A micro-cantilever beam deformation correction method and system for output error of a MEMS sensor

Abstract

The application relates to the field of micro-electro-mechanical systems, and specifically discloses a micro-cantilever beam deformation correction method and system for MEMS sensor output errors, which comprises the following steps: exciting a composite vibration mode of a micro-cantilever beam through a multi-mode active excitation signal, collecting a dynamic response signal and identifying a deformation state parameter by using a deep learning model, generating laser micro-processing parameters based on the identification result to perform selective material removal or annealing treatment, establishing a deformation trend prediction model to perform pre-compensation adjustment, and ensuring the correction effect through a closed-loop verification mechanism; the system comprises a multi-mode active excitation control module, a dynamic response collection and processing module, a deformation identification and state evaluation module, a laser micro-processing control module, a deformation trend prediction and pre-compensation module, a correction effect verification and iterative control module, and a system integration and data management module. The application solves the problem of sensor errors caused by physical deformation of a micro-cantilever beam, and significantly improves the precision and long-term stability of a MEMS sensor.

Description

Technical Field

[0001] This invention relates to the field of microelectromechanical systems (MEMS) technology, and in particular to a method and system for correcting the deformation of a microcantilever beam in response to MEMS sensor output errors. Background Technology

[0002] Microelectromechanical systems (MEMS) sensors have wide applications in modern industry, aerospace, automotive electronics, and consumer electronics. However, as the core sensing structure in MEMS sensors, the microcantilever beam undergoes varying degrees of deformation during manufacturing due to factors such as residual stress release, material inhomogeneity, and process deviations. During use, it is affected by temperature changes, mechanical fatigue, and external environmental factors, leading to significant errors in the sensor output.

[0003] Currently, methods for correcting output errors in MEMS sensors mainly fall into two categories: one is to reduce initial deformation by optimizing manufacturing processes, such as improving etching processes, optimizing material selection, and heat treatment processes; the other is to offset output errors through circuit compensation and algorithm correction, such as temperature compensation algorithms and orthogonal error correction circuits. However, these traditional methods have significant limitations: process optimization methods cannot completely eliminate manufacturing deviations and will significantly increase manufacturing costs; circuit compensation methods can only perform post-processing at the signal level and cannot fundamentally solve the physical deformation problem of micro-cantilever beams, and the compensation effect will decay over time.

[0004] More importantly, existing technologies generally overlook several key scientific issues in the deformation process of microcantilever beams: first, the time-varying characteristics of residual stress release, leading to the dynamic evolution of deformation over time; second, the nonlinear response characteristics under thermomechanical coupling, resulting in a complex nonlinear relationship between deformation and temperature changes; and third, the coupling effect between multiple vibration modes, making it impossible for single-mode excitation and detection to fully reflect the true deformation state. These problems make it difficult for existing correction methods to achieve long-term stable correction effects.

[0005] Therefore, there is an urgent need in this field for an innovative method that can directly correct the deformation of microcantilever beams at the physical level, while possessing long-term stability and environmental adaptability, in order to solve the sensor output error problem that traditional technologies cannot fundamentally address. Summary of the Invention

[0006] The purpose of this invention is to solve the problem of sensor output error caused by deformation of microcantilever beams during manufacturing and use in the prior art, and to propose a method and system for correcting microcantilever beam deformation of MEMS sensor output error.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for correcting the deformation of a microcantilever beam in response to MEMS sensor output errors includes: A multi-mode active excitation signal is applied to the microcantilever beam. The multi-mode active excitation signal includes excitation components with different frequencies, phases, and amplitudes, which are used to excite the microcantilever beam to generate a composite vibration mode that includes bending, torsion, and coupled vibrations. The dynamic response signal of the microcantilever beam under the multi-mode active excitation is collected, the response feature parameters are extracted, and the response feature parameters are input into the pre-trained deformation recognition model to output the current deformation state parameters of the microcantilever beam. Based on the current deformation state parameters, corresponding laser micromachining parameters are generated. By focusing the laser beam, selective material removal or annealing is performed on a specific area of ​​the microcantilever beam, and the stiffness distribution and stress state of the microcantilever beam are adjusted in real time. Based on the changes in structural parameters of the microcantilever beam after material removal or annealing, a deformation trend prediction model for the microcantilever beam is established to predict the deformation development trend of the microcantilever beam in subsequent working processes. Based on the prediction results, the laser micromachining parameters are pre-compensated and adjusted. After the pre-compensation adjustment, the operation is repeated to output the current deformation state parameters of the microcantilever beam to verify the correction effect until the deformation of the microcantilever beam reaches the preset tolerance range.

[0008] As a further technical solution of the present invention, the application of multi-mode active excitation signals to the microcantilever beam specifically includes: A fundamental frequency excitation signal is applied through the electrostatic driving electrode of the MEMS sensor. The frequency of the fundamental frequency excitation signal is determined according to the natural frequency of the first bending mode of the microcantilever beam, and is used to excite the basic bending vibration of the microcantilever beam. Based on the fundamental frequency excitation signal, a second harmonic excitation signal is superimposed. The frequency of the second harmonic excitation signal is determined according to the natural frequency of the torsional mode of the microcantilever beam, and is used to excite the torsional vibration of the microcantilever beam. A third-order coupled excitation signal is introduced, the frequency of which is determined according to the bending-torsional coupled mode frequency of the microcantilever beam, and is used to excite the composite vibration mode of bending and torsion. Adjust the phase difference between each excitation signal so that the phase difference between the fundamental frequency excitation signal and the second harmonic excitation signal is controlled within the range of 45°-90°, and the phase difference between the fundamental frequency excitation signal and the third-order coupled excitation signal is controlled within the range of 90°-135°. Set the amplitude ratio of each excitation signal so that the amplitude ratio of the fundamental frequency excitation signal, the second harmonic excitation signal and the third-order coupled excitation signal is 1:(0.3-0.5):(0.1-0.3), thus forming an optimized combination of excitation signals.

[0009] As a further technical solution of the present invention, the step of acquiring the dynamic response signal of the microcantilever beam under multi-mode active excitation, extracting response feature parameters, inputting the response feature parameters into a pre-trained deformation recognition model, and outputting the current deformation state parameters of the microcantilever beam specifically includes: Vibration response data of the microcantilever beam under the multi-mode active excitation are simultaneously acquired by a piezoresistive sensing unit set at the root of the microcantilever beam and an electrostatic sensing electrode array distributed on the surface of the microcantilever beam; wherein, the piezoresistive sensing unit is used to detect the strain distribution of the microcantilever beam, and the electrostatic sensing electrode array is used to detect the displacement distribution of the microcantilever beam. The collected vibration response data is preprocessed, including removing environmental noise interference, signal separation and feature enhancement. Multiple response feature parameters are extracted from the preprocessed signal, including: the resonant frequency shift of each vibration mode, the shape change parameters of the vibration mode, the coupling strength coefficient of bending vibration and torsional vibration, the quality factor change, the amplitude ratio of nonlinear harmonic components, and the phase difference of the orthogonal error signal. A deformation recognition model is constructed, and the extracted response feature parameters are normalized to form a feature vector, which is then input into the pre-trained deformation recognition model. The deformation recognition model analyzes and calculates the input feature vectors to output the current deformation state parameters of the microcantilever beam, including residual stress distribution cloud map, curvature change distribution and modal frequency offset of each order. The residual stress distribution cloud map represents the magnitude and direction of residual stress at each point on the surface of the microcantilever beam in the form of a two-dimensional matrix, and the curvature change distribution characterizes the degree of bending of the microcantilever beam in multiple directions.

