A method and system for analyzing the quality trend of electrical discharge machining

Abstract

The application discloses a kind of EDM processing quality trend analysis method and system, it is related to EDM processing technical field, the transient temperature field distribution in workpiece is solved, and the etching pit radius and etching pit depth are extracted from workpiece material melting point, spherical crown geometric analytical model is established and single pulse material removal volume is calculated, theoretical material removal rate and theoretical surface roughness are calculated in combination with effective discharge frequency calculation theory, the architecture of KAN network is initialized, open-circuit voltage, charging capacity and pulse width are corresponded to input layer, material removal rate and surface roughness are corresponded to output layer, activation function is defined, KAN agent model is initialized, process parameter combination is generated and prediction value is output, the same batch of process parameter combination is executed step S1 and step S2 to obtain physical reference value, iteratively trains until KAN agent model converges, generates multidimensional response surface, constructs and obtains the extreme point of processing quality comprehensive evaluation function to obtain preferred process parameter interval.

Description

Technical Field

[0001] This invention relates to the field of electrical discharge machining (EDM) technology, and in particular to a method and system for analyzing the quality trends of EDM. Background Technology

[0002] Electrical discharge machining (EDM), a non-contact machining method that uses the heat energy generated by pulsed discharge to erode workpieces, is widely used in the aerospace and precision mold industries for manufacturing high-hardness and complex curved surface parts. Machining quality is a core indicator for evaluating EDM processes, and these indicators are influenced by the nonlinear coupling of multi-dimensional process parameters, exhibiting extremely complex evolutionary patterns. Therefore, accurately and efficiently analyzing the trend of machining quality changes with process parameters and optimizing these parameters has become a crucial problem that urgently needs to be solved.

[0003] Currently, Chinese invention application number 202510954242.2 discloses a method for optimizing dynamic parameters in electrical discharge machining. A high-frequency acoustic emission sensor is installed on the machine tool to collect signals. Combined with the current feedback of the spindle motor, the signal energy and peak intensity are extracted and compared with a preset threshold. When abnormal discharge or insufficient energy is detected, the current amplitude, pulse width and servo voltage are dynamically adjusted to maintain machining stability. However, existing technologies suffer from the following shortcomings: they rely on physical trial and error, lacking predictability, and primarily focus on real-time correction and stability control during processing. Adjustments can only be made after processing begins and signals are generated, making it impossible to predict processing quality trends across the entire parameter space offline before processing. This hinders guidance for process engineers to directly identify the optimal parameter range before processing, resulting in high initial trial and error costs. Furthermore, they employ black-box control with opaque mechanisms, establishing statistical correlations between current / acoustic signals and discharge states, lacking a physical description of the discharge pit formation mechanism and failing to reveal how process parameters specifically affect the geometry of the etched pits. This makes it difficult to accurately quantify the numerical evolution of material removal rate and surface roughness at the microscopic mechanism level. Finally, they lack global optimization capabilities. Such dynamic adjustments are typically local fine-tuning near the current operating point, making it difficult to traverse the entire process parameter space to construct a global quality response surface. This easily leads to getting trapped in local optima and prevents true global quality trend analysis. Summary of the Invention

[0004] The technical problem solved by this invention is that existing technologies are unable to efficiently reveal the complex nonlinear coupling evolution law between multidimensional process parameters and processing quality in electrical discharge machining while ensuring prediction accuracy. They cannot overcome the dual defects of high computational cost and excessive time consumption of simple physical simulation traversing the entire parameter space, and the dependence of traditional neural network models on massive experimental samples and lack of physical interpretability. This makes it difficult to quickly obtain the full-domain processing quality response surface, resulting in low efficiency in process parameter optimization and difficulty in predicting processing quality trends.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for analyzing the quality trend of electrical discharge machining, comprising the following steps: Step S1: Construct a Gaussian heat flux density distribution function as a thermal boundary condition, establish a transient heat conduction differential equation, solve for the transient temperature field distribution inside the workpiece, and extract the radius and depth of the etched pit based on the melting point of the workpiece material. Step S2: Based on the radius and depth of the etched pit, establish a geometric analytical model of the spherical cap and calculate the single-pulse material removal volume. Combine the effective discharge frequency to calculate the theoretical material removal rate and theoretical surface roughness. Step S3: Initialize the architecture of the KAN network, map the open-circuit voltage, charging capacitance, and pulse width to the input layer, map the material removal rate and surface roughness to the output layer, and define the activation function; Step S4: Based on the KAN network architecture, initialize the KAN surrogate model, generate process parameter combinations and output predicted values. Perform steps S1 and S2 on the same batch of process parameter combinations to obtain physical baseline values, construct a comprehensive weighted loss function, adjust and update the learnable parameters, and repeat iterative training until the KAN surrogate model converges. Step S5: Perform gridded traversal calculations based on the convergent KAN surrogate model to generate a multidimensional response surface. Construct a comprehensive evaluation function for processing quality within the remaining feasible regions that satisfy the constraints. Obtain the optimal process parameter range based on the extreme points of the comprehensive evaluation function for processing quality.

[0006] Preferably, step S1 includes the following sub-steps: Step S101: Set the heat flux density in the discharge channel to follow a Gaussian distribution in the radial direction. Calculate the peak heat flux density of the discharge channel based on the preset energy distribution coefficient, discharge voltage, and discharge current. Combine this with the preset energy distribution radius to construct a Gaussian heat flux density distribution function. Use the Gaussian heat flux density distribution function as the thermal boundary condition applied to the workpiece surface. Step S102: Import the nonlinear data table of thermal conductivity, specific heat capacity and density of the workpiece material as a function of temperature, introduce the latent heat of phase change parameters during the melting and vaporization process of the material to correct the equivalent specific heat capacity, and establish the transient heat conduction differential equation, which includes temperature gradient term, material density term, specific heat capacity term and thermal conductivity term. Step S103: Discretize the workpiece model into a mesh using a finite element solver, apply the Gaussian heat flux density distribution function as a heat load to the mesh nodes, use a preset pulse width as the heat load application time, solve the transient heat conduction differential equation, and obtain the transient temperature field distribution inside the workpiece. In the transient temperature field distribution, the node regions with temperatures higher than the melting point of the workpiece material are locked. The maximum span of the node region in the radial direction is extracted as the radius of the etch pit, and the maximum coordinate value of the node region in the axial depth direction is extracted as the depth of the etch pit.

