Dynamic analysis method of MEMS sensor for outdoor cold state measurement

Abstract

The invention relates to the field of MEMS sensors, and discloses a dynamic analysis method of an MEMS sensor for outdoor cold state measurement, comprising the following steps: S1, collecting tilt or motion data of a plurality of MEMS sensors mounted on the same building; according to the method, through multi-sensor linkage analysis, identification and removal of respective uncorrected drift influence, the precision of building inclination measurement in the outdoor cold state environment is remarkably improved, state expression is carried out by adopting quaternion or Lie group SO (3), the problem of poles and singular points is effectively avoided, fine inclination changes in a three-dimensional space can be accurately described, and meanwhile, the precision of building inclination measurement in the outdoor cold state environment is improved. A measurement factor, a linkage common mode factor and a physical information constraint factor are introduced under a factor graph framework, abnormal equipment data are eliminated in combination with a robust kernel function, a structural stiffness model of a building is introduced to constrain an angular velocity change rate, MEMS high-frequency white noise is filtered out, the robustness of the analysis method is remarkably enhanced, and the analysis accuracy is improved. Therefore, the system can adapt to a complex and changeable outdoor cold-state environment.

Description

Technical Field

[0001] The present invention relates to the field of MEMS sensors, and particularly to a dynamic analysis method for MEMS sensors used in outdoor cold-state measurement. Background Art

[0002] MEMS (Micro-Electro-Mechanical System) sensors are widely used in the field of outdoor building monitoring for measuring dynamic parameters such as inclination and motion. However, in an outdoor cold-state environment, multiple MEMS sensors installed on the same building are often affected by factors such as zero drift, temperature, air pressure, and humidity, resulting in similarity but also significant differences in measurement data. These differences mainly stem from their respective uncorrected drifts and cannot accurately reflect the true changes of the building.

[0003] In the prior art, sensor data processing usually adopts single-device calibration or simple averaging methods. However, these methods ignore the common-mode changes in multi-sensor linkage, cannot effectively remove drift noise, and are difficult to handle the fine inclination description in three-dimensional space, prone to pole and singularity problems. In addition, the existing dynamic analysis methods lack robustness, cannot eliminate abnormal device data, and do not incorporate the physical structure constraints of the building, resulting in low analysis accuracy and poor real-time performance. In practical applications, such as building inclination monitoring, these problems may lead to the accumulation of measurement errors, affecting safety assessment and maintenance decisions, and further resulting in the problems of insufficient accuracy and difficult drift calibration of the existing MEMS sensor linkage analysis methods. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention provides a dynamic analysis method for MEMS sensors used in outdoor cold-state measurement, which solves the above problems.

[0005] To achieve the above objectives, the present invention is realized through the following technical solutions: A dynamic analysis method for MEMS sensors used in outdoor cold-state measurement, comprising the following steps: S1: Collect the inclination or motion data of multiple MEMS sensors installed on the same building; S2: Identify the common changes between the data of the multiple MEMS sensors, infer the true dynamic changes of the building, and remove the influence of their respective uncorrected drifts; S3: Construct a state vector based on quaternion or Lie group SO(3) using the inclination angle and azimuth angle to avoid pole and singularity problems, and obtain the global optimal inclination quaternion of the building through vector summation and averaging; S4: Introduce measurement factors, linkage common-mode factors, and physical information constraint factors in the factor graph framework, and combine recursive least squares or expectation maximization algorithms to achieve dynamic drift self-calibration.

[0006] Preferably, the state vector ,in This is the globally optimal tilt quaternion for the building. This is the real-time integrated drift bias for the i-th sensor, including the second-order terms caused by zero position and temperature.

[0007] Preferably, the measurement factor describes the relationship between sensor readings and the actual state, utilizing the physical model of the MEMS accelerometer: ,in It is the gravity vector. For rotation matrix, It is a nonlinear function affected by temperature, air pressure, and humidity. This refers to random noise in sensor measurements.

