming problem solved by the temporary model of the candidate child node to the condition number of the parent node exceeds a threshold determined based on the sample size; training a twin support vector regression model with an insensitive loss function and upper and lower bound cross-penalty constraints at the leaf nodes to generate two non-parallel velocity prediction hyperplanes. The output module is used to input the process parameters to be optimized into the model, address the leaf node along the inclined split hyperplane path, calculate the upper and lower bounds of the production line speed prediction interval using the twin support vector regression model at the leaf node, generate the risk preference coefficient based on the Hessian matrix condition number mapping of the leaf node, calculate the target speed setpoint by weighted averaging the upper and lower bounds using the risk preference coefficient, and output the result.

[0012] Preferably, the composite index, after dimensionless processing of the statistical variance of the candidate child node data cutting accuracy and the velocity interval width predicted by the temporary twin support vector regression model, includes: Calculate the mean of the cutting accuracy within the candidate child nodes, and obtain the statistical variance by summing the squares of the differences between the accuracy of each sample and the mean, and dividing by the total number of samples. A temporary twin support vector regression model is constructed, and the average difference between the upper and lower bounds of the predicted velocity interval for all samples of the node is calculated to obtain the velocity interval width. The composite index is obtained by multiplying the statistical variance and the speed interval width by a preset precision weighting coefficient and speed weighting coefficient, respectively, after performing dimensionless processing.

[0013] Preferably, the step of performing kernel principal component analysis on the current node process parameters and generating inclined splitting hyperplane partitioning data based on the first principal component vector and the splitting points includes: Calculate the kernel matrix of the process parameter set within the current node using the Gaussian kernel function; The kernel matrix is ​​decomposed into eigenvalues, and the eigenvector corresponding to the largest eigenvalue is extracted to obtain the first principal component vector; The kernel matrix column vectors corresponding to the process parameters are projected onto the first principal component vector, and the projection value of the first principal component corresponding to the split point is used as a threshold to construct an inclined splitting hyperplane for data partitioning.

[0014] Preferably, stopping the splitting when the ratio of the Hessian matrix condition number to the parent node condition number in the quadratic programming problem solved by the temporary model of the candidate child node exceeds a threshold determined based on the sample size includes: Calculate the ratio of the largest eigenvalue to the smallest non-zero eigenvalue of the Hessian matrix corresponding to the temporary model and the parent node model respectively as their condition numbers; Calculate the ratio of the number of temporary model conditions for the left and right candidate child nodes to the number of conditions for the parent node, respectively; Set the stability threshold T = α + β·N / (N + N0), where α, β and N0 are positive empirical constants, and N is the number of candidate child node data samples; When the ratio corresponding to any candidate child node is greater than its corresponding stability threshold T, the node splitting termination condition is triggered, and the splitting stops.

[0015] Preferably, the step of training a twin support vector regression model at the leaf nodes, incorporating an insensitive loss function and upper / lower bound cross-penalty constraints, to generate two non-parallel velocity prediction hyperplanes includes: We construct two dual quadratic programming problems with upper and lower bound cross-penalty constraints, and set different penalty parameters and asymmetric tolerance hyperparameters for the upper and lower bound prediction hyperplanes. By solving the two quadratic programming problems, the first weight vector and the first bias are used to construct the upper bound prediction hyperplane of the velocity interval, and the second weight vector and the second bias are used to construct the lower bound prediction hyperplane of the velocity interval.

[0016] Preferably, the step of generating risk preference coefficients based on the condition number mapping of the leaf node Hessian matrix, and using the risk preference coefficients to calculate and output the target speed setpoint by weighted averaging of the upper and lower bounds, includes: Obtain the Hessian matrix condition number saved during the training phase for the currently arrived leaf node, and generate a risk preference coefficient using a negative exponential mapping relationship with the condition number as the independent variable. The risk preference coefficient decreases as the Hessian matrix condition number increases, and its value range is greater than 0 and less than or equal to 1. The upper and lower bounds of the speed range output by the leaf nodes are weighted and averaged, with the risk preference coefficient as the weight of the upper bound of the speed range and the difference between 1 and the risk preference coefficient as the weight of the lower bound of the speed range. The target speed setpoint is calculated and output.

