A calibration method and apparatus for a triaxial vibration sensor based on the Stewart platform

Abstract

This application provides a calibration method and apparatus for a triaxial vibration sensor based on the Stewart platform, belonging to the field of sensor calibration technology. The method provided in this application involves: acquiring a laser spot motion sequence image of the Stewart platform and a triaxial output voltage sequence of the triaxial vibration sensor; calculating a triaxial excitation displacement sequence based on the laser spot motion sequence image; calculating the triaxial excitation acceleration peak value based on the triaxial excitation displacement sequence; fitting the triaxial output voltage sequence using a sine approximation method to obtain the triaxial voltage peak value; calculating the sensitivity of the triaxial vibration sensor based on the ratio of the triaxial voltage peak value to the triaxial excitation acceleration peak value; determining the bending angle of the Stewart platform; and correcting the sensitivity based on the bending angle. The calibration method and apparatus for a triaxial vibration sensor based on the Stewart platform provided in this application are used to calibrate the sensitivity of multi-axis sensors.

Description

Technical Field

[0001] This application relates to the field of sensor calibration technology, and in particular to a calibration method and apparatus for a triaxial vibration sensor based on the Stewart platform. Background Technology

[0002] Currently, calibration methods for low-frequency multi-axis vibration sensors are mainly divided into two categories. One is the step-by-step calibration method based on traditional single-axis vibration tables, which involves repeatedly disassembling and reassembling the sensor to perform single-axis excitation calibration on the X, Y, and Z axes, and then integrating the multi-axis sensitivity results. The other is the synchronous calibration method based on multi-axis motion platforms (such as the Stewart platform), which utilizes the multi-degree-of-freedom motion characteristics of the platform to provide three-dimensional spatial excitation to the sensor in one go, and uses laser interferometers or visual measurement techniques to obtain excitation parameters to achieve multi-axis synchronous calibration. Among them, the single-axis step-by-step calibration method is widely used in small and medium-scale calibration scenarios due to its low equipment cost and simple operation logic; while the Stewart platform synchronous calibration method, with its advantages of not requiring repeated disassembly and reassembly and high calibration efficiency, is gradually becoming the mainstream technology for high-end multi-axis sensor calibration, especially suitable for high-precision sensor calibration that is sensitive to installation errors.

[0003] However, for the single-axis step-by-step calibration method, the sensor needs to be disassembled and reassembled multiple times to switch calibration axes. The alignment deviation between the sensor coordinate system and the vibration table excitation axis accumulates during each installation, leading to poor consistency in multi-axis sensitivity and low calibration efficiency. While the synchronous calibration method based on the Stewart platform solves the installation error problem, the platform's worktable is affected by factors such as rigid structural deformation and sensor mass load. This results in a bending angle between the actual motion trajectory and the theoretical spatial excitation axis, introducing an additional gravitational acceleration component. This causes a mismatch between the measured excitation acceleration and the actual excitation received by the sensor, further increasing the sensitivity calibration error. In addition, existing vision measurement solutions mostly rely on binocular vision or complex optical systems, which are costly and complex to operate, making them difficult to widely apply in industrial scenarios. Summary of the Invention

[0004] In view of this, this application provides a calibration method and apparatus for a triaxial vibration sensor based on the Stewart platform, for the purpose of sensitivity calibration of the triaxial vibration sensor.

[0005] Specifically, this application is implemented through the following technical solution:

[0006] The first aspect of this application provides a calibration method for a triaxial vibration sensor based on the Stewart platform, the method comprising:

[0007] Acquire the laser spot motion sequence images of the Stewart platform and the triaxial output voltage sequence of the triaxial vibration sensor;

[0008] Calculate the triaxial excitation displacement sequence based on the laser spot motion sequence image;

[0009] Calculate the peak value of the triaxial excitation acceleration based on the triaxial excitation displacement sequence;

[0010] The triaxial output voltage sequence is fitted using the sinusoidal approximation method to obtain the triaxial voltage peak value;

[0011] The sensitivity of the triaxial vibration sensor is calculated based on the ratio of the peak value of the triaxial voltage to the peak value of the triaxial excitation acceleration. The bending angle of the Stewart platform is then determined, and the sensitivity is corrected based on the bending angle.

[0012] The second aspect of this application provides a calibration device for a triaxial vibration sensor based on the Stewart platform, the device including a data acquisition module and a calculation module;

[0013] The acquisition module acquires the laser spot motion sequence images of the Stewart platform and the triaxial output voltage sequence of the triaxial vibration sensor;

[0014] The calculation module is used to calculate the triaxial excitation displacement sequence based on the laser spot motion sequence image;

[0015] The calculation module is also used to calculate the peak value of the triaxial excitation acceleration based on the triaxial excitation displacement sequence;

[0016] The calculation module is also used to fit the triaxial output voltage sequence based on the sine approximation method to obtain the triaxial voltage peak value;

[0017] The calculation module is also used to calculate the sensitivity of the triaxial vibration sensor based on the ratio of the triaxial voltage peak value to the triaxial excitation acceleration peak value, determine the bending angle of the Stewart platform, and correct the sensitivity based on the bending angle.

