Air film hole laser three-dimensional intelligent hole making method and system

Abstract

The application provides a gas film hole laser three-dimensional intelligent drilling method and system, comprising the following steps: constructing a multi-layer material digital twin model, establishing a laser-material interaction physical model and converting it into a boundary value problem of an energy conservation system, numerically solving to obtain a three-dimensional energy distribution field, combining deep reinforcement learning to realize processing parameter optimization, and generating an optimal processing track; the core feature of the method is to construct a three-level closed-loop control system including inner ring parameter regulation, middle ring track adjustment and outer ring quality optimization, to adopt multi-modal sensors to monitor the processing process in real time, to integrate multi-source data through a sensor fusion algorithm, to input real-time feedback information into a digital twin model for simulation prediction, and to dynamically adjust laser parameters and processing tracks. The application significantly improves the gas film hole processing precision and consistency, reduces defect formation, and provides an advanced solution for the manufacturing of hot end parts of an aero-engine.

Description

Technical Field

[0001] This invention relates to the field of laser processing technology, and in particular to a method and system for three-dimensional intelligent laser-based fabrication of air film cooling holes, which is used for processing air film cooling holes in high-temperature components such as combustion chamber flame tubes and nozzles of aero-engines. Background Technology

[0002] High-temperature components such as the combustion chamber flame tube and nozzles of aero-engines require numerous film cooling holes to ensure their reliability and service life in extreme operating environments. The shape, size, distribution, and angle of these cooling holes have a decisive impact on the cooling effect, thus placing extremely high demands on machining accuracy and consistency.

[0003] Traditional methods for machining film holes primarily employ electrical discharge machining (EDM) or mechanical drilling. While EDM can machine holes with complex shapes, it suffers from low efficiency and is prone to creating heat-affected zones. Mechanical drilling, on the other hand, has significant limitations when machining non-straight holes and is susceptible to defects such as coating peeling and delamination when working with composite materials like thermal barrier coatings. Laser processing, due to its non-contact nature and high precision, is gradually becoming an important method for machining film holes.

[0004] Existing laser 3D hole-making technology typically employs an open-loop processing mode with preset parameters. Parameters such as laser power and pulse width are set based on experience, and the process is completed according to a preset trajectory. This approach cannot adjust in real-time to factors such as changes in material properties, thermal accumulation effects, and plasma shielding generated during processing. This results in problems such as large variations in hole shape accuracy, difficulty in controlling processing depth, and poor batch consistency.

[0005] Furthermore, existing technologies cannot effectively predict and compensate for changes in energy absorption and material removal behavior during the processing of complex aero-engine components such as Y-shaped holes, cat-ear-shaped holes, and carbon-based composite materials (CMC). This makes it difficult to achieve high-precision closed-loop control, resulting in unstable processing quality and affecting component performance and service life. Summary of the Invention

[0006] This invention provides a method and system for three-dimensional intelligent laser-based air film hole fabrication, aiming to solve the technical problems of large differences in hole shape accuracy, difficulty in controlling processing depth, and poor batch consistency caused by the inability of existing laser three-dimensional hole fabrication technology to make real-time adjustments to factors such as changes in material properties, thermal accumulation effects, and plasma shielding formed during processing.

[0007] To achieve the above objectives, the present invention provides a method for laser-based three-dimensional intelligent hole fabrication for air film pores, comprising:

[0008] Obtain multi-dimensional feature data of the workpiece, preprocess the multi-dimensional feature data, and generate a standardized dataset;

[0009] Based on the standardized dataset, a workpiece state model is established using a stochastic time delay model, and a digital twin model is constructed by combining numerical analysis and deep learning methods to obtain the parameters of the digital twin model.

[0010] Based on the parameters of the digital twin model, a physical model of laser-material interaction is established, transforming the laser-material interaction problem into a boundary value problem of an energy-conserving system. The boundary value problem is solved using a numerical solver, outputting a three-dimensional energy distribution field. A mapping relationship between processing parameters and processing quality is established, and an intelligent optimization algorithm is used to solve the parameter optimization problem, generating a dynamic parameter adjustment strategy and the optimal processing trajectory.

[0011] Based on the dynamic parameter adjustment strategy and the optimal processing trajectory, a multi-level closed-loop control system is constructed. Real-time feedback information is obtained by collecting processing process information in real time through sensors. The real-time feedback information is input into the digital twin model for simulation calculation to obtain the prediction result of the development trend of the processing process. The laser processing parameters and processing trajectory are dynamically adjusted according to the prediction result and the real-time feedback information to complete the air film hole processing.

[0012] Furthermore, the multi-dimensional feature data includes geometric morphology data, internal structure data, material energy absorption characteristics data, thermal barrier coating thickness data, and surface roughness data.

[0013] Furthermore, the preprocessing of the multi-dimensional feature data to generate a standardized dataset includes:

[0014] The geometric morphology data of the outer surface of the workpiece is obtained by a high-precision three-dimensional laser scanner, the internal structure data of the workpiece is obtained by X-ray computational tomography, and the material energy absorption characteristics data, thermal barrier coating thickness data and surface roughness data of the workpiece are collected by thermal imager and ultrasonic detector to obtain multi-source heterogeneous data.

[0015] The multi-source heterogeneous data is filtered to remove noise interference, and the filtered data is registered to unify the coordinate system of the multi-source heterogeneous data. The registered data is then fused to generate a standardized dataset.

[0016] Furthermore, the process involves establishing a workpiece state model using a stochastic time-delay model, and constructing a digital twin model by combining numerical analysis and deep learning methods to obtain digital twin model parameters, including:

[0017] Geometric parameters, material property parameters, and thermal barrier coating parameters of the workpiece are extracted from the standardized dataset as initial state variables. Based on the initial state variables, a workpiece state vector is constructed. The workpiece state vector is represented as a stochastic time-delay differential equation with Markov switching characteristics. The workpiece state vector is affected by the time-delay function, the Markov chain, and the stochastic process. The Markov chain represents the random switching of the processing environment. A workpiece state model is established.

[0018] The workpiece state model is associated with historical processing data, and a deep neural network is used to learn the mapping relationship between the workpiece state vector and the processing response. Combined with numerical analysis methods, a temperature field evolution model, stress field evolution model and material removal model of the workpiece in the laser processing process are established to construct a digital twin model.

[0019] By training the deep neural network, the network weights, bias parameters, and model hyperparameters are obtained. Combined with numerical analysis methods and the initial state variables, the thermal conductivity coefficient of the temperature field evolution model, the elastic modulus of the stress field evolution model, and the removal rate coefficient of the material removal model are determined, thus obtaining the parameters of the digital twin model.

[0020] Furthermore, after obtaining the digital twin model parameters, the process also includes:

[0021] During laser processing, sensor data is collected in real time by deployed sensors, including temperature distribution data, stress and strain data, and material removal depth data of the workpiece. The sensor data is then converted into a real-time state vector with the same dimension as the workpiece state vector.

[0022] The real-time state vector is compared with the workpiece state vector. When the deviation between the real-time state vector and the workpiece state vector exceeds a preset threshold, it is determined that the workpiece state has changed, and the model update process is triggered.

[0023] The sensor data, corresponding processing parameters, and processing quality evaluation results are used as new historical processing experience and merged with the historical processing data to form an updated historical processing dataset. An incremental learning algorithm is used to continuously optimize the parameters of the digital twin model from the historical processing dataset to ensure the consistency between the digital twin model and the actual workpiece state.

[0024] Furthermore, the establishment of a physical model for the interaction between laser and materials transforms the laser-material interaction problem into a boundary value problem of an energy-conserving system, including:

[0025] Based on the parameters of the digital twin model, and combined with the optical, thermal and mechanical properties of the material, a physical model of the interaction between laser and multilayer material is established. The physical model includes the light absorption process, heat conduction process, phase transition process and plasma formation and shielding process, forming a set of partial differential equations describing energy transfer.

[0026] The partial differential equations are transformed into boundary value problems of Hamiltonian systems based on the principle of energy conservation. A complete description of the boundary value problems is established for different material interfaces and boundary conditions.

[0027] Furthermore, the step of using a numerical solver to solve the boundary value problem and output a three-dimensional energy distribution field includes:

[0028] The complete boundary value problem is discretized, and the solution domain is divided into grid elements using the finite element method, thus transforming the boundary value problem of the Hamiltonian system into a large-scale linear equation system.

[0029] The large-scale linear equation system is solved using the preconditional conjugate gradient method. The temperature field distribution, stress field distribution, and energy density distribution of each grid node are obtained through iterative calculation, and a three-dimensional energy distribution field is output.

[0030] Furthermore, the method of using intelligent optimization algorithms to solve the parameter optimization problem includes:

[0031] Based on the three-dimensional energy distribution field, a mapping relationship is established between laser power, frequency, pulse width, and focus position, and processing accuracy, surface roughness, and heat-affected zone. A stochastic time-delay differential equation is used to describe the impact of changes in laser power, frequency, pulse width, and focus position on processing accuracy, surface roughness, and heat-affected zone. The processing parameter optimization problem is constructed as a Markov decision process, where the state space is the current processing state of the workpiece, and the action space is the set of adjustable parameters for laser power, frequency, pulse width, and focus position. The reward function is designed based on the evaluation indicators of processing accuracy, surface roughness, and heat-affected zone. The state transition probability is calculated by combining the parameters of the digital twin model and the three-dimensional energy distribution field. A deep reinforcement learning algorithm is used to solve the Markov decision process, generating dynamic parameter adjustment strategies for different workpiece processing states.

[0032] Furthermore, the optimal processing trajectory is generated, including:

[0033] Based on the dynamic parameter adjustment strategy, the target aperture is discretized into a grid representation to generate a set of processing points. The spatial coordinates, energy requirements, and temporal constraints of each processing point are used as system variables. A system matrix is ​​constructed based on the spatial adjacency, energy transfer, and temporal dependencies between processing points. The elements of the system matrix represent the correlation strength between processing points. A complex symmetric linear system for trajectory planning is established based on the system matrix. The system matrix is ​​decomposed, and an iterative method combined with a preprocessor is applied to solve the complex symmetric linear system to generate the optimal processing trajectory, which includes the laser movement path, dwell time, and incident angle.

[0034] Based on the dynamic parameter adjustment strategy, during the processing, the real-time state vector obtained by converting the real-time feedback information is compared with the expected state corresponding to the preset trajectory as real-time processing feedback, and a trajectory dynamic adjustment mechanism is established. When the real-time processing feedback shows changes in material properties or enhanced plasma shielding, the trajectory replanning process is triggered to reconstruct the system matrix and solve the complex symmetric linear system, thereby adjusting the optimal processing trajectory in real time.

[0035] Furthermore, the construction of a multi-level closed-loop control system involves real-time feedback information obtained through sensors during the processing, which is then input into the digital twin model for simulation calculations to predict the development trend of the processing process. Based on the prediction results and the real-time feedback information, the laser processing parameters and processing trajectory are dynamically adjusted to complete the film membrane hole processing. This includes:

[0036] Based on the dynamic parameter adjustment strategy and the optimal processing trajectory, a three-level closed-loop control system is constructed, which includes inner loop parameter control, middle loop trajectory adjustment and outer loop quality optimization. High-speed cameras, spectrometers and acoustic emission sensors are deployed to collect processing information in real time. Multi-source data is integrated through sensor fusion algorithms to monitor the hole formation process, material removal status and processing defects to obtain real-time feedback information.

[0037] The real-time feedback information is input into the digital twin model, and the digital twin model is used to perform simulation calculations to predict the future hole evolution, temperature field distribution and material removal rate, so as to obtain the prediction result of the development trend of the processing process. When the prediction result exceeds the preset safety range, an early warning mechanism is triggered.

[0038] Based on the inner ring parameter control, the laser power, pulse width, frequency, and focusing depth are dynamically adjusted according to the real-time feedback information and the prediction results; based on the middle ring trajectory adjustment, the laser movement path is adjusted in real time according to the abnormal processing status shown by the prediction results; based on the outer ring quality optimization, the processed film holes are detected and evaluated online, and the processing parameters, process data, and quality evaluation results are stored in the knowledge base. The parameter-quality relationship is mined through machine learning methods to continuously optimize the processing strategy and complete the film hole processing.

[0039] This invention also provides a laser-based three-dimensional intelligent hole-making system for air film pores, comprising:

[0040] The data acquisition and preprocessing module is used to acquire multi-dimensional feature data of the workpiece, preprocess the multi-dimensional feature data, and generate a standardized dataset.

[0041] The digital twin modeling module is used to establish a workpiece state model based on the standardized dataset using a stochastic time delay model, and to construct a digital twin model by combining numerical analysis and deep learning methods to obtain the parameters of the digital twin model.

[0042] The physical model solving and optimization module is used to establish a physical model of laser-material interaction based on the parameters of the digital twin model, transform the laser-material interaction problem into a boundary value problem of an energy conservation system, solve the boundary value problem using a numerical solver, output a three-dimensional energy distribution field, establish a mapping relationship between processing parameters and processing quality, solve the parameter optimization problem using an intelligent optimization algorithm, and generate a dynamic parameter adjustment strategy and optimal processing trajectory.

[0043] A multi-level closed-loop control module is used to construct a multi-level closed-loop control system based on the dynamic parameter adjustment strategy and the optimal processing trajectory. The module collects processing process information in real time through sensors to obtain real-time feedback information. The real-time feedback information is input into the digital twin model for simulation calculation to obtain the prediction result of the processing process development trend. Based on the prediction result and the real-time feedback information, the laser processing parameters and processing trajectory are dynamically adjusted to complete the air film hole processing.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. This invention applies the energy-conserving Hamiltonian boundary value method to model laser-material interaction processes, and combines it with a low-rank solver to achieve efficient calculation of the three-dimensional energy distribution field, thus solving the problem of energy transfer prediction in multilayer composite materials;

[0046] 2. This invention constructs a Markov decision process driven by stochastic time-delay differential equations, transforming the optimization of processing parameters into a reinforcement learning problem, thereby achieving dynamic self-adjustment of parameters such as laser power, pulse width, and focusing depth;

[0047] 3. This invention innovatively applies the asymmetric HSS iterative method and a preprocessor to solve complex symmetric linear systems for machining trajectory planning of complex irregular holes such as Y-shaped and cat-ear-shaped holes, thereby improving the efficiency and accuracy of trajectory planning;

[0048] 4. This invention constructs a three-level closed-loop control system consisting of an inner loop (parameter control), a middle loop (trajectory adjustment), and an outer loop (quality optimization), achieving comprehensive and precise control from the micro to the macro level, and significantly improving the processing quality and consistency of air film holes. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a schematic flowchart of the air film pore laser three-dimensional intelligent hole-making method provided in the embodiment of the present invention;

[0051] Figure 2 This is a schematic diagram of the process for obtaining parameters by constructing a digital twin model of a workpiece using a stochastic time delay model combined with numerical analysis and deep learning, as provided in an embodiment of the present invention.

[0052] Figure 3 This is a schematic diagram of the process for dynamically adjusting the trajectory of laser film hole processing parameters by combining multi-level closed-loop control with digital twin prediction, as provided in an embodiment of the present invention.

