A QT500-5 nodular cast iron surface laser hardening explainability process parameter optimization method

Abstract

The application discloses a QT500-5 nodular cast iron surface laser hardening explainable process parameter optimization method, including the following steps: constructing a finite element heat transfer model, screening a preliminary process parameter range; LHS sampling and testing are carried out in the range, and a data set is constructed; the data set is used to train an MTNN model, a BO algorithm is used for optimization, a BO-MTNN prediction model is constructed, and PCC and SHAP methods are introduced to reveal the action mechanism; a MOHOA algorithm is used for multi-objective optimization, a Pareto solution set is obtained, an EWM and TOPSIS combined decision method is used for multi-index comprehensive evaluation and sorting of the solution set, and an optimal process parameter combination is obtained by optimization; the optimal process parameter combination is verified by actual laser hardening test. The whole scheme has physical accuracy, high efficiency of prediction, multi-objective balance and decision objectivity, greatly reduces the simulation cost, improves the optimization efficiency, and can stably obtain the optimal laser process parameters considering the hardening effect and the melting control.

Description

Technical Field

[0001] This invention relates to the field of laser hardening processing technology, specifically to an interpretable process parameter optimization method for laser hardening of QT500-5 ductile iron surface. Background Technology

[0002] Ductile iron, due to its excellent casting properties and cost advantages, is widely used in key components such as large stamping dies. However, its insufficient surface hardness makes it prone to wear, deformation, and even cracking during service, affecting the die's lifespan and precision. While traditional integral heat treatment can improve hardness, it has limitations such as high energy consumption, difficulty in deformation control, and inability to selectively strengthen, making it difficult to meet the demands of precision dies for localized high performance and low cost. In contrast, laser surface strengthening technology has significant advantages. By precisely applying a high-energy laser beam to the die cavity surface, it can achieve localized phase transformation hardening or solidification strengthening, improving surface properties without affecting the matrix. Its non-contact, high-precision, and flexible characteristics are particularly suitable for localized strengthening of complex cavities, providing an efficient and economical solution for improving the surface properties of ductile iron dies.

[0003] Currently, laser surface hardening technology for molds and mechanical parts has been extensively studied. This technology can achieve martensitic phase transformation and microstructure refinement on the material surface through precise control of process parameters, significantly improving hardness and wear resistance. The surface hardness of some materials can reach 3-6 times that of the substrate. Research shows that process parameters need to be precisely matched within a narrow window, and optimization of the scanning strategy can further improve performance. This technology also exhibits good local selective strengthening capabilities. However, current research still focuses on qualitative analysis of process-performance, and an interpretable, high-precision quantitative mapping model has not yet been constructed. Furthermore, there is a lack of an intelligent process design system that integrates physical modeling, data-driven approaches, and multi-objective optimization, limiting the development of this technology towards precision and efficiency. Summary of the Invention

[0004] To address the above technical problems, this invention provides an interpretable process parameter optimization method for laser hardening of QT500-5 ductile iron surface.

[0005] The technical solution is as follows:

[0006] A method for optimizing interpretable process parameters for laser hardening of QT500-5 ductile iron surface, the key points of which include the following steps:

[0007] S1: Construct a finite element heat transfer model for phase change heat transfer during laser hardening on the surface of QT500-5 ductile iron, and use this model to screen out the preliminary range of laser hardening process parameters;

[0008] S2: Within the initial process parameter range, the Latin hypercube sampling method (LHS) is used for sampling and experimentation to construct a dataset containing "process parameters – response target".

[0009] S3: Based on the dataset, construct a multi-task neural network (MTNN) prediction model, and use the Bayesian optimization (BO) algorithm to optimize the MTNN model, thus establishing a Bayesian optimized multi-task neural network fusion prediction model BO-MTNN.

[0010] Meanwhile, Pearson correlation coefficient (PCC) and Shapley additive interpretation (SHAP) methods are introduced to reveal the mechanism and contribution of process parameters to the response target;

[0011] S4: The multi-objective Hippo Optimization Algorithm (MOHOA) is adopted, and the BO-MTNN model is used as a fast evaluator to perform multi-objective optimization on the process parameter space to obtain the Pareto solution set;

[0012] S5: A decision-making method combining entropy weight method (EWM) and TOPSIS is adopted to establish a comprehensive evaluation system, and the Pareto solution set is evaluated and ranked by multiple indicators to obtain the optimal combination of process parameters.

[0013] S6: Conduct actual laser hardening experiments to verify the optimal combination of process parameters, compare the experimental results with the model predictions, and verify the accuracy of the prediction model and the effectiveness of the optimization scheme.

[0014] Preferably, in step S1, the depth of the fused layer h and the depth of the hardened layer H are used as response targets, and the laser power P, scanning speed V, and overlap rate δ are used as experimental factors to construct a finite element heat transfer model.

[0015] The preliminary process parameters selected by the finite element heat transfer model are P∈[100-500] W, V∈[5-15] mm / s, δ∈[60-90] %.

[0016] Preferably, the finite element heat transfer model only considers the temperature field and the metal phase transition field when it is constructed. By meshing and verifying convergence, the temperature field and phase transition results of different process parameters are simulated and calculated based on the model, and a reasonable range of process parameters is selected.

[0017] The temperature field is controlled by the solid heat transfer module of COMSOL Multiphysics software, and its control equations are as follows:

[0018]

[0019]

[0020] In the formula, ρ is the material density. ; Equivalent specific heat capacity v is the fluid velocity. t represents time (s); Where is the heat flux divergence; Q is the external heat source. k is the thermal conductivity. ; Temperature gradient q is the heat flux density vector. ;

[0021] The equivalent specific heat capacity is determined by the properties of QT500-5 ductile iron material, and its formula is as follows:

[0022]

[0023] In the formula, Specific heat capacity at constant pressure L represents latent heat. ;T L The liquidus temperature (K) of QT500-5, T S The solidus temperature (K) of QT500-5;

[0024] Simultaneously, boundary conditions were set, introducing three types of boundary thermal effects: laser heat source, convective heat transfer, and thermal radiation. The governing equations are as follows:

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, is a Gaussian laser heat source; R is the spot radius (m); x and y are spatial coordinates (m); , These are the functions of laser movement along the x and y directions, respectively; For generalized inward heat flux (W / m²); The laser absorption rate of QT500-5; The convective heat transfer flux is (W / m²). The convective heat transfer coefficient of QT500-5 ; Radiative heat transfer flux (W / m²); The emissivity of QT500-5; The ambient temperature (K); The external radiation temperature (K);

[0030] The metal phase transition field includes a heating process and a cooling process. The heating process is calculated using the Leblond-Devaux model in COMSOL, and the cooling process is calculated using the Koistinen-Marburger equation. The formulas are as follows:

[0031]

[0032]

[0033] In the formula, The generation rate from the source phase to the target phase; The volume fraction of the source phase consumed; The target phase volume fraction; and This is a temperature-dependent function;

[0034] Martensite phase fraction; T is the martensitic phase transformation initiation temperature; β is the Koistinen-Marburger coefficient, with a value of 0.011; T m This is the current temperature of the QT500-5.

[0035] Further mesh generation was performed to determine a mesh scheme that met the requirements of computational accuracy and efficiency, thus completing the construction of the finite element heat transfer model.

