Microwave device brazing process optimization control method and system based on digital twinning

Abstract

This invention discloses a method and system for optimizing and controlling the brazing process of microwave devices based on digital twins. The method includes: acquiring real-time multiphysics field data of the microwave device to be brazed during the brazing process, wherein the multiphysics field data includes temperature field data and deformation field data; training the digital twin model based on a preset digital twin model with a physical information neural network as its core, inputting the multiphysics field data and associated process parameters to obtain a target model that characterizes the mapping relationship between process parameters, multiphysics field data, and the radio frequency performance of the microwave device; using the target model as a surrogate model, optimizing within a preset process parameter space using a Bayesian optimization algorithm with preset radio frequency performance indicators as the optimization objective to obtain optimal process parameters; and controlling the brazing equipment to execute the brazing process based on the optimal process parameters. This invention improves the yield and performance consistency of high-end microwave devices.

Description

Technical Field

[0001] This invention relates to the intersection of microwave communication technology and intelligent manufacturing technology. Specifically, it relates to a process optimization and quality control technology applied to the manufacturing process of high-end microwave devices, particularly a method and system for optimizing and controlling the brazing process of microwave devices based on digital twins. Background Technology

[0002] In modern high-tech fields such as wireless communication, radar detection, and satellite navigation, high-performance microwave devices play a crucial role. For example, waveguide cavity filters, duplexers, and combiners operating in the Ku and Ka bands are core components of radio frequency (RF) front-end systems, and their performance parameters directly determine the signal transmission quality, signal-to-noise ratio, and operational stability of the entire system. These complex and highly precision microwave devices are typically composed of multiple precision-machined metal parts connected and sealed using a brazing process. For microwave devices, high-quality brazing is not only a guarantee of structural implementation but also the foundation for achieving optimal RF performance.

[0003] The brazing process itself is a transient multiphysics coupling process involving thermodynamics, fluid mechanics, and materials science. During high-temperature thermal cycling, the various metal components of the device undergo complex thermal expansion and contraction, and the resulting thermal stress can lead to permanent plastic deformation at the micrometer level. For microwave signals with operating wavelengths on the order of centimeters or even millimeters, any minute geometrical change, such as the size of the resonant cavity, the aperture of the coupling structure, or the position of the tuning element, can cause significant or even catastrophic deviations in key RF performance indicators such as insertion loss, isolation, and resonant frequency. This directly results in unstable production yields, poor consistency, and high manufacturing costs for high-end microwave devices.

[0004] To address this issue, current industry-standard technical approaches have the following limitations. The first is a trial-and-error method relying on the personal experience of process engineers. This method involves repeatedly adjusting process parameters and conducting small-batch experiments to determine the optimal process window. The second is offline simulation optimization based on Computer-Aided Engineering (CAE). R&D personnel use finite element analysis software to perform thermo-structural coupling simulations of the brazing process to predict post-weld stress and deformation. The third is a quality management method based on Statistical Process Control (SPC). By monitoring production data, abnormal fluctuations in process parameters or product performance can be detected, serving as a quality alarm.

[0005] In recent years, with the development of Industrial Internet of Things (IIoT) and artificial intelligence (AI) technologies, some attempts have emerged to use machine learning models to correlate process parameters and quality results. These methods train models such as neural networks by collecting historical production data to predict product yield under specific process parameters. However, the accuracy and generalization ability of these predictions depend entirely on the quantity and quality of the training data. With limited data, the models are prone to overfitting, and their predictions may violate basic physical laws, resulting in insufficient reliability.

[0006] In summary, existing microwave device brazing process control technologies, whether relying on manual experience, offline simulation, or rudimentary digital monitoring, have failed to effectively establish a complete causal chain from process parameter setting to transient multiphysics evolution, then to structural microscopic deformation, and ultimately, the impact on RF performance indicators. The industry urgently needs a new technological solution capable of accurately predicting, intelligently optimizing, and controlling this complex process in a closed-loop manner. Summary of the Invention

[0007] This invention provides a method, system, computer equipment, and storage medium for optimizing and controlling the brazing process of microwave devices based on digital twins. It aims to solve the problem that the relationship between the brazing process and the final radio frequency performance of microwave devices is unclear in the prior art, which leads to optimization difficulties and low product yield.

[0008] To achieve the above objectives, the present invention provides a method for optimizing and controlling the brazing process of microwave devices based on digital twins, the method comprising the following steps:

[0009] First, real-time multiphysics data of the microwave device to be brazed during the brazing process is acquired. It should be noted that brazing is a dynamic process during which physical quantities such as temperature, stress, and strain fields within the device change drastically in time and space. These changes are the direct cause of final structural deformation and performance drift. Therefore, capturing the evolution data of these physical fields in real-time and in multiple dimensions is the foundation for subsequent accurate modeling. In the technical solution of this invention, the multiphysics data includes at least temperature field data and deformation field data of the device surface, which are the most critical physical quantities characterizing the state of the brazing process and most easily perceived by external sensors.

[0010] Next, based on a pre-defined digital twin model centered on a Physics-Informed Neural Network (PINN), the multi-physics data acquired in the previous step, along with process parameters synchronously associated with this data in time, are input to train the digital twin model. After training, a target model is obtained that can accurately characterize the complex mapping relationship between process parameters, multi-physics data, and the final RF performance of microwave devices. Unlike traditional purely data-driven models, PINN is a novel model that incorporates physical laws as strong constraints into the neural network training process. It not only learns from real data but must also adhere to pre-defined physical partial differential equations, thus exhibiting higher prediction accuracy, better generalization ability, and physical interpretability. It is particularly suitable for handling industrial problems with a clear physical background but sparse data.

[0011] Then, the target model trained in the previous step is used as an efficient and lightweight surrogate model. Using a Bayesian optimization algorithm, one or more preset RF performance metrics (e.g., minimizing insertion loss, maximizing isolation) are used as optimization objectives. Efficient global optimization is then performed within a preset multidimensional space composed of multiple process parameters (e.g., heating rates, holding temperatures, holding times, etc.). Bayesian optimization is a particularly suitable optimization algorithm for situations where objective function evaluation is costly (expensive black-box problems). It can intelligently find the global optimum with a very small amount of data, perfectly suited to the scenario where calling a digital twin model or conducting a real experiment is expensive. After optimization, the algorithm outputs a set of optimal process parameters.

[0012] Finally, based on this set of optimal process parameters, the process execution control module controls the brazing equipment to perform the brazing process on the microwave devices. Thus, the theoretically optimal solution found by the optimization algorithm is applied to actual production in the physical world, thereby effectively improving product quality. Furthermore, this process can form a closed loop, continuously using new production data to iterate the model and achieve iterative evolution of the process.

[0013] In one specific implementation, to acquire high-quality real-time data in a non-invasive manner, the steps for acquiring multiphysics data can be implemented as follows: Real-time temperature field data of the device surface is acquired non-contactly using an infrared thermal imager deployed outside the observation window of the brazing equipment; simultaneously, real-time deformation field data of the device surface is acquired non-contactly using a binocular vision system based on Digital Image Correlation (DIC) technology, also deployed outside the observation window. The deformation field data can intuitively reflect the displacement and strain of the device caused by thermal expansion and contraction.

[0014] Preferably, to enable the DIC technology to operate reliably in a high-temperature, dark vacuum furnace environment, a pre-processing step is included before data acquisition: preparing a ceramic random speckle pattern on the surface of the device to be observed, capable of withstanding the high temperatures of the brazing process. These speckles provide high-contrast tracking markers for the DIC algorithm.

[0015] Furthermore, to ensure that the constructed digital twin model possesses both data fidelity and physical rigor, the loss function of the digital twin model, which is based on a physical information neural network, is specifically designed to include at least two parts during the training process. The first part is the data loss term, which measures the difference between the physical field values ​​(such as temperature and displacement) predicted by the model and the actual multiphysics data collected by sensors, as well as the difference between the RF performance predicted by the model and the final measured RF performance of the device. This loss term ensures that the model is anchored to physical reality. The second part is the physical residual loss term, which calculates and minimizes the residual of the model output to one or more partial differential equations (e.g., heat conduction equations, solid mechanics equations) describing the brazing process using automatic differentiation techniques. This loss term forces the model to comply with the inherent laws of the physical world.

[0016] Specifically, the partial differential equations may include at least the three-dimensional unsteady heat conduction equation and the quasi-static thermal structure coupling equation. These two equations are the core physical models describing heat transfer and thermal deformation during the brazing process.