[0017] This invention integrates the statistical variance of cutting accuracy and the width of the speed prediction interval into a composite splitting index, and combines it with kernel principal component analysis to generate a tilted splitting hyperplane to adapt to the data partitioning requirements under varying process parameters. The node splitting process is controlled by the condition number ratio of the Hessian matrix, which helps reduce the risk of overfitting and improve solution stability. Leaf nodes employ a twin support vector regression model that introduces an insensitive loss function and upper / lower bound cross-penalty constraints to improve the adaptability of speed interval prediction. Furthermore, a risk preference coefficient is generated based on the condition number mapping, and the weights of the upper and lower bounds of speed prediction are adjusted according to the model's stability, so that the output speed is closer to the upper bound under stable conditions and closer to the lower bound under higher-risk conditions, thereby achieving a synergistic balance between production efficiency and cutting accuracy. Attached Figure Description

[0018] Figure 1 A flowchart of the first embodiment; Figure 2 A schematic diagram of the non-parallel velocity prediction hyperplane for leaf node twin support vector regression. Detailed Implementation

[0019] 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.

[0020] In the first embodiment, the present invention proposes a method for the coordinated optimization of speed and cutting accuracy in a pipe production line, such as... Figure 1 As shown, it includes the following steps: S1, acquire historical operating data of the pipe production line, including process parameters, production line speed and corresponding cutting accuracy.

[0021] The industrial programmable logic controller (PLC) collects real-time data on the operation of the pipe production line, reads historical operating data stored in comma-separated value format, and extracts process parameters including extruder temperature, traction force, and cooling water temperature, as well as production line speed and cutting accuracy. Missing data is imputed with mean, and an isolated forest algorithm is used to identify and remove outliers, mapping all features to a numerical range of 0 to 1.

[0022] S2, a decision tree twin support vector regression model is constructed based on the historical operating data. The training process of this model includes: calculating the statistical variance of the candidate child node data cutting accuracy and the composite index of the velocity interval width predicted by the temporary twin support vector regression model after dimensionless processing, and selecting the split point that minimizes the composite index; performing kernel principal component analysis on the current node process parameters, and generating a tilted splitting hyperplane to divide the data based on the first principal component vector and the split point; stopping the split when the ratio of the Hessian matrix condition number of the quadratic programming problem solved by the temporary model of the candidate child node to the condition number of the parent node exceeds the threshold determined based on the sample size; training a twin support vector regression model with an insensitive loss function and upper and lower bound cross-penalty constraints at the leaf nodes to generate two non-parallel velocity prediction hyperplanes.

[0023] At the current node of the decision tree, first perform kernel principal component analysis on all process parameter samples within that node to obtain the projection value of each sample along the first principal component direction; calculate the ten quantiles of the projection values ​​as a set of candidate split thresholds. For each candidate split threshold, divide the current node dataset into left and right candidate child node data subsets based on the relationship between the sample projection values ​​and the candidate split threshold. Calculate the statistical variance of the cutting accuracy feature for each subset, construct a temporary twin support vector regression model for each subset, and solve its corresponding dual quadratic programming problem using the interior point method or sequential minimum optimization algorithm to obtain temporary model parameters. Input the subset data into the temporary model to obtain the upper and lower limits of speed prediction. Subtract the upper and lower limits to obtain the predicted speed interval width. Perform dimensionless operations on the statistical variance and interval width respectively, and sum the dimensionless statistical variance and interval width by weight to obtain the composite index. Traverse all candidate split thresholds and select the candidate split threshold that minimizes the weighted sum of the composite indices of the left and right candidate subsets based on the sample size as the target split threshold.

[0024] Kernel principal component analysis (KPCA) based on radial basis function (RBF) is performed on the process parameter samples within the current node. The original process parameters are mapped to a high-dimensional kernel feature space, and the feature vector corresponding to the first principal component with the largest contribution rate is extracted as the splitting direction in the kernel space. The process parameter features of all sample points are projected along the direction of the first principal component to obtain the projected values, and the target splitting threshold selected by minimizing the composite index is used as the intercept. An inclined splitting hyperplane is constructed in the kernel space using the direction of the first principal component and the target splitting threshold. The sample projected values ​​are compared with the intercept. Samples with projected values ​​less than or equal to the intercept are assigned to the left child node, and samples with projected values ​​greater than the intercept are assigned to the right child node.

[0025] Extract the Hessian matrix from the objective function of the quadratic programming problem corresponding to the twin support vector regression model of the parent node. Calculate the condition number of the Hessian matrix for the parent node using the eigenvalue decomposition function. Calculate the condition numbers of the Hessian matrix for the temporary models of the left and right candidate child nodes using the same method. Divide the condition numbers of the Hessian matrix for the left and right candidate child nodes by the condition number of the parent node's Hessian matrix to obtain the condition number ratios for the left and right candidate child nodes. Determine the stability threshold based on the number of data samples for each candidate child node. Determine if the condition number ratios of the left and right candidate child nodes are greater than their respective stability thresholds. If the condition number ratio for either candidate child node is greater than its stability threshold, stop the recursive splitting process for the current node and set the current node as a leaf node. If the condition number ratios for both candidate child nodes are not greater than their respective stability thresholds, retain the splitting result and continue to the next level of downward splitting operation.