[0008] Preferably, the linkage common mode factor uses a robust kernel function to eliminate abnormal devices, forcing all sensors to point to the same building center value after eliminating their respective drift terms.

[0009] Preferably, the physical information constraint factor is introduced into the structural stiffness model of the building to constrain the rate of change of angular velocity. Filter out high-frequency white noise from MEMS.

[0010] Preferably, the recursive least squares algorithm is used to estimate the error parameters of each sensor in real time during the factor graph optimization process, and its specific implementation includes: S401: For each sensor i and each dimension dim, set the initial parameter vector. covariance matrix Forgetting factor ; S402: For each time step : Constructing regressor vectors ,in, This indicates the temperature at the current time step. This represents the square of the humidity at the current time step. This indicates the air pressure at the current time step; Calculate gain ,in, Let be the covariance matrix of the previous time step. This is the regressor vector at the current time step; Computing Innovation ,in To observe the residuals, These are predicted values ​​based on parameter estimates from the previous time step; Update parameters ,in These are the parameter estimates from the previous time step. This refers to the adjustment amount of the parameter; Update covariance ,in Let be the covariance matrix of the previous time step; S403: Estimating Drift ; S404: In the factor plot, the estimated Integrate optimization and iteratively update the whole system. and Until convergence.

[0011] Preferably, the expectation-maximization algorithm is used to process drift parameter estimation with hidden variables, and its specific implementation includes: S405, Set initial parameters for each sensor. drift mean ,variance ; S406. For the observed data Y, calculate the posterior expectation of the hidden variables; S407. Update parameters by maximizing the likelihood function based on the posterior expectation of the hidden variables. S408. Repeat S406-S407 until the parameter change is less than the threshold. S409. In the factor graph, the updated... As a priori, it is combined with other factors for optimization.

[0012] Preferably, it also includes step S5, real-time monitoring and early warning of dynamic changes in the building, specifically including: S501. Calculate the global optimal tilt quaternion of the building in real time, and calculate the tilt angle and azimuth angle of the building based on the quaternion. S502. Set threshold values ​​for changes in tilt angle and azimuth angle. When the detected changes exceed the set threshold values, an early warning signal is triggered. S503: Real-time monitoring data and early warning information are transmitted to the monitoring terminal via a wireless communication module so that maintenance measures can be taken in a timely manner.

[0013] This invention provides a dynamic analysis method for MEMS sensors used in outdoor cold-state measurements. Compared with existing technologies, it has the following advantages:

[0014] In this invention, multi-sensor linkage analysis is used to identify and remove the uncorrected drift effects of each sensor, which significantly improves the accuracy of building tilt measurement in outdoor cold environments. By using quaternions or Lie groups SO(3) for state expression, the problem of extreme singularities is effectively avoided, and the subtle tilt changes in three-dimensional space can be accurately described. At the same time, measurement factors, linkage common mode factors and physical information constraint factors are introduced under the factor graph framework. Abnormal equipment data is eliminated by combining robust kernel functions, and the structural stiffness model of the building is introduced to constrain the rate of change of angular velocity, filtering out high-frequency white noise from MEMS. This significantly enhances the robustness of the analysis method, enabling it to adapt to complex and changeable outdoor cold environments. It is not only suitable for building tilt monitoring, but can also be extended to other fields that require high-precision dynamic measurement, such as bridge monitoring, geological disaster early warning, and large structure health monitoring. Attached Figure Description