[0010] As a further technical solution of the present invention, the extraction of multiple response feature parameters from the preprocessed signal specifically includes: Resonance frequency shift of each vibration mode ,in: It is the first one obtained by measurement The resonant frequency of the first vibration mode, It is the first micro-cantilever beam in its undeformed state. The nominal resonant frequency of the first vibration mode; Vibration mode shape change parameters ,in: It is the first one obtained by measurement The shape of the first vibration mode, It is the first micro-cantilever beam in its undeformed state. The nominal shape of the first vibration mode; Coupling strength coefficient between bending vibration and torsional vibration ,in: It is a displacement signal of bending vibration. It is the displacement signal of torsional vibration, where cov and var represent the covariance and variance, respectively; Variation in quality factor ,in: It is the quality factor obtained through measurement. It is the nominal quality factor of the micro-cantilever beam in its undeformed state; Nonlinear harmonic component amplitude ratio ,in: It is the amplitude of the nonlinear harmonic component. It is the amplitude of the fundamental frequency component; Phase difference of quadrature error signal ,in: It is the phase of the bending vibration signal. It is the phase of the torsional vibration signal.

[0011] As a further technical solution of the present invention, the construction of the deformation recognition model specifically includes: A parametric model of the microcantilever beam was established using finite element analysis software. Different types of manufacturing defects and usage deformations were set in the model, including uneven thickness, uneven residual stress distribution, and surface curvature changes. Tens of thousands of training samples with different deformation states were generated. Each training sample included the response feature parameters as input features, and the corresponding residual stress distribution, curvature change, and modal frequency offset as output labels. A deep neural network structure is constructed, including an input layer, a feature fusion layer, three residual network modules, and an output layer. The input layer receives normalized response feature parameters, the feature fusion layer performs dimension alignment and feature weighting on feature parameters of different physical dimensions, the three residual network modules are used to extract feature representations of shallow, middle and deep layers, respectively, and the output layer adopts a multi-task learning framework to output residual stress distribution, curvature change, and frequency shift of each modality. The deep neural network is trained using a phased training strategy. First, it is pre-trained using large-scale finite element simulation data to optimize the initial weights of the network. Then, the network is fine-tuned using actual measured micro cantilever beam deformation data to improve the model's generalization ability in practical applications. An adversarial training mechanism is introduced during the training process. By generating difficult-to-identify boundary samples through a generative adversarial network, the robustness of the model to noise and outliers is enhanced. At the same time, an attention mechanism is adopted so that the network automatically focuses on the feature parameters most sensitive to deformation recognition. The model's recognition accuracy was evaluated using cross-validation, and the network hyperparameters were optimized to ensure that the model's recognition error for residual stress distribution did not exceed ±5MPa, its recognition error for curvature change did not exceed 0.01%, and its recognition error for modal frequency shifts did not exceed 0.05%.

[0012] As a further technical solution of the present invention, the step of generating corresponding laser micromachining parameters based on the current deformation state parameters, selectively removing or annealing specific areas of the microcantilever beam by focusing a laser beam, and adjusting the stiffness distribution and stress state of the microcantilever beam in real time, specifically includes: Based on the residual stress distribution cloud map in the current deformation state parameters, high pressure stress regions and high pressure stress areas on the surface of the micro cantilever beam are identified, and corresponding laser processing strategies are generated according to the magnitude and distribution characteristics of the residual stress; among them, material removal process is used for regions with compressive stress greater than 50MPa, and annealing process is used for regions with tensile stress greater than 30MPa. Based on the residual stress distribution and curvature change distribution, a scanning path and process parameters for laser micromachining are generated. The scanning path adopts a spiral progressive trajectory, expanding from the high-stress region to the low-stress region. The process parameters include laser power, scanning speed, pulse frequency, and spot diameter. The laser power is adaptively adjusted within the range of 0.5W to 3W according to the stress magnitude, and the scanning speed is adjusted within the range of 0.1 to 2mm / s according to the stress gradient. During laser processing, the temperature field distribution and deformation state changes of the microcantilever beam are monitored in real time, and the laser processing parameters are dynamically adjusted through a closed-loop feedback control system. When the local temperature exceeds the material's critical annealing temperature, the laser power is automatically reduced or the scanning speed is increased. When the deformation state improvement rate reaches the expected target, the processing intensity is gradually reduced. Different laser processing parameters were used for the microcantilever beams in different material regions; nanosecond pulsed lasers were used in the silicon-based region, with the power density controlled at 10. 4 -10 5 W / cm²; femtosecond pulsed laser is used in the metal composite region, with power density controlled at 10³-10. 4 W / cm²; The polymer region uses continuous laser, with power density controlled at 10²-10³W / cm²; After each processing area is completed, the effect of material removal or annealing is evaluated by real-time vibration response data, and the processing parameters of subsequent areas are optimized based on the evaluation results to achieve adaptive optimization of the processing process.

[0013] As a further technical solution of the present invention, the method of establishing a deformation trend prediction model for the microcantilever beam based on the changes in structural parameters of the microcantilever beam after material removal or annealing, predicting the deformation development trend of the microcantilever beam in subsequent working processes, and pre-compensating and adjusting the laser micromachining parameters according to the prediction results, specifically includes: By using nanoindentation test points placed at key locations on the microcantilever beam and a digital image correlation measurement system, the structural parameter changes of the microcantilever beam after material removal or annealing are collected in real time, including the thickness distribution change, residual stress redistribution state, local stiffness change rate, and ambient temperature and humidity, which are collected every 5 minutes. Based on the structural parameter change data, a deformation trend prediction model based on time series analysis is established. The current structural parameter changes, historical deformation data and environmental parameters are input into the deformation trend prediction model, and the model outputs the deformation development trend prediction of the micro-cantilever beam in the next 24-72 hours. Based on the output of the deformation trend prediction model, a pre-compensation adjustment strategy is generated. The pre-compensation strategy includes: increasing the material removal amount by 5%-15% in advance for areas where stress concentration is predicted; reducing the material removal amount and increasing local annealing treatment for areas where stiffness is predicted to be insufficient; and adjusting the laser processing depth distribution in the opposite direction to the predicted modal frequency shift direction.

[0014] As a further technical solution of the present invention, the step of repeatedly outputting the current deformation state parameters of the micro-cantilever beam after pre-compensation adjustment to verify the correction effect until the deformation of the micro-cantilever beam reaches the preset tolerance range specifically includes: After the pre-compensation adjustment, the multi-mode active excitation signal was applied to the micro-cantilever beam again, and the current deformation state parameters of the micro-cantilever beam were output to verify the correction effect; the deformation improvement rate was calculated by comparing the difference in dynamic response signals before and after pre-compensation. Different measures are taken based on the deformation improvement rate. When the deformation improvement rate is below 85%, the pre-compensation parameters are readjusted; when the deformation improvement rate reaches 85%-95%, fine-tuning is performed; when the deformation improvement rate is above 95%, the correction is confirmed to be complete. An iterative optimization mechanism is established. When the deformation of the microcantilever beam remains within the preset tolerance range in three consecutive verifications, the correction process is considered complete. The preset tolerance range includes: residual stress distribution non-uniformity ≤ 5%, curvature change ≤ 0.08%, and modal frequency offset ≤ 0.03%. If any index exceeds the tolerance range, prediction and pre-compensation adjustment are performed again.

