MEMS signal processing method and system based on RLS-VMD fusion algorithm

Abstract

The invention belongs to the technical field of MEMS sensor signal processing, and discloses an MEMS sensor signal processing method and system based on an RLS-VMD fusion algorithm, and the method comprises the steps: continuously collecting an original acceleration signal at a preset sampling frequency through an MEMS sensor; offset in the original acceleration signal is eliminated through iterative calculation based on an RLS algorithm, and an offset correction signal and a residual error are obtained; a dynamic energy threshold value is obtained based on residual calculation, and frequency characteristic secondary verification is carried out on each screened modal component; carrying out superposition reconstruction to obtain an acceleration signal; and taking the purified acceleration signal as input, performing two times of integral operation based on the Newton's law of motion to realize displacement calculation, and finally outputting a displacement signal. According to the method, a correlation mechanism of RLS offset correction and VMD screening parameters is established, deep collaboration is achieved, and finally the acceleration signal processing quality and the displacement calculation precision of the MEMS sensor are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of MEMS sensor signal processing, in particular to a MEMS signal processing method and system based on an RLS-VMD fusion algorithm. BACKGROUND

[0002] MEMS sensors have the advantages of small size, low manufacturing cost and convenient installation and deployment, and their application potential in displacement monitoring continues to expand. The core principle of displacement monitoring is to collect the acceleration signal of the target object through the built-in accelerometer, and then to obtain the velocity data and displacement data through two integral operations in sequence, and finally to output the monitoring results. However, in actual engineering application environment, the acceleration signal collected by the MEMS sensor often faces multiple error disturbances, which seriously affects the displacement calculation accuracy. Among them, the system bias error is an inherent error caused by the manufacturing process defects and circuit characteristics of the sensor itself, and this error will show dynamic drift characteristics with environmental temperature, working time and other factors; random noise is mainly derived from electromagnetic interference, mechanical vibration in the monitoring environment and thermal noise of the sensor internal circuit, which usually shows non-stationary and non-Gaussian characteristics; more importantly, the above two types of errors will produce significant cumulative effect after two integral operations, making the final output displacement data greatly deviate from the true value, which is difficult to meet the accuracy requirements of engineering monitoring.

[0003] The existing processing methods for MEMS acceleration signals have many obvious limitations. The traditional sliding window average method is a common bias estimation method, which takes the average value of the acceleration signal in a certain window to approximate the bias value, but this method has obvious lag in tracking dynamic changes of bias. When the bias slowly changes with environmental factors, the window average method cannot respond to the bias change in time, resulting in incomplete bias correction. In terms of noise suppression, a single filtering algorithm often cannot deal with complex non-Gaussian noise, and most filtering methods have poor adaptability to signals, and cannot balance noise suppression and effective signal preservation. More importantly, there is currently a lack of integrated solutions that optimize the three key links of bias estimation, noise separation and displacement calculation. The links are independent of each other, and the errors in the previous links cannot be effectively suppressed and compensated in the subsequent processing, resulting in limited overall signal processing accuracy and difficulty in fully utilizing the application value of MEMS sensors. Therefore, developing an algorithm that clearly defines the RLS bias estimation calculation logic, dynamically adjusts the VMD energy selection threshold based on the scene, and realizes the deep cooperation of the two algorithms, has become the key to breaking through the current technical bottleneck. SUMMARY

[0004] To overcome the technical defects of existing technologies, this invention provides a MEMS signal processing method and system based on the RLS-VMD fusion algorithm. It establishes a correlation mechanism between RLS bias correction and VMD screening parameters, realizes deep collaboration between the two algorithms, and ultimately improves the quality of MEMS sensor acceleration signal processing and displacement calculation accuracy.

[0005] The technical solution adopted in this invention is a MEMS signal processing method based on the RLS-VMD fusion algorithm, comprising the following steps: Step 1: Continuously acquire raw acceleration signals using a MEMS sensor at a preset sampling frequency. ; Step 2: Eliminate the original acceleration signal through iterative calculation based on the RLS algorithm. The bias is used to obtain the bias correction signal. With residual ; Step 3: Apply the VMD algorithm to the bias correction signal. Decomposition yields M modal components C. m (t), where (m=1,2,...,M), and calculate the energy and energy percentage of each modal component; Step 4: Based on residuals The dynamic energy threshold was calculated. The modal components are divided according to their energy proportions. The modal components are sorted from largest to smallest, and modal selection is performed by calculating cumulative energy. Then, the frequency characteristics of each selected modal component are verified a second time. The modal components that pass the second frequency characteristic verification are superimposed and reconstructed to obtain the purified acceleration signal. ; Step 5: Using the purified acceleration signal As input, displacement is calculated by performing two integral operations based on Newton's laws of motion, and the final output is a displacement signal. displacement signal The results are from the monitoring of MEMS sensors.

