Multi-objective process parameter optimization system for refined steel welding deformation

Abstract

The application provides a multi-target process parameter optimization system for refined steel welding deformation, and relates to the technical field of intelligent manufacturing of steel structures.The system first jointly encodes the variable-angle cutting posture parameters and multi-pass welding process parameters, maps the groove slag residue thickness and the heat-affected zone depth according to the cutting angle gradient, constructs a groove interface disturbance impedance field, then uses the impedance field to correct the arc energy corresponding to the welding control parameters, generates the interface constraint state heat input space boundary, then loads the boundary to the refined steel finite element grid for thermal elastic-plastic transient simulation, jointly evaluates the macro residual deformation and the micro surface forming polarization degree, and obtains the Pareto optimal cutting and welding joint instruction set through multi-target collaborative evolution. In this way, the heat input evaluation deviation caused by the non-uniform groove interface can be reduced, and the welding deformation control precision and the surface forming quality can be improved.

Description

Technical Field

[0001] This application relates to the field of intelligent manufacturing technology for steel structures, and more specifically, to a multi-objective process parameter optimization system for welding deformation of refined steel. Background Technology

[0002] Precision steel components are widely used in steel structures where high dimensional accuracy, connection strength, and surface quality are required. The welding process is characterized by rapid localized heating and uneven cooling, which can easily lead to residual stress within the components and defects such as angular deformation, warping, and twisting. Welding current, voltage, feed rate, and bevel geometry all affect heat transfer and the degree of deformation. Furthermore, there are nonlinear coupling relationships between these parameters. Relying solely on manual experience or single-objective adjustments is insufficient to simultaneously guarantee component deformation accuracy and bevel surface forming quality; therefore, multi-objective optimization of relevant process parameters is necessary.

[0003] Current methods for optimizing welding process parameters typically rely on an ideal bevel model. Welding current, voltage, and feed rate are selected within a preset range, and welding deformation is calculated using finite element simulation or empirical models. An evolutionary algorithm is then used to select the optimal parameter combination. However, during variable-angle laser cutting, the laser beam incident angle and molten material discharge conditions change with the cutting posture, resulting in slag residue of varying thickness and a heat-affected zone of uneven depth along the bevel. This non-uniform interface state causes arc spot migration, arc deviation, and energy density fluctuations, leading to discrepancies between the actual heat input and the ideal heat source model settings. Existing optimization methods often treat the bevel surface as a continuous, uniform ideal boundary, neglecting the impact of slag residue and the non-uniformity of the heat-affected zone on subsequent arc stability. This results in discrepancies between simulation evaluation results and actual welding conditions, making it difficult to effectively suppress localized heat accumulation, surface formation differences, and residual deformation. Furthermore, current cutting posture initialization methods typically perform random sampling of each trajectory node within a uniform angle range. For high curvature corner nodes, this method is prone to generating candidate postures that are close to the grazing angle or whose rate of change of adjacent node angles exceeds the limit. This results in a large amount of candidate data being truncated and corrected, reducing the number and diversity of effective candidate solutions in key areas, and thus affecting the convergence efficiency and result quality of process parameter optimization.

[0004] Therefore, an optimized multi-objective process parameter optimization system for welding deformation of refined steel is desired. Summary of the Invention

[0005] To address the aforementioned technical problems, this application is proposed. Embodiments of this application provide a multi-objective process parameter optimization system for weld deformation in refined steel, comprising: The joint cutting and welding population construction module is used to obtain the joint cutting and welding optimized population matrix by jointly encoding and sampling the variable angle cutting posture parameters and multi-pass welding process parameters based on the initial cutting and welding process design data. The interface disturbance impedance field mapping module is used to dynamically map the bevel interface disturbance impedance field oriented towards the chamfer gradient on the joint optimization population matrix of cutting and welding to obtain the bevel interface disturbance impedance field and a subset of welding control parameters. The arc heat input reconstruction module is used to reconstruct the actual arc heat input of a subset of welding control parameters based on the interface perturbation impedance field to obtain the spatiotemporal boundary of the interface-constrained heat input. The multi-objective fitness evaluation module is used to import the interface constraint state thermal input spatiotemporal boundary as a dynamic thermal load into the thermo-elastic-plastic finite element mesh corresponding to the three-dimensional design model of refined steel for transient simulation analysis, and combine the perturbation impedance field of the bevel interface to calculate the surface forming polarization index to obtain the multi-objective fitness evaluation vector. The co-evolutionary iterative output module is used to perform multi-objective co-evolutionary iteration on the cut-weld joint optimization population matrix based on the multi-objective fitness evaluation vector to output the Pareto optimal cut-weld joint instruction set.

[0006] Compared with existing technologies, the multi-objective process parameter optimization system for welding deformation of refined steel provided in this application incorporates variable angle cutting posture and multi-pass welding process parameters into the same optimization space. It adaptively limits the sampling range of the cutting angle based on the local curvature of the bevel trajectory to reduce extreme postures and invalid candidate solutions in high curvature regions. It characterizes the difference in slag residue and heat-affected zone depth caused by the change in cutting angle as the bevel interface disturbance state, and corrects the arc energy corresponding to the welding control parameters accordingly to obtain the heat input boundary that conforms to the actual interface conditions. It evaluates the differences in macroscopic residual deformation and microscopic surface forming of refined steel through thermo-elastic-plastic simulation, performs multi-objective collaborative optimization, and outputs joint cutting and welding commands, thereby reducing the heat input evaluation deviation caused by the ideal bevel assumption and taking into account welding deformation control, surface forming quality, and optimization efficiency. Attached Figure Description

[0007] The above and other objects, features, and advantages of this application will become more apparent from the more detailed description of the embodiments of this application in conjunction with the accompanying drawings. The drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the embodiments of this application to explain this application and do not constitute a limitation thereof. In the drawings, the same reference numerals generally represent the same components or steps.

[0008] Figure 1 This is a system block diagram of a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application; Figure 2This is a schematic diagram of the data flow of a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application; Figure 3 This is a block diagram of the cutting and welding joint population construction module in a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application; Figure 4 This is a block diagram of a cutting posture constraint sampling unit in a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application; Figure 5 This is a block diagram of the multi-objective fitness evaluation module in a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application. Detailed Implementation

[0009] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0010] To address the issues of existing optimization methods that treat the bevel as a uniform ideal interface, neglecting the impact of slag residue and heat-affected zone depth differences caused by varying angle cutting on arc stability, and the tendency for sampling within a uniform angle range to generate extreme postures and numerous invalid candidate solutions at high curvature nodes, this application proposes a multi-objective process parameter optimization system for the welding deformation of refined steel. This system first analyzes the local curvature of the refined steel bevel trajectory nodes and adjusts the feasible range of the entry angle for each node accordingly. Under the condition of satisfying the machine tool angular velocity limit, it samples the cutting posture and simultaneously integrates it with the welding current, voltage, and feed rate. The process involves joint encoding; then calculating the chamfer gradient distributed along the trajectory, converting it into a bevel interface disturbance state reflecting the residual slag thickness and heat-affected zone depth, and using this disturbance state to attenuate and project the ideal arc energy into a dynamic heat input boundary adapted to the actual bevel conditions; finally, obtaining the residual deformation of the component through thermo-elastic-plastic finite element simulation, establishing multi-objective evaluation results by combining surface forming differences, iteratively updating the joint cutting and welding parameters, and generating the optimal execution command, thereby improving the effectiveness of candidate solutions in key corner areas, reducing heat input evaluation bias, and balancing welding deformation control and surface forming quality.

[0011] Figure 1 This is a system block diagram of a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application. Figure 2 This is a schematic diagram of the data flow of a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application. Figure 1 and Figure 2As shown, the multi-objective process parameter optimization system 100 for welding deformation of refined steel according to an embodiment of this application includes: a cutting-welding joint population construction module 110, used to perform joint real-number encoding sampling of variable angle cutting posture parameters and multi-pass welding process parameters based on initial cutting-welding process design data to obtain a cutting-welding joint optimization population matrix; an interface disturbance impedance field mapping module 120, used to perform dynamic mapping of the bevel interface disturbance impedance field oriented towards the cutting angle gradient on the cutting-welding joint optimization population matrix to obtain the bevel interface disturbance impedance field and a subset of welding control parameters; and an arc heat input reconstruction module 130, used to perform arc heat input reconstruction based on the bevel interface disturbance impedance field. A subset of control parameters is used to reconstruct the actual arc heat input based on the interface perturbation field constraint to obtain the spatiotemporal boundary of the interface-constrained heat input. A multi-objective fitness evaluation module 140 is used to import the spatiotemporal boundary of the interface-constrained heat input as a dynamic thermal load into the thermo-elastic-plastic finite element mesh corresponding to the three-dimensional design model of refined steel for transient simulation analysis, and to calculate the surface forming polarization index by combining the bevel interface perturbation impedance field to obtain the multi-objective fitness evaluation vector. A co-evolutionary iterative output module 150 is used to perform multi-objective co-evolutionary iteration on the cutting-welding joint optimization population matrix based on the multi-objective fitness evaluation vector to output the Pareto optimal cutting-welding joint instruction set.

[0012] In the aforementioned multi-objective process parameter optimization system 100 for welding deformation of refined steel, the cutting-welding joint population construction module 110 is used to perform joint real-number encoding sampling of variable-angle cutting posture parameters and multi-pass welding process parameters based on the initial cutting-welding process design data to obtain a cutting-welding joint optimization population matrix. It is worth noting that the initial cutting-welding process design data here includes a three-dimensional design model of the refined steel, kinematic constraint parameters of the laser cutting machine tool, and the allowable range of basic welding process parameters. It should be understood that the generation of welding deformation in refined steel depends not only on the welding process parameters themselves but also on the bevel interface state formed by variable-angle laser cutting in the preceding process. The cutting posture parameters directly determine the slag residue and heat-affected zone distribution along the bevel line. These interface characteristics, in turn, change the actual transfer state of subsequent arc energy. Therefore, there is a cross-process physical coupling relationship between the cutting posture and welding parameters. Optimizing them separately in their respective independent spaces would fail to capture this coupling effect. Therefore, in the technical solution of this application, the variable-angle cutting posture parameters and multi-pass welding process parameters are jointly encoded and sampled based on the initial cutting and welding process design data. This incorporates the decision variables of the cutting and welding processes into a unified search space, enabling subsequent multi-objective optimization algorithms to synchronously control the combination relationship between the cutting posture and welding parameters. This allows the parameter correlation structure between the cutting and welding processes to be established during the population initialization stage, providing a complete encoding carrier for subsequent arc heat input reconstruction based on interface perturbation field constraints and multi-objective fitness joint evaluation, avoiding the loss of global solution space due to independent optimization of process parameters.