[0018] The calibration method and apparatus for a triaxial vibration sensor based on the Stewart platform provided in this application can achieve accurate calibration of the sensitivity of multiaxial sensors. Specifically, on the one hand, the method provided in this application does not require multiple disassembly and assembly of the sensor. By acquiring laser spot motion sequence images from the Stewart platform, the X, Y, and Z axis excitation displacement sequences are calculated simultaneously. Combined with the acquired triaxial output voltage sequences, the triaxial sensitivity calculation is completed in one step, significantly shortening the calibration time, avoiding the cumulative error of axis alignment caused by multiple installations, and improving the consistency of multiaxial sensitivity. On the other hand, compared with schemes that rely on complex optical systems, the triaxial excitation displacement is inferred from the laser spot motion sequence images, and the peak excitation acceleration is obtained through displacement-acceleration conversion. Combined with the voltage peak fitted by the sine approximation method, an accurate correspondence between the input excitation and the output response is established, providing a reliable benchmark for sensitivity calculation and effectively reducing the impact of excitation parameter measurement errors on the calibration results. Attached Figure Description

[0019] Figure 1 A flowchart of Embodiment 1 of the calibration method for a triaxial vibration sensor based on the Stewart platform provided in this application;

[0020] Figure 2 This is a schematic diagram of the second embodiment of the calibration device for a triaxial vibration sensor based on the Stewart platform provided in this application. Detailed Implementation

[0021] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0022] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used herein are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0023] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0024] The following specific embodiments are given to illustrate the technical solution of this application in detail.

[0025] Figure 1 This is a flowchart of Embodiment 1 of the calibration method for a triaxial vibration sensor based on the Stewart platform provided in this application. Please refer to... Figure 1 The method provided in this embodiment may include:

[0026] S101. Acquire the laser spot motion sequence image of the Stewart platform and the three-axis output voltage sequence of the three-axis vibration sensor, wherein the three axes are the X, Y, and Z axes of the three-axis vibration sensor.

[0027] Specifically, the Stewart platform is a high-precision multi-axis motion platform based on a 6-DOF parallel mechanism. Its core function is to drive the worktable to achieve a composite motion of translation and rotation in three-dimensional space through the coordinated control of 6 independently extendable drive rods (such as electric cylinders and hydraulic rods). This can simulate the spatial motion trajectory of a target object. The three-axis vibration sensor is used to sense the three-dimensional spatial vibration excitation provided by the Stewart platform and outputs X, Y, and Z axis voltage signals proportional to the excitation acceleration. The laser spot motion sequence image refers to the dynamic spot formed by three orthogonal laser beams projected onto the rear projection screen by the laser pointer when the Stewart platform moves. It is a collection of multiple frames of images continuously captured by a CMOS camera. Each frame records the position of the three laser beams (corresponding to the X, Y, and Z axes respectively) on the screen at a certain moment. The multiple consecutive frames reflect the trajectory change of the spot as the platform moves. The three-axis output voltage sequence is the collection of voltage signals that the three-axis vibration sensor outputs on the X, Y, and Z sensitive axes respectively under the three-dimensional vibration excitation provided by the Stewart platform, which vary with time. The voltage sequence for each axis exhibits a sinusoidal pattern (due to the sinusoidal motion of the platform excitation), and its amplitude is proportional to the excitation acceleration sensed by the sensor. It is a direct parameter characterizing the sensor's output response. The three-dimensional vibration excitation provided by the Stewart platform refers to the periodic vibration input applied to the triaxial vibration sensor along the three orthogonal directions of X, Y, and Z by the Stewart platform driving the worktable surface through a 6-DOF parallel mechanism. The three-axis spatial input excitation of the triaxial vibration sensor can be expressed by the following formula:

[0028] ;

[0029] in, , , These are the input excitations for the X, Y, and Z axes of the triaxial vibration sensor, respectively.

[0030] , as well as These represent the amplitudes of the excitation displacements along the X, Y, and Z axes of the triaxial vibration sensor, respectively.

[0031] , as well as These are the corresponding initial phases;

[0032] ω is the angular frequency.

[0033] Optionally, the calibration method is based on a calibration system, which includes a triaxial vibration sensor, a laser pointer, and a Stewart platform. The triaxial vibration sensor and the laser pointer are coaxially fixed at the center of the Stewart platform, and the axial coordinate system of the triaxial vibration sensor coincides with the platform coordinate system of the Stewart platform.

[0034] Specifically, it can be understood that the triaxial vibration sensor and laser pointer are mounted at the center of the Stewart platform's worktable. By mechanically and rigidly connecting the triaxial vibration sensor and laser pointer to the worktable, it is ensured that the sensor and laser pointer move in complete physical synchronization. When the platform moves, there is no relative displacement or lag between the two, avoiding inconsistencies between the laser spot movement and the actual excitation sensed by the sensor due to loose installation. Furthermore, since the center of the worktable is the area with the highest motion accuracy (the edges are prone to additional errors due to rigid deformation), fixing the two at the center can reduce the impact of the platform's own motion unevenness and ensure the stability of the excitation parameters.

[0035] Furthermore, the axial coordinate system of a triaxial vibration sensor refers to the three-dimensional rectangular coordinate system formed by the sensor's own sensitive axes. It is used to define the sensor's sensing reference for vibration excitation in different directions. Its core consists of three mutually orthogonal (perpendicular) sensitive axes (X-axis, Y-axis, and Z-axis). Usually, the origin of the coordinate system is taken as the geometric center of the sensor or the center of the sensitive element. The X-axis, Y-axis, and Z-axis are perpendicular to each other, forming a right-handed helical coordinate system. Each axis corresponds to a sensitive direction of the sensor, that is, the output voltage of the sensor in that axis direction is proportional to the vibration acceleration in that direction. For example, the X-axis primarily responds to acceleration along the X direction, the Y-axis responds to acceleration along the Y direction, and the Z-axis responds to acceleration along the Z direction. The Stewart platform's table coordinate system refers to a three-dimensional Cartesian coordinate system that defines the spatial motion of the worktable. It is used to quantify the displacement, attitude, and trajectory of the table. The origin is the geometric center of the Stewart platform's table. The X-axis and Y-axis are usually along two orthogonal directions in the table plane (such as the long and short sides of the table), and the Z-axis is perpendicular to the table plane, corresponding to the three linear motion degrees of freedom of the table: X-axis translation, Y-axis translation, and Z-axis translation.

