Silicon micro-resonant accelerometer noise suppression method and system based on improved auto-encoder

Abstract

The invention discloses a silicon micro-resonant accelerometer noise suppression method and system based on an improved auto-encoder. According to the method, output data with low typical random error parameter value and high signal-to-noise ratio of the accelerometer is screened out by using an Allan variance analysis method to serve as a training set, the data utilization rate is improved and the calculation complexity is reduced by adopting a mode of dynamically intercepting continuous intermediate data, and lightweight training is realized. The auto-encoder model adopts a two-stage training strategy: in the first stage, a high-quality input signal training model is used to reconstruct an original signal; in the second stage, a loss function introduces an output power spectral density constraint, so that a noise reduction result approaches to a reference sample frequency spectrum in a frequency domain, and typical random errors such as speed random walk, zero offset instability and acceleration random walk are optimized at the same time. The noise reduction result is verified through an Allan variance analysis method, and the method can remarkably reduce the output noise level of the accelerometer.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of MEMS accelerometers, and relates to a silicon micro resonant accelerometer signal noise suppression method based on deep learning, in particular to a silicon micro resonant accelerometer noise suppression method and system based on an improved autoencoder. BACKGROUND

[0002] The silicon micro resonant accelerometer is a new type of high-precision inertial device derived from the development of MEMS technology, and is the most mainstream navigation-level inertial device at present. The working principle thereof is that when an external acceleration acts, the size of the acceleration is sensed by detecting the change in the resonant frequency of a resonator. Compared with traditional inertial devices, the silicon micro resonant accelerometer has the advantages of a large range, a smaller size, lower power consumption, high reliability and low cost. However, in actual application, the output signal of the accelerometer is easily disturbed by noise (such as thermal noise, environmental high-frequency vibration noise, measurement quantization noise, etc.), resulting in an increase in acceleration measurement error. The Allan variance analysis method is used to quantitatively evaluate the statistical characteristics of the evolution of the above error with the average time.

[0003] Most of the factors causing the error of the silicon micro resonant accelerometer have randomness and uncertainty, and a mathematical expression can be obtained by using a statistical method and model identification theory to establish a random error model. Traditional noise reduction methods mainly rely on linear filtering technology or hardware compensation means, and have limitations. For example, Kalman filtering relies on an accurate noise model, the actual noise characteristics are complex and changeable, and model mismatch will cause the filtering effect to decrease; wavelet analysis needs to manually select a base function and a threshold, and has insufficient adaptability. Although the frequency measurement algorithms such as analog interpolation and continuous time stamp can improve the noise performance indicators to a certain extent, they need to rely on complex calculation logic to implement, which not only increases the calculation complexity of the system, but also brings a tedious debugging process, resulting in a high learning and implementation threshold. Although the optimized hardware scheme can suppress quantization noise, it needs to be additionally designed and customized, thereby increasing the debugging period and implementation cost.

[0004] In addition, the output signal of the silicon micro resonant accelerometer is a one-dimensional non-stationary time series, and the time-frequency domain aliasing characteristics of the noise and the effective signal thereof result in great limitations of traditional linear filtering methods. Therefore, it is urgent to develop a noise suppression method with self-characteristic extraction capability, low calculation complexity and without manual intervention. SUMMARY

[0005] The present application is just for the problems existing in the prior art, and provides a silicon micro resonant accelerometer noise suppression method and system based on an improved autoencoder. First, the Allan variance analysis method is used to screen output data with low typical random error parameter value and high signal-to-noise ratio as an autoencoder training data set. The intermediate continuous segment data is dynamically intercepted to avoid data waste and reduce the amount of calculation, thereby realizing lightweight calculation. The method of the present application also trains the autoencoder noise reduction model in two steps. The input data is reconstructed as much as possible under the condition of external environmental disturbance, and the accelerometer output power spectral density term is introduced into the loss function in the second stage to guide the autoencoder to approximate the spectral distribution of the reference low-noise sample in the frequency domain while reconstructing the signal, and to optimize the typical noise index term of the accelerometer. The method of the present application does not need artificial labeling of noise disturbance data, and the typical random error term of the accelerometer analyzed by the Allan variance method after noise reduction is significantly reduced, which can effectively suppress the noise of the output signal of the accelerometer.

