Method and system for realizing sensitivity analysis of capacitive accelerometer based on deep learning

Abstract

The invention relates to the technical field of deep learning, and discloses a method and system for realizing sensitivity analysis of a capacitive accelerometer based on deep learning, and the method comprises the steps: calculating the capacitance sensitivity of the capacitive accelerometer; calculating an equivalent stiffness coefficient corresponding to a U-shaped beam in the capacitive accelerometer and the mass of an inertial component so as to calculate a capacitance inherent frequency corresponding to the capacitive accelerometer; outputting a high-dimensional representation feature corresponding to the capacitive accelerometer; calculating the prediction sensitivity corresponding to the capacitive accelerometer by using a sensitivity regression layer in the optimization analysis network; and calculating a difference degree between the prediction sensitivity and the capacitance sensitivity, and when the difference degree is greater than a preset difference degree, performing sensitivity analysis on the capacitive accelerometer to obtain an analysis result. The accuracy of sensitivity analysis of the capacitive accelerometer can be improved.

Description

Technical Field

[0001] This invention relates to a method and system for sensitivity analysis of capacitive accelerometers based on deep learning, and belongs to the field of deep learning technology. Background Technology

[0002] Capacitive accelerometers are precision sensing devices widely used in consumer electronics, industrial measurement and control, and other fields. Their capacitance sensitivity and natural frequency are the core indicators for measuring measurement accuracy, which directly affect the signal response quality of the device under vibration, shock and other scenarios. Therefore, accurate analysis of these two factors is a key aspect of accelerometer design and optimization.

[0003] Existing sensitivity analyses of capacitive accelerometers often rely on empirical formulas or single-parameter modeling, such as deriving capacitive sensitivity and calculating natural frequency solely based on comb tooth dimensions. However, this approach cannot handle the coupling relationship between structural variables and performance indicators. Furthermore, factors such as temperature fluctuations and assembly errors in actual testing can cause deviations between theoretical calculations and capacitive sensitivity. These issues make existing analysis methods prone to misjudgments of parameter correlations and inaccurate attribution of deviations, thereby reducing the accuracy of accelerometer sensitivity analysis. Summary of the Invention

[0004] This invention provides a method and system for sensitivity analysis of capacitive accelerometers based on deep learning, with the main purpose of improving the accuracy of sensitivity analysis of capacitive accelerometers.

[0005] To achieve the above objectives, the present invention provides a method for sensitivity analysis of capacitive accelerometers based on deep learning, comprising: Collect structural variables and performance data of the capacitive accelerometer to calculate the capacitive sensitivity of the capacitive accelerometer; Calculate the equivalent stiffness coefficient and inertial component mass of the U-shaped beam in the capacitive accelerometer to calculate the natural frequency of the capacitor corresponding to the capacitive accelerometer. The capacitive sensitivity and the natural frequency are input into a pre-constructed optimization analysis network, and the dual-path feature extraction layer in the optimization analysis network is used to output the high-dimensional representation features corresponding to the capacitive accelerometer. Based on the high-dimensional representation features, the predicted sensitivity of the capacitive accelerometer is calculated using the sensitivity regression layer in the optimization analysis network. The difference between the predicted sensitivity and the capacitive sensitivity is calculated. When the difference is greater than a preset difference, sensitivity analysis is performed on the capacitive accelerometer to obtain the analysis results.

[0006] Optionally, the step of collecting structural variables and performance data of the capacitive accelerometer to calculate the capacitive sensitivity of the capacitive accelerometer includes: Based on the performance data, calculate the mechanical sensitivity of the capacitive accelerometer. Extract the sensitive correlation variables of the capacitive accelerometer from the structural variables; Combining the aforementioned sensitive correlation variable and the mechanical sensitivity, the capacitive sensitivity of the capacitive accelerometer is calculated using the following formula: ; Where A represents the capacitance sensitivity of the capacitive accelerometer, and N represents the number of one-sided capacitance pairs in the sensitivity correlation variable. Represents the dielectric constant. t represents the comb tooth alignment length in the sensitive correlation variables, and t represents the device thickness in the sensitive correlation variables. Indicates mechanical sensitivity. and These represent the spacing between different comb tooth structures.

[0007] Optionally, extracting the sensitive correlation variable of the capacitive accelerometer from the structural variables includes: The structural variables are sorted by importance to obtain sorted structural variables; Analyze the mapping correlation between each variable in the ranking structure and the sensitivity; Based on the mapping correlation degree, initial correlation variables are selected from the sorting structure variables; The initial correlation variables are subjected to hierarchical filtering to obtain the sensitive correlation variables of the capacitive accelerometer.

[0008] Optionally, calculating the equivalent stiffness coefficient and inertial component mass of the U-beam in the capacitive accelerometer includes: Measure the material properties and geometric parameters of the U-shaped beam in the capacitive accelerometer; Based on the aforementioned material properties, determine the elastic modulus of the material corresponding to the U-shaped beam; Based on the geometric parameters and the material elastic modulus, the equivalent stiffness coefficient of the U-shaped beam in the capacitive accelerometer is calculated using the following formula: ; Where B represents the equivalent stiffness coefficient corresponding to the U-shaped beam in the capacitive accelerometer, and E represents the material's elastic modulus. This refers to the thickness of the U-shaped beam in the geometric parameters. This refers to the width of the U-shaped beam in the geometric parameters. This indicates the effective length of the U-shaped beam in the geometric parameters; Identify the inertial components in the capacitive accelerometer and calculate the mass of the inertial components corresponding to the inertial components.