[0053] Figure 4 This is a schematic diagram of the structure of the air film pore laser three-dimensional intelligent pore-making system provided in an embodiment of the present invention. Detailed Implementation

[0054] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0055] Example 1

[0056] like Figure 1 As shown, the present invention provides a laser-based three-dimensional intelligent hole-making method for air film pores, comprising:

[0057] Step S1: Obtain multi-dimensional feature data of the workpiece, preprocess the multi-dimensional feature data, and generate a standardized dataset;

[0058] Step S2: Based on the standardized dataset, a workpiece state model is established using a stochastic time delay model, and a digital twin model is constructed by combining numerical analysis and deep learning methods to obtain the parameters of the digital twin model.

[0059] Step S3: Based on the parameters of the digital twin model, establish a physical model of laser-material interaction, transform the laser-material interaction problem into a boundary value problem of an energy conservation system, solve the boundary value problem using a numerical solver, output a three-dimensional energy distribution field, establish a mapping relationship between processing parameters and processing quality, solve the parameter optimization problem using an intelligent optimization algorithm, and generate a dynamic parameter adjustment strategy and optimal processing trajectory.

[0060] Step S4: Based on the dynamic parameter adjustment strategy and the optimal processing trajectory, a multi-level closed-loop control system is constructed. Real-time feedback information is obtained by collecting processing process information in real time through sensors. The real-time feedback information is input into the digital twin model for simulation calculation to obtain the prediction result of the development trend of the processing process. The laser processing parameters and processing trajectory are dynamically adjusted according to the prediction result and the real-time feedback information to complete the air film hole processing.

[0061] Example 2

[0062] In this embodiment, the multi-dimensional feature data includes geometric morphology data, internal structure data, material energy absorption characteristics data, thermal barrier coating thickness data, and surface roughness data.

[0063] Specifically, geometric topography data refers to the three-dimensional spatial shape characteristics of the workpiece's outer surface, including surface contour, curvature distribution, and shape deviations. This data directly affects the incident angle and energy distribution of the laser beam during laser processing. The acquisition accuracy of geometric topography data needs to reach the micrometer level to ensure the accuracy of subsequent processing planning.

[0064] Internal structural data refers to information such as the structural composition, defect distribution, and density variations within a workpiece, especially for multi-layered aero-engine components, including the interface morphology between the thermal barrier coating and the substrate material, and potential microcracks and pores. This data is crucial for predicting the propagation path and absorption characteristics of laser energy within the material.

[0065] Material energy absorption characteristics data include the absorptivity, reflectivity, and transmittance of materials under different wavelengths of laser light, as well as the changes in the thermophysical properties of materials at different temperatures. Aero-engine components are typically made of high-temperature alloys, ceramics, or composite materials, and these different materials exhibit significantly different laser absorption characteristics. Accurately obtaining this characteristic data is fundamental to accurately predicting laser energy distribution.

[0066] Thermal barrier coating (TBC) thickness data refers to the thickness distribution information of the thermal barrier coating (TBC) covering the surface of the substrate material. TBCs are typically composed of ceramic materials and possess optical and thermal properties different from the substrate material. The inhomogeneity of their thickness directly affects the absorption and conduction of laser energy. In practical applications, the thickness of the TBC can vary within the range of 50-500 micrometers, and this variation can significantly impact the laser processing.

[0067] Surface roughness data refers to the statistical characteristics of the microscopic geometry of a workpiece surface, including parameters such as arithmetic mean roughness (Ra) and maximum profile height (Rz). Surface roughness affects the scattering and absorption characteristics of laser energy; rough surfaces typically have higher laser absorptivity but also lead to more uneven energy distribution. In film borehole machining, surface roughness has a significant impact on the material removal efficiency and borehole accuracy in the initial stage.

[0068] These five types of feature data collectively constitute a comprehensive digital representation of the workpiece, providing the necessary input parameters for subsequent accurate digital twin modeling and physical process simulation. There are interrelationships and influences among these data types; for example, surface roughness affects the accuracy of geometric topography data acquisition, and the thickness of the thermal barrier coating affects the spatial distribution of the material's energy absorption characteristics. Therefore, comprehensively and accurately acquiring these multi-dimensional feature data is crucial for achieving high-precision laser processing of film holes.

[0069] Example 3

[0070] In this embodiment, the preprocessing of the multi-dimensional feature data to generate a standardized dataset includes: acquiring geometric morphology data of the workpiece's outer surface using a high-precision 3D laser scanner; acquiring internal structural data of the workpiece using X-ray computed tomography; and collecting material energy absorption characteristics, thermal barrier coating thickness data, and surface roughness data of the workpiece using a thermal imager and an ultrasonic detector to obtain multi-source heterogeneous data. The multi-source heterogeneous data is then filtered to remove noise interference; the filtered data is registered to unify the coordinate system of the multi-source heterogeneous data; and the registered data is fused to generate a standardized dataset.

[0071] The multi-source data acquisition and preprocessing module includes various sensing devices such as 3D laser scanners, X-ray CT equipment, thermal imagers, and ultrasonic detectors. These devices acquire multi-dimensional feature data of the workpiece, and the raw data is filtered, registered, and fused to generate a standardized dataset. Filtering primarily removes noise and improves data quality; registration unifies the coordinate systems of data from different sensors; and fusion integrates heterogeneous multi-source data into a unified data representation, providing a foundation for subsequent modeling and analysis.

[0072] Specifically, a high-precision 3D laser scanner with a resolution of no less than 0.01 mm is first used to perform a full-range scan of the workpiece's outer surface. The scanning process employs a multi-angle scanning strategy, scanning the workpiece from at least 12 different angles to eliminate data blind spots caused by occlusion. The resulting point cloud data density should reach at least 100 points per square millimeter to ensure complete capture of geometric details. For complex curved surface areas, such as the area around the air film inlet, a localized densification scanning strategy is used to increase the data density to over 300 points per square millimeter.

[0073] Internal structural data were acquired using industrial-grade X-ray computational computed tomography (CT) equipment. The slice thickness was set to no more than 0.05 mm, and the voltage was adjusted within the range of 120-450 kV according to the workpiece material to ensure X-ray penetration of high-density metallic materials. During the scanning process, the workpiece rotation angle step was set to 0.2°, completing a 360° full-angle scan and acquiring approximately 1800 two-dimensional projection images. These projection images were then reconstructed into three-dimensional voxel data using a filtered back projection (FBP) algorithm or an iterative reconstruction algorithm (such as SART or OS-EM), achieving a resolution of 10-20 μm, clearly displaying the internal microstructure and interface features.

[0074] Data acquisition of the material's energy absorption characteristics was achieved using a multi-wavelength thermal imager and a pulsed laser excitation system. First, the workpiece surface was irradiated with a low-power pulsed laser (typically a 1064nm Nd:YAG laser) of the same wavelength as the processing laser, while the thermal imager recorded the surface temperature change over time. By solving the inverse problem of the thermal diffusion equation, parameters such as the material's thermal diffusivity, specific heat capacity, and absorptivity at different locations were calculated. Measurements were performed at at least 20 points uniformly distributed across the workpiece surface to capture the spatial distribution differences in the material's properties.

[0075] The measurement of thermal barrier coating thickness data combines non-contact ultrasonic testing and eddy current detection techniques. The ultrasonic detector emits ultrasonic pulses at frequencies of 20-50 MHz, and the depth of the interface between the thermal barrier coating and the substrate material is calculated by analyzing the time-domain characteristics of the echo signal. To improve measurement accuracy, five repeated measurements are performed at each measurement point, and the average value is taken as the coating thickness at that point. The measurement points are arranged in a grid along the workpiece surface, with a grid spacing of no more than 5 mm. In the predetermined processing area, the grid spacing is increased to 1 mm to obtain more refined thickness distribution information.

[0076] Surface roughness data were measured with high precision using a confocal white light interferometer. The measurement area covered the predetermined machining location and its surrounding 5 mm range, with a sampling interval of 0.5 μm and a scanning range of 1 mm × 1 mm to capture microscopic surface morphology features. Three measurements were performed at each predetermined machining location, and parameters such as the arithmetic mean roughness (Ra), the average height of ten points (Rz), and the maximum height of the surface profile (Rt) were calculated to form a surface roughness distribution map.

[0077] Multi-scale adaptive filtering algorithms were employed for filtering multi-source heterogeneous data. For 3D laser scanning data, a statistical outlier detection algorithm was first applied to identify and remove outliers. Then, a bilateral filter was applied to reduce random noise while preserving edge features. The spatial kernel radius in the filtering parameters was set to 2-3 times the average spacing of the point cloud, and the range kernel parameter was adaptively adjusted according to the noise level of the point cloud. For CT data, a 3D anisotropic diffusion filter was used. The diffusion coefficient was adaptively adjusted according to local structural features, and the number of iterations was set to 15-20 to preserve the clarity of material interfaces while reducing noise. For thermal imager and ultrasonic data, wavelet transform denoising was used. The Daubechies wavelet basis was selected, and a 3-5 level decomposition was performed. Soft thresholding was applied to the high-frequency coefficients, and then the denoised signal was reconstructed.

[0078] Multi-source heterogeneous data registration is the process of unifying data collected by different sensors into a single coordinate system. Registration uses a workpiece coordinate system established from high-precision 3D laser scanning data as a reference, employing an Iterative Closest Point (ICP) algorithm combined with geometric feature matching to achieve rigid registration. During registration, at least four feature markers are first set on the workpiece surface to ensure these points can be identified in various sensor data. Then, for CT data, surface contour information is extracted and registered with the laser scanning point cloud. Initial registration uses coarse registration based on feature points, followed by fine registration using the ICP algorithm, with registration accuracy controlled within 0.05 mm. For thermal imager, ultrasonic, and surface roughness data, a coordinate transformation matrix is ​​calculated based on pre-calibrated sensor position relationships and feature point correspondences to map the data into a unified coordinate system.

[0079] Data fusion processing integrates registered multi-source heterogeneous data into a unified data representation. This embodiment employs a multi-resolution data structure based on an octree, discretizing the space into voxel units. The voxel size is adaptively adjusted according to the required accuracy; in critical areas (such as predetermined processing positions), the voxel size is set to 0.01 mm, while the size gradually increases to 0.1 mm further away from the processing area. Each voxel contains attribute information such as geometric morphology, internal structure, material properties, coating thickness, and surface roughness. For attribute information fusion, a weighted average method is used, with weights determined based on the measurement confidence of each data source. For example, in material interface regions, the weight of CT data is increased; in surface feature representation, the weight of laser scanning data is increased. The resulting standardized dataset is a voxel model containing spatial location and multi-dimensional attribute information. Each voxel contains 23 attribute parameters, comprehensively describing the geometric, physical, and material properties of the workpiece.

[0080] Multi-source heterogeneous data refers to datasets from different sensors, possessing different physical meanings, data structures, and scales. In this system, the multi-source heterogeneous data includes 3D point cloud data (from a laser scanner), voxel data (from CT scans), temporal signal data (from an ultrasonic detector), thermal image data (from a thermal imager), and height map data (from surface roughness measurements). These data exhibit significant differences in sampling rate, data dimensionality, physical units, and noise characteristics, posing technical challenges to their direct integration and utilization.

[0081] Standardized datasets are created by preprocessing, registering, and fusing multi-source heterogeneous data into a standardized data representation. Standardization processes include spatial resolution unification, numerical range normalization, and data structure consistency. In this system, the standardized dataset uses a unified voxel model. Each voxel contains location coordinates and 23 physical property parameters, including geometric feature parameters (such as surface normal vector and curvature), material parameters (such as thermal conductivity, specific heat capacity, and absorptivity), structural parameters (such as density and coating thickness), and surface characteristic parameters (such as roughness and reflection properties). The standardized dataset provides structured input for subsequent digital twin model construction, ensuring data consistency and integrity.

[0082] Example 4

[0083] like Figure 2 As shown, in this embodiment, the step of establishing a workpiece state model using a stochastic time-delay model, and constructing a digital twin model by combining numerical analysis and deep learning methods, yields digital twin model parameters, including:

[0084] Step S21: Extract the geometric parameters, material property parameters, and thermal barrier coating parameters of the workpiece from the standardized dataset as initial state variables. Construct a workpiece state vector based on the initial state variables. Represent the workpiece state vector as a stochastic time-delay differential equation with Markov switching characteristics. The workpiece state vector is affected by the time-delay function, Markov chain, and stochastic process. The Markov chain represents the random switching of the processing environment. Establish a workpiece state model.

[0085] Step S22: Associate the workpiece state model with historical processing data, use a deep neural network to learn the mapping relationship between the workpiece state vector and the processing response, and combine numerical analysis methods to establish the temperature field evolution model, stress field evolution model and material removal model of the workpiece in the laser processing process, and construct a digital twin model.

[0086] Step S23: By training the deep neural network, obtain the network weights, bias parameters and model hyperparameters, and combine numerical analysis methods and the initial state variables to determine the thermal conductivity coefficient of the temperature field evolution model, the elastic modulus of the stress field evolution model and the removal rate coefficient of the material removal model, thereby obtaining the parameters of the digital twin model.

[0087] Among them, the stochastic time-delay differential equation state model based on Markov switching represents the workpiece state as follows:

[0088] dx(t)=f(x(t),x(t-τ(t)),r(t))dt+g(x(t),x(t-τ(t)),r(t))dω(t)

[0089] Where x(t) represents the workpiece state, Let be the drift term function of the model, τ(t) be the time delay function, r(t) be the Markov chain, and ω(t) be the standard Wiener process. This is the diffusion term function of the model. This model can capture the uncertainties and time delays in material properties and processing conditions, providing a mathematical foundation for digital twin models.

[0090] Specifically, the process of extracting initial state variables from the standardized dataset first involves dimensionality reduction and data filtering using feature engineering methods. Geometric parameter extraction includes the workpiece surface curvature distribution, local thickness variations, and the three-dimensional coordinates and normal vectors of the predetermined machining position. The curvature distribution is calculated using the principal curvature calculation method, calculating the curvature values ​​in two principal directions at each vertex to form a curvature feature map. Local thickness variations are obtained by calculating the Euclidean distance from a surface point to the nearest internal interface. A 5mm × 5mm grid is used for sampling within the predetermined machining area, and the average thickness and variance are calculated within each grid to form a thickness feature vector.

[0091] During the extraction of material property parameters, thermal and optical properties are extracted separately for different material layers. Thermal properties include thermal conductivity, specific heat capacity, and thermal diffusivity, which are directly read from standardized datasets. Optical properties include absorptivity, reflectivity, and transmittance at different wavelengths, as well as the sensitivity coefficients of these parameters to temperature changes. For thermal barrier coating materials, their porous structure characteristics, including porosity distribution and average pore size, also need to be extracted; these parameters are obtained by analyzing the grayscale distribution of CT data.

[0092] In addition to the basic thickness distribution, the parameters of thermal barrier coatings also include the bonding strength between the coating and the substrate material, interfacial roughness, and thermal stress distribution. Bonding strength is assessed by analyzing the reflection characteristics of ultrasonic signals, while interfacial roughness is calculated using the fluctuations in the interfacial profile from CT data. These parameters collectively constitute a high-dimensional feature vector describing the properties of thermal barrier coatings.

[0093] Based on the extracted initial state variables, constructing the workpiece state vector involves organizing these discrete parameters into a structured vector representation. The workpiece state vector comprises three main parts: a geometric state sub-vector, a material state sub-vector, and a thermal barrier coating state sub-vector, with a total dimension typically between 50 and 100. Each sub-vector element is normalized to limit its value range to [0,1] for easier subsequent model processing. Principal component analysis (PCA) is used for dimensionality compression in the construction of the state vector, retaining principal components that explain over 95% of the variance and avoiding redundant information from interfering with model training.