[0026] Two optimization objective functions are constructed for the data subsets identified as leaf nodes. The first objective function introduces an asymmetric insensitive loss function, assigning different weights to the upper and lower biases of the upper bound prediction hyperplane relative to the actual production line speed sample values. The second objective function assigns another set of different weights to the upper and lower biases of the lower bound prediction hyperplane relative to the actual production line speed sample values. Both objective functions also incorporate upper and lower bound cross-constraints, consisting of a constant multiplied by a maximum function, to penalize cases where the upper bound prediction value is less than the lower bound prediction value, reducing the likelihood of cross-constraints in speed prediction intervals. The Lagrange multiplier method is used to transform the two constrained objective functions into a dual quadratic programming problem. Solving the two dual quadratic programming problems yields two optimal Lagrange multiplier solution vectors. Combining these with the radial basis function kernel, the weight coefficient vector and bias term constant are calculated, constructing a first non-parallel speed prediction hyperplane for outputting the upper bound of the speed and a second non-parallel speed prediction hyperplane for outputting the lower bound of the speed.

[0027] In an optional embodiment, the composite index, after dimensionless processing of the statistical variance of the candidate child node data cutting accuracy and the velocity interval width predicted by the temporary twin support vector regression model, includes: Calculate the mean of the cutting accuracy within the candidate child nodes, and obtain the statistical variance by summing the squares of the differences between the accuracy of each sample and the mean, and dividing by the total number of samples. A temporary twin support vector regression model is constructed, and the average difference between the upper and lower bounds of the predicted velocity interval for all samples of the node is calculated to obtain the velocity interval width. The composite index is obtained by multiplying the statistical variance and the speed interval width by a preset precision weighting coefficient and speed weighting coefficient, respectively, after the latter is dimensionless.

[0028] When evaluating the splitting quality of candidate child nodes, a candidate splitting threshold is first generated based on the projection value of the first principal component of the current node sample, and left and right candidate child nodes are formed according to the candidate splitting threshold. All samples within the candidate child nodes are extracted, for example, cutting precision data with a sample size M=150. The arithmetic mean of these 150 precision values ​​is calculated. The cutting precision of each sample is subtracted from this mean and the square is calculated. The sum of the squared differences of all samples is then divided by 150 to obtain the statistical variance of the cutting precision. .

[0029] On this candidate child node, a temporary twin support vector regression model is constructed using these 150 samples. The sample features are input into the temporary model to calculate the upper limit of the prediction speed for each sample. and lower limit The velocity interval differences of all samples are calculated and their average values ​​are taken as the velocity interval width ΔV of that node. A Min-Max normalization method is used to make both dimensionless. For example, using the maximum and minimum variance ranges (e.g., minimum 0.01 mm² to maximum 0.50 mm²) and velocity width ranges (e.g., minimum 0.1 m / s to maximum 2.0 m / s) pre-obtained based on historical global node statistics, the currently calculated... Mapping ΔV to the [0,1] interval yields the normalized variance. and normalized width Input the preset precision weighting coefficient. The preferred range is 0.6 to 0.8, with an example value of 0.7 and a velocity weighting coefficient. The preferred range is 0.2 to 0.4, with an example value of 0.3, and it satisfies... Through formula The composite index C is calculated. Through this process, the selection of the split point can comprehensively balance the fluctuation of cutting accuracy in local data and the adjustment margin of production line speed, so as to carry out decision tree growth with a better strategy.

[0030] In an optional embodiment, the step of performing kernel principal component analysis on the current node process parameters and generating tilted splitting hyperplane partitioning data based on the first principal component vector and the splitting points includes: Calculate the kernel matrix of the process parameter set within the current node using the Gaussian kernel function; The kernel matrix is ​​decomposed into eigenvalues, and the eigenvector corresponding to the largest eigenvalue is extracted to obtain the first principal component vector; The kernel matrix column vectors corresponding to the process parameters are projected onto the first principal component vector, and the projection value of the first principal component corresponding to the split point is used as a threshold to construct an inclined splitting hyperplane for data partitioning.

