Metal additive manufacturing three-dimensional temperature field Gaussian process prediction method

Abstract

The invention relates to a metal additive manufacturing three-dimensional temperature field Gaussian process prediction method, belongs to the technical field of material science, and particularly relates to a metal additive manufacturing three-dimensional temperature field prediction method. Logarithmic transformation is adopted to preprocess a temperature field, and prediction difficulty caused by extreme gradient near a molten pool is avoided; dividing the overall computational domain into a plurality of sub-domains by adopting a domain decomposition strategy to reduce the problem dimension; for each sub-domain, further combining singular value decomposition to extract a temperature field reduced-order base; establishing a local Gaussian process regression model based on a Maren kernel function and carrying out parallel training so as to establish rapid mapping from process parameters to reduced-order output; during online prediction, efficient and accurate prediction of a complete temperature field is realized through parallel calculation and full-field assembly of each local model.

Description

Technical Field

[0001] This invention relates to a method for predicting the three-dimensional temperature field Gaussian process in metal additive manufacturing, belonging to the field of materials science and technology, and particularly to a method for predicting the three-dimensional temperature field in metal additive manufacturing. Background Technology

[0002] Additive manufacturing (AM) has attracted increasing attention in many fields due to its superior capabilities, including the ability to manufacture parts with complex geometries, customizability, and short production cycles. It mainly consists of two types: laser powder bed fusion (LPBF) and direct energy deposition (DED). In both processes, a high-energy beam (such as a laser, electron beam, or electric arc) moves along a predefined scanning path, melting powder or filament in a pass-by-pass, layer-by-layer manner to form components. The thermal behavior during this process is closely related to the forming quality and efficiency, playing a crucial role in the relationship between process, microstructure, and material properties. In particular, the formation of manufacturing defects (such as porosity, thermal cracking, surface roughness, and warpage) is accompanied by complex evolution of the temperature field. Therefore, real-time analysis of the temperature field is urgently needed to achieve online process control and ensure part quality.

[0003] Currently, machine learning models possess the potential for real-time analysis. In the extreme conditions of metal additive manufacturing, experimental techniques often struggle to achieve continuous, full-field temperature monitoring. While physics-based computational models offer a viable alternative, their application in practical additive manufacturing problems remains limited due to their enormous computational costs at reasonable spatiotemporal discrete resolutions. In contrast, machine learning models learn from data and make predictions through regression or classification techniques, enabling online end-to-end mapping. By shifting the enormous computational burden to a one-off offline training process, machine learning models exhibit unprecedented speed in the online inference phase. This makes them well-suited for tasks requiring real-time performance and scalability. However, this efficiency comes with trade-offs, including dependence on large datasets and reduced interpretability compared to physics-based models, particularly for complex additive manufacturing problems. Therefore, developing a machine learning model with small sample sizes and interpretability to effectively predict the evolution of the three-dimensional temperature field during additive manufacturing remains a challenge.

[0004] Many studies have focused on developing data-driven machine learning models to effectively predict temperature fields in additive manufacturing. Early efforts primarily concentrated on physics-informed neural networks (PINNs), which integrate physical laws directly into the model's loss function to reduce reliance on massive datasets. While PINNs can alleviate the burden of training data generation as a scientific machine learning model, they typically introduce significant computational overhead during offline training. For PINNs that do not require labeled datasets, the challenge of optimizing complex network architectures to meet physical constraints often results in computational efficiency that is even lower than traditional numerical methods.

[0005] The pursuit of more computationally efficient methods has led to purely data-driven machine learning models that do not consider built-in physical constraints. Deep learning models are widely used for modeling thermal behavior, despite the high cost of acquiring large labeled datasets (whether experimental measurements or high-fidelity numerical simulations). These data-driven machine learning models can achieve high efficiency and accuracy, but they are limited by using finite element simulations that ignore molten pool convection to save computational costs in generating training samples. Clearly, using high-fidelity numerical models (e.g., considering thermal fluid flow within the molten pool) can improve the quality of training samples, but this significantly increases computational costs, making the acquisition of large datasets prohibitively expensive (let alone large datasets). Therefore, there is an urgent need for a predictive model that can efficiently predict the three-dimensional temperature field during additive manufacturing processes with small sample sizes.