[0013] Figure 3 This is a block diagram of the cutting and welding joint population construction module in a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application. Figure 3 As shown, the cutting-welding joint population construction module 110 includes: a bevel contour geometry analysis unit 111, used to perform geometric feature analysis on the bevel intersection contour in the three-dimensional design model of refined steel to obtain the ideal bevel spatial trajectory node set; a cutting posture constraint sampling unit 112, used to perform Monte Carlo random sampling and angular velocity threshold truncation filtering on the ideal bevel spatial trajectory node set based on the kinematic constraint parameters of the laser cutting machine tool to obtain the variable angle cutting posture parameter set; and a joint real number encoding splicing unit 113, used to uniformly distribute sampling of current, voltage and feed speed within the allowable range of basic welding process parameters, and to perform joint real number encoding concatenation splicing of the sampling results with the variable angle cutting posture parameter set to obtain the cutting-welding joint optimized population matrix.

[0014] Accordingly, the bevel contour geometric analysis unit 111 is used to perform geometric feature analysis on the bevel intersection contour in the three-dimensional design model of refined steel to obtain the ideal bevel spatial trajectory node set. It should be understood that since subsequent cutting posture constraint sampling and bevel interface disturbance impedance field mapping both use discrete spatial nodes as computational primitives, and the bevel information in the three-dimensional design model of refined steel is stored in the form of continuous parameterized surface boundaries, it cannot be directly used as the spatial positioning carrier of individual genes in a genetic algorithm. It needs to be transformed into a set of discrete three-dimensional coordinates arranged in an ordered manner along the cutting direction. Therefore, in the technical solution of this application, by performing geometric feature analysis on the bevel intersection contour in the three-dimensional design model of refined steel to obtain the ideal bevel spatial trajectory node set, the implicit bevel geometric path in the model is explicitly expressed as an ordered discrete node sequence, providing a unified geometric reference benchmark for subsequent cutting angle sampling, cutting angle gradient calculation, and impedance field spatial mounting at each node. This ensures that the entire calculation process from cutting posture sampling to the generation of the thermal input spatiotemporal boundary is carried out on the same set of spatial node coordinates, guaranteeing the spatial alignment and index consistency of data across modules.

[0015] Specifically, in a specific example of this application, the refined steel 3D design model stored in the STEP standard neutral file format is first read, and the boundary representation information of each face, the face normal direction and the edge topological connection relationship contained in the file are parsed. All face entities in the model are traversed, and the bevel face marked as the bevel attribute and the adjacent parent material plate face are identified. The common intersection edge shared between the bevel face and the parent material plate face is extracted as the bevel intersection edge profile. This intersection edge is recorded in the boundary representation structure in the form of a parametric space curve, and its parameter domain is the normalized arc length interval from the start end to the end end.

[0016] Next, parametric curve reconstruction is performed on the extracted bevel intersection profile, and the total arc length of the curve is calculated by integration along the parameter domain. Taking a precision steel plate used for steel structure node connections as an example, its bevel intersection profile has a total arc length of 2400 mm, including several straight segments and circular transition segments. Based on the spatial resolution requirements of the subsequent chamfer gradient differential operation, the discrete step size is set to 5 mm. Then, sampling is performed along the bevel intersection profile with equal arc length increments according to the set discrete step size. Starting from the beginning of the curve, the three-dimensional spatial coordinate point corresponding to the current arc length parameter is calculated for each increment, and the X, Y, and Z coordinate values ​​of all sampling points are obtained sequentially. Taking a total arc length of 2400 mm and a discrete step size of 5 mm as an example, a total of 480 spatial discrete points are sampled, and each discrete point is stored as a three-dimensional coordinate triplet in the workpiece coordinate system.

[0017] Furthermore, all sampled spatial discrete points are ordered and numbered according to the topological sequence of the laser cutting direction to generate an ideal bevel spatial trajectory node set. This set is structured as an ordered array, where the array index corresponds to the topological sequence number of a node on the cutting path, and the array element represents the three-dimensional spatial coordinates of that node. The starting index corresponds to the starting position of the cutting arc, and the ending index corresponds to the ending position. The spatial distance between adjacent indices is equal to the set discrete step size. All nodes in the ideal bevel spatial trajectory node set collectively describe the reference spatial trajectory that the laser cutting head needs to traverse under conditions of no attitude deflection.

[0018] Accordingly, the cutting posture constraint sampling unit 112 is used to perform Monte Carlo random sampling and angular velocity threshold truncation filtering on the set of ideal bevel spatial trajectory nodes based on the kinematic constraint parameters of the laser cutting machine tool to obtain a set of variable angle cutting posture parameters. It should be understood that since the set of ideal bevel spatial trajectory nodes only describes the spatial position sequence that the laser cutting head should traverse, it does not yet include the attitude deflection information of the cutting head relative to the workpiece surface at each node. Furthermore, the subsequent construction of the bevel interface disturbance impedance field depends on the gradient change of the normal entry angle at each node to calculate the slag residue thickness and the depth of the heat-affected zone. Therefore, it is necessary to generate feasible entry angle values ​​for each node while satisfying the physical motion capabilities of the machine tool. Therefore, in the technical solution of this application, Monte Carlo random sampling and angular velocity threshold truncation filtering are performed on the set of ideal bevel spatial trajectory nodes based on the kinematic constraint parameters of the laser cutting machine tool to obtain a set of variable angle cutting posture parameters. This allows for the random generation of a set of node-by-node-assigned normal entry angle sequences for each individual in the population within the entire reachable entry angle range of the machine tool, and the elimination of angle mutations exceeding the dynamic response capability of the drive axis. In this way, it can be ensured that each set of cutting angle sequences in the variable angle cutting posture parameter set not only covers sufficient search space diversity, but also does not violate the kinematic physical constraints of the machine tool hardware, thus providing a legitimate initial cutting posture candidate solution for subsequent genetic evolution iteration.

[0019] Specifically, in a particular example of this application, the minimum and maximum allowable entry angles of the cutting head are first extracted from the kinematic constraint parameters of the laser cutting machine tool as the upper and lower bounds of the global entry angle range. Simultaneously, the maximum angular velocity limit of the drive axis is extracted. Taking a five-axis laser cutting machine tool as an example, the minimum entry angle is 15 degrees, the maximum entry angle is 75 degrees, and the maximum angular velocity limit of the drive axis is 30 degrees per second. The minimum and maximum entry angles define the allowable deflection range of the laser beam normal relative to the workpiece surface normal, and the maximum angular velocity limit of the drive axis defines the maximum allowable rate of angular change of the cutting head rotation axis between adjacent nodes.

[0020] Next, for each node in the ideal slope spatial trajectory node set, a Monte Carlo random number generator is used to perform uniform random sampling without discrimination within the entire range defined by the minimum and maximum entry angles. Specifically, for each individual in the population, a uniformly distributed random number is independently generated at each node location. This random number is linearly mapped to an interval of 15 to 75 degrees, serving as the initial normal entry angle sampling value for that individual at that node. Taking a population size of 200 individuals and an ideal slope spatial trajectory node set containing 480 nodes as an example, this process generates a total of 200 x 480, or 96,000 independent initial entry angle values. Each value falls within the entire entry angle range, and the sampling between nodes is independent of each other.

[0021] Then, after initial sampling of all nodes, adjacent nodes are traversed pairwise according to topological order. A hard threshold truncation filter is applied to the rate of angle change between adjacent nodes using the maximum angular velocity limit. Specifically, the motion time interval is calculated by dividing the spatial arc distance between two adjacent nodes by the machine tool's set feed rate. The actual rate of angle change is obtained by dividing the absolute value of the difference between the entry angle of the successor node and the entry angle of the predecessor node by the motion time interval. The actual rate of angle change is compared with the maximum angular velocity limit of the drive shaft. If the actual rate of angle change does not exceed the maximum angular velocity limit of the drive shaft, the entry angle of the successor node is retained without modification. If the actual rate of angle change exceeds the maximum angular velocity limit of the drive shaft, the entry angle of the successor node is forcibly corrected to the entry angle of the predecessor node plus or minus the maximum allowable angle difference corresponding to the maximum angular velocity limit of the drive shaft multiplied by the motion time interval. The correction direction is consistent with the original angle change direction. Taking a distance of 5 mm from the ground and a feed rate of 50 mm per second as an example, with a time interval of 0.1 seconds between adjacent nodes, the maximum allowable angle difference is 30 degrees per second multiplied by 0.1 seconds, which is 3 degrees. Any angle jump between adjacent nodes exceeding 3 degrees will be cut off to 3 degrees.

[0022] Furthermore, after performing the aforementioned forward traversal truncation from the first node to the last node on each individual in the population, each individual obtains a set of compliant normal angle entry sequences with a length equal to the number of nodes. These compliant sequences from all individuals are aggregated to form a variable-angle cutting attitude parameter set. Each sequence in this set satisfies two constraints: first, the entry angle of each node is between the minimum and maximum entry angle; second, the rate of change of angle between adjacent nodes does not exceed the maximum angular velocity limit of the drive shaft.

[0023] Specifically, in the multi-objective process parameter optimization system for welding deformation of refined steel, the first embodiment of the aforementioned cutting posture constraint sampling unit 112 serves to provide high-quality candidate solutions for cutting postures for the genetic optimization algorithm during the population initialization phase. The first embodiment works as follows: extracting the minimum and maximum allowable entry angle boundaries from the machine tool kinematic constraint parameters; then, for each node in the ideal bevel space trajectory node set, using a Monte Carlo random number generator to perform uniform random sampling within the aforementioned global entry angle range; and finally, using a hard threshold to truncate the rate of change of angle between adjacent nodes by limiting the maximum angular velocity.

[0024] However, the actual profile of a refined steel bevel typically consists of a large number of straight sections and a few high-curvature corner transition sections, with fundamentally different physical tolerances for laser cutting head deflection in different regions. In high-curvature corner regions, the angle between the laser beam incident surface and the workpiece surface normal changes drastically. If the cutting angle is still randomly selected across the entire range, it is easy to generate extreme incident postures close to grazing angles, directly causing a sharp drop in the energy absorption rate of the laser on the refined steel surface, which in turn leads to severe slag accumulation and abrupt changes in the depth of the heat-affected zone. This is the root cause of the subsequent violent fluctuations in the welding arc due to microscopic disturbances. Furthermore, in terms of algorithm efficiency, uniform sampling across the entire range at high-curvature nodes generates a large number of invalid individuals that are forcibly truncated due to excessive angular velocity. The initial effective diversity of the population in these critical corner regions is essentially severely degraded, making it difficult for subsequent genetic iterations to search for the truly optimal posture solution in the corner region. The overall optimization convergence efficiency and the quality of the final solution of the system are significantly constrained.