[0036] Furthermore, the coordinate system of the triaxial vibration sensor coincides with the coordinate system of the Stewart platform, meaning that the X-axis of the triaxial vibration sensor only senses the excitation in the X direction of the platform, and the same applies to the Y and Z axes. This eliminates interference from cross axes. Additionally, the three laser beams of the laser pointer are aligned with the axes of the platform coordinate system, ensuring that the movement of the laser spot in the X direction only reflects the X-axis displacement of the platform, simplifying the decoupling calculation of the laser spot movement to the axis excitation. Therefore, by coaxially fixing the triaxial vibration sensor and the laser pointer at the center of the Stewart platform, it can be ensured that the laser spot movement accurately reflects the actual excitation of the three-dimensional vibration sensor. Ensuring that the coordinate system of the three-dimensional vibration sensor coincides with the coordinate system of the platform guarantees that the sensor output voltage corresponds to the theoretical excitation axis.

[0037] Furthermore, acquiring the laser spot motion sequence images of the Stewart platform includes:

[0038] (1) Control the laser pointer on the Stewart platform to emit three mutually perpendicular laser beams toward the projection screen;

[0039] Specifically, the laser pointer is pre-fixed at the center of the Stewart platform, and the directions of its three emitted laser beams strictly correspond to the X, Y, and Z axes of the platform coordinate system, respectively. The projection screen is placed perpendicular to the Z-axis of the platform coordinate system, and the line connecting the center of the screen and the emission center of the laser pointer is parallel to the Z-axis. The distance is set according to the laser projection range. When the laser pointer is powered on, the three laser beams are controlled to be turned on synchronously through the drive circuit. The laser power is adjusted to stabilize the grayscale value of the light spot on the screen at 200-240 (8-bit grayscale to avoid overexposure or underexposure). At the same time, the laser turn-on time is recorded as the reference point for subsequent timing synchronization.

[0040] (2) Start the Stewart platform to move according to the preset sinusoidal three-dimensional trajectory;

[0041] Specifically, the sinusoidal motion parameters of the Stewart platform's X, Y, and Z axes are determined based on a preset sinusoidal three-dimensional trajectory, including frequency, peak displacement, and initial phase. After determining the sinusoidal motion parameters of the Stewart platform's X, Y, and Z axes, a start command is sent to the Stewart platform to control it to move according to the sinusoidal motion parameters of the X, Y, and Z axes. At this time, the laser pointer on the platform will move with the platform, thereby forming a laser spot motion trajectory on the projection screen.

[0042] (3) Acquire the motion sequence image of the laser spot formed by the three laser beams on the projection screen during the motion.

[0043] Specifically, a CMOS camera is fixed directly in front of the projection screen (opposite to the laser pointer; that is, if the CMOS camera is in front of the projection screen, the laser pointer is behind it). The lens optical axis is perpendicular to the screen plane and aligned with the center of the screen. A trigger signal is used to synchronize the platform movement with the camera's data acquisition (error ≤ 10μs), continuously acquiring images for at least n vibration cycles. In other words, as the Stewart platform moves, the CMOS camera captures the laser spot emitted by the laser pointer on the projection screen in real time, combining this with the movement time to form a sequence of laser spot motion images.

[0044] By ensuring the laser's perpendicularity, the movement of the laser spot corresponds one-to-one with the axis system, avoiding directional coupling. This allows the Stewart platform to move along a sinusoidal trajectory, guaranteeing the periodicity and modelability of the excitation, adapting to subsequent data fitting, and simultaneously acquiring data to eliminate timing deviations, ensuring the correspondence between the laser spot position and the moment of motion.

[0045] Furthermore, after acquiring the laser spot motion sequence images of the Stewart platform, the method provided in this embodiment includes:

[0046] (1) For each frame of the laser spot motion sequence image, calculate the gray value of all pixels in each frame;

[0047] Specifically, the raw data of a single frame image is read, the image is converted into a grayscale image using an image processing library, each pixel coordinate of the image is traversed, the corresponding grayscale value is stored in a two-dimensional array to form a grayscale matrix, and the grayscale matrix is ​​normalized and preprocessed to eliminate the overall grayscale shift caused by ambient light fluctuations.

[0048] (2) Filter the pixels in each frame of the image based on the grayscale threshold to determine the initial spot area;

[0049] Specifically, the grayscale values ​​of all pixels in each frame are compared with a grayscale threshold. Pixels with grayscale values ​​greater than or equal to the grayscale threshold are retained. The initial spot area of ​​each frame is determined based on the retained pixels. It should be noted that the grayscale threshold is set according to actual needs, and is not limited in this embodiment.

[0050] (3) Determine the region of interest within a preset range, centered on the pixel with the largest gray value within the initial spot area;

[0051] Specifically, for each initial spot region, all pixels within it are traversed to find the pixel with the highest grayscale value. Using this pixel as the center, a region of interest (ROI) of a preset area is determined. It should be noted that the preset area is set according to actual needs and is not limited in this embodiment. This focuses on the core region of the spot, eliminating interference from the spot edges and background, significantly reducing the amount of data required for subsequent fitting calculations and improving processing efficiency. Using the pixel with the highest grayscale value as the center ensures that the ROI includes the area with the most concentrated spot energy, providing high-quality data for Gaussian fitting.