[0007] Preferably, step S2 includes the following sub-steps: Step S201: Based on the radius and depth of the etched pit, the etched pit generated by a single discharge is equivalent to a spherical cap geometry, and a spherical cap geometric analytical model is established. The single-pulse material removal volume under single-discharge conditions is calculated based on the spherical cap geometric analytical model. The mathematical expression for the single-pulse material removal volume is: ; in, Remove volume for single-pulse materials. To remove the radius of the pit, To remove the depth of the pit.

[0008] Preferably, step S2 further includes the following sub-steps: Step S202: Obtain the effective discharge frequency under the current open circuit voltage, charging capacitor and pulse width parameters, multiply the single-pulse material removal volume by the effective discharge frequency, calculate the total volume removal amount per unit time, and obtain the theoretical material removal rate. Step S203: Introduce an overlap factor that characterizes the degree of spatial stacking of adjacent etched pits, establish a mapping function between surface roughness and etched pit depth, substitute the etched pit depth into the mapping function and correct it using the overlap factor, and calculate the theoretical surface roughness.

[0009] Preferably, step S3 includes the following sub-steps: Step S301: Initialize the architecture of the KAN network. The architecture of the KAN network includes an input layer, an intermediate hidden layer and an output layer. The input layer is set to include three neurons, which correspond to the open circuit voltage, the charging capacitance and the pulse width respectively. The output layer is set to include two neurons, which correspond to the material removal rate and the surface roughness respectively. An intermediate hidden layer of a predetermined number of layers is set between the input layer and the output layer. Step S302: For each connection edge between adjacent neurons in the KAN network, a parameterized univariate function is defined as the activation function. The activation function is a linear combination of a residual basis function and a B-spline function, wherein the control point coefficients of the B-spline function are learned parameters during the training process of the KAN network. Step S303: Set the input value of one of the back layer neurons in the KAN network to be equal to the sum of the output values ​​of all the front layer neurons connected to the one of the back layer neurons after being transformed by the activation function on the connection edge. By superimposing a preset number of univariate functions, a multivariate nonlinear function between process parameters and processing quality is obtained.

[0010] Preferably, step S4 includes the following sub-steps: Step S401: Construct a KAN proxy model based on the KAN network architecture, initialize the control point coefficients of the B-spline function in the KAN proxy model, generate process parameter combinations using a Latin hypercube sampling strategy within the preset process parameter value range, input the process parameter combinations into the KAN proxy model, and output the corresponding predicted values ​​through KAN network hierarchy. The predicted values ​​include predicted material removal rate and predicted surface roughness.

[0011] Preferably, step S4 further includes the following sub-steps: Step S402: For the same batch of process parameter combinations, execute step S1 to calculate the radius and depth of the etched pits corresponding to the same batch of process parameter combinations. Based on the radius and depth of the etched pits corresponding to the same batch of process parameter combinations, execute step S2 to calculate the theoretical material removal rate and theoretical surface roughness corresponding to the same batch of process parameter combinations. Use the theoretical material removal rate and theoretical surface roughness corresponding to the same batch of process parameter combinations as physical reference values. The predicted values ​​and physical reference values ​​are normalized respectively, and weight coefficients are assigned according to the preset attention to construct a comprehensive weighted loss function, which includes a material removal rate error term and a surface roughness error term. Step S403: Calculate the gradient of the integrated weighted loss function with respect to the B-spline control point coefficients in the KAN network, and adjust and update the learnable parameters using the backpropagation algorithm; Determine whether the current comprehensive weighted loss function value is less than the preset convergence threshold. If the comprehensive weighted loss function value is greater than or equal to the preset convergence threshold, it is determined that the KAN surrogate model has not converged. Return to step S401 to regenerate the next batch of process parameter combinations and repeat the iterative training. If the overall weighted loss function value is less than the preset convergence threshold, the KAN surrogate model is determined to have converged, training ends, and the converged KAN surrogate model is output.

[0012] Preferably, step S5 includes the following sub-steps: Step S501: Within the feasible range of open-circuit voltage, charging capacitance, and pulse width, preset the discrete step length and construct a high-density grid matrix covering the entire parameter space. Each set of parameters in the high-density grid matrix is ​​input into the converged KAN surrogate model to calculate and output the corresponding global material removal rate prediction value and global surface roughness prediction value in batches. Step S502: Using process parameters as independent variable coordinates and material removal rate and surface roughness as dependent variable coordinates, the discrete points of the global prediction are fitted into a continuous and smooth multidimensional response surface using an interpolation algorithm. The gradient vectors at each point on the multidimensional response surface are calculated, and the sensitivity and monotonicity of the influence of changes in various process parameters on the processing quality index are analyzed, revealing the nonlinear dynamic evolution law of processing quality with changes in process parameters.

[0013] Preferably, step S5 further includes the following sub-steps: Step S503: The upper limit threshold of surface roughness and the lower limit threshold of material removal rate are preset as constraints. Region clipping and screening are performed on the multidimensional response surface to retain the remaining feasible regions that meet the constraints. Using the predicted values ​​of global material removal rate and global surface roughness in the remaining feasible region, a comprehensive evaluation function of processing quality is constructed by normalized weighted summation. Search for the extreme points of the comprehensive evaluation function of processing quality within the remaining feasible region, and take the range of process parameters corresponding to the extreme points as the preferred process parameter range.

[0014] An electrical discharge machining quality trend analysis system includes a simulation module, a solution module, a construction module, a training module, and an analysis module; The simulation module is used to construct a Gaussian heat flux density distribution function as a thermal boundary condition, establish a transient heat conduction differential equation, use a finite element solver to solve the transient temperature field distribution inside the workpiece, and extract the radius and depth of the etched pit based on the melting point of the workpiece material. The calculation module is used to establish a spherical cap geometric analytical model based on the radius and depth of the etched pit and to calculate the single-pulse material removal volume. It also calculates the theoretical material removal rate and theoretical surface roughness by combining the effective discharge frequency. The construction module is used to initialize the architecture of the KAN network, map open-circuit voltage, charging capacitance and pulse width to the input layer, map material removal rate and surface roughness to the output layer, define parameterized univariate functions on the network connection edges as activation functions, and use the superposition of univariate functions to obtain the multivariate nonlinear function between process parameters and processing quality. The training module is used to construct a KAN proxy model based on the KAN network architecture, initialize the KAN proxy model, generate process parameter combinations and output predicted values. For the same batch of process parameter combinations, steps S1 and S2 are executed to calculate the physical baseline value, construct a comprehensive weighted loss function, use the backpropagation algorithm to adjust and update the learnable parameters, and repeat iterative training until the KAN proxy model converges. The analysis module is used to perform gridded traversal calculations on the preset full process parameter space based on the convergent KAN surrogate model, generate a multidimensional response surface, construct a comprehensive evaluation function for processing quality within the remaining feasible region that meets the constraints, and obtain the optimal process parameter range based on the extreme points of the comprehensive evaluation function for processing quality.

