A physical prior bayesian calibration method for micro-hemispherical resonator torch position

Abstract

The present application relates to the technical field of micro-hemispherical resonator gyroscope design and manufacturing, and particularly relates to a physical prior Bayesian calibration method for the position of a micro-hemispherical resonator torch. The method comprises the following steps: constructing a physical deformation prior mean model and a Gaussian process residual compensation model based on physical prior Bayesian optimization; establishing an initial data set; model calibration and prediction, calibrating the parameters of the physical deformation prior mean model using the data set, and fitting and predicting the bias through the Gaussian process residual compensation model; finding the optimal coordinates, calculating the expected improvement acquisition function of each candidate coordinate point, and selecting the optimal torch coordinate for the next round; closed-loop iterative experiment, cyclically executing model calibration and prediction and finding the optimal coordinates until the height difference meets the process requirements or the preset number of iterations is reached. The present application aims to solve the technical problems of the prior art, i.e., not using physical laws to guide rapid convergence, and not effectively compensating for actual random process noise in the high-efficiency position process.

Description

Technical Field

[0001] This invention relates to the field of micro-hemispherical resonator gyroscope design and manufacturing technology, and in particular to a physical prior Bayesian calibration method for the position of the torch of a micro-hemispherical resonator. Background Technology

[0002] The geometric symmetry of the microhemispherical resonator, the core component of a microhemispherical resonator gyroscope, directly determines key indicators such as frequency fragmentation and zero-bias stability. In the high-temperature microglass blowing process using fused silica, the radial alignment accuracy between the thermal center of the high-temperature torch flame and the physical center of the graphite mold is crucial for ensuring the geometric uniformity of the resonator. If there is a positional deviation, it will lead to an asymmetrical temperature field distribution during the glass softening stage, introducing a first-order harmonic height error into the height profile of the formed resonator. This geometric defect disrupts the modal degeneracy of the resonator, causing severe frequency fragmentation and significantly degrading the long-term stability of the gyroscope. In actual manufacturing, the alignment and calibration of the torch and mold have long relied on manual trial and error based on experience, which is not only extremely inefficient but also faces problems such as high cost of fused silica wafers and easy oxidation and wear of the mold, making it difficult to meet the needs of mass production.

[0003] Existing research on improvements to the forming process of micro-hemispherical resonators mainly focuses on mold structure design and macroscopic process parameter optimization. For example, authorized invention CN118687596B discloses a method for forming a highly symmetric micro-hemispherical resonator structure, authorized invention CN117142749B discloses a mold structure for thermoforming micro-hemispherical resonators, and authorized invention CN120445270B discloses a method for fabricating a resonator for a micro-hemispherical resonant gyroscope. Furthermore, some existing technologies attempt to introduce standard data-driven algorithms (such as standard Bayesian optimization) to achieve automated process optimization. However, the above methods and existing algorithms have not effectively solved the problem of automated calibration of the alignment error between the torch and the mold, and face the following limitations: (1) Existing forming patents mostly rely on hardware structure improvements and lack quantitative inversion and automatic compensation mechanisms for torch position deviation; (2) Standard Bayesian optimization uses zero-mean Gaussian process priors, which lack physical constraints in the early stage of optimization, resulting in blind spatial exploration and requiring a large number of expensive physical samples to converge; (3) If the optimal position is derived by simply relying on deterministic physical deformation equations, although it can reflect the macro trend, it cannot be compatible with the inherent random baseline noise in the manufacturing environment and is very easy to get trapped in local optima. Therefore, there is an urgent need for an efficient automatic position calibration method that can both use physical laws to guide rapid convergence and effectively compensate for actual random process noise. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a physical prior Bayesian calibration method for the position of a micro-hemispherical resonator torch. This method aims to solve the technical problems of existing technologies that do not utilize physical laws to guide rapid convergence and do not effectively compensate for actual random process noise in efficient positioning.

[0005] To achieve the above objectives, in a first aspect, the present invention proposes a physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch, comprising the following steps:

[0006] S1. Construct a total prediction model based on physical prior Bayesian optimization, wherein the total prediction model includes a physical deformation prior mean model and a Gaussian process residual compensation model.