[0052] (4) Fit all pixels in the region of interest based on a two-dimensional Gaussian function, and determine the center of the spot based on the fitting result.

[0053] Specifically, the two-dimensional Gaussian function can be represented by the following formula:

[0054] ;

[0055] Where K is the peak gray level of the light spot;

[0056] ( () represents the center coordinates of the fitted light spot;

[0057] The coordinates of the pixels;

[0058] and These are the standard deviations of the image spot along the X and Y axes, respectively.

[0059] Furthermore, for the pixel grayscale values ​​within the region of interest, aiming to minimize the sum of the squared differences between the theoretical and actual values, the model parameters are solved using the least squares method to obtain the optimal solutions for the X and Y axis coordinates, which are then used as the spot centers in each frame of the image. It should be noted that only the calculation of the spot center for one laser beam is described here; the calculation of the spot centers for the other two laser beams is similar. In this way, the spot centers of all three laser beams in each frame of the image can be obtained.

[0060] Since the spread function of the laser spot generated by the laser projector can be regarded as a Gaussian distribution, and the Gaussian method can make the most of all the information of the laser spot and quickly and accurately obtain the center position of the laser spot, the accurate spot center can be obtained by fitting the two-dimensional Gaussian function.

[0061] S102. Calculate the triaxial excitation displacement sequence based on the laser spot motion sequence image.

[0062] Specifically, before calculating the triaxial excitation displacement based on the laser spot motion sequence image, the method provided in this embodiment includes:

[0063] (1) Construct the laser coordinate system, the table coordinate system, and the projection world coordinate system;

[0064] Specifically, a laser coordinate system O is constructed with the geometric center of the laser pointer as the origin, the X-axis as the direction of the X-ray laser beam emitted by the laser pointer, the Y-axis as the direction of the Y-ray laser beam, and the Z-axis as the direction of the Z-ray laser beam. l -X l Y l Z l A table coordinate system O is constructed with the geometric center of the Stewart platform's worktable (coinciding with the mounting centers of the laser pointer and triaxial vibration sensor) as the origin, the X-axis (e.g., the long side of the table) along a preset reference direction within the table plane, the Y-axis perpendicular to the X-axis and within the table plane, and the Z-axis perpendicular to the table plane and upwards (consistent with the platform's vertical movement direction) as the Z-axis. m -X m Y m Z m A projection world coordinate system is constructed with the geometric center of the projection screen as the origin, the X-axis extending horizontally to the right along the screen plane, the Y-axis extending vertically upwards along the screen plane, and the Z-axis pointing perpendicularly to the screen plane towards the laser pointer. c -X c Y c Z c .

[0065] (2) Determine the first rotation matrix based on the attitude deflection of the laser coordinate system relative to the platform coordinate system, and determine the second rotation matrix based on the attitude deflection of the laser coordinate system relative to the projection world coordinate system;

[0066] Specifically, the rotation matrix is ​​a 3×3 orthogonal matrix that describes the attitude deflection relationship between the two coordinate systems and is calculated using Euler angles.

[0067] Furthermore, the angles between the X-axis in the laser coordinate system and the X-axis in the table coordinate system (rotation about the Z-axis of the table coordinate system), and the angles between the Z-axis (rotation about the Y-axis of the table coordinate system) are measured using a high-precision inclinometer to obtain the Euler angles (since the installation calibration ensures that the deflection about the X-axis is negligible), and the first rotation matrix is ​​calculated according to the following formula:

[0068] ;

[0069] in, The angle between the X-axis in the laser coordinate system and the X-axis in the table coordinate system.

[0070] Furthermore, similarly, the second rotation matrix can be calculated using the following formula:

[0071] ;

[0072] in, The angle between the X-axis in the laser coordinate system and the X-axis in the projection world coordinate system.

[0073] (3) Determine the first translation matrix based on the offset of the laser coordinate system relative to the origin of the platform coordinate system, and determine the second translation matrix based on the offset of the laser coordinate system relative to the origin of the projection world coordinate system;

[0074] Specifically, the first translation matrix can be calculated using the following formula:

[0075] ;

[0076] in, , , This represents the translation distance of the laser coordinate system after the first rotation matrix transformation.

[0077] Furthermore, the second translation matrix can be calculated using the following formula:

[0078] ;

[0079] in, This is the distance from the laser pointer to the rear projection screen.

[0080] (4) Based on the first rotation matrix, the second rotation matrix, the first translation matrix and the second translation matrix, realize the coordinate transformation between the laser coordinate system, the table coordinate system and the projection world coordinate system.

[0081] Specifically, the coordinate transformation between the laser coordinate system and the table coordinate system can be achieved using the following formula:

[0082] ;

[0083] in, These are the coordinates in the table coordinate system;

[0084] The coordinates are in the laser coordinate system;

[0085] This is the first rotation matrix;

[0086] This is the first translation matrix.

[0087] Furthermore, the coordinate transformation between the laser coordinate system and the projection world coordinate system can be achieved using the following formula:

[0088] ;

[0089] in, The coordinates are in the laser coordinate system;

[0090] The coordinates are in the world coordinate system for projection;

[0091] This is the second rotation matrix;

[0092] This is the second translation matrix.

[0093] The attitude deviation was corrected by the rotation matrix to ensure directional consistency, and the position offset was quantified by the translation matrix to ensure origin alignment. The transformation operation realized accurate mapping across coordinate systems, providing a mathematical basis for calculating the laser spot pixel coordinates to the excitation displacement on the platform, and ultimately supporting the accurate calibration of the triaxial vibration sensor.