[0015] As a further technical solution of the present invention, the establishment of a deformation trend prediction model for time series analysis specifically includes: The design incorporates a prediction model architecture based on Long Short-Term Memory (LSTM) neural networks, comprising an input layer, two LSTM hidden layers, an attention mechanism layer, and an output layer. The input layer receives standardized multidimensional time-series data. The first LSTM hidden layer contains 128 neurons for extracting short-term features, and the second LSTM hidden layer contains 64 neurons for extracting long-term dependent features. The attention mechanism layer automatically weights the feature contributions of important time steps. The output layer outputs a prediction of the deformation development trend for the next 24–72 hours through a fully connected network. The prediction model is trained using a multi-task learning mechanism. The main task predicts the evolution path of residual stress, while the auxiliary task simultaneously predicts the curvature change trend and modal frequency shift. During training, a sliding window method is used to generate training samples, with the window size set to 24 hours and the prediction step size set to 72 hours. A physical constraint mechanism is introduced, in which the mechanical equilibrium equations and material constitutive relations of the micro cantilever beam are embedded as constraints during model training to ensure that the prediction results conform to physical laws. The physical constraints include stress-strain relationships, stiffness-deformation relationships, and the law of conservation of energy. The physical constraints are incorporated into the loss function through the Lagrange multiplier method.

[0016] A microcantilever beam deformation correction system for MEMS sensor output error, used to implement a method for correcting microcantilever beam deformation for MEMS sensor output error, comprising: The multi-mode active excitation control module is used to apply multi-mode active excitation signals containing different frequencies, phases, and amplitudes to the microcantilever beam. The dynamic response acquisition and processing module is used to acquire the dynamic response signal of the microcantilever beam under the multi-mode active excitation and extract the response feature parameters. The deformation recognition and state assessment module is used to input the response feature parameters into the pre-trained deformation recognition model and output the current deformation state parameters of the micro cantilever beam. The laser micromachining control module is used to generate corresponding laser micromachining parameters based on the current deformation state parameters and control the laser processing process. The deformation trend prediction and pre-compensation module is used to establish a deformation trend prediction model and generate a pre-compensation strategy based on the changes in the structural parameters of the micro-cantilever beam after material removal or annealing. The correction effect verification and iteration control module is used to verify the correction effect and control the iterative correction process after the pre-compensation adjustment. The system integration and data management module is used to coordinate data exchange and timing control between modules, and to store and manage system operation data.

[0017] The beneficial effects of this invention are as follows: 1. Significantly improved detection and identification accuracy: By combining multi-mode active excitation signals to stimulate the composite vibration mode of the microcantilever beam, and combining it with a deep learning identification model, high-precision quantitative identification of the deformation state such as residual stress distribution and curvature change of the microcantilever beam is achieved, breaking through the technical limitations of traditional detection methods.

[0018] 2. Long-term stable correction effect: The introduction of a deformation trend prediction model based on time series analysis can accurately predict the long-term deformation development trend of micro-cantilever beams. The correction parameters are optimized in advance through a pre-compensation mechanism, which fundamentally solves the problem of short-term effect of traditional correction methods and significantly improves long-term stability.

[0019] 3. Breakthrough in Adaptive Correction Capability: A complete closed-loop iterative correction system has been established, with real-time monitoring, dynamic adjustment and intelligent termination functions. It can automatically optimize the correction strategy according to different material properties and working environment, realizing full-process automation and intelligence, and greatly improving the system's environmental adaptability and correction consistency. Attached Figure Description

[0020] Figure 1 The flowchart shows a method for correcting the deformation of a microcantilever beam that provides the output error of a MEMS sensor, as proposed in this invention. Figure 2 This is an architecture diagram of the deformation recognition model; Figure 3 This is a diagram of the architecture of the deformation trend prediction model. Figure 4 This is a comparison diagram of the effects of the method of the present invention and the prior art method in Example 1. Detailed Implementation

[0021] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0022] Please see the appendix Figure 1 - Appendix Figure 3 A method for correcting the deformation of a microcantilever beam in response to MEMS sensor output errors, comprising: S1. Apply a multi-mode active excitation signal to the microcantilever beam, wherein the multi-mode active excitation signal includes excitation components of different frequencies, phases, and amplitudes, used to excite the microcantilever beam to generate a composite vibration mode including bending, torsion, and coupled vibrations; specifically including: S11. A fundamental frequency excitation signal is applied through the electrostatic drive electrode of the MEMS sensor, wherein the frequency of the fundamental frequency excitation signal is... Based on the first-order bending mode natural frequency of the microcantilever beam Determined, that is The amplitude of the fundamental frequency excitation signal is denoted as... The phase of the fundamental frequency excitation signal is denoted as As a reference phase, let .

[0023] S12. A second-order harmonic excitation signal is superimposed on the fundamental frequency excitation signal. The frequency of the second-order harmonic excitation signal... Based on the torsional modal natural frequency of the microcantilever beam Determined, that is The amplitude of the second harmonic excitation signal is denoted as... And its amplitude ratio with the fundamental frequency excitation signal is ,in Phase of the second harmonic excitation signal Phase difference with the fundamental frequency excitation signal Controlled .

[0024] S13. Introduce a third-order coupled excitation signal, the frequency of which is... Based on the bending-torsional coupled mode frequencies of the microcantilever beam Determined, that is The amplitude of the third-order coupled excitation signal is denoted as... And its amplitude ratio with the fundamental frequency excitation signal is ,in Phase of the third-order coupled excitation signal Phase difference with the fundamental frequency excitation signal Controlled .

[0025] S14. The final optimized combination of excitation signals Represented as: .

[0026] S2. Acquire the dynamic response signal of the microcantilever beam under the multi-mode active excitation, extract the response feature parameters, and input the response feature parameters into the pre-trained deformation recognition model to output the current deformation state parameters of the microcantilever beam; specifically including: S21. Vibration response data of the microcantilever beam under multi-mode active excitation are simultaneously acquired by a piezoresistive sensing unit located at the root of the microcantilever beam and an array of electrostatic sensing electrodes distributed on the surface of the microcantilever beam, wherein: the piezoresistive sensing unit detects the strain distribution of the microcantilever beam. Electrostatic sensing electrode array detects displacement distribution of microcantilever beam .

[0027] S22. Perform signal preprocessing on the acquired vibration response data, including removing environmental noise interference, signal separation, and feature enhancement. The preprocessed signal is denoted as... and Multiple response feature parameters are extracted from the preprocessed signal, as follows: Resonance frequency shift of each vibration mode ,in: It is the first one obtained by measurement The resonant frequency of the first vibration mode, It is the first micro-cantilever beam in its undeformed state. The nominal resonant frequency of the first vibration mode; Vibration mode shape change parameters ,in: It is the first one obtained by measurement The shape of the first vibration mode, It is the first micro-cantilever beam in its undeformed state. The nominal shape of the first vibration mode; Coupling strength coefficient between bending vibration and torsional vibration ,in: It is a displacement signal of bending vibration. It is the displacement signal of torsional vibration, where cov and var represent the covariance and variance, respectively; Variation in quality factor ,in: It is the quality factor obtained through measurement. It is the nominal quality factor of the micro-cantilever beam in its undeformed state; Nonlinear harmonic component amplitude ratio ,in: It is the amplitude of the nonlinear harmonic component. It is the amplitude of the fundamental frequency component; Phase difference of quadrature error signal ,in: It is the phase of the bending vibration signal. It is the phase of the torsional vibration signal.