[0036] Preferably, in step S2, the Latin hypercube sampling method is used to sample within the initial process parameter range. After sampling, the finite element heat transfer model is used for simulation calculation to obtain the dataset of "process parameters - response target".

[0037] The dataset is scored and adjusted using applied course learning strategies to make it more regular. The scoring formula is as follows:

[0038]

[0039] In the formula, and These are the values ​​of h and H, respectively; and They are respectively and The weights are each set to 0.5; This is the weighted value.

[0040] Preferably, in step S3, the dataset after course learning is normalized using Min-Max, scaling the data to [0,1], as shown in the formula:

[0041]

[0042] In the formula, X is the normalized value, and X0 is the original data value. The minimum value of the original data. The maximum value of the original data;

[0043] Based on the normalized dataset, the mapping relationship between process parameters and response targets is learned, and the MTNN prediction model is trained. The trained MTNN prediction model is then fused with the BO algorithm to optimize the hyperparameters of the MTNN prediction model, forming the BO-MTNN fusion prediction model.

[0044] Preferably, the MTNN prediction model includes a backbone network and branch networks. The process parameters are input into the backbone network of the MTNN prediction model after Min-Max normalization. The general features of the process parameters are extracted, and then the general features are input into two independent branch networks. Through the exclusive mapping of the branch networks, the predicted values ​​of the molten layer depth h and the hardened layer depth H are output simultaneously.

[0045] The BO algorithm has 10 initial sampling points, 100 iterations, and uses the root mean square error as the fitness function.

[0046] Preferably, the PCC in step S3 is used to measure the strength and direction of the linear relationship between process parameters and the response target, and its formula is as follows:

[0047]

[0048] In the formula, Let x be the Pearson correlation coefficient between variables x and y. , Let x and y be the variable values ​​of the i-th x, y sample set. Let x be the mean of the sample. Let y be the mean of the sample y;

[0049] The SHAP method can fully explain the nonlinear patterns and feature interactions captured by machine learning models. The mean absolute SHAP value is the marginal contribution of a feature parameter to the model output, representing the offset of a feature value relative to the baseline prediction. Its formula is:

[0050]

[0051] In the formula, Let S be the SHAP value of the i-th feature, where S is a subset of the entire feature set N, excluding feature i. The total number of features is |N| = 3, and |S|!(|N|-|S|-1)! is the number of permutations in which feature i is added after subset S. The model's predicted value f(S) is obtained by using a subset S and adding feature i, and the model's predicted value is obtained by using only the features in the subset S.

[0052] Preferably, the objective function and constraints for multi-objective optimization in step S4 are as follows:

[0053]

[0054]

[0055] The MOHOA algorithm is used for multi-objective optimization. The MOHOA algorithm first uses a random sampling method to initialize the population. In the population iteration and update phase, random walk and elite guidance are used to improve the global exploration ability and convergence speed.

[0056] Secondly, the differential evolution mutation strategy is integrated to further perturb the hippo search, improving the distribution and convergence of the frontier solutions. The environment selection mechanism adopts an elite retention strategy for fast non-dominated sorting, dividing the merged population into multiple frontier levels and prioritizing the retention of high-level non-dominated solutions. When the number of solutions in the same level exceeds the population capacity, crowding distance calculation is introduced to select solutions with more uniform distribution to maintain the extensibility of the Pareto solution set frontier.

[0057] Preferably, the specific steps of the comprehensive evaluation system established by the decision-making method combining EWM and TOPSIS in step S5 are as follows:

[0058] S5.1 Establish the decision matrix and standard matrix;

[0059]

[0060]

[0061]

[0062] In the formula, the Pareto solution set constitutes the decision matrix. There are m sets of process parameter combinations to be decided, m=50, and n evaluation indicators, n=2; This is the matrix obtained through forward transformation; For standard matrices;

[0063] S5.2 Calculate the weight values ​​of each objective;

[0064]

[0065]

[0066] In the formula, This is the information entropy value; These are weight values;

[0067] S5.3 calculates the Euclidean distance and outputs a comprehensive score. The optimal combination of process parameters is selected based on the comprehensive score.

[0068]

[0069]

[0070]

[0071] In the formula, and Depend on It consists of the maximum and minimum values ​​of each column of elements; and Let be the distance between the i-th solution and the optimal and worst solutions; Rate it.

[0072] Preferably, the optimal process parameters are selected for verification, which includes actual laser testing, finite element heat transfer model simulation calculation, hardness testing before and after laser testing, microstructure characterization observation, reciprocating friction test, and fixed-point quantitative analysis by energy dispersive spectrometer.

[0073] Compared with existing technologies, the beneficial effects of this invention are as follows: This application establishes a finite element heat transfer model coupled with a temperature field and a phase transition field, constructs a Bayesian optimized multi-task neural network prediction model, and introduces the Shapley additive interpretation method to reveal the parameter contribution mechanism. Then, it achieves process parameter optimization and experimental verification through a multi-objective optimization algorithm. It not only provides an optimized parameter combination for laser hardening of QT550-5 ductile iron, but more importantly, it proposes and verifies the integrated research framework of "physical modeling-data-driven-optimization decision-making". It can combine physical accuracy, prediction efficiency, multi-objective balance and decision objectivity, greatly reduce simulation costs, improve optimization efficiency, and stably obtain the optimal laser process parameters that take into account both hardening effect and melting control. Attached Figure Description

[0074] Figure 1 This is a schematic diagram of the process of the present invention;

[0075] Figure 2 The graph shows the variation of thermophysical properties of QT500-5 ductile iron.

[0076] Figure 3 This is a diagram showing the grid distribution.

[0077] Figure 4 Cross-sectional views of the temperature field of different grids at the same time;

[0078] Figure 5 This is a finite element temperature field simulation diagram;

[0079] Figure 6 The figure shows the simulation results of the metal phase transformation field;

[0080] Figure 7 This is a cross-sectional view of the laser-hardened material.

[0081] Figure 8 A table of data sets;

[0082] Figure 9 The initial state of the dataset and the sorting state after course learning are shown in the diagram.

[0083] Figure 10 A comparison table of prediction model performance;

[0084] Figure 11 A heatmap of the Pearson correlation coefficients among the parameter variables;

[0085] Figure 12 A comparison chart ranking the importance scores of SHAP features;

[0086] Figure 13 Here is a flowchart of the MOHOA algorithm;

[0087] Figure 14 The Pareto solution set graph obtained by each optimization algorithm;

[0088] Figure 15 This is a cross-sectional view of the hardening test;

[0089] Figure 16 Validate the phase fraction of the model;

[0090] Figure 17 This is a comparison chart of cross-sectional hardness;

[0091] Figure 18 Microscopic images of the solidified and hardened layers after laser hardening;

[0092] Figure 19 Images of the substrate and wear marks after laser hardening;

[0093] Figure 20 This is a graph showing the results of the energy spectrum scan.

[0094] Figure 21 Microscopic images of different regions after laser hardening;

[0095] Figure 22 Table of EDS fixed-point and quantitative analysis results for each region. Detailed Implementation

[0096] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0097] like Figure 1As shown, an interpretable process parameter optimization method for laser hardening of QT500-5 ductile iron surface includes the following steps:

[0098] S1: Construct a finite element heat transfer model for phase change heat transfer during laser hardening on the surface of QT500-5 ductile iron, and use this model to screen out the preliminary range of laser hardening process parameters;

[0099] S2: Within the initial process parameter range, the Latin hypercube sampling method (LHS) is used for sampling and experimentation to construct a dataset containing "process parameters – response target".