[0006] In existing technologies, physics-based numerical simulation methods cannot meet the real-time monitoring requirements of metal additive manufacturing processes due to their high computational costs; physical information neural networks are difficult to implement due to their low offline training efficiency; and while pure data-driven deep learning models offer fast prediction speeds, their training relies on massive amounts of data, making acquisition extremely costly. Furthermore, traditional Gaussian process regression (GPR) models, suitable for few-shot learning, encounter severe problems of the curse of dimensionality and insufficient representational ability when facing the ultra-high dimensional output of a three-dimensional temperature field with local extreme gradients and strong nonlinear characteristics, resulting in low prediction accuracy and poor physical consistency. Summary of the Invention

[0007] To address the aforementioned problems, this invention aims to provide a rapid prediction method for three-dimensional temperature fields based on partitioned discrete learning and Gaussian process regression.

[0008] The technical solution of this invention is: A method for predicting the three-dimensional temperature field in metal additive manufacturing, the method comprising the following steps: The first step is to perform high-fidelity simulation of the complete material domain in metal additive manufacturing using the multiphysics material point method, and obtain training samples of the three-dimensional temperature field evolution over time in the material domain under different process parameters. The second step is to construct a global snapshot matrix describing the dynamics of the entire material domain from the three-dimensional temperature field training samples generated in the first step, and then preprocess the snapshot matrix. The third step is to discretize the complete material domain in the first step into several subdomains, and based on the global snapshot matrix obtained in the second step, construct a local snapshot matrix for each subdomain. Then, the local snapshot matrix of each subdomain is reduced in dimension by principal component analysis (PCA) to extract the local reduced basis and local reduced output under the local snapshot matrix of each subdomain. The fourth step involves training a locally reduced Gaussian process regression (GPR) model for each subdomain based on the process parameters from the first step and the locally reduced output of each subdomain extracted in the third step. The optimal hyperparameters of each locally reduced GPR model are determined by maximizing its marginal likelihood function. The fifth step is to call the local reduced-order GPR model from the fourth step to quickly predict its expected output value in the reduced-order space for new process parameter inputs. The sixth step involves using the local reduced-order basis obtained in the third step to reconstruct the expected output value predicted in the fifth step into the full-order temperature field of the corresponding subdomain, and finally integrating it into the temperature field response of the complete material domain.

[0009] In the first step, a three-dimensional temperature field training sample is obtained by solving the following control equations; The governing equations are:

[0010] in, For speed, Representing variables The mass derivative, where t is time. Indicates temperature. Indicates density, Indicates the shear viscosity coefficient. Indicates fluid pressure. Indicates the permeability coefficient. Indicates fluid volume fraction. It is a relatively small constant. Represents gravity. Indicates recoil pressure, Indicates surface tension. For specific heat, This represents the volume fraction of the metallic material. Density of metallic materials For latent heat of fusion, Indicates the thermal conductivity coefficient. This indicates the laser thermal input.

[0011] In the first step, multiple high-fidelity simulations are performed by changing the laser power and scanning speed process parameters to obtain a sequence of three-dimensional temperature field training samples covering different process parameters. The three-dimensional temperature field training samples are spatially discrete in regular grid cells of 151×76×46 and temporally contain temperature field data at five specific moments that characterize typical thermal processes.

[0012] In the second step, the three-dimensional temperature field data at each time step are stretched into column vectors according to the spatial dimension order of x→y→z, and the column vectors of all time steps are spliced ​​together in chronological order to construct a global snapshot matrix describing the dynamics of the material domain.

[0013] In the second step, the global snapshot matrix undergoes a logarithmic transformation preprocessing, and the logarithmic transformation formula is as follows:

[0014] in, The original temperature field in the snapshot matrix. The transformed temperature field, These are process parameters.