[0015] The beneficial effects of this invention are as follows: By constructing a KAN proxy model that integrates physical mechanisms, and replacing the fixed activation functions of traditional multilayer perceptrons with learnable spline activation functions located on network connection edges, the excellent local approximation capability of spline functions is used to accurately characterize the nonlinear evolution trend between open-circuit voltage, charging capacitance, pulse width, and processing quality. Furthermore, by combining the physical and geometric calculation steps of constructing a Gaussian heat flux density distribution function, solving transient heat conduction differential equations, and deriving theoretical material removal rate and theoretical surface roughness using the spherical cap volume calculation formula, physical benchmark values ​​are embedded into the training process of the KAN proxy model, achieving rapid model convergence with minimal physical computing power consumption. The KAN proxy model replaces the complex finite element solver to complete high-density mesh traversal of the entire parameter space, generating high-precision multidimensional response surfaces and locking the optimal process parameter range, significantly improving the efficiency of trend analysis and parameter optimization while ensuring physical authenticity. Attached Figure Description

[0016] Figure 1 A flowchart illustrating the steps of an electrical discharge machining quality trend analysis method according to an embodiment of the present invention; Figure 2 This is a basic flowchart of an electrical discharge machining quality trend analysis system provided in one embodiment of the present invention. Detailed Implementation

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0018] Example 1, referring to Figure 1 This paper provides a method for analyzing the quality trends of electrical discharge machining, which includes the following steps: Step S1: Construct a Gaussian heat flux density distribution function as the thermal boundary condition, establish a transient heat conduction differential equation, use a finite element solver to solve the transient temperature field distribution inside the workpiece, and extract the radius and depth of the etched pit based on the melting point of the workpiece material.

[0019] Step S2: Based on the radius and depth of the etched pit, establish a geometric analytical model of the spherical cap and calculate the single-pulse material removal volume. Combine the effective discharge frequency to calculate the theoretical material removal rate and theoretical surface roughness.

[0020] Step S3: Initialize the architecture of the KAN network, map the open-circuit voltage, charging capacitor and pulse width to the input layer, map the material removal rate and surface roughness to the output layer, define the parameterized univariate functions on the network connection edges as activation functions, and use the superposition of univariate functions to obtain the multivariate nonlinear function between process parameters and processing quality.

[0021] Step S4: Construct a KAN proxy model based on the KAN network architecture, initialize the KAN proxy model, generate process parameter combinations and output predicted values. For the same batch of process parameter combinations, execute steps S1 and S2 to calculate the physical baseline values, construct a comprehensive weighted loss function, use the backpropagation algorithm to adjust and update the learnable parameters, and repeat iterative training until the KAN proxy model converges.

[0022] Step S5: Based on the convergent KAN surrogate model, perform gridded traversal calculations on the preset full process parameter space to generate a multidimensional response surface. Construct a comprehensive evaluation function for processing quality within the remaining feasible regions that meet the constraints. Obtain the optimal process parameter range based on the extreme points of the comprehensive evaluation function for processing quality.

[0023] This invention constructs a KAN surrogate model that integrates physical mechanisms. It replaces the fixed activation functions of traditional multilayer perceptron nodes with learnable spline activation functions located on network connection edges. It utilizes the excellent local approximation capability of spline functions to accurately characterize the nonlinear evolution trend between open-circuit voltage, charging capacitance, pulse width, and processing quality. Furthermore, it combines the physical and geometric calculation steps of constructing a Gaussian heat flux density distribution function, solving transient heat conduction differential equations, and deriving theoretical material removal rate and theoretical surface roughness using the spherical cap volume calculation formula. The physical benchmark values ​​are embedded into the training process of the KAN surrogate model, achieving rapid model convergence with minimal physical computational power consumption. The KAN surrogate model replaces the complex finite element solver to complete the high-density mesh traversal of the entire parameter space, generating a high-precision multidimensional response surface and locking the optimal process parameter range. While ensuring physical authenticity, it significantly improves the efficiency of trend analysis and parameter optimization.

[0024] In a specific embodiment, step S1 includes the following sub-steps: Step S101: Set the heat flux density in the discharge channel to follow a Gaussian distribution in the radial direction. Calculate the peak heat flux density of the discharge channel based on the preset energy distribution coefficient, discharge voltage, and discharge current. Combine this with the preset energy distribution radius to construct a Gaussian heat flux density distribution function that describes the change of heat flux density with radial distance. Use the Gaussian heat flux density distribution function as the thermal boundary condition applied to the workpiece surface.

[0025] Step S102: Import the nonlinear data table of thermal conductivity, specific heat capacity, and density of the workpiece material as a function of temperature; introduce the latent heat of phase change parameters during the melting and vaporization process of the material to correct the equivalent specific heat capacity; establish the transient heat conduction differential equation, which includes temperature gradient terms, material density terms, specific heat capacity terms, and thermal conductivity terms. The transient heat conduction differential equation is used to characterize the nonlinear heat transfer behavior inside the workpiece.

[0026] Step S103: Discretize the workpiece model using a finite element solver, apply the Gaussian heat flux density distribution function as a heat load to the grid nodes, use the preset pulse width as the heat load application time, solve the transient heat conduction differential equation, and obtain the transient temperature field distribution inside the workpiece.

[0027] Lock the node region where the temperature is higher than the melting point of the workpiece material, extract the maximum span of the node region in the radial direction as the radius of the etch pit, and extract the maximum coordinate value of the node region in the axial depth direction as the depth of the etch pit.

[0028] In this embodiment, the construction of the Gaussian heat flux density distribution function specifically includes: During electric spark discharge, the energy within the discharge channel is not uniformly distributed, but rather exhibits a pattern of high energy at the center and low energy at the edges. This embodiment uses a Gaussian distribution to describe the heat flux density. Let the center of the discharge channel be the origin of the coordinate system, and the heat flux density... radial distance The mathematical expression for the Gaussian heat flux density distribution function is as follows: ; in, The value of the Gaussian heat flux density distribution function, i.e., the distance from the discharge center. Surface heat flux density at the location, in units of , Open circuit voltage, unit: , Discharge current, in units of The open-circuit voltage and discharge current are determined by the currently input process parameters. The energy distribution coefficient represents the proportion of the total discharge energy transferred to the workpiece.