[0100] S3: Based on the dataset, construct a multi-task neural network (MTNN) prediction model, and use the Bayesian optimization (BO) algorithm to optimize the hyperparameters of the MTNN model, and establish a Bayesian optimized multi-task neural network fusion prediction model BO-MTNN.

[0101] Meanwhile, Pearson correlation coefficient (PCC) and Shapley additive interpretation (SHAP) methods are introduced to reveal the mechanism and contribution of process parameters to the response target;

[0102] S4: The multi-objective Hippo Optimization Algorithm (MOHOA) is adopted, and the BO-MTNN model is used as a fast evaluator to perform multi-objective optimization on the process parameter space to obtain the Pareto solution set;

[0103] S5: A decision-making method combining entropy weight method (EWM) and TOPSIS is adopted to establish a comprehensive evaluation system, and the Pareto solution set is evaluated and ranked by multiple indicators to obtain the optimal combination of process parameters.

[0104] S6: Conduct actual laser hardening experiments to verify the optimal combination of process parameters, compare the experimental results with the model predictions, and verify the accuracy of the prediction model and the effectiveness of the optimization scheme.

[0105] Example

[0106] S1: Finite element heat transfer model construction to determine the preliminary process parameter range;

[0107] In laser hardening experiments, process parameters such as laser power P, scanning speed V, and overlap ratio δ significantly affect the thermal process of the material surface. Excessive P and insufficient V lead to excessive energy input, causing surface melting or evaporation and resulting in poor hardening. Conversely, insufficient P and excessive V result in insufficient heat input, leading to a shallow hardened layer. δ, by controlling the degree of overlap of the scanning trajectory, affects the laser hardening effect and efficiency. Therefore, this application uses the fused layer depth h and the hardened layer depth H as evaluation indicators, and P, V, and δ as experimental factors to establish a finite element heat transfer model for QT550-5 ductile iron, systematically studying the temperature field evolution and metal phase transformation behavior.

[0108] To simplify the model building process, and to ignore the errors caused by other uncontrollable factors, we only consider the temperature field and the metal phase transition field, and make the following six assumptions:

[0109] 1) The material is isotropic and homogeneous;

[0110] 2) Changes in thermophysical properties are only related to temperature;

[0111] 3) Oxidation processes are not considered during metal hardening;

[0112] 4) The absorption rate of the metal surface to the laser is set to a constant;

[0113] 5) The simulated object is a rectangular sample with limited dimensions and a uniform initial temperature field distribution;

[0114] 6) In the laser hardening process, only the melting of the metal is considered, the temperature of the molten pool is lower than the boiling point, and the evaporation of the metal and the generation of plasma are not considered.

[0115] The thermal properties of materials such as density, thermal conductivity, and specific heat capacity depend only on temperature. The thermal properties of QT550-5 ductile iron are as follows: Absorption rate... 0.56, emissivity 0.5, latent heat of fusion (L / ) Heat transfer coefficient / ;

[0116] The graph showing the variation of thermophysical properties of QT550-5 ductile iron is as follows: Figure 2 As shown, the temperatures of its solidus and liquidus are 1421 K and 1573 K, respectively, and its liquid fraction can be calculated using the following formula:

[0117]

[0118] In the formula, The liquid phase fraction; The liquidus temperature (K); T is the solidus temperature (K); T is the current temperature (K).

[0119] Considering the solid-state transformation and latent heat of fusion during continuous laser hardening, the equivalent specific heat capacity method is used for calculation:

[0120]

[0121] In the formula, Specific heat capacity at constant pressure L represents latent heat. ;T L The liquidus temperature (K) of QT500-5, T SThe solidus temperature (K) of QT500-5;

[0122] Based on the above assumptions, the temperature field is controlled by the solid heat transfer module of the COMSOL Multiphysics software, and its control equations are as follows:

[0123]

[0124]

[0125] In the formula, ρ is the material density. ; Equivalent specific heat capacity v is the fluid velocity. t represents time (s); Where is the heat flux divergence; Q is the external heat source. k is the thermal conductivity. ; Temperature gradient q is the heat flux density vector. ;

[0126] Boundary conditions were set, and preliminary crack prevention experiments were conducted. It was determined that QT500-5 ductile iron should be preheated to 473 K. This temperature aims to alleviate its low-temperature brittleness tendency, thereby suppressing the thermal stress and cracking risk induced by the high thermal gradient during rapid laser heating. This temperature selection balances material performance optimization and process feasibility. The ambient temperature and pressure were 293 K and 1.013 × 10⁵ Pa, respectively. Three types of boundary thermal effects were introduced: laser heat source, convective heat transfer, and thermal radiation. The laser heat source accurately simulates the spatial distribution and input method of laser energy, serving as the core boundary for "energy input" in the simulation. Convective heat transfer simulates heat dissipation between the material surface and the air, preventing overestimation of the temperature field. Radiation heat transfer compensates for thermal radiation losses at high temperatures, making the temperature field calculation more comprehensive and closer to real-world conditions. The governing equations are shown below:

[0127]

[0128]

[0129]

[0130]

[0131] In the formula, is a Gaussian laser heat source; R is the spot radius (m); x and y are spatial coordinates (m); , These are the functions of laser movement along the x and y directions, respectively; For generalized inward heat flux (W / m²); The laser absorption rate of QT500-5; The convective heat transfer flux is (W / m²). The convective heat transfer coefficient of QT500-5 ; Radiative heat transfer flux (W / m²); The emissivity of QT500-5; The ambient temperature (K); The external radiation temperature (K);

[0132] The laser hardening process of QT550 ductile iron mainly includes two stages: heating and cooling. In the initial state, the ductile iron matrix consists of ferrite, pearlite, and spheroidal graphite. Ferrite, pearlite, austenite, and ledeburite undergo diffusion-type phase transformations, and their phase fractions can be calculated using a concentration field and diffusion time interpolation function. Martensite undergoes a non-diffusion-type phase transformation, and its volume fraction is only temperature-dependent. During laser scanning, the material temperature rises to A... C1 After austenitization, the substrate is further heated to a molten state and then cooled, resulting in a eutectic reaction at 1421 K to form ledeburite. The phase fractions of austenite and ledeburite were calculated using the Leblond-Devaux model in COMSOL. The substrate was then cooled to the martensitic point M. S In the following cases, the austenite transforms into martensite, and the phase fraction is solved using the Koistinen-Marburger equation, with the following formulas:

[0133]

[0134]

[0135] In the formula, The generation rate from the source phase to the target phase; The volume fraction of the source phase consumed; The target phase volume fraction; and This is a temperature-dependent function;

[0136] Martensite phase fraction; T is the martensitic phase transformation initiation temperature; β is the Koistinen-Marburger coefficient, with a value of 0.011; T m This is the current temperature of the QT500-5.

[0137] Based on the assumptions of the finite element model, a geometric model with dimensions of 15 mm × 8 mm × 1 mm was constructed within the software. To balance simulation accuracy, computational efficiency, and convergence, the mesh of the constructed geometric model was customized. The mesh size distribution is as follows. Figure 3 As shown, the partitions are M1, M2, and M3 respectively. The results of the grid independence verification are as follows:

[0138] The maximum element size of M1 is 0.18 mm, the minimum element size is 0.004 mm, the maximum element growth rate is 1.3, the resolution in narrow regions is 0.85, h is 225 μm, H is 495 μm, and t is 18108 s.