[0015] In the third step, the material domain is divided into several regular subdomains according to the thermal field distribution characteristics in the additive manufacturing process. The specific division method is as follows: the spatial continuity of the temperature field along the laser scanning path is maintained, and no partitioning is performed in the scanning direction; regions in the thermal field with temperatures not lower than the solidus temperature of the material are identified as high-gradient subdomains and divided separately, including the complete heat-affected zone of the molten pool and its surrounding high-gradient region, which is contained in a single cubic subdomain as much as possible; the remaining regions with relatively uniform thermal field distribution are divided as uniform subdomains.

[0016] The subdomain partitioning is achieved through the vertical scan path. and The spatial partition boundary is defined by two directions; let the spatial domain be defined by... and Limited, along Axis in position The division is as follows: , ,and ; along the z-axis at position The division is as follows: , ,and .

[0017] Having arbitrary spatial coordinates Data points are assigned to subdomains If and only if its coordinates simultaneously satisfy and Spatial index Mapping relationships correspond to subdomain indexes Its formula is:

[0018] The subdomains in The number of grid points in a direction is determined by calculating the coordinates of the defined subdomain boundary:

[0019] in The entire domain is respectively Grid spacing in the direction. and Representing the material domain in Spatial range of direction Representing subfields respectively exist The number of discrete units in a direction.

[0020] For subdomains Filtering from the global snapshot matrix by spatial coordinates Extract the corresponding temperature data; based on the defined subdomain boundary conditions, identify all conditions that satisfy the conditions. and The system generates a set of spatial coordinate points, then extracts the full-time-step temperature data of these spatial points from the global snapshot matrix, and arranges them in chronological order to form a subdomain. Local snapshot matrix .

[0021] Dimensionality reduction is achieved by using PCA to reduce the dimensionality of the local snapshot matrix of each subdomain, specifically through singular value decomposition of the local snapshot matrix. For each subdomain... The local snapshot matrix, whose singular value decomposition is expressed as:

[0022] in It is a left singular matrix. It is a singular value matrix. It is a right singular matrix.

[0023] The method for extracting the local order reduction basis is as follows: from Before the election The column forms a local reduced-order basis. ,Right now:

[0024] The method for calculating the locally reduced-order output is as follows:

[0025] in For subdomain The local reduced-order output.

[0026] In the fourth step, for the subdomain Based on process parameter inputs and locally reduced-order outputs, a locally reduced-order Gaussian regression (GPR) model is trained to characterize the mapping relationship between process parameters and the local temperature field. The Gaussian process regression model is expressed as follows:

[0027] in, and Let these represent the mean and covariance functions, respectively. For noise variance, It is a unit tensor. The mean function is the zero-mean function, i.e. =0; the covariance function is expressed as:

[0028] in, This represents the total number of samples. For anisotropic Matérn function kernels, for any two training samples Its formula is:

[0029] in, For signal variance, For smoothness, They represent the training samples respectively. The first in One input dimension, For the first The length scale of each input dimension This is a modified Bessel function of the second kind.

[0030] In the fifth step, the hyperparameters in the GPR model Determined by maximizing the marginal likelihood function.

[0031]

[0032] The logarithmic form of the marginal likelihood function is expressed as:

[0033] The hyperparameter optimization employs a gradient-based numerical optimization method, specifically the conjugate gradient method. The optimization process involves multiple iterations until the convergence condition is met.

[0034] in The preset gradient tolerance threshold, For the first The hyperparameter values ​​for the next iteration.

[0035] In the fifth step, the new process parameters are input. Based on the local GPR model, subdomain Predicted reduced-order output The distribution is as follows:

[0036] Forecast Mean Covariance They are respectively:

[0037] Among them, subdomain The average of the reduced-order output is:

[0038] In the sixth step, for the subdomain Based on the extracted local reduction basis The reduced-order prediction output is obtained through linear transformation. Reconstructed into a subdomain temperature field:

[0039] in, For subdomain The corresponding subdomain temperature field matrix.