[0006] Preferably, in step 2, the original acceleration signal is eliminated through iterative calculation based on the RLS algorithm. The bias is used to obtain the bias correction signal. With residual The method is to take the initial parameters as the starting point and... Initial bias estimate The initial error covariance matrix and For each sampling time, the forgetting factor is used. Perform three iterative operations: The first step is to calculate the gain coefficient. : In this formula It is the error covariance matrix of the previous time step; The second step iteratively updates the bias estimate. : In this formula It is the residual at the current moment, that is, the difference between the original acceleration signal and the bias estimate at the previous moment; The third step is to update the error covariance matrix: ,in It refers to the identity matrix.

[0007] Preferably, the obtained bias correction signal With residual The method is, After the iteration is completed, the bias correction signal is calculated. Simultaneously record residuals .

[0008] Preferably, the method for calculating displacement by performing two integral operations based on Newton's laws of motion in step 5 is to first calculate the velocity, and then... From the initial moment Integrating up to the current time t, the formula is: ,in The initial velocity (in the initial monitoring state, the target object is usually in a stationary state, therefore...) =0, unit: Next, displacement calculation is performed on the velocity signal. from Perform a second integral up to t, the formula is: ,in This represents the initial displacement; the final output displacement signal. .

[0009] Preferably, in step 3, the modal components are distinguished into effective low-frequency components and noise high-frequency components by a preset frequency threshold, wherein the modal components below or equal to the preset frequency threshold contain effective displacement information, and the modal components above the preset frequency threshold are random noise.

[0010] Preferably, the method for performing secondary frequency characteristic verification on each selected modal component in step 4 is to retain the effective low-frequency components with frequencies less than or equal to a preset frequency threshold in the selected modes, and to remove the noise high-frequency components with frequencies greater than the preset frequency threshold; if the energy proportion of the noise high-frequency component is high, it is still determined to be noise.

[0011] Preferably, establish residuals With dynamic energy threshold Association rules: when At this time, noise interference is weak, so the dynamic energy threshold is lowered. Avoid missing low-energy effective modes; when At the same time, balance screening accuracy and signal integrity; when At the same time, increase the dynamic energy threshold. Eliminate high-energy noise modes.

[0012] Preferably, the modal components The energy is calculated by using an integral form to calculate C for each modal component. m The energy E of (t) m The formula is Where t0 is the initial sampling time, t k This represents the current sampling time.

[0013] Preferably, the modal component C m (t) energy percentage The calculation formula is shown below. .

[0014] The MEMS sensor signal processing system based on the RLS-VMD fusion algorithm implements the above-mentioned MEMS signal processing method based on the RLS-VMD fusion algorithm, including an RLS module, a VMD module, and a displacement calculation module. The RLS module eliminates the original acceleration signal through iterative calculation. The bias in the output bias correction signal With residual ; The VMD module is used for bias correction signals. Decomposition yields M modal components C. m (t), where m=1,2,...,M, and calculate the energy and energy percentage of each modal component, based on the residual. The dynamic energy threshold was calculated. The modal components are divided according to their energy proportions. The modal components are sorted from largest to smallest, and modal selection is performed by calculating cumulative energy. Then, the frequency characteristics of each selected modal component are verified a second time. The modal components that pass the second frequency characteristic verification are superimposed and reconstructed to output the purified acceleration signal. .

[0015] The displacement calculation module uses the purified acceleration signal As input, displacement is calculated by performing two integral operations based on Newton's laws of motion, and the final output is a displacement signal. displacement signal The results are from the monitoring of MEMS sensors.

[0016] The beneficial effects of this invention are as follows: By clarifying the specific iterative formula and parameter definition of the RLS bias estimate, this invention improves the stability and operability of bias correction; by constructing a VMD dynamic energy screening threshold based on scene noise intensity, it achieves accurate mode purification under different interference environments; by establishing a correlation mechanism between RLS bias correction and VMD screening parameters, it achieves deep collaboration between the two algorithms, ultimately improving the quality of MEMS sensor acceleration signal processing and displacement calculation accuracy. Attached Figure Description

[0017] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0018] Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the RLS calculation process of the present invention; Figure 3 This is a schematic diagram of the VMD calculation process of the present invention; Figure 4 A comparison chart of bias correction errors for various algorithms in MEMS sensors; Figure 5 This is a comparison chart of the signal-to-noise ratio of various algorithms in MEMS sensors under different noise scenarios; Figure 6 This is a comparison chart of the relative errors of various algorithms for MEMS sensors throughout the entire process. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the various embodiments of this invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this invention to facilitate a better understanding of this application. However, the technical solutions claimed in the claims of this application can be implemented even without these technical details and with various variations and modifications based on the following embodiments.