[0139] The maximum cell size of M2 is 0.2 mm, the minimum cell size is 0.01 mm, the maximum cell growth rate is 1.35, the resolution in narrow regions is 0.9, h is 215 μm, H is 510 μm, and t is 10296 s.

[0140] The maximum element size of M3 is 1.2 mm, the minimum element size is 0.15 mm, the maximum element growth rate is 1.45, the resolution in narrow regions is 0.95, h is 280 μm, H is 640 μm, and t is 6592 s.

[0141] Under the same process parameters, the calculation results of different meshes were compared: when the mesh was refined from M3 to M2, the change rates of h and H both exceeded 20%, indicating that the M3 mesh was too coarse and did not converge; while when the mesh was further refined from M2 to M1, the change rates of h and H both dropped to less than 5%, and the results tended to stabilize. Moreover, the M2 mesh had the shortest calculation time and the highest efficiency. Figure 4 To compare the temperature field distribution under the same time and cross-section for three customized mesh specifications, meshes M1 and M2 both reflect the symmetry and uniformity of the laser heat source characteristics; mesh M3 shows an asymmetric deviation in its temperature field distribution. Meshes M1 and M2 have similar temperature field distribution characteristics, but mesh M2 exhibits superior computational efficiency. Therefore, mesh parameters M2 are ultimately adopted for mesh generation.

[0142] By constructing and verifying a finite element heat transfer-phase change coupled model, multiple sets of simulation calculations were performed within a relatively wide range of initial parameters to obtain the melting layer depth h and hardening layer depth H corresponding to each set of parameters. Qualified parameters were screened according to the judgment criteria, and abnormal intervals were eliminated. Finally, a stable and reliable preliminary process parameter range was determined, specifically: P∈[100-500] W, V∈[5-15] mm / s, δ∈[60-90] %.

[0143] To verify the accuracy of the finite element heat transfer model for laser hardening, process parameters P = 200 W and V = 10 mm·s were selected. -1Simulation was performed with δ=65%. For example... Figure 5 As shown in Figure a, the material surface undergoes rapid heating and cooling. When the temperature rises sharply, ferrite and pearlite transform into austenite. With continuous energy input, localized melting of the surface layer forms a molten pool. After the laser is removed, the molten zone cools rapidly, undergoing a eutectic reaction at 1421 K to form ledeburite. The unmelted region below the molten pool undergoes austenitization followed by rapid cooling, transforming into martensite. Ledeburite's brittleness significantly reduces the material's overall mechanical properties, and its formation should be suppressed as much as possible; while martensite is the target phase required for laser hardening. Therefore, during laser hardening, the transformation of QT550-5 from "ferrite + pearlite" in the matrix to "martensite" should meet the following two conditions:

[0144] 1) The temperature rises to the austenite transformation temperature A. C1 Above, and below the melting temperature of 1573 K;

[0145] 2) The cooling rate is greater than the critical transformation rate of martensite in order to obtain a martensitic structure.

[0146] The actual heating temperature of ductile iron should exceed the austenitizing temperature A. C1 The above range is 50~250 K. This application uses an overheating level of 123 K, which is equivalent to the A value of QT550-5. C1 The temperature is 1123 K. During laser processing, the material experiences an extremely high cooling rate, far exceeding the critical cooling rate required for martensitic transformation, thus satisfying the second condition mentioned above. In summary, the temperature in region H is above 1123 K, and the temperature in region h is above 1573 K.

[0147] Figure 5 b and Figure 5 c represents the center of the laser spot during the second pass (t=1.44 s) of the laser scanning process. Figure 5 Temperature field cross-sectional diagram at the cross-section shown in figure a. Figure 5 d represents the light spot center at different depths ( Figure 5 The temperature change curve (at the position of the dashed line) shows that, by analyzing the temperature change of the substrate, the h value is 146 μm and the H value is 282 μm under these process parameters.

[0148] To further quantify h and H, this paper introduces an interface determination method based on phase fraction distribution. This method uses the spatial distribution of phase transformation products as a basis to define the interlayer interface distance: the section where the ledeburite phase fraction first drops to 0 is defined as the lower boundary of h, the core of which is that a ledeburite fraction of "0" indicates that the material has not undergone a melting-solidification process; the section where the martensite phase fraction drops to "0" is taken as the lower boundary of H, indicating that no martensitic phase transformation has occurred below this depth. Figure 6 The simulation results of the phase distribution at the cross section corresponding to the temperature field are presented. Figure 6 d is along Figure 6 Figure b shows the phase fraction variation curves with depth along the dashed path (depth 0~300 μm). Two key transition points are visible in the figure: at a depth of 151 μm, the ledeburite phase fraction drops to 0, indicating that at... Figure 6 The region above depth a undergoes a melting-solidification process, hence h is 151 μm; at a depth of 292 μm, the martensite phase fraction also drops to 0, indicating that in Figure 6 In b, the region above this depth undergoes complete austenitization, therefore H is 292 μm.

[0149] To further quantify h and H, an interface determination method based on phase fraction distribution is introduced. This method uses the spatial distribution of phase transformation products as a basis to define the interlayer interface distance: the section where the ledeburite phase fraction first drops to 0 is defined as the lower boundary of h, the core of which is that a ledeburite fraction of "0" indicates that the material has not undergone a melting-solidification process; the section where the martensite phase fraction drops to "0" is taken as the lower boundary of H, indicating that no martensitic phase transformation has occurred below this depth. Figure 6 The simulation results of the phase distribution at the cross section corresponding to the temperature field are presented. Figure 6 d is along Figure 6 Figure b shows the phase fraction variation curves with depth along the dashed path (depth 0~300 μm). Two key transition points are visible in the figure: at a depth of 151 μm, the ledeburite phase fraction drops to 0, indicating that at... Figure 6 The region above depth a undergoes a melting-solidification process, hence h is 151 μm; at a depth of 292 μm, the martensite phase fraction also drops to 0, indicating that in Figure 6 In b, the region above this depth undergoes complete austenitization, therefore H is 292 μm.

[0150] Laser hardening experiments were conducted under the same process parameters. Specifically, a FANUC six-axis robot equipped with an RFL-C3000 semiconductor laser and a TS-6A laser head was used for laser hardening, supplemented by a TFLW-3000 water-cooling system. The laser working point was 14 mm from the workpiece, the laser beam was a Gaussian beam, and the spot diameter was 1 mm. Argon gas was introduced as an auxiliary gas during the experiment at a flow rate of 13 L / min. -1 To inhibit metal surface oxidation and improve surface quality;

[0151] The QT500-5 laser was cut to a size of 200 mm × 20 mm × 20 mm. Before the test, to obtain a good initial surface, the workpiece surface underwent a series of treatments including grinding, rust removal, degreasing, ultrasonic cleaning, and drying. During the test, the hardened area was set to 10 mm × 10 mm, and the laser was scanned in a straight line to avoid corners that could cause poor processing quality. After laser hardening, the samples were cut into 15 mm × 15 mm × 20 mm samples using wire EDM, cleaned and dried again, and then bagged for subsequent measurements. After the test, the depth of the fused layer (h) and the depth of the hardened layer (H) perpendicular to the laser scanning path were measured using a super depth-of-field microscope (LEICA DVM6). To reduce random errors in single-point measurements, the depth values ​​of h and H were the average of multiple measurements. The hardness of h and H was measured using a Vickers microhardness tester (HV-1000B) with a loading force of 500 g and a holding time of 10 s. Three points were randomly measured in each area, and the average value was taken. The microstructure of the interface was observed and elemental analyzed using scanning electron microscopy (TESCAN VEGACOMPACT) and energy dispersive spectroscopy (Bruker QUANTAX Compact).