[0017] Another aspect of the present invention is to provide a microwave device brazing process optimization control system based on digital twins for implementing the above-described method. The system includes: a data acquisition module for acquiring real-time multiphysics field data of the microwave device to be brazed during the brazing process, wherein the multiphysics field data includes at least temperature field data and deformation field data of the device surface; a data processing and modeling module for training the digital twin model based on a preset digital twin model with a physical information neural network as its core, by inputting the multiphysics field data and process parameters associated with the multiphysics field data, to obtain a target model capable of characterizing the mapping relationship between process parameters, multiphysics field data, and the final radio frequency performance of the microwave device; an intelligent optimization decision module for using the target model as a surrogate model, and through a Bayesian optimization algorithm, optimizing one or more preset radio frequency performance indicators within a preset process parameter space to obtain a set of optimal process parameters; and a process execution control module for controlling the brazing equipment to perform the brazing process on the microwave device based on the optimal process parameters.

[0018] In a preferred implementation, to improve the accuracy and robustness of data acquisition, the data acquisition module specifically includes an infrared thermal imager and a binocular vision system based on DIC technology.

[0019] In a specific system design, the physical information neural network running in the data processing and modeling module has a special dual-output head structure, including a shared backbone network, a physical field output head connected to the shared backbone network, and an RF performance proxy output head. The shared backbone network is responsible for learning the low-level feature representations of spatiotemporal coordinates and process parameters. The physical field output head outputs the instantaneous temperature and displacement of the device at any spatiotemporal point during the brazing process, directly corresponding to the physical state of the process. The RF performance proxy output head is a lightweight sub-network that receives the final deformation field output by the physical field output head at the end of brazing as input and quickly predicts the final RF performance of the device. This design achieves decoupling and proxy modeling from the thermodynamic simulation domain to the electromagnetic simulation domain, greatly improving the efficiency of end-to-end prediction.

[0020] Furthermore, to further improve optimization efficiency, the Bayesian optimization algorithm running in the intelligent optimization decision module can be specifically configured as follows: a Gaussian Process Regression (GPR) model is used as a probabilistic surrogate model to estimate the mean and uncertainty of the output of the PINN target model; and an Expected Improvement (EI) function is used as the acquisition function to intelligently select the next process parameter point to be evaluated by balancing "exploration" (sampling in regions with high uncertainty) and "utilization" (sampling in regions with known optimality).

[0021] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it can implement any of the above methods.

[0022] The present invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program being configured to perform any of the above methods when executed on a computer.

[0023] In summary, the core technical solution of this invention lies in the construction of an intelligent process optimization and control scheme that can completely connect the entire chain of microwave device brazing, from "process parameters - transient physical field evolution - final structural deformation - RF performance indicators," by deeply integrating multi-physics field sensing technology, digital twin modeling technology based on physical information neural networks, and efficient Bayesian global optimization algorithms. This system, with a high-fidelity digital twin model at its core, transforms the traditional "black box" process, which relies on experience and trial and error, into a "white box" process that is accurately predictable, deeply insightful, and intelligently optimized. Driven by both data and physical models, the system can not only accurately predict product performance under any combination of process parameters, but also autonomously search for the process scheme that achieves the best performance and highest yield in a vast parameter space with extremely high efficiency. Finally, it implements this scheme through closed-loop control, thereby simultaneously improving the efficiency and quality of the precision manufacturing process for high-end microwave devices. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic diagram of the overall functional architecture of a microwave device brazing process optimization control system based on digital twin according to an embodiment of the present invention.

[0026] Figure 2 This is an overall flowchart of a digital twin-based microwave device brazing process optimization and control method according to an embodiment of the present invention.

[0027] Figure 3 This is a schematic diagram of sensor deployment for multiphysics data acquisition of microwave devices in a vacuum brazing furnace environment according to an embodiment of the present invention.

[0028] Figure 4 This is a schematic diagram of the network structure and loss function of a Physical Information Neural Network (PINN) digital twin model according to an embodiment of the present invention.

[0029] Figure 5 This is a schematic diagram illustrating the iterative process of optimizing process parameters through interaction between a Bayesian optimization algorithm and a PINN digital twin model, according to an embodiment of the present invention.

[0030] Figure 6This is a comparison chart of the optimization effect according to an embodiment of the present invention, which includes a comparison of the process temperature curves before and after optimization and a comparison of the corresponding key RF performance of the duplexer (S21 insertion loss).

[0031] Figure 7 This is a multi-scale causal chain mapping diagram of process parameters-physical field-RF performance according to an embodiment of the present invention.

[0032] Figure 8 This is a cross-sectional view of the brazing thermal deformation mechanism of a microwave duplexer according to an embodiment of the present invention.

[0033] Figure 9 This is a comparison curve of insertion loss and isolation frequency response characteristics according to an embodiment of the present invention.

[0034] Figure 10 This is a statistical analysis chart of production yield and batch consistency according to an embodiment of the present invention.

[0035] Figure 11 This is a process optimization efficiency and cost-effectiveness evaluation diagram according to an embodiment of the present invention.

[0036] Explanation of reference numerals in the attached figures:

[0037] 100 - Data Acquisition Module; 101 - Infrared Thermal Imager; 102 - Observation Window; 103a, 103b - Industrial Cameras; 104 - PLC Controller; 105 - Edge Computing Unit; 200 - Data Processing and Modeling Module; 201 - Server / Workstation; 210 - Shared Backbone Network; 211 - Physical Field Output Head; 212 - RF Performance Proxy Output Head; 300 - Intelligent Optimization Decision Module; 400 - Process Execution Control Module; 500 - Vacuum Brazing Equipment. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Example 1

[0040] This embodiment details the specific steps and flow of a microwave device brazing process optimization and control method based on digital twins. This method aims to solve the "black box" problem where the relationship between process parameters and final RF performance during microwave device brazing is unclear. (Refer to...) Figure 2The complete process of this method can be divided into two major stages: the offline model building and optimization stage (Phase I) and the online closed-loop control and iteration stage (Phase II).

[0041] First, the offline model building and optimization phase is executed. This phase is the core of the system's initial deployment or the process development for a new type of microwave device.

[0042] The first step is system deployment and calibration (step S201). Before implementing this method, a physical measurement environment and data acquisition link need to be constructed. (Refer to...) Figure 1 and Figure 3 The system shown deploys the hardware of the data acquisition module 100 onto a vacuum brazing machine 500. Specifically, a high-resolution long-wave infrared thermal imager 101 is mounted outside the quartz observation window 102 of the furnace body via an airtight flange, ensuring its field of view completely covers the microwave device 300 to be brazed. Simultaneously, two high-speed industrial cameras 103a and 103b form a binocular vision system, also deployed outside the observation window 102, aiming at the device from different angles. These two cameras are used for digital image correlation (DIC) measurements. Furthermore, communication is established between the edge computing unit 105 and the PLC controller 104 of the brazing machine via an industrial Ethernet or corresponding fieldbus interface. After the hardware deployment is complete, a series of calibration tasks are required, such as multi-point temperature-emissivity correction of the infrared thermal imager to ensure the accuracy of temperature measurements at different temperatures; and stereo calibration of the binocular camera system using a high-precision calibration board to obtain its internal and external parameters and spatial position relationships. In addition, a key preliminary step in the deployment is to prepare a layer of ceramic random speckle that can withstand the high temperature of brazing on the surface of the microwave device to be observed (e.g., the cover plate that is most sensitive to the impact of radio frequency performance) through processes such as spraying, so as to provide high-contrast features for subsequent DIC measurements.

[0043] The second step is initial data acquisition (step S202). To train the subsequent digital twin model, an initial "seed" dataset containing sufficient information is needed. For this purpose, several sets of differentiated process parameter schemes are selected for brazing experiments. For example, 3 to 5 sets of experiments can be set up. The first set uses the baseline process currently used on the production line, while the remaining sets, based on the baseline process, make significant adjustments to key parameters such as the maximum brazing temperature, peak holding time, and cooling rate. Throughout each brazing experiment, the data acquisition module operates continuously, synchronously recording the temperature field video stream captured by the infrared thermal imager, the speckle image sequence captured by the DIC system, and the actual operating parameters of the equipment read from the PLC. After each experiment is completed and the device cools to room temperature, a comprehensive test of the device's RF performance is performed using precision instruments such as a vector network analyzer (VNA), recording its S-parameters and other key indicators. Finally, the complete process data (time series of temperature, deformation, and equipment parameters) collected from each experiment are strictly timestamped and correlated with the final performance data (S-parameter test results) to form an initial training dataset containing multiple complete samples.

[0044] The third step is to train the PINN digital twin model (step S203). The initial training dataset obtained in the previous step is sent to the data processing and modeling module 200 deployed on the high-performance server 201. The core of this module is an algorithm based on the Physical Information Neural Network (PINN). Following the method detailed in Example 2, the network topology of the PINN model is constructed, and its inputs (spatiotemporal coordinates, process parameters) and outputs (instantaneous physical field, final S-parameters) are defined. The key is to design its unique loss function, which includes not only a data loss term penalizing the difference between the model's predicted values ​​and the actual sensor data, but also a physical residual loss term penalizing the model's output for violating physical laws such as heat conduction and thermo-coupling. Subsequently, using the server's GPU computing resources, the PINN network is trained end-to-end using optimization algorithms such as gradient descent. The training process continues until the total loss function converges to a preset small value, and the model exhibits high prediction accuracy on the validation data that was not used in the training. After this step is completed, a digital twin model capable of simulating the brazing process with high fidelity is successfully constructed.

