MEMS acceleration sensor ultra-low frequency weak vibration detection and adaptive compensation method

Abstract

A method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer includes: a multi-channel parallel coherent modulation and demodulation module acquiring differential capacitance signals of the sensitive units in the MEMS accelerometer through n parallel coherent detection links, and then synchronously modulating and coherently demodulating the differential capacitance signals to obtain n baseband signals; an adaptive weighted fusion module evaluating the signal-to-noise ratio (SNR) of each baseband signal, and then weighting and fusing the n baseband signals using the square of the SNR as a weighting coefficient to obtain a fused signal; a dynamic temperature drift compensation module performing temperature drift compensation on the fused signal to obtain a compensated signal; and a variational mode decomposition adaptive filtering module performing adaptive filtering on the compensated signal to output the final acceleration signal. The effect is to improve the detection of ultra-low frequency weak vibrations in a MEMS accelerometer and enhance the accuracy of wide-temperature-range dynamic temperature drift compensation.

Description

Technical Field

[0001] This invention relates to the field of MEMS accelerometer temperature compensation technology, and in particular to a method for detecting and adaptively compensating for ultra-low frequency weak vibrations in MEMS accelerometers. Background Technology

[0002] MEMS accelerometers, with their advantages of small size, low power consumption, low cost, and ease of integration, have been widely used in structural health monitoring (such as bridges, wind turbine blades, and precision machine tools), aerospace, autonomous driving, and industrial equipment fault diagnosis. However, as the requirements for vibration monitoring accuracy in high-end equipment continue to increase, existing MEMS accelerometer detection and signal processing technologies have revealed the following core technical bottlenecks, none of which can be systematically resolved by current solutions:

[0003] (1) The ability to detect ultra-low frequency weak vibrations is seriously insufficient.

[0004] Existing weak signal detection solutions for MEMS accelerometers mostly employ a single-channel capacitor-to-voltage conversion followed by direct filtering and amplification architecture. The 1 / f noise of these interface circuits deteriorates sharply in the ultra-low frequency band (<10Hz), resulting in a signal-to-noise ratio of less than 10dB for ultra-low frequency micro-vibrations below 5μg. The effective signal is completely drowned out by noise, failing to meet the μg-level detection requirements for health monitoring of large structures and micro-deformation monitoring of precision equipment. Existing coherent detection solutions can only suppress some carrier noise and cannot solve the problem of fusion suppression of multi-link random noise, offering limited performance improvement in the low-frequency band.

[0005] (2) Insufficient accuracy of dynamic temperature drift compensation over a wide temperature range

[0006] Most existing temperature drift compensation schemes are based on polynomial fitting of static calibration at room temperature, which can only compensate for static temperature drift with zero bias. They cannot cover sensitivity temperature drift and cross-axis coupling temperature drift over a wide temperature range (-40℃ to 125℃), nor can they adapt to dynamic temperature drift effects when the temperature changes rapidly. In wide temperature range scenarios such as outdoor, automotive, and aerospace applications, the measurement error of existing schemes generally exceeds 5% across the entire temperature range, exhibiting poor long-term stability and failing to meet the requirements for high-precision measurement.

[0007] (3) The strong binding between range and resolution cannot be overcome.

[0008] There is an inherent strong bond between the hardware range and resolution of MEMS accelerometers: high-range models have low resolution and cannot detect micro-vibrations; high-resolution models have small ranges and cannot withstand abnormal impacts, making them prone to signal saturation. Existing technologies cannot achieve adaptive compatibility between high-range impacts (±100g) and high-resolution micro-vibrations (μg level) without modifying the hardware structure. This means that a single sensor cannot simultaneously cover micro-vibration monitoring under normal operating conditions and impact capture under abnormal operating conditions, severely limiting its application scenarios.

[0009] (4) Existing technologies lack a systematic optimization solution for the entire supply chain.

[0010] Existing research focuses on single-point performance optimization, failing to coordinate the optimization of three core issues: weak signal low-noise detection, full-temperature-range dynamic compensation, and range adaptive adaptation. This makes it impossible to achieve a performance leap for MEMS accelerometers across all scenarios, temperature ranges, and dynamic ranges. Furthermore, the solutions have poor compatibility, require customized hardware design, and result in high industrialization costs and long development cycles. Summary of the Invention

[0011] The present invention provides a method for detecting and adaptively compensating for ultra-low frequency weak vibrations in MEMS accelerometers, which can improve the detection of ultra-low frequency weak vibrations in MEMS accelerometers and improve the accuracy of dynamic temperature drift compensation over a wide temperature range.

[0012] To achieve the above objectives, this invention provides a method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer, which, as a key feature, includes the following steps:

[0013] Step 1: Construct an ultra-low frequency weak vibration detection and adaptive compensation system for MEMS accelerometers. This ultra-low frequency weak vibration detection and adaptive compensation system is equipped with a multi-channel parallel coherent modulation and demodulation module, an adaptive weighted fusion module, a dynamic temperature drift compensation module, and a variational mode decomposition adaptive filtering module connected in sequence.

[0014] Step 2: The multi-channel parallel coherent modulation and demodulation module acquires the differential capacitance signal X of the sensitive unit in the MEMS accelerometer through n parallel coherent detection links, and then performs synchronous modulation and coherent demodulation on the differential capacitance signal X to obtain n baseband signals. , i∈[1,n], and sent to the adaptive weighted fusion module;

[0015] Step 3: The adaptive weighted fusion module evaluates and obtains the baseband signal for each path. signal-to-noise ratio Then with the aforementioned signal-to-noise ratio The square of is the weighting coefficient for n baseband signals. Weighted fusion is performed to obtain the fused signal. And send it to the dynamic temperature drift compensation module;

[0016] Step 4: The dynamic temperature drift compensation module applies the fused signal. Perform temperature drift compensation to obtain the compensated signal. And send it to the variational mode decomposition adaptive filtering module;

[0017] Step 5: The variational mode decomposition adaptive filtering module uses the variational mode decomposition algorithm (VMD) to process the compensated signal. Adaptive filtering is performed to output the final acceleration signal Y.

[0018] Through the above design, this invention achieves low-noise extraction of ultra-low frequency μg-level weak vibration signals by using a signal extraction architecture of multi-channel parallel coherent detection modulation and demodulation + signal-to-noise ratio weighted adaptive fusion, combined with VMD adaptive filtering; and improves the accuracy of dynamic temperature drift compensation over a wide temperature range through a dynamic temperature drift compensation module.

[0019] Preferably, the channel parallel coherent modulation and demodulation module is provided with an orthogonal carrier generation unit and n parallel coherent detection links, each of which is provided with a modulation unit, a programmable gain amplifier, an ADC sampling unit and a coherent demodulation unit connected in sequence.

[0020] The orthogonal carrier generation unit is used to generate n pairs of orthogonal carrier signals and transmit them to the modulation units of the n coherent detection links. The n carrier signals correspond one-to-one with the n coherent detection links.