[0006] To achieve the above purpose, the technical scheme adopted by the present application is: a silicon micro resonant accelerometer noise suppression system based on an improved autoencoder, at least comprising a data preprocessing module, an autoencoder noise reduction module and a performance verification module,

[0007] The data preprocessing module: uses the Allan variance analysis method to screen output data with low typical random error parameter value and high signal-to-noise ratio of the accelerometer as sample training data of the autoencoder model, normalizes the sample training data, and dynamically calculates the midpoint to intercept the data in the middle continuous data segment as the training data of the autoencoder model;

[0008] The autoencoder noise reduction module: includes an autoencoder noise reduction model comprising an encoder and a decoder, and trains the autoencoder noise reduction model in two stages. The loss function of the first stage is mean square error, and the sample training data of the data preprocessing module is used as the input of the noise reduction model. The power spectral density constraint term of the accelerometer is introduced into the loss function of the second stage;

[0009] The performance verification module: checks whether the data meets the input requirements of the autoencoder noise reduction model, then performs dynamic interception processing, and reduces the noise of the verification data through the autoencoder, to verify the actual noise reduction capability of the model. The verification index includes but is not limited to the typical random error (such as velocity random walk, zero bias instability, acceleration random walk, etc.) based on Allan variance analysis before and after noise reduction; the precision index (such as root mean square error RMSE); and the signal quality index (such as signal-to-noise ratio SNR).

[0010] As an improvement of the present invention, in the autoencoder denoising model, the encoder sequentially includes an input layer, a fully connected layer, and a ReLU layer, and the decoder sequentially includes a fully connected layer, a ReLU layer, and an output layer. The input layer receives the data normalized by the data preprocessing module, the encoder encodes the input data into a low-dimensional representation, and the nonlinear activation layer uses the ReLU activation function to introduce nonlinearity into the model. The decoder decodes the low-dimensional representation back to the original input size through the fully connected layer, and then outputs the reconstructed data through the output layer.

[0011] As another improvement of the present invention, the calculation method of the verification indicators in the performance verification module is as follows: The verification indicators include at least Allan variance, typical random error of the accelerometer obtained by further analysis of Allan variance, root mean square error, and signal-to-noise ratio. The typical random error of the accelerometer includes velocity random walk, zero-bias instability, and acceleration random walk. The specific calculation methods for each indicator are as follows:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] in, To be at the sampling time Allan variance value, The root mean square error, For signal-to-noise ratio, For the Allan variance term corresponding to the velocity random walk, This represents the Allan variance term corresponding to zero-bias instability. Let N be the Allan variance term corresponding to the acceleration random walk, and let N, B, and K be the velocity random walk coefficient, the zero-bias instability coefficient, and the acceleration random walk coefficient, respectively. Indicates the accelerometer's first Group 1 One output acceleration data, Indicates the first Group Data, For the first The average value of the group's acceleration input data. The total number of data points. Indicates the first Training data for each sample, Indicates the first Noisy test data.

[0020] To achieve the above objectives, the present invention also adopts the following technical solution: a noise suppression method for silicon micro-resonant accelerometers based on an improved self-encoder, comprising the following steps:

[0021] S1: Acquire the raw output signal of the silicon micro-resonant accelerometer under static conditions at room temperature, and use the Allan variance analysis method to screen out the output data with low typical random error parameter values ​​and high signal-to-noise ratio of the accelerometer, which will be used as the target clean sample for training the autoencoder noise reduction model; the training sample data is obtained by splicing and merging multiple test data of the same accelerometer prototype.

[0022] S2: After normalizing the sample data obtained in step S1, the midpoint is dynamically calculated to extract the data within the continuous data segment in the middle as training data, with a data length of ≥3601 sampling points.

[0023] S3: Construct an autoencoder denoising model and train it in two stages. The loss function in the first stage is the mean square error, and the input is the sample training data. The loss function in the second stage introduces the accelerometer power spectral density constraint term to guide the autoencoder to optimize the accelerometer performance index while reconstructing the signal.

[0024] S4: Place the accelerometer in different test environments and use its output signal data as the validation data for the denoising model. After normalizing the validation data, input it into the trained autoencoder denoising model, and compare the output results after inverse normalization to verify the denoising effect of the model.

