A large pipe diameter steel pipe multi-axis robot welding deformation self-adaptive control system

Abstract

The application provides a large-diameter steel pipe multi-axis robot welding deformation adaptive control system, which comprises the following steps: obtaining a variable-density feature point set by discretizing a welding track according to a three-dimensional model of a steel pipe and the welding track, combining a curvature change rate and a stress sensitive area; matching each group of process parameters by relying on low-difference sequence sampling, and completing welding deformation grading by means of finite element simulation, training a multi-classification support vector machine, constructing a multi-parameter constraint polyhedron for each feature point, and demarcating an initial feasible process parameter domain; collecting a margin vector of a process parameter relative to a constraint boundary of a welded point, combining a heat accumulation effect between points to construct a non-isotropic affine transformation matrix, and correcting the feasible domain of the process parameter; taking welding efficiency, deformation level and system stability as multi-objectives to carry out Pareto optimization to solve optimal process parameters, issuing a controller to complete arc welding, and realizing online regulation and control of welding deformation.

Description

Technical Field

[0001] This application belongs to the field of large-diameter steel pipes, and particularly relates to an adaptive control system for welding deformation of large-diameter steel pipes using a multi-axis robot. Background Technology

[0002] With the continuous development of modern industrial technology, large-diameter steel pipes play a vital foundational role in key sectors of the national economy, such as petrochemicals, long-distance oil and gas transportation, urban underground utility tunnels, marine engineering, and large-scale building structures. Due to the characteristics of large-diameter steel pipes, such as thick walls, wide diameters, and complex spatial structures, traditional manual welding methods are no longer sufficient to meet the demands of high-efficiency, high-quality industrial manufacturing. In recent years, multi-axis robotic welding technology, with its advantages of high degree of freedom, strong flexibility, and high stability in continuous operation, has gradually become an important process in the manufacturing and on-site construction of large-diameter steel pipes. However, during the continuous welding process of large-diameter steel pipes using multi-axis robots, the pipe body is prone to uneven thermal expansion and contraction due to the heat source of the electric arc, leading to welding deformation. This type of welding deformation not only compromises the geometric accuracy of the steel pipe, making subsequent pipe segment assembly difficult, but may also create residual stress inside the pipe wall, weakening the overall load-bearing capacity and long-term service safety of the pipeline system. Therefore, effectively controlling the welding deformation of large-diameter steel pipes using multi-axis robots has become a crucial issue affecting the quality of high-end equipment manufacturing.

[0003] The curvature characteristics and stress distribution of large-diameter steel pipes along the welding trajectory exhibit significant spatial differences. Traditional globally consistent process parameter settings struggle to address the specific control requirements of local stress-sensitive areas. Furthermore, the long-range continuous welding process is accompanied by significant heat accumulation effects. Heat input and actual parameter fluctuations in the preceding welding stages continuously influence the temperature and stress field distributions in subsequent regions, making pre-set static process parameters prone to becoming inapplicable in the later stages of welding. In addition, actual industrial production requires controlling welding deformation while simultaneously considering operational efficiency and system anti-interference stability. However, most existing control strategies lack the ability to perform multi-objective collaborative optimization within a dynamically evolving parameter space, making it difficult to adjust subsequent process parameters in real-time and continuously based on the welded state. This results in the final welding deformation control effect failing to achieve the expected accuracy. Therefore, there is an urgent need to propose a control method that can combine spatial trajectory characteristics and preceding heat accumulation effects to achieve multi-objective optimization of process parameters, thereby improving the adaptive control capability of welding deformation in large-diameter steel pipes. Summary of the Invention

[0004] According to a first aspect of the present invention, an adaptive control system for the welding deformation of large-diameter steel pipes by a multi-axis robot is proposed to solve the problem that existing methods cannot cope with the thermodynamic evolution under spatial trajectory, and includes the following modules:

[0005] The generation module is used to discretize the welding trajectory into a set of variable density feature points based on the three-dimensional model of the steel pipe and the welding trajectory, combined with the curvature change rate and the preset stress sensitive area. For each feature point, a combination of process parameters is generated by low difference sequence sampling. The welding deformation is predicted by finite element simulation and the welding deformation is divided into multiple levels. The calculation module is used to train a multi-class support vector machine model, and to construct a multi-parameter constraint polyhedron for each feature point to define the initial feasible process parameter domain using the multi-class support vector machine model. The decision boundary of the multi-parameter constraint polyhedron is set by multiple sets of fused algebraic constraints. When performing welding operations along the trajectory, the margin vector of the actual process parameters of the previously welded feature points relative to their own multi-parameter constraint polyhedron decision boundary is extracted and calculated. The execution module is used to construct an isotropic affine transformation matrix based on the margin vector and the thermal accumulation effect between the two feature points. The isotropic affine transformation matrix is ​​used to transform the three-dimensional boundary of the initial feasible process parameter domain to generate a real-time process parameter space. In the real-time process parameter space, Pareto optimization is performed with welding efficiency, predicted deformation level, and system stability represented by the distance from the parameter to the boundary in the dimensionless space as multi-dimensional optimization objectives. The optimal combination of process parameters is determined and sent to the controller to execute the solid arc welding operation.

[0006] According to a second aspect of the present invention, an adaptive control method for welding deformation of large-diameter steel pipes using a multi-axis robot is proposed, comprising the following steps: Based on the three-dimensional model of the steel pipe and the trajectory to be welded, the trajectory to be welded is discretized into a set of variable density feature points by combining the curvature change rate and the preset stress sensitive area. For each feature point, a combination of process parameters is generated by low difference sequence sampling. The welding deformation is predicted by finite element simulation and the welding deformation is divided into multiple levels. Based on this, a multi-class support vector machine model is trained, and the multi-class support vector machine model is used to construct a multi-parameter constraint polyhedron for each feature point to define the initial feasible process parameter domain. The decision boundary of the multi-parameter constraint polyhedron is set by multiple sets of fused algebraic constraints. When performing welding operations along the trajectory, the margin vector of the actual process parameters of the previously welded feature points relative to their own multi-parameter constraint polyhedron decision boundary is extracted and calculated. Based on the thermal accumulation effect between the margin vector and the two feature points, an isotropic affine transformation matrix is ​​constructed. The three-dimensional boundary of the initial feasible process parameter domain is transformed using the isotropic affine transformation matrix to generate a real-time process parameter space. In the real-time process parameter space, Pareto optimization is performed with welding efficiency, predicted deformation level, and system stability represented by the distance from the parameter to the boundary in the dimensionless space as multi-dimensional optimization objectives. The optimal combination of process parameters is determined and sent to the controller to execute the solid arc welding operation.