[0029] In this embodiment, for steel workpiece materials, The value range is set to 0.18 to 0.25 for cemented carbide materials. The value range is set to 0.25 to 0.35. In actual simulations, It can also be obtained through calibration using a single discharge experiment. The energy distribution radius, i.e., the discharge channel radius, is expressed in units of... Since the discharge channel expands with current and time, this embodiment uses the following empirical formula to determine... Value: ; in, Pulse width (unit: ), , , This is an empirical constant. For example, for mold steel materials, take... .

[0030] The thermal boundary conditions for finite element analysis are defined by how heat is applied to the upper surface of the workpiece.

[0031] After heat enters the workpiece, it is transferred according to Fourier's law of thermal conduction. Considering that electrical discharge machining involves the melting and vaporization of materials, the thermal properties of the material are nonlinear functions of temperature. In this embodiment, an axisymmetric transient heat conduction differential equation is established in cylindrical coordinates. The mathematical expression of the transient heat conduction differential equation is: ; in, The transient temperature field distribution is represented by coordinates. and time The function, The density of the material as a function of temperature, in units of... , Thermal conductivity as a function of temperature, in units of , This is the corrected equivalent specific heat capacity, in units of... .

[0032] To address the latent heat of phase change generated during material melting, this embodiment does not directly use ordinary specific heat capacity, but instead employs the equivalent heat capacity method. That is, within the solid-liquid phase transition temperature range of the material (… to Within this range, the latent heat of phase change is superimposed on the specific heat capacity, and the mathematical expression for the corrected equivalent specific heat capacity is: ; in, The latent heat of fusion of the material, Solidus temperature This is the liquidus temperature.

[0033] Solving using a finite element solver (such as ANSYS or ABAQUS) specifically includes: Initial conditions: Set the initial temperature of the workpiece to room temperature. .

[0034] Loading process: The calculation in step S101 is performed... As a surface thermal load, the load is applied to the mesh nodes, and the load duration is equal to the input pulse width. .

[0035] Solution results: By iteratively solving the transient heat conduction differential equation in step S102, the transient temperature field distribution inside the workpiece at the end of the pulse width is obtained. .

[0036] The logic for extracting the etch size is as follows: Read the melting point of the workpiece material (For example, steel is approximately 1700K). Traverse the finite element mesh nodes and erode the radius of the pit. To be on the upper surface of the workpiece ( ), find the satisfying The maximum radial coordinate value.

[0037] Depth of erosion pits For the discharge center axis ( ), find the satisfying The maximum axial depth coordinate value.

[0038] This invention addresses the problem of inaccurate etch-out size calculations caused by neglecting the nonlinear changes in high-temperature thermal properties of materials and the endothermic effect of phase transition in existing EDM simulation models. It introduces a latent heat parameter of phase transition to correct the equivalent specific heat capacity. By combining the Gaussian heat flux density distribution function with a nonlinear data table of material properties, a transient heat conduction differential equation is established. A finite element solver accurately analyzes the transient temperature field distribution inside the workpiece, realistically reproducing the energy transfer and phase transition process at the moment of discharge. By locking node regions with temperatures higher than the melting point of the workpiece material, the radius and depth of the etch-out pits are directly extracted. This solves the problem of large prediction deviations in traditional simplified models under extreme thermal loads, providing rigorously physical benchmark data for subsequent KAN proxy models.

[0039] In a specific embodiment, step S2 includes the following sub-steps: Step S201: Based on the radius and depth of the etched pit, the etched pit generated by a single discharge is equivalent to a spherical cap geometry. A spherical cap geometric analytical model is established, and the single-pulse material removal volume under single-discharge conditions is calculated according to the spherical cap geometric analytical model. The mathematical expression for the single-pulse material removal volume is: ; in, The volume removed from the material in a single pulse, in units of , To remove the radius of the pit, To remove the depth of the pit.

[0040] Step S202: Obtain the effective discharge frequency under the current open circuit voltage, charging capacitor and pulse width parameters, multiply the single-pulse material removal volume by the effective discharge frequency, calculate the total volume removal amount per unit time, and obtain the theoretical material removal rate.

[0041] Step S203: Introduce an overlap factor that characterizes the degree of spatial stacking of adjacent etched pits, establish a mapping function between surface roughness and etched pit depth, substitute the etched pit depth into the mapping function and correct it using the overlap factor, and calculate the theoretical surface roughness.

[0042] In this embodiment, the logic for obtaining the theoretical material removal rate is as follows: To translate the microscopic volume of a single pulse into macroscopic removal efficiency, the effective number of discharges per unit time must be determined. Although the input layer parameters only include pulse width... However, in the actual control logic of the EDM power supply, pulse width and pulse interval... Typically, a specific duty cycle relationship is maintained, or the pulse interval is a function of the pulse width.

[0043] This embodiment sets the duty cycle. For a fixed value (e.g.) Then, a single discharge cycle Meanwhile, considering that not all pulses can successfully form a discharge channel during the processing, such as short circuits, open circuits, or arcs, an effective discharge rate coefficient is introduced. , Typically, it is taken as 0.8. Therefore, the effective discharge frequency is... The mathematical expression is: ; in, For the effective discharge frequency, The input pulse width, Duty cycle, This is the effective discharge rate coefficient.

[0044] Based on the single-pulse material removal volume and the effective discharge frequency, the theoretical material removal rate can be expressed mathematically as follows: ; in, Theoretical material removal rate, in units of The theoretical material removal rate is used as a physical baseline value for subsequent calculations of the MRR error term in the KAN model output.

[0045] The logic for obtaining the theoretical surface roughness is as follows: Surface roughness depends on the depth of the discharge pits and the stacking of adjacent pits. This embodiment constructs a nonlinear mapping function based on pit depth and introduces an overlap rate factor for correction. Overlap rate factor In continuous discharge machining (CDM), new discharge pits will partially cover older pits. The overlap factor characterizes the degree of overlap between pits, and its value ranges from [value missing]. . The value is related to the servo feed speed and discharge frequency. In the trend analysis of this embodiment, it is set to... Based on the radius of the etched pit The empirical function, the mathematical expression for the overlap factor, is: ; in, This represents the average discharge step distance.

[0046] In this embodiment, a fixed empirical value can be used. .