[0007] S2. Establish the initial dataset; conduct multiple initial blowing experiments, and record the torch coordinates and the corresponding measured height difference for each experiment;

[0008] S3, Model Calibration and Prediction: The parameters of the physical deformation prior mean model are calibrated using the initial dataset and the dataset in S5. The prediction bias is fitted by the Gaussian process residual compensation model, and the prediction mean and variance of each candidate coordinate point in the workspace are calculated.

[0009] S4. Find the optimal coordinates. Calculate the expected improved acquisition function of each candidate coordinate point based on the predicted mean and variance. Select the coordinates of the point with the largest function value as the best torch coordinates for the next round.

[0010] S5. Closed-loop iterative experiment: Move the blowtorch to the optimal blowtorch coordinates for a new round of blowing, measure the new height difference and import it into the dataset, and repeat S3 to S4 until the height difference meets the process requirements or reaches the preset number of iterations.

[0011] As a preferred method, the overall prediction model based on physical prior Bayesian optimization includes the following steps:

[0012] S101, Define the radial alignment error distance; let the theoretical center coordinates of the mold be ( , The actual planar coordinates of the center of the blowtorch flame are ( ). , The radial alignment error distance is defined as...

[0013] ;in It is a two-dimensional position vector containing the actual planar coordinates of the blowtorch;

[0014] S102. Establish a priori mean model of physical deformation; introduce parameters representing the inherent noise of manufacturing equipment. Establish a prior mean model of physical deformation between height difference and radial alignment error distance. :

[0015] ;in, and Let these be the linear deformation coefficient and the cubic deformation coefficient, respectively. The set of parameters to be optimized for the physical deformation prior mean model is defined as follows: ;

[0016] S103. Establish a Gaussian process residual compensation model.

[0017] As a preferred method, the method for establishing a Gaussian process residual compensation model includes the following steps:

[0018] Calculate historical observation datasets The actual height difference observed in each instance Compared with the predicted value of the physical prior mean model Local asymmetric residuals between , Indicates the total number of observations The first in Second observation;

[0019] Using the selected Matérn 5 / 2 kernel function Calculate any two known observation points and The spatial correlation between them is expressed as ;in, The variance of the signal; Represents two coordinate points and The Euclidean distance between them; The feature length scale; Indicates the total number of observations The first in Second observation;

[0020] based on Build covariance matrix : ; where the matrix Let be a noise-free covariance matrix, and its i-th Line number The elements of the column are ; For size The identity matrix; This represents the variance of the observation noise.

[0021] As a preferred method, establishing a Gaussian process residual compensation model also includes optimizing the hyperparameter set by maximizing the marginal likelihood function. ; Apply gradient descent to the function Find the maximum value; where, Given an input matrix containing all known coordinates, Covariance matrix The determinant, For data fitting terms, This is a penalty term for model complexity. This is the normalization constant.

[0022] As a preferred method, the method for establishing the Gaussian process residual compensation model also includes, after the hyperparameter optimization is completed, calculating new candidate coordinate points for any unknown candidate torch coordinate point in the workspace that has not yet undergone blowing experiments. With all The column vector of cross-covariance among historical observation points for

[0023] Define the weight vector The calculation formula is Output residual prediction mean and prediction variance ;in , .

[0024] As a preferred method, the initial dataset is to set three discrete coordinates with reasonable spatial distance as the torch pose for the initial cold start experiment, and perform three independent high-temperature formings while maintaining the same process parameters. After each forming and cooling, the height difference between the highest and lowest points of the harmonic oscillator profile is measured. The planar coordinates and height differences obtained from these three tests are then integrated to construct the initial historical observation dataset.

[0025] Preferably, the method for calibrating the parameters of the prior mean model of physical deformation in model calibration and prediction includes the following steps:

[0026] S301. During the first round of active iteration based on the initial dataset in step S2, in order to solve the underdetermined inverse problem caused by solving the physical parameters in the parameter set, the inherent noise parameters in the parameter set are forcibly locked to zero, and the unobserved theoretical center coordinate space is anchored to the geometric centroid of the initial observation point coordinates and regularized. During the second round of active iteration, the locking of the inherent noise parameters is released, so that they can participate in the joint optimization of the overall parameters.