[0007] This invention generates a variable-density feature point set by combining the rate of curvature change and the stress-sensitive region, which can accurately characterize the geometric changes and local stress state of large-diameter steel pipes along the welding trajectory, improving the targeting of feature extraction and the accuracy of welding deformation prediction. By constructing a multi-parameter constrained polyhedron through low-difference sequence sampling, finite element simulation, and a multi-class support vector machine model, the search complexity of the high-dimensional process parameter space is reduced, and a safe and reliable initial feasible parameter boundary can be quickly defined. Simultaneously, based on the margin vector of previously welded points and the thermal accumulation effect, an isotropic affine transformation matrix is ​​constructed to dynamically map and correct the parameter domain boundary, reducing the impact of heat accumulation and execution deviation on subsequent welding parameters. Furthermore, Pareto optimization is performed in the real-time process parameter space, integrating welding efficiency, deformation level, and system stability, taking into account low deformation control, high production efficiency, and anti-interference stability, further improving the deformation adaptive control effect in multi-axis robot solid welding operations. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the curves showing the rate of change of curvature of the arc length of the trajectory to be welded and the distribution curves of the variable density sampling step size. Figure 2 This is a bar chart showing the length distribution of the axial difference between dimensionless process coordinate axes. Detailed Implementation

[0009] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0010] In the first embodiment, the present invention proposes an adaptive control system for the deformation of multi-axis robot welding of large-diameter steel pipes, comprising the following modules: The generation module is used to discretize the welding trajectory into a set of variable density feature points based on the three-dimensional model of the steel pipe and the welding trajectory, combined with the curvature change rate and the preset stress sensitive area. For each feature point, a combination of process parameters is generated by low difference sequence sampling. The welding deformation is predicted by finite element simulation and the welding deformation is divided into multiple levels.

[0011] Import the standard format 3D model file of the large-diameter steel pipe, extract the discrete point set on the welding trajectory, and evaluate the rate of curvature change of the trajectory surface. Read the preset spatial coordinate interval of the stress-sensitive area. When the discrete point is located in an area where the rate of curvature change is greater than a preset threshold or within the stress-sensitive area, decrease the discrete step size to increase the feature point density; conversely, increase the discrete step size to discretize the welding trajectory into a variable-density feature point set. For each feature point, uniformly sample within the upper and lower limits of the set welding current, welding voltage, and welding speed parameters to generate multiple sets of process parameter combinations. Input the above process parameter combinations into the finite element analysis software Abaqus for thermo-mechanical coupling transient analysis, calculate the maximum residual deformation of the pipe wall node in the surface normal direction, and divide the deformation into multiple continuous deformation levels from Level 1 to Level 5 according to the distribution interval of the predicted welding deformation, to ensure consistency in the number of training labels and hierarchical logic of the subsequent support vector machine model. The distribution of the rate of curvature change corresponding to the arc length of the welding trajectory and the segmented sampling step size settings are as follows: Figure 1 As shown.

[0012] In an optional embodiment, the step of discretizing the weldable trajectory into a set of variable-density feature points based on the three-dimensional model of the steel pipe and the trajectory to be welded, combined with the rate of curvature change and a preset stress-sensitive area, includes: Sampling points are extracted along the welding trajectory at preset intervals, and the change in the normal vector at each sampling point over a unit arc length is calculated as the rate of curvature change. Based on the finite element model, the surface tensile and compressive stress distribution of the welding trajectory after heating is predicted. The closed area formed by extending the continuous closed boundary line with the absolute value of tensile and compressive stress greater than the preset threshold outward by a preset distance is set as the preset stress sensitive area. On trajectory segments where the rate of curvature change is greater than the curvature threshold or located within the preset stress-sensitive area, feature points are densely collected according to the first step length. On the trajectory segment where the rate of curvature change is not greater than the curvature threshold and is located outside the preset stress-sensitive area, feature points are sparsely collected at a second step length greater than the first step length, and all feature points are merged to generate a variable density feature point set.

[0013] For a 3D model of a steel pipe to be welded with an outer diameter of 800 to 1200 mm (e.g., 1000 mm) and a wall thickness of 10 to 20 mm (e.g., 15 mm), the preset interval for extracting sampling points on the trajectory is set to 5 to 10 mm, preferably 5 mm. The normal vector of each sampling point is extracted, and the first derivative of the normal vector along a unit arc length is calculated. The curvature change rate corresponding to each local bending section, bevel transition section, or elbow connection section of the weld path is obtained, in radians per millimeter. The curvature threshold for distinguishing between smooth and abrupt regions is set to 0.05 radians per millimeter. The curvature change rate is used to characterize the degree of local normal change of the welding trajectory, and does not only refer to the overall constant curvature of the circumferential surface of the large-diameter steel pipe. A thermo-elastic-plastic finite element model is established, and after applying a double ellipsoidal moving heat source, the distribution of the first principal stress or equivalent stress on the structural surface is extracted.

[0014] A preset threshold is set to 60% to 80% of the yield strength of the target pipe material, for example, 200 MPa for Q345 steel. Closed, continuous high-stress boundaries with absolute tensile or compressive stress values ​​greater than 200 MPa are extracted from the model. These closed boundary lines are then uniformly offset outwards along the normal direction by 15 to 30 mm, preferably 20 mm, to generate a preset stress-sensitive zone. This zone encloses potential high-deformation-risk sources with a certain margin. For weldable trajectory segments that meet the condition of a curvature change rate greater than 0.05 radians per millimeter, or whose three-dimensional spatial coordinates fall within the aforementioned preset stress-sensitive zone, the weldable trajectory segment is determined to be in a high-deformation-sensitive state. A high-frequency discretization mode is activated, using a smaller first-step length of 1 to 3 mm, preferably 2 mm, to densely generate trajectory feature points, ensuring high data resolution and controlled sampling rate in this area. Conversely, for trajectory segments with a curvature change rate not greater than 0.05 radians per millimeter and located outside the preset stress-sensitive zone, they are considered smooth segments, and a larger second-step length of 8 to 15 mm, preferably 10 mm, is used to generate sparse point sets. The two types of spatial coordinate point matrices generated with different time lengths are merged according to the sequence of spatial movement of the welding robot, and the output is a variable density feature point set that can reduce the subsequent computing power burden and ensure high-density correction in sensitive deformation areas.