[0025] To address the aforementioned technical deficiencies, a second embodiment is proposed. Specifically, in another specific example of this application, Figure 4 This is a block diagram of a cutting posture constraint sampling unit in a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application. Figure 4 As shown, the cutting posture constraint sampling unit 112 includes: a node discrete curvature estimation subunit 1121, used to perform discrete curvature estimation on the spatial triangle formed by each internal node and its adjacent nodes in the ideal bevel spatial trajectory node set to obtain a node local curvature feature sequence; an adaptive cutting angle domain construction subunit 1122, used to construct a node-level adaptive cutting angle feasible domain based on the node local curvature feature sequence; and a curvature-aware sampling truncation verification subunit 1123, used to perform Monte Carlo random sampling within the node-level adaptive cutting angle feasible domain and use the maximum angular velocity limit to perform threshold truncation verification on the angle change rate between adjacent nodes to obtain a variable angle cutting posture parameter set.

[0026] More specifically, the node discrete curvature estimation subunit 1121 is used to perform discrete curvature estimation on the spatial triangle formed by each internal node and its adjacent nodes in the ideal bevel spatial trajectory node set to obtain a node local curvature feature sequence. It should be understood that since the profile of the refined steel bevel is not straight everywhere in space, the difference in the degree of bending at different nodes directly reflects the tightness of the physical constraints faced by the laser cutting head when performing attitude adjustments at that location. The aforementioned first embodiment uses a uniform global cutting angle range for indiscriminate sampling of all nodes, failing to distinguish the essential difference in physical tolerance windows between straight sections and corner transition areas. Therefore, it is necessary to first quantitatively characterize the local geometric bending characteristics of each node in the ideal bevel spatial trajectory node set as a driving signal for subsequent adaptive narrowing of the sampling domain. Therefore, in the technical solution of this application, the geometric curvature information originally implicit in the discrete coordinate sequence is explicitly extracted into node-by-node quantitative scalar data by performing discrete curvature estimation on the spatial triangle formed by each internal node and its adjacent nodes in the ideal bevel spatial trajectory node set. This provides a physical driving signal for the subsequent construction of the node-level adaptive cutting angle feasible region. In this way, the subsequent sampling domain adjustment can have the ability to actively perceive the local morphology of the bevel contour, automatically identify key nodes with limited cutting head attitude deflection in high curvature corner areas, and maintain a loose sampling exploration range in low curvature straight sections.

[0027] In a specific example of this application, the range of nodes for which discrete curvature estimation needs to be performed is first determined. The first and last nodes in the ideal bevel spatial trajectory node set, as boundary endpoints, do not have adjacent nodes on both sides; therefore, curvature calculation is performed only on internal nodes indexed from the 2nd to the 479th. For each internal node, the node itself, its predecessor node, and its successor node in the trajectory topological order are taken, and the three-dimensional coordinates of the three nodes determine a triangle in space.

[0028] Next, the reciprocal of the radius of the circumcircle of the spatial triangle is calculated using the circumcircle method of adjacent three points, and this value is used as the discrete local spatial curvature value at the current node. The formula for calculating the node local curvature feature sequence is as follows: in, This represents the discrete local space curvature value calculated at the i-th trajectory node; This represents the spatial vector pointing from the (i-1)th node to the ith node; This represents the spatial vector pointing from the i-th node to the (i+1)-th node; This represents the spatial vector pointing from the (i-1)th node to the (i+1)th node; This is the cross product operation for vectors in three-dimensional space; the absolute value sign in the numerator represents the Euclidean magnitude of the cross product vector, and the absolute value sign in the denominator represents the Euclidean length of each edge vector. The numerator of this formula... The calculation calculates the magnitude of the cross product between the spatial vector from the predecessor node to the current node and the spatial vector from the current node to the successor node. This magnitude reflects the degree of deflection between two adjacent edge vectors. When the bevel profile bends more sharply at the node, the directional difference between the two edge vectors is greater, and the magnitude of the cross product is larger. The denominator is the product of the Euclidean lengths of the three edge vectors, which serves as a geometric normalization, eliminating the influence of node spacing on the curvature value and making the curvature values ​​comparable under different discrete step length conditions. The coefficient 2 originates from the geometric relationship between the circumcircle radius and the triangle area, ensuring that the calculation result is strictly equal to the reciprocal of the circumcircle radius.

[0029] Next, we analyze the extreme cases of the above formula. When three adjacent nodes tend to be collinear, the cross product modulus approaches zero, the numerator approaches zero, and the curvature value approaches zero. This corresponds to the straight section in the bevel profile. At this type of node, the laser cutting head does not need to make a large attitude deflection, and its physical tolerance window for the entry angle deviating from the normal of the workpiece surface is relatively wide. When three adjacent nodes form an acute triangle, the directional deflection amplitude between the two side vectors increases, the cross product modulus increases significantly, and the increase in the numerator value leads to an increase in the curvature value. This corresponds to the corner transition area in the bevel profile. The laser cutting head needs to complete a larger attitude deflection within a shorter spatial displacement, and its physical tolerance window for the entry angle deviating from the normal is narrower. Taking a certain arc transition section in the bevel of a precision steel plate as an example, if the circumscribed circle radius at this point is 50 mm, the corresponding discrete curvature value is 0.02 per millimeter, indicating that the degree of bending of the bevel profile at this node is much higher than the near-zero curvature value of the straight section.

[0030] Furthermore, the discrete local spatial curvature values ​​of all internal nodes are arranged in an ordered manner according to the trajectory topology. The curvature values ​​of their nearest-neighbor internal nodes are then assigned to the first and last boundary endpoints as supplementary values, generating a node local curvature feature sequence. The length of this sequence is consistent with the number of nodes in the ideal bevel spatial trajectory node set, and each element in the sequence corresponds to the degree of curvature of the bevel profile at the index node. Through this step, the geometric curvature information originally implicit in the discrete coordinate sequence is explicitly extracted as quantitative sequence data that can directly drive subsequent sampling domain adjustment, providing a physical driving signal for establishing a curvature-aware sampling strategy. The node local curvature feature sequence serves as the input for the next step of constructing the node-level adaptive cutting angle feasible region, controlling the narrowing of the cutting angle sampling range at each node.

[0031] More specifically, the adaptive cutting angle domain construction subunit 1122 is used to construct a node-level adaptive cutting angle feasible domain based on the node local curvature feature sequence. It should be understood that since the node local curvature feature sequence has explicitly quantified the degree of bending at each node of the bevel profile, the curvature value itself cannot be directly used to constrain the angle range of Monte Carlo sampling. It is necessary to transform geometrically perceived information into a dynamic adjustment capability for the feasible sampling interval of the cutting angle, in order to achieve an adaptive sampling strategy that actively narrows high-curvature regions and maintains a loose low-curvature region. Therefore, in the technical solution of this application, a node-level adaptive cutting angle feasible domain is further constructed based on the node local curvature feature sequence. This generates upper and lower bounds for the cutting angle sampling of each trajectory node that match its local curvature, thus constraining the sampling range of high-curvature corner nodes within a safe window close to the normal direction of the workpiece surface, while maintaining the sampling range of low-curvature straight nodes close to the full domain width. In this way, we can avoid the sharp drop in laser energy absorption rate and the deterioration of slag due to the grazing angle in the corner area from a physical perspective, while retaining the degree of freedom of attitude exploration in the straight section, and increasing the proportion and diversity of the initial effective feasible solutions in the population.

[0032] Specifically, in the embodiments of this application, the adaptive inclination angle domain construction subunit is used to: perform a shrinkage factor transformation on the node local curvature feature sequence based on the Sigmoid-type saturation mapping function to obtain a node-by-node sampling domain shrinkage factor; and based on the node-by-node sampling domain shrinkage factor, perform proportional compression on the full domain half-width with the median of the inclination angle full domain range as the center of symmetry to obtain a node-level adaptive inclination angle feasible domain.

[0033] In a specific example of this application, the global limits of the approach angle, namely the minimum and maximum approach angles, as well as the maximum angular velocity limit, are first extracted from the kinematic constraint parameters of the laser cutting machine tool. Taking a five-axis laser cutting machine tool as an example, the minimum approach angle is 15 degrees and the maximum approach angle is 75 degrees. The median value of the global range of approach angles is calculated as the center of symmetry for subsequent proportional compression.

[0034] Next, a contraction factor transformation is applied to the curvature values ​​of each node in the local curvature feature sequence using a monotonically decreasing saturation mapping function, as shown below: in, This represents the sampling domain shrinkage factor obtained after mapping the i-th node, and its value ranges between 0 and 1; The steepness control parameter of the sigmoid function determines the sensitivity of the curvature change to the narrowing response. The larger the value, the steeper the drop in the contraction factor near the reference threshold; This is the local spatial curvature value of the node output in the previous step; This is a preset reference curvature threshold used to calibrate the boundary sensitivity benchmark between the straight section and the corner transition section in the bevel of refined steel. In this formula, the Sigmoid function uses the reference curvature threshold... As a boundary benchmark, continuous curvature values ​​in the nodal local curvature feature sequence are mapped to contraction factors between 0 and 1. The numerator is always 1, and the exponential term in the denominator... This reflects the nonlinear response amplified by the steepness parameter, indicating the deviation of the current node curvature from the reference threshold. When the node curvature... Much smaller than the reference curvature threshold When the difference within the parentheses is negative, the exponent term tends towards negative infinity, the denominator approaches 1, and the contraction factor... Approaching 1, the feasible region of the incision angle at that node maintains a near-global width, and the laser cutter has the maximum degree of freedom for attitude exploration in the flat region. When the node curvature... Significantly exceeds the reference curvature threshold When the difference within the parentheses is positive and relatively large, the exponent term tends towards positive infinity, the denominator tends towards infinity, and the contraction factor... Approaching zero, the feasible region at this node is significantly compressed to a narrow central band. The laser cutting head is constrained within a safe window close to the normal direction of the workpiece surface, physically avoiding the sharp drop in energy absorption rate and slag buildup caused by the grazing angle in the corner area. Taking a refined steel bevel with a reference curvature threshold of 0.01 mm and a steepness control parameter of 500 as an example, the curvature value of the nodes in the straight section is close to zero, and the corresponding shrinkage factor is close to 1. However, when the curvature value of the nodes in the corner transition area is 0.02 mm, the corresponding shrinkage factor is about 0.007, and the feasible region width is less than one percent of the entire region.

