A physical feature construction method for manufacturing parameter prediction of micro-hemisphere resonator

Abstract

The present application relates to the technical field of micro-hemispherical resonator gyroscope design and manufacturing, and particularly relates to a physical feature construction method for manufacturing parameter prediction of a micro-hemispherical resonator, comprising the following steps: determining a manufacturing parameter to be predicted, and obtaining a basic design parameter set of the micro-hemispherical resonator required by the manufacturing parameter; defining the basic design parameter set as an input parameter, obtaining a corresponding manufacturing parameter as an output parameter, constructing a first physical feature representing mold thermal asymmetry, and constructing a second physical feature representing glass material deformation strain energy density; combining the first physical feature and the second physical feature to form an enhanced feature set for manufacturing parameter prediction, taking the enhanced feature set as an input and taking a manufacturing parameter as an output, and training a prediction model by using a deep learning method to quantify the contribution of each input feature to the final prediction result, so as to realize physical interpretability of model decision, and the present application aims to solve the technical problem that the prior art lacks a theory and method system of a prediction feature with clear physical meaning.

Description

Technical Field

[0001] This invention relates to the field of micro-hemispherical resonator gyroscope design and manufacturing technology, and in particular to a method for constructing physical characteristics for predicting manufacturing parameters of a micro-hemispherical resonator. Background Technology

[0002] As a core component of high-performance gyroscopes, the microspherical resonator's manufacturing process relies heavily on a series of key geometric and physical parameters, or performance parameters, that directly determine the final product's performance and yield. These manufacturing parameters, such as the critical forming height, quality factor, and resonant frequency, collectively constitute the constraints and quality characteristics of the resonator from design to manufacturing. Accurately predicting these parameters is a prerequisite for precisely defining the process window, avoiding processing defects, and conducting efficient design iterations. However, the high-temperature glass blowing process involves material nonlinearity, large geometric deformation, and complex thermo-mechanical coupling, making the accurate prediction of these manufacturing parameters a significant challenge.

[0003] Traditional prediction methods primarily rely on physics-based finite element numerical simulations or experience-based trial-and-error methods. While the finite element method can accurately describe process physics, its complex modeling and extremely high computational cost severely hinder its application in multi-parameter optimization and rapid design verification. Trial-and-error methods depend on physical experiments, which are costly, time-consuming, and lack universality and predictive foresight. With the development of data science, establishing a direct mapping relationship from design parameters to manufacturing goals using machine learning models has become an emerging approach. However, existing data-driven methods typically use basic geometric dimensions directly as model inputs, failing to extract essential characteristics from complex physical phenomena. Under the constraints of scarce and costly manufacturing data, these methods struggle to fully learn deep nonlinear physical laws, resulting in weak model generalization ability, insufficient prediction stability, and their "black box" nature makes the prediction results lack physical interpretability, failing to effectively guide process improvement and design optimization.

[0004] In existing technologies, research on micro-hemispherical harmonic oscillators largely focuses on specific process implementations. For example, authorized invention CN117142749B relates to a thermoforming mold and method for micro-hemispherical harmonic oscillators based on full mold constraint, and CN119426791A discloses a system for processing micro-hemispherical harmonic oscillators using carbon dioxide lasers. In addition, some research focuses on using machine learning to predict certain final performance indicators of the harmonic oscillator. However, the above research has significant limitations: firstly, process-related patents do not address the problem of forward-looking prediction of key parameters in the manufacturing process; secondly, existing prediction methods mostly focus on building "end-to-end" prediction models, and their input features often remain at the level of original design parameters, lacking a systematic, physical mechanism-based feature construction methodology, and failing to transform domain knowledge into high-value features that can enhance model performance and interpretability.

[0005] In summary, the existing technologies have the following shortcomings: (1) High-precision physical simulation calculation efficiency is low and it is difficult to support rapid design exploration; (2) Pure data-driven methods have limited performance under small sample conditions and the input features fail to fully characterize the physical nature of the manufacturing process; (3) The predictive models have poor interpretability, the decision logic is disconnected from the physical mechanism, and the engineering guidance value is limited; (4) A general theoretical and methodological system that constructs predictive features with clear physical meaning from the perspective of manufacturing physics has not yet been formed. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for predicting the critical height of a micro-hemispherical harmonic oscillator, which aims to solve the technical problems mentioned in the background art.