[0015] In an optional embodiment, for each feature point, a combination of process parameters is generated using low-difference sequence sampling. The welding deformation is then predicted via finite element simulation and classified into multiple levels, including: Welding current, welding voltage, and welding speed are selected as independent variables in the three-dimensional orthogonal control parameter space; The Sobol low-difference sequence sampling algorithm is used to extract a preset number of process parameter combinations in the three-dimensional orthogonal control parameter space; The process parameters are input into a pre-built thermo-elastic-plastic finite element model to perform thermo-mechanical coupling calculations, and the distance of the steel pipe from the initial state in the normal direction of the surface after cooling is obtained as the corresponding welding deformation. The predicted distribution range of welding deformation is divided into multiple consecutive numerical segments, and the welding deformation falling into each numerical segment is labeled as the corresponding deformation level, thus classifying the welding deformation into multiple levels.

[0016] When determining the optimization range of independent variables in the three-dimensional orthogonal control parameter space, based on the preset properties of the steel pipe base material and the characteristics of the matched welding wire, the welding current is used as the first dimension variable and limited to a safe range of 150 to 300 amps; the welding voltage is used as the second dimension variable and limited to a range of 20 to 35 volts; and the welding speed, representing the movement efficiency of the end effector, is used as the third dimension variable and limited to a range of 200 to 600 mm / min. In this three-dimensional orthogonal space composed of parameters, to reduce the experimental sample size while ensuring the uniformity of the global parameter combination distribution and avoiding model distortion caused by sample aggregation, uniform sampling is performed across the entire domain. By setting a preset sampling quantity of 500 to 1000 sets, for example, selecting 500 sets, an orthogonal process parameter combination feature matrix covering each boundary and intermediate gradient is generated. The control system uses the 500 sets of three-dimensional process parameter matrices as boundary load conditions and substitutes them into the thermo-elastic-plastic finite element model. The external convective heat transfer coefficient of the welding surface is set to 20 W / (m²·K), and the thermal emissivity is set to 0.8. Transient nonlinear thermo-mechanical coupling calculations are then initiated. After simulating the entire trajectory heat flow transfer process and ensuring all nodes in the workpiece model have completely cooled to a room temperature of 25 degrees Celsius, the residual deformation geometric displacement at the weldable feature point along the normal direction of the outer surface of the pipe wall is obtained. It is assumed that the extracted node displacements caused by each sample are continuously distributed within the range of 0.5 to 5.0 mm, which are then used as the corresponding single-point welding deformation. To transform this continuous variable into classification labels, the continuous deformation range of 0.5 to 5.0 mm was divided into 5 continuous numerical segments with an equal step size of 0.9 mm. The simulated deformation results falling within the numerical segments of 0.5 mm to 1.4 mm, 1.4 mm to 2.3 mm, 2.3 mm to 3.2 mm, 3.2 mm to 4.1 mm, and 4.1 mm to 5.0 mm were labeled as Level 1 to Level 5, respectively. Except for the last numerical segment which contains the right endpoint, the other numerical segments all contain the left endpoint and do not contain the right endpoint, thus completing the dimensionality reduction transformation from simulated data to discrete multi-level deformation labels.

[0017] When the number of feature points in the variable density feature point set exceeds a preset threshold, the feature points are first clustered according to the curvature change rate, stress sensitivity zone level, weld spatial location, and material thickness parameters. Representative feature points are then selected from each class to perform low-difference sequence sampling and thermo-elastic-plastic finite element simulation calculations. For non-representative feature points within the same class, the welding deformation level, support vector machine classification boundary, and initial feasible process parameter domain corresponding to the representative feature points are interpolated, translated, or reused based on the arc length distance, curvature change rate difference, and stress sensitivity level difference between the non-representative feature points and the representative feature points. This reduces the number of finite element simulations and the amount of offline modeling calculations.

[0018] The computation module is used to train a multi-class support vector machine model and construct a multi-parameter constraint polyhedron for each feature point to define the initial feasible process parameter domain using the multi-class support vector machine model. The decision boundary of the multi-parameter constraint polyhedron is set by multiple sets of fused algebraic constraints. When performing welding operations along the trajectory, the margin vector of the actual process parameters of the previously welded feature points relative to their own multi-parameter constraint polyhedron decision boundary is extracted and calculated.

[0019] Using combinations of process parameters as input features and corresponding deformation levels as labels, a linear support vector classifier module is invoked to train a multi-class support vector machine model under a one-to-many strategy for each feature point. Each classification boundary corresponds to a hyperplane in a high-dimensional space. The normal vector weight matrix and intercept term of each hyperplane are extracted, and multiple sets of fused linear inequality algebraic constraints are constructed. Using a half-space intersection algorithm module, the centroid of the parameter set corresponding to the target deformation level or the center point of the preset upper and lower limit parameters are used as feasible interior points to solve the geometric space defined by the inequality, thus constructing a multi-parameter constrained polyhedron defining the initial feasible process parameter domain for each feature point. When a multi-axis robot performs actual welding operations along a trajectory, sensors collect and extract in real time the actual welding current, welding voltage, and welding speed of the preceding welded feature points adjacent to the current point. First, the signed distance from the actual process parameter point to each decision boundary hyperplane of the corresponding polyhedron is calculated. The absolute value of the signed distance is used to filter the nearest decision boundary section. Then, the normal vector of the actual process parameter point pointing to the nearest decision boundary section is projected along the three parameter axes of welding current, welding voltage, and welding speed to obtain three-dimensional axial difference length data. The three-dimensional axial difference length data is used to form a margin vector representing the safety margin of the current parameters of the system.

[0020] In an optional embodiment, the multi-class support vector machine model is trained accordingly, and the multi-class support vector machine model is used to construct a multi-parameter constrained polyhedron for each feature point, defining the initial feasible process parameter domain. The decision boundary of the multi-parameter constrained polyhedron is set by multiple sets of fused algebraic constraints, including: The process parameter combinations and corresponding welding deformation levels are constructed as feature input-output data pairs. The feature input and output data are used to train the multi-class support vector machine model based on the linear kernel function, and multiple hyperplane equations that separate each welding deformation level are obtained in the three-dimensional orthogonal control parameter space. Select a target deformation level that can limit the deformation amount to within the allowable range. Take the intersection of the separating hyperplane equation of the parameter set corresponding to the target deformation level with the preset upper and lower limit constraints of welding current, welding voltage and welding speed. Construct the polyhedral region formed by the intersection as the initial feasible process parameter domain. Each surface of the polyhedral region is the decision boundary of the multi-parameter constrained polyhedron set by multiple sets of fused algebraic constraints.

