A vibration sensor adaptive virtual leveling system and method based on Rodrigues transformation
Patent Information
- Application Number
- CN202610965540.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-30
- Publication Date
- 2026-10-13
AI Technical Summary
1. 物理调平机构：采用物理水平仪和机械微调底座进行人工对准，但这种方法会增加传感器节点的硬件成本和体积，而且在设备强振动工况下，物理对准机构容易发生松动或走位
本发明公开的基于 Rodrigues 变换的振动传感器自适应虚拟调平系统及方法，通过全软件级自补偿，免去物理调平机构，替代了机械调平硬件，降低了传感器的安装部署与维护成本，有利于避免物理微调底座因机械强振动发生松动或走位的隐患，此外还降低了计算开销，适应边缘端部署：通过对 Rodrigues 三维空间旋转矩阵 R在条件下的降维简化，免去了三角函数开销，旋转矩阵构建过程仅包含 7 次乘法（或二次化简至5 次乘法），可降低边缘微处理器（如 Cortex-M 内核）的运算开销，有利于降低功耗，延长传感器节点的运行寿命，此外，通过奇异边界自适应判定防死锁：针对传感器接近水平姿态（s → 0, c > 0）或颠倒安装（s → 0, c < 0）等工况，设立判定分支直接赋予常数矩阵，可避免分母为零引发的硬件除零异常，有利于提升算法在各种安装倾角下的运行稳定性，最后本发明还能降低轴间信号串扰：作为信号链前端的预处理步骤，能够降低轴间耦合串扰，有助于提高电机故障诊断的准确率。
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Figure CN122900832A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of rotating machinery condition monitoring and vibration signal processing technology, and more specifically, to an adaptive virtual leveling system and method for vibration sensors based on Rodrigues transform. Background Technology
[0002] In vibration monitoring of rotating machinery (such as electric motors, reciprocating compressors, oil pumps, etc.), triaxial accelerometers are the core components for acquiring mechanical vibration characteristics. When performing fault diagnosis using expert systems or machine learning algorithms, it is usually necessary to decompose the vibration signals collected by the sensors into pure radial (horizontal and vertical) and pure axial vibrations.
[0003] However, when deployed in industrial settings, due to irregular equipment surface shapes, narrow installation locations, or human error, it is difficult to achieve physical horizontal and angular alignment of sensors (i.e., the three axes are difficult to align with the radial and axial directions of the equipment). This leads to inter-axis signal coupling: radial vibrations may leak into the axial channel, or axial vibrations may be mapped into the radial channel, causing distortion in the extracted fault feature frequency amplitudes. This may result in misdiagnosis of faults such as misalignment and imbalance by the expert system.
[0004] To address this problem, existing technologies mainly offer the following solutions: 1. Physical leveling mechanism: Manual alignment is performed using a physical level and a mechanical fine-tuning base. However, this method increases the hardware cost and size of the sensor nodes, and the physical alignment mechanism is prone to loosening or displacement under strong vibration conditions.
[0005] 2. Digital Gravity Debiasing: This method directly subtracts the mean (DC component) from the triaxial acceleration signal. However, this method can usually only reduce the numerical influence of static gravitational acceleration, and it is difficult to solve the problems of inter-axis angle and signal leakage caused by sensor tilt.
[0006] 3. Euler Angle Rotation Matrix Alignment: This method constructs a coordinate system aligned by multiplying a cubic rotation matrix by calculating the Euler angles of rotation around three axes. However, the Euler angle method involves numerous trigonometric function operations (sine, cosine, arctangent), which incurs computational overhead in edge microprocessors (MCUs) with limited computing power. Furthermore, when the tilt angle reaches its limit (e.g., pitch angle...), the alignment becomes problematic. When this happens, a "gimbal lock" will be triggered, causing the rotation matrix to become algebraically singular and fail.
[0007] Therefore, it is necessary to propose an adaptive virtual leveling system and method for vibration sensors based on Rodrigues transform to solve the above problems. Summary of the Invention
[0008] To overcome at least one of the defects (deficiencies) of the prior art described above, the present invention provides an adaptive virtual leveling system and method for vibration sensors based on Rodrigues transform.