[0094] Furthermore, the specific implementation steps for calculating the triaxial excitation displacement sequence based on the laser spot motion sequence image include:

[0095] (1) Obtain the camera's model parameter matrix;

[0096] Specifically, the Zhang Zhengyou calibration method is used to calibrate the CMOS camera. 10-20 chessboard images with different poses are taken. The pixel coordinates and world coordinates of the chessboard corner points are extracted by corner detection. The intrinsic parameter matrix is ​​determined based on the camera's focal length, principal point coordinates, and distortion coefficients. The extrinsic parameter matrix is ​​determined based on the pose of the camera coordinate system relative to the world coordinate system and the position of the camera origin relative to the world origin. The camera's model parameter matrix is ​​calculated based on the product of the intrinsic and extrinsic parameter matrices.

[0097] (2) Determine the pixel coordinates of the laser spot center based on the laser spot motion sequence image;

[0098] Specifically, based on the above description, the calculated center of the light spot is determined as the pixel coordinates of the light spot center.

[0099] (3) Combine the model parameter matrix to convert the pixel coordinates into three-dimensional coordinates in the projection world coordinate system;

[0100] Specifically, the three-dimensional coordinates can be calculated using the following formula:

[0101] ;

[0102] in, The coordinates are in the world coordinate system for projection;

[0103] It is the inverse of the model parameter matrix;

[0104] These are pixel coordinates.

[0105] (4) Call the first rotation matrix and the first translation matrix to convert the three-dimensional coordinates in the laser coordinate system into three-dimensional coordinates in the table coordinate system;

[0106] Specifically, the three-dimensional coordinates in the table coordinate system can be calculated using the following formula:

[0107] ;

[0108] in, These are the coordinates in the table coordinate system;

[0109] The coordinates are in the world coordinate system for projection;

[0110] This is the rotation matrix of the platform coordinate system relative to the projection world coordinate system;

[0111] This is the translation matrix of the platform coordinate system relative to the projection world coordinate system;

[0112] Based on the above description, by measuring the attitude deflection of the platform coordinate system relative to the projection world coordinate system and the offset of the origin position, the rotation matrix and translation matrix of the platform coordinate system relative to the projection world coordinate system can be obtained, which will not be elaborated here.

[0113] (5) Taking the center of the spot in the first frame of the laser spot motion sequence image as the zero point, calculate the difference between the center of the spot in each frame of the laser spot motion sequence image and the center of the spot in the first frame image, and use it as the excitation displacement. The three-axis excitation displacement sets are used to form a three-axis excitation displacement sequence.

[0114] Specifically, the center of the laser spot in the first frame of the laser spot motion sequence image is taken as the zero point, i.e. the initial point. The displacement difference between the center of the laser spot in each subsequent frame and the center of the laser spot in the first frame is calculated. The displacement differences are sorted by time to form a triaxial excitation displacement sequence.

[0115] Using the initial static position as a reference, the influence of the coordinate system origin offset on displacement calculation is eliminated, so that the displacement value directly reflects the vibration amplitude of the platform. The serialized displacement data completely records the entire journey of the platform motion, providing a time-domain excitation signal for subsequent peak acceleration calculation, and ensuring that the excitation parameters correspond to the time sequence of the sensor response.

[0116] S103. Calculate the peak value of the triaxial excitation acceleration based on the triaxial excitation displacement sequence.

[0117] Specifically, the specific steps for calculating the peak triaxial excitation acceleration based on the triaxial excitation displacement sequence include:

[0118] (1) Fit the triaxial excitation displacement sequence and sampling time sequence based on the sinusoidal approximation method, construct the fitting function, and obtain the displacement peak value of the three axes;

[0119] Specifically, the fitting function can be represented by the following formula:

[0120] ;

[0121] in, , , , The parameters are sinusoidal and are obtained by solving N equations based on the measured displacement and sampling time.

[0122] This is a triaxial excitation displacement sequence;

[0123] It is a sampling time series;

[0124] ω is the angular frequency.

[0125] (2) Substitute the peak displacement of the three axes into the fitting function to obtain the sinusoidal displacement function, and perform second derivative of the sinusoidal displacement function to obtain the peak excitation acceleration of the three axes.

[0126] Specifically, based on the above description, the corresponding peak acceleration is calculated according to the solved sine parameters:

[0127] ;

[0128] in, Peak acceleration;

[0129] , The parameter is sinusoidal;

[0130] ω is the angular frequency.

[0131] This can be expressed using Euler's formula as follows:

[0132] ;

[0133] Where i is the imaginary unit;

[0134] , , The peak value of the triaxial excitation acceleration obtained from the fitting;

[0135] , , The initial phases of the X, Y, and Z axes.

[0136] The peak acceleration is directly calculated using analytical formulas based on peak displacement and frequency, without the need for complex time-domain signal processing (such as peak detection algorithms). This method offers high computational efficiency and controllable error. The peak acceleration directly quantifies the input excitation intensity provided by the Stewart platform and is the core input parameter for subsequent sensor sensitivity calculations. Its accuracy directly determines the accuracy of the calibration results.

[0137] S104. Fit the triaxial output voltage sequence based on the sinusoidal approximation method to obtain the triaxial voltage peak value.

[0138] Specifically, based on the above description, the same sinusoidal function model as used for fitting the displacement sequence is employed to approximate the voltage sequence for each axis, and the voltage peak value in the model parameters is solved. Since the excitation of the Stewart platform is sinusoidal motion, the sensor output voltage is linearly related to the excitation acceleration; therefore, the voltage sequence also follows a sinusoidal law, and the voltage fitting equation can be calculated using the following formula:

[0139] ;

[0140] in, This represents the peak voltage.