[0009] Optionally, calculating the inertial component mass corresponding to the inertial component includes: The inertial component is modeled with high precision to obtain a digital model of the component; The key dimensional parameters of the mass frame of the inertial component are extracted from the component's digital model. Measure the material density, width, length, and additional width of the mass frame; Combining the material density, the mass frame length, the mass frame width, the additional width of the mass frame, and the key dimensional parameters, the mass of the inertial assembly corresponding to the inertial assembly is calculated using the following formula: ; Where m represents the mass of the inertial component. Indicates the density of the material. This represents the structural thickness in the critical dimension parameter, and M represents the number of movable comb tooth pairs in the critical dimension parameter. This indicates the width of a single comb tooth, a key dimensional parameter. This indicates the length of a single comb tooth in the key dimension parameters, where h represents the width of the mass frame. Indicates the length of the mass frame. This indicates the additional width of the quality frame.

[0010] Optionally, the step of using the dual-path feature extraction layer in the optimized analysis network to output the high-dimensional representation features corresponding to the capacitive accelerometer includes: The capacitance sensitivity is input into the first feature extraction path of the dual-path feature extraction layer for feature transformation to obtain the sensitivity depth feature. The inherent frequency is input into the second feature extraction path of the dual-path feature extraction layer for frequency domain feature extraction to obtain frequency depth features; The sensitivity depth feature and the frequency depth feature are concatenated using the feature fusion layer in the dual-path feature extraction layer to obtain a preliminary fused feature; The dimensionality of the preliminary fused features is compressed using the dimensionality reduction processing layer in the dual-path feature extraction layer to obtain the high-dimensional representation features corresponding to the capacitive accelerometer.

[0011] Optionally, the step of using the feature fusion layer in the dual-path feature extraction layer to concatenate the sensitivity depth feature and the frequency depth feature to obtain preliminary fused features includes: Calculate the dimensionality importance factor of each feature dimension in the sensitivity depth feature and the frequency depth feature respectively; Construct a sensitivity-frequency dual-dimensional feature weighting matrix based on the aforementioned dimensional importance factors; The sensitivity depth feature and the frequency depth feature are adaptively weighted and fused using the feature weighting matrix to obtain the weighted fused feature. The weighted fusion features are subjected to cross-channel feature enhancement processing to obtain cross-channel enhanced features; The cross-channel enhancement features are subjected to redundancy filtering to obtain the preliminary fusion features.

[0012] Optionally, based on the high-dimensional representation features, the predicted sensitivity of the capacitive accelerometer is calculated using the sensitivity regression layer in the optimized analysis network, including: The high-dimensional representation features are standardized by using the feature preprocessing layer in the sensitivity regression layer to obtain standard high-dimensional features. The standard high-dimensional features are mapped and regressed using the multivariate regression layer in the sensitivity regression layer to obtain the sensitivity vector. The sensitivity coefficients corresponding to the sensitivity vector are calculated using the optimization calculation layer in the sensitivity regression layer. Based on the sensitivity coefficient, the predicted sensitivity of the capacitive accelerometer is obtained.

[0013] Optionally, calculating the sensitivity coefficient corresponding to the sensitivity vector using the optimization calculation layer in the sensitivity regression layer includes: The error component in the initial sensitivity vector is extracted using the residual analyzer in the optimization calculation layer. Calculate the statistical distribution of the error components; Based on the statistical distribution, the residual dispersion and feature contribution corresponding to the initial sensitivity vector are calculated using the statistical functions in the optimization calculation layer. By combining the residual dispersion and the feature contribution, the sensitivity confidence corresponding to the initial sensitivity vector is calculated; Based on the sensitivity confidence level, the sensitivity coefficient corresponding to the initial sensitivity vector is obtained.

[0014] To address the aforementioned problems, this invention also provides a deep learning-based sensitivity analysis system for capacitive accelerometers, the system comprising: The sensitivity calculation module is used to collect structural variables and performance data of the capacitive accelerometer in order to calculate the capacitive sensitivity of the capacitive accelerometer. The capacitor natural frequency calculation module is used to calculate the equivalent stiffness coefficient and inertial component mass of the U-shaped beam in the capacitor accelerometer, so as to calculate the capacitor natural frequency of the capacitor accelerometer. The feature extraction module is used to input the capacitance sensitivity and the natural frequency into a pre-constructed optimization analysis network, and use the dual-path feature extraction layer in the optimization analysis network to output the high-dimensional representation features corresponding to the capacitance accelerometer. The predicted sensitivity calculation module is used to calculate the predicted sensitivity of the capacitive accelerometer based on the high-dimensional representation features and using the sensitivity regression layer in the optimization analysis network. The sensitivity analysis module is used to calculate the difference between the predicted sensitivity and the capacitive sensitivity. When the difference is greater than a preset difference, sensitivity analysis is performed on the capacitive accelerometer to obtain the analysis results.

[0015] Compared to the problems described in the background art, this invention, by collecting structural variables and performance data of a capacitive accelerometer to calculate its capacitive sensitivity, can correlate the intrinsic mapping between structural parameters and sensitivity, providing a reliable quantitative basis for subsequent comprehensive analysis based on deep learning. Furthermore, by calculating the equivalent stiffness coefficient of the U-beam and the mass of the inertial components, this invention can establish a correlation between structural mechanical properties and vibration characteristics, providing mechanical parameter support for the accurate derivation of the capacitor's natural frequency. Further, by inputting the capacitive sensitivity and natural frequency into an optimization analysis network, this invention can establish an intrinsic connection between electrical and mechanical properties, and then extract comprehensive features affecting performance through deep learning. Furthermore, by using the sensitivity regression layer in the optimization analysis network based on the high-dimensional representation features, this invention can calculate the predicted sensitivity of the capacitive accelerometer, thus predicting its sensitivity characteristics. Finally, by calculating the difference between the predicted sensitivity and the actual capacitive sensitivity, and when the difference exceeds an allowable range, this invention performs sensitivity analysis on the capacitive accelerometer to obtain the analysis results, thereby improving the accuracy of the sensitivity analysis. Therefore, the deep learning-based method and system for sensitivity analysis of capacitive accelerometers provided in this embodiment of the invention can improve the accuracy of sensitivity analysis of capacitive accelerometers. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a method for sensitivity analysis of a capacitive accelerometer based on deep learning, provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of a deep learning-based sensitivity analysis system for capacitive accelerometers, provided as an embodiment of the present invention.