[0035] Then, using the obtained node-by-node sampling domain shrinkage factor, a proportional compression with the median as the center of symmetry is performed on the entire range of the cutting angle to generate a node-level adaptive cutting angle feasible region, as follows: in, This represents the normal angle of inclination generated by the final sampling of the kth individual in the population at the i-th node; The median of the angle of entry over the entire region, i.e. ; and These are the maximum and minimum limit values ​​of the global angle of entry extracted from the kinematic constraint parameters of the machine tool, respectively. This is the sampling domain shrinkage factor for the node calculated above. In this formula, the median of the global tangent angle is used. As the geometric center of symmetrical compression, the contraction factor is used. For the full half-width Perform proportional scaling to generate the actual feasible sampling radius for the current node. (When the shrinkage factor...) When the value equals 1, the upper and lower bounds of the feasible region degenerate into: and The sampling range is equivalent to the entire range, and the laser cutting head maintains the same degree of freedom of exploration at this flat node as in the first embodiment. When the shrinkage factor... As the value approaches 0, both the upper and lower bounds of the feasible region converge to the median. The sampling range degenerates into an extremely narrow window centered on the normal direction, and the laser cutter head is forcibly constrained to a safe posture near this high-curvature corner node. Taking a minimum entry angle of 15 degrees and a maximum entry angle of 75 degrees as an example, the median is 45 degrees, and the full half-width is 30 degrees. If the shrinkage factor of a corner node is 0.1, then the feasible region of that node is 42 degrees to 48 degrees, which is significantly narrowed to only 6 degrees compared to the full width of 60 degrees, effectively avoiding the extreme incident posture of close to the grazing angle at this point.

[0036] After calculating the shrinkage factor and constructing the feasible region for each node in the ideal bevel spatial trajectory node set, each node obtains a pair of upper and lower bounds for the entry angle that are adapted to its local curvature. The upper and lower bounds of the feasible region of all nodes are arranged in the order of the trajectory topology to form a complete node-level adaptive entry angle feasible region. This feasible region will serve as the constraint boundary for subsequent Monte Carlo random sampling, replacing the uniform global sampling strategy used for all nodes in the first embodiment. This ensures that when random sampling is performed in this feasible region, the candidate entry angle values ​​generated at high curvature nodes are naturally concentrated within the safety window, reducing the number of invalid individuals truncated due to angular velocity exceeding the limit from the source and improving the initial effective feasible solution density in the key corner region.

[0037] More specifically, the curvature-aware sampling truncation verification subunit 1123 is used to perform Monte Carlo random sampling within the node-level adaptive entry angle feasible region and to perform threshold truncation verification on the rate of angle change between adjacent nodes using the maximum angular velocity limit, so as to obtain a set of variable angle cutting posture parameters. It should be understood that since the node-level adaptive entry angle feasible region only defines the static upper and lower bounds of the entry angle at each node, and has not yet actually generated a specific numerical sequence, and the angle jump between adjacent nodes is still constrained by the dynamic response capability of the machine tool drive axis, random numerical filling and dynamic compliance verification need to be completed within this feasible region in order to generate a complete cutting posture candidate solution that can be used for joint encoding. Therefore, in the technical solution of this application, Monte Carlo random sampling is performed within the node-level adaptive entry angle feasible region, and the rate of angle change between adjacent nodes is threshold truncation verification using the maximum angular velocity limit to obtain a set of variable angle cutting posture parameters. This generates a set of node-by-node-allocated entry angle values ​​for each individual in the population under the constraint of the curvature-aware sampling region, and ensures that the angle transition rate between adjacent nodes does not exceed the physical execution capability of the machine tool. In this way, through the dual constraints of curvature-aware sampling and dynamic verification, each sequence in the variable angle cutting posture parameter set can meet both the safe posture window allowed by the local curvature of each node and the dynamic response limit of the machine tool drive axis, providing legal and high-quality cutting posture candidate genes for subsequent joint real number encoding splicing.

[0038] Specifically, in a concrete example of this application, for each individual in the population, Monte Carlo random sampling is first performed within the node-level adaptive cutting angle feasible region after curvature adaptive compression to generate the initial cutting angle value at each node. Specifically, for each node in the ideal bevel spatial trajectory node set, the upper and lower bounds of the feasible region corresponding to that node are read, and a uniformly distributed random number is generated using a Monte Carlo random number generator. This random number is linearly mapped to the upper and lower bounds of the node's feasible region, serving as the initial normal cutting angle sampling value for that individual at that node. Since the feasible region of high-curvature corner nodes has been significantly compressed to a narrow central band by the contraction factor, the initial cutting angle values ​​generated there naturally concentrate within a safe range close to the normal direction of the workpiece surface. Meanwhile, the feasible region of straight section nodes maintains a width close to the entire region, and the cutting angle values ​​there possess sufficient random exploration diversity.

[0039] Next, after initial sampling of all nodes, a threshold truncation check is performed on the rate of angle change between adjacent nodes using the maximum angular velocity limit. Specifically, following the trajectory topology, adjacent nodes are traversed pair by pair starting from the first node. The motion time interval is calculated by dividing the spatial arc distance between two adjacent nodes by the machine tool's set feed speed. The actual rate of angle change is obtained by dividing the absolute value of the difference between the entry angle of the successor node and the entry angle of the predecessor node by the motion time interval. If the angle difference between adjacent nodes divided by the motion time interval exceeds the maximum angular velocity limit, a forced truncation correction is applied to the successor node. The entry angle of the successor node is corrected to the entry angle of the predecessor node plus or minus the maximum allowable angle difference corresponding to the maximum angular velocity limit multiplied by the motion time interval. The correction direction is consistent with the original angle change direction. Taking a distance of 5 mm, a feed speed of 50 mm / s as an example, a motion time interval of 0.1 seconds, and a maximum angular velocity limit of 30 degrees / s, the maximum allowable angle difference between adjacent nodes is 3 degrees. Any angle jump exceeding 3 degrees is truncated to 3 degrees. Since the sampling range at high curvature nodes has been actively compressed to a physically feasible range, the angle difference between adjacent nodes at that location is small, and the probability of it being corrected due to truncation is greatly reduced.

[0040] Then, after performing the aforementioned forward traversal truncation on each individual in the population, each individual obtains a set of compliant normal angle sequences with a length equal to the number of nodes. These compliant sequences from all individuals are aggregated to form a variable-angle cutting attitude parameter set. Each sequence in this set simultaneously satisfies two constraints: first, a curvature-aware spatial constraint, meaning that the angle of each node lies between the upper and lower bounds of the adaptive feasible region corresponding to that node; and second, a dynamic time constraint, meaning that the rate of change of angle between adjacent nodes does not exceed the maximum angular velocity limit of the drive shaft.

[0041] After the dual constraints of curvature-aware sampling and dynamic verification, the second embodiment endows the genetic optimization algorithm with the ability to actively perceive the geometry of the bevel of the refined steel during the population initialization stage. In the high-curvature corner region, the feasible sampling domain of the cutting angle is automatically constrained within a safe window close to the normal of the workpiece surface. This physically avoids the sudden drop in laser energy absorption rate, the deterioration of slag on the bevel surface, and the drastic change in the depth of the heat-affected zone caused by grazing angle incidence. These are the microscopic root causes of subsequent welding arc fluctuations and local deformation of the refined steel. In terms of algorithm efficiency, since the sampling range at high-curvature nodes has been actively compressed to the physically feasible range, the proportion of invalid individuals in the population that are forcibly truncated due to excessive angular velocity is significantly reduced. The initial effective feasible solution density in the key corner region is significantly improved, and the search efficiency and convergence speed of the genetic iteration are substantially enhanced. The final Pareto optimal cut-weld joint instruction set is significantly improved in the welding deformation control accuracy in the corner transition zone. The set of variable angle cutting posture parameters, as the front-end gene input of the joint real number encoding splicing unit, will be assembled together with the welding control parameter sequence into a complete chromosome in the cutting-welding joint optimization population matrix, for subsequent bevel interface disturbance impedance field mapping and multi-objective cooperative evolution iteration.

[0042] Accordingly, the joint real-number encoding splicing unit 113 is used to uniformly sample the current, voltage, and feed rate within the allowable range of the basic welding process parameters, and to perform joint real-number encoding concatenation splicing of the sampling results with the variable-angle cutting posture parameter set to obtain the joint optimization population matrix for cutting and welding. It should be understood that since the variable-angle cutting posture parameter set only covers the pose decision variables of the cutting process, it does not yet include the current, voltage, and feed rate information that determine the heat input intensity in the welding process. The subsequent multi-objective fitness evaluation needs to calculate the perturbation impedance field and thermo-elastic-plastic deformation results of the groove interface based on both the cutting posture and welding parameters. The two types of parameters must be carried by a unified chromosome structure in order to achieve synchronous crossover mutation and collaborative optimization in the process of genetic evolution. Therefore, in the technical solution of this application, within the allowable range of basic welding process parameters, current, voltage, and feed speed are uniformly sampled, and the sampling results are concatenated and spliced ​​with the set of variable angle cutting posture parameters using joint real-number encoding to obtain a cutting-welding joint optimization population matrix. This encapsulates all decision variables of the cutting and welding processes into a complete chromosome for each individual in the population, enabling subsequent crossover and mutation operations of evolutionary operators to act on both types of parameters simultaneously within the same encoding space. This ensures that each row vector in the cutting-welding joint optimization population matrix carries complete process information from cutting posture to welding heat, providing a structurally unified computational carrier for subsequent dynamic mapping of the bevel interface disturbance impedance field and multi-objective collaborative evolution iteration.

[0043] Specifically, in a specific example of this application, the upper and lower limits of welding current, welding voltage, and welding feed rate are first read from the allowable range of basic welding process parameters. Taking gas shielded welding of refined steel as an example, the allowable range of welding current is 120 amperes to 280 amperes, the allowable range of welding voltage is 18 volts to 32 volts, and the allowable range of welding feed rate is 200 mm / min to 600 mm / min. For each individual in the population, a set of welding current values, a set of welding voltage values, and a set of welding feed rate values ​​are generated for that individual using uniformly distributed random numbers within the above three parameter ranges. In the case of multi-pass welding, the bevel of refined steel needs to be filled in three passes. Therefore, each weld pass is independently sampled with a set of ternary parameters including current, voltage, and feed rate. The length of the welding control parameter sequence for that individual is equal to the number of weld passes multiplied by the dimension of a single pass parameter, that is, 3 passes multiplied by 3 parameters, totaling 9 consecutive real values.