[0021] The n coherent detection links are used to acquire the differential capacitance signal X, and then the differential capacitance signal X is synchronously modulated and coherently demodulated using the corresponding carrier signal to obtain n baseband signals. .

[0022] Each coherent detection link uses an independent orthogonal carrier signal, with the carrier frequency set to twice the resonant frequency of the MEMS sensitive unit to avoid the 1 / f noise inflection point frequency, typically set to 10kHz~50kHz; the n carriers are orthogonal to each other, and the differential capacitor signal X is synchronously modulated and coherently demodulated to shift the effective signal from the low frequency band to the high frequency carrier band, avoiding the influence of 1 / f noise.

[0023] Preferably, the adaptive weighted fusion module evaluation setup includes a real-time signal-to-noise ratio evaluation unit and an adaptive weighted signal fusion calculation unit connected in sequence.

[0024] The input terminals of the real-time signal-to-noise ratio evaluation unit and the adaptive weighted signal fusion calculation unit are respectively connected to the output terminals of the n coherent detection links, and are used to acquire the n baseband signals. ;

[0025] The real-time signal-to-noise ratio evaluation unit is used to evaluate each baseband signal obtained. signal-to-noise ratio The expression is:

[0026] ;

[0027] in, Let be the effective signal power of the i-th signal. Let be the noise power of the i-th signal; For the i-th signal in the i-th... The instantaneous amplitude at each sampling point The baseline estimate of the noise power of the i-th channel is obtained by noise statistics of the sensor in a stationary state or by real-time updates of high-frequency noise power. This is the index of the latest sampling point. The sliding window length is typically N=1024 or 2048, balancing real-time performance and estimation accuracy. For the first One sampling point, This represents the total average power of the i-th signal within the current window.

[0028] The adaptive weighted signal fusion calculation unit is used to calculate the signal-to-noise ratio. The square of is the weighting coefficient for n baseband signals. The weighted fusion calculation is expressed as follows:

[0029] ;

[0030] in, For the i-th baseband signal, For the i-th baseband signal The real-time signal-to-noise ratio, where n is the number of parallel channels and i is the channel index. This algorithm is used to fuse signals. It can significantly suppress uncorrelated random noise and residual 1 / f noise, thereby improving the signal-to-noise ratio of the effective signal.

[0031] Preferably, the dynamic temperature drift compensation module is provided with a temperature change rate calculation module, a temperature drift prediction module and an acceleration compensation module connected in sequence.

[0032] The temperature change rate calculation module is used to calculate the temperature change rate based on the real-time temperature data of the sensing unit in the MEMS accelerometer.

[0033] The temperature drift prediction module is used to predict the zero-bias compensation value of the MEMS accelerometer sensor based on the real-time temperature data, temperature change rate, and triaxial raw acceleration data of the MEMS accelerometer sensor's sensing unit. Sensitivity compensation coefficient and cross-axis coupling compensation matrix ;

[0034] The acceleration compensation module is used to calculate the zero-bias compensation value. Sensitivity compensation coefficient and cross-axis coupling compensation matrix For the fused signal Compensation is performed to obtain the compensated signal. .

[0035] The variational mode decomposition adaptive filtering module uses variational mode decomposition (VMD) to filter the compensated signal. Perform ultra-low frequency adaptive filtering, with preset mode number A=4~6 and penalty factor α=1000~3000, and then apply the compensation to the signal. Decompose into multiple Intrinsic Mode Functions (IMFs); calculate the relationship between each IMF and the original compensated signal. By using the Pearson correlation coefficient, noise modes and trend terms with correlation coefficients less than 0.1 are removed, and effective vibration modes are retained and the signal is reconstructed, ultimately achieving effective extraction of μg-level ultra-low frequency weak vibration signals.

[0036] As a preferred embodiment, the temperature drift prediction module has a built-in multi-output regression XGBoost temperature drift prediction model, which is used to simultaneously predict the true value of the zero-bias output, the true value of the sensitivity coefficient, and the true value of the cross-axis coupling coefficient.

[0037] The input feature vector of the multi-output regression XGBoost temperature drift prediction model is:

[0038] ;

[0039] in, This is the real-time temperature data of the sensitive unit at the current moment. The rate of temperature change at the current moment. This provides the current moment's raw triaxial acceleration data from the MEMS accelerometer.

[0040] The output vector of the multi-output regression XGBoost temperature drift prediction model is:

[0041] ;

[0042] in, The model outputs the true values ​​of the three-axis zero-bias predictions. The true values ​​of the triaxial sensitivity coefficients predicted by the model. The true values ​​of the triaxial cross-axis coupling coefficients predicted by the model;

[0043] The multi-output regression XGBoost temperature drift prediction model is an additive ensemble model, and the predicted value is obtained by accumulating the structure of k regression trees. The model prediction expression is:

[0044] ;

[0045] in, For the output vector The m-th element in the equation is the predicted true value of the m-th temperature drift parameter. For the input feature vector, Let be the mapping function for the j-th regression tree. For the function space of all regression trees, This represents the total number of regression trees;

[0046] The temperature drift prediction module calculates parameter compensation values ​​based on the true values ​​of the parameters predicted by the multi-output regression XGBoost temperature drift prediction model. The expression is as follows:

[0047] ;

[0048] ;

[0049] ;

[0050] in, The zero bias compensation value This is the sensitivity compensation coefficient. This is the cross-axis coupling compensation matrix. The true value matrix of cross-axis coupling predicted by the model The inverse matrix; It is a diagonal matrix.

[0051] Preferably, the acceleration compensation module calculates the zero-bias compensation value. Sensitivity compensation coefficient and cross-axis coupling compensation matrix For the fused signal The compensation is expressed as follows:

[0052] ;

[0053] in, This is a fused signal, i.e., a compensated input signal; The signal after compensation.

[0054] Preferably, the dynamic temperature drift compensation module is also connected to a temperature sensor, which is built into the sensitive unit of the MEMS accelerometer.

[0055] The dynamic temperature drift compensation module is also connected to the original acceleration output terminal of the MEMS accelerometer.

[0056] The temperature sensor is used to collect real-time temperature data of the sensitive unit in the MEMS accelerometer and provide it to the temperature change rate calculation module and the temperature drift prediction module.

[0057] The dynamic temperature drift compensation module uses a temperature sensor to collect the current temperature of the MEMS sensitive unit in real time at a frequency of 10Hz~50Hz, calculates the temperature change rate, inputs the feature values ​​into the pre-trained temperature drift prediction model, and outputs full parameter compensation values ​​in real time. It performs synchronous compensation for zero bias, sensitivity, and cross-axis coupling on the fused acceleration signal to eliminate dynamic temperature drift error in a wide temperature range.

[0058] The raw acceleration output terminal of the MEMS accelerometer is used to output triaxial raw acceleration data to the temperature drift prediction module.