[0027] S302, Establish a system to minimize the actual height difference Compared with the predicted value of the physical prior mean model The sum of squared errors between the two is the nonlinear cost function of the objective. The specific expansion is as follows: ;

[0028] S303 is the parameter set. Set upper and lower bound constraints that conform to the actual manufacturing process and the physical limits of machine tools. Using a nonlinear optimization solver with boundary constraints, an iterative search is performed within the aforementioned physical constraint space to find a solution that satisfies the cost function. Optimal parameter vector for obtaining the global minimum , .

[0029] As a preferred method, the method of compensating for model fitting and prediction bias by Gaussian process residuals in model calibration and prediction includes the following steps:

[0030] S304, Utilize the updated parameter set Recalculate the local asymmetric residuals at all observation points in the historical dataset. Based on the Gaussian process residual compensation model, regression prediction is performed on any candidate coordinate point within the blowtorch workspace that has not yet undergone a blowing experiment, and the mean value of the residual prediction is obtained. ;

[0031] S305. Calculate the overall forecast mean and forecast variance. The overall forecast mean is... Candidate coordinate points The original prediction variance at is ;

[0032] S306. Implement a positive lower bound truncation mechanism for the prediction variance; introduce a pre-set minimal positive real number as the lower bound tolerance threshold for variance safety at the algorithm's underlying layer. By applying a hard lower bound comparison and truncation constraint to the original prediction variance, candidate coordinate points are obtained. The final valid effective prediction variance adopted by the algorithm is The predicted standard deviation was obtained as follows: .

[0033] As a preferred method, the method for finding the optimal coordinates includes the following steps:

[0034] S401. The high-precision XY plane working space equipped with the graphite mold is uniformly discretized into a fixed two-dimensional search grid.

[0035] S402. Calculate the desired improved acquisition function for each candidate grid coordinate point in the search grid;

[0036] S403, Define a preset physical repulsion radius. Traverse the search grid. If there exists a candidate grid point whose spatial Euclidean distance to any known observation point in the historical observation dataset is less than the repulsion radius, then... If so, then the expected improved acquisition function value is forced to be negative infinity;

[0037] S404. Select the grid point coordinates that enable the desired improved acquisition function to achieve the global maximum value as the optimal blowtorch coordinates for the next closed-loop blowing experiment.

[0038] As a preferred method, the method for calculating the desired improved acquisition function for each candidate grid coordinate point in the search grid includes the following steps:

[0039] Define the expected error improvement margin as ;in This represents the smallest first-order harmonic height difference that has been actually measured and recorded in the current historical observation dataset. This indicates an exploration of jitter control parameters;

[0040] The standardization improvement margin is calculated as follows: ;in coordinate point Forecast standard deviation;

[0041] The expected improved acquisition function is calculated as follows: ;in The standard normal cumulative distribution function is... Let be the probability density function.

[0042] 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 on which the storage medium is located executes the physical prior Bayesian calibration method for the position of the micro-hemispherical resonator torch of the first aspect.

[0043] To achieve the above objectives, in a third aspect, the present invention proposes a processor for running a program, wherein the program, when running, executes the physical prior Bayesian calibration method for the position of the micro-hemispherical harmonic oscillator torch of the first aspect.

[0044] Compared with existing technologies, the physical prior Bayesian calibration method for the nozzle position of a micro-hemispherical resonator provided by this invention has the following advantages: 1. Breaking the bottleneck of blind search and significantly reducing the cost of physical sampling. This invention explicitly embeds the thermomechanical deformation mechanism model as a Gaussian process prior, and uses the natural deterministic gradient direction of the physical equations to guide the algorithm convergence. Only a very small amount of initial cold start and a few active iterations are needed to accurately lock the optimal global alignment coordinates, greatly saving debugging time and expensive fused silica consumables. 2. Possessing strong noise resistance and robustness, effectively overcoming the local extremum trap of pure physical models. Effectively overcoming the problem of not being able to characterize complex background noise such as asymmetric flame pulsation in blow molding. 3. Greatly improving the modal degeneracy performance of the resonator from the source of physical structure. This invention provides an excellent processing strategy for achieving highly consistent forming of micro-hemispherical resonators, significantly reducing the process debugging cycle, and has clear engineering application value and promotion potential in the field of precision instrument and MEMS device manufacturing. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating a physical prior Bayesian calibration method for the position of a micro-hemispherical resonator torch provided by the present invention.

[0046] Figure 2 A comparative analysis of the convergence trajectories of different optimization algorithms for first-order height error. Detailed Implementation

[0047] 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.

[0048] 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.