[0044] Next, the cutting posture parameter segment corresponding to the individual in the variable angle cutting posture parameter set is used as the first gene segment of the chromosome. This segment is a sequence of normal cutting angles with a length equal to the number of nodes in the ideal bevel spatial trajectory node set. Taking 480 nodes as an example, the length of the first gene segment is a 480-dimensional real vector, and each dimension corresponds to the compliant normal cutting angle value at the corresponding node after curvature-aware sampling and dynamic truncation verification. Then, the welding control parameter sequence generated by the above uniformly distributed sampling is used as the second gene segment of the chromosome, and it is concatenated and spliced ​​with the first gene segment along the column dimension using real-number encoding. Specifically, the 480-dimensional cutting angle vector of the first gene segment is concatenated end-to-end with the 9-dimensional welding parameter vector of the second gene segment to form a joint real-number encoded chromosome with a total length of 489 dimensions. The first 480 gene positions of this chromosome carry the spatial posture information of the cutting process, and the last 9 gene positions carry the heat control information of the welding process. The two gene segments are distinguished by position indexes and can be accurately separated by preset truncation points during subsequent chromosome decoding.

[0045] Furthermore, the above welding parameter sampling and cascade splicing operations were repeated for all individuals in the population. The joint chromosomes of 200 individuals were stacked row by row to obtain the cut-weld joint optimization population matrix. The matrix has a dimension of 200 rows by 489 columns. Each row represents a complete cut-weld joint candidate scheme covering cutting posture and welding parameters. The number of rows is equal to the population size, and the number of columns is equal to the sum of the length of the cutting posture gene locus and the length of the welding control gene locus. The first segment of the genes of each individual in the cut-weld joint optimization population matrix has been subject to dual constraints of curvature-aware sampling and angular velocity threshold truncation. The second segment of the genes covers a uniform random distribution within the allowable range of welding process parameters. Together, they constitute the unified input data structure for the subsequent bevel interface perturbation impedance field mapping module and the multi-objective co-evolution iteration module.

[0046] In the aforementioned multi-objective process parameter optimization system 100 for welding deformation of refined steel, the interface perturbation impedance field mapping module 120 is used to dynamically map the bevel interface perturbation impedance field oriented towards the chamfer gradient on the cut-weld joint optimization population matrix to obtain the bevel interface perturbation impedance field and a subset of welding control parameters. It should be understood that since the cut posture gene and welding control gene are encapsulated in the cut-weld joint optimization population matrix in the form of joint real-number encoding, but the numerical sequence in this encoding state has not yet been transformed into physically meaningful bevel interface feature information, and subsequent arc heat input reconstruction and multi-objective fitness evaluation both require correction of the ideal arc energy model based on the actual slag residue state and heat-affected zone depth distribution on the bevel surface, it is necessary to transform the spatial angle change information implicit in the cut posture gene into quantifiable interface physical features. Therefore, in the technical solution of this application, the joint cutting and welding population matrix is ​​further dynamically mapped to the bevel interface perturbation impedance field oriented towards the cutting angle gradient to obtain the bevel interface perturbation impedance field and a subset of welding control parameters. This allows the spatial angle abrupt change of the cutting posture to be quantitatively mapped to the slag residue thickness and non-uniform depth of the heat-affected zone on the bevel surface, and the welding control gene is simultaneously separated for subsequent heat input reconstruction. In this way, the posture dynamics of the preceding cutting process can be transformed into the physical constraints of the arc stability of the subsequent welding process, enabling the multi-objective optimization system to perceive the true non-uniform state of the bevel interface when evaluating welding deformation, rather than calculating based on the assumption of an ideal homogeneous surface.

[0047] Specifically, in this embodiment, the interface disturbance impedance field mapping module includes: a chromosome decoding and feature separation unit, used to perform joint population chromosome decoding and feature separation on the joint optimization population matrix of cutting and welding to obtain the current generation of variable angle cutting posture parameter subset and welding control parameter subset; a chamfer gradient differential calculation unit, used to perform node-by-node differential calculation of the normal chamfer angle sequence in the current generation of variable angle cutting posture parameter subset with respect to the spatial arc length between adjacent nodes to obtain the spatial chamfer gradient distribution vector; and a thermodynamic impedance field construction unit, used to perform thermodynamic mapping of the spatial chamfer gradient distribution vector with slag residual thickness and heat-affected zone depth and perform tensor concatenation with the node spatial coordinates to obtain the bevel interface disturbance impedance field.

[0048] More specifically, in a concrete example of this application, the chromosome decoding and feature separation unit first performs joint population chromosome decoding and feature separation on the joint optimization population matrix of welding and cutting. Based on the preset truncation point position, each chromosome is hard-truncated along the column dimension. Taking the aforementioned 489-dimensional chromosome as an example, the truncation point is set to column 480. The gene segments from column 1 to column 480 are completely stripped to generate the current generation's variable angle cutting posture parameter subset, and the gene segments from column 481 to column 489 are completely stripped to generate the welding control parameter subset. The welding control parameter subset is not modified in this step and is directly used as output data for subsequent arc heat input reconstruction module use.

[0049] Next, the chamfer gradient differential calculation unit performs node-by-node differential calculations on the normal chamfer angle sequence in the current generation's variable angle cutting attitude parameter subset regarding the spatial arc length between adjacent nodes. Specifically, for the chamfer angle sequence of each individual in the population, it traverses from the second node according to the trajectory topology order, using the forward difference method to calculate the difference between the chamfer angle of the current node and the chamfer angle of the predecessor node, and divides it by the spatial arc length distance between the two nodes to obtain the chamfer gradient value at the current node. Taking a distance of 5 mm as an example, if an individual has a chamfer angle of 38 degrees at the 127th node and a chamfer angle of 35 degrees at the 126th node, then the spatial chamfer gradient at that node is 3 degrees divided by 5 mm, which is 0.6 degrees per millimeter. The chamfer gradient values ​​at all nodes of each individual are arranged in topological order to form a spatial chamfer gradient distribution vector. The larger the value of the node position in this vector, the more drastic the attitude change of the laser cutting head at that location, and the more significant the changes in the slag discharge conditions and energy absorption distribution on the bevel surface.

[0050] Then, the thermodynamic impedance field construction unit performs a thermodynamic mapping of the spatial chamfer gradient distribution vector to the residual slag thickness and the depth of the heat-affected zone. The absolute values ​​of the chamfer gradients at each node in the spatial chamfer gradient distribution vector are substituted into the preset laser-metal thermodynamic absorption equation to calculate the residual slag thickness and the non-uniform depth of the heat-affected zone at that node. The calculation formulas are as follows: in, This represents the residual slag thickness of the k-th individual in the population at the i-th node; This represents the non-uniform depth of the heat-affected zone of the k-th individual at the i-th node; This represents the fundamental thermodynamic constant related to laser power density and slag viscosity; This is a nonlinear sensitivity coefficient characterizing the effect of the cutting angle gradient on the degree of slag discharge deterioration; This is a fundamental constant relating laser absorptivity to the thermal diffusivity of materials. The sensitivity coefficient for characterizing the extent to which the shear angle gradient affects the thermally affected zone; This represents the absolute value of the spatial chamfer gradient at that node. The first formula uses an exponential growth function to characterize the physical relationship where the residual slag thickness deteriorates rapidly with increasing chamfer gradient. As the laser cutting head deflection rate increases, the pneumatic discharge channel of the molten material is compressed, leading to a sharp decrease in slag discharge efficiency, and the slag accumulates exponentially on the bevel surface. The second formula uses a logarithmic function to characterize the physical relationship where the depth of the heat-affected zone increases with increasing chamfer gradient but gradually approaches saturation. Due to the self-limiting effect of material thermal diffusion, the growth rate of the heat-affected zone depth gradually slows down with increasing gradient.

[0051] Furthermore, the slag residue thickness and heat-affected zone depth of each node calculated above are tensor-cascaded and stitched together with the corresponding three-dimensional spatial coordinates of that node. The three-dimensional spatial coordinates are derived from the positional information of each node in the ideal bevel spatial trajectory node set generated during the bevel profile geometric analysis stage. The spatial coordinates are stitched together with the microscopic interface features along the attribute dimension, so that each node simultaneously carries its spatial position and physical interface state. The cascaded features of all individuals in the population along all trajectory nodes are aggregated to formally construct the bevel interface perturbation impedance field. Each record in this impedance field contains three types of information: the three-dimensional spatial position coordinates of the node, the corresponding slag residue thickness, and the heat-affected zone depth, which fully describes the non-uniform interface state left on the bevel surface by the previous variable angle cutting.

[0052] In the aforementioned multi-objective process parameter optimization system 100 for welding deformation of refined steel, the arc heat input reconstruction module 130 is used to reconstruct the actual arc heat input of a subset of welding control parameters based on the interface perturbation impedance field to obtain the spatiotemporal boundary of the interface-constrained heat input. It should be understood that while the interface perturbation impedance field has quantified the slag residue thickness and non-uniform depth of the heat-affected zone at each trajectory node, these microscopic interface characteristic parameters have not yet established a physical relationship with the arc energy in the subset of welding control parameters. Subsequent thermo-elastic-plastic finite element simulation requires a heat flux density field reflecting the actual arc perturbation state as the load input. If a static heat source model based on the ideal current-voltage product is still used, it cannot capture the arc energy fluctuations caused by the non-uniform interface. Therefore, in the technical solution of this application, the welding control parameter subset is reconstructed based on the interface perturbation impedance field to reconstruct the actual arc heat input constrained by the interface perturbation field. This allows the nonlinear attenuation penalty to be applied to the ideal arc energy density using the non-uniform physical state of the bevel surface, and the corrected energy value is projected into a four-dimensional spatiotemporal domain to form a dynamic thermal load file that can drive the finite element solver. In this way, the heat source load used in subsequent transient simulations can truly reflect the energy dissipation and high-frequency oscillations that occur when the arc travels on the non-uniform bevel surface, avoiding deformation prediction deviations caused by the ideal heat source assumption and improving the physical accuracy of multi-objective fitness assessment.

[0053] Specifically, in this embodiment, the arc heat input reconstruction module includes: a physical impedance fluctuation coefficient conversion unit, used to perform physical impedance characteristic analysis and fluctuation coefficient conversion on the variables of slag residue thickness and heat-affected zone depth in the perturbation impedance field of the bevel interface to obtain a high-frequency fluctuation coefficient matrix of the arc morphology; a transient energy attenuation reconstruction unit, used to use the high-frequency fluctuation coefficient matrix of the arc morphology as a penalty term to perform ideal arc parameter analysis and transient energy attenuation reconstruction on a subset of welding control parameters to obtain a transient energy density matrix of the perturbation arc; and a four-dimensional energy gradient mounting unit, used to project the transient energy density matrix of the perturbation arc as the peak energy amplitude onto the spatial node coordinates corresponding to the perturbation impedance field of the bevel interface to perform four-dimensional energy gradient mounting to obtain the spatiotemporal boundary of the interface constraint state heat input.