[0025] As an improvement to the present invention, the normalization process for the sample training data in step S2 specifically includes:

[0026]

[0027] Wherein, trainData is a set of training sample data points containing each acceleration, formed by merging different cell arrays; trainMean is the arithmetic mean of all data points in this set; and trainStd is the standard deviation of all data points in this set.

[0028] As another improvement of the present invention, the method for dynamically calculating the midpoint to extract data within a continuous intermediate data segment is specifically as follows:

[0029] Starting Index End of index

[0030] Where L is the total data length and N is the target truncation length.

[0031] As another improvement of the present invention, the loss function of the first stage of the autoencoder denoising model is the mean square error (MSE), specifically:

[0032]

[0033] in For the corresponding sample training data points, Let N be the i-th data point output by the autoencoder, and N be the total length of the data input to the autoencoder.

[0034] As another improvement of the present invention, the loss function of the second stage of the autoencoder denoising model is specifically as follows:

[0035]

[0036] Where α and β are the weighting coefficients of the mean square error and the power spectral density, and satisfy the normalization condition α + β = 1. For the corresponding sample training data, the first Data points, The first output after noise reduction by the self-encoder Data points, This represents the total number of discrete frequency points involved in the power spectral density calculation. The total length of the input data to the autoencoder. and The training signal and the autoencoder output signal are respectively represented at the 1st... Power spectral density values ​​at discrete frequency points; power spectral density and The calculation formula is: ;

[0037] in This represents the signal length (number of sampling points). For the nth value of the sample training data, Let be the output signal value of the nth autoencoder. Introducing power spectral density into the loss function can constrain the energy distribution of the denoised signal, preventing the autoencoder from losing important frequency domain structural features by only optimizing MSE. Allan variance is the mainstream time-domain index for inertial device noise analysis, but it is essentially equivalent to the weighted integral of power spectral density under different window functions (frequency domain representation). Therefore, directly introducing PSD constraints into the loss function is a frequency-domain equivalent method for optimizing Allan variance.

[0038] As a further improvement of the present invention, the training of the autoencoder denoising model also includes an L2 regularization method to improve the denoising model. For the weight matrix W of the model, the L2 regularization term is defined as follows: ,in It is a hyperparameter of regularization strength, which can be adjusted by... The value is optimized to improve the generalization ability of the denoising model.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] (1) This invention adopts a dynamic data segment extraction technology. Based on the characteristics of signal data, an adaptive data segment extraction algorithm is constructed, which can flexibly adapt to input signal data of different lengths. Through the automatic analysis and screening of data segments by the algorithm, the stable region in the data is accurately located and extracted, avoiding the tedious process and subjective error of manual data annotation. At the same time, based on the lightweight computing architecture design, the consumption of computing resources and processing time costs are reduced, and efficient and accurate noise reduction processing is achieved.

[0041] (2) The present invention standardizes the input data through normalization, eliminating the need to introduce random noise during training. It dynamically adjusts the training parameters according to the data distribution, which significantly improves the model's adaptability to different data distribution characteristics.

[0042] (3) The model constructed by this invention can complete the training process in a shorter time, effectively preserve the temporal continuity characteristics of the one-dimensional acceleration output signal, and ensure that the temporal characteristics of the signal are not destroyed. Compared with the prior art, the noise reduction method of this invention exhibits unique effectiveness and reliability.

[0043] (4) This invention introduces a power spectral density (PSD) constraint term into the loss function of the second stage of autoencoder training, incorporating frequency domain characteristics into the optimization objective and guiding the model output signal to approximate the low-noise reference sample in terms of spectral distribution. Considering that Allan variance can be regarded as the integral of PSD under a specific window function, this method can effectively improve typical random errors of accelerometers such as velocity random walk, zero-bias instability, and acceleration random walk. Compared with traditional optimization methods based solely on time domain errors, frequency domain constraints have stronger globality and specificity, which helps to improve signal stability and measurement accuracy. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the neural network structure of the autoencoder noise reduction model in the system of the present invention;

[0045] Figure 2 This is a flowchart illustrating the steps of the noise suppression method for silicon microresonant accelerometers based on an improved self-encoder according to the present invention.