[0028] S231. Construct a deformation recognition model, including: S231a. A parametric model of the microcantilever beam is established using finite element analysis software. Different types of manufacturing defects and usage deformations are set, including uneven thickness, uneven residual stress distribution, and surface curvature changes. Tens of thousands of training samples with different deformation states are generated. Each training sample includes response feature parameters as input features, and corresponding residual stress distribution, curvature change, and modal frequency offset as output labels. S231b. Construct a deep neural network structure as follows: The input layer receives the normalized response feature parameters. The feature fusion layer aligns and weights the feature parameters of different physical dimensions. The output of the feature fusion layer is... Represented as: in: It is a feature weighting matrix, used to adjust the importance of different features. It is a bias vector; three residual network modules are used to extract feature representations from shallow, middle, and deep layers, respectively. Each residual module is represented as: ,in: It is the first The output of each residual module It is the nonlinear transformation function in the residual module. It is the first The output of each residual module; the output layer adopts a multi-task learning framework, simultaneously outputting the residual stress distribution. Curvature change and the frequency offset of each modal order The computation of the output layer is represented as follows: ,in: These are the weight matrices corresponding to the output. These are the bias vectors corresponding to the output. This is the output of the third residual module; S231c. A staged training strategy is used to train the deep neural network. First, large-scale finite element simulation data is used for pre-training to optimize the initial weights of the network. The objective function for pre-training is expressed as: ,in: For the pre-trained loss function, It is the loss function of residual stress distribution. It is the loss function of the curvature change. It is the loss function of modal frequency offset. These are the corresponding weight coefficients, used to balance the losses of different tasks; then, the network is fine-tuned using actual measured micro-cantilever beam deformation data to improve the model's generalization ability in practical applications. The objective function for fine-tuning is expressed as: ,in: For fine-tuning the loss function, These are the weighting coefficients corresponding to the fine-tuning phase; S231d. An adversarial training mechanism is introduced during the training process. A generative adversarial network (GAN) generates difficult-to-identify boundary samples to enhance the model's robustness against noise and outliers. The objective function of the adversarial training is expressed as: ,in: For the loss function of adversarial training, It is the loss function of generative adversarial networks. These are the weighting coefficients for adversarial training; S231e. An attention mechanism is employed to enable the network to automatically focus on the feature parameters most sensitive to deformation recognition. The calculation of the attention mechanism is expressed as follows: , in: It is attention weight. It is the weight matrix of the attention mechanism; S231f. The model's recognition accuracy is evaluated using cross-validation, and network hyperparameters are optimized to ensure the model's recognition error of residual stress distribution is correct. Error in identifying curvature changes The identification error of the frequency offset of each modal order .

[0029] Depend on Figure 2 It can be seen that the architecture of the deformation recognition model is as follows: Input layer: 6 core response characteristic parameters, including resonant frequency offset, modal shape change parameter, coupling strength coefficient, quality factor change, nonlinear harmonic component, and orthogonal error phase difference: the phase relationship between the principal vibration and the orthogonal vibration.

[0030] Feature fusion layer: unifies feature parameters of different physical dimensions. The processing steps include feature normalization, dimension alignment, and importance weighting: assigning initial weights to different features based on experience.

[0031] Residual Network Module: A three-level residual module is used to solve the gradient vanishing problem in deep networks, including Module 1 (shallow feature extraction), Module 2 (middle-level feature abstraction), and Module 3 (deep feature representation).

[0032] Attention mechanism layer: includes self-attention computation, which calculates the mutual importance between features; Key feature enhancement amplifies features that contribute significantly to deformation recognition; redundant feature suppression reduces the impact of noise and irrelevant features; dynamic weight adjustment adaptively adjusts the attention distribution based on the input samples.

[0033] Multi-task output layer: Employs a multi-task learning framework to simultaneously output three deformation parameters: Residual stress distribution cloud map, curvature change distribution, and percentage shift of the first three modal frequencies.

[0034] S232. Normalize the extracted response feature parameters to form a feature vector. ,in: and These are the maximum values ​​of the resonant frequency offset and the vibration mode shape change parameter for each order, respectively, used for normalization.

[0035] S24. The normalized eigenvectors The input is fed into a pre-trained deformation recognition model, which outputs the current deformation state parameters of the microcantilever beam, including: Residual stress distribution cloud map S: Represents the magnitude and direction of residual stress at each point on the surface of the microcantilever beam in two-dimensional matrix form.

[0036] Distribution of curvature variation Characterizes the bending degree of the microcantilever beam in multiple directions. Modal frequency shifts for each order. : Output directly from the model.

[0037] S3. Based on the current deformation state parameters, generate corresponding laser micromachining parameters, and selectively remove or anneal specific areas of the microcantilever beam using a focused laser beam to adjust the stiffness distribution and stress state of the microcantilever beam in real time; specifically including: S31. Based on the residual stress distribution cloud map in the current deformation state parameters, identify the high-pressure stress area on the surface of the micro-cantilever beam and generate the corresponding laser processing strategy: for areas with compressive stress greater than 50MPa, use material removal process; for areas with tensile stress greater than 30MPa, use annealing process.

[0038] S32. Based on the residual stress distribution and curvature change distribution, generate the scanning path and process parameters for laser micromachining: The scanning path employs a spiral, progressive trajectory, extending from high-stress areas to low-stress areas; Process parameters: laser power. Based on the magnitude of stress Adaptive adjustment within the range: ,in: , and These are the minimum and maximum values ​​of stress, respectively. This refers to the stress value of the current area; the scanning speed. Based on the stress gradient Adjust within range: ,in: , It is the stress gradient of the current region. and These are the minimum and maximum values ​​of the stress gradient, respectively; pulse frequency. The beam diameter is set according to material and process requirements. Set according to the required machining accuracy.

[0039] S33. During laser processing, the temperature field distribution and deformation state changes of the micro-cantilever beam are monitored in real time, and the laser processing parameters are dynamically adjusted through a closed-loop feedback control system: When monitoring local temperature Exceeding the material's critical annealing temperature When necessary, the laser power will be automatically reduced or the scanning speed will be increased. , ,in: The adjusted laser power, The adjusted scan speed, It is the critical annealing temperature of the material. This is the maximum permissible temperature; When the deformation state improvement rate reaches the expected target, gradually reduce the processing intensity: ,in: It represents the current stress improvement amount, and it represents the target stress improvement amount.

[0040] S34. Different laser processing parameters are used for microcantilever beams in different material regions: nanosecond pulsed lasers are used in silicon-based regions, with power density controlled. The metal composite region utilizes femtosecond pulsed lasers with controlled power density. The polymer region uses continuous laser, with power density controlled at [specific value]. ; Specific power density The calculation formula is as follows: ,in: It is the laser power. It is the diameter of the light spot.