[0021] In the preparation phase of machine learning training data, a 500-row process parameter matrix containing the three feature columns of welding current, voltage, and speed generated above is extracted. To remove the influence of dimensional differences on kernel function optimization, max-min normalization is used to map all current, voltage, and speed values ​​to a scale range of 0 to 1, and the minimum, maximum, and range values ​​corresponding to each parameter dimension are saved as a unified scale for subsequent dimensionless and denormalization conversions in the online stage. Subsequently, the data is matched and concatenated with the corresponding Level 1 to Level 5 discrete deformation level labels by row dimension to construct 500 pairs of feature input-output data containing three-dimensional input feature vectors and one-dimensional target output levels. This standardized training set is loaded into a support vector machine model configured using a one-to-many parallel multi-classification strategy. The support vector machine model includes an input variable receiving part, a parallel linear discriminant function calculation part, and a classification output part. The input variable receiving part receives the process parameter combination matrix data composed of the aforementioned dimensionless three-dimensional feature variables, where the three-dimensional feature variables correspond to the real values ​​of welding current, welding voltage, and welding speed, respectively. The parallel linear discriminant function computation part consists of multiple independent linear binary discriminant functions. Each linear binary discriminant function contains a normal weight vector and an intercept bias term, used to calculate the inner product score of each category in the high-dimensional feature space. The classification output part outputs the aforementioned predicted deformation level, that is, it makes a judgment based on the calculated scores of each linear binary discriminant function and outputs the final determined classification label of the corresponding target deformation level to the outside world.

[0022] Set the training penalty factor C of the key parameter to a stable value between 1.0 and 10.0, for example, take C=5.0 to balance the soft margin boundary. Initiate multiple iterations of the built-in optimization algorithm suitable for linear support vector classifiers to calculate several hyperplane geometric analytical equations, each composed of a normal weight vector w and an intercept bias term b, which can isolate the five different thermal deformation levels in a three-dimensional orthogonal parameter space. Equations. When constructing the boundary polyhedron, considering the quality inspection requirements of industrial welded pipe fittings, such as allowing extreme value constraints to produce a relative deformation of no more than 2.3 mm, the corresponding Level 1 and Level 2 are extracted as compliant target deformation levels. From the generated library of multiple linear hyperplane models, a set of peripheral separating hyperplanes capable of isolating the parameter distribution clusters of these two safety levels from the Level 3 equal-height deformation distribution cluster is selected, with the number set to 4 to 6 plane equations. These equations of isolated hyperplanes are then transformed into a first-order fusion algebraic constraint system based on inequality symbols, in the form of... and A set of polynomials, combined with preset upper and lower limits for welding current, welding voltage, and welding speed, are intersected in a virtual three-dimensional orthogonal parameter space to construct a polyhedral geometric region as the initial feasible process parameter domain. When the intersection is empty or does not meet the preset volume threshold, a new set of peripheral separating hyperplanes corresponding to the target deformation level is selected, or a preset safety parameter upper and lower limit region is used as a supplementary feasible domain. The vertices and face elements of this convex polyhedron are denormalized, restoring and recombining them into the original three-dimensional control optimization space containing dimensional parameters such as amperes, volts, and millimeters per minute. The three-dimensional region constructed by this set of real dimensional inequalities becomes the adjustable parameter boundary range, and the boundary surfaces constitute the multi-parameter constrained polyhedron decision boundary system.

[0023] In an optional embodiment, the step of extracting and calculating the margin vector of the actual process parameters of the previously welded feature points relative to the decision boundary of the multi-parameter constrained polyhedron during the welding operation along the trajectory includes: Extract the actual current, actual voltage, and actual welding speed values ​​applied at the previously welded feature points recorded by the controller, and form an actual process parameter vector; The actual process parameter vector and its corresponding multi-parameter constrained polyhedron decision boundary are dimensionless, and the spatial shortest distance from the dimensionless actual process parameter vector to each constituent section of the dimensionless multi-parameter constrained polyhedron decision boundary is calculated. The decision boundary section with the smallest distance is selected, and the dimensionless normal vector of the actual process parameter vector to the section is calculated. The normal vector is projected according to the orthogonal axis of the three-dimensional parameters to obtain three corresponding axial difference length data. The axial difference length data are used to form an array with direction and magnitude attributes as a margin vector.

[0024] When performing closed-loop control welding operations along a discrete spatial trajectory, it is assumed that the motion control system is currently in the calculation stage of the k-th current feature point. The main control unit will read the actual sensor closed-loop feedback values ​​cached in the welding controller's historical memory corresponding to the immediately preceding (k-1)-th welded feature point via the bus. For example, the measured parameters obtained at the previous welded point are the actual operating current of 220 amps, the actual voltage at both ends of the arc of 26 volts, and the actual welding line speed of 400 mm / min. These three key parameters are extracted to form a transposed single-column actual process parameter vector containing 220, 26, and 400. To eliminate the influence of dimensional differences between electrical signal quantities and machine kinematic quantities, a maximum-minimum normalization process consistent with the training phase was adopted. Based on the minimum, maximum, and range values ​​of current, voltage, and welding speed stored during the training phase, this process was applied. The column vectors and the linear section boundary equations of the 3D initial multi-parameter constrained polyhedron, constructed and assigned separately around the preceding point, are dimensionless. After completing the dimensionless spatial reconstruction, the analytical expression based on the signed distance from the point to the plane is... Calculate the spatial test points represented by the current dimensionless actual process parameter vectors respectively. The signed distances to each boundary section of the multi-parameter constrained polyhedron on the outer side are calculated, and the direction of the parameter point is determined according to the inequality corresponding to the safety region to determine whether the parameter point is inside the safety region or outside the danger region; at the same time, the signed distances to each boundary section of the multi-parameter constrained polyhedron on the outer side are calculated. As a distance metric, it is used to filter the nearest decision boundary section.

[0025] A distance set is created from the obtained distance values, assuming it includes 0.15, 0.32, 0.08, 0.45, and 0.22. The decision boundary plane section containing the smallest distance (0.08) is selected. This section represents the current control output closest to the critical boundary that may cause deformation deterioration. Dimensionless parameter points are then extracted by combining the positive and negative directions of the corresponding signed distances. The perpendicular normal vector pointing to the plane section with the minimum distance. This normal vector is decomposed and orthogonally projected onto the X-axis (representing the dimensionless current component), the Y-axis (representing the voltage component), and the Z-axis (representing the velocity component). The lengths of the projected line segments, each with a sign, are independently extracted along the axes of the three coordinate systems; these are the axial difference lengths, for example, Δx=0.04, Δy=-0.06, and Δz=0.03. These three directional data are then reconstructed into a margin vector M, possessing characteristics of deviation direction and margin size, as a quantitative reference representing the parameter's safety toughness and correction limit. The dimensionless axial difference length data corresponding to each process axis are as follows: Figure 2As shown. The margin vector is preferably used for adjacent or near-neighbor feature points where the distance between the previously welded feature point and the current feature point does not exceed a preset heat-affected distance threshold. When the spatial distance between two feature points exceeds the preset heat-affected distance threshold, the weight of the margin vector in the affine transformation matrix is ​​reduced, or the initial feasible process parameter domain corresponding to the current feature point is used for optimization. Furthermore, each axial weighted scaling factor is set with a preset upper limit and a preset lower limit, and the dimensional offset is set with absolute process upper and lower limit constraints to avoid excessive contraction or expansion of the real-time process parameter space caused by the cross-point transmission of the margin vector.