[0054] More specifically, in a concrete example of this application, the physical impedance fluctuation coefficient conversion unit first performs physical impedance characteristic analysis and fluctuation coefficient conversion on the variables of slag residue thickness and heat-affected zone depth in the perturbation impedance field of the bevel interface. Specifically, the two microscopic characteristic variables, slag residue thickness and heat-affected zone non-uniform depth, are extracted node by node from the perturbation impedance field of the bevel interface, while the three-dimensional spatial coordinates contained therein are separated and retained for subsequent spatiotemporal projection. According to the physical impedance response mechanism of electric arc plasma, the greater the slag residue thickness, the stronger the electrical insulation damping effect of the bevel surface; the more severe the non-uniformity of the heat-affected zone depth, the greater the fluctuation of the micro-metallurgical thermal conductivity of the matrix. The combined effect of these two factors leads to high-frequency jumping of the arc anode spot. Using the nonlinear combination relationship of weight superposition and square amplification, the fluctuation coefficient conversion calculation is performed on the two microscopic variables at each node, as expressed by the following formula: in, This represents the high-frequency fluctuation coefficient of the arc morphology calculated for the kth individual in the population at the ith trajectory node. This indicates the residual slag thickness at that node, extracted from the perturbation impedance field of the bevel interface. This indicates the non-uniform depth of the heat-affected zone at that node, extracted from the perturbation impedance field of the bevel interface. The first-order weighting coefficient for the physical insulation damping effect of the electric arc caused by the slag thickness; This is the second-order sensitivity amplification factor for the fluctuations in microscopic metallurgical thermal conductivity caused by variations in the depth of the heat-affected zone. The first term in this formula... The linear proportion reflects the direct insulating and blocking effect of molten slag accumulation on the conductive path of the electric arc; the thicker the molten slag, the greater the impedance that needs to be overcome for arc initiation and arc maintenance. (Second term) The nonlinear perturbation effect of the depth difference of the heat-affected zone on the thermal properties of the matrix is ​​characterized by a square magnification method. The deeper the heat-affected zone, the more severe the grain coarsening and phase transformation in that region, leading to a quadratic deviation in local resistivity and thermal conductivity. The high-frequency fluctuation coefficient matrix of the arc morphology is constructed by arranging the fluctuation coefficients calculated for all individuals in the population at all trajectory nodes in a row and column manner.

[0055] Next, the transient energy attenuation reconstruction unit uses the arc morphology high-frequency fluctuation coefficient matrix as a penalty term to perform ideal arc parameter analysis and transient energy attenuation reconstruction on the subset of welding control parameters. In this embodiment, the transient energy attenuation reconstruction unit is used to: multiply the ideal welding voltage value and ideal welding current value of each individual in the subset of welding control parameters and combine them with the basic welding arc thermal efficiency constant to obtain the theoretical reference thermal power density; and use the arc morphology high-frequency fluctuation coefficient in the arc morphology high-frequency fluctuation coefficient matrix as a penalty factor for the exponential attenuation function to perform nonlinear energy reduction calculation on the theoretical reference thermal power density to obtain the perturbed arc transient energy density matrix.

[0056] Specifically, the ideal welding voltage and ideal welding current values ​​represented by the genes of each individual population are extracted from the subset of welding control parameters. These two values ​​are then multiplied by the basic welding arc thermal efficiency constant to obtain the theoretical reference heat power density without any interface disturbance. The fluctuation coefficient of the corresponding node in the high-frequency fluctuation coefficient matrix of the arc morphology is introduced as a penalty factor for the exponential decay function to perform forced energy reduction calculations on the theoretical reference heat power density. The formula is as follows: in, This represents the actual transient effective power density of the perturbation arc injected into the parent material at the i-th node by the k-th individual after nonlinear attenuation reconstruction; This represents the thermal efficiency constant of the basic welding arc under ideal conditions without interface disturbance. This represents the ideal welding voltage value of the k-th individual decoded from the subset of welding control parameters; This represents the ideal welding current value of the kth individual decoded from the subset of welding control parameters; This represents the interface penalty damping attenuation constant, used to control the sensitivity of the fluctuation coefficient to the exponential dissipation of energy absorption. This represents the high-frequency fluctuation coefficient of the arc morphology at this node, calculated in the previous step. In this formula... Part of the calculation is based on the reference power density generated by ideal voltage and ideal current under standard thermal efficiency in the welding control parameter subset, representing the total effective heat that the arc should inject into the base material when the bevel surface is in an ideal homogeneous state. (Exponential decay term) The value of is between 0 and 1. When the fluctuation coefficient at a node approaches zero, the exponential term approaches 1, and the actual power density is close to the ideal value, indicating that the bevel surface at that point is relatively smooth and there is no significant residue accumulation. When the fluctuation coefficient is large, the exponential term decays sharply and approaches zero, and the actual power density is significantly lower than the ideal value, indicating that the bevel interface at that point is severely non-uniform, and the arc energy is largely dissipated in overcoming surface impedance and high-frequency oscillations, and cannot be effectively transferred to the base material. The actual effective power density of all individuals at all nodes is matrix-encapsulated to output the transient energy density matrix of the perturbed arc.

[0057] Then, the four-dimensional energy gradient mounting unit projects the transient energy density matrix of the perturbed arc as the peak energy amplitude onto the spatial node coordinates corresponding to the perturbed impedance field at the bevel interface for four-dimensional energy gradient mounting. Specifically, the Goldak double ellipsoidal heat source model is selected as the basic distributed mathematical framework, and the coordinate values ​​of each discrete node are extracted from the previously separated and retained three-dimensional spatial position coordinates as the instantaneous geometric center of the heat source trajectory. The actual effective power density value of the corresponding node in the transient energy density matrix of the perturbed arc is injected into the double ellipsoidal heat source model as the peak energy amplitude parameter. Combined with the welding feed rate and the preset time evolution step included in the welding control parameter subset, the heat flux density distribution at each grid point in three-dimensional space during the heat source's trajectory advancement is calculated. Taking three-pass welding of refined steel plates as an example, the shape parameters of the front and rear semi-ellipsoids of the double ellipsoidal heat source are calibrated according to the actual weld width and penetration depth. The center of the heat source advances gradually along the trajectory nodes according to the feed rate, and within each time step, the effective power density at that instantaneous position decays and diffuses to the surrounding space according to a Gaussian distribution. After projecting all trajectory nodes and all time steps, the non-uniform heat flux density field containing three-dimensional spatial coordinates and one-dimensional time attributes is packaged and output to generate the interface-constrained thermal input spatiotemporal boundary. The interface-constrained thermal input spatiotemporal boundary, as the output of this step, is essentially a time-evolving four-dimensional heat flux density load file. Each record in the file corresponds to the heat flux density value that a spatial coordinate point should experience at a certain moment. The heat flux density values ​​in this load file have been corrected for nonlinearity of the bevel interface perturbation impedance field. In the corner transition region with severe non-uniformity on the bevel surface, the heat flux density is significantly lower than the ideal value, while in the relatively flat straight section region of the bevel surface, the heat flux density is close to the ideal value.

[0058] In the aforementioned multi-objective process parameter optimization system 100 for welding deformation of refined steel, the multi-objective fitness evaluation module 140 is used to import the spatiotemporal boundary of the interface-constrained thermal input as a dynamic thermal load into the thermo-elastic-plastic finite element mesh corresponding to the three-dimensional design model of the refined steel for transient simulation analysis, and to calculate the surface forming polarization index by combining the perturbation impedance field of the bevel interface to obtain the multi-objective fitness evaluation vector. It should be understood that since the spatiotemporal boundary of the interface-constrained thermal input has encoded the attenuation effect of the bevel interface non-uniformity on the arc energy as a four-dimensional heat flux density load, but this load has not yet been applied to the mechanical model of the refined steel component to calculate the actual deformation result, and the multi-objective co-evolution iteration needs to judge the merits of each individual in the population based on both the macroscopic residual warpage of the component and the microscopic surface smoothness of the bevel region, it is necessary to complete the physical solution from thermal load to deformation response within the finite element framework and establish a fitness evaluation system that includes both macroscopic and microscopic dimensions. Therefore, in the technical solution of this application, the spatiotemporal boundary of the interface-constrained thermal input is further introduced as a dynamic thermal load into the thermo-elastic-plastic finite element mesh corresponding to the three-dimensional design model of the refined steel for transient simulation analysis. The surface forming polarization index is calculated by combining the perturbation impedance field of the bevel interface to obtain a multi-objective fitness evaluation vector. This transforms the deformation response of the refined steel component and the degree of degradation of the bevel micro-quality under the perturbed thermal input condition into a numerical fitness index that can be used for ranking by the evolutionary algorithm. In this way, the fitness values ​​upon which subsequent non-dominated ranking and evolutionary iteration are based can simultaneously reflect the macroscopic dimensional accuracy of the component and the micro-forming quality of the bevel surface, ensuring that the Pareto optimal solution achieves a physically meaningful trade-off between the two objectives.

[0059] Figure 5 This is a block diagram of the multi-objective fitness evaluation module in a multi-objective process parameter optimization system for welding deformation of refined steel according to an embodiment of this application. Figure 5 As shown, the multi-objective fitness evaluation module 140 includes: a thermo-elastic-plastic transient solution unit 141, used to apply the interface constraint state thermal input spatiotemporal boundary as a dynamic thermal load to the finite element mesh corresponding to the three-dimensional design model of the refined steel for nonlinear thermo-elastic-plastic transient solution to obtain the overall three-dimensional node deformation displacement matrix of the refined steel; a macroscopic warping deformation evaluation unit 142, used to evaluate the macroscopic residual warping deformation fitness of the overall three-dimensional node deformation displacement matrix of the refined steel to obtain the welding macroscopic residual deformation fitness function value; a microscopic surface polarization evaluation unit 143, used to evaluate the microscopic surface forming polarization of the depth of the heat-affected zone between adjacent nodes in the perturbation impedance field of the bevel interface to obtain the bevel microscopic surface forming polarization fitness function value; and a multi-objective vector assembly unit 144, used to assemble the welding macroscopic residual deformation fitness function value and the bevel microscopic surface forming polarization fitness function value into a multi-objective vector to obtain a multi-objective fitness evaluation vector.