[0059] Preferably, the dynamic temperature drift compensation module is also connected to an online adaptive calibration module, which is used to monitor the fused signal in real time. The variance of the fused signal The variance is less than a preset threshold for a continuous set time period, such as 10 seconds. When the MEMS accelerometer is determined to be stationary, online self-calibration is automatically triggered.

[0060] Preferably, the online adaptive calibration module uses the compensated signal from the current static state. Based on this, the Least Mean Square (LMS) algorithm is used to iteratively update the temperature drift compensation parameters; the iteration step size is set to 0.005~0.01 to avoid parameter jumps, correct model prediction errors, and improve the long-term stability of the sensor.

[0061] This invention employs a parameterized gradient descent iterative strategy for zero-bias compensation values. Sensitivity compensation coefficient and cross-axis coupling compensation matrix Each update rule is designed separately, and all updates are based on the minimum mean square error criterion (minimizing) It can be executed in real time in an embedded MCU without complex matrix inversion operations.

[0062] ① Zero bias compensation value Iterative updates:

[0063] Zero bias compensation value The update rule directly affects the compensated baseline offset:

[0064] ;

[0065] in, For the first The zero-bias compensation value of the next iteration The iteration step size, For the first Sensitivity compensation coefficient for the next iteration. For the first Cross-axis coupling compensation matrix of the next iteration. For the first The compensation error signal for the next iteration; For the first The transpose of the product of the sensitivity compensation coefficient and the cross-axis coupling compensation matrix in the next iteration is the gradient term of the LMS algorithm, ensuring that the iteration direction of zero bias compensation is consistent with the error descent direction.

[0066] ② Sensitivity compensation coefficient Iterative updates:

[0067] Sensitivity compensation coefficient Since the matrix is ​​diagonal, only the diagonal elements need to be updated. The update is performed iteratively along the X, Y, and Z axes, with the following update rules:

[0068] ;

[0069] ;

[0070] in, For the first The sensitivity compensation coefficient for the q-axis in the next iteration; For the first The q-axis compensation error signal in the next iteration; is the intermediate signal of the i-th axis after zero bias and cross-axis compensation, and is the gradient term of sensitivity compensation.

[0071] ③ Cross-axis coupling compensation matrix Iterative updates:

[0072] The update of the cross-axis coupling compensation matrix focuses on the six off-diagonal cross-coupling coefficients. The diagonal elements are fixed at 1 and do not need to be updated. The update is applied to the off-diagonal elements. H≠h, and its update rule is:

[0073] ;

[0074] ;

[0075] in, is the cross-coupling compensation coefficient between the h-axis and the H-axis in the r-th iteration; This is the H-axis compensation error signal for the r-th iteration; The h-th axis sensitivity compensation coefficient for the r-th iteration; is the intermediate signal of the h-th axis after zero bias compensation, and is the gradient term of the cross-axis coupling compensation.

[0076] Preferably, the dynamic temperature drift compensation module is also connected to a range-resolution adaptive switching module, which is used to monitor the compensated signal in real time. The peak value and dynamic range, and then based on the compensated signal. The sampling mode is switched between peak value and dynamic range;

[0077] Sampling modes include high-resolution mode, balanced mode, and high-range mode;

[0078] When the range-resolution adaptive switching module detects the compensated signal When the peak value is below the micro-vibration threshold for M consecutive sampling points, switch to high resolution mode;

[0079] When the compensated signal When the peak value is within the normal range for M consecutive sampling points, switch to balanced mode;

[0080] When the compensated signal When the peak value is greater than the impact threshold for M consecutive sampling points, switch to high range mode.

[0081] During mode switching, a linear interpolation algorithm is used to compensate for the transition of signals before and after the switch, eliminating signal jumps and data gaps caused by mode switching and achieving seamless connection.

[0082] The beneficial effects of this invention are:

[0083] (1) Weak vibration detection performance: Improved the 1 / f noise suppression capability of MEMS accelerometer in ultra-low frequency band, effectively extracting weak vibration signals at the μg level, and significantly improving the detection signal-to-noise ratio and detection limit in ultra-low frequency band.

[0084] In the ultra-low frequency band of 0.1Hz to 10Hz, the noise density is reduced to below 0.1μg / √Hz, and the signal-to-noise ratio is increased to more than 30dB. It can stably detect ultra-low frequency micro-vibrations at the 2μg level. Compared with the existing single-channel detection scheme, the signal-to-noise ratio in the low frequency band is improved by more than 20dB, and the detection limit is reduced by an order of magnitude.

[0085] (2) Temperature drift compensation performance: It can adapt to full parameter compensation of dynamic temperature drift in a wide temperature range, which significantly reduces the measurement error in the full temperature range and improves the long-term stability of MEMS accelerometer.

[0086] Within the full temperature range of -40℃ to 125℃, the zero bias temperature drift is reduced to within ±50μg / ℃, the sensitivity temperature drift is reduced to within ±50ppm / ℃, and the cross-axis coupling error is reduced to within ±0.5%. Compared with the existing static polynomial compensation scheme, the measurement error in the full temperature range is reduced by more than 80%, and the long-term zero bias stability is improved by an order of magnitude.

[0087] (3) Range adaptation performance: It can achieve adaptive and seamless switching between high range and high resolution without modifying the hardware structure of MEMS sensitive unit.

[0088] Without modifying any hardware structure of the MEMS sensing unit, a maximum measurement range of ±100g can be achieved, while a detection resolution of 2μg can be achieved in high-resolution mode, completely breaking through the strong binding limitation between range and resolution. A single sensor can simultaneously cover both micro-vibration monitoring and impact detection scenarios.

[0089] (4) Industrialization advantages: The solution is fully compatible with the existing commercial capacitive MEMS accelerometer sensitive core. Performance improvement can be achieved simply by optimizing the embedded algorithm and detection link. No customized hardware development is required, the development cycle is shortened by more than 60%, the industrialization cost is greatly reduced, and it can be quickly adapted to multiple high-end scenarios such as structural health monitoring, industrial diagnosis, and aerospace. Attached Figure Description

[0090] Figure 1 This is a block diagram of the ultra-low frequency weak vibration detection and adaptive compensation system of the MEMS accelerometer in Example 1;

[0091] Figure 2 This is a schematic diagram illustrating the principle of multi-channel parallel coherent detection and adaptive weighted fusion in Example 1;

[0092] Figure 3 This is a flowchart of the full-temperature-range dynamic adaptive temperature drift compensation method in Example 1;

[0093] Figure 4 This is a schematic diagram of the range-resolution adaptive switching threshold logic and state machine in Example 1;

[0094] Figure 5 This is a flowchart illustrating the timing of algorithm execution in Example 2;

[0095] Figure 6 This is a system structure block diagram for Example 2;