[0046] Figure 3 This is a double logarithmic curve of the Allan standard deviation of the random error term of the accelerometer in Embodiment 2 of the present invention. Detailed Implementation

[0047] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0048] Example 1

[0049] The silicon microresonant accelerometer noise suppression system based on the improved autoencoder automatically extracts signal features through an unsupervised deep learning model, suppresses noise interference, improves frequency measurement accuracy and system stability, and reduces computational resource consumption to meet real-time requirements.

[0050] This system aims to achieve the following objectives: unsupervised feature extraction, i.e., extracting essential features of noise and effective acceleration information directly from one-dimensional time-series signals without manual data labeling; adaptive noise reduction, enabling the model to adapt to environmental noise of varying intensities; and a lightweight design that optimizes the neural network structure and hardware deployment to meet the low-latency real-time output and low logic unit occupancy requirements of the FPGA platform. Therefore, this invention's silicon microresonator accelerometer noise suppression system based on an improved autoencoder consists of three core modules: a data preprocessing module, an autoencoder noise reduction module, and a performance verification module. The frequency measurement algorithms for both the sample dataset and the verification dataset of the silicon microresonator accelerometer employ a multi-cycle synchronous counting method.

[0051] The data preprocessing module uses Allan variance analysis to select output test data with low typical random error parameter values ​​and high signal-to-noise ratio from the accelerometer as sample training data for the autoencoder model. The sample training data is then normalized, and the midpoint is dynamically calculated to extract data from the middle continuous data segment as training data.

[0052] The autoencoder denoising module includes an autoencoder denoising model comprising an encoder and a decoder. The model is trained in two stages. In the first stage, the loss function is the mean squared error (MSE), and the input is the sample training data. In the second stage, the loss function incorporates an accelerometer power spectral density (PSD) constraint term, directly improving the noise characteristic parameters of Allan variance analysis by optimizing the PSD. The autoencoder denoising model used in this invention has a one-dimensional time series input, requiring the preservation of feature representation while avoiding information loss. The ReLU function is chosen for the activation layer to enhance nonlinearity, and the output layer uses the mean squared error (MSE) loss function to reconstruct the input. Its typical network configuration is as follows: Figure 1 As shown.

[0053] In the autoencoder denoising model, the encoder consists of an input layer, a fully connected layer, and a ReLU layer, while the decoder consists of a fully connected layer, a ReLU layer, and an output layer. The input layer receives normalized data with an input size of 1, representing one-dimensional time series data. The encoder layer encodes the input data into a low-dimensional representation with a size of 10 layers. The nonlinear activation layer uses the ReLU activation function to introduce nonlinearity into the model. The decoder layer decodes the low-dimensional representation back to the original input size through the fully connected layer. The output layer uses a regression layer to output the reconstructed data.

[0054] The performance verification module checks whether the data meets the input requirements of the autoencoder denoising model, then performs dynamic truncation processing, and denoises the verification data through the autoencoder to verify the actual denoising capability of the model. The verification indicators include, but are not limited to, typical random errors based on Allan variance analysis before and after denoising (such as velocity random walk, zero-bias instability, acceleration random walk); accuracy indicators (such as root mean square error RMSE); and signal quality indicators (such as signal-to-noise ratio SNR).

[0055] Example 2

[0056] A noise suppression method for silicon microresonant accelerometers based on an improved self-encoder, using the system described in Example 1, specifically as follows: Figure 2 As shown, it includes the following steps:

[0057] Step S1: Under a controlled temperature and humidity environment with minimal external interference, the raw 1Hz output signal of the silicon micro-resonator accelerometer was repeatedly acquired at room temperature static conditions (±0g, ±1g). Allan variance analysis was used to select output data with low typical random error parameter values ​​and high signal-to-noise ratios for use as clean sample data for training the autoencoder denoising model.

[0058] The accelerometer under test is fixed using fixtures to ensure its stability and controllable installation error during testing. The customized fixture with the fixed accelerometer is then mounted on a high-precision single-axis turntable, enabling accurate performance testing of the accelerometer. To effectively isolate the test results from interference from external high-frequency vibrations, the test platform must be installed on a vibration-isolated foundation, providing a stable physical basis for the test. This embodiment is conducted in a standard test environment with a controlled indoor temperature of approximately 25°C and RH of 40% (strict temperature and humidity control is not required for verification data acquisition). The acquired test data exhibits high reliability and low interference, providing a high-quality and effective sample dataset for the subsequent construction and optimization of the noise reduction model.