[0007] To achieve the above objectives, in a first aspect, the present invention proposes a method for constructing physical features for predicting manufacturing parameters of a micro-hemispherical harmonic oscillator, comprising the following steps:

[0008] S1. Determine the manufacturing parameters to be predicted and obtain the basic design parameter set of the micro-hemispherical resonator required for these manufacturing parameters;

[0009] S2. Define the basic design parameter set as input parameters and obtain the corresponding manufacturing parameters as output parameters;

[0010] S3. Based on the aforementioned set of basic design parameters, construct a first physical characteristic characterizing the thermal asymmetry of the mold;

[0011] S4. Based on the aforementioned set of basic design parameters, construct a second physical characteristic characterizing the deformation strain energy density of the glass material;

[0012] S5. Combine the basic design parameters with the first physical feature and the second physical feature to form an enhanced feature set for manufacturing parameter prediction;

[0013] S6. Using the enhanced feature set as input and the manufacturing parameters as output, a prediction model is trained using deep learning methods. After training, the prediction model is analyzed to quantify the contribution of each input feature to the final prediction result, thereby achieving physical interpretability of the model's decision.

[0014] Preferably, the manufacturing parameters in S1 include, but are not limited to, the critical height of the glass blowing forming stage, the quality factor of the resonator, and the operating frequency of the resonator; the basic design parameter set includes the resonator radius, anchor point radius, thickness, and mold forming section radius; the graphite mold is a stepped shaft structure including an upper forming section and a lower support base, and the mold forming section radius is the same as the upper forming section radius.

[0015] As a preferred method, the method for obtaining the corresponding manufacturing parameters includes the following steps:

[0016] S201, Planning parameter combinations; Based on the basic design parameter set determined in step S1, systematically plan multiple sets of representative parameter combinations to cover the expected design space;

[0017] S202. Perform simulation calculations or experiments and collect output data; for the parameter combination planned in S201, perform finite element simulation or experimental measurement, accurately extract or measure the required manufacturing parameter results, and use them as the output parameters corresponding to the input parameters, thereby constructing the initial dataset of input and output.

[0018] As a preferred embodiment, the method for constructing a first physical characteristic characterizing the thermal asymmetry of the mold includes the following steps:

[0019] S301, Calculate the width of the mold edge support;

[0020] S302. Define and construct the first physical feature as a dimensionless parameter, which is the ratio of the width of the mold edge support to the radius of the anchor point.

[0021] Preferably, the method for the second physical characteristic includes the following steps:

[0022] S401. The harmonic oscillator is considered as a geometric body formed by rotating a beam around its central axis. The membrane strain energy is described by the membrane strain energy of the beam. The relationship between the membrane strain energy and the strain of the beam width and the radial length of the beam is established.

[0023] S402. Establish the relationship between the strain of the beam's radial length and the width of the edge support and the radius of the anchor point;

[0024] S403. The deformation strain energy density of the constructed material is defined as the second physical characteristic by means of membrane strain energy.

[0025] As a preferred option, the radius of the harmonic oscillator is limited to... Anchor point radius is Thickness is The radius of the forming section of the mold is Then the edge support width It can represent Edge support width Physically, it characterizes the radial support dimension of the portion of the quartz glass sheet that extends beyond the outline of the target harmonic oscillator during the initial formation stage.

[0026] As a preferred embodiment, the first physical characteristic is defined as P, which is used to quantify the thermal asymmetry of the mold; its expression is: .