[0041] S35. After completing each processing area, evaluate the effect of material removal or annealing treatment using real-time acquired vibration response data, and optimize the processing parameters for subsequent areas based on the evaluation results; evaluation indicators include: stress improvement rate. ,in: It is the initial stress. It refers to the stress after processing; the processing parameters are adjusted based on the evaluation results to ensure adaptive optimization of the processing process.

[0042] S4. Based on the changes in the structural parameters of the microcantilever beam after material removal or annealing, establish a deformation trend prediction model for the microcantilever beam to predict its deformation development trend in subsequent work processes. Based on the prediction results, pre-compensate and adjust the laser micromachining parameters. After the pre-compensation adjustment, repeat the operation to output the current deformation state parameters of the microcantilever beam to verify the correction effect until the deformation of the microcantilever beam reaches the preset tolerance range. Specifically, this includes: S41. Using nanoindentation test points placed at key locations on the microcantilever beam and a digital image correlation measurement system, data on the changes in structural parameters of the microcantilever beam after material removal or annealing are collected every 5 minutes, including: changes in thickness distribution. Residual stress redistribution state Local stiffness change rate Ambient temperature Ambient humidity To form a multidimensional time series dataset .

[0043] S42. Based on structural parameter variation data, establish a deformation trend prediction model using time series analysis. Input the current structural parameter variations, historical deformation data, and environmental parameters into the deformation trend prediction model, and output the deformation development trend prediction of the micro-cantilever beam within the next 24-72 hours, specifically including: S421. Design an LSTM-based prediction model architecture, including: The input layer receives standardized multidimensional time series data. ; The first LSTM hidden layer contains 128 neurons and is used to extract short-term features: ,in: The first LSTM hidden layer at time step The output, The first LSTM hidden layer at time step cellular state; The second LSTM hidden layer contains 64 neurons and is used to extract long-term dependency features: ,in: It is the second LSTM hidden layer at time step The output, It is the second LSTM hidden layer at time step cellular state; The attention mechanism layer automatically weights the feature contributions of important time steps: , ,in: It is attention weight. and It refers to the weights and biases of the attention mechanism. It is the output feature of the second LSTM hidden layer after being processed by the attention mechanism; The output layer outputs a prediction of the deformation development trend for the next 24-72 hours through a fully connected network: ,in: It is the output prediction result. and These are the weights and biases of the output layer.

[0044] S422. A multi-task learning mechanism is used to train the prediction model. The main task predicts the evolution path of residual stress, while the auxiliary task simultaneously predicts the curvature change trend and modal frequency shift. The loss of the main task is the loss of the residual stress evolution path. The auxiliary task loss is the loss based on the curvature change trend. and the loss of modal frequency shift Total loss function: ,in: For the total loss, These are weighting coefficients; During training, a sliding window method is used to generate training samples, with a window size of 24 hours and a prediction step size of 72 hours.

[0045] S423. Introduce a physical constraint mechanism by embedding the mechanical equilibrium equations and material constitutive relations of the micro-cantilever beam as constraint conditions during model training: The stress-strain relationship is as follows: ,in: It is stress. It is the elastic modulus. It is strain; the loss term in the stress-strain relationship. ,in: It is the sample size. and These are the stress and strain predicted by the model, respectively. The stiffness-deformation relationship is: ,in: It's stiffness. It is a force. It is the amount of deformation; the loss term in the stiffness-deformation relationship. ,in: and These are the stiffness and deformation predicted by the model, respectively. These are known forces; The law of conservation of energy is: ,in: It is the amount of deformation. It is volume; the loss term of the law of conservation of energy. ,in: It is the known volume of the material; Incorporating physical constraints into the loss function using the Lagrange multiplier method: ,in: It is a Lagrange multiplier.

[0046] Depend on Figure 3 It can be seen that the architecture of the deformation trend prediction model is as follows: Input layer: Input multi-source time series data, including thickness distribution change sequence, residual stress redistribution sequence, local stiffness change sequence, ambient temperature sequence, and ambient humidity sequence.

[0047] Data preprocessing layer: Sliding window processing is used, including data standardization, unifying data scale, and eliminating the influence of units; missing value imputation, which fills in missing data based on time series interpolation; Outlier detection: Identify and process abnormal sensor readings.

[0048] LSTM network layer: A two-layer LSTM structure is adopted to capture features at different time scales, including LSTM hidden layer 1 (short-term feature extraction) and LSTM hidden layer 2 (long-term dependency modeling).

[0049] Attention mechanism layer: Time step attention calculation to evaluate the importance of each time step; key time point focus to highlight the key moments that affect the prediction; dynamic weight allocation to adaptively adjust the attention distribution according to the input sequence; temporal pattern enhancement to strengthen temporal features such as periodicity and trend.

[0050] Physical constraint embedding layer: The mechanical laws of the micro cantilever beam are used as soft constraints to embed into the model.

[0051] Multi-task prediction output layer: Employs a multi-task learning framework to simultaneously predict multiple key parameters.

[0052] S43. Based on the output of the deformation trend prediction model, generate a pre-compensation adjustment strategy: Increase the amount of material removed in advance in stress concentration areas. , ,in: It is the amount of raw material removed. This refers to the amount of material removed after adjustment in the stress concentration area. ; In areas with insufficient stiffness, reduce the amount of material removed and increase local annealing treatment. , ,in: This represents the adjusted material removal amount for areas with insufficient stiffness. It is a reduction in the proportion of material removed. The adjusted annealing time. It is an increase in the annealing process ratio. This is the original annealing time; The modal frequency shift direction is reversed to adjust the laser processing depth distribution. ,in: The adjusted modal frequencies, It is an adjustment factor. It is the modal frequency offset.

[0053] S44. After pre-compensation adjustment, apply multi-mode active excitation signals to the micro-cantilever beam again and output the current deformation state parameters of the micro-cantilever beam to verify the correction effect; calculate the deformation improvement rate by comparing the difference in dynamic response signals before and after pre-compensation: ,in: It is the initial stress. It is the adjusted stress; Different measures are taken based on the value of the deformation improvement rate: For deformation improvement rates below a certain threshold... The pre-compensation parameters were readjusted, and the deformation improvement rate reached [percentage missing]. Fine-tuning was performed, resulting in a deformation improvement rate higher than [previous figure]. Correction confirmed.

[0054] S45. Establish an iterative optimization mechanism. The correction process is considered complete when the deformation of the micro-cantilever beam remains within a preset tolerance range in three consecutive verifications. The preset tolerance range includes: Non-uniformity of residual stress distribution : ,in: For residual stress non-uniformity, It is the average stress. These represent the maximum and minimum stress values, respectively; and the change in curvature. ; Modal frequency offsets : ,in: The frequency offset for each modal is denoted as . It is the nominal modal frequency; If any indicator exceeds the tolerance range, the forecast and pre-compensation adjustment will be carried out again.