[0009] To solve the above technical problems, the technical solution of the present invention is as follows: an adaptive virtual leveling system for vibration sensors based on Rodrigues transform, comprising a raw signal acquisition module, a DC gravity extraction module, a vector normalization module, a singular degradation adaptive module, a matrix construction module, and an in-situ coverage rotation module; The original signal acquisition module is used to acquire the time-domain acceleration sequences x(t), y(t), and z(t) collected by a triaxial accelerometer mounted on the surface of rotating machinery; The DC gravity extraction module, connected to the original signal acquisition module, is used to perform moving average filtering on the received time-domain acceleration sequence and calculate the static gravity acceleration projection vector within a set time window. .
[0010] The vector normalization module, connected to the DC gravity extraction module, is used to calculate and normalize the magnitude of the gravity acceleration projection vector calculated by the DC gravity extraction module, and to calculate the source gravity unit vector. Align unit vector with target ; The singular degradation adaptive module, connected to the vector normalization module, is used to calculate the sine and cosine values of the rotation angle s and c in real time, and to determine when... The singular boundary states at time are directly assigned to the corresponding constant rotation matrix to avoid division by zero errors; The matrix construction module is connected to the vector normalization module and the singular degeneracy adaptive module, respectively, and is used to determine whether the system state is normal, i.e., the sine value of the rotation angle. At that time, the rotation axis is normalized, and the Z component of the unit rotation axis is always zero. Under specific conditions, construct the dimensionality-reduced Rodrigues 3D space rotation matrix R; The in-situ covering rotation module is connected to the matrix construction module and is used to call the constructed Rodrigues three-dimensional space rotation matrix R to perform in-situ linear coordinate transformation on each sampling point of the original time-domain acceleration sequence, eliminate the interference of static gravity components in the original vibration sequence, reduce the cross-coupling error between axes, and finally output accurate radial and axial vibration signals to complete the adaptive virtual leveling of the vibration sensor. This invention also discloses an adaptive virtual leveling method for vibration sensors based on the Rodrigues transform, comprising the following steps: S101: Data acquisition is performed using the original signal acquisition module to obtain the time-domain acceleration sequences x(t), y(t), and z(t) collected by the triaxial accelerometer arranged on the surface of the rotating machinery; S102: Using the DC gravity extraction module, the acquired time-domain acceleration sequence is subjected to long sliding window mean low-pass filtering. By constructing a calculation window with a time period T or selecting N sampling points, the window mean is calculated for the time-domain acceleration sequence to obtain the static gravity acceleration projection vector. ; in, ; S103: Utilize the vector normalization module to perform vector normalization processing and anomaly detection, and calculate the magnitude of the gravitational acceleration projection vector. ; like If the value is less than the preset threshold of 1mg, the data is determined to be abnormal or the sensor is in a state of weightlessness, and the current leveling process is terminated directly. like If the value is not less than a preset threshold, then the gravitational acceleration projection vector is normalized to obtain the source gravity unit vector. : ; Define the target alignment gravity unit vector This means aligning the gravity to the Z-axis; S104: Solving for rotational parameters and determining singular degeneracy using a singular degeneracy adaptive module, and solving for the source gravity unit vector through outer product operations. Align unit vector with target And calculate the rotation axis vector. Because the target is aligned with the unit gravity vector Therefore, the outer product operation is greatly simplified to: ; Then calculate the sine of the rotation angle s and the cosine of the rotation angle c, where the sine of the rotation angle s is: ; The cosine value of the rotation angle c: ; Based on the numerical relationship between the sine and cosine values of the rotation angle s and c, three decision branches are defined: If the sine value And since the cosine value c > 0, the sensor is determined to be in a near-horizontal alignment posture, requiring no adjustment. The Rodrigues 3D rotation matrix R is directly assigned as the identity matrix. ; If the sine value If the cosine value c < 0, the sensor is determined to be in an inverted installation position. A reflection transformation matrix is assigned, and the physical directions of the Y-axis and Z-axis are reversed to maintain a right-handed coordinate system. ; like The orientation is determined to be a normal tilt. The rotation axis vector is normalized to obtain a unit rotation axis vector with a Z component that is always zero. ,because Here, the Z component of the unit rotation axis is always zero: ; S105: Construct a one-time Rodrigues 3D rotation matrix R using the matrix construction module. Based on the Rodrigues rotation formula, the Rodrigues 3D rotation matrix R can be