[0027] Preferably, the membrane strain energy of the beam is defined as follows: ,but ;in Indicates Young's modulus. Indicates the width of the beam. The strain representing the radial length of the beam can be expressed as: ;in This indicates the length of the cavity section in the forming segment of the graphite mold. This represents the length of the beam after deformation within the cavity of the forming section of the graphite mold following high-temperature blow molding; the strain of the beam. It is a uniform membrane strain energy Simplified to When the anchor point radius When the value is very small, the strain is the greatest, and the length is the longest. It has a maximum value The strain is approximately equal to the sum of the length of the beam cavity section and the radius of a circle that is one-quarter the length of the beam cavity section. Maximum value It can be represented as When the anchor point radius When the value is particularly large, the strain is minimal, and the edge support width is [missing information]. With anchor point radius Equivalent, length It has a minimum value Approximately equal to the length of a semicircular arc with a radius half the length of the beam cavity interval, under this condition, the strain... Minimum value It can be represented as Linearization approximation is used for... To express ;

[0028] Membrane strain energy of beam It can be represented as Second physical characteristic Used to quantify the strain energy density of material deformation .

[0029] Preferably, the method for constructing and training the prediction model involves matching the output parameters in the initial dataset constructed in step S2 with the input vectors of the enhanced feature set constructed in step S5 to form a paired sample set, and normalizing all features to eliminate the influence of dimensions and improve the stability of model training. The paired sample set is divided into a training set and a test set, wherein the training set is used for model parameter learning and the test set is used to evaluate the generalization performance of the model. A prediction model suitable for small sample regression tasks is selected, and the enhanced feature vectors of the training set are used as inputs and the corresponding manufacturing parameters are used as outputs to train the model. During the training process, cross-validation and early stopping strategies are adopted to prevent overfitting and optimize model performance.

[0030] The method to achieve physical interpretability of model decisions is to analyze the prediction model after training and validation using the Shapley additive interpretation method. By sampling the test samples multiple times and propagating the model forward, the Shapley additive value of each input feature is calculated and summarized. This value quantitatively reflects the contribution of each feature to a single prediction result. Based on the Shapley additive analysis results, the physical quantities of the input features that show the main contribution to the output are identified, so that the prediction results have clear physical interpretability, so as to better guide the design and optimization of the harmonic oscillator.

[0031] To achieve the above objectives, in a second aspect, the present invention proposes a storage medium comprising a stored program, wherein, when the program is executed, the device containing the storage medium is controlled to perform the physical feature construction method for predicting the manufacturing parameters of the micro-hemispherical harmonic oscillator of the first aspect.

[0032] To achieve the above objectives, in a third aspect, the present invention proposes a processor for running a program, wherein the program executes the physical feature construction method for predicting the manufacturing parameters of a micro-hemispherical harmonic oscillator according to the first aspect.

[0033] Compared with existing technologies, the physical feature construction method for predicting manufacturing parameters of micro-hemispherical harmonic oscillators provided by this invention has the following advantages: it effectively overcomes the core limitations of traditional methods, such as insufficient mining of physical mechanisms at the feature construction level, weak generalization ability of prediction models under small sample conditions, and lack of interpretability in the decision-making process. Existing technologies either rely on computationally expensive finite element simulations for trial and error or only use basic geometric parameters as inputs to data-driven models, resulting in low prediction efficiency and difficulty in capturing the complex physical essence of the manufacturing process when data is scarce. This method creatively integrates the physical phenomena revealed by finite element simulations with the derivation of solid mechanics theory to construct feature parameters with clear physical meaning, providing downstream prediction models with high information density and strong physical interpretability. In particular, the constructed features can not only serve as a rapid qualitative criterion for manufacturing feasibility, but also significantly improve the accuracy and robustness of various prediction models in small sample scenarios. In addition, through the Shapley additive interpretation analysis tool, the contribution of each physical feature to the prediction results can be clearly quantified, mapping the model decision back to an understandable physical mechanism, and realizing closed-loop guidance for prediction and design. This invention provides a novel and universal underlying feature engineering solution for the efficient and reliable design and manufacturing optimization of micro-hemispherical resonators, significantly reducing the reliance on high-cost trial and error and "black box" models, and possessing good mechanism transparency and engineering promotion value. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the physical feature construction method for predicting manufacturing parameters of a micro-hemispherical harmonic oscillator, as provided by the present invention.

[0035] Figure 2 This is a schematic diagram of the strain length variation of the harmonic oscillator in this invention.

[0036] Figure 3 This is a schematic diagram showing the critical height of the harmonic oscillator in an embodiment of the present invention.

[0037] Figure 4 The diagram shows the additive analysis results of sapride in an embodiment of the present invention.

