Accelerometer vibration rectification error analysis method

Abstract

The invention relates to the technical field of data processing, in particular to an accelerometer vibration rectification error analysis method, which comprises the steps of receiving multiple paths of accelerometer original current signals, processing acquired data and outputting a feature point coordinate sequence with confidence; according to the confidence and the optimization algorithm combination in the frequency band distribution characteristic dynamic scheduling knowledge base, calculating a local statistical data set; inputting the data set into a mechanical dynamics model to execute trajectory simulation, and inputting a control model reconstruction signal to compare a dual-path positioning drift distance difference to generate an error correction coefficient matrix; outputting a knowledge base updating instruction and a parameter resetting instruction by adopting a matrix reconstruction vibration rectification error quantized value; a quantized value is imported to calculate theoretical angle deviation and verify convergence, and the neural network is triggered to be retrained when the deviation exceeds a threshold value. Through a non-smooth feature extraction algorithm and a closed-loop feedback mechanism, the problem of signal distortion caused by smooth operation in the prior art is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data processing, and in particular to an accelerometer vibration rectification error analysis method. BACKGROUND

[0002] The accelerometer vibration rectification error is a measurement distortion phenomenon that occurs in a vibration environment, and is essentially due to the nonlinear characteristics of the accelerometer, which rectifies the alternating vibration signal into a false direct current component. When the accelerometer is subjected to vibration, the second-order or high-order nonlinear terms of the internal transfer function of the accelerometer will cause the vibration acceleration with a mean value of zero to produce a non-zero average output offset. This offset will be mistaken for a real direct current acceleration signal in static or low frequency measurement scenarios, for example, causing angle calculation deviation in inclination detection, or introducing positioning drift in inertial navigation. The amplitude of the vibration rectification error is closely related to the vibration intensity and spectral distribution, and is modulated by factors such as the sensor structure resonance characteristics, packaging stiffness, and the relative angle between the vibration direction and the input axis, especially under multi-axis coupled vibration or specific frequency phase combinations.

[0003] The existing accelerometer vibration rectification error has the following technical problems in analysis. In the data processing algorithm, the smoothing operation introduces signal distortion risk. The reason is that the acceleration signal in the vibration test scene has non-stationary characteristics. Although the smoothing process reduces noise, it can easily weaken the authenticity of high-frequency transient components. For example, vibration rectification error analysis needs to capture accurate extreme points, but the smoothing process can average the rapid changes in actual vibration events, causing the error calculation result to deviate from the actual physical response. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application provides an accelerometer vibration rectification error analysis method. The present application solves the technical problem that the smoothing operation in the data processing of non-stationary vibration signals introduces signal distortion, causing the vibration rectification error calculation result to deviate from the actual physical response.

[0005] To solve the above technical problems, the content of the present application is as follows: The present application provides an accelerometer vibration rectification error analysis method, comprising: Step 1: receiving the original current signals of multiple accelerometers under vibration excitation, synchronizing the channel data with time stamps, and outputting the original non-stationary vibration data set that retains high-frequency components; Step 2: based on the original non-stationary vibration data set, performing short-time Fourier transform to identify the vibration energy concentrated frequency band, using Zernike moment algorithm to detect the transient shock waveform boundary, fitting the extreme envelope line in the marked interval by Hermite interpolation, and outputting the feature point coordinate sequence with confidence; Step 3: Based on the confidence level and frequency band distribution characteristics of the feature point coordinate sequence, dynamically schedule the optimization algorithm combination in the knowledge base, call the scheduled algorithm combination to calculate and output the local statistical data set. The knowledge base includes the Levenberg-Marquardt method, simulated annealing algorithm, and particle swarm optimization. Step 4: Input the local statistical data set into the mechanical dynamics model to perform trajectory simulation, and simultaneously input the control model to reconstruct the signal output, compare the difference in positioning drift between the two paths, and generate the error correction coefficient matrix; Step 5: Use the error correction coefficient matrix to reconstruct the vibration rectification error quantization value, input it into the self-organizing map neural network to perform error distribution clustering, and when the clustering detects an abnormal pattern, it outputs the knowledge base update instruction and the feature point detection parameter reset instruction; Step 6: Import the quantized value of the vibration rectification error into the inclination detection model to calculate the theoretical angle deviation. Input the vibration table test data to verify the convergence. When the deviation exceeds the threshold, trigger the neural network retraining and return to the process of step 5 to reconstruct the quantized value of the vibration rectification error.