[0017] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0018] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0019] This application provides a method for sensitivity analysis of capacitive accelerometers based on deep learning. The execution entity of this method includes, but is not limited to, at least one of the following electronic devices that can be configured to execute the method provided in this application: a server, a terminal, etc. In other words, the method for sensitivity analysis of capacitive accelerometers based on deep learning can be executed by software or hardware installed on a terminal device or a server device. The server includes, but is not limited to, a single server, a server cluster, a cloud server, or a cloud server cluster.

[0020] Reference Figure 1 The diagram shown is a flowchart illustrating a deep learning-based method for sensitivity analysis of a capacitive accelerometer, according to an embodiment of the present invention. In this embodiment, the deep learning-based method for sensitivity analysis of a capacitive accelerometer includes: S1. Collect the structural variables and performance data of the capacitive accelerometer to calculate the capacitive sensitivity of the capacitive accelerometer.

[0021] This invention calculates the capacitive sensitivity of a capacitive accelerometer by collecting its structural variables and performance data. It establishes an intrinsic mapping between structural parameters and sensitivity, providing a reliable quantitative basis for subsequent deep learning-based comprehensive analysis. The structural variables include, but are not limited to, electrode spacing, electrode area, and mass weight. The performance data includes, but is not limited to, output voltage, capacitance change, and temperature characteristics. Furthermore, the structural variables and performance data of the capacitive accelerometer can be collected using a high-precision optical measuring instrument and a dynamic performance testing platform.

[0022] As an embodiment of the present invention, the step of collecting structural variables and performance data of the capacitive accelerometer to calculate the capacitive sensitivity of the capacitive accelerometer includes: Based on the performance data, calculate the mechanical sensitivity of the capacitive accelerometer. Extract the sensitive correlation variables of the capacitive accelerometer from the structural variables; The capacitive sensitivity of the capacitive accelerometer is calculated by combining the aforementioned sensitive correlation variable and the mechanical sensitivity.

[0023] The performance data refers to measured data reflecting the dynamic response characteristics of the accelerometer, including the capacitor output signal and the displacement of the movable structure under different acceleration loads; the mechanical sensitivity is the displacement generated by the movable component under unit acceleration, which is the core performance parameter connecting mechanical motion and electrical signal; the structural variables are a set of design parameters describing the physical structure of the accelerometer; and the sensitivity correlation variables are structural parameters that directly participate in the capacitor sensitivity calculation formula, and their numerical accuracy directly affects the reliability of the calculation results.

[0024] Furthermore, based on the measured results of multiple sets of acceleration loads and corresponding movable structure displacements recorded in the performance data, the correlation between acceleration and displacement is fitted by linear regression, and then the mechanical sensitivity of the capacitive accelerometer is calculated.

[0025] Furthermore, as another embodiment of the present invention, the capacitive sensitivity of the capacitive accelerometer is calculated using the following formula, combining the sensitive correlation variable and the mechanical sensitivity: ; Where A represents the capacitance sensitivity of the capacitive accelerometer, and N represents the number of one-sided capacitance pairs in the sensitivity correlation variable. Represents the dielectric constant. t represents the comb tooth alignment length in the sensitive correlation variables, and t represents the device thickness in the sensitive correlation variables. Indicates mechanical sensitivity. and These represent the spacing between different comb tooth structures.

[0026] Wherein, the comb tooth facing length is the tooth length in a capacitive accelerometer where the moving comb tooth and the fixed comb tooth face each other and can generate effective capacitive coupling; the device thickness is the dimension of the core functional structure of the capacitive accelerometer (such as the comb tooth, mass frame, etc.) in the direction perpendicular to the comb tooth plane; the comb tooth structure spacing is the gap distance between comb teeth (or between tooth grooves) in a capacitive accelerometer, which is a key structural parameter that directly affects the initial value and change of capacitance.

[0027] Furthermore, as an optional embodiment of the present invention, the extraction of the sensitive correlation variable of the capacitive accelerometer from the structural variables includes: The structural variables are sorted by importance to obtain sorted structural variables; Analyze the mapping correlation between each variable in the ranking structure and the sensitivity; Based on the mapping correlation degree, initial correlation variables are selected from the sorting structure variables; The initial correlation variables are subjected to hierarchical filtering to obtain the sensitive correlation variables of the capacitive accelerometer.

[0028] Wherein, the sorted structure variable is an ordered set of parameters formed after the structure variables are sorted by importance quantification; the mapping correlation degree represents the nonlinear correlation strength and influence weight between each variable in the sorted structure variable and the sensitivity; the initial correlation variable is a subset of parameters with a correlation degree higher than a preset threshold selected from the sorted structure variables based on the mapping correlation degree.

[0029] Furthermore, the structural variables can be sorted by importance using a gradient boosting tree algorithm (such as XGBoost) to obtain sorted structural variables; the mapping correlation between each variable in the sorted structural variables and the sensitivity can be analyzed using the kernel partial least squares (KPLS) algorithm; based on the mapping correlation, initial correlated variables can be selected from the sorted structural variables by setting a dynamic threshold (such as taking the top 30% quantile value of the correlation); the initial correlated variables can be hierarchically filtered by combining the capacitance sensitivity calculation formula to perform parameter correlation verification, thereby obtaining the sensitivity correlated variables of the capacitive accelerometer.