[0096] Figure 7The timing diagram is shown for the algorithm in Example 2. Detailed Implementation

[0097] The present invention will be further described in detail below with reference to the accompanying drawings and specific examples. The following embodiments or drawings are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0098] Example 1: A method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer, comprising the following steps:

[0099] Step 1: Construct an ultra-low frequency weak vibration detection and adaptive compensation system for MEMS accelerometers. This system includes a multi-channel parallel coherent modulation and demodulation module, an adaptive weighted fusion module, a dynamic temperature drift compensation module, and a variational mode decomposition adaptive filtering module connected in sequence. Figure 1 As shown;

[0100] Step 2: The multi-channel parallel coherent modulation and demodulation module acquires the differential capacitance signal X of the sensitive unit in the MEMS accelerometer through n parallel coherent detection links, and then performs synchronous modulation and coherent demodulation on the differential capacitance signal X to obtain n baseband signals. , i∈[1,n], and sent to the adaptive weighted fusion module;

[0101] Step 3: The adaptive weighted fusion module evaluates and obtains the baseband signal for each path. signal-to-noise ratio Then with the aforementioned signal-to-noise ratio The square of is the weighting coefficient for n baseband signals. Weighted fusion is performed to obtain the fused signal. And send it to the dynamic temperature drift compensation module;

[0102] Step 4: The dynamic temperature drift compensation module applies the fused signal. Perform temperature drift compensation to obtain the compensated signal. And send it to the variational mode decomposition adaptive filtering module;

[0103] Step 5: The variational mode decomposition adaptive filtering module uses the variational mode decomposition algorithm (VMD) to process the compensated signal. Adaptive filtering is performed to output the final acceleration signal Y.

[0104] The variational mode decomposition adaptive filtering module uses variational mode decomposition (VMD) to process the compensated signal. Perform ultra-low frequency adaptive filtering, with preset mode number A=4~6 and penalty factor α=1000~3000, and then apply the compensation to the signal. Decompose into multiple Intrinsic Mode Functions (IMFs); calculate the relationship between each IMF and the original compensated signal. By using the Pearson correlation coefficient, noise modes and trend terms with correlation coefficients less than 0.1 are removed, and effective vibration modes are retained and the signal is reconstructed, ultimately achieving effective extraction of μg-level ultra-low frequency weak vibration signals.

[0105] like Figure 2 As shown, the channel parallel coherent modulation and demodulation module is equipped with an orthogonal carrier generation unit and four parallel coherent detection links. Each coherent detection link is equipped with a modulation unit, a programmable gain amplifier, an ADC sampling unit and a coherent demodulation unit connected in sequence.

[0106] The orthogonal carrier generation unit is used to generate four pairs of orthogonal carrier signals, which are then transmitted to the modulation units of the four coherent detection links. The four carrier signals correspond one-to-one with the four coherent detection links.

[0107] The four coherent detection links are used to acquire the differential capacitance signal X, and then the differential capacitance signal X is synchronously modulated and coherently demodulated using the corresponding carrier signal to obtain four baseband signals. .

[0108] Each coherent detection link uses an independent orthogonal carrier signal, with the carrier frequency set to twice the resonant frequency of the MEMS sensitive unit to avoid the 1 / f noise inflection point frequency, typically set to 10kHz~50kHz; the n carriers are orthogonal to each other, and the differential capacitor signal X is synchronously modulated and coherently demodulated to shift the effective signal from the low frequency band to the high frequency carrier band, avoiding the influence of 1 / f noise.

[0109] The adaptive weighted fusion module evaluation setup includes a real-time signal-to-noise ratio evaluation unit and an adaptive weighted signal fusion calculation unit connected in sequence.

[0110] The input terminals of the real-time signal-to-noise ratio evaluation unit and the adaptive weighted signal fusion calculation unit are respectively connected to four coherent detection links to acquire four baseband signals. ;

[0111] The real-time signal-to-noise ratio evaluation unit is used to evaluate each baseband signal obtained. signal-to-noise ratio The expression is:

[0112] ;

[0113] in, Let be the effective signal power of the i-th signal. Let be the noise power of the i-th signal; For the i-th signal in the i-th... The instantaneous amplitude at each sampling point The baseline estimate of the noise power of the i-th channel is obtained by noise statistics of the sensor in a stationary state or by real-time updates of high-frequency noise power. This is the index of the latest sampling point. The sliding window length is typically N=1024 or 2048, balancing real-time performance and estimation accuracy. For the first One sampling point, This represents the total average power of the i-th signal within the current window.

[0114] The adaptive weighted signal fusion calculation unit is used to calculate the signal-to-noise ratio. The square of is the weighting coefficient for n baseband signals. The weighted fusion calculation is expressed as follows:

[0115] ;

[0116] in, For the i-th baseband signal, For the i-th baseband signal The real-time signal-to-noise ratio, where n is the number of parallel channels (n=4 in this embodiment), and i is the channel index. For fused signals.

[0117] The dynamic temperature drift compensation module is equipped with a temperature change rate calculation module, a temperature drift prediction module, and an acceleration compensation module connected in sequence.

[0118] The temperature change rate calculation module is used to calculate the temperature change rate based on the real-time temperature data of the sensing unit in the MEMS accelerometer.

[0119] The temperature drift prediction module is used to predict the zero-bias compensation value of the MEMS accelerometer sensor based on the real-time temperature data, temperature change rate, and triaxial raw acceleration data of the MEMS accelerometer sensor's sensing unit. Sensitivity compensation coefficient and cross-axis coupling compensation matrix ;

[0120] The acceleration compensation module is used to calculate the zero-bias compensation value. Sensitivity compensation coefficient and cross-axis coupling compensation matrix For the fused signal Compensation is performed to obtain the compensated signal. .

[0121] The dynamic temperature drift compensation module is also connected to a temperature sensor, which is built into the sensitive unit of the MEMS accelerometer.

[0122] The dynamic temperature drift compensation module is also connected to the original acceleration output terminal of the MEMS accelerometer.

[0123] The temperature sensor is used to collect real-time temperature data of the sensitive unit in the MEMS accelerometer and provide it to the temperature change rate calculation module and the temperature drift prediction module.

[0124] The raw acceleration output terminal of the MEMS accelerometer is used to output triaxial raw acceleration data to the temperature drift prediction module.

[0125] The temperature change rate calculation module calculates the temperature change rate using the following expression:

[0126] ;

[0127] in, This represents the rate of temperature change at the current moment, calculated from the temperature difference between adjacent sampling moments. Indicates the temperature sampling period. Indicates the current temperature. This indicates the temperature at the previous sampling time.

[0128] The temperature drift prediction module has a built-in multi-output regression XGBoost temperature drift prediction model, which is used to simultaneously predict the true value of the zero-bias output, the true value of the sensitivity coefficient, and the true value of the cross-axis coupling coefficient.