expressed using a unit rotation axis. The sine and cosine of the included angle are expressed as: ; in, It is the unit axis of rotation Antisymmetric matrix: ; Combined unit rotation axis By substituting and expanding the components under the constraints, a specific algebraic dimensionality reduction is performed on the 3x3 rotation matrix to eliminate all constraints. The operation terms, the expansion of the nine analytical coefficients of the Rodrigues three-dimensional rotation matrix R is as follows: ; By introducing intermediate product variables The calculation of the 9 matrix components in the above equation can be transformed into: ; The entire process avoids the use of trigonometric functions and obtains the Rodrigues three-dimensional rotation matrix R through only a finite number of multiplication operations; S106: In-situ covering vibration signal correction is performed using an in-situ covering rotation module. The obtained Rodrigues three-dimensional spatial rotation matrix R is used to perform an in-situ linear transformation on each sampling point of the time-domain acceleration sequence acquired by the triaxial accelerometer. ; After transformation, the rotationally corrected result is obtained. and This is a purely radial plane vibration signal perpendicular to the vertical direction of gravity. It is a pure axial vibration signal, eliminating gravity component interference and inter-axis signal crosstalk, and completing the sensor's adaptive virtual leveling.
[0011] Furthermore, in S102, the long sliding window mean low-pass filter is used to filter out the quasi-periodic alternating vibration signal of the rotating machinery and retain the static gravity DC component. The number of sampling points N of the sliding window is adaptively configured according to the equipment type and vibration frequency of the rotating machinery.
[0012] Furthermore, in S104, the gravity unit vector is aligned by fixing the target. This achieves a fixed simplification of the outer product operation, ensuring that the Z component of the rotation axis vector is always zero, thus providing a prerequisite constraint for subsequent dimensionality reduction and simplification of the rotation matrix.
[0013] Furthermore, in S104, the singular degradation adaptive determination mechanism, for the two extreme singular conditions of sensor horizontal alignment and inverted installation, completely avoids the abnormal operation of the normalization denominator being zero when s→0 by replacing the conventional solution operation with a predefined constant rotation matrix, thus solving the gimbal deadlock problem of the traditional Euler angle algorithm.
[0014] Furthermore, in S105, based on The specific constraints reduce the dimensionality of the Rodrigues rotation matrix, simplifying traditional complex matrix operations to 7 multiplication operations. This eliminates the need to call sine, cosine, and arctangent trigonometric functions, significantly reducing the computing power and operating power consumption of edge microprocessors.
[0015] Furthermore, in S106, the in-situ linear transformation adopts the same memory space data update method, which does not require additional cache memory and is suitable for embedded wireless sensor node deployment scenarios with low memory and low computing power.
[0016] Furthermore, the triaxial accelerometer is suitable for various types of rotating machinery, and can perform real-time adaptive virtual leveling when the equipment is running smoothly or stopped. The output decoupled vibration signal is used for equipment fault diagnosis and operating condition identification.
[0017] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: This invention discloses an adaptive virtual leveling system and method for vibration sensors based on Rodrigues transform. Through fully software-level self-compensation, it eliminates the need for physical leveling mechanisms, replaces mechanical leveling hardware, reduces sensor installation, deployment, and maintenance costs, and helps avoid the risk of loosening or displacement of the physical fine-tuning base due to strong mechanical vibration. Furthermore, it reduces computational overhead and is suitable for edge deployment: by applying the Rodrigues three-dimensional spatial rotation matrix R... The dimensionality reduction simplification under the given conditions eliminates the overhead of trigonometric functions. The rotation matrix construction process only involves 7 multiplications (or quadratic simplification to 5 multiplications), which can reduce the computational overhead of edge microprocessors (such as Cortex-M cores), thus helping to reduce power consumption and extend the operating life of sensor nodes. In addition, deadlock prevention is achieved through singular boundary adaptive decision-making: for working conditions such as sensors being in near-horizontal posture (s → 0, c > 0) or inverted installation (s → 0, c < 0), a decision branch is set up to directly assign a constant matrix, which can avoid hardware division by zero caused by the denominator being zero, thus improving the stability of the algorithm under various installation tilt angles. Finally, this invention can also reduce inter-axis signal crosstalk: as a preprocessing step at the front end of the signal chain, it can reduce inter-axis coupling crosstalk, which helps to improve the accuracy of motor fault diagnosis. Attached Figure Description
[0018] Figure 1 This is a schematic diagram of the structure of the vibration sensor adaptive virtual leveling system based on Rodrigues transform in this invention.