[0045] The fourth step is to perform Bayesian optimization-based process optimization (step S204). After obtaining a fast and accurate digital twin model, virtual optimization of process parameters can be performed efficiently. The intelligent optimization decision module 300 is activated, which runs the Bayesian optimization algorithm. First, based on the product design requirements, a mathematical optimization objective function is defined, for example, a weighted utility function aimed at minimizing insertion loss while maximizing isolation. Then, the process parameters to be optimized and their reasonable value ranges are set, for example, the final brazing temperature range is 820-880℃. The Bayesian optimization algorithm uses the PINN model as a "proxy" for its internal evaluation objective function, intelligently performing sequential sampling and evaluation in the multi-dimensional parameter space through an "exploration-exploitation" strategy. After a set number of iterations (e.g., 100), the algorithm automatically converges and outputs a set of process parameter combinations P* considered optimal.

[0046] Step 5: Optimal process verification (Step S205). To confirm the validity of the virtual optimization results in the physical world, verification experiments are required. The process parameter combination P* obtained in the previous step is compiled into an executable program for the device, sent to the brazing furnace, and a verification production run is conducted on the new device. After production, rigorous S-parameter tests are performed on the finished product. The test results are compared with the predicted values ​​of the PINN model. If the actual test performance is highly consistent with the predicted values ​​and significantly better than the baseline process, it indicates that the offline model construction and optimization phase has been successful.

[0047] Next, we enter the online closed-loop control and iteration stage, which is the stage in which this method continues to play a role in subsequent large-scale production.

[0048] Step 6: Deploy the optimal process (step S206). The optimal process parameters P* that were successfully verified in the previous step are used as standard operating procedures (SOPs) and incorporated into the process recipe library of the production line to guide the mass production of all subsequent products of the same model.

[0049] Step 7: Real-time monitoring of the production process (step S207). During daily batch production, the data acquisition module 100 does not stop working but switches to monitoring mode. In each production task, it continues to collect data such as temperature field and deformation field in real time. This real-time data can be compared in real time with the evolution trajectory of the "ideal" physical field corresponding to the optimal process P* stored in the digital twin model, forming a digital twin mirror image of the production process.

[0050] Step 8: Anomaly detection and alarm (step S208). During real-time monitoring, if the system detects that the actual physical field data stream deviates significantly from its ideal trajectory—for example, the heating rate in a certain area is much lower than the set value, or the strain in a certain part suddenly shows an abnormal jump—the system will determine that a production anomaly may have occurred. These anomalies may stem from localized hardware failures (such as aging of a heating unit), loosening or deformation of tooling fixtures, etc. The system will immediately trigger an alarm mechanism, sending alarm information to on-site engineers, and may even automatically interrupt the production process in pre-set emergency situations, thereby preventing larger-scale waste generation.

[0051] Step 9: Perform periodic model retraining and process fine-tuning (Step S209). As production progresses, the system continuously accumulates new and effective data. To address the slow drift of the process window caused by factors such as equipment aging and batch-to-batch variations in raw materials, a period can be set, such as monthly or after producing a certain number of products, to add the new data accumulated during this period (especially data that has undergone final performance testing) to the historical database. The system can automatically or manually trigger an incremental training or fine-tuning of the PINN model. The retrained model will be closer to the current "healthy state" of the production line. If the updated model shows that the original optimal process P* is no longer the optimal point under the current conditions, the system can restart the Bayesian optimization algorithm on a small scale to quickly fine-tune P*, find a new optimal point, and thus achieve continuous self-improvement and evolution of the process solution.

[0052] Through the complete cycle of the above two major stages and nine steps, the method of the present invention not only solves the optimization problem in the new process development stage, but also establishes an intelligent quality assurance system that integrates real-time monitoring, anomaly early warning and continuous self-learning in the mass production stage.

[0053] Example 2

[0054] This embodiment will provide a more detailed description of the specific implementation methods of two key technical means in the method of this invention—the construction of the Physical Information Neural Network (PINN) digital twin model and the process optimization decision based on Bayesian optimization. These two technologies are the cornerstones for achieving "accurate prediction" and "efficient optimization," respectively.

[0055] First, the construction of the Physical Information Neural Network (PINN) digital twin model is explained in detail. This model aims to create a virtual agent that is both constrained by real data and strictly adheres to the principles of physics.

[0056] Reference Figure 4 The implementation of the PINN model includes the following core aspects.

[0057] Regarding the input and output definitions of the model, the core of the model is a deep neural network, whose input vector is designed as [t, x, y, z, P]. Here, t is the time variable, (x, y, z) are the spatial coordinates within the microwave device's geometric model, and P is a vector representing adjustable process parameters, such as P = {R1, T1, t1, R2, T2, t2, R_cool}, representing key process control quantities such as multi-stage heating rate, holding temperature, holding time, and cooling rate, respectively. Using P as input enables the trained model to have generalization ability, capable of predicting results under any given process parameters. The model's output vector is [T, u, v, w, S_params]. Here, T is the instantaneous temperature prediction value at that spatiotemporal point, and (u, v, w) are the displacement component prediction values ​​of that point in three-dimensional space, which together constitute the instantaneous temperature field and displacement field. S_params, on the other hand, is the predicted value of the final RF performance indicators of the device (such as S21 insertion loss and S31 isolation) after the entire process is completed.

[0058] In terms of neural network architecture design, to efficiently handle cross-scale, cross-domain prediction tasks from transient physical fields to final RF performance, this embodiment employs a dual-output head architecture that differs from existing technologies. The core of the network is a shared backbone network 210, consisting of 8 to 12 fully connected hidden layers, each containing, for example, 256 neurons, and employing smooth activation functions such as tanh to facilitate the calculation of higher-order derivatives. This backbone network is responsible for learning a shared, deep feature representation from the input spatiotemporal coordinates and process parameters. The backbone network branches into two branches: the first is the physical field output head 211, which is a simple fully connected layer that directly outputs 4 neurons, corresponding to the instantaneous physical quantities (T,u,v,w). The second is the RF performance proxy output head 212, which is a small multilayer perceptron (MLP) that receives the final deformation field (i.e., displacement distribution) distributed across the critical surfaces of the device, output by the backbone network at the process end time t = t_final, as input. After undergoing several layers of nonlinear transformations, it outputs a prediction of the final S-parameters. This design avoids the time-consuming full-wave electromagnetic simulation in every prediction. Instead, it uses a lightweight proxy network to achieve a fast mapping from "deformation" to "performance", which is the key to achieving efficient optimization.

[0059] In one specific implementation, the RF performance proxy output head 212 receives the displacement field (i.e., deformation) distributed across the critical geometric surfaces of the device (such as the inner wall of the resonant cavity) predicted by the backbone network at a specific moment (at the end of the brazing process, t=t_final), and may combine it with key process parameters P as input. This sub-network outputs the predicted S-parameters through 2-3 smaller hidden layers. This structure is an innovation of the present invention, which cleverly decouples the thermo-mechanical coupling simulation domain from the electromagnetic simulation domain, replacing the huge computational overhead of calling full-wave electromagnetic simulation (such as HFSS) every time with a lightweight proxy model, thereby achieving fast end-to-end prediction.

[0060] In terms of implementing physical constraints, the essence of PINN lies in the design of its loss function. The total loss function L_total is composed of three parts through a weighted sum: L_total = λ_data * L_data + λ_pde * L_pde + λ_bc_ic * L_bc_ic.

[0061] The first term, L_data, represents the data loss. It calculates the mean square error (MSE) between the model's predicted values ​​and the actual measured data. Specifically, it includes three parts: the MSE of the model's predicted temperature and displacement versus the actual measured values ​​at spatiotemporal points where measurement data is available from the thermal imager and DIC system; and the MSE of the S-parameters predicted by the RF performance output head versus the measured S-parameters from the VNA for each complete process sample. This term firmly "anchors" the model to physical reality.

[0062] L_data = MSE_T + MSE_U + MSE_S

[0063] MSE_T: The mean square error between the network-predicted temperature T_pred and the actual measured value T_data at the thermal imager temperature measurement point.

[0064] MSE_U: The mean square error between the network-predicted displacement U_pred and the actual measured value U_data at the DIC measurement point.

[0065] MSE_S: The mean square error between the predicted S_params_pred from the RF performance output head and the actual measured S_params_data from the network analyzer (VNA) for a completed process batch.