[0030] S2. Calculate the equivalent stiffness coefficient and inertial component mass of the U-shaped beam in the capacitive accelerometer to calculate the natural frequency of the capacitor corresponding to the capacitive accelerometer.

[0031] This invention establishes the correlation between structural mechanical properties and vibration characteristics by calculating the equivalent stiffness coefficient and inertial component mass of a U-shaped beam, providing mechanical parameter support for the accurate derivation of the natural frequency of the capacitor. The equivalent stiffness coefficient reflects the U-shaped beam's ability to resist deformation, and the inertial component mass affects the dynamic response characteristics of the accelerometer.

[0032] As an embodiment of the present invention, the calculation of the equivalent stiffness coefficient and inertial component mass corresponding to the U-shaped beam in the capacitive accelerometer includes: Measure the material properties and geometric parameters of the U-shaped beam in the capacitive accelerometer; Based on the aforementioned material properties, determine the elastic modulus of the material corresponding to the U-shaped beam; Based on the geometric dimensions and the material elastic modulus, the equivalent stiffness coefficient corresponding to the U-shaped beam in the capacitive accelerometer is calculated. Identify the inertial components in the capacitive accelerometer and calculate the mass of the inertial components corresponding to the inertial components.

[0033] The material properties are a set of parameters reflecting the mechanical and physical characteristics of the U-shaped beam material, including elastic modulus, density, Poisson's ratio, etc.; the geometric dimensional parameters are key dimensions describing the spatial structure of the U-shaped beam, including width, thickness, effective length, and radius of curvature of the bending segment, etc.; the material elastic modulus is the ratio coefficient of stress to strain when the material undergoes elastic deformation, reflecting the material's ability to resist elastic deformation; the inertial assembly is a movable structure in the accelerometer that generates displacement with acceleration, including components such as the mass frame, movable comb teeth, and connecting beams.

[0034] Furthermore, the material properties can be determined using a Dynamic Mechanical Analyzer (DMA), which accurately obtains the elastic modulus by applying dynamic loads and monitoring deformation; the geometric parameters are obtained by scanning with a white light interferometer, and the microstructure of the U-shaped beam is reconstructed using the principle of optical interference; based on the material properties, the elastic modulus of the material corresponding to the U-shaped beam is determined by extracting the linear segment of the material stress-strain curve and calculating the slope; the structural morphology can be observed using a scanning electron microscope to distinguish between movable parts and fixed substrates, and to identify the inertial components in the capacitive accelerometer.

[0035] Furthermore, as another embodiment of the present invention, the equivalent stiffness coefficient corresponding to the U-shaped beam in the capacitive accelerometer is calculated using the following formula based on the geometric dimensional parameters and the material elastic modulus: ; Where B represents the equivalent stiffness coefficient corresponding to the U-shaped beam in the capacitive accelerometer, and E represents the material's elastic modulus. This refers to the thickness of the U-shaped beam in the geometric parameters. This refers to the width of the U-shaped beam in the geometric parameters. This indicates the effective length of the U-shaped beam in the geometric parameters.

[0036] Furthermore, as an optional embodiment of the present invention, calculating the inertial component mass corresponding to the inertial component includes: The inertial component is modeled with high precision to obtain a digital model of the component; The key dimensional parameters of the mass frame of the inertial component are extracted from the component's digital model. Measure the material density, width, length, and additional width of the mass frame; The mass of the inertial component corresponding to the inertial component is calculated by combining the material density, the length of the mass frame, the width of the mass frame, the additional width of the mass frame, and the key dimension parameters.

[0037] The high-precision modeling process refers to the process of creating a precise digital representation of the inertial component through 3D scanning or computer-aided design software; the component digital model is a 3D digital representation of the inertial component, containing its complete geometric shape and structural information; the mass frame is an abstract cuboid model defined to simplify calculations and containing the main mass characteristics of the inertial component; the key dimensional parameters include geometric parameters affecting mass calculations such as the height of the mass frame, chamfer dimensions, and cutout feature dimensions; the material density is the mass per unit volume of the material used to manufacture the inertial component; the mass frame width is the dimension of the mass frame in the X-axis direction; the mass frame length is the dimension of the mass frame in the Y-axis direction; and the additional width of the mass frame is the additional dimension of the non-primary structural parts within the mass frame.

[0038] Furthermore, the high-precision modeling process can be achieved through a 3D laser scanner or an industrial CT scanning device; the analysis of the component digital model can be completed through the measurement tools of CAD software (such as SolidWorks, Pro / Engineer); the measurement of the material density, width, length and additional width of the mass frame can be achieved through corresponding tools, such as a high-precision electronic balance (for measuring material density) or a white light interferometer (for measuring width, length and additional width).

[0039] Furthermore, as another embodiment of the present invention, the mass of the inertial component corresponding to the inertial component is calculated using the following formula, combining the material density, the length of the mass frame, the width of the mass frame, the additional width of the mass frame, and the key dimensional parameters: ; Where m represents the mass of the inertial component. Indicates the density of the material. This represents the structural thickness in the critical dimension parameter, and M represents the number of movable comb tooth pairs in the critical dimension parameter. This indicates the width of a single comb tooth, a key dimensional parameter. This indicates the length of a single comb tooth in the key dimension parameters, where h represents the width of the mass frame. Indicates the length of the mass frame. This indicates the additional width of the quality frame.