[0006] Furthermore, the accelerometer vibration rectification error analysis method of the present invention, step 1 includes: Receive parallel data stream from vibration tooling AD conversion module; Use GPS disciplined clock source to mark absolute timestamps for parallel data streams; Perform impedance matching on the timestamped data to suppress reflection interference; The processed data are integrated to generate a raw data matrix with absolute time scale.

[0007] Furthermore, in the accelerometer vibration rectification error analysis method of the present invention, step 2 includes: Perform short-time Fourier transform on the original non-stationary vibration data set to generate a time-frequency spectrum and calculate the spectral entropy value to quantify the energy concentration of the frequency band; The waveform curvature feature projection value is calculated based on the time-frequency spectrum, and the transient shock waveform boundary is adaptively determined using the Otsu method. Call cubic Hermite interpolation to locate the extreme point coordinates in the boundary interval; Perform Monte Carlo repeated sampling on the extreme point coordinates to calculate the confidence interval and output a sequence of feature point coordinates with confidence intervals.

[0008] Furthermore, in the accelerometer vibration rectification error analysis method of the present invention, step 3 includes: Establish an algorithm and feature mapping rule table and define the following correspondences: steady-state sinusoidal vibration corresponds to the Levenberg-Marquardt method, impulse response corresponds to the simulated annealing algorithm, and broadband random vibration corresponds to particle swarm optimization; Receiving confidence interval attributes and frequency band distribution characteristic data of a feature point coordinate sequence; Perform cosine similarity matching on the confidence interval attributes and frequency band distribution feature data of the feature point coordinate sequence and the rule table, and output the optimization algorithm combination; The optimization algorithm is used to process the feature point coordinate sequence, and the local curvature characteristics are fitted by the Levenberg-Marquardt method to extract the average value of the trend component. The maximum sequence of the envelope profile is searched by simulated annealing algorithm; The minimum value of the non-stationary interval is located through particle swarm optimization, and the envelope maximum value sequence and the local statistical data set of the minimum value of the non-stationary interval are output.

[0009] Furthermore, in the accelerometer vibration rectification error analysis method of the present invention, step 4 includes: In the mechanical dynamics model, the virtual vibration table is driven by using the maximum value and minimum value data in the partition parameter set to generate first trajectory data, wherein the first trajectory data represents a simulation result of the mechanical dynamics model; Injecting vibration environment interference noise into the control model to reconstruct the theoretical output current signal and generate second trajectory data, the second trajectory data representing the reconstructed signal of the control model; A dynamic time warping algorithm is executed on the first trajectory data and the second trajectory data to align the motion trajectories to obtain an aligned dual path, a root mean square error value of the aligned dual path is calculated, and an error correction coefficient matrix is ​​output.

[0010] Furthermore, in the accelerometer vibration rectification error analysis method of the present invention, step 5 includes: Perform weighted processing on the original non-stationary vibration data set in step 1 and the error correction coefficient matrix; Perform Gaussian process regression on the weighted data to compensate for system deviation and reconstruct the quantized value of vibration rectification error; The ring topology self-organizing map network is called to perform cluster analysis on the vibration rectification error quantization value. When the proportion of abnormal vibration modes in the clustering results exceeds the preset threshold, the weight update instruction is transmitted to the knowledge base in step 3 and the parameter reset instruction is transmitted to step 2.

[0011] Furthermore, in the accelerometer vibration rectification error analysis method of the present invention, step 6 includes: When receiving the feature point detection parameter reset instruction, execute the following sequence to clear the currently cached feature point coordinate sequence; Reload the original non-stationary vibration data set from step 1 and recalculate the Otsu method adaptive threshold based on the reloaded data set; The optimization algorithm combination scheduling of step 3 is suspended until step 2 outputs the updated feature point coordinate sequence, which is generated by step 2 based on the reloaded dataset.