[0031] When partitioning the data at the current node, process parameters of M samples within that node are collected, such as pipe outer diameter, wall thickness, material hardness, heating temperature, and other multi-dimensional features. For example, the dimension is 8, and Gaussian kernel function and radial basis function (RBF) are used. The kernel width parameter σ is preferably in the range of 0.5 to 5.0, with an example value of 2.0. The nonlinear similarity between pairs of samples is calculated, constructing a symmetric kernel matrix K of size M×M. To reduce the influence of the origin offset in the data space, a centering matrix processing formula is used to center the kernel matrix K to obtain the matrix... For the centered kernel matrix Eigenvalue decomposition is performed to obtain the set of eigenvalues ​​and the corresponding eigenvector matrix. The eigenvalues ​​are then sorted in descending order, and the largest eigenvalue, such as the dominant eigenvalue that accounts for 65% of the total variance, is extracted as the unit eigenvector. This vector is the high-dimensional representation of the first principal component in the kernel space.

[0032] Each sample in the current node Mapping vectors in kernel space, i.e., matrices The i-th column vector and the first principal component vector Perform inner product operation to obtain the projection value of each sample along the direction of the first principal component. According to the projection value Generate a set of candidate split thresholds, for example, by taking the decimal points of the projected value sequence or the midpoint of adjacent sorted projected values ​​as candidate split thresholds; for each candidate split threshold, according to the sample projected values... The left and right candidate child nodes are divided according to the magnitude of the candidate splitting threshold, and the corresponding weighted sum of composite indices is calculated; the candidate splitting threshold that minimizes the weighted sum of composite indices is determined as the target splitting threshold. and with equation This serves as the tilted splitting hyperplane for that node. Compare the sample projection values. and The size of the projection value will be less than or equal to the size of the projection value. The sample is assigned to the left child node, and the projection value is greater than 1. The sample is assigned to the right child node. Through this projection in nonlinear space, candidate threshold evaluation, and target splitting threshold determination, it is helpful to ensure that the splitting evaluation process is consistent with the actual tilted hyperplane partitioning process.

[0033] In an optional embodiment, stopping the splitting when the ratio of the Hessian matrix condition number to the parent node condition number in the quadratic programming problem solved by the temporary model of the candidate child node exceeds a threshold determined based on the sample size includes: Calculate the ratio of the largest eigenvalue to the smallest non-zero eigenvalue of the Hessian matrix corresponding to the temporary model and the parent node model respectively as their condition numbers; Calculate the ratio of the number of temporary model conditions for the left and right candidate child nodes to the number of conditions for the parent node, respectively; Set the stability threshold T = α + β·N / (N + N0), where α, β and N0 are positive empirical constants, and N is the number of candidate child node data samples; When the ratio corresponding to any candidate child node is greater than its corresponding stability threshold T, the node splitting termination condition is triggered, and the splitting stops.

[0034] For the currently constructed candidate child node temporary twin support vector regression model and its corresponding parent node model, extract the Hessian matrix from the quadratic programming objective function of both. and Perform singular value decomposition or eigenvalue solving algorithms on these two symmetric positive semidefinite matrices to extract the maximum eigenvalue of each matrix. and the smallest non-zero eigenvalue The Hessian condition number of the candidate child nodes is calculated by dividing the largest eigenvalue by the smallest non-zero eigenvalue. For example, 350.5 and the condition number of the Hessian matrix of the parent node. For example, 200.2, find the ratio of the two. The calculated value is 1.75, which represents the increase in model instability caused by the reduction of local node data.

[0035] A stability threshold T for stopping splitting is set based on the number of data samples N of candidate child nodes. A base threshold α, a sample size adjustment coefficient β, and a reference sample size N0 are pre-defined, where α, β, and N0 are all positive empirical constants. The stability threshold is calculated as T = α + β·N / (N + N0), ensuring a lower stability threshold when the number of candidate child node samples is small, making it easier to trigger splitting cessation; and a higher stability threshold when the number of candidate child node samples is large, allowing continued splitting when data support is sufficient. For example, with α = 1.2, β = 0.8, and N0 = 100, T is approximately 1.33 when the number of candidate child node samples N is 20, and approximately 1.64 when the number of candidate child node samples N is 120.

[0036] For the left and right candidate child nodes formed by the same candidate split threshold, calculate the corresponding condition number ratio. and And calculate the corresponding stability threshold based on the number of samples of the left and right candidate child nodes respectively. and .like Greater than or Greater than If the current candidate split is determined to cause numerical ill-conditioned quadratic programming of at least one child node's temporary model and increase the risk of overfitting, the termination condition is triggered, the current node is stopped from continuing to split, and the current node is set as a leaf node; if Not greater than and Not greater than If the candidate split result is not found, the split will be retained and the split will continue downwards.