[0020] like Figures 1 to 3 As shown, this embodiment provides a MEMS signal processing method based on the RLS-VMD fusion algorithm, where RLS represents the recursive least squares algorithm and VMD represents the dynamic energy threshold variational mode decomposition algorithm, including the following steps: Step 1: Continuously acquire raw acceleration signals using a MEMS sensor at a preset sampling frequency. .

[0021] Step 2: Eliminate the original acceleration signal through iterative calculation based on the RLS algorithm. The bias is used to obtain the bias correction signal. With residual The core is to clarify the iterative calculation logic, parameter definition, and dynamic adjustment rules of the bias estimate Bk, so as to provide a high-quality bias correction signal for subsequent VMD calculations.

[0022] Step 3: Apply the VMD algorithm to the bias correction signal. Perform decomposition, setting the number of decomposition modes M and the penalty factor. Regarding convergence accuracy, by constructing a constrained variational problem and using the alternating direction multiplier algorithm to decompose A1(t), M eigenmode components C are obtained. m (t) (m=1,2,...,M), and calculate the energy and energy percentage of each modal component; among them, the effective low-frequency component (frequency≤5Hz, the effective signal in displacement monitoring is mostly in this range) mainly contains effective displacement information, and the noise high-frequency component (frequency>5Hz) is mainly random noise.

[0023] Step 4: Based on residuals The dynamic energy threshold was calculated. The modal components are divided according to their energy proportions. The modal components are sorted from largest to smallest, and modal selection is performed by calculating cumulative energy. Then, the frequency characteristics of each selected modal component are verified a second time. The modal components that pass the second frequency characteristic verification are superimposed and reconstructed to obtain the purified acceleration signal. This signal has effectively removed bias errors and random noise, providing high-quality input for subsequent displacement calculations.

[0024] Step 5: Using the purified acceleration signal As input, displacement is calculated by performing two integral operations based on Newton's laws of motion, and the final output is a displacement signal. displacement signal The results are from the monitoring of MEMS sensors.

[0025] In step 2, the original acceleration signal is eliminated through iterative calculation based on the RLS algorithm. The bias is used to obtain the bias correction signal. With residual The method is to take the initial parameters as the starting point and... Initial bias estimate The initial error covariance matrix and For each sampling time, the forgetting factor is used. Perform three iterative operations: The first step is to calculate the gain coefficient. : In this formula It is the error covariance matrix of the previous time step; The second step iteratively updates the bias estimate. : In this formula It is the residual at the current moment, that is, the difference between the original acceleration signal and the bias estimate at the previous moment; in this way, dynamic tracking can be achieved by using the residual between the original signal and the bias at the previous moment.

[0026] The third step is to update the error covariance matrix: ,in This refers to the identity matrix, thus providing the next time step G. k Calculations provide accurate information.

[0027] The obtained bias correction signal and residual Difference The method is to calculate the bias correction signal after the iteration is completed. Simultaneously record residuals As the criterion for determining the dynamic energy threshold in VMD calculation, A1(t) and Res are compared. k Synchronously transferred to VMD computation.

[0028] The method for secondary verification of the frequency characteristics of each selected modal component in step 4 is to retain the effective low-frequency components with a frequency ≤ 5Hz in the selected modes and remove the noise high-frequency components with a frequency > 5Hz; if the energy proportion of the noise high-frequency component is high, it is still determined to be noise.

[0029] The method for calculating displacement in step 5, which involves two integral operations based on Newton's laws of motion, is to first calculate the velocity. From the initial moment Integrating up to the current time t, the formula is: ,in The initial velocity (in the initial monitoring state, the target object is usually in a stationary state, therefore...) =0, unit: Next, displacement calculation is performed on the velocity signal. from Perform a second integral up to t, the formula is: ,in The initial displacement (monitoring at the initial moment, with the sensor installation position as the reference point, so S0=0, unit: m); the final output displacement signal. .