[0019] Figure 2 This is the overall control flowchart of the virtual leveling method based on the Rodrigues rotation formula in this invention.
[0020] Figure 3 This is the algebraic self-healing and branch decision logic diagram of the numerical singular state in step S104 of the present invention.
[0021] Figure 4 This is a schematic diagram of radial / axial vibration leakage caused by the arbitrary angle of the triaxial accelerometer being attached and tilted in this invention.
[0022] Figure 5 This is a schematic diagram of the decoupled distribution of vibration after Rodrigues rotation leveling and alignment in this invention.
[0023] In the figure, 1 is the original signal acquisition module, 2 is the DC gravity extraction module, 3 is the vector normalization module, 4 is the singular degradation adaptive module, 5 is the matrix construction module, and 6 is the in-situ coverage rotation module. Detailed Implementation
[0024] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. To better illustrate this embodiment, some components in the drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions of the product. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.
[0025] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. The technical solution of this invention will be further described below with reference to the accompanying drawings and embodiments.
[0026] like Figure 1-5 As shown, a Rodrigues transform-based adaptive virtual leveling system for vibration sensors includes a raw signal acquisition module 1, a DC gravity extraction module 2, a vector normalization module 3, a singular degradation adaptive module 4, a matrix construction module 5, and an in-situ coverage rotation module 6. The raw signal acquisition module 1 acquires the time-domain acceleration sequences x(t), y(t), and z(t) collected by a triaxial accelerometer mounted on the surface of rotating machinery. The DC gravity extraction module 2, connected to the raw signal acquisition module 1, performs sliding mean filtering on the received time-domain acceleration sequences to calculate the static gravity acceleration projection vector within a set time window. Vector normalization module 3, connected to DC gravity extraction module 2, is used to calculate and normalize the magnitude of the gravity acceleration projection vector calculated by DC gravity extraction module 2, and to calculate the source gravity unit vector. Align unit vector with target The singular degeneracy adaptive module 4, connected to the vector normalization module 3, is used to calculate the sine and cosine values of the rotation angle s and c in real time, and to determine when... The singular boundary state is determined and the corresponding constant rotation matrix is directly assigned to it to avoid division by zero error; the matrix construction module 5 is connected to the vector normalization module 3 and the singular degeneracy adaptive module 4 respectively, and is used to determine the normal state of the system, i.e., the sine value of the rotation angle. At that time, the rotation axis is normalized, and the Z component of the unit rotation axis is always zero. Under specific conditions, a dimension-reduced Rodrigues 3D spatial rotation matrix R is constructed; the in-situ covering rotation module 6, connected to the matrix construction module 5, is used to call the constructed Rodrigues 3D spatial rotation matrix R, and perform in-situ linear coordinate transformation on each sampling point of the original time-domain acceleration sequence to eliminate the interference of static gravity components in the original vibration sequence, reduce the cross-coupling error between axes, and finally output accurate radial and axial vibration signals to complete the adaptive virtual leveling of the vibration sensor; This invention also discloses an adaptive virtual leveling method for vibration sensors based on the Rodrigues transform, comprising the following steps: S101: Data acquisition is performed using the original signal acquisition module to obtain the time-domain acceleration sequences x(t), y(t), and z(t) collected by the triaxial accelerometer arranged on the surface of the rotating machinery; S102: Using the DC gravity extraction module, the acquired time-domain acceleration sequence is subjected to long sliding window mean low-pass filtering. By constructing a calculation window with a time period T or selecting N sampling points, the window mean is calculated for the time-domain acceleration sequence to obtain the static gravity acceleration projection vector. ; in, ; S103: Utilize the vector normalization module to perform vector normalization processing and anomaly detection, and calculate the magnitude of the gravitational acceleration projection vector. : ; like If the value is less than the preset threshold of 1mg, the data is determined to be abnormal or the sensor is in a state of weightlessness, and the current leveling process is terminated directly. like If the