[0038] Figure 5 This is a comparison chart of the first root mean square error of the model before and after the introduction of physical features in an embodiment of the present invention.

[0039] Figure 6 This is a comparison chart of the second root mean square error of the model before and after the introduction of physical features in an embodiment of the present invention.

[0040] Figure 7 This is a comparison chart of the third root mean square error of the model before and after the introduction of physical features in an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. However, it should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0042] In the description of this invention, it should be noted that when an element is referred to as being "fixed to" or "set on" another element, it can be directly on or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to or indirectly connected to the other element.

[0043] This invention proposes a method for constructing physical features to predict manufacturing parameters of micro-hemispherical harmonic oscillators. The core of this invention is not to replace specific prediction models, but to solve a key upstream bottleneck: by integrating finite element simulation insights with solid mechanics theoretical derivations, it abstracts and constructs intrinsic feature parameters from the complex manufacturing physics process that profoundly reflect deformation and constraint mechanisms. The features constructed by this method have universal physical meaning and can be injected as powerful prior knowledge into various downstream prediction models, thereby significantly improving prediction accuracy, robustness, and model transparency under small sample conditions. This provides an innovative underlying feature engineering solution for the intelligent manufacturing and collaborative design of micro-hemispherical harmonic oscillators. See appendix. Figure 1 A method for constructing physical features for predicting manufacturing parameters of a micro-hemispherical harmonic oscillator, comprising the following steps:

[0044] S1. Determine the required manufacturing parameters and obtain the basic design parameter set of the micro-hemispherical resonator needed for these manufacturing parameters. The parameter set includes at least the resonator radius. Anchor point radius ,thickness and the radius of the forming section of the mold .

[0045] Furthermore, the specific plan for step S1 is as follows:

[0046] S101. Determine the specific manufacturing parameters for the micro-hemispherical resonator. The manufacturing parameters include, but are not limited to, the critical height during the glass blowing process, the quality factor of the resonator, or the operating frequency of the resonator.

[0047] S102. Determine the basic design parameters of the resonator required to obtain these manufacturing parameters, including: resonator radius. That is, the radius of the hemispherical profile to be achieved after forming; anchor point radius. That is, the radius of the central support structure; degrees. The initial thickness of the quartz glass sheet used for blowing; the radius of the forming section of the die. Graphite molds typically have a stepped shaft structure, consisting of an upper forming section and a lower support base. The radius of the forming section of the mold is... That is, the radius of the upper forming section.

[0048] S2. Define a set of basic design parameters as input parameters, and obtain the data values ​​of manufacturing parameters corresponding to the parameters as output parameters through finite element simulation or experimental measurement, thereby constructing the initial dataset of input and output.

[0049] Furthermore, the specific plan for step S2 is as follows:

[0050] S201. Planning Parameter Combinations. Based on the basic design parameters determined in step S1, systematically plan multiple sets of representative parameter combinations to cover the expected design space;

[0051] S202. Perform simulation calculations or experiments and collect output data. For the parameter combination planned in S201, perform finite element simulation or experimental measurement to accurately extract or measure the required manufacturing parameter results, which are used as the output parameters corresponding to the input parameters, thereby constructing the initial dataset of input and output.

[0052] S3. Based on the aforementioned set of basic design parameters, construct the first physical feature characterizing the thermal asymmetry of the mold.

[0053] Furthermore, the specific plan for step S3 is as follows:

[0054] S301, Calculate the width of the mold edge support. The radial direction of the forming section of a graphite mold can be divided into three intervals: the anchor point radius interval, the cavity interval, and the edge support interval. Edge support width... It can be represented as: Edge support width Physically, it characterizes the radial support dimension of the portion of the quartz glass sheet that extends beyond the outline of the target harmonic oscillator during the initial formation stage.

[0055] S302. Define and construct the first physical feature. The expression for quantifying the thermal asymmetry of a mold is: This feature As a dimensionless parameter, its physical meaning lies in characterizing the radial geometric ratio between the anchor point of the forming region and the surrounding region; ratio The larger the value, the more significant the asymmetry of the thermal field distribution in the mold, which makes the glass material more prone to non-uniform deformation towards the anchor point during the blowing process, thus directly affecting the geometric shape of the harmonic oscillator.