[0040] This invention, by calculating the natural frequency of the capacitor corresponding to the capacitive accelerometer, can reveal the dynamic response characteristics and effective measurement bandwidth of the capacitive accelerometer, providing a basis for ensuring measurement accuracy and optimizing its structure. The natural frequency reflects the system's response characteristics to external stimuli. Furthermore, the formula for calculating the natural frequency of the capacitor corresponding to the capacitive accelerometer is: Natural frequency = .

[0041] S3. Input the capacitance sensitivity and the natural frequency into a pre-constructed optimization analysis network, and use the dual-path feature extraction layer in the optimization analysis network to output the high-dimensional representation features corresponding to the capacitive accelerometer.

[0042] This invention establishes an intrinsic connection between electrical and mechanical properties by optimizing the analysis network based on capacitance sensitivity and inherent frequency inputs. Then, it extracts comprehensive features affecting performance through deep learning. The optimization analysis network is a computational architecture specifically designed to handle the correlation features of multiple physical quantities. The dual-path feature extraction layer can process sensitivity features and frequency features separately, and finally merge them into a unified high-dimensional representation feature.

[0043] As an embodiment of the present invention, the step of using the dual-path feature extraction layer in the optimized analysis network to output the high-dimensional representation features corresponding to the capacitive accelerometer includes: The capacitance sensitivity is input into the first feature extraction path of the dual-path feature extraction layer for feature transformation to obtain the sensitivity depth feature. The inherent frequency is input into the second feature extraction path of the dual-path feature extraction layer for frequency domain feature extraction to obtain frequency depth features; The sensitivity depth feature and the frequency depth feature are concatenated using the feature fusion layer in the dual-path feature extraction layer to obtain a preliminary fused feature; The dimensionality of the preliminary fused features is compressed using the dimensionality reduction processing layer in the dual-path feature extraction layer to obtain the high-dimensional representation features corresponding to the capacitive accelerometer.

[0044] The first feature extraction path is a feature processing module adapted to the capacitance sensitivity characteristics, consisting of three fully connected multilayer perceptrons, used to convert one-dimensional sensitivity values ​​into multi-dimensional feature vectors. The sensitivity depth feature is a feature set obtained after nonlinear mapping by the first path, containing implicit correlation information between capacitance sensitivity and structural parameters. The second feature extraction path is a processing module designed for the frequency domain characteristics of the inherent frequency, consisting of two 1D convolutional layers and one pooling layer, used to capture the local patterns of frequency variation with structure. The frequency depth feature is the frequency domain correlation feature extracted by the second path, reflecting the dynamic distribution attributes of the inherent frequency. The feature fusion layer is a network unit that combines two types of features, integrating feature information of different dimensions through vector concatenation. The preliminary fusion feature is a high-dimensional vector obtained by directly concatenating the sensitivity depth feature and the frequency depth feature, with a dimension equal to the sum of the dimensions of the two types of features. The dimensionality reduction processing layer is a module that reduces feature redundancy, using average pooling or fully connected compression to retain core features. The high-dimensional representation feature is a simplified feature vector obtained after dimensionality reduction, containing key characterization information of the capacitance accelerometer's performance.

[0045] Furthermore, the feature transformation in the first feature extraction path is implemented through a multilayer perceptron, using the ReLU activation function to enhance nonlinear expressive power; the frequency domain feature extraction in the second feature extraction path adopts a one-dimensional convolutional neural network, capturing multi-scale information of frequency features through convolutional kernels of different sizes; the dimensionality reduction layer adopts principal component analysis to retain the main feature components while reducing the feature dimension.

[0046] Furthermore, as an optional embodiment of the present invention, the step of using the feature fusion layer in the dual-path feature extraction layer to concatenate the sensitivity depth feature and the frequency depth feature to obtain preliminary fused features includes: Calculate the dimensionality importance factor of each feature dimension in the sensitivity depth feature and the frequency depth feature respectively; Construct a sensitivity-frequency dual-dimensional feature weighting matrix based on the aforementioned dimensional importance factors; The sensitivity depth feature and the frequency depth feature are adaptively weighted and fused using the feature weighting matrix to obtain the weighted fused feature. The weighted fusion features are subjected to cross-channel feature enhancement processing to obtain cross-channel enhanced features; The cross-channel enhancement features are subjected to redundancy filtering to obtain the preliminary fusion features.

[0047] The dimension importance factor is a quantitative indicator that measures the contribution of a single feature dimension to the performance characterization of the accelerometer. It is obtained by calculating the correlation coefficient between the feature value of the dimension and the measured performance of the accelerometer, and the value ranges from [0,1]. The larger the value, the more critical the effective information contained in the dimension. The feature weighting matrix of the sensitivity-frequency dual dimension is a two-dimensional matrix of dimension M×N (M is the number of sensitivity feature dimensions, and N is the number of frequency feature dimensions). The matrix elements are the product of the corresponding dimension importance factors, which are used to quantify the correlation weight between the two types of feature dimensions. The weighted fusion feature is a feature set obtained after weighting, which integrates the core information of sensitivity and frequency features, and has a dimension of M+N. The cross-channel enhancement feature is a feature vector after enhancement processing, in which the signal intensity of high-value features is amplified by 1.2-2.0 times. The redundancy filtering process is the process of removing duplicate or low-information dimensions from the features, which is achieved by calculating the cosine similarity between features.

[0048] S4. Based on the high-dimensional representation features, the predicted sensitivity of the capacitive accelerometer is calculated using the sensitivity regression layer in the optimization analysis network.

[0049] This invention calculates the predicted sensitivity of a capacitive accelerometer based on the high-dimensional representation features using a sensitivity regression layer in the optimized analysis network. This allows for the prediction of the sensitivity characteristics of the capacitive accelerometer. The sensitivity regression layer is a network layer specifically designed to regress sensitivity values ​​from the high-dimensional features, and the predicted sensitivity is a theoretical sensitivity value calculated based on the network.