[0026] The execution module is used to construct an isotropic affine transformation matrix based on the margin vector and the thermal accumulation effect between the two feature points. The isotropic affine transformation matrix is ​​used to transform the three-dimensional boundary of the initial feasible process parameter domain to generate a real-time process parameter space. In the real-time process parameter space, Pareto optimization is performed with welding efficiency, predicted deformation level, and system stability represented by the distance from the parameter to the boundary in the dimensionless space as multi-dimensional optimization objectives. The optimal combination of process parameters is determined and sent to the controller to execute the solid arc welding operation.

[0027] When the current feature point is the first feature point of the trajectory to be welded, the thermal accumulation effect is set as the baseline thermal accumulation effect, and an initial margin vector is generated based on the boundary distance of the preset initial process parameters relative to the corresponding initial feasible process parameter domain, or Pareto optimization is performed directly within the initial feasible process parameter domain of the first feature point. The time interval is obtained by calculating the spatial distance between the previously welded feature point and the current feature point, dividing it by the actual welding speed, and then substituting it into the one-dimensional thermal conductivity exponential decay equation to calculate the thermal accumulation effect factor. The three-dimensional axial difference length data in the margin vector and the thermal accumulation effect factor are input together into a preset mapping relationship to calculate the weighted scaling factor of the current axis, voltage axis, and welding speed axis, respectively, and the weighted scaling factor is limited to a preset positive value range; wherein, the smaller the margin or the stronger the thermal accumulation effect, the feasible spatial scaling factor corresponding to the current axis and voltage axis decreases, and the adjustment direction corresponding to the welding speed axis is determined according to the rule of enhancing heat dissipation. Simultaneously, the dimensionless offset of each axis is output from the preset mapping relationship. Then, according to the inverse normalization scale corresponding to the dimensionless processing of each axis, the dimensionless offset is converted into a dimensioned offset corresponding to the current, voltage and welding speed respectively, and a scaling matrix and offset vector in the form of a diagonal matrix are constructed.

[0028] The scaling matrix and offset vector are combined to obtain a fourth-order anisotropic affine transformation matrix. This matrix is ​​used to perform a linear spatial mapping transformation on the coordinates of each vertex of the initial multi-parameter constrained polyhedron. The transformed vertices are then used to reconstruct a real-time process parameter space adapted to the current thermal state. This reconstructed real-time process parameter space is then constrained by intersecting with preset absolute upper and lower limits for welding current, welding voltage, and welding speed to obtain the final real-time process parameter space used for optimization. Within this real-time process parameter space, welding speed is set as the evaluation index for welding efficiency, the predicted deformation level output by the multi-class support vector machine model is set as the evaluation index for predicted deformation, and the minimum distance from parameter points to the boundary interfaces of the real-time polyhedron is set as the evaluation index for system stability. With the multi-dimensional optimization objectives of maximizing welding speed, minimizing deformation level, and maximizing system stability, an iterative search is performed within the real-time process parameter space to obtain the Pareto front solution set. The optimal process parameter combination with the highest comprehensive score is selected from the Pareto front solution set and converted into a communication message format supported by a programmable logic controller (PLC). This PLC is then sent to the motion controller at the bottom layer of the multi-axis robot via a communication protocol to drive the welding torch to perform solid arc welding operations.

[0029] In an optional embodiment, the step of constructing an isotropic affine transformation matrix based on the thermal accumulation effect between the margin vector and the two feature points, and using the isotropic affine transformation matrix to transform the three-dimensional boundary of the initial feasible process parameter domain to generate a real-time process parameter space, includes: Obtain the spatial distance, moving speed, time variables, measured temperature of the substrate surface, and material thermal diffusion attenuation parameters from the previously welded feature point to the current feature point; When the measured temperature of the substrate surface cannot be obtained, the welding heat input and equivalent energy-temperature conversion coefficient at the previously welded feature point are obtained as alternative sources of temperature rise. The predicted heat accumulation absolute temperature at the current feature point is calculated based on the heat conduction exponential decay model that includes both time decay and spatial decay. The heat accumulation effect is represented by the ratio of the predicted heat accumulation absolute temperature to the reference absolute temperature; The axial difference length data of each dimension in the margin vector are mapped to the preset mapping relationship of the thermal accumulation effect, and the weighted scaling factor and the dimensionless offset of each axis are calculated respectively. Based on the inverse normalization scale corresponding to the dimensionless processing of each axis, the dimensionless offset is converted into a dimensionless offset corresponding to the welding current, welding voltage and welding speed respectively. Among them, the dimensionless offset and dimensionless offset corresponding to the welding current axis and welding voltage axis are negatively adjusted as the heat accumulation effect increases, while the dimensionless offset and dimensionless offset corresponding to the welding speed axis are positively adjusted as the heat accumulation effect increases. A fourth-order anisotropic affine transformation matrix is ​​constructed using the weighted scaling factor of each axis as the main diagonal element and combined with the dimensional offset. After converting the three-dimensional boundary coordinate vertices of the initial feasible process parameter domain into four-dimensional homogeneous coordinates, the four-dimensional homogeneous coordinates corresponding to the three-dimensional boundary coordinate vertices are linearly transformed using the fourth-order isotropic affine transformation matrix to obtain the three-dimensional volume boundary set after spatial scaling and offset, thereby generating the real-time process parameter space.