[0094] The stochastic time-delay differential equation model is one of the core innovations of this invention, used to describe the dynamic changes in the workpiece state with time and processing conditions. The stochastic time-delay characteristic is reflected in the time delay effects of energy transfer and material response during laser processing; for example, heat conduction from the surface to the interior takes time, and material phase transitions and stress release also exhibit lag. The Markov switching characteristic reflects the stochastic changes in the processing environment, such as the influence of uncertainties like laser energy fluctuations, ambient temperature changes, and plasma shielding effects.

[0095] In its implementation, the stochastic time-delay differential equation is constructed through the following steps: First, a time-delay function τ(t) is defined to represent the delay characteristics of different physical processes. For heat conduction processes, the time-delay function is related to the material thickness and thermal diffusivity; for phase transition processes, the time-delay function is related to the latent heat of the material and the local temperature gradient. Then, a Markov chain r(t) is constructed to describe the state transitions of the processing environment. The Markov chain typically contains 3-5 discrete states, such as normal processing state, plasma shielding enhancement state, and material phase transition state. The transition probability matrix between states is obtained by analyzing historical processing data. Finally, the Wiener process ω(t) is combined to describe the random perturbations of the system, thus completing the stochastic time-delay differential equation model.

[0096] The process of associating the workpiece state model with historical processing data is a crucial step in building a digital twin model. Historical processing data includes records of processing procedures and result evaluations for different workpieces, materials, and processing parameters. After cleaning, labeling, and structuring, this data forms a training dataset. Data association employs a multi-level alignment method: first, coarse-grained matching is performed based on material type and geometric features; then, fine-grained association is performed based on the similarity calculation of state vectors; finally, the most relevant case set from historical data is found for the current workpiece.

[0097] The deep neural network employs a hybrid architecture, comprising a Convolutional Neural Network (CNN) and a Long Short-Term Memory (LSTM) network. The CNN extracts spatial features from the workpiece state vector, including geometric and material distribution characteristics; the LSTM captures temporal dependencies during processing and predicts state evolution over time. The overall network structure consists of 5 convolutional layers, 3 LSTM layers, and 2 fully connected layers, with a total number of parameters ranging from 2 million to 5 million. The convolutional layers use 3×3 kernels, the LSTM layers have a hidden state dimension of 128, the fully connected layers use the ReLU activation function, and the output layer selects an appropriate activation function based on the task type.

[0098] The temperature field evolution model is based on the heat conduction equation, but introduces stochastic time delay terms and nonlinear boundary conditions to accurately describe the complex heat transfer phenomena during laser processing. The model is solved using the finite element method, discretizing the workpiece space into a tetrahedral mesh, with a significantly increased mesh density in the processing region. The thermal conductivity coefficient is set as a function of temperature, varying with increasing temperature, exhibiting significant nonlinearity, especially as the material approaches its phase transition point. The boundary conditions consider the combined effects of laser irradiation, thermal radiation, convective heat dissipation, and plasma shielding.

[0099] The stress field evolution model, based on elastoplastic mechanics theory, describes the stress distribution and evolution of materials under thermal gradients. The model considers the thermal expansion characteristics of the material, the variation of yield strength with temperature, and the interfacial stress concentration caused by the difference in thermal expansion coefficients between the thermal barrier coating and the substrate material. By solving the thermo-structural coupling equations, the model can predict defects such as thermal stress cracks and coating peeling that may occur during processing.

[0100] The material removal model, based on laser ablation theory and phase transformation kinetics, describes the removal mechanisms and rates of different materials under high-energy laser irradiation. The model distinguishes three main material removal modes: evaporation removal, melt jetting, and mechanical fragmentation, automatically determining the dominant removal mode based on local energy density and material properties. For multilayer composite materials, the model considers the influence of interface effects and abrupt changes in material properties on the removal process, accurately predicting the formation process of complex pores.

[0101] The training of the deep neural network employs a phased strategy. The first phase uses historical data for supervised learning, minimizing the mean squared error between predicted values ​​and actual processing results. The second phase combines numerical simulation with semi-supervised learning, using the output of the physical model to guide network optimization. The third phase fine-tunes network parameters through reinforcement learning to optimize performance for specific processing tasks. The training process uses the Adam optimizer, with an initial learning rate of 0.001, gradually reduced using cosine annealing. To prevent overfitting, L2 regularization and Dropout mechanisms are introduced, along with an early stopping strategy.

[0102] Network weights and bias parameters are direct results of deep neural network training; they define the connection strength and activation threshold between neurons in the network. In this system, the network weight matrix is ​​sparsified, removing weight values ​​close to zero to reduce model complexity and improve inference speed. These weights and bias parameters are saved as binary files for real-time prediction.

[0103] Model hyperparameters are high-level parameters that control the model structure and training process, including the number of network layers, number of neurons, learning rate, batch size, etc. These parameters are determined through grid search and Bayesian optimization methods. For different types of workpieces and processing tasks, the system maintains a hyperparameter template library, which can automatically select the most suitable hyperparameter combination according to the characteristics of the current task.

[0104] Digital twin model parameters are a comprehensive set of parameters containing multi-layered information, including three main categories: network parameters, physical model parameters, and state representation parameters. Network parameters define the structure and behavior of the deep learning model; physical model parameters control the accuracy and characteristics of the numerical simulation; and state representation parameters describe the current state and historical trajectory of the workpiece. These parameters together constitute the core of the digital twin model, supporting real-time model operation and prediction.

[0105] Example 5

[0106] In this embodiment, after obtaining the digital twin model parameters, the process further includes: during laser processing, real-time acquisition of workpiece temperature distribution data, stress-strain data, and material removal depth data using deployed sensors to obtain sensing data; converting the sensing data into a real-time state vector with the same dimension as the workpiece state vector; comparing the real-time state vector with the workpiece state vector; when the deviation between the real-time state vector and the workpiece state vector exceeds a preset threshold, determining that the workpiece state has changed and triggering a model update process; using the sensing data, corresponding processing parameters, and processing quality evaluation results as new historical processing experience, merging them with the historical processing data to form an updated historical processing dataset; and continuously optimizing the digital twin model parameters from the historical processing dataset using an incremental learning algorithm to ensure the consistency between the digital twin model and the actual workpiece state.

[0107] Specifically, the sensor system deployed during laser processing adopts a multimodal, multi-scale design concept, forming a comprehensive monitoring network. Temperature distribution data is acquired using a high-speed infrared thermal imager with a resolution of 640×512 pixels, a sampling frequency of no less than 200Hz, a temperature measurement range of 200-3000℃, and an accuracy of ±1% or ±1℃. The thermal imager is mounted around the laser processing head, coaxially designed with the processing optical path to ensure that the center of the field of view coincides with the laser focal point. To reduce interference from plasma radiation on the measurement, the thermal imager is equipped with an optical filter, allowing only specific bands of infrared radiation to pass through.

[0108] The acquisition of stress-strain data combines acoustic emission sensors and a laser speckle interferometry system. The acoustic emission sensors are arranged on the workpiece fixture, forming a triangulation network of at least three sensing points. The sampling frequency is set to 5MHz, and the signal preamplifier gain is 40dB. By analyzing the arrival time difference, amplitude, and spectral characteristics of the acoustic emission signals, the initiation and propagation of cracks within the material can be monitored in real time. The laser speckle interferometry system operates during processing intervals, analyzing changes in the speckle pattern on the workpiece surface to calculate the micro-strain distribution, achieving a resolution at the micro-strain level (10⁻⁶). -6 ).

[0109] The acquisition of material removal depth data employs a combination of confocal displacement sensors and structured light scanning. The confocal displacement sensor is mounted on the side of the laser processing head at a fixed angle to the processing optical path, with a measurement range of 10 mm, a resolution of 0.1 μm, and a sampling frequency of 10 kHz. During laser pulse intervals, the displacement sensor rapidly scans the aperture contour, recording depth changes. The structured light scanning system operates during processing pauses, projecting a specifically coded grating pattern. A camera captures the deformed pattern, reconstructing the three-dimensional morphology of the aperture with an accuracy of 5-10 μm.

[0110] The preprocessing of sensor data first involves targeted processing based on the characteristics of various sensors. For temperature data, a combination of mean filtering and Gaussian filtering is used to remove noise, and then a radiometric correction algorithm is used to compensate for the non-uniformity and temperature dependence of material emissivity. For acoustic emission data, wavelet decomposition is used for noise reduction, and then time-frequency analysis is used to extract characteristic parameters of acoustic emission events. For displacement and structured light data, a point cloud registration algorithm is applied to align depth information collected at different times to generate a continuous aperture evolution sequence.

[0111] Converting sensor data into real-time state vectors is a crucial step in achieving real-time updates to the digital twin model. The conversion process employs a feature mapping method, mapping multi-source sensor data to the same feature space as the workpiece state vector. First, statistical and physical features are extracted for each type of sensor data, forming feature sub-vectors. Statistical features include mean, standard deviation, peak value, and valley value, while physical features include temperature gradient, heat flux density, and strain rate. Then, a pre-trained autoencoder network compresses these feature sub-vectors into a latent space corresponding to the workpiece state vector, ensuring dimensionality matching and semantic consistency.

[0112] The comparison between the real-time state vector and the workpiece state vector employs a multi-index evaluation method. First, the Euclidean distance between the two vectors is calculated as a measure of overall deviation. Then, the cosine similarity between each sub-vector is calculated to assess directional consistency. Finally, the point-to-point deviation of key feature elements is analyzed to identify the main dimensions of change. A preset threshold is dynamically adjusted based on different processing tasks and material types, typically set to 2-3 times the standard deviation. When the overall deviation exceeds the preset threshold, or the deviation of any key feature element exceeds its specific threshold, the system determines that the workpiece state has changed significantly.

[0113] The model update process is triggered immediately upon detecting a change in the workpiece state and includes three stages: parameter identification, model structure update, and parameter re-optimization. The parameter identification stage uses the latest observation data and maximum likelihood estimation to re-identify key parameters in the stochastic time-delay differential equation, including time-delay function parameters and random perturbation strength. The model structure update stage evaluates the adaptability of the existing model structure, adjusting the number of network layers, neuron connection patterns, or introducing new feature extraction modules as necessary. The parameter re-optimization stage, while maintaining the overall model structure, uses incremental learning to update model parameters, performing local optimization only on a subset of parameters that have changed significantly, thus significantly improving update efficiency.

[0114] The integration of sensor data, machining parameters, and machining quality assessment results employs a structured data storage mechanism. Each set of machining experience is organized into a data package, containing fields such as timestamp, workpiece ID, material type, machining parameter set, sensor data sequence, machining quality indicators, and anomaly event markers. Quality indicators include quantitative metrics such as aperture accuracy (error < ±5μm), shape consistency (roundness deviation < 3μm), surface roughness (Ra < 0.8μm), and heat-affected zone width (< 30μm), obtained through offline measurement or online evaluation. After verification, the data package is stored in a distributed database, and the knowledge graph is updated simultaneously to establish relationships between different machining experiences.

[0115] The expansion and management of historical processing datasets employ a hierarchical storage structure. The latest processing experience is stored in a cache layer for fast access; validated and stable data is stored in the master data layer; and large amounts of historical data accumulated over a long period are compressed and feature-extracted before being stored in the archive layer. Data retrieval utilizes a multi-dimensional indexing method, supporting fast similarity-based queries and providing accurate historical reference cases for model updates and parameter optimization.

[0116] Incremental learning algorithms are learning methods that incrementally update the existing model based on new data, without retraining the entire model. This system employs an incremental learning algorithm based on Elastic Weight Consolidation (EWC). By calculating the Fisher information matrix of the model parameters, it identifies parameters important to the learned task and applies protective constraints to these parameters during the update process to prevent catastrophic forgetting. The algorithm executes in three steps: First, it calculates the parameter importance matrix of the existing model on historical data; second, it calculates the gradient on new data and updates the model parameters, while considering the importance constraints; finally, it updates the parameter importance matrix, integrating the influence of old and new data.

[0117] The workpiece state vector is a high-dimensional mathematical representation of the current physical state of the workpiece, typically with a dimension between 50 and 100, containing information such as geometric features, material properties, and processing status. In this system, the workpiece state vector is organized into a hierarchical structure: the top layer contains global features, such as workpiece type, material category, and processing stage; the middle layer contains regional features, such as temperature distribution, stress state, and material removal status in different regions; and the bottom layer contains local features, such as temperature values, strain values, and microstructural parameters at specific points. Each element of the state vector is normalized to distribute it within the [0,1] interval, facilitating model processing and comparison.

[0118] The real-time state vector is a representation of the current state of the workpiece constructed in real time based on sensor data. Its structure and dimensions are consistent with the workpiece state vector, but its source and construction method differ. The workpiece state vector is mainly constructed based on initial data and model predictions, while the real-time state vector is constructed entirely based on real-time sensor observation data. Comparing the two can reveal the deviation between model predictions and actual conditions, serving as an important basis for evaluating model accuracy and triggering updates.

[0119] The consistency of a digital twin model refers to the degree to which the model accurately reflects the state and behavior of the actual physical object. In this system, consistency is evaluated at three levels: static consistency, which assesses the accuracy of the model's representation of the workpiece's current state; dynamic consistency, which assesses the accuracy of the model's prediction of changes in workpiece behavior; and functional consistency, which assesses the model's effectiveness in guiding processing decisions. Through sensor feedback and incremental learning, the system can continuously improve model consistency, ensuring that the digital twin model remains highly synchronized with the actual workpiece, providing a reliable foundation for precise control of the laser processing process.

[0120] The update mechanism of the digital twin model ensures its real-time performance and accuracy. When a significant change in the workpiece's state is detected, the model update process is automatically triggered, optimizing the model parameters through an incremental learning algorithm. This dynamic update mechanism enables the digital twin model to adapt to changes in the workpiece's state and maintain synchronization with the physical workpiece.

[0121] Example 6

[0122] In this embodiment, establishing a physical model of laser-material interaction, transforming the laser-material interaction problem into a boundary value problem of an energy-conserving system, includes: based on the parameters of the digital twin model, and combined with the optical, thermal, and mechanical properties of the material, establishing a physical model of laser-multilayer material interaction, the physical model including light absorption, heat conduction, phase transition, and plasma formation and shielding processes, forming a set of partial differential equations describing energy transfer; transforming the set of partial differential equations into a boundary value problem of a Hamiltonian system based on the principle of energy conservation, and establishing a complete boundary value problem description for different material interfaces and boundary conditions.

[0123] Among them, the Hamiltonian boundary value problem transforms the laser-material interaction problem into an energy-conserving system:

[0124] H(q,p)=T(p)+V(q)

[0125] Where H represents the Hamiltonian of the system, q represents the system position (spatial distribution), p represents momentum (energy transfer rate), T represents kinetic energy, and V represents potential energy; this mathematical description can accurately reflect the distribution and evolution of energy in space, laying the foundation for subsequent numerical solutions.

[0126] Specifically, when constructing a physical model of the interaction between laser and materials, it is first necessary to clarify the energy transfer process in laser processing. Aero-engine components are typically composed of multiple layers of composite materials, including a matrix material and a thermal barrier coating. The responses of different material layers to laser energy vary significantly. Based on the material parameters and geometric information provided by the digital twin model, four key sub-models were constructed: a light absorption model, a heat conduction model, a phase transition model, and a plasma shielding model. These sub-models together describe the complete chain of physical phenomena in the laser processing process.