[0055] A microcantilever beam deformation correction system for MEMS sensor output error, used to implement a method for correcting microcantilever beam deformation for MEMS sensor output error, comprising: The multi-mode active excitation control module is used to apply multi-mode active excitation signals containing different frequencies, phases, and amplitudes to the micro-cantilever beam; specifically, it includes: A digital signal generator used to simultaneously generate a fundamental frequency excitation signal, a second-order harmonic excitation signal, and a third-order coupled excitation signal; Phase control circuit, used to precisely control the phase difference between each excitation signal within the range of 45°-135°; An amplitude regulator is used to adjust the amplitude of each excitation component according to a ratio of 1:(0.3-0.5):(0.1-0.3); The drive mode switching unit is used to support automatic switching between three drive modes: electrostatic drive, piezoelectric drive, and electromagnetic drive.

[0056] The dynamic response acquisition and processing module is used to acquire the dynamic response signal of the micro-cantilever beam under the multi-mode active excitation and extract response feature parameters; specifically, it includes: A piezoresistive sensing unit array is arranged at the root of the microcantilever beam to detect the strain distribution of the microcantilever beam. An electrostatic sensing electrode array covers the surface of a microcantilever beam to measure the displacement distribution of the microcantilever beam. Digital signal processors are used to execute signal denoising, separation, and feature enhancement algorithms in real time. The characteristic parameter calculation unit is used to automatically calculate characteristic parameters such as resonant frequency shift, modal shape change, and coupling strength coefficient.

[0057] The deformation recognition and state assessment module is used to input the response feature parameters into a pre-trained deformation recognition model and output the current deformation state parameters of the micro-cantilever beam; specifically, it includes: GPU computing units are used to accelerate the inference process of deep neural network models; Model storage unit, used to store deformation recognition models pre-trained with limited metadata; The parameter calculation unit is used to output residual stress distribution cloud map, curvature change and modal frequency offset; The model update interface is used to support incremental learning and parameter optimization of the model.

[0058] The laser micromachining control module is used to generate corresponding laser micromachining parameters based on the current deformation state parameters and control the laser processing process; specifically, it includes: Multi-mode laser source, integrating nanosecond, femtosecond and continuous laser modes, to meet the processing needs of different materials; A three-dimensional motion platform is used to achieve spiral progressive scanning path control; Temperature monitoring system is used to detect the temperature distribution in the processing area in real time; The parameter adjustment unit is used to adaptively adjust the processing parameters such as laser power, scanning speed, and pulse frequency.

[0059] The deformation trend prediction and pre-compensation module is used to establish a deformation trend prediction model and generate a pre-compensation strategy based on the changes in the structural parameters of the micro-cantilever beam after material removal or annealing; specifically, it includes: LSTM prediction model unit, used to perform 24-72 hour deformation trend prediction; A multi-task learning framework for simultaneously predicting stress evolution, curvature changes, and frequency shifts; A physical constraint correction mechanism is used to correct prediction results based on mechanical laws.

[0060] The correction effect verification and iteration control module is used to verify the correction effect and control the iterative correction process after pre-compensation adjustment; specifically, it includes: The verification test execution unit is used to automatically execute the effect verification test after the correction. Improvement rate calculation unit, used to calculate the deformation improvement rate before and after pre-compensation; The indicator monitoring unit is used to monitor key indicators such as residual stress non-uniformity, curvature change, and frequency offset. The iterative control logic unit is used to intelligently control the iterative correction process based on a preset threshold.

[0061] The system integration and data management module is used to coordinate data exchange and timing control between modules, and to store and manage system operation data; specifically, it includes: A distributed system architecture is used to coordinate data exchange and timing control between modules; The central database is used to store historical correction records, model parameters, and performance data; A graphical user interface for real-time display of correction progress and effect evaluation; A remote monitoring interface is used to support remote operation and fault diagnosis functions.

[0062] Example 1 1. Experimental Setup 1.1 Test Samples: Ten groups of MEMS gyroscope chips from the same batch were selected as test objects. All samples exhibited micro-cantilever beam deformation due to the manufacturing process. The samples were divided into two groups: the experimental group (5 chips) was corrected using the method of this invention, and the control group (5 chips) was corrected using the traditional circuit compensation method.

[0063] 1.2 Test environment: Temperature range: -40℃~+85℃, vibration environment: 10-2000Hz, 5gRMS, test duration: 500 hours of continuous accelerated life test.

[0064] 2. Experimental Methods 2.1 Experimental group implementation process: The following steps were performed according to the method of this invention: Step 1: Multi-mode active excitation, with excitation parameters set as follows: fundamental frequency excitation f1 = 12.5kHz, phase 0°, amplitude 1V; second harmonic excitation f2 = 34.8kHz, phase 90°, amplitude 0.4V; Third-order coupling f3 = 28.3kHz, phase 135°, amplitude 0.2V.

[0065] Step 2: Dynamic response acquisition. Vibration response data is acquired through a piezoresistive sensing array and electrostatic sensing electrodes at a sampling rate of 500 kS / s.

[0066] Step 3: Deformation identification. Using a pre-trained deep neural network model, identify the current deformation state: the residual stress distribution is a maximum compressive stress of 68 MPa and a maximum tensile stress of 42 MPa. The curvature change is 0.15%; the first-order modal frequency shift is +1.2%.

[0067] Step 4: Laser micromachining correction. The processing parameters are: laser power 2.5W and scanning speed 0.5mm / s in the high-pressure stress area; laser power 1.2W and scanning speed 1.2mm / s in the low-stress area; the total processing time is 45 minutes.

[0068] Step 5: Based on the LSTM model, predict the deformation trend in the next 72 hours and implement pre-compensation: increase the material removal amount by 12% in areas of expected stress concentration and decrease the material removal amount by 8% in areas of weak stiffness.

[0069] 2.2 Control Group Implementation Process Using traditional methods: circuit gain compensation is adjusted within a range of ±15%, temperature drift compensation is achieved by second-order polynomial fitting, and orthogonal error compensation is achieved by phase adjustment of ±5°.

[0070] 3. Test Results The effects of the method of this invention and the traditional method are compared in Table 1 below. Figure 4 As shown: Table 1: Comparison of Results The orthogonal error correction effect was tested at room temperature (25℃): the orthogonal error of the experimental group decreased from 52.8° / s before correction to 15.3° / s; the orthogonal error of the control group decreased only from 53.1° / s to 38.5° / s.

[0071] Temperature adaptability test: In the temperature cycling test from -40℃ to +85℃, the output change of the experimental group was ≤0.25° / s / ℃ across the entire temperature range; the output change of the control group reached 0.82° / s / ℃.

[0072] Long-term stability test results after 500 hours of accelerated life testing: the performance degradation rate of the experimental group was ≤4.2%; the performance degradation rate of the control group reached 18.5%.

[0073] 4. Results Analysis This invention corrects the deformation of microcantilever beams at the physical level, rather than through traditional signal-level compensation; it significantly improves long-term operational stability through trend prediction and pre-compensation mechanisms; it exhibits excellent stability across the entire temperature range; it successfully induces bending, torsion, and coupled vibrations to obtain richer deformation information; the deformation identification accuracy reaches ±5MPa, far exceeding traditional methods; it achieves micron-level precision in material removal and stress adjustment; and the deformation trend prediction accuracy reaches 92.3%.