[0056] S4. Based on the aforementioned set of basic design parameters, construct a second physical characteristic that characterizes the deformation strain energy density of the glass material.

[0057] Furthermore, the specific plan for step S4 is as follows:

[0058] S401. A harmonic oscillator can be considered as a geometric body formed by rotating a beam around its central axis. Its membrane strain energy can be expressed as the membrane strain energy of the beam. To describe: .

[0059] in Indicates Young's modulus. Indicates the width of the beam. The strain representing the radial length of a beam can be expressed as: .in This indicates the length of the cavity section in the forming segment of the graphite mold. It indicates the length of the beam after deformation within the cavity of the forming section of the graphite mold following high-temperature blow molding.

[0060] Since the beam is uniformly heated, the strain of the beam can be approximated. It is uniform, membrane strain energy It can be simplified to: .

[0061] S402, Confirm The expression. See appendix. Figure 2 The resonator is typically shaped like a hemisphere, and its profile is related to the radius of the anchor point. When the anchor point radius... The strain is greatest in extremely small times. It has a maximum value It is approximately equal to the sum of the length of the beam cavity section and the radius of a circle that is one-quarter the length of the beam cavity section. Under this condition, It has a maximum value It can be represented as: .

[0062] See appendix Figure 2 When the anchor point radius When the value is particularly large, the strain is minimal, and the edge support width is [missing information]. With anchor point radius quite, It has a minimum value It is approximately equal to the length of a semicircular arc with a radius equal to half the length of the beam cavity section. Under this condition, It has a minimum value It can be represented as: .

[0063] Using linearized approximations To describe: .

[0064] S403, Define and construct the second physical feature Membrane strain energy of beam It can be represented as: .

[0065] Second physical characteristic Used to quantify the strain energy density of material deformation: .

[0066] Second physical characteristic From the perspective of the energy of the material to resist deformation, it provides a more fundamental input variable for predicting manufacturing parameters such as critical height; the larger the value, the higher the deformation potential of the material system under the same blowing conditions, which usually corresponds to a larger achievable forming height.

[0067] S5. Combine the basic design parameters with the constructed physical features to form an enhanced feature set for manufacturing parameter prediction.

[0068] Furthermore, the specific plan for step S5 is as follows:

[0069] S501. Based on the basic design parameter set defined in S2, the first physical characteristic corresponding to each set of parameters is calculated by S302 and S403. The numerical value and second physical characteristics The value.

[0070] S502, Combine the basic design parameter set with the physical characteristics of the structure ( , They are integrated to form an enhanced dataset as the input vector.

[0071] S6. Using the enhanced feature set as input and the manufacturing parameters as output, train the model using a deep learning method. After training, analyze the prediction model using the Shapley additive interpretation method to quantify the contribution of each input feature to the final prediction result, thereby achieving the physical interpretability of the model's decision.

[0072] Furthermore, the specific plan for step S6 is as follows:

[0073] S601. Data Preprocessing and Partitioning. The output parameters in the initial dataset constructed in step S2 are matched one-to-one with the input vectors of the enhanced feature set constructed in step S5 to form a paired sample set. All features are normalized to eliminate the influence of unit dimensions and improve model training stability. The paired sample set is divided into a training set and a test set, where the training set is used for model parameter learning, and the test set is used to evaluate the model's generalization performance.

[0074] S602. Model Selection and Training: Select a prediction model suitable for small-sample regression tasks. Use the enhanced feature vectors of the training set as input and the corresponding manufacturing parameters as output to train the model. Cross-validation and early stopping strategies can be used during training to prevent overfitting and optimize model performance.

[0075] S603. Interpretability Analysis Based on Shapley Additive Interpretation. For the trained and validated prediction model, the Shapley additive interpretation method is used for analysis. Through multiple samplings of test samples and model forward propagation, each input feature (including...) is calculated and summarized. , The Shapley property value is used to quantitatively reflect the contribution of each feature to a single prediction result.