[0066] The second term, L_pde, is the physical residual loss. This term is the core difference between PINN and traditional neural networks. It does not rely on any labeled data, but instead randomly samples a large number of virtual points called "placement points" throughout the entire solution domain (including time and space). At each placement point, using the powerful automatic differentiation capabilities of deep learning frameworks, it calculates the partial derivatives of the model output (T, u, v, w) with respect to the input (t, x, y, z). Then, these derivatives are substituted into predefined physical partial differential equations (PDEs) to calculate the residuals of the equations. In this embodiment, these PDEs include at least the three-dimensional unsteady-state heat conduction equations describing heat transfer. Coupled with the quasi-static thermal structure equations describing thermally induced deformation These are the mean square errors of the residuals of these physical equations across all points. Minimizing this term is equivalent to forcing the solution of the neural network to actively satisfy the fundamental laws of thermodynamics.

[0067] L_pde = MSE_heat + MSE_mech

[0068] MSE_heat: The mean square error of the value of the three-dimensional unsteady heat conduction equation f_heat at the placement point, which is made to approach 0.

[0069] MSE_mech: The mean square error of the quasi-static thermal-structural coupling equation f_mech value calculated at the placement point, making it approach 0.

[0070] The network outputs the derivatives of each order with respect to t, x, y, z. This is achieved precisely and efficiently through automatic differentiation, which is a core function of modern deep learning frameworks.

[0071] In the three-dimensional unsteady-state heat conduction equation, ρ is the material density, c is the specific heat capacity, and k is the thermal conductivity (these physical properties can be functions of temperature to improve accuracy). ∇· is the divergence operator. This equation constrains the network-predicted temperature field T(t, x, y, z) to satisfy the law of conservation of energy.

[0072] In the quasi-static thermal-structural coupling equations, F represents volume forces (such as gravity, which can be neglected), and σ is the stress tensor. The stress σ is connected to the strain ε through constitutive relations. The total strain ε consists of two parts: mechanical strain ε_mech and thermal strain ε_th. Thermal strain is caused by temperature changes. It is the coefficient of thermal expansion. The strain ε is directly related to the displacement field U. This equation tightly couples the change in the temperature field T predicted by the network with the change in the structural displacement field U that it must cause.

[0073] The third term, L_bc_ic, represents the boundary and initial condition losses. It ensures that the model's solution conforms to physical reality at the spacetime boundaries. L_ic: Initial condition loss, for example, the mean square error between T(0,x,y,z) and the initial room temperature at t=0. L_bc: Boundary condition loss. For example, on the device surface, heat flow must satisfy the boundary conditions of thermal radiation and convection.

[0074] During model training, advanced optimizers such as Adam or L-BFGS are used to minimize the total loss function, thereby simultaneously optimizing all weights and bias parameters of the network. After training, a high-fidelity and differentiable digital twin model is obtained.

[0075] In one specific implementation, the network's weights and bias parameters are trained by minimizing the total loss function L_total. An optimizer such as Adam or L-BFGS is used, with a large number of "process parameter-sensor data-final performance" data pairs obtained from simulations or a small batch of experiments as input. After training, a lightweight, differentiable, high-fidelity digital twin model is obtained. This model can respond to a query in milliseconds: given a set of process parameters P, it can quickly predict the physical field evolution throughout space and time, as well as the final key RF performance S_params.

[0076] Next, the process optimization decision-making process based on Bayesian optimization will be described in detail. (Refer to...) Figure 5 The implementation process of Bayesian optimization (BO) is as follows.

[0077] First, in defining the objective function and parameter space, the engineering objective needs to be transformed into a mathematical optimization problem. The optimization objective function f(P) is designed as a scalar to evaluate the quality of a set of process parameters P. f(P) = w1 * S21_loss(P) - w2 * S31_iso(P) + Penalty(P), where w1 and w2 are weighting coefficients reflecting the emphasis on different performance indicators. S21_loss(P) and S31_iso(P) are predicted values ​​obtained by calling the PINN digital twin model. Penalty(P) is a penalty term used to handle process constraints, such as imposing a large penalty value when the total process time exceeds the upper limit. The ultimate goal is to find the process parameters P* that minimize f(P). For example, f(P) = 10 * |S21_loss(P) - (-0.4)| + 1 * |S31_iso(P) - 85|, the goal is to minimize this f(P), where S21_loss(P) and S31_iso(P) are the predicted values ​​obtained by calling the PINN model. The optimized parameter space is a 7-dimensional hypercube consisting of 7 process parameters (as defined by the P vector above) and their respective ranges (e.g., T2 is between [820, 880] degrees Celsius).

[0078] In this embodiment, the complex brazing temperature profile has been parameterized for optimization. For example, a typical heating-holding-cooling process can be described by the following seven key parameters P:

[0079] P = {R1, T1, t1, R2, T2, t2, R_cool}

[0080] - R1: First stage heating rate (°C / min)

[0081] - T1: Temperature of the first insulation platform (°C)

[0082] - t1: First insulation time (min)

[0083] - R2: Second stage heating rate (°C / min)

[0084] - T2: Final brazing temperature (°C)

[0085] - t2: Final brazing time (min)

[0086] - R_cool: Average cooling rate of the forced cooling section (°C / min)

[0087] The optimizer will search for the optimal solution within this 7-dimensional hypercube.

[0088] Secondly, the core components of Bayesian optimization consist of two parts. The first is the probabilistic surrogate model, which in this embodiment uses Gaussian Process Regression (GPR). GPR learns a posterior probability distribution about the objective function f(P) based on existing "process parameter-performance score" observation data for {(P1,y1), ...}. This means that for any unknown process parameter point P_new, GPR can not only predict a performance mean μ(P_new), but also provide a measure of uncertainty about this prediction, namely the variance σ²(P_new). The second is the acquisition function, which in this embodiment uses the classic Expected Improvement (EI) function. The role of the EI(P) function is to quantify the expected benefits that can be obtained by conducting the next "virtual experiment" at point P. The calculation of this function considers both the performance prediction mean given by GPR (preferring to "utilize" near known advantages) and the uncertainty variance (preferring to "explore" in unknown, highly uncertain regions).

[0089] In the iterative optimization process, starting with a small initial dataset (steps S501-S502), Bayesian optimization enters a loop. In each loop, the GPR model is first updated based on all currently known observation data (step S503). Then, in the entire process parameter space, a numerical optimization method is used to find the point P_next that maximizes the acquisition function EI(P) (step S504). This P_next is the point that the algorithm considers most worthwhile to evaluate. Next, the time-consuming trained PINN digital twin model is called to evaluate the value of f(P_next), obtaining a new data pair (P_next, y_next) (step S505). Finally, this new data pair is added to the observation dataset, and it is checked whether the termination condition is met (such as reaching the maximum number of iterations). If not, the next loop begins (step S506). The whole process is like a clever experimenter, choosing the most informative experimental point each time, thereby finding the global optimum with the fewest number of experiments (step S507).

[0090] This embodiment uses the classic Expected Improvement (EI) function as the sampling function. The EI function calculates how much improvement is expected compared to the currently found optimal value y* when sampling at a point P for the next time. Its analytical form is: ,in , and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively. Ultimately, we only need to find the point P_next that maximizes the acquisition function EI(P) in the entire parameter space using an efficient optimization algorithm (such as L-BFGS-B). This point is the optimal choice for the next evaluation.

[0091] like Figure 7 As shown, a specific implementation reveals a complete multi-scale causal chain mapping relationship between soldering process parameters and final RF performance. The causal chain comprises four levels, with each level interconnected through causal relationships of varying strengths.

[0092] The process parameter layer contains seven key parameter nodes: heating rate R1, holding temperature T1, holding time t1, heating rate R2, brazing temperature T2, brazing time t2, and cooling rate Rcool. Among them, the brazing temperature T2 has the most significant impact on the subsequent physical field, and its node size is the largest.

[0093] In the multiphysics layer, the four physical quantities—transient temperature field T(t,x,y,z), stress field, strain field, and heat flux density—are directly driven by process parameters. The influence coefficient of T2 on the temperature field is 0.92, the influence coefficient on the stress field is 0.85, and the influence coefficient of the cooling rate on the stress field is 0.76, all indicated by thick solid lines.

[0094] In the structural deformation layer, the temperature field primarily drives changes in cavity dimensions (influence coefficient 0.88), while the stress field primarily drives the tilt and displacement of the resonator (influence coefficient 0.83). In the RF performance layer, the tilt of the resonator has a strong impact on S21 insertion loss (0.87), S31 isolation (0.81), and center frequency drift (0.85), while the influence coefficient of cavity dimension changes on center frequency drift is 0.90. The thickness of the connecting lines is divided into three visual levels, corresponding to strong, medium, and weak influences, respectively.

[0095] Through the detailed technical implementation described above, this invention deeply applies artificial intelligence models and efficient optimization algorithms to complex industrial manufacturing scenarios, providing a complete and feasible technical path for solving long-standing process problems.