[0127] The optical absorption process model describes the mechanism by which laser radiation energy is absorbed by the surface and interior of materials. For Nd:YAG lasers (wavelength 1064 nm) or fiber lasers (wavelength 1070 nm), the model considers four main absorption mechanisms: surface absorption, volumetric absorption, plasmon-enhanced absorption, and multiple scattering absorption. Surface absorption is calculated using a modified Fresnel formula, treating the material's complex refractive index as a function of temperature and wavelength, while also considering the modulation effect of surface roughness on the absorptivity. For ceramic thermal barrier coatings, the Kubelka-Munk scattering theory is used to handle their translucent properties, calculating the depth-dependent volumetric absorptivity. The absorptivity is no longer a simple constant but is expressed as a complex function of spatial location, material temperature, surface state, and laser parameters. In the high energy density region, nonlinear optical effects, such as two-photon absorption and photoionization, on the alteration of material absorption characteristics are also considered.

[0128] The heat conduction process model employs a nonlinear, non-Fourier heat conduction equation to describe the diffusion of energy within the material. Traditional Fourier heat conduction theory assumes an instantaneous response between heat flow and temperature gradient; however, this assumption no longer applies in the ultrafast heating environment of laser processing. The system introduces a thermal wave model (hyperbolic heat conduction equation) to consider the finite propagation speed of heat diffusion, thus more accurately describing the rapid thermal processes under nanosecond pulsed lasers. The thermal conductivity coefficient is set as a nonlinear function of temperature, exhibiting significant changes, especially near the material's phase transition temperature. For multilayer composite materials, the model addresses the thermal resistance effect and discontinuous thermal characteristics at the interface, resolving the continuity of heat flow at the heterogeneous interface by setting contact thermal resistance and a transition layer.

[0129] The phase transition process model describes the state transitions of materials at high temperatures and the corresponding energy absorption / release. For metallic materials, solid-liquid phase transitions (melting) and liquid-gas phase transitions (vaporization) are considered; for ceramic materials, decomposition and sublimation processes are considered. The model handles the latent heat of phase transition using the effective heat capacity method, introducing a temperature-dependent equivalent specific heat capacity within the phase transition temperature range to avoid the discontinuity problem in numerical calculations of the traditional enthalpy method. Simultaneously, a phase field variable is introduced to track the spatial distribution of material phase states, accurately simulating the movement and morphological evolution of phase interfaces. For non-equilibrium phase transition processes, a kinetically corrected phase transition temperature is used, considering the superheating / supercooling effects under rapid heating conditions.

[0130] A plasma formation and shielding process model describes the plasma cloud formed in the high-temperature region of laser processing and its impact on laser transmission. When the material surface temperature reaches a sufficiently high level, a large amount of evaporated material is ionized under the influence of the laser beam to form plasma. Plasma formation is calculated using the Saha ionization equation, considering the effects of temperature, pressure, and material composition on the degree of ionization. Once formed, the plasma absorbs and scatters laser energy through inverse bremsstrahlung and light scattering processes, creating a shielding effect. The model evaluates the attenuation effect on laser transmission by calculating the complex refractive index and extinction coefficient of the plasma. Under pulsed laser conditions, the temporal evolution characteristics of the plasma, including plasma expansion, cooling, and recombination processes, are also considered; these factors collectively determine the dynamic strength of the plasma shielding.

[0131] The four sub-models mentioned above are coupled together through the principle of energy conservation, forming a set of partial differential equations describing energy transfer. The light absorption model provides the heat source term for the heat conduction model, the heat conduction model provides the temperature field for the phase transition model, the phase transition model in turn affects the heat conduction parameters, and the plasma model modulates the spatial distribution of laser energy. This multi-physics coupled set of equations typically contains highly nonlinear terms and spatiotemporal dependencies, making direct solution extremely challenging.

[0132] To efficiently solve this complex system of equations, this invention innovatively transforms the problem into a boundary value problem of a Hamiltonian system. The Hamiltonian system is a mathematical framework in physics describing energy-conserving systems, possessing excellent structural properties and numerical stability. The transformation process first defines generalized coordinates and generalized momentum, treating physical quantities such as temperature, displacement, and the degree of phase transition as generalized coordinates, and heat flow, stress, and phase transition rate as generalized momentum. Then, the system's Hamiltonian is constructed, representing the system's total energy, including kinetic energy terms (such as thermal energy and kinetic energy) and potential energy terms (such as elastic potential energy, latent heat of phase transition, and surface energy).

[0133] The boundary value problem description of a Hamiltonian system consists of three parts: system equations, boundary conditions, and initial conditions. The system equations adopt the standard Hamiltonian canonical equation form, describing the evolution of generalized coordinates and generalized momentum. Boundary conditions are set according to the physical context, including surface thermal boundary conditions (such as laser heat source input, convective heat dissipation, and radiative heat dissipation), mechanical boundary conditions (such as displacement constraints and force constraints), and phase transition boundary conditions. For the interface between the thermal barrier coating and the substrate material, a special interface continuity condition is set to ensure that heat flux and displacement satisfy the physical conservation requirements at the interface. Initial conditions are set according to the initial state of the workpiece, including the initial temperature field, initial stress field, and initial phase distribution.

[0134] A key feature of this model is its handling of interfaces between different materials. Aero-engine components typically contain multiple layers of heterogeneous materials, such as a nickel-based superalloy matrix, an MCrAlY transition layer, and a ceramic thermal barrier coating. The interface treatment between these layers employs "conservative interface conditions" to ensure that heat flux, stress, and mass flux are conserved at the interface, while also considering potential contact thermal resistance, stress concentration, and diffusion phenomena. For phase transitions and chemical reactions at the interface, an interfacial reaction kinetic model is introduced to describe the element diffusion and compound formation that may occur at the interface under high-temperature conditions.

[0135] The boundary conditions are designed to fully account for the complexity of the actual processing environment. In the laser-irradiated area, the boundary conditions employ a spatiotemporally varying heat flux density distribution, reflecting the spatial distribution (typically Gaussian) and temporal characteristics (continuous or pulsed) of the laser beam. In the unirradiated area, natural convection and radiative heat dissipation are considered, with the heat dissipation coefficient dynamically varying with temperature and environmental conditions. For radiative heat dissipation under high-temperature conditions, a modified Stefan-Boltzmann law is used, taking into account the material emissivity variation with temperature.

[0136] The Hamiltonian system boundary value problem provides a mathematically rigorous and physically sound framework, expressing the laser-material interaction process as an energy-conserving system. This representation not only conforms to the physical essence but also possesses favorable numerical properties, laying the foundation for subsequent efficient and stable numerical solutions. Using this method, the system can accurately simulate complex physical phenomena during laser processing, including heat-affected zone formation, phase transition boundary movement, thermal stress distribution, and plasma shielding effects, providing a reliable basis for optimizing film aperture processing parameters and formulating control strategies.

[0137] Example 7

[0138] In this embodiment, the step of using a numerical solver to solve the boundary value problem and output a three-dimensional energy distribution field includes: discretizing the complete boundary value problem description; dividing the solution domain into grid cells using the finite element method; transforming the boundary value problem of the Hamiltonian system into a large-scale linear equation system; solving the large-scale linear equation system using the preconditioned conjugate gradient method; obtaining the temperature field distribution, stress field distribution, and energy density distribution of each grid node through iterative calculation; and outputting a three-dimensional energy distribution field.

[0139] The numerical solution process employs the finite element method and the preconditional conjugate gradient method, which can efficiently solve large-scale linear equation systems and obtain accurate three-dimensional energy distribution fields. These numerical methods are characterized by high computational efficiency and good convergence, and are suitable for solving complex boundary value problems.

[0140] Specifically, to numerically solve the boundary value problem of a Hamiltonian system, it is first necessary to transform the continuous problem description into a discrete form. This system employs a strategy combining spatial and temporal discretization to achieve complete discretization of the problem. Spatial discretization uses the finite element method, while temporal discretization uses an implicit time integration scheme. This combination ensures both computational accuracy and good numerical stability.

[0141] Spatial discretization involves dividing the three-dimensional continuous solution domain into discrete mesh elements, approximating the unknown function with a shape function within each element. Considering the multi-scale characteristics of film borehole machining (the borehole diameter is typically 0.3-1.0 mm, while the workpiece size can reach tens of centimeters), this system employs an adaptive mesh refinement strategy to increase mesh density in key regions. Specifically, an initial tetrahedral mesh is first constructed based on the workpiece's geometric model, using the Delaunay triangulation algorithm to ensure mesh quality. Then, mesh refinement is performed near the expected laser interaction area and material interface, with the element size gradually decreasing as a function of distance from the laser center. The minimum mesh size can reach 5-10 micrometers, sufficient to capture the fine physical processes of laser machining.

[0142] To accurately handle multi-layered material structures, the mesh generation process pays special attention to the treatment of material interfaces. Interface-aligned meshing techniques are employed in the interface regions to ensure precise alignment of the mesh boundaries with the material interfaces, avoiding numerical errors caused by mesh mismatch. For thin-layer structures such as thermal barrier coatings, anisotropic mesh design is used, maintaining sufficient mesh resolution (at least 5-10 mesh layers) in the thickness direction while maintaining a relatively large mesh size in the lateral direction, balancing computational accuracy and efficiency. The final generated mesh typically contains 500,000 to 2,000,000,000 tetrahedral elements, accurately representing the workpiece's geometric features and the expected scale of physical phenomena.

[0143] The core of discretizing the boundary value problem of a Hamiltonian system is to construct the discrete form of the Hamiltonian and its canonical equations. This system employs the hybrid finite element method, simultaneously discretizing generalized coordinates (such as temperature and displacement) and generalized momentum (such as heat flux and stress), thus avoiding the locking phenomenon and instability that may occur in traditional methods. For the temperature field, linear or quadratic Lagrangian elements are used; for the displacement field, quadratic Lagrangian elements are used to accurately capture bending deformation; for phase field variables, linear elements are sufficient to express their variation characteristics.

[0144] At each finite element node, the unknowns include temperature, three-dimensional displacement components, and the degree of phase transition, totaling six degrees of freedom. For a mesh with N nodes, the total number of degrees of freedom is 6N, forming a large-scale linear system of equations. The structure of the coefficient matrix of the equation system reflects the coupling relationships between different physical fields: diagonal blocks describe the correlation within a single physical field (e.g., temperature versus temperature), while off-diagonal blocks describe the coupling between different physical fields (e.g., temperature versus displacement). This structure makes the coefficient matrix exhibit obvious blocky sparsity characteristics, which can be efficiently represented using a special storage format (e.g., Block Compacted Row Storage, BCSR).

[0145] The time discretization employs an implicit backdating difference method. While this method involves significant computational cost per step, it offers unconditional stability and allows for larger time steps. To address the multi-timescale characteristics of laser processing, the system adopts an adaptive time step strategy: during laser pulses, microsecond-level or smaller time steps are used to capture rapid thermal processes; during pulse intervals, millisecond-level time steps are used to improve computational efficiency. The time step adjustment is automatically controlled based on the rate of temperature change and phase transition rate, ensuring numerical accuracy while optimizing computational performance.

[0146] Solving large-scale linear equation systems is the core and computational bottleneck of the entire numerical computation process. Considering the scale (typically reaching millions) and sparsity of these systems, direct solution methods such as LU decomposition are computationally and memory-intensive, necessitating iterative methods. This system selects the preconditioned conjugate gradient (PCG) method as the primary solver. This method exhibits good convergence for symmetric positive definite systems and is easily parallelized.

[0147] Preconditioning techniques are crucial for improving the convergence speed of iterative methods. This system employs a combination of several preconditioning strategies: diagonal blocks utilize algebraic multigrid (AMG) preconditioning, which effectively handles multi-scale problems by constructing multi-level representations of the equations; coupled blocks employ physics-based Schur complement preconditioning, fully utilizing the scale separation characteristics between different physical fields. For thermo-structure coupled problems, a field splitting iteration strategy is adopted: first, the temperature field is solved; then, based on the updated temperature field, the displacement field is solved; finally, a fully coupled iteration is performed. This strategy significantly reduces memory requirements.

[0148] Considering the nonlinear nature of the problem, the system employs a modified Newton-Raphson method for nonlinear iteration. In each nonlinear iteration step, the coefficient matrix and right-hand side are first calculated based on the current solution. Then, the linear system is solved to obtain the increment, the solution is updated, and convergence is checked. The convergence criterion comprehensively considers the residual norm and the change in the solution; when both are simultaneously below a preset threshold (typically 10), convergence occurs. -6 When the nonlinear iteration converges, it is assumed to be convergent. To improve robustness, line search techniques and adaptive damping factors are introduced to handle numerical difficulties in strongly nonlinear regions (such as phase transition fronts).

[0149] To improve computational efficiency, the system implements a multi-layered parallel computing architecture. In thread-level parallelism, OpenMP is used to achieve multi-core parallelism on a single node; in node-level parallelism, MPI is used to achieve distributed computing across nodes. The computation domain is partitioned using the METIS algorithm to optimize load balancing and communication overhead. Specifically, for matrix-vector multiplication operations in the iterative solver, GPU acceleration technology is utilized to achieve hardware acceleration of key computational cores, increasing computational speed by 5-10 times.

[0150] The calculation of the three-dimensional energy distribution field is the final output of the numerical solution. The energy distribution field is not a direct solution of variables, but rather a result of comprehensive calculations based on the temperature field, stress field, and phase transition field. At each grid node, the system calculates the total energy density, including thermal energy (related to temperature), elastic energy (related to stress and strain), surface energy (related to the interface), and chemical energy (related to phase transition). These energy components together constitute the complete three-dimensional energy distribution field, reflecting the energy absorption, transfer, and conversion processes of the material under laser irradiation.

[0151] Post-processing and visualization of the energy distribution field are crucial aspects of the results analysis. The system supports various data extraction methods, including arbitrary cross-sections, isosurfaces, time-history curves, and spatial distribution statistics. For the temperature field, particular attention is paid to the location of the highest temperature point and the temperature gradient distribution; for the stress field, the focus is on analyzing the distribution of the maximum principal stress and potential stress concentration regions; for the phase transition field, the movement and morphological evolution of the phase interface are tracked. These analytical results are presented in the form of color contour maps, vector maps, and dynamic evolution videos, intuitively demonstrating the physical phenomena during laser processing.

[0152] The accuracy of the energy distribution field is verified using a combination of methods. First, the discretization accuracy is verified through mesh convergence studies, progressively refining the mesh in key regions until the variation in results is less than a preset threshold (typically 1%). Then, the correctness of the algorithm implementation is verified by comparing it with analytical solutions. For simplified cases (such as transient heat conduction in a semi-infinite body), the deviation between the numerical and analytical solutions is calculated to ensure that the deviation is within an acceptable range (typically less than 5%). Finally, the physical accuracy of the model is verified by comparing it with experimental data. The predicted aperture, molten pool size, and heat-affected zone range are compared with the actual measurement results, and the model parameters are adjusted until a satisfactory agreement is achieved.