[0012] Furthermore, in the accelerometer vibration rectification error analysis method of the present invention, step 6 further includes: The vibration rectification error quantization value is implanted into the finite element model to calculate the theoretical inclination angle and output the theoretical angle data; The actual displacement data of the vibration table is obtained through the laser interferometer; Calculate the actual angle data by performing coordinate transformation based on the actual displacement data; The least square method is used to fit the deviation curve between theoretical angle data and actual angle data; Extract the amplitude fluctuation parameters and frequency domain distribution parameters of the deviation curve; The fluctuation parameter and distribution parameter are substituted into the dynamic threshold function to judge the convergence. When the output value of the function exceeds the set threshold, a retraining trigger pulse is generated.

[0013] Furthermore, in the accelerometer vibration rectification error analysis method of the present invention, step 6 further includes: The dynamic threshold function receives the amplitude fluctuation parameter and the frequency domain distribution parameter, and outputs the convergence criterion by calculating the function value including the frequency, amplitude and the logarithm of the vibration energy; When the retraining trigger pulse arrives, the weight matrix of the self-organizing map neural network is cleared and the structural parameters are initialized; The initialized neural network re-receives the vibration rectification error quantization value reconstructed in step 5 to perform cluster analysis.

[0014] Furthermore, in the accelerometer vibration rectification error analysis method of the present invention, step 6 further includes: Generate dynamic scheduling priority data based on the feature point coordinate sequence and perform sorting operations on the algorithm combinations in the knowledge base; The clustering results are used to extract waveform curvature feature correction parameters and update the Otsu method adaptive threshold calculation parameters; According to the convergence criterion output by the dynamic threshold function, the weight distribution ratio in the rule table is reconstructed, and the weight distribution ratio in the replacement algorithm and feature mapping rule table is replaced; The updated rule table drives the cosine similarity matching process in step 3, forming a feedback control loop for the cross-step error analysis process.

[0015] Beneficial effects of the present invention: The beneficial effects brought by the technical solution of the present invention are reflected in three aspects: in the data processing link, the high-frequency components are retained by aligning the channel data through time stamp synchronization and Hermite interpolation is used to fit the extreme envelope, avoiding the weakening of transient characteristics by smoothing operations and maintaining the true physical form of the vibration signal; in the error modeling link, the dynamic scheduling knowledge base matching optimization algorithm is used to combine and process the feature point coordinate sequence, and the positioning drift difference is compared and positioned in combination with the dual-path trajectory simulation to solve the error transmission problem of single model analysis; in the closed-loop control link, the abnormal mode is identified by clustering the self-organizing map network to trigger the parameter reset instruction, and the dynamic threshold function convergence criterion is linked to update the weight distribution ratio of the rule table, forming a cross-step feedback control loop to continuously optimize the feature extraction accuracy, so that the vibration rectification error quantization result closely fits the physical response characteristics under complex vibration environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solution of the present invention, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, for ordinary technicians in this field, other drawings can be obtained based on the drawings without paying any creative labor.

[0017] Figure 1 This is a flow chart of a method for analyzing accelerometer vibration rectification errors provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0018] To make the technical solution of the present invention clearer, the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. The present invention provided by each embodiment of the present invention is described in detail below in conjunction with the drawings. In order to better understand the purpose of the present invention, the present invention is further described below.