[0152] Its cross-sectional morphology is as follows Figure 7 As shown, a three-layer structure can be observed, consisting of a fused layer (ledeburite), a hardened layer (martensite + ledeburite), and a matrix (ferrite + pearlite + spheroidal graphite). According to the phase fraction interface determination method, as shown in the figure below, the section above which the ledeburite is "0" under an electron microscope represents the fused layer. The bottom of the hardened layer is a mixture of martensite and ferrite. The section where the martensite is "0" is the interface between the hardened layer and the matrix; the section above this section is the hardened layer. The measured h is 162 μm, and H is 303 μm. Compared with the temperature field simulation results, the relative errors are 9.88% and 6.93%, respectively; compared with the phase fraction simulation results, the relative errors are 6.79% and 3.63%, respectively, both less than 10%, and the phase fraction simulation results are closer to the experimental values. In summary, the laser hardening phase transformation heat transfer simulation results show a high degree of agreement with the experimental results, and the layer depth finite element simulation based on phase fraction can provide data support for subsequent prediction modeling.

[0153] S2: Latin hypercube sampling to construct a dataset of "process parameters - response target";

[0154] Latin Hypercube Sampling (LHS) was used to sample parameter combinations within the initial process parameter range. After sampling, the data was further simulated using a finite element heat transfer model, resulting in a specific dataset of "process parameters - response target." The details of this dataset are as follows... Figure 8 As shown.

[0155] like Figure 9 As shown in Figure a, the LHS-generated data is messy and disordered, making the model training process susceptible to noise interference. To improve model training, a course learning strategy is applied, assigning a difficulty score to the original data. A higher score indicates higher sample complexity, and vice versa. The core theory of the course learning strategy is to quantify sample difficulty, allowing the model to learn progressively from simple to complex. The adjusted overall distribution is as follows. Figure 9 As shown in b, the recombined dataset exhibits a certain regular distribution. The grading formula for the course is:

[0156]

[0157] In the formula, and These are the values ​​of h and H, respectively; and They are respectively and The weights are each set to 0.5; This is the weighted value.

[0158] S3: Construction of BO-MTNN fusion prediction model, and introduction of PCC and SHAP methods to reveal the mechanism and contribution of process parameters to the response target;

[0159] S3.1 Prediction Model Construction

[0160] In the laser hardening process, there is often a nonlinear mapping relationship between process parameters and response targets. Therefore, the Multi-Task Neural Network (MTNN) model is adopted to accurately model the coupling relationship of multiple parameters in laser hardening through its powerful nonlinear fitting ability.

[0161] The dataset after the course in step S2 is subjected to Min-Max normalization, scaling the data to [0,1]. The formula is as follows:

[0162]

[0163] In the formula, X is the normalized value, and X0 is the original data value. The minimum value of the original data. The maximum value of the original data;

[0164] Based on the normalized dataset, the mapping relationship between process parameters and response targets is learned, and an MTNN prediction model is trained. The trained MTNN prediction model is then optimized using the Bayesian Optimization (BO) algorithm to optimize the hyperparameters of the MTNN prediction model, forming a BO-MTNN fusion prediction model.

[0165] The MTNN prediction model comprises a backbone network and branch networks. The process parameters, after Min-Max normalization, are input into the backbone network of the MTNN prediction model to extract the common features of the process parameters. These common features are then input into two independent branch networks. Through the dedicated mapping of the branch networks, the predicted values ​​of the molten layer depth h and the hardened layer depth H are output simultaneously. The mean square error (MSE) loss function is used to constrain and optimize the parameters of the shared layer and the output layer, respectively, to achieve high-precision prediction of the model.

[0166] The fitting performance of the MTNN model is closely related to the selection of hyperparameters such as hidden layers, learning rate, batch size, and pattern. However, manually selecting these hyperparameters alone is insufficient to obtain the optimal combination. Therefore, Boolean optimization (BO) is used to optimize the hyperparameters of the MTNN model to construct a more accurate prediction model. The BO algorithm starts with 10 sampling points, performs 100 iterations, and uses the root mean square error as the fitness function.

[0167] To evaluate the predictive performance of the BO-MTNN model, we compared and analyzed the Back Propagation Neural Network (BPNN), Random Forest (RF), eXtreme Gradient Boosting (XGBOOST), and MTNN models. We used three metrics for comprehensive evaluation: coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE). A closer R² to 1 and a closer MAE and RMSE to 0 indicate a higher model fit and better predictive performance. The formulas are as follows:

[0168]

[0169] In the formula, y1 is the actual value. y1 is the predicted value, y2 is the mean of the actual values, and n is the number of samples.

[0170] The prediction performance results of each model are as follows: Figure 10 As shown, the BO-MTNN model is the best in all metrics and has the highest prediction accuracy, providing a reliable foundation for subsequent model interpretability analysis.

[0171] S3.2 PCC Correlation Analysis

[0172] In order to study the influence of P, V, and δ on h and H during the experiment, and to avoid extreme cases where h is too large or H is too small due to improper combination of different process parameters, Pearson correlation analysis was conducted.

[0173] The Pearson correlation coefficient (PCC) measures the strength and direction of the linear relationship between two variables, and is an important basis for analyzing the linear dependence between variables. The calculation formula is as follows:

[0174]

[0175] In the formula, Let x be the Pearson correlation coefficient between variables x and y. , Let x and y be the variable values ​​of the i-th x, y sample set. Let x be the mean of the sample. Let y be the mean of the sample y.

[0176] The results are as follows Figure 11 As shown, there is a very strong positive correlation between h and H, with a correlation coefficient r = 0.98. The physical mechanism is that both are determined by the laser energy input: when P increases or V decreases, the strong heat input causes the surface layer to melt and form h, while the heat conducted inward causes the subsurface layer to undergo a phase transition and form H. The specific correlations between each process parameter and the response target are as follows: the correlation coefficients between P and h and H are 0.96 and 0.95, respectively, showing a strong positive correlation and being the decisive factor; V shows a weak negative correlation with h and H, with coefficients of -0.10 and -0.17, respectively, indicating that within the parameter range studied in this paper, changing V has a limited effect on the layer depth. δ shows a weak positive correlation with h and H, with coefficients of 0.11 and 0.13, respectively, and its effect is not significant. Based on the magnitude of the absolute value of the linear correlation coefficient, the order of influence of each parameter on h is: P > δ > V, and the order of influence on H is: P > V > δ.

[0177] Implementation of S3.3 SHAP

[0178] The black-box nature of data-driven machine learning models can lead to interpretability difficulties and reduced interpretability. Therefore, the Shapley Additive Explanations (SHAP) method is introduced to explain these "black-box" models. Based on game theory, SHAP can fully explain the nonlinear patterns and feature interactions captured by machine learning models, thus overcoming the limitations of PCC in this regard. The mean absolute SHAP value is the marginal contribution of a feature parameter to the model output, representing the offset of a feature value relative to the baseline prediction. Its formula is as follows:

[0179]

[0180] In the formula, Let S be the SHAP value of the i-th feature, where S is a subset of the entire feature set N, excluding feature i. The total number of features is |N| = 3, and |S|!(|N|-|S|-1)! is the number of permutations in which feature i is added after subset S. The model's predicted value f(S) is obtained by using a subset S and adding feature i, and the model's predicted value is obtained by using only the features in the subset S.