[0153] The Hamiltonian system is a mathematical framework for describing energy-conserving dynamical systems, using generalized coordinates and generalized momentum as a complete description of the system's state. In this invention, the Hamiltonian system provides a unified mathematical framework for handling multiphysics coupling problems. Traditional thermal-structure-phase transition coupling analysis typically employs a method of separate solutions followed by iterative coupling, while the Hamiltonian system method treats different physical fields as different aspects of a unified system, intrinsically linking them through energy functions (Hamiltonian quantities). This approach is more consistent with the physical essence and provides better numerical properties.

[0154] The preconditioning conjugate gradient method is an efficient iterative method for solving large-scale symmetric positive definite linear equation systems. "Preconditioning" refers to constructing a preconditioning matrix that approximates the inverse matrix of the original system, thereby improving the condition number of the original system and accelerating iterative convergence. In this system, the construction of preconditions fully utilizes the physical characteristics and matrix structure of the problem. For example, the multigrid method is used to handle multi-scale effects in the temperature field, and the Schur complement method is used to handle the coupling relationships between different physical fields. These targeted preconditioning strategies improve the solution speed by 5-10 times compared to conventional methods, providing a computational foundation for real-time simulation and control.

[0155] A three-dimensional energy distribution field is a comprehensive physical quantity describing the spatial distribution of energy during laser processing. It includes not only the thermal energy distribution reflected in temperature fields, but also the elastic energy distribution reflected in stress fields, and the chemical energy distribution reflected in phase transition fields. By analyzing the three-dimensional energy distribution field, energy-dense regions and energy transfer paths can be identified, and material removal areas and potential defect formation areas can be predicted. This comprehensive energy analysis method surpasses traditional single-physics field analysis, enabling a more comprehensive understanding of the complex physical processes of laser-material interaction and providing a more reliable theoretical basis for optimizing processing parameters and formulating control strategies.

[0156] Example 8

[0157] In this embodiment, the method of solving the parameter optimization problem using an intelligent optimization algorithm includes: establishing a mapping relationship between laser power, frequency, pulse width, and focus position, and processing accuracy, surface roughness, and heat-affected zone based on the three-dimensional energy distribution field; describing the impact of changes in laser power, frequency, pulse width, and focus position on processing accuracy, surface roughness, and heat-affected zone using stochastic time-delay differential equations; constructing the processing parameter optimization problem as a Markov decision process, where the state space is the current processing state of the workpiece, the action space is the set of adjustable parameters of laser power, frequency, pulse width, and focus position; designing the reward function based on the evaluation indicators of processing accuracy, surface roughness, and heat-affected zone; calculating the state transition probability by combining the parameters of the digital twin model and the three-dimensional energy distribution field; and solving the Markov decision process using a deep reinforcement learning algorithm to generate the dynamic parameter adjustment strategy for different workpiece processing states.

[0158] Among them, parameter optimization based on deep reinforcement learning constructs the processing parameter optimization problem as a Markov decision process, and learns the optimal parameter policy through deep reinforcement learning algorithms. This method can handle the uncertainty and randomness in the processing process and generate highly adaptive dynamic parameter adjustment policies.

[0159] Specifically, establishing the mapping relationship between laser parameters and processing quality indicators based on the three-dimensional energy distribution field is the foundation of parameter optimization. First, a multi-factor orthogonal experimental scheme is designed for the specific material combination and geometric characteristics of the workpiece to systematically explore the parameter space. The experimental scheme includes four key parameters: laser power (400-1200W), pulse frequency (10-50kHz), pulse width (50-500ns), and focusing position (-2mm to +2mm, relative to the workpiece surface). Each parameter is set with 5-7 levels, forming a complete parameter combination matrix. For each parameter combination, the three-dimensional energy distribution field is calculated using the aforementioned digital twin model and physical solver, and processing quality-related characteristic parameters are extracted from it.

[0160] The machining quality assessment employs three key indicators: machining accuracy, surface roughness, and heat-affected zone (HAZ) extent. Machining accuracy is quantified by two parameters: aperture error (the difference between the expected and actual diameter) and roundness deviation (the maximum deviation of the actual profile from the ideal circle), with target values ​​within ±5 μm and 3 μm, respectively. Surface roughness is characterized by the arithmetic mean roughness Ra, with a target value below 0.8 μm. The HAZ extent is defined as the width of the region where the temperature exceeds half the material's phase transition temperature, with a target value typically not exceeding 50 μm. These indicators are calculated by analyzing the temperature gradient, maximum temperature range, and energy density distribution in the three-dimensional energy distribution field, forming the assessment function.

[0161] To accurately describe the dynamic impact of laser parameter variations on processing quality, a stochastic time-delay differential equation model is introduced. This model considers the time delay characteristics and random disturbances between parameter adjustment and quality response, better reflecting the physical nature of actual processing. The stochastic time-delay differential equation is expressed as a set of coupled stochastic differential equations, where the quality index serves as the state variable, the laser parameters as the control input, the time-delay term reflects the delay effects of energy accumulation and material response, and the random term describes the uncertainties caused by the processing environment and material inhomogeneities.

[0162] The determination of the time delay function is based on a combination of physical mechanism analysis and data fitting. For heat conduction processes, the time delay is directly proportional to the square of the material thickness and inversely proportional to the thermal diffusivity; for phase transition processes, the time delay is directly proportional to the latent heat and inversely proportional to the energy input rate. By analyzing the temporal relationship between parameter adjustments and quality changes in historical processing data, the parameters of the time delay function are identified using the maximum likelihood estimation method, forming a time delay function library for different materials and processing conditions.

[0163] The characteristics of the random term are determined by analyzing the dispersion of repeated experimental results. Multiple repeated experiments are conducted under the same parameter conditions, and the fluctuation range and distribution characteristics of the quality indicators are statistically analyzed to fit the intensity and probability distribution of the random perturbation. The study found that in most cases, the random perturbation can be approximated as additive white Gaussian noise. However, under high-power conditions with significant plasma shielding, the perturbation exhibits non-Gaussian characteristics, requiring a more complex stochastic process model for description.

[0164] Constructing the parameter optimization problem as a Markov Decision Process (MDP) is a key step in applying reinforcement learning methods. A Markov Decision Process is a mathematical framework describing sequential decision problems, comprising four core elements: state space, action space, state transition probabilities, and reward function. In this system, the state space is defined as a high-dimensional vector describing the current processing state of the workpiece, containing physical quantities such as current processing depth, surface morphology, temperature distribution, and material removal rate, as well as historical processing trajectories and parameter sequences. The state dimension is typically between 50 and 100.

[0165] The motion space is defined as the adjustable set of laser parameters, including power adjustment range (±20%, step size 5%), frequency adjustment range (±5kHz, step size 1kHz), pulse width adjustment range (±50ns, step size 10ns), and focus position adjustment range (±0.5mm, step size 0.1mm). Considering the response characteristics of actual processing systems, a rate limit is set for parameter adjustments to ensure the smoothness and feasibility of parameter changes. The total dimension of the motion space is the number of combinations of power × frequency × pulse width × focus position, typically between 1000 and 3000.

[0166] The design of the reward function directly affects the achievement of the optimization objective and is a key factor in the success of reinforcement learning. A multi-objective weighted reward function is adopted, comprehensively considering three quality indicators: processing accuracy, surface roughness, and heat-affected zone. The reward function R is defined as a weighted combination of these three indicators, with the weighting coefficients dynamically adjusted according to the specific application's quality requirements. For each quality indicator, a nonlinear mapping function is designed to map the indicator value to a reward value in the interval [-1, 1]. The mapping function has its maximum gradient near the target value, encouraging the system to converge towards the optimal quality region. Simultaneously, a parameter smoothing term is introduced into the reward function to penalize excessively drastic parameter changes, improving the stability of the processing.

[0167] The calculation of state transition probabilities combines physical model predictions with historical data statistics. Based on a digital twin model and a three-dimensional energy distribution field, the system can predict the deterministic component of evolution to the next state given the current state and action; by combining the characteristics of the stochastic terms in the stochastic time-delay differential equation, the stochastic component of state transition is calculated. Finally, the state transition probability is expressed as a conditional probability distribution P(s'|s,a), that is, the probability that the system will transition to state s' after taking action a in the current state s. This physical-based probabilistic model is more reliable than purely data-driven methods, especially when training data is limited.

[0168] The choice of deep reinforcement learning algorithm considered the high dimensionality, continuity, and partial observability of the problem. A proximal policy optimization (PPO) algorithm based on the Actor-Critic architecture was adopted, which achieves a good balance between stability and sample efficiency. The Actor network is responsible for policy learning, mapping observed states to parameter adjustment actions; the Critic network is responsible for value evaluation, predicting the long-term cumulative reward of the current state. Both networks are implemented using deep neural networks, including feature extraction layers, memory layers, and decision layers.

[0169] The Actor network structure consists of 3 convolutional layers (for handling spatially distributed data), 2 long short-term memory layers (for capturing temporal dependencies), and 3 fully connected layers (for comprehensive decision-making). The input layer receives a state vector, and the output layer generates the probability distribution of parameter adjustment actions. The network uses a softmax function to output the probability of discrete parameter selection, or a hyperbolic tangent function (tanh) to output the magnitude of continuous parameter adjustments. The Critic network structure is similar to Actor, but its output layer has only one neuron, used to predict state values.

[0170] The network training employs a phased strategy. The first phase takes place in a simulated environment, utilizing a digital twin model and a physical solver to construct a virtual processing environment, accelerating strategy exploration and initial convergence. The second phase incorporates actual processing experiments, using data generated from real processing equipment to further optimize network parameters and bridge the gap between the model and reality. The training process employs an experience replay mechanism, storing historical experience in a replay buffer and randomly sampling for network updates, breaking down correlations between samples and improving learning stability. Simultaneously, a priority experience replay strategy is adopted to increase the probability of selecting rare but information-rich samples.

[0171] To address the diversity of material properties and the complexity of operating conditions in aero-engine components, a meta-learning framework is introduced, enabling the algorithm to rapidly adapt to new materials and operating conditions. Meta-learning constructs general knowledge for parameter tuning by pre-training basic strategies under various materials and operating conditions, and then fine-tunes them with a small number of samples on specific tasks, achieving rapid adaptation. This approach significantly reduces the learning curve for new materials and operating conditions, improving the system's versatility and engineering practicality.

[0172] The generation of dynamic parameter adjustment strategies is the final output of deep reinforcement learning. The strategy is represented as a mapping function from state to action, outputting the optimal parameter adjustment decision given the current workpiece processing state. To improve the interpretability and credibility of the strategy, it also outputs the decision confidence level and the expected quality improvement magnitude, helping operators understand and evaluate the automatically generated parameter recommendations. The strategy also includes anomaly detection and handling mechanisms; when abnormal states are detected in the processing (such as excessive plasma shielding or material anomalies), it can generate a safety recovery strategy to prevent the expansion of processing defects.

[0173] Stochastic time-delay differential equations are a special type of differential equation that combines the characteristics of stochastic differential equations and time-delay differential equations, simultaneously describing the time delay effect and the influence of random disturbances in a system. In the context of laser processing, the time delay effect manifests as the delay between energy input and material response, such as the time required for heat conduction from the surface to the interior, and the incubation period for material phase transitions; random effects arise from uncertainties such as laser energy fluctuations, material inhomogeneities, and environmental disturbances. Traditional differential equations struggle to characterize both effects simultaneously, while stochastic time-delay differential equations provide a unified mathematical framework, more accurately describing the dynamic characteristics of laser processing.

[0174] Markov Decision Processes (MDFs) are the theoretical foundation of reinforcement learning. They describe a class of sequential decision-making problems where the system state evolves over time according to the Markov property (the next state depends only on the current state and action, independent of historical paths), and the decision-maker maximizes long-term cumulative rewards by choosing actions. In this system, MDFs provide a formal expression for the parameter optimization problem, viewing the process as a trajectory of a series of parameter decision points, with the goal of finding the parameter sequence that optimizes the quality index. Although the actual process may not perfectly satisfy the Markov property (due to time delays), by incorporating historical information into the state definition, the system constructs an augmented state space that satisfies the Markov property, enabling the effective application of reinforcement learning methods.

[0175] The dynamic parameter adjustment strategy is the core output of this system. It is a mapping function from processing state to parameter decisions, capable of adaptively adjusting laser parameters based on the real-time state of the workpiece. Compared with traditional fixed-parameter schemes, the dynamic adjustment strategy can cope with changes in material properties, geometric shapes, and processing environment disturbances, maintaining stable processing quality. The "dynamic" nature of the strategy is reflected in three levels: spatial dynamics, adjusting parameters according to the geometry and material properties of the processing position; temporal dynamics, adjusting parameters according to the processing stage and cumulative thermal effects; and responsive dynamics, adjusting parameters based on real-time feedback information. This multi-layered dynamism enables the strategy to cope with various complex situations, significantly improving processing quality and stability.

[0176] Example 9

[0177] In this embodiment, generating the optimal processing trajectory includes: discretizing the target aperture shape into a grid representation based on the dynamic parameter adjustment strategy to generate a set of processing points; using the spatial coordinates, energy requirements, and temporal constraints of each processing point as system variables; constructing a system matrix based on the spatial adjacency, energy transfer, and temporal dependencies between processing points, where the elements of the system matrix represent the correlation strength between processing points; establishing a complex symmetric linear system for trajectory planning based on the system matrix; decomposing the system matrix; applying an iterative method combined with a preprocessor to solve the complex symmetric linear system to generate an optimal processing trajectory including the laser movement path, dwell time, and incident angle; based on the dynamic parameter adjustment strategy, comparing the real-time state vector obtained by converting the real-time feedback information with the expected state corresponding to the preset trajectory during processing as real-time processing feedback, establishing a dynamic trajectory adjustment mechanism; when the real-time processing feedback shows changes in material properties or enhanced plasma shielding, triggering a trajectory replanning process, reconstructing the system matrix and solving the complex symmetric linear system, and adjusting the optimal processing trajectory in real time.

[0178] The trajectory planning algorithm discretizes the target hole shape into a set of processing points and generates the optimal processing trajectory by solving a complex symmetric linear system. A dynamic trajectory adjustment mechanism is also established, which can adjust the trajectory based on real-time processing feedback to adapt to state changes during the processing.

[0179] Specifically, the first step in generating the optimal processing trajectory based on the dynamic parameter adjustment strategy is to convert the target aperture shape into a computer-processable discrete representation. The system employs a multi-resolution mesh discretization method, determining the mesh density based on the aperture shape's geometric characteristics and accuracy requirements. For standard film pores (typically 0.3-1.0 mm in diameter, with an aspect ratio of 3:1 to 5:1), a uniform mesh is used in the internal region, with a mesh cell size of 10-20 μm, sufficient to represent fine geometric features; adaptive mesh refinement is used in the edge region, with the mesh size refined to 5 μm to accurately characterize the contour features; and a gradually sparser mesh is used in the far-field region to optimize computational resources. The mesh generation process considers the material hierarchy, ensuring mesh node alignment at different material interfaces to avoid discretization errors.

[0180] The generation of the processing point set is based on mesh representation and material removal strategy. The system first determines the voxel regions where material needs to be removed based on the 3D geometry of the target aperture, then maps these voxels to surface processing points, taking into account the laser beam's penetration capability and the material removal mechanism. For multilayer composite materials, the system identifies key interface locations and sets control points at these locations to ensure the accuracy of interface processing. The processing point density is proportional to the local geometric complexity, increasing the point density in regions with large curvature changes. The final generated processing point set typically contains hundreds to thousands of points, each containing 3D spatial coordinates and expected removal depth information.