[0060] More specifically, in a concrete example of this application, the thermo-elastic-plastic transient solver first applies the interface-constrained thermal input spatiotemporal boundary as a dynamic thermal load to the finite element mesh corresponding to the three-dimensional design model of refined steel for nonlinear thermo-elastic-plastic transient solution. Specifically, using the three-dimensional design model of refined steel as the geometric basis, a three-dimensional solid finite element mesh containing the nonlinear temperature-dependent properties of the material is generated using a mesh generation algorithm. These material properties include the yield strength versus temperature curve, the coefficient of thermal expansion versus temperature curve, and the elastic modulus versus temperature curve. The heat flux density values ​​at each spatial coordinate point recorded in the interface-constrained thermal input spatiotemporal boundary at each time step are gradually applied to the corresponding nodes of the finite element mesh as a time-evolving thermal load. A nonlinear thermo-elastic-plastic solver is initiated, employing the Newton-Raphson incremental iteration method to solve for the temperature field distribution caused by the thermal load at each time step. This temperature field is then used as the volume load to drive the incremental solution of the elasto-plastic equilibrium equations. The nodal displacement increments across all time steps are accumulated until the welding process ends and the material cools to room temperature. The final residual displacements of each mesh node are then compiled and output as the overall three-dimensional nodal deformation displacement matrix of the refined steel. Taking a refined steel plate with approximately 12,000 nodes in its finite element mesh as an example, the overall three-dimensional nodal deformation displacement matrix of the refined steel has dimensions of 12,000 rows by 3 columns, with each row corresponding to the cooling residual displacement components of a node in the X, Y, and Z directions.

[0061] Next, the macroscopic warping deformation evaluation unit evaluates the macroscopic residual warping deformation fitness of the overall refined steel three-dimensional node deformation displacement matrix. Specifically, it iterates through each row of the overall refined steel three-dimensional node deformation displacement matrix, calculates the composite absolute value of the displacement components in the three directions of each grid node, searches for the maximum extreme value among all the composite absolute values ​​of node displacements to characterize the maximum local warping amplitude of the refined steel component, and simultaneously calculates the spatial variance of all the composite absolute values ​​of node displacements to characterize the degree of unevenness in the deformation distribution on the component. The maximum extreme value and spatial variance are linearly combined and normalized using preset weighting coefficients to output the welding macroscopic residual deformation fitness function value, expressed by the following formula: in, This represents the fitness function value for macroscopic residual deformation during welding; the smaller the value, the smaller the macroscopic deformation of the component. This represents the absolute value of the combined residual displacement components of the cooling in the three directions of the j-th finite element mesh node; This represents the maximum extreme value of the absolute value of the composite displacement among all grid nodes; This represents the total number of nodes in the finite element mesh model of refined steel. This represents the arithmetic mean of the absolute values ​​of the composite displacements of all grid nodes; and These are the expert experience weighting coefficients assigned to the maximum extremum and spatial variance, respectively. The first term in this formula... It captures the warping amplitude of the single point on the component where deformation is most severe, reflecting whether the refined steel will cause out-of-tolerance fit due to local bulges or depressions during assembly. (Second item) The variance component captures the spatial uniformity of deformation distribution across the entire component surface. Even if the maximum extreme value is acceptable, extremely uneven deformation distribution can still cause visible wavy undulations on the surface of refined steel. The weighted combination of the two components allows the fitness function to penalize both extreme local warping and global non-uniform deformation.

[0062] Then, the micro-surface polarization evaluation unit evaluates the depth of the heat-affected zone between adjacent nodes in the perturbation impedance field of the bevel interface using micro-surface forming polarization. Specifically, it extracts the non-uniform depth feature sequence of the heat-affected zone at each trajectory node from the perturbation impedance field of the bevel interface, calculates the absolute difference of the heat-affected zone depth between adjacent nodes according to the trajectory topology, and accumulates and averages the absolute differences of all adjacent node pairs to output the micro-surface forming polarization fitness function value of the bevel, expressed by the following formula: in, This represents the polarization fitness function value for bevel micro-surface forming; the smaller the value, the smoother the bevel micro-surface. This represents the total number of spatial nodes discrete along the cutting trajectory; and These represent the non-uniform depths of the heat-affected zone (HAZ) of the k-th individual in the perturbation impedance field at the adjacent ith and (i+1)-th nodes, respectively. This formula calculates the average absolute gradient of the HAZ depth along the trajectory direction. A greater difference in HAZ depth between adjacent nodes indicates a more pronounced hot spot abrupt change and grain coarsening jump on the bevel surface at that location. After welding, refined steel will exhibit visible color differences and microscopic unevenness in this area, directly affecting surface aesthetics and coating adhesion.

[0063] Furthermore, a multi-objective vector assembly unit assembles the fitness function value of the macroscopic residual deformation of welding and the fitness function value of the microscopic surface forming polarization of the bevel into a multi-objective vector. Specifically, the two fitness scalar values ​​are concatenated in a fixed order as a one-dimensional array. The first element is the fitness function value of the macroscopic residual deformation of welding, and the second element is the fitness function value of the microscopic surface forming polarization of the bevel, which is encapsulated as the bi-objective evaluation vector of the individual in the population. The entire process from finite element simulation to fitness calculation is repeated for all individuals in the population. The bi-objective evaluation vector of each individual is stacked row by row, and finally, a multi-objective fitness evaluation vector is output. Each row in this vector corresponds to the comprehensive quality score of an individual in the joint optimization population matrix of welding and cutting. The number of rows is equal to the population size, and the number of columns is equal to the number of objective dimensions, i.e., 2 columns, which are used for subsequent non-dominated sorting and crowding calculation.

[0064] In the aforementioned multi-objective process parameter optimization system 100 for welding deformation of refined steel, the co-evolutionary iterative output module 150 is used to perform multi-objective co-evolutionary iteration on the cutting-welding joint optimization population matrix based on the multi-objective fitness evaluation vector to output the Pareto optimal cutting-welding joint instruction set. It should be understood that since the multi-objective fitness evaluation vector has provided each individual in the cutting-welding joint optimization population matrix with a two-dimensional score including macroscopic residual deformation fitness and microscopic surface polarization fitness, but the current population is still in a random initialization or intermediate evolutionary state, its individual distribution may not be concentrated in the optimal region of the Pareto front. It is necessary to drive the population towards the Pareto front through multiple generations of genetic evolution operations, and after satisfying the termination condition, extract the most representative individual from the final front as the output solution. Therefore, in the technical solution of this application, a multi-objective co-evolutionary iteration is further performed on the cutting-welding joint optimization population matrix based on the multi-objective fitness evaluation vector to output the Pareto optimal cutting-welding joint instruction set. This is achieved by screening dominant individuals through non-dominated sorting and generating a new generation of candidate schemes in the joint encoding space using crossover and mutation operators. After multiple rounds of iterative iteration, the population gradually converges to the optimal compromise region between welding deformation and surface forming quality. Finally, the optimal individual is decoded into a cutting and welding joint control file that can be executed in the workshop. In this way, a global Pareto optimal solution can be obtained in the joint search space of cutting posture and welding parameters, ensuring that the output cutting-welding joint instructions achieve the best physical balance between macroscopic deformation control and microscopic surface quality.

[0065] Specifically, in this embodiment, the co-evolutionary iterative output module includes: a non-dominated sorting crowding calculation unit, used to perform non-dominated sorting and front-end crowding calculation on all individuals in the cut-weld joint optimization population matrix based on the multi-objective fitness evaluation vector to obtain the global Pareto level and crowding set; a population evolution iterative update unit, used to update the cut-weld joint optimization population matrix based on the global Pareto level and crowding set and return to the bevel interface perturbation impedance field mapping step to execute a new round of iteration when the iteration counter has not reached the preset maximum evolution generation threshold; and an elite extraction reverse encoding output unit, used to extract the elite chromosome with the largest crowding distance from the first front of the global Pareto level and crowding set when the iteration counter reaches the maximum evolution generation threshold, and perform reverse encoding conversion through CNC post-processing and welding robot protocol parsing to output the Pareto optimal cut-weld joint instruction set.

[0066] More specifically, in a concrete example of this application, the non-dominated sorting crowding calculation unit first performs non-dominated sorting and front crowding calculation on all individuals in the joint welding-cutting population matrix based on the multi-objective fitness evaluation vector. Specifically, it reads the welding macroscopic residual deformation fitness function value and the bevel microscopic surface forming polarization fitness function value of each individual in the multi-objective fitness evaluation vector, and compares the pairwise dominance relationships of all individuals in the population. If an individual is not inferior to another individual in both objective dimensions and is strictly superior to that individual in at least one dimension, then the former is determined to dominate the latter. According to the hierarchy of dominance relationships, all individuals are divided into different Pareto front levels. Individuals not dominated by any other individual are assigned to the first front, those dominated only by individuals in the first front are assigned to the second front, and so on. For individuals within the same front level, they are sorted in ascending order according to their fitness values ​​in each objective dimension. The perimeter of the rectangle formed by each individual and its two adjacent individuals in the objective space is calculated as the crowding distance. Individuals located at the front boundary are assigned infinite crowding to protect diversity. The Pareto front level identifier of each individual is structurally bound to the crowding distance value to generate a global Pareto level and crowding set. Taking a population size of 200 individuals as an example, after non-dominated sorting, the first front contains about 15 to 30 individuals, the second front contains about 30 to 50 individuals, and the remaining individuals are distributed in the lower-level fronts.

[0067] Next, the population evolution iteration update unit determines whether the current iteration counter has reached the preset maximum generation threshold. Taking a maximum generation threshold of 150 generations as an example, if the current iteration counter has not yet reached 150 generations, the cut-weld joint optimization population matrix is ​​updated based on the global Pareto level and crowding set. Specifically, a binary tournament selection method is used to select parent individuals from the current population. The selection rule is to prioritize individuals with lower Pareto levels. If two candidate individuals have the same level, the individual with a larger crowding distance is selected to maintain solution set diversity. A simulated binary crossover operator is executed on the selected parent individuals, generating two offspring individuals in the real-number encoding space of the joint chromosome. The crossover operation simultaneously acts on the cutting posture genes in the front segment of the chromosome and the welding control genes in the back segment, enabling the parameters of the cutting and welding processes to achieve coordinated recombination in the same crossover operation. A polynomial mutation operator is executed on the offspring individuals, slightly perturbing random gene positions in the chromosome with a preset mutation probability. After merging the generated offspring population with the parent population, a new non-dominated sort is performed. Following the Pareto rank priority and crowding distance as the second-best rule, the number of individuals is truncated to the same size as the original population, forming an updated cut-weld joint optimization population matrix. This updated cut-weld joint optimization population matrix is ​​then returned to the bevel interface perturbation impedance field mapping step to execute a new round of iterations. This involves re-performing the complete process of chromosome decoding, bevel gradient differential calculation, impedance field construction, arc heat input reconstruction, finite element simulation, and fitness evaluation, with the iteration counter incremented by one.