[0059] The turntable was operated to keep the accelerometer input shaft horizontal (+0g), while maintaining a constant temperature in the chamber throughout the experiment to effectively suppress the impact of ambient temperature drift on the test results. During this stage, the accelerometer was only powered on, without any output data acquisition. Half an hour after power-on, 1Hz output data was acquired for one hour, after which the power was turned off and the output data was saved. This stage aimed to minimize temperature drift caused by the accelerometer's internal temperature due to power-on heating, and to eliminate interference introduced by sudden environmental changes or transient circuit responses at the beginning and end of the signal. The above process was repeated to obtain multiple sets of experimental data as a training dataset.

[0060] One hour after data collection, the accelerometer was powered off, and the output acceleration data was saved. This process was repeated multiple times. Accelerometer output test data with low typical random error parameter values ​​and high signal-to-noise ratios, selected using Allan variance analysis, were used as clean sample data for the autoencoder target.

[0061] Step S2: After normalizing the sample data obtained in step S1, dynamically calculate the midpoint and use the data within the continuous data segment in the middle as training data, with a data length of ≥3601 sampling points.

[0062] For data collected after controlling the test environment, the midpoint position is dynamically calculated to extract the middle data segment, avoiding interference introduced at the beginning and end of the signal due to sudden environmental changes or transient circuit response.

[0063] In the autoencoder noise reduction module, the cell array stores multiple training datasets. This cell array is formed by splicing and merging the raw acceleration signals generated by the same accelerometer prototype in different rounds of experiments, where each cell element corresponds to the raw acceleration signal of one experiment.

[0064] Based on the merged acceleration training data `trainData`, its mean `trainMean` and standard deviation `trainStd` are calculated accordingly. Then, the obtained mean and standard deviation are used to normalize the training data. This normalization aims to enhance the model's generalization ability, ensuring stable and good noise reduction performance under different scenarios and data inputs. The normalization calculation formula is as follows:

[0065]

[0066] To adapt to the specific requirements of the autoencoder model for input data length while reducing computational load, this invention employs a dynamic data segment extraction method. This method effectively avoids transient noise interference generated during the accelerometer startup phase by calculating the midpoint position of the data sequence. Based on the design requirements of the autoencoder model, a minimum data length of 3601 data points is pre-set. After obtaining the total length of the normalized data, the start and end indices of the data segments are dynamically calculated based on the aforementioned minimum data length requirement. This index calculation mechanism accurately extracts intermediate data segments from the normalized data, thereby forming training data that conforms to the model input specifications, ensuring efficient and accurate model training. In the field of MEMS inertial devices, Allan variance is an important time-domain analysis method for evaluating the stability of frequency sources (such as the operating frequency of an accelerometer resonator). This method effectively quantifies the short-term fluctuations and random noise characteristics of data by calculating the squared average of the frequency differences within adjacent time intervals. Furthermore, performing Allan variance analysis on the MEMS accelerometer output signal and plotting its double logarithmic curve as a function of average time can effectively distinguish and calculate random noise components with different characteristics. Among them, bias instability (BI), velocity random walk (VRW), and acceleration random walk (ARW) are the three most significant sources of random error in the output signal of silicon micro-resonant accelerometers. Allan variance is the time period. The functions, different The corresponding Allan variance is used to analyze the characteristics of noise in different frequency bands. Therefore, the proportion of each typical error component before and after noise reduction can be intuitively obtained from its double logarithmic curve. Figure 3 The graph shows the Allan standard deviation of the random noise term of the accelerometer in a double logarithmic curve. The zero-bias instability corresponds to the segment with a slope of 0 in the double logarithmic curve, which is the minimum value position in the double logarithmic curve; the velocity random walk corresponds to the segment with a slope of -0.5 in the double logarithmic curve; and the acceleration random walk corresponds to the segment with a slope of 0.5 in the double logarithmic curve.

[0067] Step S3: Construct an autoencoder denoising model and train it in two stages. The loss function in the first stage is the mean square error. The sample training data obtained in step S2 is used as input for training. The power spectral density constraint term of the accelerometer is introduced into the loss function in the second stage to guide the autoencoder to optimize the accelerometer performance index while reconstructing the signal.