[0181] Determining the energy requirement for each processing point is a crucial step in trajectory planning. The energy requirement is not a simple fixed value, but rather the result of comprehensive calculations based on multiple factors. First, the system considers local material properties such as thermal conductivity, specific heat capacity, melting point, and latent heat, parameters extracted from a digital twin model. Second, it considers local geometric characteristics such as surface normals, curvature, and thickness variations, factors that affect laser energy absorption and propagation. Third, it considers the required processing depth; greater depth requires higher energy, but the relationship is usually non-linear. Finally, it considers the energy accumulation effect in adjacent areas to avoid quality problems caused by overheating. Taking all these factors into account, the system calculates the energy demand density (J / mm²) for each processing point. 3 ) and total energy demand (J).

[0182] Setting time constraints ensures a balance between processing time efficiency and heat accumulation control. Time constraints fall into several categories: absolute time constraints, such as total processing time limits; relative time constraints, such as processing sequence requirements for specific areas; and cooling time constraints, ensuring sufficient cooling time for heat-sensitive areas. These constraints are represented by time window parameters, assigning each processing point an earliest possible processing time and a latest required processing time, forming a set of time constraints. The setting of time constraints considers the thermophysical properties of the material and the dynamic response characteristics of the laser equipment, maximizing processing efficiency while ensuring quality.

[0183] Constructing the system matrix is ​​a core step in expressing the complex relationships between processing points. The system matrix is ​​an N×N square matrix, where N is the number of processing points, and the matrix element Aij represents the correlation strength between point i and point j. The correlation strength is determined by three main factors: spatial adjacency, energy transfer, and temporal dependency. Spatial adjacency is calculated based on Euclidean distance; the closer the distance, the stronger the correlation. Energy transfer considers the heat conduction path and the range of heat influence, using a heat diffusion model to calculate the energy transfer coefficient. Temporal dependency considers the impact of processing order on quality; the influence of earlier processing points on later processing points is usually greater than the reverse influence. The construction of the system matrix integrates these three relationships, forming a weighted sum. The weight coefficients are determined through model optimization and experimental verification.

[0184] The system matrix possesses several important properties: First, it is a sparse matrix because the correlation between distant points is usually negligible, with most elements approaching zero; second, it is a symmetric matrix, i.e., Aij = Aji, reflecting the reciprocity of the relationships between points; and third, it is a positive semi-definite matrix, satisfying the principle of energy conservation. These properties provide the conditions for efficient numerical solutions. The calculation of matrix elements employs a block-parallel method, performing accurate calculations for nearest-neighbor pairs and using approximate models for distant pairs, thus balancing accuracy and computational efficiency.

[0185] Establishing trajectory planning for complex symmetric linear systems based on the system matrix is ​​a key step in transforming the optimization problem into a solution problem. The basic form of a linear system is Ax'=b, where A is the system matrix, x' is the vector of the processing point access order and dwell time to be solved, and b is the vector of energy demand and constraints. The system construction follows the principle of minimum energy, that is, finding the minimum energy path that satisfies the energy demand and constraints. This mathematical expression transforms the complex trajectory planning problem into a standard linear system solution problem, making efficient numerical methods possible.

[0186] Decomposing the system matrix is ​​a preparatory step before solving the problem, aiming to reduce computational complexity and improve numerical stability. Considering the sparsity and symmetry of the matrix, the Cholesky decomposition method is adopted, decomposing matrix A into the form LLᵀ, where L is a lower triangular matrix. Cholesky decomposition is the most efficient decomposition method for symmetric positive definite matrices, with lower computational complexity and storage requirements than general matrix decomposition. For large-scale problems (more than 1000 processing points), incomplete Cholesky decomposition is used, sacrificing some accuracy for a significant speed improvement, as a preprocessing step.

[0187] The solution of complex symmetric linear systems employs an iterative approach combined with a preprocessor. The primary solver is the conjugate gradient method (CG), one of the most efficient iterative methods for solving symmetric positive definite systems. The preprocessor is dynamically selected based on the problem size and characteristics: for small to medium-sized problems (processing points < 1000), complete Cholesky decomposition is used as the direct preprocessor; for large-scale problems, incomplete Cholesky decomposition or algebraic multigrid (AMG) is used as the iterative preprocessor. This preprocessing technique significantly improves the iteration convergence speed; for typical-sized problems (processing points 500-2000), the solution time is reduced from tens of seconds to a few seconds, meeting real-time computing requirements.

[0188] The initial results obtained from the solution are the access sequence and dwell time of the processing points, which require further processing to form a complete processing trajectory. First, the discrete processing point sequence is converted into a continuous path, and spline interpolation is used to generate a smooth path curve to ensure the stability of the laser head movement. Then, the optimal incident angle for each point is calculated, considering the surface normal vector, material properties, and laser absorption characteristics. Typically, the incident angle deviates from the surface normal by no more than 30 degrees to ensure energy absorption efficiency. Finally, the dwell time distribution is optimized to ensure that the energy input matches the demand, while also considering material heat dissipation and thermal accumulation effects. The complete processing trajectory includes three core elements: spatial path (XYZ coordinate sequence), dwell time (the time spent at each position), and incident angle (the angle between the laser beam and the surface).

[0189] Real-time processing feedback is the foundation for dynamically adjusting the trajectory. Processing information is collected through multiple sensors and converted into a real-time state vector. Key sensor information includes: the temperature field of the processing area (acquired by a high-speed infrared camera), plasma intensity (monitored by a photomultiplier tube), material removal depth (measured by a confocal sensor), and surface morphology (acquired through structured light scanning). This raw sensor data is filtered, registered, and feature-extracted, transforming it into a real-time state vector with the same dimension as the workpiece state vector, achieving a unified representation of the state space.

[0190] The real-time state vector is compared with the desired state corresponding to the preset trajectory to generate real-time processing feedback. The system defines multi-level comparison indicators: the first-level indicator is the absolute deviation of key state parameters (such as maximum temperature and removal depth); the second-level indicator is the statistical deviation of state distribution characteristics (such as temperature gradient and surface roughness); and the third-level indicator is the matching degree of state evolution trends. These indicators are weighted and combined to form a comprehensive evaluation indicator, which serves as the decision-making basis for triggering trajectory adjustments. The evaluation adopts a sliding window method to ensure insensitivity to instantaneous fluctuations while rapidly responding to persistent deviations.

[0191] The trajectory dynamic adjustment mechanism includes three levels of adjustment strategies: parameter fine-tuning, local trajectory adjustment, and global trajectory replanning. Parameter fine-tuning is the most basic adjustment, adjusting laser power, pulse frequency, or movement speed while keeping the path unchanged; it is suitable for minor deviations. Local trajectory adjustment addresses significant deviations in a specific area, replanning the access sequence, incident angle, or dwell time for that area without affecting other areas. Global trajectory replanning is the most thorough adjustment, triggered when a significant change in material properties or a significant enhancement in plasma shielding is detected; it reconstructs the entire system matrix and solves for a new optimal trajectory. The selection of the adjustment level is based on the degree and nature of the deviation, following the "principle of minimum intervention," minimizing the adjustment amplitude while ensuring processing quality.

[0192] Detecting changes in material properties is a crucial condition for triggering trajectory reprogramming. By analyzing the spatiotemporal evolution of the temperature field, changes in the material's thermophysical properties are identified. Under normal circumstances, the diffusion rate and peak temperature of the temperature field have a deterministic relationship with material properties; when a significant deviation from the expected temperature response is detected, the system determines that the material properties have changed. Typical examples include changes in thermal conductivity (manifested as an abnormal thermal diffusion rate), specific heat capacity (manifested as an abnormal heating rate), and phase transition characteristics (manifested as an abnormal temperature plateau). An adaptive threshold judgment criterion is established, with the threshold value determined based on historical data statistics and physical model predictions, and dynamically adjusted as processing experience accumulates.

[0193] Enhanced plasma shielding is another key condition for triggering trajectory reprogramming. Plasma shielding is a common phenomenon in high-power laser processing. When the material surface temperature is extremely high, the evaporated material is ionized by the laser to form a plasma cloud, which absorbs or scatters some of the laser energy, reducing the effective energy reaching the workpiece surface. The strength of the plasma shielding is monitored by a dedicated photoelectric detection system, measuring the radiation intensity within a specific wavelength range. When the detected plasma intensity exceeds a preset threshold (typically three times the baseline value) and the duration exceeds a critical value (typically 100-200 μs), the system determines that the plasma shielding is significantly enhanced.

[0194] The trajectory replanning process is a complete optimization calculation. First, based on the latest real-time status and sensor data, the parameters of the digital twin model are updated, especially adjusting the material property parameters related to the current deviation. Then, the energy requirements for the remaining processing points are recalculated, considering the actual situation of completed processing and the latest material properties. Next, the system matrix is ​​reconstructed, and the relationships between processing points are updated. Finally, the updated complex symmetric linear system is solved to generate a new optimal trajectory. The entire replanning process is typically completed within 50-200ms, meeting the timeliness requirements of real-time adjustment.

[0195] To ensure trajectory continuity and smooth transition, the system employs a special connection strategy during replanning. The new trajectory starts from the current laser position, and the system is designed with a smooth transition curve connecting the end point of the original trajectory and the starting point of the new trajectory, avoiding sudden acceleration or directional changes of the laser head. Simultaneously, the laser parameters are also designed with a gradual adjustment process, transitioning from the original parameters to the new parameters gradually within 0.1-0.5 seconds to avoid abrupt changes in processing quality. This smooth transition strategy ensures that the processing maintains stability and continuity even after trajectory replanning.

[0196] The performance evaluation of dynamic trajectory adjustment was conducted in two ways: offline evaluation and online evaluation. Offline evaluation used historical processing data to simulate the impact of trajectory adjustment on processing quality and calculate the degree of quality improvement before and after adjustment. Online evaluation collected adjustment effect data in real time during actual processing and statistically analyzed the correlation between adjustment triggering conditions and quality results. Evaluation results showed that dynamic trajectory adjustment technology can effectively cope with material changes and plasma interference, reducing the standard deviation of processing accuracy by 40-60%, and significantly improving processing stability and yield.

[0197] The system matrix is ​​a mathematical structure describing the complex relationships between processing points. Unlike traditional adjacency or distance matrices, it contains richer physical information. In this system, each element Aij of the system matrix comprehensively expresses the thermal influence, material interaction, and temporal constraints between processing points i and j, which can be understood as a kind of "coupling degree" or "interference intensity." This representation transforms complex physical relationships into mathematical forms, enabling the trajectory optimization problem to be solved using mature numerical methods. The construction process of the system matrix is ​​essentially extracting and encoding the knowledge implicit in the physical model into the matrix elements. It considers both first principles of physics (such as the law of heat conduction) and data-driven empirical rules (such as the statistical properties of material parameters).

[0198] Complex symmetric linear systems are a special class of linear equation systems whose coefficient matrices satisfy symmetry (A=A). TThis linear system also possesses complex structural characteristics (such as block sparsity and multi-scale properties). In this system, this linear system is the mathematical expression of the trajectory planning problem, and its solution corresponds to the optimal processing trajectory. Compared with traditional optimization algorithms (such as genetic algorithms and simulated annealing), transforming the problem into a linear system solution has two significant advantages: first, it has high computational efficiency, especially for large-scale problems, where the algorithm complexity of linear system solutions is usually lower than that of combinatorial optimization algorithms; second, it has good numerical stability, is not prone to getting trapped in local optima, and has less dependence on initial values. This method integrates the advantages of optimization theory and numerical computation methods, and is an innovative approach to solving high-dimensional complex optimization problems.

[0199] Real-time machining feedback is a comprehensive real-time evaluation mechanism, unlike traditional single-parameter monitoring. Traditional methods typically monitor only a single physical quantity (such as temperature or position), while real-time machining feedback is based on state vector comparison, comprehensively considering multi-dimensional machining state information. The state vector includes physical quantities such as temperature distribution, phase transition degree, material removal depth, and surface morphology, comprehensively describing the current state of the workpiece. Comparing the real-time state with the expected state not only determines the magnitude of the deviation but also analyzes the nature and cause of the deviation, providing more targeted information for adjusting strategies. This state-space based feedback mechanism is the key to the system's ability to achieve intelligent adaptive control, enabling the system not only to react to "what" but also to reason about "why," thereby achieving a higher level of machining intelligence.

[0200] Example 10

[0201] like Figure 3 As shown, in this embodiment, the construction of a multi-level closed-loop control system involves real-time feedback information obtained by sensors collecting processing information in real time. This real-time feedback information is then input into the digital twin model for simulation calculations to obtain a prediction of the processing trend. Based on the prediction results and the real-time feedback information, the laser processing parameters and processing trajectory are dynamically adjusted to complete the film membrane hole processing. This includes:

[0202] Step S41: Based on the dynamic parameter adjustment strategy and the optimal processing trajectory, a three-level closed-loop control system is constructed, which includes inner loop parameter control, middle loop trajectory adjustment and outer loop quality optimization. High-speed cameras, spectrometers and acoustic emission sensors are deployed to collect processing information in real time. Multi-source data is integrated through sensor fusion algorithms to monitor the hole formation process, material removal status and processing defects to obtain real-time feedback information.

[0203] Step S42: Input the real-time feedback information into the digital twin model, use the digital twin model to perform simulation calculations, predict the hole evolution, temperature field distribution and material removal rate at future moments, and obtain the prediction result of the development trend of the processing process. When the prediction result exceeds the preset safety range, trigger the early warning mechanism.

[0204] Step S43: Based on the inner ring parameter control, dynamically adjust the laser power, pulse width, frequency, and focusing depth according to the real-time feedback information and the prediction results; based on the middle ring trajectory adjustment, adjust the laser movement path in real time according to the abnormal processing status shown by the prediction results; based on the outer ring quality optimization, perform online detection and evaluation of the processed film holes, store the processing parameters, process data, and quality evaluation results in the knowledge base, mine the parameter-quality relationship through machine learning methods, continuously optimize the processing strategy, and complete the film hole processing.

[0205] The multi-level closed-loop control system includes three levels of closed-loop control: inner loop parameter adjustment, middle loop trajectory adjustment, and outer loop quality optimization. The inner loop is responsible for real-time adjustment of laser parameters, the middle loop is responsible for dynamic trajectory optimization, and the outer loop is responsible for continuous improvement of processing quality. All control loops work together to achieve comprehensive and precise control from micro to macro levels.

[0206] Specifically, constructing a multi-level closed-loop control system is a key step in achieving high-precision film aperture laser processing. This system, based on a hierarchical control concept, decomposes the complex processing control task into different functional levels, each focusing on a specific control objective and time scale. The three-level closed-loop control architecture consists of inner-loop parameter control, middle-loop trajectory adjustment, and outer-loop quality optimization, forming a complete control system from micro to macro, and from rapid response to long-term optimization. This hierarchical design fully considers the multi-scale and multi-physics characteristics of the laser processing process, enabling more precise and comprehensive control of the processing.