[0040] In the sixth step, following the reverse process of the defined spatial dimensional order x→y→z, the subdomain temperature field is rearranged through dimensional reordering. Reconstructed into three-dimensional temperature field data:

[0041] in This indicates the total number of test samples.

[0042] For subdomains According to the defined boundary coordinates Determine the spatial location index range of this subdomain within the complete material domain:

[0043]

[0044] Subdomain Reconstructed temperature field Place it in the corresponding position within the complete temperature field:

[0045] Beneficial effects 1. A data-driven method for rapid prediction of temperature field in metal additive manufacturing process, which uses logarithmic transformation to preprocess the temperature field to avoid prediction difficulties caused by extreme gradients near the molten pool; 2. A domain decomposition strategy is adopted to divide the overall computational domain into several subdomains to reduce the problem dimensionality; for each subdomain, singular value decomposition is further combined to extract the reduced-order basis of the temperature field; 3. Establish a local Gaussian process regression model based on the Matérn kernel function and train it in parallel to establish a fast mapping from process parameters to reduced-order output; during online prediction, achieve efficient and accurate prediction of the complete temperature field through parallel computation of each local model and assembly of the whole field.

[0046] The rapid temperature field prediction method for metal additive manufacturing processes provided in this application effectively solves the core problems of high cost and low efficiency in high-fidelity numerical simulation through a series of innovative technological combinations, and produces multiple synergistic technical benefits. A detailed analysis follows: (1) Through the architectural innovation of “domain decomposition + local order reduction modeling”, the computational efficiency was improved by an order of magnitude, solving the problem of “slow computation”. Technical Solution Relatedness: This invention does not choose to directly predict the computationally intensive global temperature field, but instead adopts a "domain decomposition" strategy to break down the complex global temperature field prediction problem into a series of sub-problems. Based on this, PCA is applied to each subdomain to extract reduced-order basis, projecting the high-dimensional temperature field onto a low-dimensional feature space, and then a lightweight GPR model is independently trained for each subdomain.

[0047] Mechanism of Effect: This architecture brings triple efficiency gains: First, domain decomposition "divides and conquers" large-scale problems, reducing the complexity of individual problems and laying the foundation for parallel computing. Second, PCA dimensionality reduction simplifies the input-output relationship that the GPR model needs to learn from "process parameters → hundreds of thousands of node temperatures" to "process parameters → thousands of reduced-order outputs," greatly reducing model complexity and training / prediction costs. Finally, the local GPR model only requires simple matrix operations to achieve rapid prediction of the global temperature field during online prediction.

[0048] Technical benefits achieved: This method shifts the main computational burden to the offline stage. During online prediction, the system quickly assembles a series of pre-trained small GPR models to obtain the overall prediction. Compared to traditional computational fluid dynamics (CFD) simulations that take hours to days, this method can achieve real-time / near real-time predictions in seconds or minutes, improving computational efficiency by 2-3 orders of magnitude. This makes it possible to perform large-scale parameter scanning and rapid feedback in scenarios such as process design and online monitoring.

[0049] (2) By combining the "standardized preprocessing" and the "Matérn kernel function", the robustness and prediction accuracy of the model are guaranteed, thus solving the problem of "how to ensure accuracy". Related technical solutions: This invention explicitly includes data preprocessing steps (such as logarithmic transformation of temperature data), and its core adopts a PCA-based data-driven order reduction method.

[0050] Mechanism of effect: The role of data preprocessing: Logarithmic data processing mitigates the adverse effects of the magnitude difference in raw temperature data on model training. It makes optimization algorithms (such as maximizing marginal likelihood) more stable and efficient in finding GPR hyperparameters, and avoids certain dimensional features dominating model training. This is a key prerequisite for building a high-precision and robust GPR model.

[0051] The role of the Matérn kernel function: Compared with the commonly used quadratic exponential kernel function, the Matérn kernel function can generate non-infinitely smooth function responses. This allows it to more accurately capture and characterize the local variations such as the sharp temperature gradients and melt pool boundaries that are prevalent in the temperature field of additive manufacturing, thus providing the model with stronger mathematical expressive power and making its predictions more consistent with physical reality.