[0050] As an embodiment of the present invention, based on the high-dimensional representation features, the predicted sensitivity of the capacitive accelerometer is calculated using the sensitivity regression layer in the optimized analysis network, including: The high-dimensional representation features are standardized by using the feature preprocessing layer in the sensitivity regression layer to obtain standard high-dimensional features. The standard high-dimensional features are mapped and regressed using the multivariate regression layer in the sensitivity regression layer to obtain the sensitivity vector. The sensitivity coefficients corresponding to the sensitivity vector are calculated using the optimization calculation layer in the sensitivity regression layer. Based on the sensitivity coefficient, the predicted sensitivity of the capacitive accelerometer is obtained.

[0051] The feature preprocessing layer adjusts the numerical range of the high-dimensional representation features to a form suitable for regression analysis and is composed of the Z-score standardization function. The multivariate regression layer is a computational layer that fits the standard high-dimensional features to a linear or nonlinear relationship and is constructed using the least squares regression algorithm. The optimization calculation layer is a calculation unit used to correct the accuracy of the initial sensitivity vector. The sensitivity output layer is composed of a linear combination function.

[0052] Furthermore, as another optional embodiment of the present invention, the step of calculating the sensitivity coefficient corresponding to the sensitivity vector using the optimization calculation layer in the sensitivity regression layer includes: The error component in the initial sensitivity vector is extracted using the residual analyzer in the optimization calculation layer. Calculate the statistical distribution of the error components; Based on the statistical distribution, the residual dispersion and feature contribution corresponding to the initial sensitivity vector are calculated using the statistical functions in the optimization calculation layer. By combining the residual dispersion and the feature contribution, the sensitivity confidence corresponding to the initial sensitivity vector is calculated; Based on the sensitivity confidence level, the sensitivity coefficient corresponding to the initial sensitivity vector is obtained.

[0053] The error component is the deviation from the theoretical prediction value in the initial sensitivity vector (including systematic deviations such as measurement noise and model simplification errors). The residual dispersion and the feature contribution represent the degree of dispersion of the error component (the lower the dispersion, the more concentrated the error) and the influence weight of each feature dimension on the sensitivity vector, respectively (the higher the contribution, the stronger the determination of the feature on the sensitivity). The sensitivity confidence is a probabilistic index used to quantify the reliability of the sensitivity coefficient (the value ranges from 0 to 1, and the higher the value, the more reliable the coefficient).

[0054] Furthermore, the residual analyzer is compiled using Python (based on the residual analysis module of the Scikit-learn library to adaptively extract error components); the statistical distributions corresponding to the error components can be calculated using kernel density estimation (e.g., the mean, variance, and quantiles of errors from 100 consecutive sets of sampled data); the statistical function is composed of a coefficient of variation function (for calculating residual dispersion) and a random forest feature importance function (for calculating feature contribution); the calculation process for the sensitivity confidence level corresponding to the initial sensitivity vector is as follows: normalize the residual dispersion and take its reciprocal (to obtain the reliability baseline score), multiply it by the weighted sum of feature contributions (weights are allocated according to the importance of physical dimensions), and then normalize it to the 0-1 interval using Max-Min, which is the sensitivity confidence level; the sensitivity coefficient corresponding to the initial sensitivity vector is obtained by multiplying the initially calculated coefficient value by the sensitivity confidence level (the higher the confidence level, the higher the coefficient retention).

[0055] S5. Calculate the difference between the predicted sensitivity and the capacitive sensitivity. When the difference is greater than a preset difference, perform sensitivity analysis on the capacitive accelerometer to obtain the analysis results.

[0056] This invention improves the accuracy of sensitivity analysis by calculating the difference between the predicted sensitivity and the capacitive sensitivity. When the difference exceeds an allowable range, sensitivity analysis is performed on the capacitive accelerometer to obtain the analysis results. The difference is the degree of deviation between the predicted value and the actual value, such as relative error or absolute deviation. Optionally, the difference can be calculated using difference operations or percentage calculations. For example, the ratio of the absolute difference between the two sensitivities to the capacitive sensitivity can be used as the difference index. When this index exceeds a preset threshold, it indicates an abnormality in the sensitivity output, requiring further analysis of the accelerometer's internal state. By detecting the sensitivity output curve characteristics or signal response features and comparing them with historical data, the specific cause of the sensitivity abnormality can be determined. Finally, based on the analysis results, it is determined whether the capacitive accelerometer needs adjustment or maintenance.

[0057] Compared to the problems described in the background art, this invention, by collecting structural variables and performance data of a capacitive accelerometer to calculate its capacitive sensitivity, can correlate the intrinsic mapping between structural parameters and sensitivity, providing a reliable quantitative basis for subsequent comprehensive analysis based on deep learning. Furthermore, by calculating the equivalent stiffness coefficient of the U-beam and the mass of the inertial components, this invention can establish a correlation between structural mechanical properties and vibration characteristics, providing mechanical parameter support for the accurate derivation of the capacitor's natural frequency. Further, by inputting the capacitive sensitivity and natural frequency into an optimization analysis network, this invention can establish an intrinsic connection between electrical and mechanical properties, and then extract comprehensive features affecting performance through deep learning. Furthermore, by using the sensitivity regression layer in the optimization analysis network based on the high-dimensional representation features, this invention can calculate the predicted sensitivity of the capacitive accelerometer, thus predicting its sensitivity characteristics. Finally, by calculating the difference between the predicted sensitivity and the actual capacitive sensitivity, and when the difference exceeds an allowable range, this invention performs sensitivity analysis on the capacitive accelerometer to obtain the analysis results, thereby improving the accuracy of the sensitivity analysis. Therefore, the deep learning-based method and system for sensitivity analysis of capacitive accelerometers provided in this embodiment of the invention can improve the accuracy of sensitivity analysis of capacitive accelerometers.