[0030] During the operating cycle, the spatial arc length distance L from the previously welded feature point to the current target feature point is extracted using forward kinematics. If the extracted distance is 2 mm, the real-time system welding travel speed is also extracted. For example, 400 millimeters per minute translates to 6.67 millimeters per second. The time difference between two points is obtained analytically through a division operation. The calculated time is 0.3 seconds. Based on the extracted historical data and the formula... ,in To convert the welding travel speed to millimeters per second, the effective utilization coefficient of the heat transfer arc, η, is taken as 0.8. The calculated heat input released to the pipe base material at the preceding node is 686 joules per millimeter. Simultaneously, the initial measured temperature value of the surface of the steel pipe substrate before cooling is obtained by a non-contact infrared thermal imager mounted around the welding torch, for example, 423.15 Kelvin, or 150 degrees Celsius. Based on this, a one-dimensional transient heat conduction exponential decay function that simultaneously incorporates time decay and spatial decay is constructed. Where α is the time decay coefficient and β is the spatial decay coefficient. This is the initial temperature rise; when the measured temperature of the substrate surface is obtained... season When the measured temperature of the substrate surface is not obtained, let ,in , This is the equivalent energy-temperature conversion factor. The measured temperature of the substrate surface and the welding heat input are not directly added as two temperature rise terms. The predicted cumulative absolute temperature of the target welding point due to residual heat transfer is derived from the above variables, assuming a calculated value of 380 Kelvin; this absolute temperature is then proportionally divided with a preset reference absolute temperature, such as 298.15 Kelvin, to obtain a dimensionless scaling multiplier, which is used to represent the intensity of the cumulative heat effect.

[0031] Based on this model, the margin vector M, which contains deviation information of three orthogonal parameters obtained in the previous analysis, is composed of three axial differences. , as well as This involves performing a multi-parameter spatial mapping transformation operation. Since parameters such as voltage and current possess positive temperature gradients, and the moving speed exhibits heat dissipation characteristics, the spatial difference between the current and voltage dimensions, which have heat-generating characteristics, is substituted into a multiplicative mapping relationship containing a negatively correlated attenuation gain coefficient to calculate the contraction ratio. and The gain ratio is obtained by applying a positive correlation amplification factor to the velocity dimension. The weighted scaling factors representing the degree of scaling along the three-dimensional axes are extracted. Based on the denormalized scales of current, voltage, and welding speed saved during the training phase, the dimensionless offset results are converted into offsets in amperes, volts, and millimeters per minute (mm / min). For example, dimensional offsets of -5 A, -1 V, and +20 mm / min are calculated for the X, Y, and Z axes. The calculated weighted scaling factors for different axial dimensions are then used to calculate the offsets. , and The numerical value 1 is sequentially filled into the diagonal of the square matrix, and the calculated offset vector is embedded into the fourth column at the end of the matrix to construct a 4×4 fourth-order anisotropic affine transformation matrix with displacement and spatial scaling properties. The coordinates of each three-dimensional vertex of the initial feasible convex polyhedron of the current feature point are extracted, and the last position is filled with the number 1 to transform it into a homogeneous four-dimensional geometric space point coordinate column matrix format. The left multiplication operation is performed on the matrix determined above to remove the processed fourth dimension, which is transformed into a three-dimensional volume envelope surface set enclosed by the new vertices, generating a real-time process parameter space that combines the accumulated heat state and safety bias.

[0032] In an optional embodiment, the step of performing Pareto optimization within the real-time process parameter space, using welding efficiency, predicted deformation level, and system stability represented by the distance from the parameters to the boundary in the dimensionless space as multi-dimensional optimization objectives, to determine the optimal combination of process parameters and send it to the controller to execute the solid arc welding operation, includes: Welding speed is used as the evaluation target for welding efficiency; The deformation level predicted by the support vector machine for the current test process point is used as the evaluation target for predicted deformation. The minimum distance from the normalized process parameter point to the multidimensional real-time boundary interface is used as the system stability evaluation target. The three evaluation objectives are introduced as independent objective functions into a multi-objective genetic algorithm for crossover and mutation iteration operations to generate a set of Pareto optimal solutions that are not mutually dominant. The optimal process parameter combination is selected from the Pareto optimal solution set, which satisfies the comprehensive evaluation index of high efficiency, low deformation and maximum tolerance. This optimal process parameter combination is then sent to the multi-axis robot controller to perform solid arc welding.

[0033] For the set of parameter test points within the real-time process parameter space, three evaluation objective models are constructed during the search and optimization phase. The first objective is to improve welding efficiency, by extracting the third component parameter, namely the welding speed, from the column vector of each set of three-dimensional test parameters. The objective function for evaluating welding efficiency is millimeters per minute. The second objective is to control deformation. This involves inputting the three-dimensional test current, voltage, and velocity data into a trained and converged support vector machine prediction model for classification and discrimination. The returned Level 1 to Level 5 deformation rating index labels are then used as the target for minimizing the predicted deformation. In this system, Level 1 to Level 5 are mapped to values ​​1 to 5, with smaller values ​​indicating smaller predicted deformations. The third measure improves system stability by projecting the current process test points back into the dimensionless spatial domain, calculating the distances from the test points in the current dimensionless space to each boundary interface of the real-time polyhedron, and taking the minimum distance value as the system stability evaluation target. The three established evaluation objectives are then input into a fast, non-dominated sorting genetic algorithm with an elitist strategy and a crowding calculation mechanism, such as the NSGA-II algorithm module. The population base is configured to randomly generate 100 to 200 individuals, with the best individuals selected to form the parent population. Based on the selected parents, the crossover / recombination probability is set to 0.9 and the mutation probability to 0.1, and iterative calculations are performed for 50 to 100 generations. This iterative operation generates a set of optimal solutions for non-dominated Pareto first front candidate parameter combinations.

[0034] To meet the real-time requirements of online control between adjacent feature points, the system pre-generates candidate Pareto solution sets for different thermal accumulation effect intervals, margin vector intervals, and deformation level constraints during the offline phase, and stores these candidate Pareto solution sets as a parameter lookup table. During the online welding phase, the controller selects initial candidate solutions from the parameter lookup table based on the current thermal accumulation effect, margin vector, and real-time process parameter space, using the optimal process parameter combination of the previous feature point as the initial population center. It performs rapid iterative optimization within a limited number of generations only in the local neighborhood. When the online computation time reaches a preset time limit, the current local iteration process is stopped, and the currently obtained non-dominated solution set is used as the candidate solution set to be evaluated. Before calculating the comprehensive score, the welding speed, deformation level, and system stability index are normalized, and the deformation level is converted into a reverse normalized index, where a larger value indicates better deformation control performance. The weights for the normalized welding speed, the inverse normalized deformation control index, and the normalized stability index were set to 0.4 and 0.2 respectively. The node closest to the ideal solution with the highest comprehensive score was extracted from all non-dominated solution combinations. For example, the parameter combination with the highest comprehensive score was determined to be 210 amps current, 25 volts voltage, and a welding speed of 420 mm / min. After completing the data packet construction, the data was sent to the multi-axis robot controller, triggering the welding machine's arc control power supply to perform closed-loop tracking and deformation compensation correction for the steel pipe butt welding.