[0052] The achieved technical results are as follows: preprocessing ensures that the model "learns stably," and the Matérn kernel function ensures that the model "learns accurately." The synergistic effect of the two enables the final model to not only predict quickly, but also to reproduce key physical features, including melt pool morphology, high-temperature regions, and steep temperature gradients, with prediction errors controlled within a low level permissible by engineering.

[0053] (3) By constructing a clear "offline-online" system architecture, the engineering practicality and versatility of the method are greatly enhanced. Technical Solution Relationship: This invention clearly divides the process into an offline "data preparation and model training" stage and an online "rapid prediction" stage, and clarifies the corresponding hardware implementation.

[0054] Mechanism of Effect: This architectural design allows computationally demanding tasks (CFD simulation, PCA, GPR training) to be performed upfront on a high-performance computing platform. The end user (such as a process engineer) receives a pre-trained, lightweight model integrated into a dedicated prediction system. Users do not need to understand complex CFD theory or the details of the reduced-order model, nor do they need to configure expensive simulation software. They simply set process parameters through the system's input devices, and the processor can access the model, providing visualized temperature field results within one minute via the output devices.

[0055] Technical benefits achieved: In addition to the core advantages of speed and accuracy, this method also brings significant additional technical benefits: Ease of use and accessibility: It greatly lowers the technical barrier to use, enabling non-CFD experts to make high-precision temperature field predictions.

[0056] Feasibility of optimization: The extremely high prediction speed makes this method an ideal tool for optimizing process parameters based on simulation. It can quickly traverse a huge parameter space, thereby significantly shortening the process development cycle of additive manufacturing. Attached Figure Description

[0057] Figure 1 A Gaussian process regression prediction method for the three-dimensional temperature field in metal additive manufacturing is proposed, where “PCA↓” and “PCA↑” represent PCA dimensionality reduction and reconstruction in the material domain subdomain, respectively. Figure 2 Numerical model for heat transfer problems in metal additive manufacturing; Figure 3 Material domain division in metal additive manufacturing; Figure 4 The results show the predicted three-dimensional temperature field under certain processes. Detailed Implementation

[0058] The present invention will be further described below with reference to the accompanying drawings, tables, and embodiments.

[0059] A method for predicting the three-dimensional temperature field Gaussian process in a metal additive manufacturing method, such as Figure 1 As shown, the steps of this method include: The first step involves obtaining the three-dimensional temperature field data through high-fidelity numerical simulation by solving the governing equations within the multiphysics material point method framework. The geometric extent of the numerical model is 0.6 mm × 0.3 mm × 0.18 mm (e.g., ...). Figure 2 Discretization was performed using a 4 µm element size, and the simulation physical time was 7.5 × 10⁻⁶. -4 s, and with 1 × 10 -5Temperature field data is output at time intervals of s; the material of the model is 316L stainless steel with an energy absorption rate of 0.38. Other material parameters are shown in Tables 1 and 2. The heat source is a Gaussian laser heat source with a radius of 35 µm acting on the material surface; the simulated process parameters include laser power and scanning speed, wherein the laser power is taken in 20 W intervals within the range of 160 W to 340 W, and the scanning speed is taken in 80 mm / s intervals within the range of 480 mm / s to 760 mm / s.

[0060] The second step involves arranging all the three-dimensional temperature field data obtained from the numerical simulation in the order of laser power, scanning speed, and time. The temperature field data for each time step is flattened into a column vector, which fully contains the temperature values ​​of all spatial units within the material domain at that moment. Subsequently, the column vectors corresponding to all time steps are arranged strictly from left to right according to their temporal sequence, ultimately constructing a two-dimensional global snapshot matrix. The row dimension of this matrix corresponds to the total number of spatial units within the material domain, and the column dimension is equal to the product of the total number of time steps and the number of different process parameter combinations. Then, the global snapshot matrix undergoes a logarithmic transformation preprocessing. Perform calculations, where The original temperature field in the snapshot matrix. This represents the transformed temperature field.