[0015] Figure 1 This is a flowchart of a dynamic analysis method for an outdoor cold-state measurement MEMS sensor proposed in this invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Please see Figure 1 The present invention provides the following technical solutions, specifically including the following embodiments: Example 1: A dynamic analysis method for outdoor cold-state measurement MEMS sensors includes the following steps: S1. Collect tilt or motion data from multiple MEMS sensors installed on the same building; S2. Identify common changes among multiple MEMS sensor data, infer the true dynamic changes of the building, and remove the uncorrected drift effects of each individual sensor. S3. Construct a state vector based on quaternions or Lie groups SO(3) using tilt angle and azimuth angle to avoid extreme singularity problems, and obtain the global optimal tilt quaternion of the building by vector summation and averaging. ,in This is the globally optimal tilt quaternion for the building. The real-time integrated drift bias of the i-th sensor includes the second-order terms caused by zero position and temperature. S4. Within the factor graph framework, measurement factors, linkage common mode factors, and physical information constraint factors are introduced. Dynamic drift self-calibration is achieved by combining recursive least squares or expectation-maximization algorithms. The measurement factors describe the relationship between sensor readings and the true state, utilizing the physical model of the MEMS accelerometer. ,in It is the gravity vector. For rotation matrix, It is a nonlinear function affected by temperature, air pressure, and humidity. To mitigate random noise in sensor measurements, a common-mode factor is implemented using a robust kernel function to eliminate faulty devices, forcing all sensors to point to the same building center value after removing their respective drift terms. A physical information constraint factor is introduced into the building's structural stiffness model to constrain the rate of change of angular velocity. To filter out high-frequency white noise in MEMS, a recursive least squares algorithm is used to estimate the error parameters of each sensor in real time during factor graph optimization. The specific implementation includes: S401: For each sensor i and each dimension dim, set the initial parameter vector. covariance matrix Forgetting factor ; S402: For each time step : Constructing regressor vectors ,in, This indicates the temperature at the current time step. This represents the square of the humidity at the current time step. This indicates the air pressure at the current time step; Calculate gain ,in, Let be the covariance matrix of the previous time step. This is the regressor vector at the current time step; Computing Innovation ,in To observe the residuals, These are predicted values ​​based on parameter estimates from the previous time step; Update parameters ,in These are the parameter estimates from the previous time step. This refers to the adjustment amount of the parameter; Update covariance ,in Let be the covariance matrix of the previous time step; S403: Estimating Drift ; S404: In the factor plot, the estimated Integrate optimization and iteratively update the whole system. and Until convergence.

[0018] The expectation-maximization algorithm is used to handle drift parameter estimation with hidden variables. Specific implementations include: S405, Set initial parameters for each sensor. drift mean ,variance ; S406. For the observed data Y, calculate the posterior expectation of the hidden variables; S407. Update parameters by maximizing the likelihood function based on the posterior expectation of the hidden variables. S408. Repeat S406-S407 until the parameter change is less than the threshold. S409. In the factor graph, the updated... As a priori, it is combined with other factors for optimization.

[0019] Preferably, it also includes step S5, real-time monitoring and early warning of dynamic changes in the building, specifically including: S501. Calculate the global optimal tilt quaternion of the building in real time, and calculate the tilt angle and azimuth angle of the building based on the quaternion. S502. Set threshold values ​​for changes in tilt angle and azimuth angle. When the detected changes exceed the set threshold values, an early warning signal is triggered. S503: Real-time monitoring data and early warning information are transmitted to the monitoring terminal via a wireless communication module so that maintenance measures can be taken in a timely manner.

[0020] Example 2: Based on Example 1, the effectiveness of this method was verified by using 5 MEMS sensors and 100 sampling points to simulate a small tilt of a building (true acceleration based on gravity g=[0,0,-9.81]), with drift affected by temperature T, air pressure P, and humidity H. The error index is the mean square error (MSE). The calculation process of MSE is as follows, comparing this method (RLS and EM variants) with the traditional simple averaging method; In cold outdoor environments, building tilt monitoring is crucial for safety assessment and maintenance. Due to changes in environmental factors (such as temperature, air pressure, and humidity), the measurement data of MEMS sensors are often affected by drift. To improve measurement accuracy and reliability, this embodiment uses the recursive least squares (RLS) algorithm to perform real-time calibration of the sensor's dynamic drift.