[0047] Theoretically, surface roughness is related to the depth of the etched pits. Proportional. For an ideal, continuously overlapping surface of spherical cap-shaped pits, the mathematical expression for the theoretical surface roughness is: ; in, For theoretical surface roughness, The depth of the etched pit is expressed in units of . , Let be a geometric shape constant. For a spherical cap geometry, take . That is, the roughness is about 1 / 3 of the pit depth. This is an overlap correction term, used to characterize the effect of overlap reducing the height difference between surface wave peaks and troughs. In this embodiment, an exponent is set. This is to reflect the nonlinear characteristics.

[0048] This invention addresses the problems in existing technologies where single-pulse thermal field simulation data is difficult to directly quantify macroscopic processing efficiency, and multi-pulse continuous erosion simulation involves complex dynamic mesh reconstruction leading to low computational efficiency. By constructing a spherical cap geometric analytical model, the radius and depth of the microscopic erosion pits are equivalent to a spherical cap geometry to calculate the single-pulse material removal volume. Combined with the effective discharge frequency, the theoretical material removal rate is quickly derived. Considering the formation mechanism of surface morphology, an overlap rate factor characterizing the spatial stacking degree of adjacent erosion pits is introduced to establish a mapping function to correct the theoretical surface roughness. This cleverly avoids the cumbersome geometric simulation and mesh reconstruction process, achieving the effect of rapidly and accurately analyzing macroscopic processing quality indicators based solely on the physical characteristics of a single pulse.

[0049] In a specific embodiment, step S3 includes the following sub-steps: Step S301: Initialize the architecture of the KAN network. The architecture of the KAN network includes an input layer, an intermediate hidden layer and an output layer. The input layer is set to include three neurons, which correspond to the open circuit voltage, the charging capacitance and the pulse width respectively. The output layer is set to include two neurons, which correspond to the material removal rate and the surface roughness respectively. An intermediate hidden layer of a predetermined number of layers is set between the input layer and the output layer.

[0050] KAN is a novel neural network architecture based on the Kolmogorov-Arnold representation theorem. Unlike traditional multilayer perceptrons (MLPs), KAN does not fix the activation function on the nodes, but instead places it on the network connection edges. Traditional neural networks (MLPs) use fixed activation functions, such as ReLU and Sigmoid. When fitting highly nonlinear and high-dimensional physical processes like electrical discharge machining (EDM), they often require extremely deep network layers, resulting in a large number of parameters and a lack of interpretability. The core advantage of KAN lies in the fact that the activation function on the edge defines each connection edge as a learnable B-spline function, meaning the network can adaptively learn the complex nonlinear curve relationship between process parameters (voltage, pulse width) and machining quality. The calculation between layers is no longer a simple linear weighting, but a superposition of univariate nonlinear functions. This allows KAN to achieve higher fitting accuracy than MLPs with very few parameters, making it very suitable for scenarios like this one where sample acquisition costs are high.

[0051] Step S302: For each connection edge between adjacent neurons in the KAN network, define a parameterized univariate function. As the activation function, the activation function is a linear combination of a residual basis function and a B-spline function, where the control point coefficients of the B-spline function serve as learnable parameters during the training process of the KAN network.

[0052] Step S303: Set the input value of one of the back layer neurons in the KAN network to be equal to the sum of the output values ​​of all the front layer neurons connected to one of the back layer neurons after being transformed by the activation function on the connection edge. By superimposing a preset number of univariate functions, a multivariate nonlinear function between process parameters and processing quality is obtained.

[0053] In this embodiment, the learnable spline activation function located on the connection edge of the KAN network is a univariate function. The mathematical expression for a single-variable function is: ; in, The output value of the front layer neurons. As the basis function weights, The weights of the spline function and the weights are both used as learnable parameters of the KAN network. For the residual basis functions, the SiLU function is preferably used in this embodiment. The mathematical expression is: ; The SiLU function is mainly used to preserve the nonlinear characteristics of the input signal and prevent gradient vanishing.

[0054] It is a B-spline function used to capture local nonlinear variations. The mathematical expression is: ; in, For learnable control point coefficients, It is a B-spline basis defined based on a preset grid.

[0055] To ensure the model's ability to fit the complex nonlinear laws of electrical discharge machining while also considering computational efficiency, the B-spline is set to order 3 in this embodiment to ensure the smoothness of the curve (second-order continuous differentiability). The initial number of B-spline grids is set to 5 to 10. As training progresses, a grid refinement strategy can be used to gradually increase the grid density to improve accuracy.

[0056] This invention addresses the problem that traditional neural network models, which use fixed activation functions for nodes, struggle to accurately represent the strong nonlinear coupling relationships between multidimensional parameters in electrical discharge machining (EDM). By employing a KAN network architecture, open-circuit voltage, charging capacitance, and pulse width are mapped to the input layer. This eliminates nonlinear transformations at nodes and instead defines a parameterized univariate function—a linear combination of residual basis functions and B-spline functions—as the activation function on each connection edge between neurons in adjacent layers. The control point coefficients of the B-spline function are set as learnable parameters. Utilizing the superposition principle of univariate functions, by accumulating the output values ​​of previous neurons after transformation by the activation functions on the connection edges, the complex multivariate nonlinear function between process parameters and machining quality can be accurately fitted with a more flexible topology, significantly improving the model's ability to express and predict the evolution of machining quality.

[0057] In a specific embodiment, step S4 includes the following sub-steps: Step S401: Construct a KAN surrogate model based on the KAN network architecture, initialize the control point coefficients of the B-spline function in the KAN surrogate model, generate process parameter combinations using a Latin hypercube sampling strategy within the preset process parameter value range, input the process parameter combinations into the KAN surrogate model, and output the corresponding predicted values ​​through the KAN network hierarchy. The predicted values ​​include the predicted material removal rate and the predicted surface roughness.

[0058] Step S402: For the same batch of process parameter combinations, execute steps S101 to S103 to calculate the radius and depth of the etched pits corresponding to the same batch of process parameter combinations. Based on the radius and depth of the etched pits corresponding to the same batch of process parameter combinations, execute steps S201 to S203 to calculate the theoretical material removal rate and theoretical surface roughness corresponding to the same batch of process parameter combinations. Use the theoretical material removal rate and theoretical surface roughness corresponding to the same batch of process parameter combinations as physical reference values.

[0059] The predicted values ​​and physical baseline values ​​are normalized respectively, and weight coefficients are assigned according to the preset attention to construct a comprehensive weighted loss function. The comprehensive weighted loss function includes a material removal rate error term and a surface roughness error term.