[0061] The third step is to spatially divide the complete material domain into multiple subdomains arranged regularly along the y and z directions, such as... Figure 3 As shown. The y-direction is divided into five sub-intervals based on the given coordinates 0, 48, 100, 204, 256, and 300µm: [0,48), [48, 100), [100, 204), [204, 256), and [256, 300]. The z-direction is also divided into five sub-intervals based on the given coordinates 0, 40, 80, 120, 160, and 180µm: [0, 40), [40, 80), [80, 120), [120, 160), and [160, 180]. Each y-sub-interval and z-sub-interval together define a subdomain. In the time dimension, according to 1 × 10⁻⁶... -5 s, 2 × 10 -5 s, 3 × 10 -5 s, 4 × 10 -5 s, 5 × 10 -5The uniform time scale is selected. Based on the subdomain range, temperature data of all spatial points satisfying different subdomains at different times are extracted from the global snapshot matrix and arranged in chronological order to form the local snapshot matrix of that subdomain. Subsequently, principal component analysis is performed on the local snapshot matrix of each subdomain, and the eigenvalues ​​and eigenvectors of the covariance matrix are calculated through eigenvalue decomposition. The first 60 principal eigenvectors are selected to form the local reduced-order basis of that subdomain. Based on the obtained local reduced-order basis, the high-dimensional temperature field data of each subdomain is projected onto the low-dimensional space to obtain the local reduced-order output of each subdomain.

[0062] The fourth step involves constructing 25 local Gaussian process regression models based on process parameter inputs and local order-reduced outputs. Laser power, scanning speed, and time are used as input features, and the local order-reduced output of the subdomain is used as the target variable. The hyperparameters of each of the 25 local Gaussian process regression models are then optimized using the conjugate gradient method. Maximize the marginal likelihood function to obtain the optimal hyperparameter configuration for each local model.

[0063] The fifth step is to achieve rapid prediction of the temperature field for new combinations of process parameters and prediction time. In this step, the new laser power value, scanning speed value and target time are simultaneously input into 25 local Gaussian process regression models that have obtained the best hyperparameters. Each model performs prediction in parallel and outputs the predicted reduced-order output of the corresponding subdomain.

[0064] The sixth step involves multiplying the predicted reduced-order output of each subdomain with the corresponding local reduced-order basis through linear transformation to reconstruct the temperature field distribution of each subdomain. Following the reverse process of the spatial dimension order x→y→z, the temperature field data of all subdomains are reorganized and stitched together according to their original spatial positions. The reconstructed temperature field of each subdomain is then precisely placed into the corresponding spatial position of the complete three-dimensional temperature field to form the final temperature field prediction result.

[0065] Step 7: Evaluation of Gaussian process regression models. The 25 local Gaussian process regression models trained using the above methods can quickly and accurately predict the three-dimensional temperature field at a given moment and any combination of process parameters in the parameter space. This modeling method has high computational efficiency, capable of predicting the global temperature field in seconds, which would require several hours of computation in traditional numerical simulations (Table 3). The model prediction results are as follows: Figure 4 As shown in the figure, the model clearly demonstrates the temperature field prediction effect under the test process parameters, verifying the effectiveness and practicality of the method of the present invention.

[0066] Based on the prediction results of the aforementioned Gaussian process regression model, a leap from passive simulation to active optimization can be achieved. This model can quickly and accurately predict the global temperature field, providing strong support for process optimization: by traversing massive combinations of process parameters in seconds, it precisely locks the optimal process window, effectively replacing costly physical trial and error. Furthermore, the model's real-time prediction capability makes it an ideal virtual sensor, which can be deeply integrated into production systems to achieve real-time monitoring of processing status and defect early warning. It can also further construct adaptive control loops to proactively adjust process parameters to ensure consistent product quality.