[0049] This invention proposes a physical prior Bayesian calibration method for the position of the blowtorch in a micro-hemispherical resonator. This method uses the deterministic physical deformation equation as the mean prior of a Gaussian process, constructing a Bayesian optimization framework that fuses physical information. While utilizing physical laws to guide the global convergence direction, it effectively fits and compensates for actual random process noise through a Gaussian process. This method can achieve high-precision inversion and position compensation of the alignment deviation between the blowtorch thermal center and the mold physical center under minimal physical sampling conditions, thereby significantly suppressing the first harmonic error in the height direction of the resonator. It provides an efficient and low-cost automated calibration method for improving the height symmetry of micro-hemispherical resonator forming. The physical prior Bayesian calibration method for the position of the blowtorch in a micro-hemispherical resonator is described in detail below.

[0050] See appendix Figure 1 A physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch includes the following steps:

[0051] S1. Construct a total prediction model based on physical prior Bayesian optimization. The total prediction model includes a physical deformation prior mean model with baseline noise parameters (i.e., inherent noise parameters) and a Gaussian process residual compensation model.

[0052] Furthermore, the specific plan for step S1 is as follows:

[0053] S101, Define the radial alignment error distance. Let the theoretical center coordinates of the mold be ( , The actual planar coordinates of the center of the blowtorch flame are ( ). , The radial alignment error distance is defined as: .in It is a two-dimensional position vector containing the actual planar coordinates of the blowtorch, i.e. , This represents the transpose of a matrix.

[0054] S102. Establish a priori mean model of physical deformation. Introduce parameters representing the inherent noise of the manufacturing equipment. Establish a prior mean model of physical deformation between height difference and radial alignment error distance. : .in, and Let these be the linear deformation coefficient and the cubic deformation coefficient, respectively. The set of parameters to be optimized for the physical deformation prior mean model is defined as follows: .

[0055] S103. Establish a Gaussian process residual compensation model.

[0056] Calculate historical observation datasets The actual height difference observed in each instance Compared with the predicted value of the physical prior mean model Local asymmetric residuals between , Indicates the total number of observations The first in This observation. Using position coordinate vectors. For input, residual Output the target.

[0057] Using position coordinate vector For input, residual For the target output, use the selected Matérn 5 / 2 kernel function. Calculate any two known observation points and Spatial correlation between them Indicates the total number of observations The first in Second observation: .in, The signal variance represents the global maximum amplitude of local manufacturing residual fluctuations caused by unknown process disturbances; Represents two coordinate points and The Euclidean distance between them; The characteristic length scale represents the spatial extent of the correlation influence of local residuals.

[0058] Build covariance matrix : Among them, matrix Let be a noise-free covariance matrix, and its i-th Line number The elements of the column are ; For size The identity matrix; This represents the observation noise variance, which includes the inherent system detection noise floor of the measuring instrument itself, as well as the completely random white noise in the actual manufacturing environment.

[0059] Optimize the set of hyperparameters by maximizing the marginal likelihood function. Find the maximum value of the following function (log marginal likelihood function) using gradient descent: .in, Given an input matrix containing all known coordinates, Covariance matrix The determinant of the objective function. The first term on the right-hand side of the objective function equation is the data fitting term, which physically measures the model's ability to capture the physical laws of existing residuals; the second term is the model complexity penalty term, which physically prevents the model from overfitting local extreme measurement noise; the third term is the normalization constant, which does not affect the selection of hyperparameters during optimization.

[0060] After hyperparameter optimization, for any unknown candidate blowtorch coordinate point in the workspace that has not yet undergone blowing experiments, the model can calculate a set of distance weights based on its distance correlation with all historically known observation points. Calculate new candidate coordinate points. With all The column vector of cross-covariance among historical observation points : .

[0061] Define weight vector The calculation formula is: .

[0062] This reflects the "empirical contribution" of each known historical processing point to the prediction result of the current unknown candidate point. In terms of spatial distance... The closer the historical point and the stronger its physical correlation, the greater the influence weight the model assigns to its residuals. The Gaussian process model calculates and outputs information about the candidate coordinate points. Two key data points: the first key data point is the mean of the residual predictions. This represents the best expected estimate of the height error:

[0063] .

[0064] The second key data point is the prediction variance. The uncertainty of the model in predicting the above mean is characterized as follows: .