[0030] The following section provides a detailed description of the specific implementation of this invention, including algorithm parameter configuration, implementation steps, performance verification, and application adaptation: I. Algorithm Parameter Configuration Regarding basic parameter configuration, the sampling frequency of the MEMS sensor is set to 50-200Hz according to the dynamic characteristics of the monitored target, corresponding to the sampling interval. For static scenarios such as building static settlement (displacement change rate ≤ 1 mm / d), a sampling frequency of 50-100 Hz is selected. The results show that at this frequency, the computation time for a single algorithm operation is ≤0.008ms, which is much lower than the sampling interval. This avoids the computational resource redundancy caused by high-frequency sampling while ensuring the complete capture of static displacement changes. For dynamic scenarios such as excavation deformation of foundation pits (displacement change rate 3-13mm / min), a sampling frequency of 150-200Hz was selected. It can completely reproduce the rapid displacement dynamic process of 13mm / min without signal aliasing or information loss, providing high-quality raw data for subsequent bias correction and noise suppression.

[0031] Initial bias estimate This value is based on the inherent bias range of mainstream MEMS accelerometers ( The initial value was determined, and verification showed that this initial value can shorten the initial convergence time of the algorithm to 5 sampling periods, which is 60% more efficient than the random initial value (convergence time of 12 sampling periods); the initial error covariance matrix Set diagonal elements as This conforms to the error distribution characteristics of the sensor in its initial power-on state, laying a stable foundation for subsequent iterations; forgetting factor An adaptive residual adjustment strategy is adopted: for static scenes, the residual is set to 0.98-0.99, and for static scenes, it is set to 0.95-0.97 to ensure timely correction of bias drift.

[0032] The VMD module parameter configuration balances decomposition accuracy and computational efficiency. The number of decomposition modes M is adjusted according to the vibration characteristics of the monitored object: for sandy slope monitoring scenarios (single vibration frequency, mainly concentrated in 1-3Hz, weak noise interference), M=3 is used; for cohesive soil slope monitoring scenarios (complex vibration frequencies, distributed in 0.5-5Hz, with blurred boundaries between noise and effective signal frequencies), M=4-5 is used; the penalty factor is fixed at 2000; and the convergence accuracy is fixed at [value missing]. To ensure the stability and repeatability of decomposition results under different noise scenarios; dynamic energy threshold. Residual based on RLS module output Real-time adjustments can accurately separate effective modes from noise modes, providing a high signal-to-noise ratio signal for displacement calculation.

[0033] Algorithm implementation steps: The algorithm is divided into three core stages: RLS dynamic bias estimation, dynamic energy threshold VMD mode purification, and displacement calculation. Each stage achieves deep collaboration through data interaction. All steps have been verified by experimental code to ensure the operability and stability of engineering deployment.

[0034] II. RLS Dynamic Bias Estimation and Correction Stage Define core parameters: Let t k Let A0(t) be the sampling time point at time k. k ) represents the original acceleration signal at time k (unit: ), B k The bias value at time k (unit: ), B k-1 G is the bias estimate at time k-1. k P represents the gain coefficient of the RLS algorithm at time k (unitless, controlling the step size of the bias update). k The error covariance matrix at time k is a 3×3 diagonal matrix, where the diagonal elements correspond to the uncertainties in the estimation of acceleration, velocity, and displacement, respectively, with units of ( , ), is the forgetting factor (ranging from 0.95 to 0.99, giving higher weight to recent signals to track dynamic bias), and I is a 3×3 identity matrix.

[0035] Bias estimate B k Real-time updates are achieved through three-level iterative calculations, with the specific process as follows: First, calculate the gain coefficient G. k The formula is G k = In this formula, Reflecting the uncertainty of the bias estimate at the previous moment, when When G increases (e.g., due to sudden changes in ambient temperature causing drastic fluctuations in bias), k As it increases, the bias update rate is accelerated to adapt to the drift; when When the bias decreases (while the bias is in a steady state), G k Reduce, to avoid estimation fluctuations caused by over-adjustment.

[0036] Then iteratively update the bias estimate B. k The formula is .in, The residual between the current original signal and the bias at the previous time step (denoted as Res) k The larger the residual, the greater the deviation between the current bias and the true value, and the larger the bias update amplitude, ensuring timely tracking of dynamic bias.

[0037] Finally, update the error covariance matrix P. k The formula is Through the forgetting factor With gain coefficient G k The linkage dynamically adjusts the "memory" of the covariance matrix—when the bias drift is fast, Take a smaller value (0.95-0.97) to reduce the weight of historical data; when the bias is stable, A larger value (0.98-0.99) is chosen to enhance the weight of historical data and provide an accurate basis for calculating the gain coefficient at the next time step.