[0037] In an optional embodiment, training a twin support vector regression model at the leaf nodes, incorporating an insensitive loss function and upper / lower bound crossover penalties, to generate two non-parallel velocity prediction hyperplanes includes: We construct two dual quadratic programming problems with upper and lower bound cross-penalty constraints, and set different penalty parameters and asymmetric tolerance hyperparameters for the upper and lower bound prediction hyperplanes. By solving the two quadratic programming problems, the first weight vector and the first bias are used to construct the upper bound prediction hyperplane of the velocity interval, and the second weight vector and the second bias are used to construct the lower bound prediction hyperplane of the velocity interval.

[0038] Two sets of quadratic programming problems are constructed based on the samples inside the leaf nodes: For the upper bound prediction hyperplane, a penalty parameter is applied. The preferred range is 10 to 100, with an example value of 50, and an upper bound insensitivity tolerance hyperparameter is set. The preferred range is 0.05 to 0.15, with an example value of 0.1; different penalty parameters are used for the lower bound prediction hyperplane. The preferred range is 10 to 100, with an example value of 80, and a lower bound insensitivity tolerance hyperparameter is set. To improve the conservatism and constraint sensitivity of the lower bound prediction, Set to less than The example value is 0.05. Additional upper and lower bound crossover penalty terms are added to the objective function, for example, the crossover penalty coefficient is set to... =20. When the lower bound prediction value trained by the model exceeds the upper bound prediction value, the positive overlap difference between the two is calculated, and a penalty is applied to the overlap difference, thereby reducing the probability of the upper and lower bounds of the velocity prediction interval crossing or diverging significantly.

[0039] The original objective problem constructed above is transformed into a computationally efficient dual quadratic programming problem using Lagrange multipliers. This dual problem is then solved using the interior-point method or sequential minimum optimization algorithm to obtain the objective Lagrange multiplier vectors α and γ. Then, based on the KKT conditions and the correspondence between the dual and original variables, a reverse calculation is performed to extract the decision variables from the original problem, yielding the first weight vector corresponding to the upper bound prediction hyperplane. The example consists of a high-dimensional column vector with dimensions consistent with those after kernel mapping and a first bias scalar. Example value is 2.3, and the second weight vector of the lower bound prediction hyperplane. Second bias scalar The example value is 1.8. Substitute any input process feature vector x into the formula. Output the upper limit of the speed range, substitute it The lower bound of the output velocity range is used to establish two sets of non-parallel velocity prediction hyperplanes with cross constraints. The non-parallel velocity prediction hyperplanes for leaf node twin support vector regression are shown below. Figure 2 As shown.

[0040] S3. Input the process parameters to be optimized into the model, address the leaf node along the inclined split hyperplane path, use the twin support vector regression model at the leaf node to calculate the upper and lower bounds of the production line speed prediction interval, generate the risk preference coefficient based on the Hessian matrix condition number mapping of the leaf node, use the risk preference coefficient to calculate the target speed setpoint by weighted averaging the upper and lower bounds and output it.

[0041] The same normalization transformation is performed on the real-time acquired process parameters to be optimized. Starting from the root node of the decision tree, the system searches downwards, calculating the query projection value of the process parameters to be optimized in the first principal component direction of the current node according to the kernel principal component analysis parameters, the first principal component vector, and the target splitting threshold saved at each node during the training phase. If the query projection value is less than or equal to the intercept of the tilted splitting hyperplane of the current node, the system enters the left subtree; otherwise, it enters the right subtree. This process is iterated until the system reaches the terminal leaf node.

[0042] The process parameters to be optimized are substituted into the expressions of the first and second non-parallel velocity prediction hyperplanes of the leaf node to calculate the upper and lower bounds of the production line velocity prediction interval. The Hessian matrix condition number saved by the leaf node during the training phase is extracted. The product of the negative constant and the condition number is used as the exponent, and the exponentiation is performed with the natural constant e as the base to generate a risk preference coefficient. The upper bound is multiplied by the risk preference coefficient to obtain the upper bound weighted component. The difference between 1 and the risk preference coefficient is used as the lower bound weight. The lower bound weight is multiplied by the lower bound of the velocity interval to obtain the lower bound weighted component. The upper bound weighted component and the lower bound weighted component are added together to calculate the target velocity setpoint. Based on the normalized mapping relationship established for the production line velocity variables during the training phase, the calculated target velocity setpoint is subjected to an inverse scaling transformation to restore the normalized value to the production line velocity control quantity in the actual velocity dimension. This value is then sent to the pipe production line equipment controller for control via the industrial Ethernet communication protocol.