value is not less than a preset threshold, then the gravitational acceleration projection vector is normalized to obtain the source gravity unit vector. : ; Define the target alignment gravity unit vector This means aligning the gravity to the Z-axis; S104: Solving for rotational parameters and determining singular degeneracy using a singular degeneracy adaptive module, and solving for the source gravity unit vector through outer product operations. Align unit vector with target And calculate the rotation axis vector. Because the target is aligned with the unit gravity vector Therefore, the outer product operation is greatly simplified to: ; Then calculate the sine of the rotation angle s and the cosine of the rotation angle c, where the sine of the rotation angle s is: ; The cosine value of the rotation angle c: ; Based on the numerical relationship between the sine and cosine values of the rotation angle s and c, three decision branches are defined: If the sine value And since the cosine value c > 0, the sensor is determined to be in a near-horizontal alignment posture, requiring no adjustment. The Rodrigues 3D rotation matrix R is directly assigned as the identity matrix. ; If the sine value If the cosine value c < 0, the sensor is determined to be in an inverted installation position. A reflection transformation matrix is assigned, and the physical directions of the Y-axis and Z-axis are reversed to maintain a right-handed coordinate system. ; like The orientation is determined to be a normal tilt. The rotation axis vector is normalized to obtain a unit rotation axis vector with a Z component that is always zero. ,because Here, the Z component of the unit rotation axis is always zero: ; S105: Construct a one-time Rodrigues 3D rotation matrix R using the matrix construction module. Based on the Rodrigues rotation formula, the Rodrigues 3D rotation matrix R can be expressed using a unit rotation axis. The sine and cosine of the included angle are expressed as: ; in, It is the unit axis of rotation Antisymmetric matrix: ; Combined unit rotation axis By substituting and expanding the components under the constraints, a specific algebraic dimensionality reduction is performed on the 3x3 rotation matrix to eliminate all constraints. The operation terms, the expansion of the nine analytical coefficients of the Rodrigues three-dimensional rotation matrix R is as follows: ; By introducing intermediate product variables The calculation of the 9 matrix components in the above equation can be transformed into: ; The entire process avoids the use of trigonometric functions and obtains the Rodrigues three-dimensional rotation matrix R through only a finite number of multiplication operations; S106: In-situ covering vibration signal correction is performed using an in-situ covering rotation module. The obtained Rodrigues three-dimensional spatial rotation matrix R is used to perform an in-situ linear transformation on each sampling point of the time-domain acceleration sequence acquired by the triaxial accelerometer. ; After transformation, the rotationally corrected result is obtained. and This is a purely radial plane vibration signal perpendicular to the vertical direction of gravity. It is a pure axial vibration signal, eliminating gravity component interference and inter-axis signal crosstalk, and completing the sensor's adaptive virtual leveling.
[0027] In S102 of the present invention, the long sliding window mean low-pass filter is used to filter out the quasi-periodic alternating vibration signal of the rotating machinery and retain the static gravity DC component. The number of sampling points N of the sliding window is adaptively configured according to the equipment type and vibration frequency of the rotating machinery.
[0028] In S104 of the present invention, the gravity unit vector is aligned by fixing the target. This achieves a fixed simplification of the outer product operation, ensuring that the Z component of the rotation axis vector is always zero, thus providing a prerequisite constraint for subsequent dimensionality reduction and simplification of the rotation matrix.
[0029] In S104 of this invention, the singular degradation adaptive determination mechanism, for the two extreme singular working conditions of sensor horizontal alignment and inverted installation, replaces the conventional solution operation with a predefined constant rotation matrix, completely avoiding the operation abnormality of the normalization denominator being zero when s→0, and solving the gimbal deadlock problem of the traditional Euler angle algorithm.
[0030] In S105 of the present invention, based on The specific constraints reduce the dimensionality of the Rodrigues rotation matrix, simplifying traditional complex matrix operations to 7 multiplication operations. This eliminates the need to call sine, cosine, and arctangent trigonometric functions, significantly reducing the computing power and operating power consumption of edge microprocessors.