[0021] Implementation steps S1. Collect tilt or motion data from 5 MEMS sensors installed on the same building, and collect data results under three different environmental conditions: normal environment, high temperature change environment, and high noise environment. S2. Identify common changes among multiple MEMS sensor data, infer the true dynamic changes of the building, and remove the uncorrected drift effects of each individual sensor. S3. Construct a state vector based on quaternions or Lie groups SO(3) using tilt angle and azimuth angle to avoid extreme singularity problems, and obtain the global optimal tilt quaternion of the building by vector summation and averaging. ,in This is the globally optimal tilt quaternion for the building. The real-time integrated drift bias of the i-th sensor includes the second-order terms caused by zero position and temperature. S4. Within the factor graph framework, measurement factors, linkage common mode factors, and physical information constraint factors are introduced. Dynamic drift self-calibration is achieved by combining recursive least squares or expectation-maximization algorithms. The measurement factors describe the relationship between sensor readings and the true state, utilizing the physical model of the MEMS accelerometer. ,in It is the gravity vector. For rotation matrix, It is a nonlinear function affected by temperature, air pressure, and humidity. To mitigate random noise in sensor measurements, a common-mode factor is implemented using a robust kernel function to eliminate faulty devices, forcing all sensors to point to the same building center value after removing their respective drift terms. A physical information constraint factor is introduced into the building's structural stiffness model to constrain the rate of change of angular velocity. To filter out high-frequency white noise in MEMS, a recursive least squares algorithm is used to estimate the error parameters of each sensor in real time during factor graph optimization. The specific implementation includes: S401: For each sensor i and each dimension dim, set the initial parameter vector. covariance matrix Forgetting factor ; S402: For each time step : Constructing regressor vectors ,in, This indicates the temperature at the current time step. This represents the square of the humidity at the current time step. This indicates the air pressure at the current time step; Calculate gain ,in, Let be the covariance matrix of the previous time step. This is the regressor vector at the current time step; Computing Innovation ,in To observe the residuals, These are predicted values ​​based on parameter estimates from the previous time step; Update parameters ,in These are the parameter estimates from the previous time step. This refers to the adjustment amount of the parameter; Update covariance ,in Let be the covariance matrix of the previous time step; S403: Estimating Drift ; S404: In the factor plot, the estimated Integrate optimization and iteratively update the whole system. and Until convergence.

[0022] The expectation-maximization algorithm is used to handle drift parameter estimation with hidden variables. Specific implementations include: S405, Set initial parameters for each sensor. drift mean ,variance ; S406. For the observed data Y, calculate the posterior expectation of the hidden variables; S407. Update parameters by maximizing the likelihood function based on the posterior expectation of the hidden variables. S408. Repeat S406-S407 until the parameter change is less than the threshold. S409. In the factor graph, the updated... As a priori, it is combined with other factors for optimization.

[0023] The calculation process for MSE is as follows:

[0024] in, (Number of sampling points) The estimated acceleration vector (3D). For the simulated real acceleration vector, It is the square of the Euclidean norm (i.e., the sum of the squares of the three dimensions).

[0025] The following is a table showing the data results from the above embodiments:

[0026] Conclusions: In normal environments (temperature variation ±10°C, noise σ=0.01): Traditional method MSE=0.171996; this method RLS MSE=0.000017; EM MSE=0.003451; In high-temperature variable environments (temperature variation ±30°C): Traditional method MSE=0.184349; RLS MSE=0.000014; EM MSE=0.009598. RLS performs excellently under high variability due to its recursive adaptation; In high-noise environments (noise σ=0.1): Traditional method MSE=0.171051; RLS MSE=0.001245; EM MSE=0.005777. EM is sensitive to noise but still outperforms the traditional method.

[0027] Example 3: Five MEMS sensors and 100 sampling points were used to simulate the slight tilt of a building (true acceleration based on gravity g=[0,0,-9.81]), with drift affected by temperature T, air pressure P, and humidity H. The error metric was mean square error (MSE). The calculation process of MSE was compared between this method (RLS and EM variants) and the traditional simple averaging method as follows; In cold outdoor environments, building tilt monitoring is crucial for safety assessment and maintenance. Due to changes in environmental factors (such as temperature, air pressure, and humidity), the measurement data of MEMS sensors are often affected by drift. To improve measurement accuracy and reliability, this embodiment uses the recursive least squares (RLS) algorithm to perform real-time calibration of the sensor's dynamic drift.