[0076] S604. Result Interpretation. Based on the Shapley additive analysis results, identify the input characteristic physical quantities that contribute significantly to the output, so that the prediction results have clear physical interpretability, in order to better guide the design optimization of the harmonic oscillator.

[0077] Furthermore, embodiments of this application also provide a storage medium for storing a computer program, wherein the computer program, when running, controls the device where the storage medium is located to execute the above-described... Figures 1-3 A method for constructing physical characteristics for predicting the manufacturing parameters of a micro-hemispherical harmonic oscillator.

[0078] Furthermore, embodiments of this application also provide a processor for running a program, wherein the program executes the above-described... Figures 1-3A method for constructing physical characteristics for predicting the manufacturing parameters of a micro-hemispherical harmonic oscillator.

[0079] This invention presents a physical feature construction method for predicting manufacturing parameters of micro-hemispherical harmonic oscillators, addressing the limitations of traditional data-driven methods in predictive model accuracy, weak generalization ability, and insufficient decision interpretability caused by the unclear physical meaning of input features under data-scarce conditions. This invention integrates physical phenomena revealed by finite element simulation with derivations from solid mechanics theory, extracting and constructing physical features characterizing the thermal asymmetry of the mold and the deformation strain energy density of the glass material from the complex glass blowing process. This provides high-value input for predictive models of various manufacturing parameters. This method significantly improves prediction accuracy and robustness in small-sample learning scenarios and injects physical insights into the model, enhancing its engineering guidance value. This invention provides a novel, mechanism-driven feature engineering solution for the design and manufacturing of micro-hemispherical harmonic oscillators, overcoming the limitations of relying solely on geometric parameters or "black box" models, and facilitating efficient and reliable design iteration and process optimization.

[0080] Specific experimental procedure: To verify the feasibility of this invention, an experiment was conducted on the physical feature construction method for predicting the manufacturing parameters of a micro-hemispherical harmonic oscillator, according to the method provided in this invention. See appendix. Figure 3 As the blow molding process progresses, the outer edge of the resonator gradually approaches the side wall of the mold. When the outer edge of the resonator is about to contact the side wall of the mold, the height of the resonator is the critical height. If this height is exceeded, the outer edge of the resonator will contact the side wall of the mold, causing the shape of the resonator to be distorted.

[0081] Determine the fundamental design parameters of the resonator required to obtain these manufacturing parameters. The radius of the microhemispherical resonator. The radius of the mold forming section is set to 5mm. It is 8mm. In addition, the anchor point radius... and thickness It will also affect the critical height of the harmonic oscillator.

[0082] The critical height of the resonator was obtained through a blow molding simulation experiment using ANSYS POLYFLOW. The geometric parameters of the micro-hemispherical resonator in the simulation experiment were determined: the simulation value ranges for the resonator anchor point radius and thickness are shown in Table 1.

[0083] Table 1: Simulation Value Range of Geometric Parameters for the Microhemispherical Resonator

[0084] During the blow molding simulation, a 1.5 × 10⁻⁶ layer was applied to the upper surface of the fused silica sheet. 6 The heat flux density is set at W / m², and the surface is designed to withstand a pressure of 50 kPa. The coupling coefficient for heat exchange is 500 W / (m²).2 K), and other relevant physical parameters of the material are detailed in Table 2. The corresponding critical height dataset was obtained.

[0085] Table 2: Material Parameters for Finite Element Blow Molding

[0086] Expand the input dataset. Utilize the radius of the harmonic oscillator. radius of mold forming section Anchor point radius and thickness Calculate the first physical feature corresponding to each simulation. The numerical value and second physical characteristics The values ​​will be based on the set of basic design parameters ( , , , ) and the physical characteristics of the structure ( , They are integrated to form an enhanced dataset as the input vector.

[0087] The Transformer-LSTM model was used for training. After training, the Shapley additive interpretation method was used for analysis, and the results are shown in the appendix. Figure 4 .because and Since it's a fixed value, no analysis is performed. The analysis results show that the variable with the greatest impact on the critical height is the anchor point radius. ,thickness It has a relatively small impact on the critical height. and Their importance scores were all significantly higher than This confirms and The parameters do indeed capture the deep physical mechanisms that affect the deformation process, rather than simply geometric dimensions.