[0207] The inner loop parameter control layer, located at the bottom of the control system, is responsible for real-time adjustment of laser parameters, including four key parameters: power, pulse width, frequency, and depth of focus. The inner loop is characterized by fast response speed (typically microseconds to milliseconds), high update frequency (up to the kilohertz level), and high control accuracy (power control accuracy better than ±1%, pulse width control accuracy better than ±5ns). The inner loop controller employs an adaptive PID (proportional-integral-derivative) structure, automatically adjusting control parameters according to the processing status. A feedforward compensation mechanism is introduced into the control algorithm, adjusting parameters in advance based on predictions from a digital twin model to reduce system lag. The inner loop also includes an anomaly detection and rapid response module. When anomalies such as plasma shielding or material mutations are detected, a preset safety response strategy can be executed within microseconds to prevent the formation of processing defects.

[0208] The intermediate trajectory adjustment layer, located in the middle layer of the control system, is responsible for the dynamic optimization of the laser movement path, with a time scale ranging from milliseconds to seconds. Based on machining state assessment and prediction results, the intermediate control dynamically adjusts the laser beam's trajectory, incident angle, and dwell time on the workpiece surface. The intermediate controller employs a model predictive control (MPC) framework, using a digital twin model to predict system behavior over several future time steps, solving a rolling optimization problem, and generating the optimal control sequence. To address the challenges of real-time computation, an approximate MPC method is used, compressing computation time to the millisecond level through pre-computed control law libraries and fast interpolation techniques, meeting real-time control requirements. The intermediate loop also includes a path planner, which can quickly generate new path schemes when a significant change in machining strategy is detected, ensuring machining continuity and smooth transitions.

[0209] The outer-loop quality optimization layer, located at the outermost layer of the control system, is responsible for the overall assessment and long-term optimization of processing quality, with a time scale ranging from minutes to hours. Based on the quality assessment results of the complete processing cycle, the outer loop optimizes control strategies and parameter settings, improving the system's adaptability and intelligence. The outer-loop control employs a data-driven optimization method, combining empirical models and machine learning techniques to mine parameter-quality relationships from historical processing data and continuously improve processing strategies. The outer loop also includes a knowledge management system, which structurally stores the parameters, process data, and quality assessment results of each processing cycle, forming a continuously expanding knowledge base to support experience accumulation and knowledge transfer. Through long-term optimization by the outer loop, it can adapt to changes such as new materials, new processes, and equipment aging, maintaining stable processing quality.

[0210] The coordinated operation of a multi-level closed-loop control system relies on efficient information flow and decision-making mechanisms. The three control loops interact through hierarchical data interfaces: the inner loop provides parameter adjustment status and constraints to the middle loop, while the middle loop provides trajectory execution status and abnormal event records to the outer loop. Decision-making authority is allocated according to urgency; the inner loop can override instructions from the middle and outer loops to handle emergencies, and the middle loop can override instructions from the outer loop to handle anomalies of moderate urgency. A conflict resolution mechanism is also designed; when decisions from different control loops conflict, consensus is reached through preset priority rules and negotiation algorithms. This coordination mechanism ensures stable operation and consistent decision-making within a complex and ever-changing processing environment.

[0211] The sensor system is a critical infrastructure for acquiring real-time processing information, employing a multimodal, multi-scale sensor deployment scheme. High-speed cameras are the core of visual monitoring, using a dual-camera configuration: one high-frame-rate camera (10,000-20,000 frames / second) focuses on the laser's point of action, capturing rapid dynamic processes; the other high-resolution camera (resolution > 4MP) monitors the entire working area, providing a global view. The cameras are equipped with special optical filters to filter out the laser's operating wavelength, preventing overexposure and enhancing the observation capabilities of the plasma and molten pool. The video stream undergoes real-time image processing to extract key features such as aperture shape, molten pool size, and plasma morphology.

[0212] The spectrometer is used to monitor spectral information during processing, capturing characteristic spectral lines of material elements and plasma luminescence properties. The system employs a high-resolution (<0.1 nm), wide spectral range (200-1100 nm) spectrometer with a sampling frequency of 1 kHz. Spectral data is analyzed in real-time using a characteristic spectral line recognition algorithm to identify changes in material composition, phase transition processes, and plasma characteristics. In particular, by monitoring the intensity ratio of characteristic spectral lines of specific elements (such as Ni, Cr, and Al), the penetration state and interface positions of multilayer materials can be determined, providing crucial information for precise control. The spectrometer is also equipped with a time-resolved function, which can distinguish the spectral characteristics of different stages during the laser pulse process, revealing more detailed physical processes.

[0213] Acoustic emission sensors are used to capture acoustic signals during the machining process, which contain rich information about material deformation, phase transitions, and defect formation. A network of 4-8 high-sensitivity (>60dB), wide-bandwidth (50kHz-1MHz) acoustic emission sensors is deployed to locate the sound source. The sensors are fixed around the workpiece using specially designed waveguides to maximize signal transmission efficiency. After pre-amplification (40dB gain) and bandpass filtering, the acoustic emission signals enter a high-speed data acquisition system (sampling rate >5MHz). Real-time signal processing algorithms extract characteristic parameters from the acoustic emission waveforms, such as ring count, energy, peak frequency, and duration, to identify material removal mechanisms and potential defects. By analyzing the time difference of arrival of the acoustic emission signals, the system can accurately locate the sound source and correlate it with a specific machining area.

[0214] In addition to the core sensors mentioned above, a variety of auxiliary sensing devices are integrated: a thermal imager monitors the temperature field distribution on the workpiece surface, a displacement sensor measures workpiece deformation, a power meter monitors the laser output power in real time, and a reflective photodetector monitors the laser reflection on the workpiece surface. These sensors form a comprehensive monitoring network, capturing information about the processing from different angles.

[0215] Sensor fusion algorithms are a key technology for integrating heterogeneous data from multiple sources, enabling the acquisition of comprehensive information that a single sensor cannot provide. The fusion process consists of three levels: data-level fusion, feature-level fusion, and decision-level fusion. Data-level fusion first addresses the time synchronization problem of sensor data by aligning data from different sampling rates onto a unified time axis using high-precision timestamps (accuracy <1μs) and interpolation algorithms. Then, it handles the spatial registration problem, establishing precise transformation relationships between different sensor coordinate systems and mapping all observation data to a unified workpiece coordinate system.

[0216] Feature-level fusion combines feature parameters extracted from different sensors into a multimodal feature vector. It reduces the dimensionality of the feature space through feature selection algorithms and feature transformation methods (such as principal component analysis and autoencoders), extracting the most informative combined features. The fusion employs a weighted combination method, with weights dynamically adjusted based on sensor reliability and feature correlation. For example, under high-power conditions, plasma shielding can affect the reliability of visual data; therefore, the system will reduce the weight of visual features and increase the weight of acoustic emission features.

[0217] The decision-level fusion adopts the Dempster-Shafer evidence theory framework, treating the judgment results of different sensors as uncertain evidence, and deriving a comprehensive judgment through evidence synthesis rules. This method can effectively handle sensor conflicts and uncertainties, improving the robustness of the system. For example, when the vision system judges the aperture to be normal but the acoustic emission system detects an abnormal signal, the fusion algorithm will provide a comprehensive evaluation result and confidence level based on historical experience and current reliability.

[0218] Through sensor fusion, comprehensive monitoring of the processing is achieved. For the hole formation process, the fusion algorithm comprehensively utilizes visual, spectral, and acoustic emission data to track changes in hole diameter, depth, and shape in real time with an accuracy of ±10μm. For material removal, it can identify different removal mechanisms (evaporation, melt jetting, or mechanical fragmentation) and estimate the removal rate, providing a basis for parameter adjustment. For processing defects, the system can detect potential problems such as microcracks, unfused areas, and interface delamination at an early stage, triggering corresponding intervention measures.

[0219] Inputting real-time feedback information into the digital twin model is a crucial step in achieving predictive control. The feedback information first undergoes data preprocessing, including noise filtering, outlier detection, and data normalization, before being injected into the digital twin model via the model interface. Data injection employs a state estimation method, combining sensor observations with model predictions to update the model's state variables. The system uses an ensemble Kalman filter (EnKF) to achieve state estimation for high-dimensional nonlinear systems. This method represents the state distribution through a set of multiple model instances (typically 20-50), effectively handling uncertainties in both the model and observations.

[0220] The digital twin model employs a multi-timescale, multi-resolution computational strategy. For short-term predictions (milliseconds), the model uses complete physical equations to accurately simulate the laser-material interaction process; for medium-term predictions (seconds), the model appropriately simplifies the physical process while retaining key influencing factors; for long-term predictions (minutes), the model is further abstracted, using simplified models and statistical prediction methods. This hierarchical computational strategy balances prediction accuracy and computational efficiency, enabling the system to achieve multi-timescale predictions with limited computing resources.

[0221] Aperture evolution prediction is one of the core functions of a digital twin model. Based on the current processing state and future control inputs, it predicts changes in aperture, depth, and shape. The prediction process considers various physical processes such as material removal mechanisms, thermal effects, and material flow, accurately simulating the formation of complex geometric features. The aperture prediction results are represented as a 3D mesh model with a resolution of 5-10 μm, sufficient to capture fine structural features. The prediction results also include uncertainty estimates, displayed as confidence intervals for aperture wall positions, helping the control system assess the reliability of the predictions.

[0222] The temperature field distribution prediction is based on heat conduction and energy input models, taking into account the nonlinear thermal properties and latent heat of phase change of the material. The prediction results show the three-dimensional temperature distribution inside the workpiece, focusing on the extent of the heat-affected zone, the location of the highest temperature, and the temperature gradient distribution. The system pays special attention to regions where the temperature exceeds the material's melting point or decomposition temperature, where uncontrollable material removal or defect formation may occur. The temperature field prediction also considers thermal cycling effects, simulating the heat accumulation and material property changes caused by multiple laser scans.

[0223] Material removal rate prediction is crucial for optimizing processing efficiency and quality. The prediction model, based on energy balance principles and material response characteristics, calculates the instantaneous removal rate and cumulative removal amount at different locations. The model distinguishes between different removal mechanisms (such as evaporation, melt jetting, and mechanical fragmentation) and considers their interactions. The removal rate prediction results are presented as a spatial distribution map, showing high and low removal rate regions, guiding the optimization and adjustment of processing parameters and trajectories.

[0224] The early warning mechanism is a crucial component for ensuring processing safety and quality. The system defines multiple levels of safety ranges: a soft limit range (the system issues a warning but continues processing when the material approaches this range); a hard limit range (the system intervenes when this range is exceeded); and an emergency limit range (the system executes an emergency stop procedure when this range is exceeded). Safety range parameters include maximum temperature (typically limited to 200-300°C below the material's boiling point), temperature gradient (typically limited to below 500°C / mm), stress level (limited to below 80% of the material's yield strength), and plasma intensity (limited to below a threshold level). Warning information is presented to operators through both visual and audible means, simultaneously triggering corresponding automatic intervention procedures.

[0225] Inner-loop parameter control is the most basic control level, responsible for adjusting the laser's output parameters in real time. Power control, based on feedback temperature information and predicted energy demand, achieves precise control through a sophisticated power modulator (response time <100μs). The system employs a combined feedforward and feedback control strategy; the feedforward part calculates the ideal power curve based on model predictions, while the feedback part corrects for actual deviations. The power adjustment range is typically 70%-120% of the nominal power, with an adjustment accuracy better than 1%.

[0226] Pulse width modulation (PWM) is used for pulsed lasers to control the duration of a single pulse. The pulse width directly affects the energy transfer depth and the size of the heat-affected zone (HAZ). Shorter pulse widths (e.g., 50-100 ns) are suitable for fine surface machining, while longer pulse widths (e.g., 200-500 ns) are suitable for deep hole machining. PWM is based on the material removal state and predicted thermal accumulation effects, optimizing energy distribution while maintaining stable average power. The pulse width adjustment process considers the physical limitations and response delay of the laser, employing pre-compensation techniques to improve control accuracy.

[0227] Frequency modulation is used to control the repetition rate of a pulsed laser, affecting the temporal distribution of energy input. Higher frequencies result in more uniform energy input but lower single-pulse energy; lower frequencies result in higher single-pulse energy but may lead to uneven energy input. Frequency modulation is based on the material's thermal properties and removal mechanisms, employing different frequency strategies for different processing stages. For example, in the initial stage of hole preparation, lower-frequency (10-20kHz) high-energy pulses are used to rapidly penetrate the surface layer, while in the finishing stage, higher-frequency (30-50kHz) low-energy pulses are used to improve surface quality.

[0228] Depth-of-focus control manages the distance between the laser beam's focal point and the workpiece surface, directly affecting energy density distribution and machining depth. The system employs a fast focusing system (such as an acousto-optic deflector or liquid lens) to achieve millisecond-level focus position adjustment. The focus position control strategy dynamically adjusts based on the current machining depth and the expected hole shape. For example, in multi-layer material machining, when the laser penetrates a new material layer, the system adjusts the focal point position according to the material properties to optimize energy distribution. Depth-of-focus control considers the beam's propagation characteristics within the material, including effects such as refraction, scattering, and absorption.

[0229] The mid-loop trajectory adjustment is based on processing status assessment and prediction results, dynamically optimizing the laser beam's movement path. When the prediction model indicates an abnormal processing status, the mid-loop control system triggers the trajectory adjustment process. Abnormal states include various situations: excessively high local temperatures, potentially leading to over-ablation; excessive temperature gradients, potentially causing thermal cracking; enhanced plasma shielding, reducing energy transfer efficiency; and changes in material properties, such as encountering hard phases or pores. The system selects appropriate adjustment strategies based on the type of abnormality, ranging from simple local avoidance to complex global replanning.

[0230] The trajectory adjustment employs a real-time path planning algorithm to generate new movement paths while ensuring processing continuity. The algorithm is based on fast Marsher distance field calculations, marking abnormal areas as high-cost regions and using an improved A* algorithm to search for the optimal path. To improve computational efficiency, the system adopts a hierarchical planning strategy: first, a global path is planned on a coarse-grained grid, and then local details are optimized on a fine-grained grid. The entire planning process is typically completed within 10-50ms, meeting the requirements for real-time adjustment.

[0231] Path adjustment involves not only spatial trajectory but also time scheduling and parameter configuration. The system recalculates the dwell time at each point to ensure that energy input matches material requirements. Simultaneously, it adjusts the laser incident angle, optimizes energy absorption efficiency, and controls the reflection direction to avoid interference from reflected light on already processed areas. For areas requiring reprocessing, the system schedules cooling time, waiting for the temperature to drop to a safe range before proceeding with further processing.

[0232] Outer ring quality optimization focuses on overall processing quality and process improvement, continuously optimizing processing strategies through online inspection, evaluation, and knowledge accumulation. The online inspection system integrates multiple measurement technologies: a 3D optical scanner measures hole geometry with an accuracy of ±5μm; a confocal microscope assesses surface roughness with a resolution of 0.1μm; a thermal imaging system detects residual thermal stress distribution; and an ultrasonic testing system detects internal defects and interface quality. These inspection devices perform measurements immediately during or after processing pauses, providing comprehensive quality data.

[0233] The quality assessment employs a multi-index comprehensive scoring system, with indicators including geometric accuracy (aperture, roundness, taper deviation), surface quality (roughness, microcracks, slag), internal quality (interface bonding, heat-affected zone width, residual stress), and functional performance (flow rate testing, film cooling efficiency estimation). Each indicator is assigned a weight based on application requirements, and a comprehensive quality score is calculated. The system also performs a stability assessment of the processing, analyzing parameter fluctuations, trajectory deviations, and quality consistency to identify unstable factors and potential improvement points.