[0038] After completing the bias estimation at time k, the real-time bias estimate is subtracted from the original acceleration signal to obtain the bias-corrected acceleration signal. Simultaneously record residuals (The magnitude of the residual directly reflects the noise intensity of the current scene; the larger the residual, the stronger the noise interference.) Compare A1(t) with Res... k The data are jointly transmitted to the VMD modal purification module to provide a basis for determining the dynamic energy threshold.

[0039] III. Dynamic Energy Threshold (VMD) Modal Purification Stage This stage represents the core innovation of the algorithm, aiming to remove random noise from A1(t) and output a purified signal A2(t) with a high signal-to-noise ratio. The key lies in utilizing Res... k Achieve scenario adaptation for energy thresholds.

[0040] First, perform VMD basic mode decomposition: set the number of decomposition modes M (range 3-5, determined based on the characteristic that most effective signals in displacement monitoring are low-frequency components, to avoid over-decomposition increasing the computational load or insufficient decomposition missing effective information), and a penalty factor. =2000 (Balances the compactness and smoothness of modal decomposition to ensure clear modal frequency characteristics), convergence accuracy (To ensure the stability and repeatability of the decomposition results). By constructing a constrained variational problem, the alternating direction multiplier algorithm is used to decompose A1(t) to obtain M eigenmode components C. m (t) (m=1,2,...,M), where the effective low-frequency component (frequency≤5Hz, the effective signal in displacement monitoring is mostly in this range) mainly contains effective displacement information, and the noise high-frequency component (frequency>5Hz) is mainly random noise.

[0041] Then, dynamic energy threshold calculation and mode selection are performed, with the following specific steps: The first step is to calculate the modal energy and energy percentage: calculate each modal component using an integral form. Energy Em The formula is Where t0 is the initial sampling time, t k At the current sampling moment, the integral form can accurately quantify the energy contribution of each mode; further calculation of the energy percentage is then performed. It intuitively reflects the proportion of a single mode in the total energy.

[0042] The second step is to determine the dynamic energy threshold. Based on the residual Resk passed by the RLS module, the scene noise intensity is determined, and association rules are established. (In low-noise scenarios, such as indoor building static settlement) At this point, noise interference is weak, so lowering the threshold avoids missing low-energy effective modes (such as low-frequency weak signals generated by slow settling); when (In medium-noise scenarios, such as monitoring ordinary sandy slopes) Balancing screening accuracy with signal integrity; when (In high-noise scenarios, such as deformation of a foundation pit at a construction site) To improve the threshold for eliminating high-energy noise modes and avoid interfering with subsequent displacement calculations, a dynamic energy screening threshold based on scene noise intensity is constructed to achieve accurate separation of effective modes and noise modes, while also cooperating with the RLS algorithm.

[0043] The third step is modal screening and signal reconstruction: Each modal component is sorted according to its energy percentage. Sort by size from largest to smallest, and calculate the cumulative energy percentage by adding them up sequentially. When the cumulative value reaches the dynamic energy threshold, the screening stops. At the same time, combined with the secondary verification of frequency characteristics, the effective low-frequency components with a frequency ≤ 5Hz in the screened modes are retained, and the noise high-frequency components with a frequency > 5Hz are removed (even if some noise high-frequency components have a high energy ratio, they are still judged as noise). Finally, the modal components that have passed the secondary verification are superimposed and reconstructed to obtain the purified acceleration signal A2(t). This signal has effectively removed the bias error and random noise, providing a high-quality input for subsequent displacement calculation.

[0044] IV. Displacement Calculation Stage Based on Purified Signal This stage utilizes the high signal-to-noise ratio A2(t) to achieve accurate displacement calculation. The core employs the trapezoidal integration method to balance accuracy and efficiency, avoiding the error accumulation of traditional integration. Using A2(t) as input, two integrations are performed based on Newton's laws of motion: the first step calculates the velocity signal and initializes the initial velocity. (Assuming the target is stationary in the initial state), perform a trapezoidal integral on A2(t) from the initial time t0 to the current time t, the formula is as follows: The second step is to solve the displacement signal, where For the initial displacement (monitoring at the initial moment, with the sensor installation position as the reference point, so S0=0, unit: m), Performing the second trapezoidal integral, the formula is: Finally, S(t) is converted to commonly used engineering units and output to the display terminal or data storage module of the monitoring system, while simultaneously entering the next sampling cycle.