[0129] The input feature vector of the multi-output regression XGBoost temperature drift prediction model is:

[0130] ;

[0131] in, This is the real-time temperature data of the sensitive unit at the current moment. The rate of temperature change at the current moment. This provides the current moment's raw triaxial acceleration data from the MEMS accelerometer.

[0132] The output vector of the multi-output regression XGBoost temperature drift prediction model is:

[0133] ;

[0134] in, The model outputs the true values ​​of the three-axis zero-bias predictions. The true values ​​of the triaxial sensitivity coefficients predicted by the model. The true values ​​of the triaxial cross-axis coupling coefficients predicted by the model correspond to the 6 off-diagonal elements of the 3×3 cross-axis coupling matrix;

[0135] The multi-output regression XGBoost temperature drift prediction model is an additive ensemble model, and the predicted value is obtained by accumulating the structure of k regression trees. The model prediction expression is:

[0136] ;

[0137] in, For the output vector The m-th element in the equation is the predicted true value of the m-th temperature drift parameter. For the input feature vector, Let be the mapping function for the j-th regression tree. Let be the function space of all regression trees; The total number of regression trees is set to 200 during the pre-training phase.

[0138] The objective function for training the multi-output regression XGBoost temperature drift prediction model is:

[0139] ;

[0140] in, The squared loss function, To calibrate the true value of the m-th temperature drift parameter for the i-th sample in the sample library, This is a regularization term used to control model complexity and avoid overfitting.

[0141] The temperature drift prediction module predicts the true value based on the parameters output by the multi-output regression XGBoost temperature drift prediction model. The parameter compensation value is calculated using the following expression:

[0142] ;

[0143] ;

[0144] ;

[0145] in, The zero bias compensation value This is the sensitivity compensation coefficient. This is the cross-axis coupling compensation matrix. The true value matrix of cross-axis coupling predicted by the model The inverse matrix; It is a diagonal matrix.

[0146] The acceleration compensation module is based on the zero bias compensation value. Sensitivity compensation coefficient and cross-axis coupling compensation matrix For the fused signal The compensation is expressed as follows:

[0147] ;

[0148] in, This is a fused signal, i.e., a compensated input signal; The signal after compensation.

[0149] like Figure 3 As shown: The multi-output regression XGBoost temperature drift prediction model is obtained through the following training:

[0150] (1) Construction and pre-training of the full temperature range sample library: In the full temperature range of -40℃ to 125℃, a calibration temperature point is set every 5℃, covering three typical temperature change rates of 1℃ / min, 2℃ / min, and 5℃ / min. The true values ​​of the zero bias output, sensitivity coefficient, and triaxial cross-coupling coefficient of the MEMS accelerometer are collected under each working condition to construct the temperature drift sample library; Based on the temperature drift sample library, the multi-output regression gradient boosting tree XGBoost temperature drift prediction model is trained, and the input feature of the model is the current temperature. Rate of temperature change Triaxial raw acceleration values The model output is the true value of the three-axis zero-bias output. True values ​​of triaxial sensitivity coefficients True values ​​of the three-axis cross-axis coupling coefficients .

[0151] The parameters collected in the temperature drift sample library, i.e., the calibration true values, are defined as follows:

[0152] At each calibrated temperature point and under each temperature change rate condition, the true temperature drift error parameters of the MEMS accelerometer were collected through high-precision gravity field calibration and high-precision single-axis turntable calibration, and used as label values ​​for model training.

[0153] Zero bias output truth value The true value of the deviation between the triaxial output of the MEMS accelerometer and the ideal zero input in a static state, i.e., the true value of the zero bias error;

[0154] True value of sensitivity coefficient The true value of the ratio between the triaxial output of the MEMS accelerometer and the actual acceleration input, i.e., the true value of the sensitivity;

[0155] True value of triaxial cross-coupling coefficient A 3x3 cross-coupling matrix, with diagonal elements equal to 1 and off-diagonal elements equal to 0. This represents the true value of the coupling coefficient between the y-axis acceleration input and the x-axis output, characterizing the cross-interference error between the three axes.

[0156] The model output compensation value, i.e., the error correction amount, is defined as follows:

[0157] The compensation value / compensation matrix output by the model in real time is a correction amount used to offset the above-mentioned true temperature drift error, and its correspondence with the calibration true value is as follows:

[0158] Zero bias compensation value : Equal in magnitude but opposite in sign to the zero bias truth value, i.e. This is used to directly offset zero bias error;

[0159] Sensitivity compensation coefficient : is the reciprocal of the true value of sensitivity, i.e. This is used to correct sensitivity deviations;

[0160] Cross-axis coupling compensation matrix : is the inverse of the truth matrix of cross-coupling, i.e. It is used to eliminate cross-coupling interference between the three axes.

[0161] (2) Calibration implementation method: During the temperature drift sample library construction stage, the MEMS accelerometer is placed in a high and low temperature chamber and kept at each set temperature point for no less than 30 minutes until the chip core temperature collected by the on-chip temperature sensor built into the MEMS sensitive unit reaches a steady-state equilibrium with the ambient temperature set in the high and low temperature chamber. Then, parameter calibration is carried out to ensure that the temperature data in the sample library is completely matched with the corresponding temperature drift parameters.

[0162] (3) Real-time operation: The high-precision temperature acquisition channel built into the MEMS accelerometer and the same chip as the sensing unit is used to collect the core temperature of the chip in real time at a sampling frequency of 20Hz. The temperature characteristics are completely identical to those of the sample library, eliminating the dynamic compensation error caused by thermal hysteresis and solving the pain point that the existing technology cannot adapt to the rapid temperature change scenario using ambient temperature.

[0163] The dynamic temperature drift compensation module is also connected to an online adaptive calibration module, which is used to monitor the fused signal in real time. The variance of the fused signal The variance is less than a preset threshold for a continuous set time period, such as 10 seconds. When the MEMS accelerometer is determined to be stationary, online self-calibration is automatically triggered.

[0164] The online adaptive calibration module uses the compensated signal from the current static state. Based on this, the Least Mean Square (LMS) algorithm is used to iteratively update the temperature drift compensation parameters; the iteration step size is set to 0.005~0.01 to avoid parameter jumps, correct model prediction errors, and improve the long-term stability of the sensor.

[0165] (a) The prerequisite parameters for online adaptive calibration are as follows:

[0166] Criteria for determining static state: fused signals within 10 consecutive seconds variance The sensor is determined to be in a stationary state.

[0167] Desired output d in a stationary state: In a stationary state, the sensor is only affected by gravitational acceleration. The desired output is the projection component of gravitational acceleration onto the three axes of the sensor, which is a 3×1 column vector, expressed as:

[0168] ;

[0169] in,( These are the components of gravitational acceleration along the X, Y, and Z axes. If the sensor is mounted horizontally, the typical value is... , This is the local gravitational acceleration; the desired output can be obtained through initial installation attitude calibration, or locked by low-pass filtering in the initial stationary state.