[0181] like Figure 12 As shown, based on the mean absolute SHAP value, the predicted h and H of the model are interpreted qualitatively and quantitatively, and the mean SHAP values ​​of several prediction models such as BO-MTNN, MTNN, BPNN, XGBOOST and RF are compared.

[0182] In the graph, the vertical axis represents each process parameter, and the horizontal axis represents the mean absolute value (SHAP). The magnitude of the SHAP value directly characterizes the importance of the corresponding process parameter to the output of the prediction model. The red bar represents the contribution of h, and the green bar represents the contribution of H. A larger mean absolute value indicates a greater influence of that feature variable on the response variable of the prediction model output. Model evaluation metrics show that the BO-MTNN model has the highest fitting accuracy. Figure 12 As shown in Figure a, the SHAP analysis based on this model reveals that for h, the importance ranking of each process parameter is P>V>δ; for H, the importance ranking is P>V>δ. This indicates that P has a dominant influence on both response indicators. Further analysis of the mean absolute SHAP value shows that when P increases, its effect on h is more significant; while when V increases, its effect on H is more pronounced; and the influence of δ on both is relatively weak.

[0183] Comparing different models reveals that in the BO-MTNN, MTNN, and BPNN models with higher fitting accuracy, the length of the SHAP bar charts for each process parameter is relatively long, indicating that the model assigns significant importance to the parameters. Conversely, in the XGBOOST and RF models with lower fitting accuracy, the bar chart lengths are generally shorter, indicating that the mean absolute SHAP value is distorted due to poor model performance. In summary, model fitting accuracy is a crucial prerequisite for ensuring the reliability of the SHAP interpretability method's output. Based on the mean absolute SHAP value of BO-MTNN, it is clear that P is the key influencing factor, while the influence of δ is negligible. SHAP provides a reference for accurately understanding the impact of process parameters in specific predictions.

[0184] S4: MOHOA performs multi-objective optimization of laser hardening process parameters;

[0185] The objective function and constraints for the multi-objective optimization are as follows:

[0186]

[0187]

[0188] like Figure 13 As shown, the Multi-Objective Hippopotamus Optimization Algorithm (MOHOA) is used to optimize the laser hardening process parameters in multiple objectives. MOHOA is a multi-objective extension of the Hippopotamus Optimization Algorithm, introducing differential evolution mutation and environment selection mechanisms. The algorithm first initializes the population using random sampling. During the population iteration and update phase, random walks and elite-guided approaches are used to improve global exploration capabilities and convergence speed. Secondly, a differential evolution mutation strategy is incorporated to further perturb the Hippopotamus search, improving the distribution and convergence of the leading edge solutions. The environment selection mechanism uses an elite retention strategy for fast non-dominated sorting, dividing the merged population into multiple leading edge levels and prioritizing the retention of higher-level non-dominated solutions. When the number of solutions at the same level exceeds the population capacity, crowding distance calculation is introduced to select solutions with a more even distribution to maintain the extensibility of the Pareto solution set front. This two-stage selection strategy ensures convergence while avoiding local clustering of optimal solutions.

[0189] To verify that the Pareto solution set calculated by the MOHOA algorithm is superior, the Multiple Objective Particle Swarm Optimization (MOPSO) algorithm and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm are introduced for comparison.

[0190] While MOPSO converges quickly, it is prone to getting trapped in local optima and has poor solution set distribution. NSGA-II has stable distribution and robustness, but its convergence speed is relatively slow. MOHOA, by integrating differential evolution mutation and environment selection mechanisms, significantly enhances global exploration capabilities and convergence efficiency while maintaining good solution set distribution. It is more suitable for engineering parameter optimization problems with complex solution spaces, strong objective conflicts, and the need to balance convergence speed and frontier coverage, providing a high-quality and uniformly distributed Pareto solution set.

[0191] like Figure 14The distribution of the first 50 Pareto solutions for the three optimization algorithms is shown. MOHOA maintains good convergence while exhibiting a more uniform solution distribution and a more complete boundary cover, demonstrating its excellent diversity preservation ability. In contrast, although MOPSO and NSGA-II have strong convergence, their solution distribution is more concentrated, and the front ends are not fully covered, which may result in missing key boundary solutions.

[0192] To evaluate the overall performance of different optimization algorithms, hypervolume (HV) and inverted generational distance (IGD) are used as evaluation metrics. HV measures the diversity and distribution rationality of the solution set by calculating the volume of the region enclosed between the Pareto solution set and the reference point, while IGD evaluates the convergence and uniformity of the solution set by calculating the average distance from sample points on the ideal target front to the nearest point in the algorithm's solution set.

[0193] The comparison results show that MOHOA's HV is 3.71 × 10⁻⁶. 5 The IGD was 4.24; the HV of MOPSO was 2.14 × 10⁻⁶. 5 The HV of NSGA-II is 2.57 × 10⁻⁶. 5 The IGD value is 4.63. Among them, MOHOA has the highest HV metric, indicating better diversity in its solution set; simultaneously, it has the lowest IGD value, reflecting better convergence and uniformity of the solution set. In summary, the MOHOA algorithm exhibits superior overall performance in multi-objective optimization.

[0194] S5: Based on EWM-TOPSIS decision-making, establish a comprehensive evaluation method and perform comprehensive ranking to select the optimal combination of process parameters;

[0195] S5.1 Establish the decision matrix and standard matrix;

[0196]

[0197]

[0198]

[0199] In the formula, the Pareto solution set constitutes the decision matrix. There are m sets of process parameter combinations to be decided, m=50, and n evaluation indicators, n=2; This is the matrix obtained through forward transformation; For standard matrices;

[0200] S5.2 Calculate the weight values ​​of each objective;

[0201]

[0202]

[0203] In the formula, This is the information entropy value; These are weight values;

[0204] S5.3 calculates the Euclidean distance and outputs a comprehensive score. The optimal combination of process parameters is selected based on the comprehensive score.

[0205]

[0206]

[0207]

[0208] In the formula, and Depend on It consists of the maximum and minimum values ​​of each column of elements; and Let be the distance between the i-th solution and the optimal and worst solutions; Rate it.

[0209] Following the steps outlined above, the Pareto solutions obtained from MOHOA optimization were comprehensively evaluated and ranked, identifying the top 5 optimal combinations of process parameters, specifically:

[0210] 1: P = 201.8 W, V = 5.0 mm·s -1 , δ=86.9%, H=245.9 μm, h=73.5 μm, =0.62;

[0211] 2: P = 207.6 W, V = 5.0 mm·s -1 , δ=88.5%, H=243.2 μm, h=72.5 μm, =0.61;

[0212] 3: P = 207.6 W, V = 5.1 mm·s -1 , δ=88.5%, H=243 μm, h=72.3 μm, =0.59;

[0213] 4: P = 206.6 W, V = 5.3 mm·s -1 , δ=87.6%, H=250.3 μm, h=79.3 μm, =0.56;

[0214] 5: P=208 W, V=5.4 mm·s -1 , δ=82.8%, H=304.5 μm, h=135.8 μm, =0.54.