[0019] See also Figure 1 The present invention provides an accelerometer vibration rectification error analysis method, comprising: Step 1: Receive the original current signals of multiple accelerometers under vibration excitation, align the channel data using time stamp synchronization, and output the original non-stationary vibration data set that retains the high-frequency components; Step 2: Based on the original non-stationary vibration data set, a short-time Fourier transform is performed to identify the frequency band where vibration energy is concentrated. The Zernike moment algorithm is used to detect the boundary of the transient impact waveform. The extreme envelope is fitted within the marked interval through Hermite interpolation, and a sequence of feature point coordinates with confidence is output. Step 3: Based on the confidence level and frequency band distribution characteristics of the feature point coordinate sequence, dynamically schedule the optimization algorithm combination in the knowledge base, call the scheduled algorithm combination to calculate and output the local statistical data set. The knowledge base includes the Levenberg-Marquardt method, simulated annealing algorithm, and particle swarm optimization. Step 4: Input the local statistical data set into the mechanical dynamics model to perform trajectory simulation, and simultaneously input the control model to reconstruct the signal output, compare the difference in positioning drift between the two paths, and generate the error correction coefficient matrix; Step 5: Use the error correction coefficient matrix to reconstruct the vibration rectification error quantization value, input it into the self-organizing map neural network to perform error distribution clustering, and when the clustering detects an abnormal pattern, it outputs the knowledge base update instruction and the feature point detection parameter reset instruction; Step 6: Import the quantized value of the vibration rectification error into the inclination detection model to calculate the theoretical angle deviation. Input the vibration table test data to verify the convergence. When the deviation exceeds the threshold, trigger the neural network retraining and return to the process of step 5 to reconstruct the quantized value of the vibration rectification error.

[0020] The system receives raw current signals generated by multiple accelerometers under vibration excitation and transmits them to the processing system via parallel data channels. A high-precision clock source is used to timestamp the multi-channel data streams, eliminating time deviations caused by transmission delays. Impedance matching is performed on the time-aligned data to suppress interference caused by signal reflections. The processed multi-channel data is integrated to generate a non-stationary vibration dataset with an absolute time stamp, fully preserving the high-frequency transient components of the vibration signals. This dataset serves as the basis for subsequent analysis, preventing smoothing from degrading high-frequency features.

[0021] A short-time Fourier transform is performed on the original non-stationary vibration dataset to generate a time-frequency domain distribution map and calculate spectral entropy values ​​to quantify the energy concentration in different frequency bands. The waveform curvature feature projection values ​​are calculated based on the time-frequency spectrum, and an adaptive threshold segmentation algorithm is used to determine the boundary interval of the transient impact waveform. Within the marked boundary range, the extreme value envelope of the vibration signal is fitted using a cubic Hermite interpolation function. Probability distribution sampling is performed on the extracted extreme points, and a sequence of feature point coordinates with confidence intervals is output, ensuring that transient feature extraction is unaffected by smoothing.

[0022] Based on the confidence level and frequency band energy distribution characteristics of the feature point coordinate sequence, a combination of optimization algorithms from the knowledge base is dynamically scheduled. The knowledge base includes three algorithms: the Levenberg-Marquardt method, simulated annealing, and particle swarm optimization. Using the algorithm and feature mapping rule table, cosine similarity matching is performed between the feature attributes and the optimization algorithm. The matching algorithm combination is then called to collaboratively process the feature point coordinate sequence: the Levenberg-Marquardt method fits local curvature features to extract the average value of the trend component; the simulated annealing algorithm searches for the maximum sequence of the envelope profile; and the particle swarm optimization locates the minimum value of the non-stationary interval. The output is a partition parameter set containing the average, maximum, and minimum values.

[0023] The partitioned parameter set is input into the mechanical dynamics model, driving a virtual vibration table to generate simulated motion trajectory data. Environmental interference noise is injected into the control model, reconstructing the theoretical output current signal and generating corresponding trajectory data. A dynamic time warping algorithm is applied to the two trajectory data to eliminate time scale differences and align the trajectory paths. The positioning drift of the aligned dual paths is calculated, and the root mean square error (RMS) is evaluated to generate an error correction coefficient matrix to quantify the deviation between the model and the actual response.

[0024] The original non-stationary vibration dataset is weighted and corrected using an error correction coefficient matrix. Gaussian process regression is then used to compensate for inherent system biases and reconstruct the quantized vibration rectification error. A ring-topology self-organizing map network is then used to perform cluster analysis on the quantized vibration rectification error to identify abnormal distribution patterns. When the proportion of abnormal vibration patterns in the clustering results exceeds a preset threshold, a weight update instruction is sent to the knowledge base, and a parameter reset instruction is sent to the feature extraction module, triggering the reinitialization of the feature extraction process.