[0065] S2. Establish an initial dataset, conduct multiple initial blowing experiments, and record the torch coordinates and the corresponding measured height difference for each experiment. Ideally, three initial blowing experiments should be conducted.

[0066] Furthermore, the specific plan for step S2 is as follows:

[0067] Within the operating workspace, three discrete coordinates with reasonable spatial distances are set as the torch pose for the initial cold start experiment using initial visual or optical aids. The same blowing time and temperature and other process parameters are maintained for three independent high-temperature forming processes. After each forming and cooling, the height difference between the highest and lowest points of the harmonic oscillator profile is measured. The "planar coordinate-height difference" data obtained from these three processes are integrated to construct an initial historical observation dataset, providing basic physical samples for subsequent Bayesian optimization.

[0068] S3. Model calibration and prediction: The parameters of the physical model are calibrated using the datasets (initial dataset and datasets in S5), and the prediction bias is fitted by a Gaussian process model to calculate the prediction mean and variance of each candidate coordinate point in the workspace.

[0069] Furthermore, the specific plan for step S3 is as follows:

[0070] S301. Determine the optimization state and execute parameter constraints. In the first round of active iteration based solely on the initial cold-start experimental data from step S2, for the solution... The underdetermined inverse problem arising from the five physical parameters in the parameter set will affect the baseline noise parameters in the parameter set. Forced to lock to zero, and the unobserved theoretical center coordinates ( , The spatial anchor is regularized at the geometric centroid of the three initial observation points; during the second round of active iteration, the baseline noise parameters are removed. The locking mechanism allows it to participate in the joint optimization of overall parameters.

[0071] S302. Construct the prediction error cost function. Establish a function that minimizes the actual height difference. Compared with the predicted value of the physical prior mean model The sum of squared errors between the two is the nonlinear cost function of the objective. The specific expansion is as follows: .

[0072] S303, Perform nonlinear constraint solving for optimization. The parameter vector to be optimized is... Set upper and lower bound constraints that conform to the actual manufacturing process and the physical limits of machine tools. Using a nonlinear optimization solver with boundary constraints, an iterative search is performed within the defined physical constraint space to find a solution that satisfies the cost function. Optimal parameter vector for obtaining the global minimum : .

[0073] S304. Calculate the residual prediction distribution. Using the updated parameter set. Recalculate the local asymmetric residuals at all observation points in the historical dataset. Then, based on the Gaussian process residual compensation model in step S103, the coordinates of any candidate mesh point within the torch workspace that has not yet undergone a forming experiment are calculated. Perform regression prediction to obtain the mean of the predicted residuals. .

[0074] S305. Calculate the overall forecast mean and forecast variance.

[0075] Overall forecast mean : .

[0076] Candidate grid coordinates Original prediction variance at : .

[0077] S306. Implement a positive lower bound truncation mechanism for the prediction variance. A pre-defined, minimal positive real number is introduced at the algorithm's underlying level as a tolerance threshold for the variance's safe lower bound. By applying a hard lower bound comparison and truncation constraint to the original prediction variance, the coordinate points are obtained. The final valid and effective prediction variance adopted by the algorithm : .

[0078] Final coordinates Predicted standard deviation : .

[0079] This truncation mechanism mathematically guarantees that the standard deviation of any point within the workspace is always greater than zero.

[0080] S4. Find the optimal coordinates. Calculate the expected improved acquisition function for each candidate point based on the predicted mean and variance, and select the point with the largest function value as the best torch coordinates for the next round.

[0081] Furthermore, the specific plan for step S4 is as follows:

[0082] S401. Discretization of the working space. The high-precision XY plane working space of the graphite mold is uniformly discretized into a fixed two-dimensional search grid.

[0083] S402. Calculate the desired improved acquisition function for each candidate grid coordinate point in the search grid. Define the expected error improvement margin. : .in, This represents the smallest first-order harmonic height difference that has been actually measured and recorded in the current historical observation dataset; This indicates an exploration of controllable jitter parameters.

[0084] Standardization improvement margin This reflects the ratio of the potential improvement in the expected height error of the candidate point to its own prediction uncertainty risk: .in, coordinate point Forecast standard deviation.

[0085] Expected improvement of the acquisition function : .in, It is the standard normal cumulative distribution function; Let be the probability density function.