[0058] like Figure 2 The diagram shown is a functional block diagram of the capacitive accelerometer sensitivity analysis system based on deep learning, as described in this invention.

[0059] The deep learning-based capacitive accelerometer sensitivity analysis system 200 described in this invention can be installed in an electronic device. Depending on the functions implemented, the deep learning-based capacitive accelerometer sensitivity analysis system may include a sensitivity calculation module 201, a capacitance natural frequency calculation module 202, a feature extraction module 203, a predicted sensitivity calculation module 204, and a sensitivity analysis module 205. The module described in this invention can also be called a unit, referring to a series of computer program segments that can be executed by the processor of an electronic device and perform a fixed function, stored in the memory of the electronic device.

[0060] In this embodiment of the invention, the functions of each module / unit are as follows: The sensitivity calculation module 201 is used to collect the structural variables and performance data of the capacitive accelerometer in order to calculate the capacitive sensitivity of the capacitive accelerometer. The capacitor natural frequency calculation module 202 is used to calculate the equivalent stiffness coefficient and inertial component mass of the U-shaped beam in the capacitor accelerometer, so as to calculate the capacitor natural frequency of the capacitor accelerometer. The feature extraction module 203 is used to input the capacitance sensitivity and the natural frequency into a pre-constructed optimization analysis network, and use the dual-path feature extraction layer in the optimization analysis network to output the high-dimensional representation features corresponding to the capacitance accelerometer. The predicted sensitivity calculation module 204 is used to calculate the predicted sensitivity of the capacitive accelerometer based on the high-dimensional representation features and using the sensitivity regression layer in the optimization analysis network. The sensitivity analysis module 205 is used to calculate the difference between the predicted sensitivity and the capacitive sensitivity. When the difference is greater than a preset difference, sensitivity analysis is performed on the capacitive accelerometer to obtain the analysis result.

[0061] In detail, the modules in the deep learning-based capacitive accelerometer sensitivity analysis system 200 described in this embodiment of the invention employ the same methods as described above. Figure 1 The technique used is the same as the deep learning-based method for sensitivity analysis of capacitive accelerometers described above, and it can produce the same technical effect, so it will not be repeated here.

[0062] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0063] Finally, it should be noted that in the above embodiments, each embodiment can be combined with each other or independent. Deleting any one of them will not affect the technical implementation of other embodiments. The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for sensitivity analysis of capacitive accelerometers based on deep learning, characterized in that, The method includes: Collect structural variables and performance data of the capacitive accelerometer to calculate the capacitive sensitivity of the capacitive accelerometer; Calculate the equivalent stiffness coefficient and inertial component mass of the U-shaped beam in the capacitive accelerometer to calculate the natural frequency of the capacitor corresponding to the capacitive accelerometer. The capacitive sensitivity and the natural frequency are input into a pre-constructed optimization analysis network, and the dual-path feature extraction layer in the optimization analysis network is used to output the high-dimensional representation features corresponding to the capacitive accelerometer. Based on the high-dimensional representation features, the predicted sensitivity of the capacitive accelerometer is calculated using the sensitivity regression layer in the optimization analysis network. The difference between the predicted sensitivity and the capacitive sensitivity is calculated. When the difference is greater than a preset difference, sensitivity analysis is performed on the capacitive accelerometer to obtain the analysis results.

2. The method for sensitivity analysis of a capacitive accelerometer based on deep learning as described in claim 1, characterized in that, The process of acquiring structural variables and performance data from the capacitive accelerometer to calculate its capacitive sensitivity includes: Based on the performance data, calculate the mechanical sensitivity of the capacitive accelerometer. Extract the sensitive correlation variables of the capacitive accelerometer from the structural variables; Combining the aforementioned sensitive correlation variable and the mechanical sensitivity, the capacitive sensitivity of the capacitive accelerometer is calculated using the following formula: ； Where A represents the capacitance sensitivity of the capacitive accelerometer, and N represents the number of one-sided capacitance pairs in the sensitivity correlation variable. Represents the dielectric constant. t represents the comb tooth alignment length in the sensitive correlation variables, and t represents the device thickness in the sensitive correlation variables. Indicates mechanical sensitivity. and These represent the spacing between different comb tooth structures.

3. The method for sensitivity analysis of a capacitive accelerometer based on deep learning as described in claim 2, characterized in that, The extraction of the sensitive correlation variable of the capacitive accelerometer from the structural variables includes: The structural variables are sorted by importance to obtain sorted structural variables; Analyze the mapping correlation between each variable in the ranking structure and the sensitivity; Based on the mapping correlation degree, initial correlation variables are selected from the sorting structure variables; The initial correlation variables are subjected to hierarchical filtering to obtain the sensitive correlation variables of the capacitive accelerometer.

4. The method for sensitivity analysis of a capacitive accelerometer based on deep learning as described in claim 1, characterized in that, The calculation of the equivalent stiffness coefficient and inertial component mass of the U-shaped beam in the capacitive accelerometer includes: Measure the material properties and geometric parameters of the U-shaped beam in the capacitive accelerometer; Based on the aforementioned material properties, determine the elastic modulus of the material corresponding to the U-shaped beam; Based on the geometric parameters and the material elastic modulus, the equivalent stiffness coefficient of the U-shaped beam in the capacitive accelerometer is calculated using the following formula: ； Where B represents the equivalent stiffness coefficient corresponding to the U-shaped beam in the capacitive accelerometer, and E represents the material's elastic modulus. This refers to the thickness of the U-shaped beam in the geometric parameters. This refers to the width of the U-shaped beam in the geometric parameters. This indicates the effective length of the U-shaped beam in the geometric parameters; Identify the inertial components in the capacitive accelerometer and calculate the mass of the inertial components corresponding to the inertial components.