[0028] Implementation steps S1. Collect tilt or motion data from 5 MEMS sensors installed on the same building under the same normal environmental conditions; S2. Identify common changes among multiple MEMS sensor data, infer the true dynamic changes of the building, and remove the uncorrected drift effects of each individual sensor. S3. Construct a state vector based on quaternions or Lie groups SO(3) using tilt angle and azimuth angle to avoid extreme singularity problems, and obtain the global optimal tilt quaternion of the building by vector summation and averaging. ,in This is the globally optimal tilt quaternion for the building. The real-time integrated drift bias of the i-th sensor includes the second-order terms caused by zero position and temperature. S4. Within the factor graph framework, measurement factors, linkage common mode factors, and physical information constraint factors are introduced. Dynamic drift self-calibration is achieved by combining recursive least squares or expectation-maximization algorithms. The measurement factors describe the relationship between sensor readings and the true state, utilizing the physical model of the MEMS accelerometer. ,in It is the gravity vector. For rotation matrix, It is a nonlinear function affected by temperature, air pressure, and humidity. To mitigate random noise in sensor measurements, a common-mode factor is implemented using a robust kernel function to eliminate faulty devices, forcing all sensors to point to the same building center value after removing their respective drift terms. A physical information constraint factor is introduced into the building's structural stiffness model to constrain the rate of change of angular velocity. To filter out high-frequency white noise in MEMS, a recursive least squares algorithm is used to estimate the error parameters of each sensor in real time during factor graph optimization. The specific implementation includes: S401: For each sensor i and each dimension dim, set the initial parameter vector. covariance matrix The forgetting factor is set to 1. , , ; S402: For each time step : Constructing regressor vectors ,in, This indicates the temperature at the current time step. This represents the square of the humidity at the current time step. This indicates the air pressure at the current time step; Calculate gain ,in, Let be the covariance matrix of the previous time step. This is the regressor vector at the current time step; Computing Innovation ,in To observe the residuals, These are predicted values ​​based on parameter estimates from the previous time step; Update parameters ,in These are the parameter estimates from the previous time step. This refers to the adjustment amount of the parameter; Update covariance ,in Let be the covariance matrix of the previous time step; S403: Estimating Drift ; S404: In the factor plot, the estimated Integrate optimization and iteratively update the whole system. and Until convergence.

[0029] The expectation-maximization algorithm is used to handle drift parameter estimation with hidden variables. Specific implementations include: S405, Set initial parameters for each sensor. drift mean ,variance ; S406. For the observed data Y, calculate the posterior expectation of the hidden variables; S407. Update parameters by maximizing the likelihood function based on the posterior expectation of the hidden variables. S408. Repeat S406-S407 until the parameter change is less than the threshold. S409. In the factor graph, the updated... As a priori, it is combined with other factors for optimization.

[0030] The following is a table showing the data results from the above embodiments:

[0031] Conclusion: RLS forgetting factor λ: MSE = 0.000012 when λ = 0.9; MSE = 0.000015 when λ = 0.95; MSE = 0.000017 when λ = 0.99. A smaller λ adapts to rapid changes and improves accuracy, but may increase noise sensitivity; EM iteration count: MSE is 0.003451 for 5, 10, and 20 iterations (due to the rapid convergence of the simple model). In complex models, more iterations can further reduce the error, but the computational cost increases.

[0032] In summary, the experimental verification in this embodiment demonstrates that the recursive least squares algorithm can effectively calibrate the dynamic drift of MEMS sensors in outdoor cold environments, significantly improving measurement accuracy and reliability. This method is particularly suitable for practical applications such as building tilt monitoring, providing accurate data support for building safety assessment and maintenance.