[0043] In an optional embodiment, the step of generating risk preference coefficients based on the Hessian matrix condition number mapping of the leaf nodes, calculating and outputting the target velocity setpoint by weighted averaging of the upper and lower bounds using the risk preference coefficients, includes: Obtain the Hessian matrix condition number saved during the training phase for the currently arrived leaf node, and generate a risk preference coefficient using a negative exponential mapping relationship with the condition number as the independent variable. The risk preference coefficient decreases as the Hessian matrix condition number increases, and its value range is greater than 0 and less than or equal to 1. The upper and lower bounds of the speed range output by the leaf nodes are weighted and averaged, with the risk preference coefficient as the weight of the upper bound of the speed range and the difference between 1 and the risk preference coefficient as the weight of the lower bound of the speed range. The target speed setpoint is calculated and output.

[0044] After predicting the speed operating boundary under a specific production process task, a speed setpoint adjustment strategy is implemented based on the robustness of the local model data at the current leaf node. The Hessian matrix condition number λ, calculated during the twin model training phase at that leaf node, is extracted in real time. For example, λ=25 when the data in that region is complete and the matrix is ​​well-conditioned, or when the data is scattered and the matrix is ​​ill-conditioned. =400, and using mathematical formulas Generate a risk preference coefficient. The preset positive adjustment coefficient γ is typically set based on engineering parameter tuning experience and the average value of the condition number, with an optimal range limited to 0.001 to 0.01; an example value of 0.005 is used. If the Hessian matrix condition number for reaching a leaf node is small, such as λ=20, it indicates that the quadratic programming solution is relatively stable, and the reliability of the upper bound of the velocity prediction is relatively high. Substituting this into the formula, the preference coefficient ρ≈0.90 is calculated.

[0045] Extract the upper bound of the predicted velocity for this production state from the output of the non-parallel hyperplane model. For example, 2.5 m / s and the lower limit of velocity. For example, 1.8 m / s. Substituting the calculated risk preference coefficient ρ = 0.90 into the weighted average setting formula, the target speed setpoint is calculated. =2.43m / s, at which point the model is in a high reliability state, and the set speed is closer to the upper limit. Running the system helps improve production line capacity efficiency; conversely, if the computational condition number at another leaf node is high, such as λ=400, it indicates that the data features of that sub-region are missing and the model fitting has a high risk. In this case, the calculated coefficient is low, ρ≈0.135, and the target speed setpoint is calculated. =1.89m / s, and a higher weight will be assigned to the lower bound, causing the output production line speed to operate closer to the more conservative lower bound. Thus, the control system achieves a speed regulation mechanism that integrates comprehensive numerical stability assessment and equipment safety.

[0046] In the second embodiment, the present invention also proposes a system for the coordinated optimization of speed and cutting accuracy in a pipe production line, comprising the following modules: The acquisition module is used to acquire historical operating data of the pipe production line, including process parameters, production line speed and corresponding cutting accuracy. The calculation module is used to construct a decision tree twin support vector regression model based on the historical operating data. The training process of this model includes: calculating the statistical variance of the candidate child node data cutting accuracy and the composite index of the velocity interval width predicted by the temporary twin support vector regression model after dimensionless processing; selecting the split point that minimizes the composite index; performing kernel principal component analysis on the process parameters of the current node; generating a tilted splitting hyperplane to divide the data based on the first principal component vector and the split point; stopping the splitting when the ratio of the Hessian matrix condition number of the quadratic programming problem solved by the temporary model of the candidate child node to the condition number of the parent node exceeds a threshold determined based on the sample size; training a twin support vector regression model with an insensitive loss function and upper and lower bound cross-penalty constraints at the leaf nodes to generate two non-parallel velocity prediction hyperplanes. The output module is used to input the process parameters to be optimized into the model, address the leaf node along the inclined split hyperplane path, calculate the upper and lower bounds of the production line speed prediction interval using the twin support vector regression model at the leaf node, generate the risk preference coefficient based on the Hessian matrix condition number mapping of the leaf node, calculate the target speed setpoint by weighted averaging the upper and lower bounds using the risk preference coefficient, and output the result.

[0047] 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.