[0074] 5. Conclusion This verification experiment fully demonstrates the effectiveness and superiority of the method of this invention. Compared with the prior art, this invention achieves significant improvements in several key performance indicators: orthogonality error is reduced by 69.5%, frequency stability is improved by 73.9%; long-term stability is improved by 77.3%, and temperature adaptability is improved by 75.3%; it is the first to achieve accurate identification and physical correction of micro-cantilever beam deformation; and it provides a reliable performance guarantee solution for high-precision MEMS sensors.

[0075] As can be seen from the above description, the embodiments of the present invention achieve the following technical effects: 1. Revolutionary Improvement in Detection and Recognition Accuracy: This invention achieves precise identification of the deformation state of micro-cantilever beams by combining a multi-mode active excitation mechanism with a deep learning recognition model, a feat unattainable by existing technologies. Specifically: By precisely matching the fundamental frequency excitation, second-order harmonic, and third-order coupled excitation (amplitude ratio 1:0.3-0.5:0.1-3), the multi-dimensional excitation signal design successfully excited the bending, torsional, and coupled vibration modes of a microcantilever beam, obtaining rich dynamic response information that cannot be obtained by traditional single-mode excitation. Experimental data show that this method improves the completeness of vibration characteristic parameter acquisition by more than 3 times.

[0076] The deep neural network recognition model is built based on large-scale finite element training data and adopts a multi-task learning framework, which can simultaneously and accurately output residual stress distribution, curvature change, and modal frequency shift. Practical verification shows that the model achieves an accuracy of ±5MPa in recognizing residual stress distribution and a sensitivity of 0.01% in detecting curvature change, far exceeding the limits of traditional optical measurement methods (typically ±20MPa and 0.05%).

[0077] This innovation enables the precise quantification of the micro-deformation state of the micro-cantilever beam for the first time, laying a solid foundation for subsequent accurate correction.

[0078] 2. Significantly enhanced long-term effectiveness and stability of the correction effect: The deformation trend prediction and pre-compensation mechanism introduced in this invention fundamentally solves the problem of short-lived effects in traditional correction methods, achieving long-term stable correction effects. The LSTM time series prediction model, based on changes in structural parameters after material removal or annealing, can accurately predict the deformation development trend of micro-cantilever beams over the next 24–72 hours. By embedding physical constraint mechanisms, the model ensures that the prediction results conform to mechanical laws, achieving a prediction accuracy of 92.3%.

[0079] The pre-compensation adjustment strategy proactively optimizes laser micromachining parameters based on prediction results. For example, it increases material removal by 5%–15% in areas of anticipated stress concentration and reduces material removal while adding localized annealing in areas of weak stiffness. This proactive correction allows the microcantilever beam to maintain its ideal state even after stress redistribution.

[0080] Long-term test data shows that the sensor corrected using this method has a performance degradation rate of only 4.2% in a 500-hour accelerated life test, while the sensor corrected using the traditional method has a degradation rate as high as 18.5%, representing an improvement of 77.3%.

[0081] 3. A major breakthrough in adaptive correction capabilities: The closed-loop iterative correction system of this invention realizes a fully automated detection-correction-verification process and possesses powerful adaptive capabilities. The real-time monitoring and dynamic adjustment mechanism continuously monitors the temperature field distribution and deformation state changes during laser micromachining. When the local temperature exceeds the material's critical annealing temperature, it automatically reduces the laser power or increases the scanning speed, effectively avoiding irreversible damage to the material's properties.

[0082] The intelligent iterative control logic is based on strict tolerance standards (residual stress distribution non-uniformity ≤5%, curvature change ≤0.08%, modal frequency offset ≤0.03%), and automatically terminates the correction process after three consecutive verifications that meet the standards. This mechanism ensures the consistency of the correction effect while preventing over-correction.

[0083] Multi-material adaptability is achieved through intelligent switching between nanosecond pulsed lasers (silicon-based), femtosecond pulsed lasers (metal composites), and continuous lasers (polymers), adapting to the processing needs of different material regions, with power density precisely controlled within 10²-10. 5 The appropriate range for W / cm².

[0084] The system demonstrated excellent stability in the full temperature range (-40℃ to +85℃), with the temperature drift decreasing from 0.85° / s / ℃ in the traditional method to 0.21° / s / ℃, an improvement of 75.3%, fully demonstrating its strong environmental adaptability.

[0085] In summary, the beneficial effects of this invention are not only reflected in the immediate improvement in accuracy, but also in the significant breakthroughs in long-term stability, environmental adaptability, and system intelligence, providing reliable technical support for the development of high-precision MEMS sensors.

[0086] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.

[0087] This invention is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this specification. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for correcting the deformation of a microcantilever beam in relation to the output error of a MEMS sensor, characterized in that, include: Multi-mode active excitation signals are applied to the microcantilever beam to induce a composite vibration mode that includes bending, torsion, and coupled vibrations. The dynamic response signal of the microcantilever beam under the multi-mode active excitation is collected, the response feature parameters are extracted, and the response feature parameters are input into the pre-trained deformation recognition model to output the current deformation state parameters of the microcantilever beam. Based on the current deformation state parameters, corresponding laser micromachining parameters are generated. By focusing the laser beam, selective material removal or annealing is performed on a specific area of ​​the microcantilever beam, and the stiffness distribution and stress state of the microcantilever beam are adjusted in real time. Based on the changes in structural parameters of the microcantilever beam after material removal or annealing, a deformation trend prediction model for the microcantilever beam is established to predict the deformation development trend of the microcantilever beam in subsequent working processes. Based on the prediction results, the laser micromachining parameters are pre-compensated and adjusted. After the pre-compensation adjustment, the operation is repeated to output the current deformation state parameters of the microcantilever beam to verify the correction effect until the deformation of the microcantilever beam reaches the preset tolerance range.

2. The method for correcting microcantilever beam deformation of MEMS sensor output error according to claim 1, characterized in that, The application of multi-mode active excitation signals to the microcantilever beam specifically includes: A fundamental frequency excitation signal is applied through the electrostatic driving electrode of the MEMS sensor. The frequency of the fundamental frequency excitation signal is determined according to the natural frequency of the first bending mode of the microcantilever beam, and is used to excite the basic bending vibration of the microcantilever beam. Based on the fundamental frequency excitation signal, a second harmonic excitation signal is superimposed. The frequency of the second harmonic excitation signal is determined according to the natural frequency of the torsional mode of the microcantilever beam, and is used to excite the torsional vibration of the microcantilever beam. A third-order coupled excitation signal is introduced, the frequency of which is determined according to the bending-torsional coupled mode frequency of the microcantilever beam, and is used to excite the composite vibration mode of bending and torsion. Adjust the phase difference between each excitation signal and set the amplitude ratio of each excitation signal.

3. The method for correcting microcantilever beam deformation of MEMS sensor output error according to claim 1, characterized in that, The process of acquiring the dynamic response signal of the microcantilever beam under multi-mode active excitation, extracting response feature parameters, and inputting these parameters into a pre-trained deformation recognition model to output the current deformation state parameters of the microcantilever beam specifically includes: Vibration response data of the microcantilever beam under the multi-mode active excitation are simultaneously collected by a piezoresistive sensing unit set at the root of the microcantilever beam and an electrostatic sensing electrode array distributed on the surface of the microcantilever beam. The collected vibration response data is preprocessed to extract multiple response feature parameters from the preprocessed signal; A deformation recognition model is constructed, and the extracted response feature parameters are normalized to form a feature vector, which is then input into the pre-trained deformation recognition model. The deformation recognition model analyzes and calculates the input feature vectors to output the current deformation state parameters of the microcantilever beam, including residual stress distribution cloud map, curvature change distribution, and modal frequency offsets.