[0031] In S106 of the present invention, the in-situ linear transformation adopts the same memory space data update method, which does not require additional cache memory and is suitable for embedded wireless sensor node deployment scenarios with low memory and low computing power.
[0032] In this invention, the triaxial accelerometer is suitable for various types of rotating machinery. It can perform real-time adaptive virtual leveling when the equipment is running smoothly or stopped. The output decoupled vibration signal is used for equipment fault diagnosis and operating condition identification.
[0033] The positional relationships described in the figures are for illustrative purposes only and should not be construed as limiting this patent. Clearly, the above embodiments of the present invention are merely examples to clearly illustrate the invention and are not intended to limit the implementation of the invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of this invention.
Claims
1. An adaptive virtual leveling system for vibration sensors based on Rodrigues transform, characterized in that: It includes a raw signal acquisition module, a DC gravity extraction module, a vector normalization module, a singular degradation adaptive module, a matrix construction module, and an in-situ coverage rotation module; The original signal acquisition module is used to acquire the time-domain acceleration sequences x(t), y(t), and z(t) collected by a triaxial accelerometer mounted on the surface of rotating machinery; The DC gravity extraction module, connected to the original signal acquisition module, is used to perform moving average filtering on the received time-domain acceleration sequence and calculate the static gravity acceleration projection vector within a set time window. ; The vector normalization module, connected to the DC gravity extraction module, is used to calculate and normalize the magnitude of the gravity acceleration projection vector calculated by the DC gravity extraction module, and to calculate the source gravity unit vector. Align unit vector with target ; The singular degradation adaptive module, connected to the vector normalization module, is used to calculate the sine and cosine values of the rotation angle s and c in real time, and to determine when... The singular boundary states at time are directly assigned to the corresponding constant rotation matrix to avoid division by zero errors; The matrix construction module is connected to the vector normalization module and the singular degeneracy adaptive module, respectively, and is used to determine whether the system state is normal, i.e., the sine value of the rotation angle. At that time, the rotation axis is normalized, and the Z component of the unit rotation axis is always zero. Under specific conditions, construct the dimensionality-reduced Rodrigues 3D space rotation matrix R; The in-situ covering rotation module is connected to the matrix construction module and is used to call the constructed Rodrigues three-dimensional space rotation matrix R to perform in-situ linear coordinate transformation on each sampling point of the original time-domain acceleration sequence, eliminate the interference of static gravity components in the original vibration sequence, reduce the cross-coupling error between axes, and finally output accurate radial and axial vibration signals to complete the adaptive virtual leveling of the vibration sensor.
2. An adaptive virtual leveling method for vibration sensors based on Rodrigues transform, characterized in that: Includes the following steps: S101: Data acquisition is performed using the original signal acquisition module to obtain the time-domain acceleration sequences x(t), y(t), and z(t) collected by the triaxial accelerometer arranged on the surface of the rotating machinery; S102: Using the DC gravity extraction module, the acquired time-domain acceleration sequence is subjected to long sliding window mean low-pass filtering. By constructing a calculation window with a time period T or selecting N sampling points, the window mean is calculated for the time-domain acceleration sequence to obtain the static gravity acceleration projection vector. ; in, ; S103: Utilize the vector normalization module to perform vector normalization processing and anomaly detection, and calculate the magnitude of the gravitational acceleration projection vector. : ; like If the value is less than the preset threshold of 1mg, the data is determined to be abnormal or the sensor is in a state of weightlessness, and the current leveling process is terminated directly. like If the value is not less than a preset threshold, then the gravitational acceleration projection vector is normalized to obtain the source gravity unit vector. : ; Define the target alignment gravity unit vector This means aligning the gravity to the Z-axis; S104: Solving for rotational parameters and determining singular degeneracy using a singular degeneracy adaptive module, and solving for the source gravity unit vector through outer product operations. Align unit vector with target And calculate the rotation axis vector. Because the target is aligned with the unit gravity vector Therefore, the outer product operation is greatly simplified to: ; Then calculate the