[0060] In this embodiment, the construction process of the comprehensive weighted loss function specifically includes two steps: normalization and weighted summation, to eliminate the numerical differences between material removal rate and surface roughness caused by different dimensions. The first step is data normalization, because... Usually in Magnitude Usually in Due to the large magnitude and wide numerical range, direct calculation errors could cause the model to be biased towards large numerical indicators. Therefore, the Min-Max normalization method is used to process the predicted values ​​and physical baseline values ​​of the KAN surrogate model separately. By utilizing the statistical extreme values ​​in the current batch or global parameter space, the material removal rate and surface roughness are uniformly mapped to the numerical range of 0 to 1, resulting in normalized predicted values ​​and normalized physical baseline values, thus eliminating the influence of dimensional differences on the model training weights.

[0061] The second step is to perform a weighted summation. The mathematical expression for the comprehensive weighted loss function is: ; in, To calculate the overall weighted loss function value, This represents the number of samples in the current training batch. and The first The predicted material removal rate after normalization for each sample and the physical baseline material removal rate and The first The normalized predicted surface roughness of each sample compared to the physical reference surface roughness. This is the weighting coefficient for material removal rate. This is the surface roughness weighting coefficient.

[0062] If the processing objective prioritizes efficiency, i.e., in a rough processing scenario, then set... .

[0063] If the processing objective prioritizes quality, i.e., a finishing process scenario, then set... .

[0064] In general trend analysis, for the sake of balance, a setting is usually made. By minimizing the above The loss function with respect to the B-spline control point coefficients is calculated using the backpropagation algorithm. The gradient drives the KAN surrogate model to continuously approximate the processing rules established by the physical model.

[0065] Step S403: Calculate the gradient of the comprehensive weighted loss function with respect to the coefficients of the B-spline control points in the KAN network, and adjust and update the learnable parameters using the backpropagation algorithm.

[0066] Determine whether the current comprehensive weighted loss function value is less than the preset convergence threshold. If the comprehensive weighted loss function value is greater than or equal to the preset convergence threshold, it is determined that the KAN surrogate model has not converged. Return to step S401 to regenerate the next batch of process parameter combinations and repeat the iterative training.

[0067] If the overall weighted loss function value is less than the preset convergence threshold, the KAN surrogate model is determined to have converged, training ends, and the converged KAN surrogate model is output.

[0068] Preset convergence threshold During the backpropagation iteration process, when the calculated current loss function value is less than the preset convergence threshold, it is determined that the KAN surrogate model has converged and can accurately replace the physical model for prediction.

[0069] This invention addresses the problem of existing offline prediction methods requiring the pre-construction of massive physical simulation sample sets, resulting in extremely high computational costs and uneven sample distribution. It constructs a physics-driven online evolutionary training framework for the KAN surrogate model, employing a Latin hypercube sampling strategy to efficiently generate process parameter combinations within a preset range of process parameter values. The predicted values ​​output by the KAN network layers are compared with the physical baseline values ​​obtained in real-time through steps S1 and S2. By constructing a comprehensive weighted loss function including material removal rate error and surface roughness error terms, the backpropagation algorithm is used to precisely adjust the control point coefficients of the B-spline function. Based on the preset convergence threshold, the system dynamically determines whether to regenerate the next batch of process parameter combinations and repeat iterative training. This breaks the traditional static mode of full simulation followed by training, achieving a closed-loop interaction between physical simulation and model training, and driving the surrogate model to converge rapidly with minimal physical computational cost.

[0070] In a specific embodiment, step S5 includes the following sub-steps: Step S501: Within the feasible range of open-circuit voltage, charging capacitance, and pulse width, preset the discrete step length and construct a high-density grid matrix covering the entire parameter space.

[0071] Each set of parameters in the high-density grid matrix is ​​input into the converged KAN surrogate model, and the corresponding global material removal rate prediction and global surface roughness prediction are calculated and output in batches.

[0072] Step S502: Using process parameters as independent variable coordinates and material removal rate and surface roughness as dependent variable coordinates, the discrete points of the global prediction are fitted into a continuous and smooth multidimensional response surface using an interpolation algorithm.

[0073] The gradient vectors at each point on the multidimensional response surface are calculated, and the sensitivity and monotonicity of the influence of changes in various process parameters on the processing quality index are analyzed, revealing the nonlinear dynamic evolution law of processing quality with changes in process parameters.

[0074] Step S503: The upper limit threshold of surface roughness and the lower limit threshold of material removal rate are preset as constraints. Region clipping and screening are performed on the multidimensional response surface to retain the remaining feasible regions that meet the constraints.

[0075] The upper limit threshold for surface roughness is the maximum allowable roughness value determined based on the accuracy requirements of the workpiece design drawings. For example, it can be set to 0.8 during the finishing stage. Up to 1.6 During region trimming, any combination of process parameters whose predicted surface roughness by the KAN surrogate model exceeds the upper limit threshold for surface roughness will be directly discarded to ensure that the final processing quality meets the standards.

[0076] The lower limit threshold for material removal rate is the minimum allowable processing efficiency set based on production cycle and processing cost requirements. For example, it can be set to 20% in the rough processing stage. During region trimming, any combination of process parameters whose predicted material removal rate is less than the lower limit threshold of the material removal rate by the KAN surrogate model will be eliminated to prevent excessively low processing efficiency due to improper parameter selection.

[0077] Using the predicted values ​​of global material removal rate and global surface roughness within the remaining feasible region, a comprehensive evaluation function for processing quality is constructed through normalized weighted summation.

[0078] Search for the extreme points of the comprehensive evaluation function of processing quality within the remaining feasible region, and take the range of process parameters corresponding to the extreme points as the preferred process parameter range.

[0079] This invention addresses the problems of existing technologies, which suffer from excessive computational load, making it impossible to complete full parameter space traversal, obtain global quality evolution trends, and achieve multi-objective collaborative optimization. It utilizes a convergent KAN surrogate model to replace the physical solver, performing batch calculations on high-density grid matrices of open-circuit voltage, charging capacitance, and pulse width. This generates predicted values ​​for global material removal rate and global surface roughness, and fits a multi-dimensional response surface. By calculating gradient vectors, it intuitively reveals the nonlinear dynamic evolution law, sensitivity, and monotonicity of processing quality as a function of process parameters. By setting upper and lower thresholds for surface roughness and material removal rate as constraints, it performs region clipping and screening. Within the remaining feasible region, it searches for extreme points based on a comprehensive processing quality evaluation function constructed using normalized weighted summation. This efficiently solves the problem of determining the optimal process parameter range under multi-objective conflicts.