[0068] Then, when the iteration counter reaches the maximum generation threshold, the elite extraction decoding output unit extracts the elite chromosome with the largest crowding distance from the first frontier of the global Pareto level and crowding set. Specifically, from the global Pareto level and crowding set of the final generation, all individual indices with a Pareto level of the first frontier are retrieved. Among these first frontier individuals, the individual with the largest crowding distance value is searched. This individual is located in the sparse region of the Pareto front in the target space, representing the most balanced compromise between the fitness function value of the welding macroscopic residual deformation and the fitness function value of the bevel microscopic surface forming polarization. Based on the row index of this individual, a complete row of real-valued encoding sequences is extracted from the joint cutting and welding population matrix as the globally optimal elite chromosome.

[0069] Furthermore, the globally optimal elite chromosome undergoes CNC post-processing and welding robot protocol parsing through reverse encoding conversion. Based on the previously defined chromosome truncation point positions, the elite chromosome is decomposed into a front-end cutting posture gene segment and a back-end welding control gene segment. The CNC machine tool post-processor function is called to bind the normal infeed angle numerical sequence of each node in the front-end cutting posture gene segment with the three-dimensional coordinates in the ideal bevel spatial trajectory node set, converting it into spatial interpolation G-code conforming to the kinematics syntax of a five-axis laser cutting machine tool. The G-code contains the coordinate values ​​of each trajectory node and the corresponding cutting head rotation angle command. The welding robot protocol parsing function is called to map the current, voltage, and feed rate values ​​in the back-end welding control gene segment into a dynamic parameter timing allocation script recognizable by the welding robot controller, according to the weld bead sequence. The generated G-code file and the welding robot execution script file are injected into the inter-process timing synchronization identifier and packaged together, finally outputting a Pareto-optimal cut-weld joint instruction set. This instruction set can be directly issued to the workshop manufacturing execution system, and then executed sequentially by the laser cutting machine and welding robot according to the time synchronization relationship, so as to achieve optimal process parameter control for the entire process from beveling to welding.

[0070] In summary, the multi-objective process parameter optimization system for welding deformation of refined steel according to the embodiments of this application is explained. It incorporates variable-angle cutting posture and multi-pass welding process parameters into the same optimization space, and adaptively limits the sampling range of the cutting angle based on the local curvature of the bevel trajectory to reduce extreme postures and invalid candidate solutions in high curvature regions. It characterizes the difference in slag residue and heat-affected zone depth caused by the change in cutting angle as the bevel interface disturbance state, and corrects the arc energy corresponding to the welding control parameters accordingly to obtain the heat input boundary that conforms to the actual interface conditions. It evaluates the difference between macroscopic residual deformation and microscopic surface forming of refined steel through thermo-elastic-plastic simulation, performs multi-objective collaborative optimization, and outputs joint cutting and welding commands, thereby reducing the heat input evaluation deviation caused by the ideal bevel assumption, and taking into account welding deformation control, surface forming quality and optimization efficiency.

Claims

1. A multi-objective process parameter optimization system for welding deformation of refined steel, characterized in that, include: The joint cutting and welding population construction module is used to obtain the joint cutting and welding optimized population matrix by jointly encoding and sampling the variable angle cutting posture parameters and multi-pass welding process parameters based on the initial cutting and welding process design data. The interface disturbance impedance field mapping module is used to dynamically map the bevel interface disturbance impedance field oriented towards the chamfer gradient on the joint optimization population matrix of cutting and welding to obtain the bevel interface disturbance impedance field and a subset of welding control parameters. The arc heat input reconstruction module is used to reconstruct the actual arc heat input of a subset of welding control parameters based on the interface perturbation impedance field to obtain the spatiotemporal boundary of the interface-constrained heat input. The multi-objective fitness evaluation module is used to import the interface constraint state thermal input spatiotemporal boundary as a dynamic thermal load into the thermo-elastic-plastic finite element mesh corresponding to the three-dimensional design model of refined steel for transient simulation analysis, and combine the perturbation impedance field of the bevel interface to calculate the surface forming polarization index to obtain the multi-objective fitness evaluation vector. The co-evolutionary iterative output module is used to perform multi-objective co-evolutionary iteration on the cut-weld joint optimization population matrix based on the multi-objective fitness evaluation vector to output the Pareto optimal cut-weld joint instruction set.

2. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 1, characterized in that, The initial cutting and welding process design data includes a three-dimensional design model of refined steel, kinematic constraint parameters of the laser cutting machine tool, and allowable ranges of basic welding process parameters.

3. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 1, characterized in that, The joint cutting and welding population construction module includes: The bevel profile geometric analysis unit is used to perform geometric feature analysis on the bevel intersection profile in the 3D design model of refined steel to obtain the set of ideal bevel spatial trajectory nodes. The cutting posture constraint sampling unit is used to perform Monte Carlo random sampling and angular velocity threshold truncation filtering on the set of ideal bevel spatial trajectory nodes based on the kinematic constraint parameters of the laser cutting machine tool to obtain a set of variable angle cutting posture parameters. The joint real-number encoding splicing unit is used to uniformly sample current, voltage and feed speed within the allowable range of basic welding process parameters, and to perform joint real-number encoding cascade splicing of the sampling results with the set of variable angle cutting posture parameters to obtain the joint optimization population matrix of cutting and welding.

4. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 1, characterized in that, The interface disturbance impedance field mapping module includes: The chromosome decoding and feature separation unit is used to perform joint population chromosome decoding and feature separation on the cut-weld joint optimization population matrix to obtain the current generation of variable angle cutting posture parameter subset and welding control parameter subset; The tangent gradient differential calculation unit is used to perform node-by-node differential calculation of the normal ingress angle sequence in the current generation of variable angle cutting attitude parameter subset with respect to the spatial arc length between adjacent nodes to obtain the spatial tangent gradient distribution vector. The thermodynamic impedance field construction unit is used to perform thermodynamic mapping of the spatial chamfer gradient distribution vector to the slag residual thickness and the depth of the heat-affected zone, and to perform tensor concatenation with the nodal spatial coordinates to obtain the perturbation impedance field of the bevel interface.

5. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 1, characterized in that, The arc heat input reconstruction module includes: The physical impedance fluctuation coefficient conversion unit is used to perform physical impedance characteristic analysis and fluctuation coefficient conversion on the variables of slag residual thickness and heat-affected zone depth in the perturbation impedance field of the bevel interface to obtain the high-frequency fluctuation coefficient matrix of the arc morphology. The transient energy decay reconstruction unit is used to perform ideal arc parameter analysis and transient energy decay reconstruction on a subset of welding control parameters, using the high-frequency fluctuation coefficient matrix of the arc morphology as a penalty term, to obtain the transient energy density matrix of the disturbed arc. The four-dimensional energy gradient mounting unit is used to project the transient energy density matrix of the perturbed arc as the peak energy amplitude onto the spatial node coordinates corresponding to the perturbed impedance field of the bevel interface to obtain the spatiotemporal boundary of the interface constraint state thermal input.

6. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 5, characterized in that, The transient energy decay reconstruction unit is used for: The ideal welding voltage and ideal welding current values ​​of each individual in the welding control parameter subset are multiplied together and combined with the basic welding arc thermal efficiency constant to obtain the theoretical reference thermal power density. Using the high-frequency fluctuation coefficient of the arc morphology in the high-frequency fluctuation coefficient matrix of the arc morphology as the penalty factor of the exponential decay function, nonlinear energy reduction calculation is performed on the theoretical reference thermal power density to obtain the transient energy density matrix of the disturbed arc.

7. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 1, characterized in that, The multi-objective fitness evaluation module includes: The thermo-elastic-plastic transient solution element is used to apply the interface constraint state thermal input spatiotemporal boundary as a dynamic thermal load to the finite element mesh corresponding to the three-dimensional design model of refined steel for nonlinear thermo-elastic-plastic transient solution to obtain the overall three-dimensional nodal deformation displacement matrix of refined steel. The macroscopic warping deformation evaluation unit is used to evaluate the macroscopic residual warping deformation fitness of the three-dimensional node deformation displacement matrix of the whole refined steel in order to obtain the welding macroscopic residual deformation fitness function value. The micro-surface polarization evaluation unit is used to evaluate the depth of the heat-affected zone between adjacent nodes in the perturbation impedance field of the bevel interface to obtain the micro-surface polarization fitness function value of the bevel. The multi-objective vector assembly unit is used to assemble the fitness function value of the welding macroscopic residual deformation and the fitness function value of the bevel microscopic surface forming polarization to obtain the multi-objective fitness evaluation vector.

8. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 1, characterized in that, The co-evolutionary iterative output module includes: The non-dominated sorting crowding calculation unit is used to perform non-dominated sorting and front crowding calculation on all individuals in the cut-weld joint optimization population matrix based on the multi-objective fitness evaluation vector to obtain the global Pareto level and crowding set. The population evolution iteration update unit is used to update the cutting and welding joint optimization population matrix based on the global Pareto level and crowding set when the iteration counter has not reached the preset maximum evolution generation threshold, and return to the bevel interface disturbance impedance field mapping step to execute a new round of iteration. The elite extraction and reverse encoding output unit is used to extract the elite chromosome with the largest crowding distance from the first frontier of the global Pareto level and crowding set when the iteration counter reaches the maximum evolution generation threshold. The chromosome is then reverse encoded and converted through CNC post-processing and welding robot protocol parsing to output the Pareto optimal cutting and welding joint instruction set.

9. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 3, characterized in that, The cutting posture constraint sampling unit includes: The node discrete curvature estimation sub-unit is used to perform discrete curvature estimation on the spatial triangle formed by each internal node and its adjacent nodes in the ideal slope spatial trajectory node set to obtain the node local curvature feature sequence. An adaptive inclination angle domain is used to construct a sub-unit, which is used to construct a node-level adaptive inclination angle feasible region based on the node local curvature feature sequence; The curvature-aware sampling truncation verification subunit is used to perform Monte Carlo random sampling within the feasible region of the node-level adaptive cutting angle and to perform threshold truncation verification on the rate of change of angle between adjacent nodes using the maximum angular velocity limit, so as to obtain the set of variable angle cutting attitude parameters.

10. The multi-objective process parameter optimization system for welding deformation of refined steel according to claim 9, characterized in that, The adaptive in-angle domain construction subunit is used for: The node-by-node sampling domain shrinkage factor is obtained by performing a shrinkage factor transformation on the node local curvature feature sequence based on the Sigmoid-type saturation mapping function. Based on the node-by-node sampling domain shrinkage factor, the full domain half-width is compressed proportionally with the median of the ingress angle range as the center of symmetry to obtain the node-level adaptive ingress angle feasible domain.

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