[0048] 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 method for synergistic optimization of speed and cutting accuracy in a pipe production line, characterized in that, include: Acquire historical operating data of the pipe production line, including process parameters, production line speed and corresponding cutting accuracy; Based on the historical operating data, a decision tree twin support vector regression model is constructed. The training process of this model includes: calculating the statistical variance of the candidate child node data cutting accuracy and the composite index of the velocity interval width predicted by the temporary twin support vector regression model after dimensionless processing; selecting the split point that minimizes the composite index; performing kernel principal component analysis on the current node process parameters, and generating inclined splitting hyperplane partitioning data based on the first principal component vector and the split point; stopping splitting when the ratio of the Hessian matrix condition number to the parent node condition number in the quadratic programming problem solved by the temporary model of the candidate child node exceeds a threshold determined based on the sample size, wherein the temporary model of the candidate child node is a temporary twin support vector regression model; and introducing insensitivity at the leaf nodes during training. A twin support vector regression model with a loss function and upper and lower bound cross-penalty constraints generates two non-parallel velocity prediction hyperplanes. The upper and lower bound cross-penalty constraints are set by: constructing two optimization objective functions for the subset of data determined as leaf nodes; introducing an asymmetric insensitive loss function in the first optimization objective function; assigning different weights of penalty factors to the upper and lower biases of the upper bound prediction hyperplane relative to the actual production line velocity sample values; assigning another set of different weights of penalty factors to the upper and lower biases of the lower bound prediction hyperplane relative to the actual production line velocity sample values ​​in the second optimization objective function; and simultaneously adding upper and lower bound cross-penalty constraints composed of a constant multiplied by a maximum function in both optimization objective functions. The process parameters to be optimized are input into the model, and the leaf node is located along the inclined split hyperplane path. The upper and lower bounds of the production line speed prediction interval are calculated using the twin support vector regression model at the leaf node. The risk preference coefficient is generated based on the Hessian matrix condition number mapping of the leaf node. The target speed setpoint is calculated by weighted averaging the upper and lower bounds using the risk preference coefficient and then output.

2. The method according to claim 1, characterized in that, The composite index, which calculates the statistical variance of the candidate child node data cutting accuracy and the dimensionless processing of the velocity interval width predicted by the temporary twin support vector regression model, includes: Calculate the mean of the cutting accuracy within the candidate child nodes, and obtain the statistical variance by summing the squares of the differences between the accuracy of each sample and the mean, and dividing by the total number of samples. A temporary twin support vector regression model is constructed, and the average difference between the upper and lower bounds of the predicted velocity interval for all samples of the candidate child node is calculated to obtain the velocity interval width. The statistical variance and the speed interval width are respectively dimensionless, and the composite index is obtained by weighting them with preset precision weight coefficients and speed weight coefficients respectively.

3. The method according to claim 1, characterized in that, The step of performing kernel principal component analysis on the current node process parameters, and generating tilted splitting hyperplane partitioning data based on the first principal component vector and the splitting points, includes: Calculate the kernel matrix of the process parameter set within the current node using the Gaussian kernel function; The kernel matrix is ​​decomposed into eigenvalues, and the eigenvector corresponding to the largest eigenvalue is extracted to obtain the first principal component vector; The kernel matrix column vectors corresponding to the process parameters are projected onto the first principal component vector, and the projection value of the first principal component corresponding to the split point is used as a threshold to construct an inclined splitting hyperplane for data partitioning.

4. The method according to claim 1, characterized in that, The step of stopping the split when the ratio of the Hessian matrix condition number to the parent node condition number in the quadratic programming problem solved by the temporary model of the candidate child node exceeds a threshold determined based on the sample size includes: Calculate the ratio of the largest eigenvalue to the smallest non-zero eigenvalue of the Hessian matrix corresponding to the temporary model and the parent node model respectively as their condition numbers; Calculate the ratio of the number of temporary model conditions for the left and right candidate child nodes to the number of conditions for the parent node, respectively; Set the stability threshold T = α + β·N / (N + N0), where α, β and N0 are positive empirical constants, and N is the number of candidate child node data samples; When the ratio corresponding to any candidate child node is greater than its corresponding stability threshold T, the node splitting termination condition is triggered and the splitting stops.

5. The method according to claim 1, characterized in that, The twin support vector regression model, which incorporates an insensitive loss function and upper / lower bound cross-penalty constraints and is trained at the leaf nodes, generates two non-parallel velocity prediction hyperplanes, including: We construct two dual quadratic programming problems with upper and lower bound cross-penalty constraints, and set different penalty parameters and asymmetric tolerance hyperparameters for the upper and lower bound prediction hyperplanes. By solving the two quadratic programming problems, the first weight vector and the first bias are used to construct the upper bound prediction hyperplane of the velocity interval, and the second weight vector and the second bias are used to construct the lower bound prediction hyperplane of the velocity interval.

6. The method according to claim 1, characterized in that, The process of generating risk preference coefficients based on the Hessian matrix condition number mapping of the leaf nodes, and then using these risk preference coefficients to calculate and output a target speed setpoint by weighted averaging of the upper and lower bounds, includes: Obtain the Hessian matrix condition number saved during the training phase for the currently arrived leaf node, and generate a risk preference coefficient using a negative exponential mapping relationship with the condition number as the independent variable. The risk preference coefficient decreases as the Hessian matrix condition number increases, and its value range is greater than 0 and less than or equal to 1. The upper and lower bounds of the speed range output by the leaf nodes are weighted and averaged, with the risk preference coefficient as the weight of the upper bound of the speed range and the difference between 1 and the risk preference coefficient as the weight of the lower bound of the speed range. The target speed setpoint is calculated and output.