[0080] Example 2, refer to Figure 2 This paper presents an electrical discharge machining quality trend analysis system, which includes a simulation module, a solution module, a construction module, a training module, and an analysis module.

[0081] The simulation module is used to construct the Gaussian heat flux density distribution function as the thermal boundary condition, establish the transient heat conduction differential equation, use the finite element solver to solve the transient temperature field distribution inside the workpiece, and extract the radius and depth of the etched pit based on the melting point of the workpiece material.

[0082] The calculation module is used to establish a geometric analytical model of the spherical cap based on the radius and depth of the etch pit and to calculate the single-pulse material removal volume. It also combines the effective discharge frequency to calculate the theoretical material removal rate and theoretical surface roughness.

[0083] The building module is used to initialize the architecture of the KAN network, mapping open-circuit voltage, charging capacitance, and pulse width to the input layer, and mapping material removal rate and surface roughness to the output layer. It defines parameterized univariate functions on the network connection edges as activation functions, and uses the superposition of univariate functions to obtain the multivariate nonlinear function between process parameters and processing quality.

[0084] The training module is used to build a KAN proxy model based on the KAN network architecture, initialize the KAN proxy model, generate process parameter combinations and output predicted values. For the same batch of process parameter combinations, steps S1 and S2 are executed to calculate the physical baseline values, construct a comprehensive weighted loss function, use the backpropagation algorithm to adjust and update the learnable parameters, and repeat iterative training until the KAN proxy model converges.

[0085] The analysis module is used to perform gridded traversal calculations on the preset full process parameter space based on the convergent KAN surrogate model, generate multidimensional response surfaces, construct a comprehensive evaluation function for processing quality within the remaining feasible regions that meet the constraints, and obtain the optimal process parameter range based on the extreme points of the comprehensive evaluation function for processing quality.

[0086] This invention ensures the physical realism of microscopic analysis through a simulation module using the Gaussian heat flux density distribution function and transient heat conduction differential equations. A solution module obtains theoretical indices based on a spherical cap geometric analytical model. A construction module builds a KAN network architecture with parameterized single-variable functions. A training module executes a backpropagation algorithm driven by physical benchmarks for updating and iteration. Finally, an analysis module locks in the optimal process parameter range based on a multidimensional response surface and a comprehensive evaluation function of processing quality. This achieves modular integration and full-process automation from microscopic physical simulation to macroscopic process optimization, significantly improving the intelligence level and engineering practicality of trend analysis while ensuring analytical accuracy.

[0087] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0088] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the protection scope of the present invention.

Claims

1. A method for analyzing the quality trend of electrical discharge machining, characterized in that, Includes the following steps: Step S1: Construct a Gaussian heat flux density distribution function as a thermal boundary condition, establish a transient heat conduction differential equation, solve for the transient temperature field distribution inside the workpiece, and extract the radius and depth of the etched pit based on the melting point of the workpiece material. Step S2: Based on the radius and depth of the etched pit, establish a geometric analytical model of the spherical cap and calculate the single-pulse material removal volume. Combine the effective discharge frequency to calculate the theoretical material removal rate and theoretical surface roughness. Step S3: Initialize the architecture of the KAN network, map the open-circuit voltage, charging capacitance, and pulse width to the input layer, map the material removal rate and surface roughness to the output layer, and define the activation function; Step S4: Based on the KAN network architecture, initialize the KAN surrogate model, generate process parameter combinations and output predicted values. Perform steps S1 and S2 on the same batch of process parameter combinations to obtain physical baseline values, construct a comprehensive weighted loss function, adjust and update the learnable parameters, and repeat iterative training until the KAN surrogate model converges. Step S5: Perform gridded traversal calculations based on the convergent KAN surrogate model to generate a multidimensional response surface. Construct a comprehensive evaluation function for processing quality within the remaining feasible regions that satisfy the constraints. Obtain the optimal process parameter range based on the extreme points of the comprehensive evaluation function for processing quality.

2. The method for analyzing the quality trend of electrical discharge machining as described in claim 1, characterized in that, Step S1 includes the following sub-steps: Step S101: Set the heat flux density in the discharge channel to follow a Gaussian distribution in the radial direction. Calculate the peak heat flux density of the discharge channel based on the preset energy distribution coefficient, discharge voltage, and discharge current. Combine this with the preset energy distribution radius to construct a Gaussian heat flux density distribution function. Use the Gaussian heat flux density distribution function as the thermal boundary condition applied to the workpiece surface. Step S102: Import the nonlinear data table of thermal conductivity, specific heat capacity and density of the workpiece material as a function of temperature, introduce the latent heat of phase change parameters during the melting and vaporization process of the material to correct the equivalent specific heat capacity, and establish the transient heat conduction differential equation, which includes temperature gradient term, material density term, specific heat capacity term and thermal conductivity term. Step S103: Discretize the workpiece model into a mesh using a finite element solver, apply the Gaussian heat flux density distribution function as a heat load to the mesh nodes, use a preset pulse width as the heat load application time, solve the transient heat conduction differential equation, and obtain the transient temperature field distribution inside the workpiece. In the transient temperature field distribution, the node regions with temperatures higher than the melting point of the workpiece material are locked. The maximum span of the node region in the radial direction is extracted as the radius of the etch pit, and the maximum coordinate value of the node region in the axial depth direction is extracted as the depth of the etch pit.

3. The method for analyzing the quality trend of electrical discharge machining as described in claim 2, characterized in that, Step S2 includes the following sub-steps: Step S201: Based on the radius and depth of the etched pit, the etched pit generated by a single discharge is equivalent to a spherical cap geometry, and a spherical cap geometric analytical model is established. The single-pulse material removal volume under single-discharge conditions is calculated based on the spherical cap geometric analytical model. The mathematical expression for the single-pulse material removal volume is: ； in, Remove volume for single-pulse materials. To remove the radius of the pit, To remove the depth of the pit.

4. The method for analyzing the quality trend of electrical discharge machining as described in claim 3, characterized in that, Step S2 further includes the following sub-steps: Step S202: Obtain the effective discharge frequency under the current open circuit voltage, charging capacitor and pulse width parameters, multiply the single-pulse material removal volume by the effective discharge frequency, calculate the total volume removal amount per unit time, and obtain the theoretical material removal rate. Step S203: Introduce an overlap factor that characterizes the degree of spatial stacking of adjacent etched pits, establish a mapping function between surface roughness and etched pit depth, substitute the etched pit depth into the mapping function and correct it using the overlap factor, and calculate the theoretical surface roughness.