[0033] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A dynamic analysis method of a MEMS sensor for outdoor cold measurement, characterized by: Includes the following steps: S1. Collect tilt or motion data from multiple MEMS sensors installed on the same building; S2. Identify the common changes among the data from the multiple MEMS sensors, infer the true dynamic changes of the building, and remove the uncorrected drift effects of each sensor. S3. Construct a state vector based on quaternions or Lie group SO(3) using tilt angle and azimuth angle to avoid extreme singularity problems, and obtain the global optimal tilt quaternion of the building by vector summation and averaging. S4. Introduce measurement factors, linkage common mode factors, and physical information constraint factors within the factor graph framework, and combine them with recursive least squares or expectation-maximization algorithms to achieve dynamic drift self-calibration.

2. The dynamic analysis method for an outdoor cold-state measurement MEMS sensor according to claim 1, characterized in that: the state vector wherein is the global optimal tilt quaternion of the building, is the real-time integrated drift bias of the i-th sensor, including the zero offset, the temperature-induced second order term.

3. The dynamic analysis method for an outdoor cold-state measurement MEMS sensor according to claim 1, characterized in that: The measurement factor describes the relation of the sensor reading to the true state, using a physical model of the MEMS accelerometer: where is the gravity vector, is the rotation matrix, is a non-linear function influenced by temperature, air pressure, humidity, is the random noise in the sensor measurement.

4. The dynamic analysis method of a MEMS sensor for outdoor cold-state measurement according to claim 1, characterized in that: The linkage common mode factor uses a robust kernel function to eliminate abnormal devices, forcing all sensors to point to the same building center value after eliminating their respective drift terms.

5. The dynamic analysis method for an outdoor cold-state measurement MEMS sensor according to claim 1, characterized in that: The physical information constraint factor introduces a structural stiffness model of the building, constraining the angular velocity rate of change Filter out the MEMS high-frequency white noise.

6. The dynamic analysis method of a MEMS sensor for outdoor cold-state measurement according to claim 1, characterized in that: The recursive least squares algorithm is used to estimate the error parameters of each sensor in real time during the factor graph optimization process. Its specific implementation includes: S401 : Set initial parameter vector for each sensor i and each dimension dim , covariance matrix , forgetting factor ; S402: For each time step : Constructing regressor vectors where, represents the temperature at the current time step, represents the square of the humidity at the current time step, represents the air pressure at the current time step; Computing the gain where, is the covariance matrix of the previous time step, is the regressor vector of the current time step; Computing Innovation ,in To observe the residuals, These are predicted values ​​based on parameter estimates from the previous time step; Update parameters ,in These are the parameter estimates from the previous time step. This refers to the adjustment amount of the parameter; Update covariance ,in Let be the covariance matrix of the previous time step; S403: Estimating Drift ; S404: In the factor plot, the estimated Integrate optimization and iteratively update the whole system. and Until convergence.

7. The dynamic analysis method for an outdoor cold-state measurement MEMS sensor according to claim 1, characterized in that: The expectation-maximization algorithm is used to handle drift parameter estimation with hidden variables, and its specific implementation includes: S405, Set initial parameters for each sensor. drift mean ,variance ; S406. For the observed data Y, calculate the posterior expectation of the hidden variables; S407. Update parameters by maximizing the likelihood function based on the posterior expectation of the hidden variables. S408. Repeat S406-S407 until the parameter change is less than the threshold. S409. In the factor graph, the updated... As a priori, it is combined with other factors for optimization.

8. The dynamic analysis method for an outdoor cold-state measurement MEMS sensor according to claim 1, characterized in that: It also includes step S5, which involves real-time monitoring and early warning of dynamic changes in the building, specifically including: S501. Calculate the global optimal tilt quaternion of the building in real time, and calculate the tilt angle and azimuth angle of the building based on the quaternion. S502. Set threshold values ​​for changes in tilt angle and azimuth angle. When the detected changes exceed the set threshold values, an early warning signal is triggered. S503: Real-time monitoring data and early warning information are transmitted to the monitoring terminal via a wireless communication module so that maintenance measures can be taken in a timely manner.

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