[0096] Example 3

[0097] This embodiment aims to describe in detail the specific structure and implementation of the microwave device brazing process optimization control system based on digital twins, which implements the method of the present invention. This system, as a hardware and software integrated whole, is the physical carrier of the technical solution of the present invention. (Refer to...) Figure 1 The system can be divided into four core functional modules: data acquisition module 100, data processing and modeling module 200, intelligent optimization decision-making module 300, and process execution control module 400.

[0098] First, the data acquisition module 100 will be described. This module's function is to capture multi-dimensional, multi-physics field information during the brazing process in real time and synchronously. Its specific implementation is as follows:

[0099] This module consists of multiple sensors and data aggregation units deployed externally to the vacuum brazing equipment 500. The non-contact temperature field acquisition function is achieved by a long-wave infrared thermal imager 101. For example, a research-grade thermal imager with a spectral range of 8-14 μm, a resolution of at least 640x512 pixels, and a frame rate of at least 50 Hz can be selected. This wavelength effectively penetrates common residual gases such as CO2 and H2O in a vacuum and has good response to the target temperature range (room temperature to 950°C). The thermal imager lens is connected via a flange and sealed outside the quartz observation window 102 of the vacuum brazing furnace, facing the upper surface (usually the cover plate) of the duplexer 300. To achieve accurate temperature measurement, emissivity calibration is required before starting. Since the emissivity of the duplexer's base material (oxygen-free copper), the brazing filler metal (silver-copper alloy), and the fixture (graphite) differs, a lookup table (LUT) can be established for the emissivity of these materials at different temperatures through pre-experimentation. During real-time acquisition, the software automatically or manually retrieves the corresponding emissivity value to calculate the temperature based on the material and approximate temperature of the measured area. The thermal imager, through an infrared window made of ZnSe or Ge, is aimed at the microwave device 300 to be soldered inside the furnace, enabling it to capture detailed two-dimensional temperature distribution on the device surface in real time. The raw thermal radiation data stream is then transmitted to the edge computing unit 105 via high-speed digital interfaces such as GigEVision or Camera Link.

[0100] The non-contact deformation field acquisition function is achieved by a binocular stereo vision system based on digital image correlation (DIC) technology. This system includes two high-resolution, high-speed industrial cameras (e.g., cameras equipped with 2-megapixel CMOS sensors and synchronous triggering functions) 103a and 103b, and an LED illumination source that flashes in sync with the camera shutter. To avoid interference from the thermal radiation of the high-temperature object itself, narrow-band blue or green light is preferred. The binocular system captures images of pre-fabricated high-temperature speckle patterns on the device surface from different angles through the observation window 102. By analyzing the sequential changes in the speckle images, the three-dimensional displacement and strain of the entire surface field can be accurately determined.

[0101] In one specific implementation, two megapixel industrial cameras, 103a and 103b, form a binocular stereo vision system, symmetrically mounted above the observation window 102 to ensure a common, unobstructed field of view for the pre-formed speckle area. To address imaging challenges in the dark environment inside the furnace, a narrowband blue LED illumination source synchronized with the camera shutter can be used. The blue light band effectively avoids spectral crosstalk with the long-wave infrared band of the thermal imager. Before the experiment, a standard high-precision checkerboard or circular array calibration plate is used to perform stereo calibration of the binocular camera system, obtaining the intrinsic and extrinsic parameters of the two cameras and their relative positional and orientational relationships—the foundation for three-dimensional measurement.

[0102] During brazing, a binocular camera system synchronously acquires speckle image pairs at a frequency of 1-5 frames per second. The acquired image pairs are sent to the edge computing unit 105 or the backend DIC analysis software. The software first uses the first frame during the heating process (or the image at room temperature) as a reference image. For each subsequent image pair, the DIC algorithm calculates the displacement vector of the center point of each sub-region in three-dimensional space by identifying and tracking the speckle pattern within a small window (sub-region) in the image. Finally, the system outputs a series of timestamped full-field three-dimensional displacement field data U(t, x, y, z) = {u(t), v(t), w(t)}. By calculating the spatial gradient of the displacement field data, the strain tensor field ε(t, x, y) of the surface, including normal strain and shear strain, can be further calculated.

[0103] Equipment status data acquisition is achieved through communication with the PLC controller 104 of the vacuum brazing equipment 500. Using standard industrial communication protocols such as Modbus TCP / IP, OPC UA, or PROFINET, the edge computing unit 105 can poll and read a series of internal status parameters from the PLC at high frequency (e.g., 10Hz), including heating power, vacuum level, set temperature curve, and cooling water valve opening.

[0104] All these data streams from different sensors are ultimately converged in the edge computing unit 105. The core task of this unit is to achieve hardware or software synchronization of multi-source heterogeneous data, assign a unified high-precision timestamp to each data frame or data point, perform preliminary data preprocessing (such as image denoising and ROI extraction), and finally package and send the synchronized data to the backend server.

[0105] In one specific implementation, since the acquired temperature field, strain field, and PLC device parameters are three data streams from different sources and with different frequencies, they must be precisely aligned in time to serve as effective inputs for training the PINN model. This system employs a master clock synchronization scheme with the edge computing unit 105 as its core.

[0106] The edge computing unit 105 synchronizes itself with a standard time source via the Network Time Protocol (NTP). It synchronizes the image acquisition moments of the thermal imager and the two DIC cameras by triggering signal lines (hardware triggering) or precisely controlling network data packets (software triggering), ensuring that temperature and shape are captured at the same time.

[0107] For data from PLC 104, edge computing unit 105 actively polls and reads it at a high frequency (e.g., 10Hz). Upon receiving the data packet returned by PLC, it immediately appends a local high-precision timestamp to it.

[0108] Through this mechanism, all acquired data points—whether image frames from the camera or a set of parameters from the PLC—are integrated into a unified time-series database, forming records in a format similar to {timestamp:1678886401.123, T_matrix: [...], U_matrix: [...], PLC_params: {vac: 1e-4,pwr: 85%}}, providing a high-quality, synchronized dataset for subsequent modeling.

[0109] Secondly, the data processing and modeling module 200 is described. This module is responsible for running and training the PINN digital twin model, which is the core of this invention. Its specific implementation is as follows:

[0110] This module is typically deployed on one or more high-performance servers / workstations. In terms of hardware configuration, to meet the huge computational demands of training deep learning models, the server needs to be equipped with a large amount of RAM (e.g., ≥128GB), a high-speed NVMe solid-state drive array, and one or more high-end Tensor Core GPUs (e.g., NVIDIA A100 or RTX4090).

[0111] On the software level, this module runs on a Linux-based operating system, with Python as its core development environment. It integrates multiple open-source software stacks, including: using PyTorch or TensorFlow as the underlying deep learning framework; using NVIDIA CUDA and cuDNN libraries for GPU-accelerated computation; using the OpenCV library for image data processing and analysis; and using a time-series database (such as InfluxDB or Prometheus) to efficiently store, query, and manage the massive amounts of time-series data received from the data acquisition module. The core function of this module is to receive real-time or historical data and execute the entire process of defining the PINN model, constructing the loss function, and training the model, as detailed in Example 2.

[0112] Next, the intelligent optimization decision-making module 300 will be described. This module is responsible for efficiently optimizing process parameters based on the trained digital twin model. Its specific implementation is as follows:

[0113] This module is logically independent, but physically it can be deployed on the same server 201 as the data processing and modeling module 200 to reduce data communication latency. Its core is a Bayesian optimization algorithm engine. The software implementation of this engine can be based on mature open-source libraries (such as GPyOpt, BoTorch, scikit-optimize) or developed in-house. It interacts with the PINN digital twin model through a standardized interface. When the optimization task starts, the module receives the user-defined optimization objective (such as minimizing insertion loss) and parameter boundaries. Then, following the iterative process detailed in Example 2, it repeatedly: 1) constructs a Gaussian process surrogate model; 2) maximizes the acquisition function to generate the next candidate parameter point; 3) calls the PINN model to obtain a performance evaluation of that point. This loop continues until the convergence condition is met. Finally, the module outputs a set of process parameters that have been confirmed as optimal.

[0114] In one specific implementation, the optimization process for this module is as follows:

[0115] Step S501 (Initialization): In the defined 7-dimensional parameter space, 3-5 initial process parameter points {P_init} are randomly selected using methods such as Latin Hypercube Sampling.

[0116] Step S502 (Initial Evaluation): For each initial point Pi_init, call the trained PINN digital twin model to calculate its corresponding RF performance, and then obtain the objective function value yi = f(Pi_init). This forms the initial dataset D_init.

[0117] Step S503 (Constructing the GPR model): Based on the current full observation dataset D (initially D_init), fit a Gaussian process regression model.