[0141] Let be the voltage at time t;

[0142] The vibration frequency;

[0143] For a specific moment;

[0144] This is the initial phase of the voltage;

[0145] This represents the DC offset of the voltage.

[0146] For each sensitive axis in the three axes, the voltage fitting equation for each axis is formed by substituting the above formula. The parameters in the voltage fitting equation are then solved using the least squares method to obtain the peak voltage for each axis, which is taken as the triaxial voltage peak. For details on the implementation steps of solving the parameters in the voltage fitting equation using the least squares method, please refer to the descriptions in relevant technologies; they will not be repeated here. The calculated sensor output voltage can be expressed as:

[0147] ;

[0148] Where i is the imaginary unit;

[0149] , , This represents the peak value of the triaxial voltage.

[0150] , , This is the initial phase.

[0151] S105. Calculate the sensitivity of the triaxial vibration sensor based on the ratio of the peak value of the triaxial voltage to the peak value of the triaxial excitation acceleration, determine the bending angle of the Stewart platform, and correct the sensitivity based on the bending angle.

[0152] Specifically, sensitivity can be calculated using the following formula:

[0153] ;

[0154] in, The sensitivity values ​​corresponding to the X, Y, and Z axes in a triaxial vibration sensor;

[0155] This represents the peak value of the triaxial excitation acceleration.

[0156] This represents the peak value of the triaxial voltage.

[0157] By simultaneously acquiring laser spot motion sequence images from the Stewart platform and the output voltage sequence of a triaxial vibration sensor, the triaxial excitation displacement sequence is inversely derived using laser spot visual measurement as the core. Then, the displacement-acceleration conversion yields the precise peak excitation acceleration. Simultaneously, a sine approximation method is used to fit the voltage sequence and extract the peak voltage. Finally, the sensor sensitivity is calculated using the ratio of the peak voltage to the peak acceleration. This eliminates the need for repeated sensor disassembly and assembly, achieving simultaneous triaxial calibration through the Stewart platform's multi-degree-of-freedom motion, avoiding accumulated installation errors and significantly improving multi-axis sensitivity consistency. Laser visual measurement combined with sine fitting and mathematical differentiation effectively eliminates interference from environmental noise and platform motion deviations on the quantization of excitation parameters and output response, ensuring the accuracy of the calculated peak acceleration and voltage. The entire process is adaptable to low-frequency multi-axis vibration scenarios, establishing a precise correspondence between the sensor's input excitation and output response, ultimately achieving high-precision sensitivity calibration.

[0158] Furthermore, the specific implementation process of correcting the sensitivity based on the bending angle includes:

[0159] (1) Determine the bending angle between the platform of the Stewart platform and the motion axis of the spatial excitation trajectory;

[0160] Specifically, due to factors such as mass load, rigid structure and installation error, at time t, there is a bending angle between the worktable surface and its actual spatial excitation trajectory motion axis, and the bending angle will introduce additional excitation acceleration.

[0161] Furthermore, the steps for determining the bending angle between the Stewart platform's surface and the spatial excitation trajectory motion axis include:

[0162] 1.1 Control the Stewart platform to perform single-axis sinusoidal motion according to preset excitation parameters, acquire images of high-contrast markers at different positions within the motion stroke, and extract the horizontal and vertical pixel displacements of the rectangular markers at the corresponding positions from the images at different positions.

[0163] Specifically, the Stewart platform is controlled to perform sinusoidal motion along a preset single axis (usually the X-axis or Z-axis of the platform coordinate system, corresponding to the main excitation direction). The motion parameters are consistent with the excitation parameters of the subsequent sensor calibration. After the platform motion is started, the CMOS camera continuously acquires marker images at a frame rate of 50fps (50 times the platform motion frequency to ensure that 50 frames of images are acquired per cycle, covering the complete motion journey). The acquisition time is ≥3 motion cycles, and each frame of image is timestamped.

[0164] Furthermore, using the marked image acquired when the platform is stationary as the reference frame, the position of the rectangular mark is located in each subsequent frame of motion image through a template matching algorithm (using the rectangular mark in the reference frame as the template), the center pixel coordinates of the rectangular mark and the center coordinates of the reference frame are extracted, and the horizontal and vertical pixel displacements are calculated based on the difference between the center pixel coordinates of the rectangular mark and the center coordinates of the reference frame.

[0165] 1.2 Based on the model parameter matrix, the horizontal and vertical pixel displacements are converted into actual horizontal and vertical displacements in the projection world coordinate system;

[0166] Specifically, by using the inverse transformation of the model parameter matrix, the pixel displacement is converted into the actual spatial displacement, thereby obtaining the actual horizontal displacement and the actual vertical displacement. For details on the specific implementation process, please refer to the description in the relevant technologies, which will not be repeated here.

[0167] 1.3 The bending angle is calculated based on the arctangent function combined with the actual horizontal and vertical displacements.

[0168] Specifically, the bending angle can be calculated using the following formula:

[0169] ;

[0170] in, The bending angle;

[0171] This represents the actual vertical displacement.

[0172] This represents the actual horizontal displacement.

[0173] (2) Calculate the additional excitation acceleration based on the product of the gravitational acceleration and the sine function of the bending angle;

[0174] Specifically, the additional excitation acceleration can be calculated using the following formula:

[0175] ;

[0176] in, For additional acceleration;

[0177] It is the acceleration due to gravity;

[0178] The bending angle is denoted by .