[0088] Analysis results indicate that more attention needs to be paid to the harmonic oscillator during the manufacturing process. Change, and and Changes in these three parameters will cause significant fluctuations in the critical height of the harmonic oscillator. The change in [variable value] has a relatively small impact on the critical height of the resonator. Considering manufacturing errors during the design phase, it is necessary to [adjust / compare] [the value]. , and Errors are strictly controlled to minimize fluctuations in the critical height. Regarding thickness... The thickness and processing precision of the purchased raw materials can be appropriately relaxed, thereby effectively reducing the procurement cost.

[0089] Three comparative experiments were conducted based on the Transformer-LSTM model. Under the same hyperparameter settings, training was performed using both the original critical height dataset and a dataset incorporating physical features. (See attached image.) Figures 5-7 The comparison of root mean square error (RMSE) for two datasets on the test set is shown. The data shows that, compared to the original data, after using the physical feature construction method of this invention, the first ( Figure 5 ), the second time ( Figure 6 ) and the third ( Figure 7 The relative RMSE errors (the difference between the RMSE using the physical feature construction method and the RMSE without the physical feature construction method / the RMSE without the physical feature construction method) in the comparative experiments were significantly reduced by 18.47%, 5.39%, and 27.65%, respectively. The experimental results demonstrate that the method of this invention can effectively reduce model prediction errors and significantly improve prediction accuracy.

[0090] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0091] It is understood that the relevant features in the above methods and systems can be referenced interchangeably. Furthermore, the terms "first," "second," etc., in the above embodiments are used to distinguish between embodiments and do not represent the superiority or inferiority of any particular embodiment.

[0092] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0093] The algorithms and displays provided herein are not inherently related to any particular computer, virtual system, or other device. Various general-purpose systems can also be used in conjunction with the teachings herein. The required structure for constructing such systems is apparent from the above description. Furthermore, this application is not directed to any particular programming language. It should be understood that the content of this application described herein can be implemented using various programming languages, and the above description of specific languages ​​is for the purpose of disclosing the best mode of implementation of this application.

[0094] In addition, the memory may include non-permanent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM, and the memory includes at least one memory chip.

[0095] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0096] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0097] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0098] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0099] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0100] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0101] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0102] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0103] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0104] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions or improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method of constructing a physical feature for micro-hemisphere resonator manufacturing parameter prediction, characterized by, Includes the following steps: S1. Determine the manufacturing parameters to be predicted and obtain the basic design parameter set of the micro-hemispherical resonator required for these manufacturing parameters; S2. Define the basic design parameter set as input parameters and obtain the corresponding manufacturing parameters as output parameters; S3. Based on the aforementioned set of basic design parameters, construct a first physical characteristic characterizing the thermal asymmetry of the mold; S4. Based on the aforementioned set of basic design parameters, construct a second physical characteristic characterizing the deformation strain energy density of the glass material; S5. Combine the basic design parameters with the first physical feature and the second physical feature to form an enhanced feature set for manufacturing parameter prediction; S6. Using the enhanced feature set as input and the manufacturing parameters as output, a prediction model is trained using deep learning methods. After training, the prediction model is analyzed to quantify the contribution of each input feature to the final prediction result, thereby achieving physical interpretability of the model's decision-making.

2. The method of claim 1, wherein the physical feature construction method of microhemispherical resonator fabrication parameter prediction is characterized by, The manufacturing parameters in S1 include, but are not limited to, the critical height of the glass blowing forming stage, the quality factor of the resonator, and the operating frequency of the resonator; the basic design parameter set includes the resonator radius, anchor point radius, thickness, and mold forming section radius; the graphite mold is a stepped shaft structure including an upper forming section and a lower support base, and the mold forming section radius is the same as the upper forming section radius.

3. The method of claim 2, wherein the physical feature construction method is a microhemispherical resonator fabrication parameter prediction method, characterized by, The method for obtaining the corresponding manufacturing parameters includes the following steps: S201, Planning parameter combinations; Based on the basic design parameter set determined in step S1, systematically plan multiple sets of representative parameter combinations to cover the expected design space; S202. Perform simulation calculations or experiments and collect output data; for the parameter combination planned in S201, perform finite element simulation or experimental measurement, accurately extract or measure the required manufacturing parameter results, and use them as the output parameters corresponding to the input parameters, thereby constructing the initial dataset of input and output.