[0170] Current real-time output after compensation: The compensated signal calculated using the current temperature drift compensation parameters. .

[0171] The compensation error signal e: the difference between the expected output and the real-time compensated output in the static state, is a 3×1 column vector and is the core driving signal for the LMS algorithm iteration.

[0172] ;

[0173] Iteration step size The iteration update step size of the LMS algorithm is preset to a range of 0.005 ≤ ≤0.01; a small step size can avoid jumps in compensation parameters, ensure the numerical stability of the iteration process, and at the same time take into account the convergence speed.

[0174] (II) The complete iterative update rules for the temperature drift compensation parameters in the LMS algorithm are as follows:

[0175] This invention employs a parameterized gradient descent iterative strategy for zero-bias compensation values. Sensitivity compensation coefficient and cross-axis coupling compensation matrix Each update rule is designed separately, and all updates are based on the minimum mean square error criterion (minimizing) It can be executed in real time in an embedded MCU without complex matrix inversion operations.

[0176] ① Zero bias compensation value Iterative updates:

[0177] Zero bias compensation value The update rule directly affects the compensated baseline offset:

[0178] ;

[0179] in, For the first The zero-bias compensation value of the next iteration The iteration step size, For the first Sensitivity compensation coefficient for the next iteration. For the first Cross-axis coupling compensation matrix of the next iteration. For the first The compensation error signal for the next iteration; For the first The transpose of the product of the sensitivity compensation coefficient and the cross-axis coupling compensation matrix in the next iteration is the gradient term of the LMS algorithm, ensuring that the iteration direction of zero bias compensation is consistent with the error descent direction.

[0180] Physical meaning: By correcting the zero bias compensation value in real time through the error signal, the zero bias drift caused by long-term aging of the sensor and gradual changes in the environment is offset, so that the compensated output baseline is completely matched with the gravitational acceleration reference.

[0181] ② Sensitivity compensation coefficient Iterative updates:

[0182] Sensitivity compensation coefficient Since the matrix is ​​diagonal, only the diagonal elements need to be updated. The update is performed iteratively along the X, Y, and Z axes, with the following update rules:

[0183] ;

[0184] ;

[0185] in, For the first The sensitivity compensation coefficient for the q-axis in the next iteration; For the first The q-axis compensation error signal in the next iteration; is the intermediate signal of the i-th axis after zero bias and cross-axis compensation, and is the gradient term of sensitivity compensation.

[0186] Physical meaning: By correcting the sensitivity compensation coefficient in real time through the error signal, the sensitivity ratio error under wide temperature range and long-term operation is corrected, ensuring the linear correspondence between the sensor output and the actual input acceleration.

[0187] ③ Cross-axis coupling compensation matrix Iterative updates:

[0188] The update of the cross-axis coupling compensation matrix focuses on the six off-diagonal cross-coupling coefficients. The diagonal elements are fixed at 1 and do not need to be updated. The update is applied to the off-diagonal elements. H≠h, and its update rule is:

[0189] ;

[0190] ;

[0191] in, is the cross-coupling compensation coefficient between the h-axis and the H-axis in the r-th iteration; This is the H-axis compensation error signal for the r-th iteration; The h-th axis sensitivity compensation coefficient for the r-th iteration; is the intermediate signal of the h-th axis after zero bias compensation, and is the gradient term of the cross-axis coupling compensation.

[0192] (III) The physical basis and closed-loop logic of iterative updates are as follows:

[0193] Physical basis: In a stationary state, the actual input acceleration of the sensor, i.e., the component of gravitational acceleration, is a known quantity; therefore, the expected output d can be used as the true value benchmark. Through gradient descent iteration of the LMS algorithm, the temperature drift compensation parameters are continuously adjusted to ensure that the compensated output... By gradually approximating the desired output d, the prediction error of the temperature drift prediction model caused by long-term aging and gradual environmental changes is corrected. No additional high-precision calibration equipment is required, achieving "maintenance-free" online self-calibration.

[0194] Closed-loop execution logic: The complete closed-loop process of online self-calibration is as follows:

[0195] 1. Static state determination: The variance of the signal over 10 consecutive seconds is < This triggers self-calibration;

[0196] 2. Lock the desired output d: Lock the gravitational acceleration projection based on the initial installation attitude or the first static state;

[0197] 3. Calculate the current compensation output With error signal e;

[0198] 4. Iterate through the zero-bias compensation values ​​according to the update expression described above. Sensitivity compensation coefficient and cross-axis coupling compensation matrix ;

[0199] 5. The updated compensation parameters are directly used for temperature drift compensation calculation at the next sampling time, forming a real-time closed loop;

[0200] 6. When the sensor exits the static state machine, i.e., variance > Immediately stop the iteration, keep the current compensation parameters unchanged, and avoid dynamic signals interfering with the stability of the iteration.

[0201] like Figure 4 As shown, the dynamic temperature drift compensation module is also connected to a range-resolution adaptive switching module, which is used to monitor the compensated signal in real time. The peak value and dynamic range, and then based on the compensated signal. The sampling mode is switched between peak value and dynamic range;

[0202] (1) Three-level threshold dynamic monitoring: Real-time monitoring of the peak value and dynamic range of acceleration signal, and setting three-level trigger thresholds: micro-vibration threshold (<1g), conventional range threshold (1g~20g), and impact threshold (>20g). The thresholds can be adaptively adjusted according to the application scenario.

[0203] (2) Seamless switching between multiple modes:

[0204] When the range-resolution adaptive switching module detects the compensated signal When the peak value is below the micro-vibration threshold for 5 consecutive sampling points, it automatically switches to high resolution mode: hardware gain attenuation is turned off, 4-channel full-link coherent fusion is enabled, the oversampling rate is increased to 256 times, and the effective sampling bit number is increased from 16 bits to 24 bits, achieving high resolution detection at the μg level.

[0205] When the signal peak is within the normal range, switch to balanced mode: adjust the hardware gain to a moderate level, enable 2-channel coherent detection, and set the oversampling rate to 64 times to balance resolution and dynamic range.

[0206] When the signal peak triggers the impact threshold, the high range mode is switched within 1ms: hardware gain attenuation is enabled, the oversampling rate is reduced to 16 times, the dynamic range is widened to ±100g, and the impact data buffering mechanism is triggered to latch the original data for 500ms before and after the impact to avoid loss of the impact signal.

[0207] (3) Transition compensation: During mode switching, a linear interpolation algorithm is used to compensate for the transition of signals before and after switching, eliminating signal jumps and data gaps caused by mode switching, and achieving seamless connection.