[0215] S6: Optimization result verification;

[0216] Rounding the parameters of the top-ranked combination, we get P = 202 W and V = 5 mm·s. -1 The experimental verification was conducted at δ=87%. The verification included actual laser testing, finite element heat transfer model simulation calculation, hardness testing before and after laser testing, microstructure characterization observation, reciprocating friction experiment, and fixed-point quantitative analysis by energy dispersive spectroscopy.

[0217] like Figure 15 As shown in the hardening test cross-section, a fused layer exists on the surface, mainly composed of ledeburite; the subsurface layer is martensite, i.e., the hardened layer. The fused layer is located above the cross-section where ledeburite is "0", and the hardened layer is located above the cross-section where martensite is "0". The measured h is 65 μm, and H is 225 μm.

[0218] like Figure 16 As shown, Figure 16 c is along Figure 16 Phase fraction distribution at different depths (b, indicated by the dashed line): Ledeburite fraction drops to 0 at a depth of 71 μm, thus defining... Figure 16 At this depth, h is 71 μm; the martensite fraction approaches 0 at 246 μm, therefore H is 246 μm. Furthermore, the experimental results, model predictions, and simulation results are compared, and the values ​​are close, indicating that the simulation model and the prediction model have good accuracy.

[0219] like Figure 17 As shown, hardness tests were performed on the samples before and after laser hardening, and the average hardness of the matrix was 166±15 HV. 0.5 After laser hardening, the hardness of the surface molten area was significantly increased to 940±40 HV. 0.5 It is approximately 5.7 times harder than the matrix; the hardness of the hardened region is 630±30 HV. 0.5 It is much higher than the matrix, and has good comprehensive mechanical properties and hardening effect.

[0220] To investigate the relationship between tissue structure and properties, scanning electron microscopy was used to characterize the tissue morphology of the laser-hardened area. Figure 18 The microstructure under optimal parameters is shown: fused layer Figure 18 a consists of fine ledeburite, exhibiting a eutectic morphology of austenite and cementite. The dense, skeletal cementite formed under extremely high cooling rates acts as a hard and brittle phase, working in conjunction with the refined microstructure to increase the hardness to 940 HV. 0.5 Hardened layer ( Figure 18 b) Predominantly composed of acicular martensite, with needles approximately 5–20 μm in length. Martensitic phase transformation forms a carbon supersaturated solid solution, inducing lattice distortion and high dislocation density. The fine martensite needle boundaries hinder dislocation movement; the synergistic effect of phase transformation strengthening and microstructure refinement results in a hardness of 630 HV. 0.5 It is much higher than the matrix.

[0221] A reciprocating friction test (100 N, 3 Hz, 20 min) was conducted on the substrate and laser-hardened surface using an MDW-02 friction and wear testing machine. The wear mechanisms were mainly adhesive wear and abrasive wear. Figure 19 As shown, comparative analysis indicates that the substrate surface is severely worn, exhibiting deep furrows, material peeling, and a large amount of wear debris, which is the result of the combined effects of abrasive and adhesive wear; the laser-hardened surface is relatively smooth, with only slight wear marks.

[0222] Because the QT500-5 surface forms a high-hardness ledeburite and martensite structure during laser hardening, its resistance to plastic deformation and peeling is significantly improved. The friction coefficient curves show that both initially increase and then stabilize, but the steady-state friction coefficient of the laser-hardened sample decreases more significantly due to its increased hardness and improved friction performance. In summary, laser-hardened surfaces exhibit significant advantages in both microstructure and macroscopic friction properties.

[0223] like Figure 20 As shown, line scanning of h, H, and the matrix was performed using an energy dispersive spectroscopy (EDS) instrument. When the scan passed through the graphite phase, the carbon-rich characteristics of graphite led to a significant enhancement of the carbon element pulse signal. In the non-graphite phase region, the elements were evenly distributed, and no obvious elemental segregation was observed.

[0224] To quantitatively analyze the elemental distribution during the laser hardening process, EDS was used. Figure 21 Point scan analysis was performed on the intermediate fused layer, hardened layer, and substrate region. The results of selecting 3 points in each region are as follows: Figure 22 As shown, the data indicates that the average C content in both the fused and hardened layers is higher than that in the matrix, mainly due to C diffusion under laser irradiation; the fused region has the highest C content due to more complete graphite dissolution. Analysis shows that no significant macroscopic diffusion or agglomeration of the main elements occurred, indicating that the improved material properties are primarily attributed to phase transformation strengthening and microstructure refinement mechanisms.

[0225] This application employs a finite element phase change heat transfer model to obtain high-precision data on temperature field, phase fraction, and hardened layer depth. A sample set is efficiently constructed using Latin hypercube sampling. A BO-MTNN multi-task proxy model is used to achieve rapid and accurate prediction of process parameters to the depth of the fused and hardened layers. Then, a Pareto optimal solution set is obtained through MOHOA multi-objective optimization. Finally, EWM-TOPSIS is combined to complete scientific decision-making and optimal parameter selection. The entire scheme combines physical accuracy, predictive efficiency, multi-objective balance, and decision objectivity, significantly reducing simulation costs and improving optimization efficiency. It can stably obtain optimal laser process parameters that balance hardening effect and fused control.

[0226] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention. Those skilled in the art, under the guidance of the present invention, can make various similar representations without departing from the spirit and claims of the present invention, and such modifications all fall within the protection scope of the present invention.

Claims

1. A method for optimizing interpretable process parameters of laser hardening on the surface of QT500-5 ductile iron, characterized in that: Includes the following steps: S1: Construct a finite element heat transfer model for phase change heat transfer during laser hardening on the surface of QT500-5 ductile iron, and use this model to screen out the preliminary range of laser hardening process parameters; S2: Within the initial process parameter range, the Latin hypercube sampling method (LHS) is used for sampling and experimentation to construct a dataset containing "process parameters – response target"; S3: Based on the dataset, construct a multi-task neural network (MTNN) prediction model, and use the Bayesian optimization (BO) algorithm to optimize the MTNN model, thus establishing a Bayesian optimized multi-task neural network fusion prediction model BO-MTNN. Meanwhile, Pearson correlation coefficient (PCC) and Shapley additive interpretation (SHAP) methods are introduced to reveal the mechanism and contribution of process parameters to the response target; S4: The multi-objective Hippo Optimization Algorithm (MOHOA) is adopted, and the BO-MTNN model is used as a fast evaluator to perform multi-objective optimization on the process parameter space to obtain the Pareto solution set; S5: A decision-making method combining entropy weight method (EWM) and TOPSIS is adopted to establish a comprehensive evaluation system, and the Pareto solution set is evaluated and ranked by multiple indicators to obtain the optimal combination of process parameters. S6: Conduct actual laser hardening experiments to verify the optimal combination of process parameters, compare the experimental results with the model predictions, and verify the accuracy of the prediction model and the effectiveness of the optimization scheme.

2. The method for optimizing interpretable process parameters of laser hardening on the surface of QT500-5 ductile iron according to claim 1, characterized in that: In step S1, the depth of the condensed layer h and the depth of the hardened layer H are used as response targets, and the laser power P, scanning speed V, and overlap rate δ are used as experimental factors to construct a finite element heat transfer model. The preliminary process parameters selected by the finite element heat transfer model are P∈[100-500] W, V∈[5-15] mm / s, δ∈[60-90] %.