4. The method of claim 3, wherein the physical feature construction method is a microhemispherical resonator manufacturing parameter prediction method, characterized by, The method for constructing a first physical characteristic to characterize the thermal asymmetry of a mold includes the following steps: S301, Calculate the width of the mold edge support; S302. Define and construct the first physical feature as a dimensionless parameter, which is the ratio of the width of the mold edge support to the radius of the anchor point.

5. The method of claim 4, wherein the microhemispherical resonator fabrication parameter prediction physical feature construction method is characterized by, The method for the second physical characteristic includes the following steps: S401. The harmonic oscillator is considered as a geometric body formed by rotating a beam around its central axis. The membrane strain energy is described by the membrane strain energy of the beam. The relationship between the membrane strain energy and the strain of the beam width and the radial length of the beam is established. S402. Establish the relationship between the strain of the beam's radial length and the width of the edge support and the radius of the anchor point; S403. The deformation strain energy density of the constructed material is defined as the second physical characteristic by means of membrane strain energy.

6. The method for constructing physical features for predicting manufacturing parameters of a micro-hemispherical harmonic oscillator as described in claim 5, characterized in that, The radius of the harmonic oscillator is limited to Anchor point radius is Thickness is The radius of the forming section of the mold is Then the edge support width Represented as Edge support width Physically, it characterizes the radial support dimension of the portion of the quartz glass sheet that extends beyond the outline of the target harmonic oscillator during the initial formation stage.

7. The method for constructing physical features for predicting manufacturing parameters of a micro-hemispherical harmonic oscillator as described in claim 6, characterized in that, Define the first physical characteristic as P, and use it to quantify the thermal asymmetry of the mold. Its expression is: .

8. The method for constructing physical features for predicting manufacturing parameters of a micro-hemispherical harmonic oscillator as described in claim 7, characterized in that, The membrane strain energy of the beam is limited to ,but ; in Indicates Young's modulus. Indicates the width of the beam. The strain representing the radial length of the beam is expressed as... ； in This indicates the length of the cavity section in the forming segment of the graphite mold. This indicates the length of the beam after deformation within the cavity of the forming section of the graphite mold following high-temperature blow molding. Strain of the beam It is a uniform membrane strain energy Simplified to ; When the anchor point radius Especially in small hours, length It has a maximum value The strain is approximately equal to the sum of the length of the beam cavity section and the radius of a circle that is one-quarter the length of the beam cavity section. Maximum value Represented as ; When the edge support width With anchor point radius When they are equal, length It has a minimum value Approximately equal to the length of a semicircular arc with a radius half the length of the beam cavity interval, under this condition, the strain... Minimum value Represented as ; Using linearization approximation The expression is ; Membrane strain energy of beam Represented as ; Second physical characteristic Used to quantify the strain energy density of material deformation .

9. The method for constructing physical features for predicting manufacturing parameters of a micro-hemispherical harmonic oscillator as described in claim 8, characterized in that, The method for constructing and training the prediction model is as follows: the output parameters in the initial dataset constructed in step S2 are matched one-to-one with the input vector of the enhanced feature set constructed in step S5 to form a paired sample set, and all features are normalized. The paired sample set is then divided into a training set and a test set. A prediction model suitable for small sample regression tasks is selected, and the enhanced feature vector of the training set is used as input and the corresponding manufacturing parameters are used as output to train the model. Cross-validation and early stopping strategies are adopted during the training process. The method to achieve physical interpretability of model decision-making is to analyze the prediction model after training and validation using the Shapley additive interpretation method. By sampling the test samples multiple times and propagating the model forward, the Shapley additive value of each input feature is calculated and summarized. Based on the Shapley additive analysis results, the physical quantities of the input features that make the main contribution to the output are identified.

10. A processor, characterized in that, The processor is used to run a program, wherein the program executes the physical feature construction method for predicting manufacturing parameters of a micro-hemispherical harmonic oscillator as described in any one of claims 1 to 9.

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