[0179] (3) Calculate the actual excitation acceleration of the triaxial vibration sensor based on the bending angle, the additional excitation acceleration, and the peak value of the triaxial excitation acceleration;

[0180] Specifically, the actual excitation acceleration can be calculated using the following formula:

[0181] ;

[0182] in, To provide actual incentive acceleration;

[0183] This represents the peak value of the triaxial excitation acceleration.

[0184] The bending angle;

[0185] This provides additional acceleration.

[0186] (4) Substitute the actual excitation acceleration into the sensitivity calculation formula to obtain the corrected sensitivity of the triaxial vibration sensor.

[0187] Specifically, the corrected sensitivity of a triaxial vibration sensor can be calculated using the following formula:

[0188] ;

[0189] The sensitivity values ​​corresponding to the X, Y, and Z axes in a triaxial vibration sensor;

[0190] This represents the peak value of the triaxial excitation acceleration.

[0191] This represents the peak value of the triaxial voltage.

[0192] This provides additional acceleration.

[0193] The calibration method for a triaxial vibration sensor based on the Stewart platform provided in this embodiment overcomes the inherent defects of traditional single-axis step-by-step calibration, achieving multi-axis synchronous and accurate calibration. First, by coaxially fixing the triaxial vibration sensor and laser indicator to the center of the Stewart platform, the coordinate systems of both are ensured to coincide with the platform's coordinate system. This eliminates the need for multiple sensor disassemblies and reassemblies, allowing synchronous X, Y, and Z-axis excitation via the Stewart platform's motion, completely avoiding accumulated axis alignment errors caused by multiple installations, reducing multi-axis sensitivity consistency errors, and significantly improving calibration efficiency. Second, relying on the motion sequence image of three orthogonal laser beams, combined with multi-coordinate system transformation (laser, laser ... The system uses a two-dimensional Gaussian function to fit the coordinates of the platform and the projection world coordinate system, achieving sub-pixel-level spot center positioning and micrometer-level displacement calculation accuracy. Then, it uses a sine approximation method to fit the displacement sequence and obtain the acceleration peak value by second derivative. Simultaneously, it fits the voltage sequence to extract the voltage peak value, establishing a precise correspondence between input excitation and output response, effectively eliminating environmental noise and equipment deviation interference. Finally, a bending angle correction mechanism is introduced to further improve calibration accuracy. To address the issue of additional gravitational acceleration components caused by the rigid deformation of the Stewart platform platform, the system extracts displacement from high-contrast marked images and calculates the bending angle using an arctangent function, thereby correcting the actual excitation acceleration and reducing sensitivity calibration error.

[0194] Corresponding to the aforementioned embodiment of a calibration method for a triaxial vibration sensor based on the Stewart platform, this application also provides an embodiment of a calibration device for a triaxial vibration sensor based on the Stewart platform.

[0195] Figure 2 This is a schematic diagram of Embodiment 2 of the calibration device for the triaxial vibration sensor based on the Stewart platform provided in this application. Please refer to... Figure 2 The device provided in this embodiment includes a data acquisition module 210 and a calculation module 220;

[0196] The acquisition module 210 acquires the laser spot motion sequence image of the Stewart platform and the triaxial output voltage sequence of the triaxial vibration sensor;

[0197] The calculation module 220 is used to calculate a triaxial excitation displacement sequence based on the laser spot motion sequence image;

[0198] The calculation module 220 is also used to calculate the peak value of the triaxial excitation acceleration based on the triaxial excitation displacement sequence;

[0199] The calculation module 220 is also used to fit the triaxial output voltage sequence based on the sinusoidal approximation method to obtain the triaxial voltage peak value;

[0200] The calculation module 220 is also used to calculate the sensitivity of the triaxial vibration sensor based on the ratio of the triaxial voltage peak value to the triaxial excitation acceleration peak value, determine the bending angle of the Stewart platform, and correct the sensitivity based on the bending angle.

[0201] The apparatus of this embodiment can be used to perform... Figure 1 The steps of the method embodiment shown are similar in principle and process, and will not be repeated here.

[0202] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0203] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0204] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A correction method of a three-axis vibration sensor based on a Stewart platform, characterized in that, The method comprises: Collecting a laser spot motion sequence image of the Stewart platform and a three-axis output voltage sequence of the three-axis vibration sensor, wherein the three axes are X, Y and Z axes of the three-axis vibration sensor; Calculating a three-axis excitation displacement sequence based on the laser spot motion sequence image; Calculating a three-axis excitation acceleration peak value according to the three-axis excitation displacement sequence; Fitting the three-axis output voltage sequence based on a sine approximation method to obtain a three-axis voltage peak value; Calculating a sensitivity of the three-axis vibration sensor according to a ratio of the three-axis voltage peak value to the three-axis excitation acceleration peak value, determining a bending angle of the Stewart platform, and correcting the sensitivity based on the bending angle; wherein the determination of the bending angle of the Stewart platform and the correction of the sensitivity based on the bending angle comprise: Determining a bending angle between a table surface of the Stewart platform and a spatial excitation trajectory motion axis; wherein the determination of the bending angle between the table surface of the Stewart platform and the spatial excitation trajectory motion axis comprises: Controlling the Stewart platform to make a single-axis sinusoidal motion according to preset excitation parameters, collecting images of high-contrast marks at different positions within the motion stroke, and extracting horizontal and vertical pixel displacements of the rectangular marks at the corresponding positions from the images at different positions; Converting the horizontal and vertical pixel displacements into horizontal and vertical actual displacements in a projection world coordinate system based on a model parameter matrix; Calculating the bending angle based on an inverse tangent function in combination with the horizontal and vertical actual displacements; Calculating an additional excitation acceleration based on a product of a gravitational acceleration and a sine function of the bending angle; Calculating an actual excitation acceleration of the three-axis vibration sensor according to the bending angle, the additional excitation acceleration and the three-axis excitation acceleration peak value; Obtaining a corrected sensitivity of the three-axis vibration sensor by bringing the actual excitation acceleration into a calculation formula of the sensitivity.