3. The method for optimizing interpretable process parameters for laser hardening of QT500-5 ductile iron surface according to claim 2, characterized in that: The finite element heat transfer model only considers the temperature field and the metal phase transition field when it is constructed. By meshing and verifying convergence, the temperature field and phase transition results of different process parameters are simulated and calculated based on the model, and a reasonable range of process parameters is selected. The temperature field is controlled by the solid heat transfer module of COMSOL Multiphysics software, and its control equations are as follows: In the formula, ρ is the material density. ; Equivalent specific heat capacity v is the fluid velocity. t represents time (s); Where is the heat flux divergence; Q is the external heat source. k is the thermal conductivity. ; Temperature gradient q is the heat flux density vector. ; The equivalent specific heat capacity is determined by the properties of QT500-5 ductile iron material, and its formula is as follows: In the formula, Specific heat capacity at constant pressure L represents latent heat. ;T L The liquidus temperature (K) of QT500-5, T S The solidus temperature (K) of QT500-5; Simultaneously, boundary conditions were set, introducing three types of boundary thermal effects: laser heat source, convective heat transfer, and thermal radiation. The governing equations are as follows: In the formula, is a Gaussian laser heat source; R is the spot radius (m); x and y are spatial coordinates (m); , These are the functions of laser movement along the x and y directions, respectively; For generalized inward heat flux (W / m²); The laser absorption rate of QT500-5; The convective heat transfer flux is (W / m²). The convective heat transfer coefficient of QT500-5 ; Radiative heat transfer flux (W / m²); The emissivity of QT500-5; The ambient temperature (K); The external radiation temperature (K); The metal phase transition field includes a heating process and a cooling process. The heating process is calculated using the Leblond-Devaux model in COMSOL, and the cooling process is calculated using the Koistinen-Marburger equation. The formulas are as follows: In the formula, The generation rate from the source phase to the target phase; The volume fraction of the source phase consumed; The target phase volume fraction; and This is a temperature-dependent function; Martensite phase fraction; T is the martensitic phase transformation initiation temperature; β is the Koistinen-Marburger coefficient, with a value of 0.011; T m This is the current temperature of the QT500-5. Further mesh generation was performed to determine a mesh scheme that met the requirements of computational accuracy and efficiency, thus completing the construction of the finite element heat transfer model.

4. The method for optimizing interpretable process parameters of laser hardening on the surface of QT500-5 ductile iron according to claim 3, characterized in that: In step S2, the Latin hypercube sampling method is used to sample within the initial process parameter range. After sampling, the finite element heat transfer model is used for simulation calculation to obtain the dataset of "process parameters - response target". The dataset is scored and adjusted using applied course learning strategies to make it more regular. The scoring formula is as follows: In the formula, and These are the values ​​of h and H, respectively; and They are respectively and The weights are each set to 0.5; This is the weighted value.

5. The method for optimizing interpretable process parameters for laser hardening of QT500-5 ductile iron surface according to claim 4, characterized in that: In step S3, the dataset after the course is processed by Min-Max normalization, scaling the data to [0,1]. The formula is as follows: In the formula, X is the normalized value, and X0 is the original data value. The minimum value of the original data. The maximum value of the original data; Based on the normalized dataset, the mapping relationship between process parameters and response targets is learned, and the MTNN prediction model is trained. The trained MTNN prediction model is then fused with the BO algorithm to optimize the hyperparameters of the MTNN prediction model, forming the BO-MTNN fusion prediction model.

6. The method for optimizing interpretable process parameters of laser hardening on the surface of QT500-5 ductile iron according to claim 5, characterized in that: The MTNN prediction model includes a backbone network and branch networks. The process parameters are processed by Min-Max normalization and input into the backbone network of the MTNN prediction model. The general features of the process parameters are extracted and then input into two independent branch networks. Through the exclusive mapping of the branch networks, the predicted values ​​of the molten layer depth h and the hardened layer depth H are output simultaneously. The BO algorithm has 10 initial sampling points, 100 iterations, and uses the root mean square error as the fitness function.

7. The method for optimizing interpretable process parameters for laser hardening of QT500-5 ductile iron surface according to claim 5 or 6, characterized in that: In step S3, PCC is used to measure the strength and direction of the linear relationship between process parameters and the response target, and its formula is as follows: In the formula, Let x be the Pearson correlation coefficient between variables x and y. , Let x and y be the variable values ​​of the i-th x, y sample set. Let x be the mean of the sample. Let y be the mean of the sample y; The SHAP method can fully explain the nonlinear patterns and feature interactions captured by machine learning models. The mean absolute SHAP value is the marginal contribution of a feature parameter to the model output, representing the offset of a feature value relative to the baseline prediction. Its formula is: In the formula, Let S be the SHAP value of the i-th feature, where S is a subset of the entire feature set N, excluding feature i. The total number of features is |N| = 3, and |S|!(|N|-|S|-1)! is the number of permutations in which feature i is added after subset S. The model's predicted value f(S) is obtained by using a subset S and adding feature i, and the model's predicted value is obtained by using only the features in the subset S.

8. The method for optimizing interpretable process parameters of laser hardening on the surface of QT500-5 ductile iron according to claim 6, characterized in that: The objective function and constraints for the multi-objective optimization in step S4 are as follows: The MOHOA algorithm is used for multi-objective optimization. The MOHOA algorithm first uses a random sampling method to initialize the population. In the population iteration and update phase, random walk and elite guidance are used to improve the global exploration ability and convergence speed. Secondly, the differential evolution mutation strategy is integrated to further perturb the hippo search, improving the distribution and convergence of the frontier solutions. The environment selection mechanism adopts an elite retention strategy for fast non-dominated sorting, dividing the merged population into multiple frontier levels and prioritizing the retention of high-level non-dominated solutions. When the number of solutions in the same level exceeds the population capacity, crowding distance calculation is introduced to select solutions with more uniform distribution to maintain the extensibility of the Pareto solution set frontier.

9. The method for optimizing interpretable process parameters for laser hardening of QT500-5 ductile iron surface according to claim 1 or 8, characterized in that: The specific steps of the comprehensive evaluation system established by the decision-making method combining EWM and TOPSIS in step S5 are as follows: S5.1 Establish the decision matrix and standard matrix; In the formula, the Pareto solution set constitutes the decision matrix. There are m sets of process parameter combinations to be decided, m=50, and n evaluation indicators, n=2; This is the matrix obtained through forward transformation; For standard matrices; S5.2 Calculate the weight values ​​of each objective; In the formula, This is the information entropy value; These are weight values; S5.3 calculates the Euclidean distance and outputs a comprehensive score. The optimal combination of process parameters is selected based on the comprehensive score. In the formula, and Depend on It consists of the maximum and minimum values ​​of each column of elements; and Let be the distance between the i-th solution and the optimal and worst solutions; Rate it.

10. The method for optimizing interpretable process parameters of laser hardening on the surface of QT500-5 ductile iron according to claim 9, characterized in that: The optimal process parameters were selected for verification, which included actual laser experiments, finite element heat transfer model simulation calculations, hardness tests before and after laser experiments, microstructure characterization observations, reciprocating friction experiments, and point-to-point quantitative analysis by energy dispersive spectroscopy.

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