sine of the rotation angle s and the cosine of the rotation angle c, where the sine of the rotation angle s is: ; The cosine value of the rotation angle c: ; Based on the numerical relationship between the sine and cosine values of the rotation angle s and c, three decision branches are defined: If the sine value And since the cosine value c > 0, the sensor is determined to be in a near-horizontal alignment posture, requiring no adjustment. The Rodrigues 3D rotation matrix R is directly assigned as the identity matrix. ; If the sine value If the cosine value c < 0, the sensor is determined to be in an inverted installation position. A reflection transformation matrix is assigned, and the physical directions of the Y-axis and Z-axis are reversed to maintain a right-handed coordinate system. ; like The orientation is determined to be a normal tilt. The rotation axis vector is normalized to obtain a unit rotation axis vector with a Z component that is always zero. ,because Here, the Z component of the unit rotation axis is always zero: ; S105: Construct a one-time Rodrigues 3D rotation matrix R using the matrix construction module. Based on the Rodrigues rotation formula, the Rodrigues 3D rotation matrix R can be expressed using a unit rotation axis. The sine and cosine of the included angle are expressed as: ; in, It is the unit axis of rotation Antisymmetric matrix: ; Combined unit rotation axis By substituting and expanding the components under the constraints, a specific algebraic dimensionality reduction is performed on the 3x3 rotation matrix to eliminate all constraints. The operation terms, the expansion of the nine analytical coefficients of the Rodrigues three-dimensional rotation matrix R is as follows: ; By introducing intermediate product variables The calculation of the 9 matrix components in the above equation can be transformed into: ; The entire process avoids the use of trigonometric functions and obtains the Rodrigues three-dimensional rotation matrix R through only a finite number of multiplication operations; S106: In-situ covering vibration signal correction is performed using an in-situ covering rotation module. The obtained Rodrigues three-dimensional spatial rotation matrix R is used to perform an in-situ linear transformation on each sampling point of the time-domain acceleration sequence acquired by the triaxial accelerometer. ; After transformation, the rotationally corrected result is obtained. and This is a purely radial plane vibration signal perpendicular to the vertical direction of gravity. It is a pure axial vibration signal, eliminating gravity component interference and inter-axis signal crosstalk, and completing the sensor's adaptive virtual leveling.
3. The adaptive virtual leveling method for vibration sensors based on Rodrigues transform according to claim 2, characterized in that: In step S102, the long sliding window mean low-pass filter is used to filter out the quasi-periodic alternating vibration signal of the rotating machinery and retain the static gravity DC component. The number of sampling points N of the sliding window is adaptively configured according to the equipment type and vibration frequency of the rotating machinery.
4. The adaptive virtual leveling method for vibration sensors based on Rodrigues transform according to claim 2, characterized in that: In step S104, the gravity unit vector is aligned by fixing the target. This achieves a fixed simplification of the outer product operation, ensuring that the Z component of the rotation axis vector is always zero, thus providing a prerequisite constraint for subsequent dimensionality reduction and simplification of the rotation matrix.
5. The adaptive virtual leveling method for vibration sensors based on Rodrigues transform according to claim 2, characterized in that: In S104, the singular degradation adaptive determination mechanism, for the two extreme singular conditions of sensor horizontal alignment and inverted installation, completely avoids the abnormal operation of normalization denominator being zero when s→0 by replacing the conventional solution operation with a predefined constant rotation matrix.
6. The adaptive virtual leveling method for vibration sensors based on Rodrigues transform according to claim 2, characterized in that: In S105, based on The specific constraints reduce the dimensionality of the Rodrigues rotation matrix, simplifying traditional complex matrix operations to 7 multiplication operations.
7. The adaptive virtual leveling method for vibration sensors based on Rodrigues transform according to claim 2, characterized in that: In S106, the in-situ linear transformation adopts the same memory space data update method, which does not require additional cache memory and is suitable for embedded wireless sensor node deployment scenarios with low memory and low computing power.
8. The adaptive virtual leveling method for vibration sensors based on Rodrigues transform according to claim 2, characterized in that: The triaxial accelerometer is suitable for various types of rotating machinery. It can perform real-time adaptive virtual leveling when the equipment is running smoothly or stopped. The output decoupled vibration signal is used for equipment fault diagnosis and operating condition identification.