[0045] A MEMS sensor signal processing system based on the RLS-VMD fusion algorithm is used to implement the aforementioned MEMS signal processing method based on the RLS-VMD fusion algorithm, including an RLS module, a VMD module, and a displacement calculation module. The RLS module eliminates the original acceleration signal through iterative calculation. The bias in the output bias correction signal With residual ; The VMD module is used for bias correction signals. The decomposition yields M modal components. Where m = 1, 2, ..., M, and calculate the energy and energy percentage of each modal component, based on the residual. The dynamic energy threshold was calculated. The modal components are divided according to their energy proportions. The modal components are sorted from largest to smallest, and modal selection is performed by calculating cumulative energy. Then, the frequency characteristics of each selected modal component are verified a second time. The modal components that pass the second frequency characteristic verification are superimposed and reconstructed to output the purified acceleration signal. .

[0046] The displacement calculation module uses the purified acceleration signal As input, displacement is calculated by performing two integral operations based on Newton's laws of motion, and the final output is a displacement signal. displacement signal The final output of the MEMS sensor is a displacement signal based on the monitoring results. displacement signal The results are from the monitoring of MEMS sensors.

[0047] Performance verification instructions: Perform bias correction performance verification and construct a bias system. The test was conducted in three scenarios—low noise, medium noise, and high noise—with gradually changing speeds. The results are as follows: The RLS module of this invention exhibits extremely high stability and accuracy in bias correction error thanks to its residual adaptive forgetting factor strategy: the error in low-noise scenarios is... Medium noise scene High-noise scenarios are The average of the three is only All are stably controlled at Within, and the error fluctuation range between different scenarios is ≤ The accuracy did not decrease significantly due to increased noise intensity, demonstrating excellent anti-interference capability.

[0048] Traditional sliding window methods are limited by the lag of fixed windows and cannot track dynamic biases in real time. The mean value is [value missing] in low, medium, and high noise scenarios. Although noise has a relatively small impact on its error, the overall accuracy is far lower than that of this invention, and the window lag causes the bias tracking response time to be more than 3 times slower than that of this invention. Conventional RLS algorithms use a fixed forgetting factor. It cannot adapt to the bias drift rate in different scenarios, and the mean value is not suitable. Error fluctuation range When the bias drift rate increases, the fixed This results in insufficient tracking sensitivity and significantly lower accuracy compared to the present invention. The direct integration method does not perform any bias correction, relying solely on the integration of the original signal; the bias error accumulates completely, ultimately leading to an error as high as [missing information]. This far exceeds the precision requirements of bias control for engineering monitoring.

[0049] like Figure 4 As shown, through data comparison and calculation, the bias correction accuracy of the present invention is improved by 72% compared with the traditional sliding window method and by 45% compared with the conventional RLS algorithm. The error stability is improved by more than 40% compared with both comparison algorithms, which fully demonstrates its significant advantages in dynamic bias tracking and anti-interference, and can meet the high-precision bias correction requirements in complex engineering environments.

[0050] Noise suppression performance was verified for components containing effective displacement information (amplitude) in the 1-5Hz range. The standard acceleration signal was subjected to non-Gaussian noise of varying intensities, and the test results are as follows: After processing by the Dynamic Energy Threshold (VMD) module of this invention, the signal-to-noise ratio (SNR) reached 32.6 dB in low-noise scenarios, 29.5 dB in medium-noise scenarios, and 28.2 dB in high-noise scenarios, with an SNR fluctuation range ≤ 0.5 dB. The effective signal retention rate was ≥ 92% in all scenarios, with a core effective signal retention rate of 98% in the 1-3 Hz range. Figure 5 As shown: Traditional sliding window combined with VMD algorithm (fixed) The signal-to-noise ratios (SNRs) of the proposed method are 27.1 dB, 23.9 dB, and 21.8 dB, with a fluctuation range of 1.5 dB. In high-noise scenarios, the omission rate of low-energy effective modes in the 1-2 Hz range reaches 15%. The SNRs of conventional RLS combined with a fixed threshold VMD algorithm are 29.3 dB, 26.2 dB, and 24.1 dB, with a fluctuation range of 1.2 dB and an effective signal retention rate of 82%-88%. The direct integration method has an SNR of only 18-22 dB, exhibiting extremely weak noise suppression capabilities. This invention improves the SNR by 3-5 dB and the effective signal retention rate by 10%-15% compared to conventional algorithms, demonstrating that the dynamic energy threshold can accurately adapt to different noise scenarios, achieving a balance between noise suppression and effective signal retention.