[0118] Step S504 (Maximize Acquisition Function): In the entire process parameter space, find the point P_next that maximizes the acquisition function EI(P) by solving the numerical optimization method.

[0119] Step S505 (Evaluate and Update): Call the PINN model to evaluate the performance of point P_next, obtaining y_next = f(P_next). Then add the new data pair (P_next, y_next) to the dataset D, forming D_new.

[0120] Step S506 (Loop / Terminate): Check if the preset termination condition has been met, such as the number of iterations reaching the upper limit (e.g., 100 times), the maximum value of the acquisition function falling below a certain threshold, or the optimal value found in multiple consecutive iterations not showing significant improvement. If not met, return to step S503, refit the GPR model using the updated dataset D_new, and start a new round of iterations. If the termination condition is met, the optimization ends.

[0121] Step S507 (Output result): Among all the evaluated points, select the point P* that minimizes f(P), take it as the globally optimal combination of process parameters, and send it to the process execution control module 400.

[0122] Finally, the process execution control module 400 will be described. This module is crucial for achieving the control closed loop. Its specific implementation is as follows:

[0123] This module is a hardware / software interface layer. It receives a highly abstract list of optimal process parameters (e.g., a dictionary structure containing multiple temperature-time setpoints) from the intelligent optimization decision module 300. The program inside the module is responsible for "compiling" this abstract parameter list into a specific format that the PLC controller 104 of the specific brand and model of the vacuum brazing equipment 500 can understand and execute. This could be a standard recipe file or a series of operation instructions issued via a specific communication protocol. Through bidirectional communication with the PLC, this module can not only issue optimization instructions but also receive feedback from the PLC on the actual execution status during execution, compare it with the setpoints, and achieve monitoring and fine-tuning at the execution level, ensuring that the results of upper-level optimization can be accurately reproduced on the physical equipment.

[0124] These four modules work closely together through industrial Ethernet and other means to form a complete closed-loop intelligent system that goes from physical world perception to digital world modeling, cognition, and decision-making, and then back to physical world execution.

[0125] Example 4

[0126] This embodiment combines a specific industrial application scenario, namely the optimization of the vacuum brazing process of a Ku-band high-precision dielectric resonator duplexer for satellite communication systems, to fully and comprehensively demonstrate the entire process of the technical solution described in this invention from deployment, data acquisition, modeling, optimization to verification.

[0127] 1. Application Scenarios and Technical Background

[0128] The Ku-band duplexer is a key passive component in the RF transceiver front-end. Its complex structure consists of a precision-machined oxygen-free copper (OFC) cavity, eight silver-plated low-temperature co-fired ceramic (LTCC) resonator rods, and corresponding coupling and adjustment structures. To achieve cavity sealing and electrical connections between components, a vacuum brazing process using BAg-8 (72% silver, 28% copper) solder paste is required to synchronously connect all connectors in a single thermal cycle.

[0129] The technical challenge of this product lies in the significant mismatch in the coefficient of thermal expansion (CTE) between the ceramic resonator and the copper cavity material. During the high-temperature thermal cycling process of brazing, improper temperature control can easily generate excessive thermal stress at the connection between the resonator and the cavity, leading to slight tilting or displacement of the resonator after cooling. This severely affects its resonant frequency and degrades the RF performance of the duplexer. The main RF performance requirements for the product are: insertion loss (S21) must be strictly less than 0.5 dB in the 14.0-14.5 GHz passband; and isolation must be greater than 80 dB in the 12.0-12.5 GHz isolation band. Before applying this invention, the product was manufactured using traditional expert-developed processes, with a first-piece yield consistently fluctuating around 75%. The main failure modes were insertion loss exceeding specifications in the passband or unacceptable drift at the center frequency.

[0130] like Figure 8 As shown, the cross-sectional structure of the microwave duplexer involved in this embodiment includes the following key components: A is the oxygen-free copper (OFC) cavity shell, B is the LTCC ceramic resonator rod, C is the BAg-8 solder joint, D is the coupling window, and E is the thermal stress concentration area.

[0131] The oxygen-free copper cavity A is divided into multiple resonant chambers, each containing a vertically mounted LTCC ceramic resonant rod B. The bottom of the resonant rod B is brazed to the copper cavity A using BAg-8 solder C, and adjacent chambers are electromagnetically coupled through coupling windows D.

[0132] During the brazing heating and cooling process, the coefficient of thermal expansion of oxygen-free copper (CTE_Cu approximately 17 x 10⁻⁶ / K) is much greater than that of LTCC ceramic (CTE_LTCC approximately 5 x 10⁻⁶ / K). This mismatch in thermal expansion coefficients results in significant thermal stress concentration at the brazing joint. After cooling, the shrinkage of the copper cavity is greater than that of the ceramic resonator, causing the resonator to undergo micron-level tilting deformation dT and displacement dd, as shown by the dashed line in the figure.

[0133] The temperature gradient bar on the right side of the figure represents the temperature distribution from the high temperature inside the furnace (780K) to the room temperature on the outer wall (300K). The thermal mismatch deformation directly affects the electrical length and coupling spacing of the resonant rod, thus leading to a shift in radio frequency performance. This is the core technical problem that this invention aims to solve through process optimization control using a digital twin model.

[0134] 2. System deployment, calibration, and workpiece preparation

[0135] At the initial stage of implementing the method of this invention, the physical system is first built and precisely calibrated.

[0136] In terms of hardware configuration and selection, the data acquisition module 100 uses a FLIR A655sc research-grade infrared thermal imager, with a working frame rate of 50Hz and a spatial resolution of 640x480 pixels. The digital image correlation (DIC) measurement system uses two Basler acA1920-155um industrial cameras from Germany, equipped with synchronous triggers and 16mm telecentric lenses to ensure minimal imaging distortion within the working distance, with an image acquisition frequency set to 2Hz. The edge computing unit 105 for data aggregation and preliminary processing uses an industrial computer equipped with an Intel Core i7 processor and an NVIDIA Jetson AGX Xavier embedded GPU module. The back-end data processing and modeling, and intelligent optimization decision-making modules (200 and 300) run uniformly on a Dell PowerEdge R7525 server equipped with dual Intel Xeon Gold 6248R processors, 256GB ECC RAM, and two NVIDIA A100 80GB Tensor Core GPUs. The production equipment used is a machine equipped with precision programmable temperature control (temperature control accuracy ±1℃) and a high vacuum system (ultimate vacuum degree can reach 1x10⁻). 4 A vertical vacuum brazing furnace (Pa) 500.

[0137] Regarding workpiece preparation and calibration, in one specific step, the duplexer assembly to be brazed undergoes the following pretreatment: First, all components are precisely assembled in a clean room, and a measured amount of BAg-8 brazing paste is accurately applied to each joint using an automated dispensing device. Next, for DIC measurement requirements, a thin, uniform layer of white zirconium oxide high-temperature resistant primer and a layer of randomly distributed black silicon carbide high-temperature resistant speckle are sprayed sequentially onto the outer surface of its cover plate (the key area that best reflects overall deformation) using a pneumatic airbrush. This is then cured in a 150°C oven for 2 hours to form a stable speckle field capable of withstanding temperatures exceeding 1000°C.

[0138] Before loading the workpiece into the furnace, precise sensor calibration is performed. For the infrared thermal imager 101, temperature-emissivity calibration is performed in segments within the range of 200℃ to 900℃ using a calibration blackbody with multiple thermocouples, establishing accurate lookup tables for the emissivity of oxygen-free copper, silver-coated ceramics, and BAg-8 solder in different temperature ranges. For the DIC binocular camera system (103a, 103b), a high-precision checkerboard calibration board is used to perform complete stereo calibration at the furnace loading position, accurately calculating the intrinsic and extrinsic parameters of the two cameras, lens distortion coefficients, and their precise spatial poses relative to the furnace coordinate system.

[0139] 3. Collection of the initial dataset

[0140] To train a PINN model with good generalization ability, an initial dataset containing a sufficient range of process parameter variations is needed. In this embodiment, five different process schemes were carefully designed for "seed experiments":

[0141] - Process 1 (Benchmark): Adopting the expert experience process used in historical production, the maximum brazing temperature is set at 840℃, and the temperature is held for 10 minutes, followed by natural cooling with the furnace.

[0142] - Process 2 (Low Temperature / Short Time): The maximum temperature is reduced to 820℃, and the holding time is shortened to 5 minutes.

[0143] - Process 3 (Low Temperature / Long Time): The maximum temperature is 820℃, and the holding time is extended to 15 minutes.

[0144] - Process 4 (High Temperature / Short Time): The maximum temperature is raised to 860℃, and the holding time is 5 minutes.

[0145] - Process 5 (High Temperature / Long Time): Maximum temperature is 860℃, and the holding time is 15 minutes.