[0068] In the first stage, the sample training data is used as the input to the autoencoder model. The autoencoder model aims to reconstruct the sample training data and minimize the mean square error (MSE) between the input data and the reconstructed data in order to learn the original characteristics of the accelerometer output signal.

[0069] The truncated data segment `trainDataProcess` is used as input and target `x` to train the autoencoder model. By minimizing the error between the input data `x` and the reconstructed data `x'`, the model is ensured to accurately reconstruct the input data under conditions of minimal external interference. The training objective is to teach the autoencoder to perform an identity mapping on the input signal, thereby learning the signal's fundamental characteristics. The first stage ensures that the autoencoder network establishes a correct signal mapping relationship, making the performance optimization of the accelerometer prototype more effective in the second stage. The loss function chosen for the first stage is the mean squared error (MSE), calculated using the following formula:

[0070]

[0071] In the second stage, a power spectral density constraint term from the accelerometer is introduced into the loss function. (Allan variance) With the power spectral density present in the inherent random process There are fixed relationships The Allan variance is essentially the integral of the power spectral density under a specific window function. By adjusting the noise energy distribution in different frequency bands, the random noise characteristics of the accelerometer can be optimized overall. The significant advantages of this scheme are: firstly, it directly intervenes in the energy distribution dimension from the physical nature of noise, providing a more efficient control mechanism compared to traditional time-domain constraint methods; secondly, it can simultaneously manage multiple types of random error indicators through a single constraint term, avoiding the complexity of manually adjusting multiple parameters and reducing the computational load for noise reduction. Compared to the computational complexity of Allan variance (O(N²), the computational complexity of power spectral density is only O(NlogN), significantly reducing the computational burden and meeting the application requirements of lightweight and efficient implementation for noise reduction algorithms. The specific expression of its improved loss function is:

[0072]

[0073] Where α and β are the weighting coefficients of the mean square error and the power spectral density, and satisfy the normalization condition α + β = 1. For the corresponding sample training data points, The first output after noise reduction by the self-encoder Data points, This represents the total number of discrete frequency points involved in the power spectral density calculation. The total length of the input data to the autoencoder. and The training signal and the autoencoder output signal are respectively represented at the 1st... The power spectral density values ​​at discrete frequency points.

[0074] Power spectral density and The calculation formula is: ;

[0075] in This represents the signal length (number of sampling points). For the nth value of the sample training data, This is the output signal value of the nth autoencoder.

[0076] To enhance the generalization ability of the denoising model and avoid overfitting, L2 regularization is introduced during the training phase. By adding a sum-of-squares term to the loss function, large weight values ​​are penalized, thus encouraging the model to learn smoother decision boundaries. Overfitting leads to a model performing well on training data but exhibiting poor generalization ability on unseen data. An L2 regularization term is introduced into the loss function of the deep learning model, and this term is proportional to the sum of squares of the model weights. For the model's weight matrix W, the L2 regularization term is defined as... ,in This is a hyperparameter for regularization strength. The hyperparameter is adjusted during model training. The value controls the contribution of the L2 regularization term to the loss function, so as to achieve a better noise reduction effect.

[0077] Step S4: Place the accelerometer in different test environments and use its output signal data as the validation data for the denoising model. After normalizing the validation data, input it into the trained autoencoder denoising model, and compare the output results after inverse normalization to verify the denoising effect of the model.

[0078] The testing environment for the validation data should meet standard indoor temperature and humidity conditions. The accelerometer and its test platform should be placed on a marble table to isolate them from high-frequency external vibrations. The performance validation module will first check whether the data length meets the model input requirements. Then, dynamic truncation processing will be performed, and the validation data will be denoised using an autoencoder to verify the model's actual denoising capability. Typical random errors of the accelerometer (such as velocity random walk, zero-bias instability, acceleration random walk, etc.) based on Allan variance analysis before and after denoising will be calculated; accuracy indicators (such as root mean square error RMSE); and signal quality indicators (such as signal-to-noise ratio SNR) will be calculated to provide objective evidence for evaluating the model's denoising performance.