[0208] Example 2: Based on Example 1, the MEMS accelerometer ultra-low frequency weak vibration detection and adaptive compensation method provided by this invention is applied to the health monitoring scenario of large bridge structures, such as... Figure 5-7 As shown, the monitoring requirements are: to detect ultra-low frequency micro-vibrations of bridges in the range of 0.1Hz to 10Hz, with a detection limit of 2μg, an operating temperature range of -40℃ to 85℃, and the ability to capture ±20g impacts from passing vehicles, with a measurement error ≤1% across the entire temperature range. The specific steps are as follows:

[0209] Step 1: Multi-channel parallel coherent detection and signal fusion implementation

[0210] Four parallel coherent detection links are set up with a carrier frequency of 20kHz to avoid the 1 / f noise inflection point of the MEMS sensitive unit. The four carriers are pairwise orthogonal sinusoidal signals, which are used to synchronously modulate the differential capacitance signals output by the MEMS sensitive unit. The modulated signals are amplified by programmable gain and then sampled by the ADC with a sampling rate of 256kHz. The sampled digital signals are synchronously coherently demodulated in the MCU to obtain four baseband signals.

[0211] The adaptive weighted fusion module calculates the signal-to-noise ratio (SNR) of each baseband signal in real time and uses the square of the SNR as the weighting coefficient to complete the adaptive weighted fusion of the four signals. The SNR of the fused signal is improved by more than 18dB compared to the single signal.

[0212] Step 2: Implementing dynamic temperature drift compensation across the entire temperature range

[0213] Pre-calibration stage: In the high and low temperature chamber, a temperature point was set every 5℃ within the range of -40℃ to 85℃ for the sensor. After holding each temperature point for 30 minutes, the zero bias output, sensitivity coefficient and triaxial cross coupling coefficient under ±1g / ±5g / ±10g input under static conditions were collected. At the same time, temperature drift data at temperature change rates of 1℃ / min, 2℃ / min and 5℃ / min were collected to build a temperature drift sample library containing 2000 samples.

[0214] An XGBoost temperature drift prediction model was trained based on a temperature drift sample database. The tree depth was set to 6, the learning rate to 0.1, and the number of iterations to 200. The model inputs were the current temperature, the rate of temperature change, and the raw triaxial acceleration values. The outputs were the true values ​​of the triaxial zero-bias output, the true values ​​of the triaxial sensitivity coefficients, and the true values ​​of the triaxial cross-axis coupling coefficients. The model's goodness of fit was assessed. ≥0.998.

[0215] Real-time operation phase: The temperature sensor collects the current temperature at a frequency of 20Hz. The dynamic temperature drift compensation module calculates the rate of temperature change and then outputs compensation parameters in real time through the XGBoost temperature drift prediction model to perform full parameter compensation on the fused signal. Simultaneously, the online self-calibration module monitors the signal variance in real time. When the signal variance is less than [value missing] for 10 consecutive seconds... When the state is determined to be static, online self-calibration is triggered, and the zero bias compensation value is iteratively updated using the LMS algorithm with an iteration step size of 0.01.

[0216] Step 3: Implementing adaptive switching between range and resolution

[0217] The range-resolution adaptive switching module monitors the peak value of the acceleration signal in real time and has three threshold levels: micro-vibration threshold range is <1g, conventional range threshold range is 1g~20g, and impact threshold range is >20g.

[0218] When the signal peak value is less than 1g for 5 consecutive sampling points, switch to high resolution mode: set the programmable gain to 16 times, the oversampling rate to 256 times, the effective sampling bit depth to 24 bits, and enable 4-channel full fusion mode.

[0219] When the signal peak value is in the range of 1g~20g, switch to balanced mode: set the programmable gain to 2 times, the oversampling rate to 64 times, and enable 2-channel fusion mode;

[0220] When the signal peak exceeds 20g, switch to high range mode within 1ms: set the programmable gain to 0.25 times, the oversampling rate to 16 times, disable multi-channel fusion, and buffer the raw data for 500ms before and after the impact.

[0221] During mode switching, a linear interpolation algorithm is used to compensate for signal transitions and eliminate signal jumps.

[0222] Step 4: Adaptive Filtering and Signal Output

[0223] The VMD adaptive filtering module decomposes the compensated signal using the VMD algorithm, setting the number of modes K=5 and the penalty factor α=2000, resulting in 5 IMF components. The correlation coefficient between each IMF and the original signal is calculated, and noise modes and trend terms with correlation coefficients less than 0.1 are removed. The effective signal is then reconstructed, and finally, a high-precision acceleration value is output to the host computer monitoring system.

[0224] In this implementation case, the final performance indicators of the sensor are as follows:

[0225] Noise density in the 0.1Hz~10Hz frequency band: 0.08μg / √Hz, capable of stably detecting 2μg of ultra-low frequency micro-vibrations, with a signal-to-noise ratio of 32dB;

[0226] Within the full temperature range of -40℃ to 85℃, the zero-bias temperature drift is ±30μg / ℃, the sensitivity temperature drift is ±30ppm / ℃, the cross-axis coupling error is ≤0.3%, and the full temperature range measurement error is ≤0.8%.

[0227] The measurement range is ±100g, with a resolution of 1.5μg in high-resolution mode, a mode switching time of ≤1ms, and no signal jumps or data loss.

[0228] After 72 hours of continuous operation testing, the zero-bias drift was ≤10μg, demonstrating excellent long-term stability and fully meeting the application requirements for bridge structural health monitoring.

[0229] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer, characterized in that, Includes the following steps: Step 1: Construct an ultra-low frequency weak vibration detection and adaptive compensation system for MEMS accelerometers. This ultra-low frequency weak vibration detection and adaptive compensation system is equipped with a multi-channel parallel coherent modulation and demodulation module, an adaptive weighted fusion module, a dynamic temperature drift compensation module, and a variational mode decomposition adaptive filtering module connected in sequence. Step 2: The multi-channel parallel coherent modulation and demodulation module acquires the differential capacitance signal X of the sensitive unit in the MEMS accelerometer through n parallel coherent detection links, and then performs synchronous modulation and coherent demodulation on the differential capacitance signal X to obtain n baseband signals. And send it to the adaptive weighted fusion module; Step 3: The adaptive weighted fusion module evaluates and obtains the baseband signal for each path. signal-to-noise ratio Then with the aforementioned signal-to-noise ratio The square of is the weighting coefficient for n baseband signals. Weighted fusion is performed to obtain the fused signal. And send it to the dynamic temperature drift compensation module; Step 4: The dynamic temperature drift compensation module applies the fused signal. Perform temperature drift compensation to obtain the compensated signal. And send it to the variational mode decomposition adaptive filtering module; Step 5: The variational mode decomposition adaptive filtering module uses the variational mode decomposition algorithm to process the compensated signal. Adaptive filtering is performed to output the final acceleration signal Y.

2. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 1, characterized in that: The channel parallel coherent modulation and demodulation module is equipped with an orthogonal carrier generation unit and n parallel coherent detection links. Each coherent detection link is equipped with a modulation unit, a programmable gain amplifier, an ADC sampling unit and a coherent demodulation unit connected in sequence. The orthogonal carrier generation unit is used to generate n pairs of orthogonal carrier signals and transmit them to the n coherent detection links accordingly. The n coherent detection links are used to acquire the differential capacitance signal X, and then the differential capacitance signal X is synchronously modulated and coherently demodulated using the corresponding carrier signal to obtain n baseband signals. .

3. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 1, characterized in that: The adaptive weighted fusion module evaluation setup includes a real-time signal-to-noise ratio evaluation unit and an adaptive weighted signal fusion calculation unit connected in sequence. The input terminals of the real-time signal-to-noise ratio evaluation unit and the adaptive weighted signal fusion calculation unit are respectively connected to n coherent detection links to acquire n baseband signals. ; The real-time signal-to-noise ratio evaluation unit is also used to evaluate each baseband signal obtained. signal-to-noise ratio The expression is: ； in, Let be the effective signal power of the i-th signal. Let be the noise power of the i-th signal; For the i-th signal in the i-th... The instantaneous amplitude at each sampling point Let be the baseline estimate of the noise power of the i-th channel. This is the index of the latest sampling point. The length of the sliding window. For the first One sampling point, This represents the total average power of the i-th signal within the current window. The adaptive weighted signal fusion calculation unit is also used to calculate the signal-to-noise ratio. The square of is the weighting coefficient for n baseband signals. The weighted fusion calculation is expressed as follows: ； in, For the i-th baseband signal, For the i-th baseband signal The real-time signal-to-noise ratio, where n is the number of parallel channels and i is the channel index. For fused signals.

4. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 1, characterized in that: The dynamic temperature drift compensation module is equipped with a temperature change rate calculation module, a temperature drift prediction module, and an acceleration compensation module connected in sequence. The temperature change rate calculation module is used to calculate the temperature change rate based on the real-time temperature data of the sensing unit in the MEMS accelerometer. The temperature drift prediction module is used to predict the zero-bias compensation value of the MEMS accelerometer sensor based on the real-time temperature data, temperature change rate, and triaxial raw acceleration data of the MEMS accelerometer sensor's sensing unit. Sensitivity compensation coefficient and cross-axis coupling compensation matrix ; The acceleration compensation module is used to calculate the zero-bias compensation value. Sensitivity compensation coefficient and cross-axis coupling compensation matrix For the fused signal Compensation is performed to obtain the compensated signal. .

5. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 4, characterized in that: The temperature drift prediction module has a built-in multi-output regression XGBoost temperature drift prediction model, which is used to simultaneously predict the true value of the zero-bias output, the true value of the sensitivity coefficient, and the true value of the cross-axis coupling coefficient. The input feature vector of the multi-output regression XGBoost temperature drift prediction model is: ； in, This is the real-time temperature data of the sensitive unit at the current moment. The rate of temperature change at the current moment. This provides the current moment's raw triaxial acceleration data from the MEMS accelerometer. The output vector of the multi-output regression XGBoost temperature drift prediction model is: ； in, The model outputs the true values ​​of the three-axis zero-bias predictions. The true values ​​of the triaxial sensitivity coefficients predicted by the model. The true values ​​of the triaxial cross-axis coupling coefficients predicted by the model; The multi-output regression XGBoost temperature drift prediction model is an additive ensemble model, and the predicted value is obtained by accumulating the structure of k regression trees. The model prediction expression is: ； in, For the output vector The m-th element in the equation is the predicted true value of the m-th temperature drift parameter. For the input feature vector, Let be the mapping function for the j-th regression tree. For the function space of all regression trees, This represents the total number of regression trees; The temperature drift prediction module calculates parameter compensation values ​​based on the true values ​​of the parameters predicted by the multi-output regression XGBoost temperature drift prediction model. The expression is as follows: ； ； ； in, The zero bias compensation value This is the sensitivity compensation coefficient. This is the cross-axis coupling compensation matrix. The true value matrix of cross-axis coupling predicted by the model The inverse matrix; It is a diagonal matrix.

6. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 4, characterized in that: The acceleration compensation module is based on the zero bias compensation value. Sensitivity compensation coefficient and cross-axis coupling compensation matrix For the fused signal The compensation is expressed as follows: ； in, This is a fused signal, i.e., a compensated input signal; The signal after compensation.

7. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 4, characterized in that: The dynamic temperature drift compensation module is also connected to a temperature sensor, which is built into the sensitive unit of the MEMS accelerometer. The dynamic temperature drift compensation module is also connected to the original acceleration output terminal of the MEMS accelerometer. The temperature sensor is used to collect real-time temperature data of the sensitive unit in the MEMS accelerometer and provide it to the temperature change rate calculation module and the temperature drift prediction module. The raw acceleration output terminal of the MEMS accelerometer is used to output triaxial raw acceleration data to the temperature drift prediction module.

8. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 1, characterized in that: The dynamic temperature drift compensation module is also connected to an online adaptive calibration module, which is used to monitor the fused signal in real time. The variance of the fused signal When the variance of the sensor is less than a preset threshold for a continuous set time, the MEMS accelerometer is determined to be in a stationary state, and online self-calibration is automatically triggered.

9. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 8, characterized in that: The online adaptive calibration module uses the compensated signal from the current static state. Based on this, the Least Mean Square (LMS) algorithm is used to iteratively update the temperature drift compensation parameters; Zero bias compensation value The iterative update expression is: ； in, For the first The zero-bias compensation value of the next iteration The iteration step size, For the first Sensitivity compensation coefficient for the next iteration. For the first Cross-axis coupling compensation matrix of the next iteration. For the first The compensation error signal for the next iteration; Sensitivity compensation coefficient The iterative update expression is: ； ； in, For the first The sensitivity compensation coefficient for the q-axis in the next iteration; For the first The q-axis compensation error signal in the next iteration; Cross-axis coupling compensation matrix The iterative update expression is: ； ； in, is the cross-coupling compensation coefficient between the h-axis and the H-axis in the r-th iteration; This is the H-axis compensation error signal for the r-th iteration; is the sensitivity compensation coefficient for the h-th axis in the r-th iteration.

10. The method for detecting and adaptively compensating for ultra-low frequency weak vibrations in a MEMS accelerometer according to claim 1, characterized in that: The dynamic temperature drift compensation module is also connected to a range-resolution adaptive switching module, which is used to monitor the compensated signal in real time. The peak value and dynamic range, and then based on the compensated signal. The sampling mode is switched between peak value and dynamic range; Sampling modes include high-resolution mode, balanced mode, and high-range mode; When the range-resolution adaptive switching module detects the compensated signal When the peak value is below the micro-vibration threshold for M consecutive sampling points, switch to high resolution mode; When the compensated signal When the peak value is within the normal range for M consecutive sampling points, switch to balanced mode; When the compensated signal When the peak value is greater than the impact threshold for M consecutive sampling points, switch to high range mode.

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