[0051] To verify the accuracy of displacement calculation, two types of tests were conducted: static distance measurement and dynamic deformation. In the static distance measurement test, the MEMS sensor was fixed to a linear guide rail with an accuracy of 0.1 mm, and four standard distances of 40 cm, 60 cm, 80 cm, and 100 cm were set. The relative errors of the algorithm of this invention in low, medium, and high noise scenarios were 1.1%-1.8%, 1.3%-2.0%, and 1.5%-2.2%, respectively, with error fluctuations ≤0.2% at different distances. In the dynamic deformation test, the displacement changes of the foundation pit excavation were simulated (rate 3-13 mm / min). The average relative error of this invention in low, medium, and high noise scenarios were 2.5%-3.0%, 3.0%-3.5%, and 3.5%-4.0%, respectively, with error increases ≤0.3% at a displacement rate of 13 mm / min, and the error was consistently lower than the engineering allowable error (5%). Figure 6 As shown in the comparison, the traditional sliding window combined with VMD algorithm has a static error of 3.5%-5.2% and a dynamic error of 5.0%-6.5%, the conventional RLS combined with fixed threshold VMD algorithm has a static error of 2.3%-3.5% and a dynamic error of 4.5%-5.5%, and the direct integration method has a static error of 8.0%-10.5% and a dynamic error of 9.5%-12.0%, all of which cannot meet the requirements of high-precision monitoring. The static ranging accuracy of this invention is improved by 30%-40% compared with conventional algorithms, and the dynamic deformation accuracy is improved by 25%-35%, which fully meets the accuracy requirements of fields such as foundation pit deformation and geological slope monitoring in civil engineering.

[0052] This invention, in terms of dynamic bias correction performance, reduces the bias estimation lag time by more than 60% compared to the traditional sliding window averaging method by clarifying the three-level iterative formula (gain coefficient - bias value - covariance matrix) for the bias estimate Bk and the dynamic adjustment rules for the forgetting factor. In a simulated scenario with gradually changing rates (simulating bias drift caused by sudden temperature changes), the bias correction error of this invention is stably controlled within a certain range. Below, the error of the traditional sliding window algorithm exceeds... The error of the conventional RLS algorithm (with a fixed forgetting factor) is... This provides a higher quality base signal for subsequent VMD mode purification.

[0053] In terms of noise suppression and signal purification, the VMD module's dynamic energy threshold breaks through the limitations of a fixed threshold. In high-noise scenarios ( In [the context of] ), an 85% dynamic threshold improves the high-energy noise mode rejection rate to over 92%; in low-noise scenarios (…), In this module, a 75% dynamic threshold increases the effective mode retention rate to over 95%. After processing by this module, the signal-to-noise ratio is stably improved to over 28dB, reaching a maximum of 32dB, far exceeding the processing effect of conventional fixed-threshold VMD modules (with an upper limit of approximately 25dB in signal-to-noise ratio improvement), effectively solving the problem of separation when noise and effective signal frequencies overlap.

[0054] In terms of displacement calculation accuracy and module synergy, the deep synergy between RLS and VMD (residual feedback adjustment threshold) significantly enhances the end-to-end error suppression capability. The relative error of displacement calculation is strictly controlled within the range of 1.1%-4.0%, with the relative error of static distance monitoring (standard distance of 40cm-100cm) being 1.1%-2.0%, and the relative error of dynamic deformation monitoring (displacement rate of 3-13mm / min, simulating the foundation pit excavation process) being 2.5%-4.0%, fully meeting the high-precision requirements of displacement data in fields such as civil engineering and geological monitoring.

[0055] Those skilled in the art will understand that the above embodiments are specific examples of implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A MEMS signal processing method based on the RLS-VMD fusion algorithm, characterized in that, Includes the following steps: Step 1: Continuously acquire raw acceleration signals using a MEMS sensor at a preset sampling frequency. ; Step 2: Eliminate the original acceleration signal through iterative calculation based on the RLS algorithm. The bias is used to obtain the bias correction signal. With residual ; Step 3: Apply the VMD algorithm to the bias correction signal. Decomposition yields M modal components C. m (t), where m=1,2,...,M; and calculate the energy and energy percentage of each modal component; Step 4: Based on residuals The dynamic energy threshold was calculated. The modal components are divided according to their energy proportions. The modal components are sorted from largest to smallest, and modal selection is performed by calculating cumulative energy. Then, the frequency characteristics of each selected modal component are verified a second time. The modal components that pass the second frequency characteristic verification are superimposed and reconstructed to obtain the purified acceleration signal. ; Step 5: Using the purified acceleration signal As input, displacement is calculated by performing two integral operations based on Newton's laws of motion, and the final output is a displacement signal. displacement signal The results are from the monitoring of MEMS sensors.