[0035] In the second embodiment, the present invention also proposes an adaptive control method for welding deformation of large-diameter steel pipes using a multi-axis robot, comprising the following steps: Based on the three-dimensional model of the steel pipe and the trajectory to be welded, the trajectory to be welded is discretized into a set of variable density feature points by combining the curvature change rate and the preset stress sensitive area. For each feature point, a combination of process parameters is generated by low difference sequence sampling. The welding deformation is predicted by finite element simulation and the welding deformation is divided into multiple levels. Based on this, a multi-class support vector machine model is trained, and the multi-class support vector machine model is used to construct a multi-parameter constraint polyhedron for each feature point to define the initial feasible process parameter domain. The decision boundary of the multi-parameter constraint polyhedron is set by multiple sets of fused algebraic constraints. When performing welding operations along the trajectory, the margin vector of the actual process parameters of the previously welded feature points relative to their own multi-parameter constraint polyhedron decision boundary is extracted and calculated. Based on the thermal accumulation effect between the margin vector and the two feature points, an isotropic affine transformation matrix is ​​constructed. The three-dimensional boundary of the initial feasible process parameter domain is transformed using the isotropic affine transformation matrix to generate a real-time process parameter space. In the real-time process parameter space, Pareto optimization is performed with welding efficiency, predicted deformation level, and system stability represented by the distance from the parameter to the boundary in the dimensionless space as multi-dimensional optimization objectives. The optimal combination of process parameters is determined and sent to the controller to execute the solid arc welding operation.

[0036] The above description represents the preferred embodiments of the present invention. It should be noted that, for those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. An adaptive control system for welding deformation of large-diameter steel pipes using a multi-axis robot, characterized in that, Includes the following modules: The generation module is used to discretize the welding trajectory into a set of variable density feature points based on the three-dimensional model of the steel pipe and the welding trajectory, combined with the curvature change rate and the preset stress sensitive area. For each feature point, a combination of process parameters is generated by low difference sequence sampling. The welding deformation is predicted by finite element simulation and the welding deformation is divided into multiple levels. The calculation module is used to train a multi-class support vector machine model, and to construct a multi-parameter constraint polyhedron for each feature point to define the initial feasible process parameter domain using the multi-class support vector machine model. The decision boundary of the multi-parameter constraint polyhedron is set by multiple sets of fused algebraic constraints. When performing welding operations along the trajectory, the margin vector of the actual process parameters of the previously welded feature points relative to their own multi-parameter constraint polyhedron decision boundary is extracted and calculated. The execution module is used to construct an isotropic affine transformation matrix based on the margin vector and the thermal accumulation effect between the two feature points. The isotropic affine transformation matrix is ​​used to transform the three-dimensional boundary of the initial feasible process parameter domain to generate a real-time process parameter space. In the real-time process parameter space, Pareto optimization is performed with welding efficiency, predicted deformation level, and system stability represented by the distance from the parameter to the boundary in the dimensionless space as multi-dimensional optimization objectives. The optimal combination of process parameters is determined and sent to the controller to execute the solid arc welding operation.

2. The system according to claim 1, characterized in that, The process involves discretizing the steel pipe's three-dimensional model and the trajectory to be welded, combined with the rate of curvature change and a preset stress-sensitive area, into a set of variable-density feature points, including: Sampling points are extracted along the welding trajectory at preset intervals, and the change in the normal vector at each sampling point over a unit arc length is calculated as the rate of curvature change. Based on the finite element model, the surface tensile and compressive stress distribution of the welding trajectory after heating is predicted. The closed area formed by extending the continuous closed boundary line with the absolute value of tensile and compressive stress greater than the preset threshold outward by a preset distance is set as the preset stress sensitive area. On trajectory segments where the rate of curvature change is greater than the curvature threshold or located within the preset stress-sensitive area, feature points are densely collected according to the first step length. On the trajectory segment where the rate of curvature change is not greater than the curvature threshold and is located outside the preset stress-sensitive area, feature points are sparsely collected at a second step length greater than the first step length, and all feature points are merged to generate a variable density feature point set.

3. The system according to claim 2, characterized in that, For each feature point, a combination of process parameters is generated using low-difference sequence sampling. The welding deformation is then predicted through finite element simulation and divided into multiple levels, including: Welding current, welding voltage, and welding speed are selected as independent variables in the three-dimensional orthogonal control parameter space; The Sobol low-difference sequence sampling algorithm is used to extract a preset number of process parameter combinations in the three-dimensional orthogonal control parameter space; The process parameters are input into a pre-built thermo-elastic-plastic finite element model to perform thermo-mechanical coupling calculations, and the distance of the steel pipe from the initial state in the normal direction of the surface after cooling is obtained as the corresponding welding deformation. The predicted distribution range of welding deformation is divided into multiple consecutive numerical segments, and the welding deformation falling into each numerical segment is labeled as the corresponding deformation level, thus classifying the welding deformation into multiple levels.

4. The system according to claim 1, characterized in that, The multi-class support vector machine model is trained accordingly, and the multi-parameter constraint polyhedron is used to construct a multi-parameter constraint polyhedron for each feature point to define the initial feasible process parameter domain. The decision boundary of the multi-parameter constraint polyhedron is set by multiple sets of fused algebraic constraints, including: The process parameter combinations and corresponding welding deformation levels are constructed as feature input-output data pairs. The feature input and output data are used to train the multi-class support vector machine model based on the linear kernel function, and multiple hyperplane equations that separate each welding deformation level are obtained in the three-dimensional orthogonal control parameter space. Select a target deformation level that can limit the deformation amount to within the allowable range. Take the intersection of the separating hyperplane equation of the parameter set corresponding to the target deformation level with the preset upper and lower limit constraints of welding current, welding voltage and welding speed. Construct the polyhedral region formed by the intersection as the initial feasible process parameter domain. Each surface of the polyhedral region is the decision boundary of the multi-parameter constrained polyhedron set by multiple sets of fused algebraic constraints.

5. The system according to claim 1, characterized in that, The step of extracting and calculating the margin vector of the actual process parameters of previously welded feature points relative to the decision boundary of its own multi-parameter constrained polyhedron during welding operations along the trajectory includes: Extract the actual current, actual voltage, and actual welding speed values ​​applied at the previously welded feature points recorded by the controller, and form an actual process parameter vector; The actual process parameter vector and its corresponding multi-parameter constrained polyhedron decision boundary are dimensionless, and the spatial shortest distance from the dimensionless actual process parameter vector to each constituent section of the dimensionless multi-parameter constrained polyhedron decision boundary is calculated. The decision boundary section with the smallest distance is selected, and the dimensionless normal vector of the actual process parameter vector to the section is calculated. The normal vector is projected according to the orthogonal axis of the three-dimensional parameters to obtain three corresponding axial difference length data. The axial difference length data are used to form an array with direction and magnitude attributes as a margin vector.