5. The method for analyzing the quality trend of electrical discharge machining as described in claim 4, characterized in that, Step S3 includes the following sub-steps: Step S301: Initialize the architecture of the KAN network. The architecture of the KAN network includes an input layer, an intermediate hidden layer and an output layer. The input layer is set to include three neurons, which correspond to the open circuit voltage, the charging capacitance and the pulse width respectively. The output layer is set to include two neurons, which correspond to the material removal rate and the surface roughness respectively. An intermediate hidden layer of a predetermined number of layers is set between the input layer and the output layer. Step S302: For each connection edge between adjacent neurons in the KAN network, a parameterized univariate function is defined as the activation function. The activation function is a linear combination of a residual basis function and a B-spline function, wherein the control point coefficients of the B-spline function are learned parameters during the training process of the KAN network. Step S303: Set the input value of one of the back layer neurons in the KAN network to be equal to the sum of the output values ​​of all the front layer neurons connected to the one of the back layer neurons after being transformed by the activation function on the connection edge. By superimposing a preset number of univariate functions, a multivariate nonlinear function between process parameters and processing quality is obtained.

6. The method for analyzing the quality trend of electrical discharge machining as described in claim 5, characterized in that, Step S4 includes the following sub-steps: Step S401: Construct a KAN proxy model based on the KAN network architecture, initialize the control point coefficients of the B-spline function in the KAN proxy model, generate process parameter combinations using a Latin hypercube sampling strategy within the preset process parameter value range, input the process parameter combinations into the KAN proxy model, and output the corresponding predicted values ​​through KAN network hierarchy. The predicted values ​​include predicted material removal rate and predicted surface roughness.

7. The method for analyzing the quality trend of electrical discharge machining as described in claim 6, characterized in that, Step S4 further includes the following sub-steps: Step S402: For the same batch of process parameter combinations, execute step S1 to calculate the radius and depth of the etched pits corresponding to the same batch of process parameter combinations. Based on the radius and depth of the etched pits corresponding to the same batch of process parameter combinations, execute step S2 to calculate the theoretical material removal rate and theoretical surface roughness corresponding to the same batch of process parameter combinations. Use the theoretical material removal rate and theoretical surface roughness corresponding to the same batch of process parameter combinations as physical reference values. The predicted values ​​and physical reference values ​​are normalized respectively, and weight coefficients are assigned according to the preset attention to construct a comprehensive weighted loss function, which includes a material removal rate error term and a surface roughness error term. Step S403: Calculate the gradient of the integrated weighted loss function with respect to the B-spline control point coefficients in the KAN network, and adjust and update the learnable parameters using the backpropagation algorithm; Determine whether the current comprehensive weighted loss function value is less than the preset convergence threshold. If the comprehensive weighted loss function value is greater than or equal to the preset convergence threshold, it is determined that the KAN surrogate model has not converged. Return to step S401 to regenerate the next batch of process parameter combinations and repeat the iterative training. If the overall weighted loss function value is less than the preset convergence threshold, the KAN surrogate model is determined to have converged, training ends, and the converged KAN surrogate model is output.

8. The method for analyzing the quality trend of electrical discharge machining as described in claim 7, characterized in that, Step S5 includes the following sub-steps: Step S501: Within the feasible range of open-circuit voltage, charging capacitance, and pulse width, preset the discrete step length and construct a high-density grid matrix covering the entire parameter space. Each set of parameters in the high-density grid matrix is ​​input into the converged KAN surrogate model to calculate and output the corresponding global material removal rate prediction value and global surface roughness prediction value in batches. Step S502: Using process parameters as independent variable coordinates and material removal rate and surface roughness as dependent variable coordinates, the discrete points of the global prediction are fitted into a continuous and smooth multidimensional response surface using an interpolation algorithm. The gradient vectors at each point on the multidimensional response surface are calculated, and the sensitivity and monotonicity of the influence of changes in various process parameters on the processing quality index are analyzed, revealing the nonlinear dynamic evolution law of processing quality with changes in process parameters.

9. The method for analyzing the quality trend of electrical discharge machining as described in claim 8, characterized in that, Step S5 further includes the following sub-steps: Step S503: The upper limit threshold of surface roughness and the lower limit threshold of material removal rate are preset as constraints. Region clipping and screening are performed on the multidimensional response surface to retain the remaining feasible regions that meet the constraints. Using the predicted values ​​of global material removal rate and global surface roughness in the remaining feasible region, a comprehensive evaluation function of processing quality is constructed by normalized weighted summation. Search for the extreme points of the comprehensive evaluation function of processing quality within the remaining feasible region, and take the range of process parameters corresponding to the extreme points as the preferred process parameter range.

10. An electrical discharge machining (EDM) quality trend analysis system, applied in an EDM quality trend analysis method as described in any one of claims 1-9, characterized in that, It includes a simulation module, a solution module, a construction module, a training module, and an analysis module; The simulation module is used to construct a Gaussian heat flux density distribution function as a thermal boundary condition, establish a transient heat conduction differential equation, use a finite element solver to solve the transient temperature field distribution inside the workpiece, and extract the radius and depth of the etched pit based on the melting point of the workpiece material. The calculation module is used to establish a spherical cap geometric analytical model based on the radius and depth of the etched pit and to calculate the single-pulse material removal volume. It also calculates the theoretical material removal rate and theoretical surface roughness by combining the effective discharge frequency. The construction module is used to initialize the architecture of the KAN network, map open-circuit voltage, charging capacitance and pulse width to the input layer, map material removal rate and surface roughness to the output layer, define parameterized univariate functions on the network connection edges as activation functions, and use the superposition of univariate functions to obtain the multivariate nonlinear function between process parameters and processing quality. The training module is used to construct a KAN proxy model based on the KAN network architecture, initialize the KAN proxy model, generate process parameter combinations and output predicted values. For the same batch of process parameter combinations, steps S1 and S2 are executed to calculate the physical baseline value, construct a comprehensive weighted loss function, use the backpropagation algorithm to adjust and update the learnable parameters, and repeat iterative training until the KAN proxy model converges. The analysis module is used to perform gridded traversal calculations on the preset full process parameter space based on the convergent KAN surrogate model, generate a multidimensional response surface, construct a comprehensive evaluation function for processing quality within the remaining feasible region that meets the constraints, and obtain the optimal process parameter range based on the extreme points of the comprehensive evaluation function for processing quality.

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