[0234] The knowledge base serves as the system's long-term memory, storing detailed information on all historical processing steps. It employs a structured data model, comprising multiple interconnected data tables: a workpiece information table (material composition, geometric features, application scenario), a processing parameter table (laser settings, trajectory configuration, auxiliary gas parameters), a process data table (sensor records, abnormal events, adjustment history), and a quality assessment table (measured values ​​of various indicators, comprehensive score, defect records). Data storage utilizes a distributed database system, supporting high-speed writing and complex queries. Data is stored in encrypted form to ensure intellectual property security.

[0235] Machine learning methods are used to mine parameter-quality relationships from accumulated processed data, providing data-driven guidance for policy optimization. The system employs multiple algorithms: supervised learning algorithms (such as random forests and gradient boosting trees) build predictive models of parameters and quality indicators; unsupervised learning algorithms (such as cluster analysis and principal component analysis) identify patterns and associations in the data; reinforcement learning algorithms continuously optimize control strategies; and deep learning algorithms extract high-level features and complex relationships from large-scale sensor data. The machine learning process utilizes an online learning framework, continuously updating the model as new data accumulates, adapting to changes in materials, equipment, and the environment.

[0236] Continuous optimization is the core function of outer-loop control, transforming the results of knowledge base and machine learning into practical improvements to processing strategies. The optimization process includes three aspects: parameter optimization, trajectory optimization, and control strategy optimization. Parameter optimization adjusts parameter ranges and default values ​​based on quality feedback, gradually narrowing the optimal parameter window with accumulated experience. Trajectory optimization improves path generation rules and priority settings by analyzing the relationship between historical processing paths and quality. Control strategy optimization adjusts the structure and parameters of the control algorithm, such as PID controller gain, MPC prediction time domain and constraints, and reinforcement learning reward functions, gradually perfecting the control system.

[0237] A multi-level closed-loop control system is a hierarchical control architecture that decomposes complex control tasks into different functional levels, each focusing on a specific control objective and time scale. This control architecture originates from industrial control theory, but the innovation of this system lies in its application to the field of laser precision machining, integrating digital twin and artificial intelligence technologies. Multi-level closed-loop control differs from traditional single-level feedback control, which only focuses on the stability of a single parameter and struggles to handle the multi-variable, multi-objective control requirements of complex machining processes. Through hierarchical design, multi-level closed-loop control achieves comprehensive closed-loop control from micro-parameter control to macro-quality assurance, significantly improving the system's ability to cope with complex situations and the stability of machining quality.

[0238] Sensor fusion algorithms are information processing methods that comprehensively utilize data from multiple sensors, aiming to obtain complete information that a single sensor cannot provide. Unlike simple data stitching, true sensor fusion needs to consider the spatiotemporal alignment of data, the representation of uncertainty, the mining of complementarity, and conflict resolution. The sensor fusion algorithm in this system is based on a Bayesian inference framework, treating each sensor's data as an incomplete observation of the true state. By integrating these observations through a probabilistic model, the most probable true state is inferred. This probabilistic fusion method effectively handles noise, uncertainty, and inconsistency in sensor data, providing more reliable state estimates and a solid foundation for control decisions.

[0239] The prediction of process development trends is a key output of the digital twin model. It's not merely a simple extrapolation, but a comprehensive prediction based on physical models and historical data. The prediction process considers the system's nonlinear dynamic characteristics, random disturbances, and time delay effects, enabling it to capture potential abrupt changes and critical behaviors during complex processes. The prediction results include multiple possible evolutionary paths and their probability distributions, rather than just a single deterministic prediction. This allows the control system to assess the risks and benefits of different decisions and make more informed choices. The prediction timeframe is dynamically adjusted: short-term predictions (milliseconds) emphasize accuracy for immediate control decisions, while long-term predictions (seconds to minutes) focus on trend capture for strategic planning and risk warning.

[0240] like Figure 4 As shown, the present invention also provides a three-dimensional intelligent laser-based hole-making system for air film pores, comprising:

[0241] The data acquisition and preprocessing module 10 is used to acquire multi-dimensional feature data of the workpiece, preprocess the multi-dimensional feature data, and generate a standardized dataset.

[0242] The digital twin modeling module 20 is used to establish a workpiece state model based on the standardized dataset using a stochastic time delay model, and to construct a digital twin model by combining numerical analysis and deep learning methods to obtain digital twin model parameters.

[0243] The physical model solving and optimization module 30 is used to establish a physical model of laser-material interaction based on the parameters of the digital twin model, transform the laser-material interaction problem into a boundary value problem of an energy conservation system, solve the boundary value problem using a numerical solver, output a three-dimensional energy distribution field, establish a mapping relationship between processing parameters and processing quality, solve the parameter optimization problem using an intelligent optimization algorithm, and generate a dynamic parameter adjustment strategy and optimal processing trajectory.

[0244] The multi-level closed-loop control module 40 is used to construct a multi-level closed-loop control system based on the dynamic parameter adjustment strategy and the optimal processing trajectory. It collects processing process information in real time through sensors to obtain real-time feedback information, inputs the real-time feedback information into the digital twin model for simulation calculation to obtain the prediction result of the development trend of the processing process, and dynamically adjusts the laser processing parameters and processing trajectory according to the prediction result and the real-time feedback information to complete the air film hole processing.

[0245] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for laser-based three-dimensional intelligent hole fabrication for air film pores, characterized in that, include: Obtain multi-dimensional feature data of the workpiece, preprocess the multi-dimensional feature data, and generate a standardized dataset; Based on the standardized dataset, a workpiece state model is established using a stochastic time delay model, and a digital twin model is constructed by combining numerical analysis and deep learning methods to obtain the parameters of the digital twin model. Based on the parameters of the digital twin model, a physical model of laser-material interaction is established, transforming the laser-material interaction problem into a boundary value problem of an energy-conserving system. The boundary value problem is solved using a numerical solver, outputting a three-dimensional energy distribution field. A mapping relationship between processing parameters and processing quality is established, and an intelligent optimization algorithm is used to solve the parameter optimization problem, generating a dynamic parameter adjustment strategy and the optimal processing trajectory. Based on the dynamic parameter adjustment strategy and the optimal processing trajectory, a multi-level closed-loop control system is constructed. Real-time feedback information is obtained by collecting processing process information in real time through sensors. The real-time feedback information is input into the digital twin model for simulation calculation to obtain the prediction result of the development trend of the processing process. The laser processing parameters and processing trajectory are dynamically adjusted according to the prediction result and the real-time feedback information to complete the air film hole processing.

2. The method according to claim 1, characterized in that, The multi-dimensional feature data includes geometric morphology data, internal structure data, material energy absorption characteristics data, thermal barrier coating thickness data, and surface roughness data.

3. The method according to claim 2, characterized in that, The preprocessing of the multi-dimensional feature data to generate a standardized dataset includes: The geometric morphology data of the outer surface of the workpiece is obtained by a high-precision three-dimensional laser scanner, the internal structure data of the workpiece is obtained by X-ray computational tomography, and the material energy absorption characteristics data, thermal barrier coating thickness data and surface roughness data of the workpiece are collected by thermal imager and ultrasonic detector to obtain multi-source heterogeneous data. The multi-source heterogeneous data is filtered to remove noise interference, and the filtered data is registered to unify the coordinate system of the multi-source heterogeneous data. The registered data is then fused to generate a standardized dataset.

4. The method according to claim 3, characterized in that, The process involves establishing a workpiece state model using a stochastic time-delay model, and constructing a digital twin model by combining numerical analysis and deep learning methods. The resulting digital twin model parameters include: Geometric parameters, material property parameters, and thermal barrier coating parameters of the workpiece are extracted from the standardized dataset as initial state variables. Based on the initial state variables, a workpiece state vector is constructed. The workpiece state vector is represented as a stochastic time-delay differential equation with Markov switching characteristics. The workpiece state vector is affected by the time-delay function, the Markov chain, and the stochastic process. The Markov chain represents the random switching of the processing environment. A workpiece state model is established. The workpiece state model is associated with historical processing data, and a deep neural network is used to learn the mapping relationship between the workpiece state vector and the processing response. Combined with numerical analysis methods, a temperature field evolution model, stress field evolution model and material removal model of the workpiece in the laser processing process are established to construct a digital twin model. By training the deep neural network, the network weights, bias parameters, and model hyperparameters are obtained. Combined with numerical analysis methods and the initial state variables, the thermal conductivity coefficient of the temperature field evolution model, the elastic modulus of the stress field evolution model, and the removal rate coefficient of the material removal model are determined, thus obtaining the parameters of the digital twin model.

5. The method according to claim 4, characterized in that, After obtaining the digital twin model parameters, the process also includes: During laser processing, sensor data is collected in real time by deployed sensors, including temperature distribution data, stress and strain data, and material removal depth data of the workpiece. The sensor data is then converted into a real-time state vector with the same dimension as the workpiece state vector. The real-time state vector is compared with the workpiece state vector. When the deviation between the real-time state vector and the workpiece state vector exceeds a preset threshold, it is determined that the workpiece state has changed, and the model update process is triggered. The sensor data, corresponding processing parameters, and processing quality evaluation results are used as new historical processing experience and merged with the historical processing data to form an updated historical processing dataset. An incremental learning algorithm is used to continuously optimize the parameters of the digital twin model from the historical processing dataset to ensure the consistency between the digital twin model and the actual workpiece state.

6. The method according to claim 5, characterized in that, The establishment of a physical model for the interaction between laser and materials transforms the laser-material interaction problem into a boundary value problem of an energy-conserving system, including: Based on the parameters of the digital twin model, and combined with the optical, thermal and mechanical properties of the material, a physical model of the interaction between laser and multilayer material is established. The physical model includes the light absorption process, heat conduction process, phase transition process and plasma formation and shielding process, forming a set of partial differential equations describing energy transfer. The partial differential equations are transformed into boundary value problems of Hamiltonian systems based on the principle of energy conservation. A complete description of the boundary value problems is established for different material interfaces and boundary conditions.

7. The method according to claim 6, characterized in that, The process of solving the boundary value problem using a numerical solver and outputting a three-dimensional energy distribution field includes: The complete boundary value problem is discretized, and the solution domain is divided into grid elements using the finite element method, thus transforming the boundary value problem of the Hamiltonian system into a large-scale linear equation system. The large-scale linear equation system is solved using the preconditional conjugate gradient method. The temperature field distribution, stress field distribution, and energy density distribution of each grid node are obtained through iterative calculation, and a three-dimensional energy distribution field is output.

8. The method according to claim 7, characterized in that, The method of using intelligent optimization algorithms to solve parameter optimization problems includes: Based on the three-dimensional energy distribution field, a mapping relationship is established between laser power, frequency, pulse width, and focus position, and processing accuracy, surface roughness, and heat-affected zone. A stochastic time-delay differential equation is used to describe the impact of changes in laser power, frequency, pulse width, and focus position on processing accuracy, surface roughness, and heat-affected zone. The processing parameter optimization problem is constructed as a Markov decision process, where the state space is the current processing state of the workpiece, and the action space is the set of adjustable parameters for laser power, frequency, pulse width, and focus position. The reward function is designed based on the evaluation indicators of processing accuracy, surface roughness, and heat-affected zone. The state transition probability is calculated by combining the parameters of the digital twin model and the three-dimensional energy distribution field. A deep reinforcement learning algorithm is used to solve the Markov decision process, generating dynamic parameter adjustment strategies for different workpiece processing states.

9. The method according to claim 8, characterized in that, Generate the optimal processing trajectory, including: Based on the dynamic parameter adjustment strategy, the target aperture is discretized into a grid representation to generate a set of processing points. The spatial coordinates, energy requirements, and temporal constraints of each processing point are used as system variables. A system matrix is ​​constructed based on the spatial adjacency, energy transfer, and temporal dependencies between processing points. The elements of the system matrix represent the correlation strength between processing points. A complex symmetric linear system for trajectory planning is established based on the system matrix. The system matrix is ​​decomposed, and an iterative method combined with a preprocessor is applied to solve the complex symmetric linear system to generate the optimal processing trajectory, which includes the laser movement path, dwell time, and incident angle. Based on the dynamic parameter adjustment strategy, during the processing, the real-time state vector obtained by converting the real-time feedback information is compared with the expected state corresponding to the preset trajectory as real-time processing feedback, and a trajectory dynamic adjustment mechanism is established. When the real-time processing feedback shows changes in material properties or enhanced plasma shielding, the trajectory replanning process is triggered to reconstruct the system matrix and solve the complex symmetric linear system, thereby adjusting the optimal processing trajectory in real time.

10. The method according to claim 9, characterized in that, The construction of a multi-level closed-loop control system involves real-time data acquisition of processing information via sensors to obtain real-time feedback information. This real-time feedback information is then input into a digital twin model for simulation calculations to predict the development trend of the processing process. Based on the prediction results and the real-time feedback information, laser processing parameters and processing trajectories are dynamically adjusted to complete the film membrane hole processing. This includes: Based on the dynamic parameter adjustment strategy and the optimal processing trajectory, a three-level closed-loop control system is constructed, which includes inner loop parameter control, middle loop trajectory adjustment and outer loop quality optimization. High-speed cameras, spectrometers and acoustic emission sensors are deployed to collect processing information in real time. Multi-source data is integrated through sensor fusion algorithms to monitor the hole formation process, material removal status and processing defects to obtain real-time feedback information. The real-time feedback information is input into the digital twin model, and the digital twin model is used to perform simulation calculations to predict the future hole evolution, temperature field distribution and material removal rate, so as to obtain the prediction result of the development trend of the processing process. When the prediction result exceeds the preset safety range, an early warning mechanism is triggered. Based on the inner ring parameter control, the laser power, pulse width, frequency, and focusing depth are dynamically adjusted according to the real-time feedback information and the prediction results; based on the middle ring trajectory adjustment, the laser movement path is adjusted in real time according to the abnormal processing status shown by the prediction results; based on the outer ring quality optimization, the processed film holes are detected and evaluated online, and the processing parameters, process data, and quality evaluation results are stored in the knowledge base. The parameter-quality relationship is mined through machine learning methods to continuously optimize the processing strategy and complete the film hole processing.

11. A three-dimensional intelligent laser-based hole-making system for air-film pores, characterized in that, include: The data acquisition and preprocessing module is used to acquire multi-dimensional feature data of the workpiece, preprocess the multi-dimensional feature data, and generate a standardized dataset. The digital twin modeling module is used to establish a workpiece state model based on the standardized dataset using a stochastic time delay model, and to construct a digital twin model by combining numerical analysis and deep learning methods to obtain the parameters of the digital twin model. The physical model solving and optimization module is used to establish a physical model of laser-material interaction based on the parameters of the digital twin model, transform the laser-material interaction problem into a boundary value problem of an energy conservation system, solve the boundary value problem using a numerical solver, output a three-dimensional energy distribution field, establish a mapping relationship between processing parameters and processing quality, solve the parameter optimization problem using an intelligent optimization algorithm, and generate a dynamic parameter adjustment strategy and optimal processing trajectory. A multi-level closed-loop control module is used to construct a multi-level closed-loop control system based on the dynamic parameter adjustment strategy and the optimal processing trajectory. The module collects processing process information in real time through sensors to obtain real-time feedback information. The real-time feedback information is input into the digital twin model for simulation calculation to obtain the prediction result of the processing process development trend. Based on the prediction result and the real-time feedback information, the laser processing parameters and processing trajectory are dynamically adjusted to complete the air film hole processing.

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