[0086] S403. Set up a physical sampling repulsion mechanism. Define a preset physical repulsion radius. Traverse the search grid; if a candidate grid point exists... Compared with historical observation datasets The spatial Euclidean distance between any known observation point in the region is less than the repulsion radius. Then, the desired improved acquisition function value is forced to be negative infinity: .

[0087] S404. Determine and output the optimal torch alignment coordinates for the next round. Select the acquisition function that is expected to improve. The grid point coordinates that yield the global maximum value will be used as the optimal torch target coordinates for the next closed-loop blowing experiment. : .

[0088] S5. Closed-loop iterative experiment: Move the blowtorch to the optimal coordinates for a new round of blowing, measure the new height difference and import it into the dataset, and repeat S3 to S4 until the height difference meets the process requirements or reaches the preset number of iterations.

[0089] Furthermore, the specific plan for step S5 is as follows:

[0090] The high-precision XY two-dimensional displacement stage (which is an existing product available for purchase on the market) is used to precisely move the mold to the physical coordinate point. Under the condition of keeping the core forming process parameters such as heating time and temperature unchanged, a brand-new micro-glass high-temperature blow forming experiment is performed to accurately measure and extract the newly generated first-order harmonic height difference. If the height difference has dropped to the preset process tolerance threshold or the overall closed-loop optimization cycle has reached the preset maximum number of exploration iterations, the system automatically terminates the automatic calibration process and solidifies the currently determined optimal processing alignment pose; otherwise, the latest measured "planar coordinates-height difference" real physical observation data of the current round is imported and expanded into the historical observation dataset. Then the system directly returns to step S3 to start a new round of physical parameter adaptive inversion correction and Gaussian process residual compensation update until the height difference has dropped to the preset process tolerance threshold or the overall closed-loop optimization cycle has reached the preset maximum number of exploration iterations.

[0091] 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... Figure 1 A physical prior Bayesian calibration method for the position of the blowtorch of a micro-hemispherical harmonic oscillator.

[0092] Furthermore, embodiments of this application also provide a processor for running a program, wherein the program executes the above-described... Figure 1 A physical prior Bayesian calibration method for the position of the blowtorch of a micro-hemispherical harmonic oscillator.

[0093] To verify the effectiveness and advancement of the present invention, an alignment and calibration of a high-temperature blowing device for a micro-hemispherical resonator was performed according to the method provided in the present invention.

[0094] The planar relative displacement between the blowtorch and the graphite mold is performed by a high-precision XY two-dimensional displacement stage with a step resolution of 0.001 mm. The boundary of the safe search operation space for the blowtorch on the worktable is set as follows: [297.0, 298.0] and [31.5, 33.0], for biased physical deformation prior mean models Apply empirically reasonable domain constraints. Set an upper limit for the allowable baseline noise bias. 0.01 mm; Acquisition function explores control jitter parameters. To prevent the algorithm from continuously blowing materials at the same physical location, the physical repulsion radius is set to 0.015 mm.

[0095] Three independent blowing operations were performed under identical negative pressure and air supply parameters. The initial planar coordinates set for the three cold starts were [297.499, 31.701], [297.398, 31.701], and [297.499, 31.803] (mm), respectively. After the resonator to be formed cooled, its relative morphology in the height profile direction was scanned using a white light interferometer, and the first harmonic height difference was extracted. The height differences measured three times were 0.8294 mm, 0.7813 mm, and 0.7252 mm, respectively. This data constitutes the initial historical observation dataset. The first round will The value is locked at 0. Subsequently, a nonlinear programming solver is used to perform constrained optimization, and the grid expectation is calculated by combining residual compensation from a Gaussian process. Improve the maximum point and perform a fourth blow based on that point. After the fourth sample point test is completed and added to the dataset, remove the baseline noise bias. The zero-lock constraint allows this parameter to participate in joint optimization.

[0096] The total number of active iterations is set to 4. Figure 2 This paper presents the convergence trajectories of standard Bayesian optimization, pure physical models, and the Physical Prior Bayesian Optimization (PIBO) framework of this invention for the first-order height error. Throughout the convergence process, if only a pure physical model is used for fitting, the algorithm fails to effectively decouple the complex local processing perturbations, and gets stuck in the local lower bound blind zone of 0.0323 mm in the fourth active iteration. Furthermore, the standard Bayesian optimization without physical prior Bayesian optimization, even after as many as seven exploratory experiments, still shows an error high at 0.5132 mm. The framework of this invention, however, exhibits superior robustness. In the subsequent fourth round of active iteration (i.e., the seventh overall processing experiment), the measured first-order height error of the shaped resonator is 0.0130 mm, demonstrating the superiority of the proposed method.