[0146] For each process scheme, a pre-processed duplexer component was placed in a graphite fixture and sent into the brazing furnace. After vacuuming and starting the temperature control program, the data acquisition module 100 operated continuously. The edge computing unit 105 ensured that the infrared image, left and right camera images, and PLC status readings remained synchronized with microsecond-level time accuracy through hardware trigger signals. Throughout the experiment, the system recorded a complete video of the temperature field evolution, a sequence of speckle images of the deformation field, and equipment parameter logs. After the furnace temperature dropped to a safe level, the brazed duplexer was removed. Subsequently, using an Agilent N5230A vector network analyzer, its S-parameters were comprehensively tested under a standard 25℃ test environment. The test data (e.g., 501 frequency points of S21 and S31 in a specific frequency band) were packaged with the corresponding process data to form a complete sample. This process was repeated until all five sets of experiments were completed, forming the initial training dataset.

[0147] 4. Training the PINN digital twin model

[0148] The five complete "process-performance" datasets collected are transmitted to the backend server 201. The data processing and modeling module 200 first preprocesses the data, including converting infrared thermal images into temperature field matrix sequences registered onto a 3D CAD model, and batch processing speckle images using DIC commercial software (such as VIC-3D) to obtain the full-field displacement and strain matrix sequences of the cover plate surface.

[0149] Next, the training script for the PINN model is started. The shared backbone network of this model is configured with 10 hidden layers, each containing 256 neurons. In the total loss function, the weights of the data loss term are... Set to 1.0 to force the model to fit the true measurement data highly; while the weight of the physical residual loss term is... The value was set to 0.01 to regularize the network, ensuring that its solution is physically plausible. The Adam optimizer was used during training, with an initial learning rate of 1e-3 and an exponential decay strategy configured. The entire training process was performed in parallel on two A100 GPUs. After approximately 200,000 iterations, the total loss function decreased by four orders of magnitude and converged. The trained model demonstrated excellent performance in cross-validation: the root mean square error of temperature prediction at any given time inside the furnace was within 5°C, the maximum displacement prediction error of the cover plate center was within 3 μm, and the prediction error of the final S-parameter key indicators was within ±3%, proving its high fidelity.

[0150] 5. Bayesian optimization-based process optimization

[0151] After model training is complete, the intelligent optimization decision module 300 is activated. Engineers first configure the optimization task. The optimization process parameter space is defined as a seven-dimensional vector, including three heating rates, two holding periods of temperature and time, and a controlled cooling rate. Each parameter has a physically and equipment-capable reasonable boundary. The optimization objective function f(P) is carefully designed as: f(P) = 15 * max(0, S21_loss(P) - 0.45) + 1 * max(0, 80 -S31_iso(P)). This function is a penalty function; a larger penalty value is applied when the predicted insertion loss is greater than -0.45dB (i.e., the loss is worse than 0.45dB) or the isolation is less than 80dB. The weight of 15:1 reflects the higher priority given to the insertion loss metric in the current scenario.

[0152] After the optimization program started, the Bayesian optimization algorithm ran autonomously without human intervention. It first used a Gaussian process regression model to fit the initial five data points, and then entered a 120-cycle iterative optimization loop. On the server, each iteration (including calling the PINN model for a complete virtual brazing simulation evaluation) took an average of about 1 minute. The entire optimization process took approximately 2 hours in total.

[0153] 6. Optimize results analysis, verification, and effectiveness evaluation.

[0154] The optimization algorithm ultimately outputs a set of optimal process parameters. Plotting these parameters as a temperature curve yields the following result: Figure 6 The solid line in neutron plot (a) represents the optimized curve. Compared to the conventional process represented by the dashed line, the most significant feature of the optimized curve is the addition of a 5-minute preheating plateau around 780°C before reaching the final soldering temperature of 855°C. Mechanistic analysis using a trained PINN model visualized the instantaneous temperature and stress fields within the duplexer. The analysis clearly reveals that this preheating plateau provides sufficient time for the low thermal conductivity ceramic resonator to catch up with the heating rate of the external copper cavity, thereby minimizing the instantaneous temperature difference between them before the period of most rapid thermal expansion. This directly results in a reduction of approximately 35% in thermal mismatch stress at the peak temperature, which is the fundamental physical reason for the final reduction in residual deformation and improved RF performance. This finding is difficult to achieve through purely empirical trial and error.

[0155] To verify this optimization result, the optimal process curve was downloaded to the brazing furnace and used for the subsequent batch production of 50 duplexers. After production, a statistical comparative analysis of the performance of these 50 samples and another 50 samples produced using the traditional process was conducted. The results show:

[0156] Improved RF performance: Reference Figure 6 Neutron plot (b) shows the S21 insertion loss curve (solid line) of the optimized sample. Throughout the 14.0–14.5 GHz passband, the value is not only lower (closer to 0 dB), but the curve is also flatter and more consistent. Statistical results indicate that the average insertion loss of the optimized product significantly decreased from 0.58 dB to 0.42 dB, representing a 27.6% improvement in average performance; the average isolation increased from 78.5 dB to 83.1 dB.

[0157] A leap in production yield: Before optimization, the overall scrap rate due to unqualified performance indicators was approximately 24%, and the yield rate was 76%. After adopting the optimized process, the scrap rate dropped to 4%, and the overall yield rate increased significantly to 96%.

[0158] Improved product consistency: The dispersion of performance data has been significantly reduced. For example, the standard deviation of insertion loss has decreased from 0.12 dB to 0.04 dB, indicating a 3-fold improvement in consistency within product batches.

[0159] Improved R&D efficiency: For this product model, the process optimization process, from initial data collection to obtaining the validated optimal process solution, consumed only 8 physical samples (5 for training and 3 for preliminary verification), with a total time of less than 3 working days. This represents a significant leap forward in R&D efficiency and cost control compared to the traditional model that required senior engineers to spend months and scrap dozens of expensive samples for repeated trial and error.

[0160] To verify the effect of the microwave device brazing process optimization control method based on digital twins described in this invention on improving the S-parameter performance of microwave devices, frequency response characteristics were tested in the 14.0GHz-14.5GHz band for S21 insertion loss and in the 12.0GHz-12.5GHz band for S31 isolation. 501 sets of data were collected at each frequency point, and the frequency response curves and their consistency between the traditional brazing process and the optimized process of this invention were compared.

[0161] like Figure 9 As shown, the figure consists of two side-by-side subplots, corresponding to the frequency response comparison of insertion loss (S21) and isolation (S31), respectively. The solid lines in the figure represent the measurement results using the optimized process of this invention, the dashed lines represent the measurement results using the traditional process, and the gray shaded areas represent their respective ±1 standard deviation (±1 sigma) confidence bands.

[0162] son Figure 9(a) Comparison of frequency response characteristics of S21 insertion loss. The mean S21 of the traditional process is -0.58dB, and the standard deviation is 0.12dB. The curve shows obvious fluctuations and a large confidence band, indicating insufficient consistency in the brazing process. After optimization using the method of this invention, the mean S21 is improved to -0.42dB, an increase of 27.6%, and the standard deviation is reduced to 0.04dB. The curve becomes flatter, and the confidence band is significantly narrowed. Under the optimized process, S21 at all frequencies meets the -0.5dB specification line requirement (shown by the horizontal dotted line in the figure), while the traditional process shows out-of-tolerance phenomena at some frequencies.

[0163] son Figure 9 (b) Comparison of frequency response characteristics for S31 isolation. The average S31 value of the traditional process is -78.5dB, which fails to meet the -80dB specification line requirement, and the curve fluctuates significantly. After optimization using the method of this invention, the average S31 value is improved to -83.1dB, an increase of 4.6dB, meeting the specification line requirements across the entire frequency band, and the curve stability is also significantly improved. The above results demonstrate that this invention, through the synergistic effect of digital twin model prediction and Bayesian optimization algorithm, effectively improves the S-parameter performance and batch consistency of microwave devices after soldering.

[0164] To quantitatively evaluate the improvement effect of the optimized control method described in this invention on batch production yield and product consistency, 50 product samples each from the traditional brazing process and the optimized process of this invention were statistically analyzed, and the production yield and S21 insertion loss distribution characteristics were compared and tested.

[0165] like Figure 10 As shown, the figures are a bar chart comparing yield rates and a violin plot showing the performance distribution of S21.

[0166] son Figure 10 (a) is a comparison chart of production yield, using a stacked bar chart format. The darker segments represent the yield rate, and the lighter segments represent the scrap rate. The chart shows that the traditional process yields a 76% production yield and a 24% scrap rate, indicating that under traditional brazing conditions, nearly a quarter of the products are scrapped due to substandard S-parameters or welding quality. After adopting the optimized method of this invention, the production yield increases to 96%, and the scrap rate decreases to 4%, representing a 20 percentage point increase in yield and an 83.3% decrease in scrap rate, significantly improving production quality stability.