2. The MEMS signal processing method based on the RLS-VMD fusion algorithm according to claim 1, characterized in that: In step 2, the original acceleration signal is eliminated through iterative calculation based on the RLS algorithm. The bias is used to obtain the bias correction signal. With residual The method is to take the initial parameters as the starting point and... Initial bias estimate The initial error covariance matrix and For each sampling time, the forgetting factor is used. Perform three iterative operations: The first step is to calculate the gain coefficient. : In this formula It is the error covariance matrix of the previous time step; The second step iteratively updates the bias estimate. : ； In the formula It is the residual at the current moment, that is, the difference between the original acceleration signal and the bias estimate at the previous moment; The third step is to update the error covariance matrix: ,in It refers to the identity matrix.

3. The MEMS signal processing method based on the RLS-VMD fusion algorithm according to claim 1, characterized in that: The obtained bias correction signal With residual The method is, After the iteration is completed, the bias correction signal is calculated. Simultaneously record residuals .

4. The MEMS signal processing method based on the RLS-VMD fusion algorithm according to claim 1, characterized in that: The method for calculating displacement in step 5, which involves two integral operations based on Newton's laws of motion, is to first calculate the velocity. From the initial moment Integrating up to the current time t, the formula is: ,in The initial velocity is then used to calculate the displacement of the velocity signal. from Perform a second integral up to t, the formula is: ,in This represents the initial displacement; the final output displacement signal. .

5. The MEMS signal processing method based on the RLS-VMD fusion algorithm according to claim 1, characterized in that: In step 3, modal components are distinguished into effective low-frequency components and noise high-frequency components by a preset frequency threshold. Modal components that are lower than or equal to the preset frequency threshold contain effective displacement information, while modal components that are higher than the preset frequency threshold are random noise.

6. The MEMS signal processing method based on the RLS-VMD fusion algorithm according to claim 5, characterized in that: The method for performing secondary verification of the frequency characteristics of each selected modal component in step 4 is to retain the effective low-frequency components with frequencies less than or equal to a preset frequency threshold in the selected modes, and to remove the noise high-frequency components with frequencies greater than the preset frequency threshold. If the high-frequency component of noise accounts for a high proportion of energy, it is still considered noise.

7. The MEMS signal processing method based on the RLS-VMD fusion algorithm according to claim 1, characterized in that: Establish residuals With dynamic energy threshold Association rules, when At this time, noise interference is weak, so the dynamic energy threshold is lowered. Avoid missing low-energy effective modes; when At the same time, balance screening accuracy and signal integrity; when At the same time, increase the dynamic energy threshold. Eliminate high-energy noise modes.

8. The MEMS signal processing method based on the RLS-VMD fusion algorithm according to claim 1, characterized in that... Modal component C m The energy (t) is calculated by using an integral form to calculate C for each modal component. m The energy E of (t) m The formula is Where t0 is the initial sampling time, t k This represents the current sampling time.

9. The MEMS signal processing method based on the RLS-VMD fusion algorithm according to claim 1, characterized in that... Modal components Energy percentage The calculation formula is shown below. .

10. A MEMS sensor signal processing system based on the RLS-VMD fusion algorithm, used to implement the MEMS signal processing method based on the RLS-VMD fusion algorithm as described in any one of claims 1-9, characterized in that: Includes the RLS module, VMD module, and displacement calculation module; The RLS module eliminates the original acceleration signal through iterative calculation. The bias in the output bias correction signal With residual ; The VMD module is used for bias correction signals. Decomposition yields M modal components C. m (t), where m=1,2,...,M, and calculate the energy and energy percentage of each modal component, based on the residual. The dynamic energy threshold was calculated. The modal components are divided according to their energy proportions. The modal components are sorted from largest to smallest, and modal selection is performed by calculating cumulative energy. Then, the frequency characteristics of each selected modal component are verified a second time. The modal components that pass the second frequency characteristic verification are superimposed and reconstructed to output the purified acceleration signal. ; The displacement calculation module uses the purified acceleration signal As input, displacement is calculated by performing two integral operations based on Newton's laws of motion, and the final output is a displacement signal. displacement signal The results are from the monitoring of MEMS sensors.

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