[0097] Compared with existing technologies, the beneficial effects of this invention are as follows: 1. Breaking through the bottleneck of blind search and significantly reducing the cost of physical sampling. This invention explicitly embeds the thermomechanical deformation mechanism model as a Gaussian process prior, utilizing the inherent deterministic gradient direction of the physical equations to guide algorithm convergence. Only a minimal initial cold start and a few active iterations are needed to accurately lock the optimal global alignment coordinates, greatly saving debugging time and expensive fused silica consumables. 2. Possessing strong noise resistance and robustness, effectively overcoming the local extremum trap of pure physical models. It effectively overcomes the problem of being unable to characterize complex background noise such as asymmetric flame pulsation in blow molding. 3. Significantly improving the modal degeneracy performance of the resonator from the source of physical structure. This invention provides an excellent processing strategy for achieving highly consistent forming of micro-hemispherical resonators, significantly reducing the process debugging cycle, and has clear engineering application value and promotion potential in the field of precision instrument and MEMS device manufacturing.

[0098] 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.

[0099] 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.

[0100] 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.

[0101] 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.

[0102] 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.

[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] 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.

[0105] 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.

[0106] 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.

[0107] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0108] 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.

[0109] 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.

[0110] 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.

[0111] 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.

[0112] 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 physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch, characterized in that, Includes the following steps: S1. Construct a total prediction model based on physical prior Bayesian optimization, wherein the total prediction model includes a physical deformation prior mean model and a Gaussian process residual compensation model. S2. Establish the initial dataset; Multiple initial blowing experiments were conducted, and the torch coordinates and corresponding measured height differences were recorded for each experiment. S3. Model Calibration and Prediction: Using the initial dataset and the dataset in S5, the parameters of the physical deformation prior mean model are calibrated, and the prediction bias is fitted using a Gaussian process residual compensation model. The predicted mean and variance of each candidate coordinate point in the workspace are calculated. This includes the following steps: S301. During the first round of active iteration based on the initial dataset in step S2, in order to solve the underdetermined inverse problem caused by solving the physical parameters in the parameter set, the inherent noise parameters in the parameter set are forcibly locked to zero, and the unobserved theoretical center coordinate space is anchored to the geometric centroid of the initial observation point coordinates and regularized. During the second round of active iteration, the locking of the inherent noise parameters is released, so that they can participate in the joint optimization of the overall parameters. S302, Establish a system to minimize the actual height difference Compared with the predicted value of the physical prior mean model The sum of squared errors between the two is the nonlinear cost function of the objective. The specific expansion is as follows: ; S303 is the parameter set. Set upper and lower bound constraints that conform to the actual manufacturing process and the physical limits of machine tools. By utilizing a nonlinear optimization solver with boundary constraints, an iterative search is performed within a defined constraint space to find a solution that satisfies the cost function. Optimal parameter vector for obtaining the global minimum , ; S304, Utilize the updated parameter set Recalculate the local asymmetric residuals at all observation points in the historical dataset. Based on the Gaussian process residual compensation model, for any candidate coordinate point in the blowtorch workspace that has not yet undergone a blowing experiment... Perform regression prediction to obtain the mean of the predicted residuals. ; S305. Calculate the overall forecast mean and forecast variance. The overall forecast mean is... Candidate coordinate points The original prediction variance at is ; S306. Implement a positive lower bound truncation mechanism for the prediction variance; introduce a pre-set minimal positive real number as the lower bound tolerance threshold for variance safety at the algorithm's underlying layer. By applying a hard lower bound comparison and truncation constraint to the original prediction variance, candidate coordinate points are obtained. The final valid effective prediction variance adopted by the algorithm is The predicted standard deviation was obtained as follows: ; S4. Find the optimal coordinates. Calculate the expected improved acquisition function of each candidate coordinate point based on the predicted mean and variance. Select the coordinates of the point with the largest function value as the best torch coordinates for the next round. S5. Closed-loop iterative experiment: Move the blowtorch to the optimal blowtorch coordinates for a new round of blowing, measure the new height difference and import it into the dataset, and repeat S3 to S4 until the height difference meets the process requirements or reaches the preset number of iterations.