5. The method for sensitivity analysis of a capacitive accelerometer based on deep learning as described in claim 4, characterized in that, The calculation of the inertial component mass corresponding to the inertial component includes: The inertial component is modeled with high precision to obtain a digital model of the component; The key dimensional parameters of the mass frame of the inertial component are extracted from the component's digital model. Measure the material density, width, length, and additional width of the mass frame; Combining the material density, the mass frame length, the mass frame width, the additional width of the mass frame, and the key dimensional parameters, the mass of the inertial assembly corresponding to the inertial assembly is calculated using the following formula: ； Where m represents the mass of the inertial component. Indicates the density of the material. This represents the structural thickness in the critical dimension parameter, and M represents the number of movable comb tooth pairs in the critical dimension parameter. This indicates the width of a single comb tooth, a key dimensional parameter. This indicates the length of a single comb tooth in the key dimension parameters, where h represents the width of the mass frame. Indicates the length of the mass frame. This indicates the additional width of the quality frame.

6. The method for sensitivity analysis of a capacitive accelerometer based on deep learning as described in claim 1, characterized in that, The step of using the dual-path feature extraction layer in the optimized analysis network to output the high-dimensional representation features corresponding to the capacitive accelerometer includes: The capacitance sensitivity is input into the first feature extraction path of the dual-path feature extraction layer for feature transformation to obtain the sensitivity depth feature. The inherent frequency is input into the second feature extraction path of the dual-path feature extraction layer for frequency domain feature extraction to obtain frequency depth features; The sensitivity depth feature and the frequency depth feature are concatenated using the feature fusion layer in the dual-path feature extraction layer to obtain a preliminary fused feature; The dimensionality of the preliminary fused features is compressed using the dimensionality reduction processing layer in the dual-path feature extraction layer to obtain the high-dimensional representation features corresponding to the capacitive accelerometer.

7. The method for sensitivity analysis of a capacitive accelerometer based on deep learning as described in claim 6, characterized in that, The process of concatenating the sensitivity depth feature and the frequency depth feature using the feature fusion layer in the dual-path feature extraction layer to obtain preliminary fused features includes: Calculate the dimensionality importance factor of each feature dimension in the sensitivity depth feature and the frequency depth feature respectively; Construct a sensitivity-frequency dual-dimensional feature weighting matrix based on the aforementioned dimensional importance factors; The sensitivity depth feature and the frequency depth feature are adaptively weighted and fused using the feature weighting matrix to obtain the weighted fused feature. The weighted fusion features are subjected to cross-channel feature enhancement processing to obtain cross-channel enhanced features; The cross-channel enhancement features are subjected to redundancy filtering to obtain the preliminary fusion features.

8. The method for sensitivity analysis of a capacitive accelerometer based on deep learning as described in claim 1, characterized in that, Based on the high-dimensional representation features, the predicted sensitivity of the capacitive accelerometer is calculated using the sensitivity regression layer in the optimized analysis network, including: The high-dimensional representation features are standardized by using the feature preprocessing layer in the sensitivity regression layer to obtain standard high-dimensional features. The standard high-dimensional features are mapped and regressed using the multivariate regression layer in the sensitivity regression layer to obtain the sensitivity vector. The sensitivity coefficients corresponding to the sensitivity vector are calculated using the optimization calculation layer in the sensitivity regression layer. Based on the sensitivity coefficient, the predicted sensitivity of the capacitive accelerometer is obtained.

9. The method for sensitivity analysis of a capacitive accelerometer based on deep learning as described in claim 8, characterized in that, The step of calculating the sensitivity coefficient corresponding to the sensitivity vector using the optimization calculation layer in the sensitivity regression layer includes: The error component in the initial sensitivity vector is extracted using the residual analyzer in the optimization calculation layer. Calculate the statistical distribution of the error components; Based on the statistical distribution, the residual dispersion and feature contribution corresponding to the initial sensitivity vector are calculated using the statistical functions in the optimization calculation layer. By combining the residual dispersion and the feature contribution, the sensitivity confidence corresponding to the initial sensitivity vector is calculated; Based on the sensitivity confidence level, the sensitivity coefficient corresponding to the initial sensitivity vector is obtained.

10. A sensitivity analysis system for capacitive accelerometers based on deep learning, characterized in that, The system includes: The sensitivity calculation module is used to collect structural variables and performance data of the capacitive accelerometer in order to calculate the capacitive sensitivity of the capacitive accelerometer. The capacitor natural frequency calculation module is used to calculate the equivalent stiffness coefficient and inertial component mass of the U-shaped beam in the capacitor accelerometer, so as to calculate the capacitor natural frequency of the capacitor accelerometer. The feature extraction module is used to input the capacitance sensitivity and the natural frequency into a pre-constructed optimization analysis network, and use the dual-path feature extraction layer in the optimization analysis network to output the high-dimensional representation features corresponding to the capacitance accelerometer. The predicted sensitivity calculation module is used to calculate the predicted sensitivity of the capacitive accelerometer based on the high-dimensional representation features and using the sensitivity regression layer in the optimized analysis network; the sensitivity analysis module is used to calculate the difference between the predicted sensitivity and the capacitive sensitivity, and when the difference is greater than a preset difference, to perform sensitivity analysis on the capacitive accelerometer and obtain the analysis results.

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