2. The method of claim 1, wherein, The correction method is realized based on a correction system, the correction system comprises a three-axis vibration sensor, a laser pointer and a Stewart platform, the three-axis vibration sensor and the laser pointer are coaxially fixed at a center of a table surface of the Stewart platform, an axis coordinate system of the three-axis vibration sensor coincides with a table surface coordinate system of the Stewart platform.

3. The method of claim 1, wherein, Before calculating the three-axis excitation displacement based on the laser spot motion sequence image, it comprises: Constructing a laser coordinate system, a table surface coordinate system and a projection world coordinate system; Determining a first rotation matrix according to an attitude deflection of the laser coordinate system relative to the table surface coordinate system, and determining a second rotation matrix according to an attitude deflection of the laser coordinate system relative to the projection world coordinate system; Determining a first translation matrix according to an origin position offset of the laser coordinate system relative to the table surface coordinate system, and determining a second translation matrix according to an origin position offset of the laser coordinate system relative to the projection world coordinate system; The coordinate conversion between the laser coordinate system, the table coordinate system and the projection world coordinate system is realized based on the first rotation matrix, the second rotation matrix, the first translation matrix and the second translation matrix.

4. The method of claim 1, wherein, The laser spot motion sequence image of the Stewart platform is collected, including: The laser pointer on the Stewart platform is controlled to emit three mutually perpendicular laser beams to the projection screen; The Stewart platform is started to move according to a preset sinusoidal three-dimensional trajectory; The laser spot motion sequence image of the projection screen formed by the three laser beams during the movement is collected.

5. The method of claim 1, wherein, After the laser spot motion sequence image of the Stewart platform is collected, including: For each frame of image in the laser spot motion sequence image, the gray value of each pixel in each frame of image is calculated; Based on the gray threshold, the pixels in each frame of image are screened to determine the initial spot region; The region of interest within a preset range is determined with the pixel point with the maximum gray value in the initial spot region as the center; Based on the two-dimensional Gaussian function, all pixel points in the region of interest are fitted, and the spot center is determined according to the fitting result.

6. The method of claim 1, wherein, The three-axis excitation displacement sequence is calculated based on the laser spot motion sequence image, including: The model parameter matrix of the camera is obtained; The pixel coordinates of the spot center are determined based on the laser spot motion sequence image; The pixel coordinates are converted into three-dimensional coordinates under the coordinates of the projection world coordinate system in combination with the model parameter matrix; The first rotation matrix and the first translation matrix are called to convert the three-dimensional coordinates under the laser coordinate system into three-dimensional coordinates under the table coordinate system; The difference between the spot center of the first frame of image in the laser spot motion sequence image and the spot center of each frame of image is calculated as the excitation displacement, and the three-axis excitation displacement sequence is constituted by the excitation displacement of the three axes.

7. The method of claim 1, wherein, The three-axis excitation acceleration peak value is calculated according to the three-axis excitation displacement sequence, including: The three-axis excitation displacement sequence and the sampling time sequence are fitted based on the sine approximation method to construct a fitting function, and the displacement peak value of the three axes is obtained; The displacement peak value of the three axes is substituted into the fitting function to obtain a sinusoidal displacement function, and the three-axis excitation acceleration peak value is obtained by performing second-order derivation on the sinusoidal displacement function.

8. A correction device for a three-axis vibration sensor based on a Stewart platform, characterized in that The device includes a collection module and a calculation module, wherein: The collection module collects the laser spot motion sequence image of the Stewart platform and the three-axis output voltage sequence of the three-axis vibration sensor; The calculation module is configured to calculate the three-axis excitation displacement sequence based on the laser spot motion sequence image; The calculation module is further configured to calculate the three-axis excitation acceleration peak value according to the three-axis excitation displacement sequence; The calculation module is further configured to fit the three-axis output voltage sequence based on the sine approximation method to obtain the three-axis voltage peak value; The computing module is further configured to calculate sensitivity of the triaxial vibration sensor according to a ratio of the triaxial voltage peak value and the triaxial excitation acceleration peak value, determine a bending angle of the Stewart platform, and correct the sensitivity based on the bending angle; wherein the determination of the bending angle of the Stewart platform and the correction of the sensitivity based on the bending angle comprise: determining a bending angle between a table top of the Stewart platform and a spatial excitation trajectory movement axis; wherein the determination of the bending angle between the table top of the Stewart platform and the spatial excitation trajectory movement axis comprises: controlling the Stewart platform to make single-axis sinusoidal motion according to preset excitation parameters, collecting images of high-contrast marks at different positions in a motion stroke, and extracting horizontal pixel displacement and vertical pixel displacement of the rectangular marks at the corresponding positions from the images at different positions; converting the horizontal pixel displacement and the vertical pixel displacement into horizontal actual displacement and vertical actual displacement in a projection world coordinate system based on a model parameter matrix; calculating the bending angle based on an inverse tangent function in combination with the horizontal actual displacement and the vertical actual displacement; calculating an additional excitation acceleration based on a product of gravitational acceleration and a sine function of the bending angle; calculating actual excitation acceleration of the triaxial vibration sensor according to the bending angle, the additional excitation acceleration, and a triaxial excitation acceleration peak value; obtaining corrected sensitivity of the triaxial vibration sensor by bringing the actual excitation acceleration into a calculation formula of the sensitivity.

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