4. The method for correcting microcantilever beam deformation of MEMS sensor output error according to claim 3, characterized in that, The extraction of multiple response feature parameters from the preprocessed signal specifically includes: Resonance frequency shift of each vibration mode ,in: It is the first one obtained by measurement The resonant frequency of the first vibration mode, It is the first micro-cantilever beam in its undeformed state. The nominal resonant frequency of the first vibration mode; Vibration mode shape change parameters ,in: It is the first one obtained by measurement The shape of the first vibration mode, It is the first micro-cantilever beam in its undeformed state. The nominal shape of the first vibration mode; Coupling strength coefficient between bending vibration and torsional vibration ,in: It is a displacement signal of bending vibration. It is the displacement signal of torsional vibration, where cov and var represent the covariance and variance, respectively; Variation in quality factor ,in: It is the quality factor obtained through measurement. It is the nominal quality factor of the micro-cantilever beam in its undeformed state; Nonlinear harmonic component amplitude ratio ,in: It is the amplitude of the nonlinear harmonic component. It is the amplitude of the fundamental frequency component; Phase difference of quadrature error signal ,in: It is the phase of the bending vibration signal. It is the phase of the torsional vibration signal.

5. The method for correcting microcantilever beam deformation of MEMS sensor output error according to claim 4, characterized in that, The construction of the deformation recognition model specifically includes: A parametric model of the micro cantilever beam was established using finite element analysis software. Different types of manufacturing defects and usage deformations were set in the model, including uneven thickness, uneven residual stress distribution, and changes in surface curvature, generating training samples containing tens of thousands of different deformation states. Construct a deep neural network structure, including an input layer, a feature fusion layer, a three-layer residual network module, and an output layer; The deep neural network is trained using a phased training strategy. First, it is pre-trained using large-scale finite element simulation data to optimize the initial weights of the network. Then, the network is fine-tuned using actual measured micro cantilever beam deformation data to improve the model's generalization ability in practical applications. An adversarial training mechanism is introduced during the training process. By generating difficult-to-identify boundary samples through a generative adversarial network, the robustness of the model to noise and outliers is enhanced. At the same time, an attention mechanism is adopted so that the network automatically focuses on the feature parameters most sensitive to deformation recognition. The model's recognition accuracy was evaluated using cross-validation, and the network hyperparameters were optimized.

6. The method for correcting microcantilever beam deformation of MEMS sensor output error according to claim 1, characterized in that, The process involves generating corresponding laser micromachining parameters based on the current deformation state parameters, selectively removing or annealing specific areas of the microcantilever beam using a focused laser beam, and adjusting the stiffness distribution and stress state of the microcantilever beam in real time. Specifically, this includes: Based on the residual stress distribution cloud map in the current deformation state parameters, the high-pressure stress region and low-pressure stress region on the surface of the microcantilever beam are identified, and the corresponding laser processing strategy is generated according to the magnitude and distribution characteristics of the residual stress. Based on the residual stress distribution and curvature change distribution, the scanning path and process parameters for laser micromachining are generated; The temperature field distribution and deformation state changes of the microcantilever beam are monitored in real time during laser processing, and the laser processing parameters are dynamically adjusted through a closed-loop feedback control system. Different laser processing parameters are used for microcantilever beams with different material regions; After each processing area is completed, the effect of material removal or annealing is evaluated by real-time vibration response data, and the processing parameters of subsequent areas are optimized based on the evaluation results to achieve adaptive optimization of the processing process.

7. The method for correcting the deformation of a microcantilever beam in MEMS sensor output error according to claim 1, characterized in that, Based on the changes in structural parameters of the microcantilever beam after material removal or annealing, a deformation trend prediction model for the microcantilever beam is established to predict its deformation development trend during subsequent operations. Based on the prediction results, pre-compensation adjustments are made to the laser micromachining parameters, specifically including: By using nanoindentation test points placed at key locations on the microcantilever beam and a digital image correlation measurement system, the structural parameter changes of the microcantilever beam after material removal or annealing are collected in real time, including changes in thickness distribution, redistribution of residual stress, local stiffness change rate, and ambient temperature and humidity. Based on the structural parameter change data, a deformation trend prediction model based on time series analysis is established. The current structural parameter changes, historical deformation data and environmental parameters are input into the deformation trend prediction model, and the model outputs the deformation development trend prediction of the micro-cantilever beam in the next 24-72 hours. Based on the output of the deformation trend prediction model, a pre-compensation adjustment strategy is generated.

8. The method for correcting microcantilever beam deformation of MEMS sensor output error according to claim 7, characterized in that, The step of repeatedly outputting the current deformation state parameters of the microcantilever beam after pre-compensation adjustment to verify the correction effect, until the deformation of the microcantilever beam reaches the preset tolerance range, specifically includes: After the pre-compensation adjustment, the multi-mode active excitation signal was applied to the micro-cantilever beam again, and the current deformation state parameters of the micro-cantilever beam were output to verify the correction effect; the deformation improvement rate was calculated by comparing the difference in dynamic response signals before and after pre-compensation. Different measures are taken based on the value of the deformation improvement rate; An iterative optimization mechanism is established. When the deformation of the microcantilever beam remains within the preset tolerance range in three consecutive verifications, the correction process is considered complete.

9. The method for correcting the deformation of a microcantilever beam in relation to the output error of a MEMS sensor according to claim 8, characterized in that, The establishment of the deformation trend prediction model for time series analysis specifically includes: Design a prediction model architecture based on a long short-term memory neural network, including an input layer, two LSTM hidden layers, an attention mechanism layer, and an output layer; The prediction model is trained using a multi-task learning mechanism. The main task predicts the evolution path of residual stress, while the auxiliary task simultaneously predicts the curvature change trend and modal frequency shift. A physical constraint mechanism is introduced, in which the mechanical equilibrium equations and material constitutive relations of the microcantilever beam are embedded as constraint conditions during model training.

10. A microcantilever beam deformation correction system for MEMS sensor output error, characterized in that, A microcantilever beam deformation correction method for implementing the output error of a MEMS sensor as described in any one of claims 1-9 includes: The multi-mode active excitation control module is used to apply multi-mode active excitation signals containing different frequencies, phases, and amplitudes to the microcantilever beam. The dynamic response acquisition and processing module is used to acquire the dynamic response signal of the microcantilever beam under the multi-mode active excitation and extract the response feature parameters. The deformation recognition and state assessment module is used to input the response feature parameters into the pre-trained deformation recognition model and output the current deformation state parameters of the micro cantilever beam. The laser micromachining control module is used to generate corresponding laser micromachining parameters based on the current deformation state parameters and control the laser processing process. The deformation trend prediction and pre-compensation module is used to establish a deformation trend prediction model and generate a pre-compensation strategy based on the changes in the structural parameters of the micro-cantilever beam after material removal or annealing. The correction effect verification and iteration control module is used to verify the correction effect and control the iterative correction process after the pre-compensation adjustment. The system integration and data management module is used to coordinate data exchange and timing control between modules, and to store and manage system operation data.

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