[0079] The specific calculation methods for velocity random walk, zero-bias instability, acceleration random walk, and signal-to-noise ratio (SNR) based on Allan variance analysis involved in this embodiment are as follows:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] in, To be at the sampling time Allan variance value, For signal-to-noise ratio, For the Allan variance term corresponding to the velocity random walk, This represents the Allan variance term corresponding to zero-bias instability. Let N be the Allan variance term corresponding to the acceleration random walk, and let N, B, and K be the velocity random walk coefficient, the zero-bias instability coefficient, and the acceleration random walk coefficient, respectively. Indicates the accelerometer's first Group 1 One output acceleration data, Indicates the first Group Data, For the first The average value of the group's acceleration input data. The total number of data points. Indicates the first Training data for each sample, Indicates the first Noisy test data.

[0087] During the verification phase, noisy output signals from silicon microresonator accelerometers under different test environments were used as inputs. This invention employs root mean square error (RMSE) and signal-to-noise ratio (SNR) as quality evaluation indicators for the denoised signal to quantitatively assess its noise reduction performance. A higher SNR value indicates lower noise content in the denoised signal; a lower RMSE value indicates smaller error between the denoised signal and the original clean signal.

[0088] Compared to traditional filtering and noise reduction methods, autoencoders offer significant advantages in handling abrupt changes and high-frequency periodic interference signals. Autoencoder neural networks can learn the complex characteristics and patterns of accelerometer output signals, rapidly responding to abrupt changes and effectively removing high-frequency periodic interference signals. Furthermore, autoencoders can minimize the error between the input signal and the reconstructed signal through training, thereby improving the quality of signal reconstruction.

[0089] In summary, the self-encoder noise reduction scheme proposed in this invention can effectively suppress noise while preserving the effective characteristics of the original output signal of the silicon microresonator accelerometer, resulting in a clear, stable signal waveform and high transmission quality. Through parameter adjustment, various indicators obtained using Allan variance analysis are significantly improved, resulting in a high signal-to-noise ratio (SNR) for the accelerometer output signal, with a clear and stable waveform. The noise reduction model of this invention has low computational cost during training, strong generalization ability, and can effectively reduce the typical random error term of the accelerometer output signal.

[0090] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A noise suppression system for a silicon microresonant accelerometer based on an improved self-encoder, characterized in that, It includes at least a data preprocessing module, an autoencoder noise reduction module, and a performance verification module. The data preprocessing module selects output data with low typical random error parameter values ​​and high signal-to-noise ratio by using Allan variance analysis to filter them out as sample training data for the autoencoder model. It then normalizes the sample training data and dynamically calculates the midpoint to extract data from the middle continuous data segment as training data. The autoencoder denoising module includes an autoencoder denoising model containing an encoder and a decoder, and trains the autoencoder denoising model in two stages. The loss function in the first stage is the mean squared error, and the sample training data from the data preprocessing module is used as the input to the denoising model. The second-stage loss function introduces an accelerometer power spectral density constraint term; The performance verification module checks whether the data meets the input requirements of the autoencoder denoising model, then performs dynamic truncation processing, and denoises the verification data through the autoencoder to verify the actual denoising capability of the model; the verification indicators include, but are not limited to: Allan variance, typical random error parameters of accelerometer, accuracy indicators, and signal quality indicators.

2. The silicon microresonant accelerometer noise suppression system based on an improved self-encoder as described in claim 1, characterized in that: In the autoencoder denoising model, the encoder consists of an input layer, a fully connected layer, and a ReLU layer, while the decoder consists of a fully connected layer, a ReLU layer, and an output layer. The input layer receives the normalized data from the data preprocessing module, the encoder encodes the input data into a low-dimensional representation, and the nonlinear activation layer uses the ReLU activation function to introduce nonlinearity into the model. The decoder uses a fully connected layer to restore the low-dimensional representation to data of the same dimension as the original input, and then outputs the reconstructed result through the output layer.