[0067] The Gaussian process modeling method was adopted and implemented based on the gpml toolbox. It was trained on a computer equipped with a 40-core Intel(R) Xeon(R) Gold 6248 CPU @ 2.5 GHz and 192 GB RAM. The optimization process adopted the conjugate gradient method and the maximum number of optimization steps was set to 100. The hyperparameters of the Gaussian process regression model were optimized by maximizing the marginal likelihood function to obtain the optimal hyperparameter configuration of each local model.

[0068] Table 1 shows the material parameters of 316L stainless steel.

[0069] Table 2 shows the temperature-related physical properties of 316L.

[0070] Table 3 compares the prediction times of the Gaussian process regression model and the numerical model.

[0071] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the three-dimensional temperature field in metal additive manufacturing, the method comprising the following steps: The first step is to perform high-fidelity simulation of the complete material domain in metal additive manufacturing using the multiphysics material point method, and obtain training samples of the three-dimensional temperature field evolution over time in the material domain under different process parameters. The second step is to construct a global snapshot matrix describing the dynamics of the entire material domain from the three-dimensional temperature field training samples generated in the first step, and then preprocess the snapshot matrix. The third step is to discretize the complete material domain in the first step into several subdomains, and to reduce the dimensionality of the local snapshot matrix of each subdomain based on the preprocessing in the second step, so as to extract the local reduced basis and local reduced output under the local snapshot matrix of each subdomain. The fourth step involves training a locally reduced GPR model for each subdomain based on the process parameters from the first step and the locally reduced output of each subdomain extracted in the third step. The optimal hyperparameters of each locally reduced GPR model are determined by maximizing its marginal likelihood function. The fifth step is to call the local reduced-order GPR model from the fourth step to quickly predict its expected output value in the reduced-order space for new process parameter inputs. The sixth step involves using the local reduced-order basis obtained in the third step to reconstruct the expected output value predicted in the fifth step into the full-order temperature field of the corresponding subdomain, and finally integrating it into the temperature field response of the complete material domain.

2. The method for predicting the temperature field during metal additive manufacturing according to claim 1, characterized in that: In the first step, a three-dimensional temperature field training sample is obtained by solving the following control equations; The governing equations are: in, For speed, Representing variables The mass derivative, where t is time. Indicates temperature. Indicates density, Indicates the shear viscosity coefficient. Indicates fluid pressure. Indicates the permeability coefficient. Indicates fluid volume fraction. It is a relatively small constant. Represents gravity. Indicates recoil pressure, Indicates surface tension. For specific heat, This represents the volume fraction of the metallic material. Density of metallic materials For latent heat of fusion, Indicates the thermal conductivity coefficient. This indicates the laser thermal input.

3. The method for predicting the temperature field during metal additive manufacturing according to claim 2, characterized in that: The three-dimensional temperature field training samples are spatially discretized into regular grid cells of 151×76×46, and temporally contain temperature field data at five set times that characterize the thermal process.

4. The method for predicting the temperature field during metal additive manufacturing according to claim 1, characterized in that: In the second step, the training samples of the three-dimensional temperature field at each time step are stretched into column vectors according to the spatial dimension order of x→y→z, and the column vectors of all time steps are spliced ​​together in chronological order to construct a global snapshot matrix describing the dynamics of the material domain.

5. The method for predicting the temperature field during metal additive manufacturing according to claim 4, characterized in that: In the second step, the global snapshot matrix undergoes a logarithmic transformation preprocessing, and the logarithmic transformation formula is as follows: in, The original temperature field in the snapshot matrix. The transformed temperature field, These are process parameters.