7. A system for synergistic optimization of speed and cutting accuracy in a pipe production line, characterized in that, include: The acquisition module is used to acquire historical operating data of the pipe production line, including process parameters, production line speed and corresponding cutting accuracy. The computation module is used to construct a decision tree twin support vector regression model based on the historical operating data. The training process of this model includes: calculating the composite index of the statistical variance of the candidate child node data cutting accuracy and the dimensionless processing of the velocity interval width predicted by the temporary twin support vector regression model; selecting the split point that minimizes the composite index; performing kernel principal component analysis on the current node process parameters; generating inclined splitting hyperplane partitioning data based on the first principal component vector and the split point; stopping splitting when the ratio of the Hessian matrix condition number of the quadratic programming problem solved by the temporary model of the candidate child node to the condition number of the parent node exceeds a threshold determined based on the sample size; the temporary model of the candidate child node is a temporary twin support vector regression model; and training at the leaf nodes. A twin support vector regression model with an insensitive loss function and upper / lower bound cross-penalty constraints is introduced to generate two non-parallel velocity prediction hyperplanes. The upper / lower bound cross-penalty constraints are set by: constructing two optimization objective functions for the subset of data determined as leaf nodes; introducing an asymmetric insensitive loss function in the first optimization objective function; assigning different weights of penalty factors to the upper and lower biases of the upper bound prediction hyperplane relative to the actual production line velocity sample values; assigning another set of different weights of penalty factors to the upper and lower biases of the lower bound prediction hyperplane relative to the actual production line velocity sample values; and simultaneously adding upper / lower bound cross-penalty constraints composed of a constant multiplied by a maximum function in both optimization objective functions. The output module is used to input the process parameters to be optimized into the model, address the leaf node along the inclined split hyperplane path, calculate the upper and lower bounds of the production line speed prediction interval using the twin support vector regression model at the leaf node, generate the risk preference coefficient based on the Hessian matrix condition number mapping of the leaf node, calculate the target speed setpoint by weighted averaging the upper and lower bounds using the risk preference coefficient, and output the result.

8. The system according to claim 7, characterized in that, The composite index, which calculates the statistical variance of the candidate child node data cutting accuracy and the dimensionless processing of the velocity interval width predicted by the temporary twin support vector regression model, includes: Calculate the mean of the cutting accuracy within the candidate child nodes, and obtain the statistical variance by summing the squares of the differences between the accuracy of each sample and the mean, and dividing by the total number of samples. A temporary twin support vector regression model is constructed, and the average difference between the upper and lower bounds of the predicted velocity interval for all samples of the candidate child node is calculated to obtain the velocity interval width. The statistical variance and the speed interval width are respectively dimensionless and then weighted and summed using preset precision weighting coefficients and speed weighting coefficients to obtain the composite index.

9. The system according to claim 7, characterized in that, The step of performing kernel principal component analysis on the current node process parameters, and generating tilted splitting hyperplane partitioning data based on the first principal component vector and the splitting points, includes: Calculate the kernel matrix of the process parameter set within the current node using the Gaussian kernel function; The kernel matrix is ​​decomposed into eigenvalues, and the eigenvector corresponding to the largest eigenvalue is extracted to obtain the first principal component vector; The kernel matrix column vectors corresponding to the process parameters are projected onto the first principal component vector, and the projection value of the first principal component corresponding to the split point is used as a threshold to construct an inclined splitting hyperplane for data partitioning.

10. The system according to claim 7, characterized in that, The step of stopping the split when the ratio of the Hessian matrix condition number to the parent node condition number in the quadratic programming problem solved by the temporary model of the candidate child node exceeds a threshold determined based on the sample size includes: Calculate the ratio of the largest eigenvalue to the smallest non-zero eigenvalue of the Hessian matrix corresponding to the temporary model and the parent node model respectively as their condition numbers; Calculate the ratio of the number of temporary model conditions for the left and right candidate child nodes to the number of conditions for the parent node, respectively; Set the stability threshold T = α + β·N / (N + N0), where α, β and N0 are positive empirical constants, and N is the number of candidate child node data samples; When the ratio corresponding to any candidate child node is greater than its corresponding stability threshold T, the node splitting termination condition is triggered and the splitting stops.

Images