6. The system according to claim 1 or 5, characterized in that, The process of constructing an isotropic affine transformation matrix based on the thermal accumulation effect between the margin vector and two feature points, and using the isotropic affine transformation matrix to transform the three-dimensional boundary of the initial feasible process parameter domain to generate a real-time process parameter space, includes: Obtain the spatial distance, moving speed, time variables, measured temperature of the substrate surface, and material thermal diffusion attenuation parameters from the previously welded feature point to the current feature point; When the measured temperature of the substrate surface cannot be obtained, the welding heat input and equivalent energy-temperature conversion coefficient at the previously welded feature point are obtained as alternative sources of temperature rise. The predicted heat accumulation absolute temperature at the current feature point is calculated based on the heat conduction exponential decay model that includes both time decay and spatial decay. The heat accumulation effect is represented by the ratio of the predicted heat accumulation absolute temperature to the reference absolute temperature; The axial difference length data of each dimension in the margin vector are mapped to the preset mapping relationship of the thermal accumulation effect, and the weighted scaling factor and the dimensionless offset of each axis are calculated respectively. Based on the inverse normalization scale corresponding to the dimensionless processing of each axis, the dimensionless offset is converted into a dimensionless offset corresponding to the welding current, welding voltage and welding speed respectively. Among them, the dimensionless offset and dimensionless offset corresponding to the welding current axis and welding voltage axis are negatively adjusted as the heat accumulation effect increases, while the dimensionless offset and dimensionless offset corresponding to the welding speed axis are positively adjusted as the heat accumulation effect increases. A fourth-order anisotropic affine transformation matrix is ​​constructed using the weighted scaling factor of each axis as the main diagonal element and combined with the dimensional offset. After converting the three-dimensional boundary coordinate vertices of the initial feasible process parameter domain into four-dimensional homogeneous coordinates, the four-dimensional homogeneous coordinates corresponding to the three-dimensional boundary coordinate vertices are linearly transformed using the fourth-order isotropic affine transformation matrix to obtain the three-dimensional volume boundary set after spatial scaling and offset, thereby generating the real-time process parameter space.

7. The system according to claim 1, characterized in that, Within the real-time process parameter space, Pareto optimization is performed using welding efficiency, predicted deformation level, and system stability (represented by the distance from the parameters to the boundary in the dimensionless space) as multi-dimensional optimization objectives to determine the optimal combination of process parameters and send it to the controller for execution of solid arc welding operations. This includes: Welding speed is used as the evaluation target for welding efficiency; The deformation level predicted by the support vector machine for the current test process point is used as the evaluation target for predicted deformation. The minimum distance from the normalized process parameter point to the multidimensional real-time boundary interface is used as the system stability evaluation target. The three evaluation objectives are introduced as independent objective functions into a multi-objective genetic algorithm for crossover and mutation iteration operations to generate a set of Pareto optimal solutions that are not mutually dominant. The optimal process parameter combination is selected from the Pareto optimal solution set, which satisfies the comprehensive evaluation index of high efficiency, low deformation and maximum tolerance. This optimal process parameter combination is then sent to the multi-axis robot controller to perform solid arc welding.

8. An adaptive control method for welding deformation of large-diameter steel pipes using a multi-axis robot, characterized in that, Includes the following steps: Based on the three-dimensional model of the steel pipe and the trajectory to be welded, the trajectory to be welded is discretized into a set of variable density feature points by combining the curvature change rate and the preset stress sensitive area. For each feature point, a combination of process parameters is generated by low difference sequence sampling. The welding deformation is predicted by finite element simulation and the welding deformation is divided into multiple levels. Based on this, a multi-class support vector machine model is trained, and the multi-class support vector machine model is used to construct a multi-parameter constraint polyhedron for each feature point to define the initial feasible process parameter domain. The decision boundary of the multi-parameter constraint polyhedron is set by multiple sets of fused algebraic constraints. When performing welding operations along the trajectory, the margin vector of the actual process parameters of the previously welded feature points relative to their own multi-parameter constraint polyhedron decision boundary is extracted and calculated. Based on the thermal accumulation effect between the margin vector and the two feature points, an isotropic affine transformation matrix is ​​constructed. The three-dimensional boundary of the initial feasible process parameter domain is transformed using the isotropic affine transformation matrix to generate a real-time process parameter space. In the real-time process parameter space, Pareto optimization is performed with welding efficiency, predicted deformation level, and system stability represented by the distance from the parameter to the boundary in the dimensionless space as multi-dimensional optimization objectives. The optimal combination of process parameters is determined and sent to the controller to execute the solid arc welding operation.

9. The method according to claim 8, characterized in that, The process involves discretizing the steel pipe's three-dimensional model and the trajectory to be welded, combined with the rate of curvature change and a preset stress-sensitive area, into a set of variable-density feature points, including: Sampling points are extracted along the welding trajectory at preset intervals, and the change in the normal vector at each sampling point over a unit arc length is calculated as the rate of curvature change. Based on the finite element model, the surface tensile and compressive stress distribution of the welding trajectory after heating is predicted. The closed area formed by extending the continuous closed boundary line with the absolute value of tensile and compressive stress greater than the preset threshold outward by a preset distance is set as the preset stress sensitive area. On trajectory segments where the rate of curvature change is greater than the curvature threshold or located within the preset stress-sensitive area, feature points are densely collected according to the first step length. On the trajectory segment where the rate of curvature change is not greater than the curvature threshold and is located outside the preset stress-sensitive area, feature points are sparsely collected at a second step length greater than the first step length, and all feature points are merged to generate a variable density feature point set.

10. The method according to claim 8, characterized in that, For each feature point, a combination of process parameters is generated using low-difference sequence sampling. The welding deformation is then predicted through finite element simulation and divided into multiple levels, including: Welding current, welding voltage, and welding speed are selected as independent variables in the three-dimensional orthogonal control parameter space; The Sobol low-difference sequence sampling algorithm is used to extract a preset number of process parameter combinations in the three-dimensional orthogonal control parameter space; The process parameters are input into a pre-built thermo-elastic-plastic finite element model to perform thermo-mechanical coupling calculations, and the distance of the steel pipe from the initial state in the normal direction of the surface after cooling is obtained as the corresponding welding deformation. The predicted distribution range of welding deformation is divided into multiple consecutive numerical segments, and the welding deformation falling into each numerical segment is labeled as the corresponding deformation level, thus classifying the welding deformation into multiple levels.

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