3. The silicon microresonant accelerometer noise suppression system based on an improved self-encoder as described in claim 1, characterized in that: Among the verification metrics of the performance verification module, typical random errors of the accelerometer include velocity random walk, zero-bias instability, and acceleration random walk. Signal quality metrics include at least the signal-to-noise ratio. The specific calculation methods for each metric are as follows: ； ； ； ； ； ； ； in, To be at the sampling time Allan variance value, The root mean square error, For signal-to-noise ratio, For the Allan variance term corresponding to the velocity random walk, This represents the Allan variance term corresponding to zero-bias instability. Let N be the Allan variance term corresponding to the acceleration random walk, and let N, B, and K be the velocity random walk coefficient, the zero-bias instability coefficient, and the acceleration random walk coefficient, respectively. Indicates the accelerometer's first Group 1 One output acceleration data, Indicates the first Group Data, For the first The average value of the group's acceleration input data. The total number of data points. Indicates the first Training data for each sample, Indicates the first Noisy test data.

4. A noise suppression method for silicon microresonant accelerometers based on an improved self-encoder, characterized in that, Includes the following steps: S1: Collect the raw output signal of the silicon micro-resonant accelerometer under normal temperature static conditions, and use the Allan variance analysis method to screen out the output data with low typical random error parameter values ​​and high signal-to-noise ratio of the accelerometer as sample training data for the autoencoder noise reduction model; the sample data is spliced ​​and merged from data segments obtained from multiple tests of the same accelerometer prototype. S2: After normalizing the sample data obtained in step S1, dynamically calculate the midpoint to extract data within the middle continuous data segment, with a data length ≥ 3601 sampling points. S3: Construct an autoencoder denoising model and optimize it using a phased training method; In the first stage, the loss function is selected as mean square error (MSE), and the sample training data obtained in step S2 is used as the input of the denoising model to train the model to reconstruct the original signal; In the second stage, the power spectral density constraint term of the accelerometer output signal is introduced into the loss function to make the denoising result approximate the spectrum distribution of the reference sample in the frequency domain characteristics, and at the same time optimize the typical random error of the accelerometer. S4: Place the accelerometer in different test environments and use its output signal data as the validation data for the denoising model. After normalizing the validation data, input it into the trained autoencoder denoising model, and compare the output results after inverse normalization to verify the denoising effect of the model.

5. The noise suppression method for silicon microresonant accelerometers based on an improved self-encoder as described in claim 4, characterized in that: The normalization process for the sample training data in step S2 specifically involves: ； Wherein, trainData is a set of training sample data points containing each acceleration, formed by merging different cell arrays; trainMean is the arithmetic mean of all data points in this set; and trainStd is the standard deviation of all data points in this set.

6. The noise suppression method for silicon microresonant accelerometers based on an improved self-encoder as described in claim 4, characterized in that: The method for dynamically calculating the midpoint to extract data within a continuous data segment is as follows: Starting Index End of index ; Where L is the total data length and N is the target truncation length.

7. The noise suppression method for silicon microresonant accelerometers based on an improved self-encoder as described in claim 4, characterized in that: The loss function of the first stage of the autoencoder denoising model is the mean squared error (MSE), specifically: ； in For the corresponding sample training data points, Let be the i-th data point output after noise reduction by the autoencoder, and N be the total length of the data input to the autoencoder.

8. The noise suppression method for silicon microresonant accelerometers based on an improved self-encoder as described in claim 7, characterized in that: The loss function for the second stage of the autoencoder denoising model is as follows: ； Where α and β are the weighting coefficients of the mean square error and the power spectral density, and satisfy the normalization condition α + β = 1. For the corresponding sample training data points, The first output after noise reduction by the self-encoder Data points, This represents the total number of discrete frequency points involved in the power spectral density calculation. The total length of the input data to the autoencoder. and The training signal and the autoencoder output signal are respectively represented at the 1st... Power spectral density values ​​at discrete frequency points.

9. The noise suppression method for silicon microresonant accelerometers based on an improved self-encoder as described in claim 8, characterized in that: The sample training data and autoencoder output data at frequency points Power spectral density at and The calculation formula is: ; in For signal length, For the nth value of the sample training data, This is the output signal value of the nth autoencoder.

10. The noise suppression method for silicon microresonant accelerometers based on an improved self-encoder as described in claim 4, characterized in that: The training of the autoencoder denoising model also includes an L2 regularization method to improve the denoising model. For the model's weight matrix W, the L2 regularization term is defined as... ,in It is a hyperparameter of regularization strength, which can be adjusted by... The value is optimized to improve the generalization ability of the denoising model.

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