6. The method for predicting the temperature field during metal additive manufacturing according to claim 1, characterized in that: In the third step, the material domain is divided into several regular subdomains according to the thermal field distribution characteristics during the additive manufacturing process. The specific division method is as follows: the spatial continuity of the temperature field along the laser scanning path is maintained, and no partitioning is performed in the scanning direction; regions in the thermal field with temperatures not lower than the solidus temperature of the material are identified as high-gradient subdomains and divided separately, including the complete heat-affected zone of the molten pool and its surrounding high-gradient region, which is contained within a single cubic subdomain as much as possible; the remaining regions with relatively uniform thermal field distribution are divided as uniform subdomains. Subdomain partitioning is achieved through vertical scan paths. and The spatial partition boundary is defined by two directions; let the spatial domain range be determined by... and Limited, along Axis in position The division is as follows: , ,and ; Position along the z-axis The division is as follows: , ,and ; Having arbitrary spatial coordinates Data points are assigned to subdomains If and only if its coordinates simultaneously satisfy and Spatial index Mapping relationships correspond to subdomain indexes Its formula is: The subdomains in The number of grid points in a direction is determined by calculating the coordinates of the defined subdomain boundary: in The entire domain is respectively Grid spacing in the direction; and Representing the material domain in Spatial range of direction Representing subfields respectively exist The number of discrete units in a direction; For subdomains Filtering from the global snapshot matrix by spatial coordinates Extract the corresponding temperature data; based on the defined subdomain boundary conditions, identify all conditions that satisfy the conditions. and The system generates a set of spatial coordinate points, then extracts the full-time-step temperature data of these spatial points from the global snapshot matrix, and arranges them in chronological order to form a subdomain. Local snapshot matrix ; Principal component analysis is used to reduce the dimensionality of the local snapshot matrix of each subdomain, specifically by performing singular value decomposition on the local snapshot matrix; for each subdomain... The local snapshot matrix, whose singular value decomposition is expressed as: in It is a left singular matrix. It is a singular value matrix. It is a right singular matrix.

7. The method for predicting the temperature field during metal additive manufacturing according to claim 6, characterized in that: The method for extracting the local order reduction basis is as follows: from Before the election The column forms a local reduced-order basis. ,Right now: The method for calculating the locally reduced-order output is as follows: in For subdomain The local reduced-order output.

8. The method for predicting the temperature field during metal additive manufacturing according to claim 7, characterized in that: In the fourth step, for the subdomain The locally reduced-order GPR model is expressed as: in, and Let these represent the mean and covariance functions, respectively. For noise variance, As a unit tensor, the mean function is a zero-mean function, i.e. =0; the covariance function is expressed as: in, Indicates the total number of samples; For anisotropic Matérn function kernels, for any two training samples Its formula is: in, For signal variance, For smoothness, They represent the training samples respectively. The first in One input dimension, For the first The length scale of each input dimension For the modified second type of Bessel function; Hyperparameters in GPR model Determined by maximizing the marginal likelihood function; The logarithmic form of the marginal likelihood function is expressed as: The hyperparameter optimization employs a gradient-based numerical optimization method, specifically the conjugate gradient method. The optimization process involves multiple iterations until the convergence condition is met. in The preset gradient tolerance threshold, For the first The hyperparameter values ​​for the next iteration.

9. The method for predicting the temperature field during metal additive manufacturing according to claim 1, characterized in that: In the fifth step, the new process parameters are input. Based on the local GPR model, subdomain Predicted reduced-order output The distribution is as follows: Forecast Mean Covariance They are respectively: Among them, subdomain Reduced-order output mean for: 。 10. The method for predicting the temperature field during metal additive manufacturing according to claim 9, characterized in that: In the sixth step, for the subdomain Based on local order reduction basis The reduced-order prediction output is obtained through linear transformation. Reconstructed into a subdomain temperature field: in, For subdomain The corresponding subdomain temperature field matrix; In the sixth step, following the reverse process of the spatial dimensional order x→y→z, the subdomain temperature field is rearranged through dimensional reordering. Reconstructed into three-dimensional temperature field data: in Indicates the total number of test samples; For subdomains According to the boundary coordinates defined in Determine the spatial location index range of this subdomain within the complete material domain: in, Representing subfields respectively exist Start and end indices in the direction, Representing subfields respectively exist Start and end indices in the direction; Subdomain Reconstructed temperature field Place it in the corresponding position within the complete temperature field: 。

Images