[0167] son Figure 10(b) is a violin plot of the insertion loss distribution for S21, visually illustrating the difference in performance distribution patterns under the two process conditions. The violin plot for the traditional process is wide, with a median of -0.58 dB and a standard deviation (sigma) of 0.12 dB, indicating high performance dispersion, and some samples exceeding the -0.5 dB specification limit (horizontal dotted line in the figure). The violin plot for the optimized process is significantly narrower, with the median improving to -0.42 dB, the standard deviation (sigma) decreasing to 0.04 dB, and the distribution concentration increasing threefold. All samples meet the specification requirements. These statistical results demonstrate that this invention significantly improves production yield while also effectively improving batch consistency of microwave devices.

[0168] Finally, to evaluate the convergence efficiency of the Bayesian optimization method described in this invention and its improvement effect on engineering cost compared with the traditional trial-and-error method, the optimization convergence process is characterized by the curve of the objective function value f(P) changing with the number of iterations, and the sample cost of the two methods is characterized by the cumulative sample consumption, and a comparative analysis is conducted.

[0169] like Figure 11 As shown, this figure is presented as a composite graph with two vertical axes. The left vertical axis corresponds to the Bayesian optimization convergence curve (solid line), the right vertical axis corresponds to the cumulative sample consumption line of the two methods, and the horizontal axis represents the number of iterations (0 to 120). The gray-filled area below the curve on the left vertical axis represents the cumulative improvement space during the optimization process.

[0170] As shown by the convergence curve on the left vertical axis, the objective function value f(P) decreases rapidly in the early stages of iteration, enters a rapid convergence phase between the 20th and 30th iterations (the area marked by the gray rectangle in the figure), and then gradually approaches the optimal value. After 120 iterations (approximately 2 hours, with each iteration lasting about 1 minute), the objective function value converges to a value close to the minimum, indicating that the Bayesian optimization algorithm can efficiently locate the optimal combination of process parameters within a finite number of iterations.

[0171] As shown by the comparison of the broken lines on the right vertical axis, the cumulative sample consumption of the traditional trial-and-error method (dashed line) increases linearly with the number of experimental rounds. Completing a single full process optimization requires approximately 50 samples and takes about 3 months, resulting in high R&D costs. Using the method of this invention, only 5 basic samples are needed in the initial modeling stage, plus 3 verification samples, totaling 8 samples, to complete the process optimization, taking approximately 3 working days. The annotation box at the top of the figure compares the overall costs of the two methods. The above results demonstrate that this invention, by replacing a large number of physical experiments with digital twin virtual experiments and combining them with a Bayesian optimization search strategy, can reduce the sample consumption for process development to less than 16% of that of traditional methods, shortening the R&D cycle from several months to 3 working days, demonstrating significant engineering efficiency and cost advantages.

[0172] In summary, this embodiment provides a detailed, end-to-end application case, specifically demonstrating how the technical solution of this invention can be applied to solve complex industrial manufacturing problems. It not only verifies the feasibility and effectiveness of the method of this invention but also quantitatively proves its significant technical advantages and practical value in improving product performance, increasing production yield, and accelerating process development. Compared with existing technologies, the beneficial effects of this invention are as follows.

[0173] First, this invention achieves high-precision "white-box" prediction of the brazing process. By introducing Physical Information Neural Network (PINN) technology, physical partial differential equations are incorporated as strong constraints into the deep learning model. The constructed digital twin model overcomes the drawbacks of pure data-driven models, such as dependence on massive amounts of data and potential violation of physical laws. It has stronger generalization and extrapolation prediction capabilities, enabling in-depth analysis and accurate prediction of the process.

[0174] Secondly, this invention achieves efficient and intelligent optimization of process parameters. Addressing the high cost of a single evaluation in this scenario, a Bayesian optimization algorithm is selected. With its superior data efficiency, it can quickly converge to the globally optimal combination of process parameters with far fewer evaluations than traditional optimization algorithms. This completely replaces the traditional time-consuming, labor-intensive, and expensive manual trial-and-error or offline simulation process, shortening the process development cycle of new products and reducing R&D costs.

[0175] Furthermore, this invention can significantly improve product performance and yield. Through a closed-loop self-optimization process, the system can tailor the optimal soldering process curve for each specific structure and batch of microwave devices, fundamentally suppressing adverse structural deformation caused by improper thermal cycling. This significantly improves key RF indicators such as insertion loss and isolation of products like duplexers, resulting in a marked improvement in finished product yield and performance consistency.

[0176] Finally, this invention constructs an intelligent production system with online monitoring, anomaly early warning, and continuous self-learning capabilities. During mass production, the digital twin model serves as a health baseline, monitoring the production process in real time, promptly detecting anomalies, and preventing large-scale quality accidents. Simultaneously, the system can continuously learn from new production data, enabling self-iteration of the model and continuous fine-tuning of the process, thus giving the production system the ability to be upgraded.

[0177] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for optimizing and controlling the brazing process of microwave devices based on digital twins, characterized in that, include: Real-time multiphysics field data of the microwave device to be brazed during the brazing process are obtained, wherein the multiphysics field data includes at least temperature field data and deformation field data of the device surface; Based on a preset digital twin model with a physical information neural network as its core, the multi-physics field data and the process parameters associated with the multi-physics field data are input to train the digital twin model and obtain a target model that can characterize the mapping relationship between process parameters, multi-physics field data and the final radio frequency performance of microwave devices. Using the target model as a proxy model, the Bayesian optimization algorithm is used to find the optimal process parameters within a preset process parameter space, with one or more preset RF performance indicators as optimization targets. Furthermore, the brazing equipment is controlled to perform the brazing process on the microwave device based on the optimal process parameters.

2. The method according to claim 1, characterized in that, The acquisition of real-time multiphysics data of the microwave device to be brazed during the brazing process includes: Real-time temperature field data of the device surface is collected non-contactly using an infrared thermal imager deployed outside the observation window of the brazing equipment. Furthermore, real-time deformation field data of the device surface are acquired non-contactly through a binocular vision system based on digital image correlation technology deployed outside the observation window.

3. The method according to claim 2, characterized in that, Before acquiring data using the binocular vision system based on digital image correlation technology, the following steps are also included: On the surface of the device to be observed, a ceramic random speckle pattern capable of withstanding the high temperature of the brazing process is prepared.

4. The method according to claim 1, characterized in that, The digital twin model, which is based on a physical information neural network, has a loss function during training that includes at least the following: The data loss term is used to measure the difference between the predicted physical field values ​​of the model and the multi-physics data collected by the sensor, as well as the difference between the RF performance predicted by the model and the measured RF performance of the device. Additionally, a physical residual loss term is used to measure how well the model's predicted physical field values ​​conform to one or more partial differential equations describing the brazing process.

5. The method according to claim 4, characterized in that, The partial differential equations include at least three-dimensional unsteady heat conduction equations and quasi-static thermal structure coupling equations.

6. A microwave device brazing process optimization control system based on digital twin, characterized in that, include: The data acquisition module is used to acquire real-time multi-physics field data of the microwave device to be brazed during the brazing process. The multi-physics field data includes at least temperature field data and deformation field data of the device surface. The data processing and modeling module is used to train the digital twin model based on a preset digital twin model with physical information neural network as the core, by inputting the multi-physics field data and the process parameters associated with the multi-physics field data, and obtaining a target model that can characterize the mapping relationship between process parameters, multi-physics field data and the final radio frequency performance of microwave devices. The intelligent optimization decision module is used to take the target model as a proxy model and use the Bayesian optimization algorithm to find the optimal process parameters in the preset process parameter space with one or more preset RF performance indicators as optimization targets. And a process execution control module, used to control the brazing equipment to perform the brazing process on the microwave device based on the optimal process parameters.

7. The system according to claim 6, characterized in that, The data acquisition module specifically includes: An infrared thermal imager is used to collect real-time temperature field data of the surface of the device in a non-contact manner. Additionally, a binocular vision system based on digital image correlation technology is used to non-contactly acquire real-time deformation field data of the device surface.

8. The system according to claim 6, characterized in that, The physical information neural network running in the data processing and modeling module has a network architecture including a shared backbone network, a physical field output head connected to the shared backbone network, and a radio frequency performance proxy output head. The physical field output head is used to output the instantaneous temperature and displacement of the device at any point in time and space during the brazing process; The RF performance proxy output head is used to predict the final RF performance of the device based on the displacement output by the physical field output head at the end of the soldering process.

9. The system according to claim 6, characterized in that, The Bayesian optimization algorithm running in the intelligent optimization decision module is specifically configured as follows: A Gaussian process regression model is used as a probabilistic surrogate model to estimate the mean and uncertainty of the output of the target model; Furthermore, the expected improvement function is used as the acquisition function to select the next process parameter point to be evaluated within the process parameter space.

10. A computer device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor is configured to, when executing the computer program, implement the method as described in any one of claims 1-5.

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