2. The physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch as described in claim 1, characterized in that, The method for constructing a total prediction model based on physical prior Bayesian optimization includes the following steps: S101, Define the radial alignment error distance; let the theoretical center coordinates of the mold be ( , The actual planar coordinates of the center of the blowtorch flame are (x, y). The radial alignment error distance is defined as... ;in It is a two-dimensional position vector containing the actual planar coordinates of the blowtorch; S102. Establish a priori mean model of physical deformation; introduce parameters representing the inherent noise of manufacturing equipment. Establish a prior mean model of physical deformation between height difference and radial alignment error distance. : ;in, and Let these be the linear deformation coefficient and the cubic deformation coefficient, respectively. The set of parameters to be optimized for the physical deformation prior mean model is defined as follows: ; S103. Establish a Gaussian process residual compensation model.

3. The physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch as described in claim 2, characterized in that, The method for establishing a Gaussian process residual compensation model includes the following steps: Calculate historical observation datasets The actual height difference observed in each instance Compared with the predicted value of the physical prior mean model Local asymmetric residuals between , Indicates the total number of observations The first in Second observation; Using the selected Matérn 5 / 2 kernel function Calculate any two known observation points and The spatial correlation between them is expressed as ;in, The variance of the signal; Represents two coordinate points and The Euclidean distance between them; The feature length scale; Indicates the total number of observations The first in Second observation; based on Build covariance matrix : ; where the matrix Let be a noise-free covariance matrix, and its i-th Line number The elements of the column are ; For size The identity matrix; This represents the variance of the observation noise.

4. The physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch as described in claim 3, characterized in that, Methods for establishing Gaussian process residual compensation models also include optimizing the hyperparameter set by maximizing the marginal likelihood function. ; Apply gradient descent to the function Find the maximum value; where, Given an input matrix containing all known coordinates, Covariance matrix The determinant, For data fitting terms, This is a penalty term for model complexity. This is the normalization constant.

5. The physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch as described in claim 4, characterized in that, The method for establishing a Gaussian process residual compensation model also includes, after the hyperparameter optimization is completed, calculating new candidate coordinate points for any unknown candidate torch coordinate point in the workspace that has not yet undergone blowing experiments. With all The column vector of cross-covariance among historical observation points for Define the weight vector The calculation formula is Output residual prediction mean and prediction variance ;in , .

6. The physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch as described in claim 1, characterized in that, The method for establishing the initial dataset is to set three discrete coordinates with reasonable spatial distance as the torch pose for the initial cold start experiment, and to perform three independent high-temperature formings while maintaining the same process parameters. After each forming and cooling, the height difference between the highest and lowest points of the harmonic oscillator profile is measured. The planar coordinates and height differences obtained from these three tests are then integrated to construct the initial historical observation dataset.

7. The physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch as described in claim 1, characterized in that, The method for finding the optimal coordinates includes the following steps: S401. The high-precision XY plane working space equipped with the graphite mold is uniformly discretized into a fixed two-dimensional search grid. S402. Calculate the desired improved acquisition function for each candidate grid coordinate point in the search grid; S403, Define a preset physical repulsion radius. Traverse the search grid. If there exists a candidate grid point whose spatial Euclidean distance to any known observation point in the historical observation dataset is less than the repulsion radius, then... If so, then the expected improved acquisition function value is forced to be negative infinity; S404. Select the grid point coordinates that enable the desired improved acquisition function to achieve the global maximum value as the optimal blowtorch coordinates for the next closed-loop blowing experiment.

8. The physical prior Bayesian calibration method for the position of a micro-hemispherical harmonic oscillator torch as described in claim 7, characterized in that, The method for calculating the desired improved acquisition function for each candidate grid coordinate point in the search grid includes the following steps: Define the expected error improvement margin as ;in This represents the smallest first-order harmonic height difference that has been actually measured and recorded in the current historical observation dataset. This indicates an exploration of jitter control parameters; The standardization improvement margin is calculated as follows: ;in for The predicted standard deviation of the coordinate point; The expected improved acquisition function is calculated as follows: ;in The standard normal cumulative distribution function is... Let be the probability density function.

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