[0025] The quantized vibration rectification error is input into the inclination detection model to calculate the theoretical angle deviation data. Combined with the actual displacement data collected from the vibration table test, the actual angle information is generated through coordinate transformation. The least squares method is used to fit the deviation curve between the theoretical and actual angles, extracting amplitude fluctuation parameters and frequency domain energy distribution parameters. These parameters are input into a dynamic threshold function to determine system convergence. When the output value exceeds the set threshold, the neural network weight initialization is triggered and the process of reconstructing the quantized vibration rectification error value is returned.

[0026] Steps 1 and 2 complete data preprocessing and transient feature extraction; steps 3 and 4 implement feature optimization and error modeling; and steps 5 and 6 perform error verification and feedback optimization. A dynamic scheduling mechanism matches the optimization algorithm based on feature confidence, dual-path simulation verifies model reliability, and neural network clustering identifies abnormal patterns and triggers parameter reset. Knowledge base update instructions and feature parameter reset instructions form cross-step feedback, enabling the system to adapt to changes in the vibration environment. This entire process addresses signal distortion in vibration rectification error analysis by preserving high-frequency components and avoiding smoothing operations.

[0027] Specifically, the accelerometer vibration rectification error analysis method of the present invention, step 1 includes: Receive parallel data stream from vibration tooling AD conversion module; Use GPS disciplined clock source to mark absolute timestamps for parallel data streams; Perform impedance matching on the timestamped data to suppress reflection interference; The processed data are integrated to generate a raw data matrix with absolute time scale.

[0028] The vibration tooling A / D conversion module collects raw current signals generated by multiple accelerometers under vibration excitation and outputs parallel data streams. A GPS-disciplined clock source assigns nanosecond-precision absolute timestamps to each sampling point in the parallel data streams, eliminating inter-channel clock drift errors. Impedance matching is performed on the timestamped data, adjusting the ratio of the transmission line characteristic impedance to the load impedance to suppress interference caused by signal reflections. The impedance-matched multi-channel data is then integrated to generate a raw data matrix with absolute time stamps. This matrix preserves the complete high-frequency components and time synchronization of the vibration signal.

[0029] Data acquisition: The vibration tooling AD conversion module directly obtains the original current signal output by the accelerometer, avoiding the loss of high-frequency components caused by preprocessing.

[0030] Time synchronization: The GPS disciplined clock source provides a unified time reference, marking absolute timestamps for multi-channel data and solving the time asynchrony problem of distributed acquisition systems.

[0031] Signal fidelity: Impedance matching maintains signal integrity and eliminates reflection interference caused by impedance mismatch in the transmission path.

[0032] Data reconstruction: The processed multi-channel data are integrated to form a spatiotemporal correlation matrix, which provides the original input for subsequent non-stationary analysis.

[0033] A / D conversion digitizes the physical signal, clock synchronization provides the time base, impedance matching ensures signal quality, and data integration forms the foundation for analysis. The absolute time stamp of the GPS clock provides the time base for the time-frequency analysis in step 2. The retained high-frequency components support the error quantization and reconstruction in step 5. Impedance matching ensures that the feature point coordinate sequence extracted in step 3 is not affected by transmission interference. This entire process avoids smoothing operations, ensuring the accuracy of vibration rectification error analysis from the source.

[0034] Specifically, the accelerometer vibration rectification error analysis method of the present invention, step 2 includes: Perform short-time Fourier transform on the original non-stationary vibration data set to generate a time-frequency spectrum and calculate the spectral entropy value to quantify the energy concentration of the frequency band; The waveform curvature feature projection value is calculated based on the time-frequency spectrum, and the Otsu method is used to adaptively determine the boundary of the transient impact waveform. The extreme value point coordinates are located by calling the cubic Hermite interpolation function to fit the vibration signal waveform in the marked boundary interval. The confidence interval is calculated by performing Monte Carlo repeated sampling on the extreme value point coordinates, and the feature point coordinate sequence with a confidence interval is output.

[0035] The short-time Fourier transform is performed on the original non-stationary vibration data set output in step 1 to generate a time-frequency spectrum including the time-frequency-energy three-dimensional relationship. The spectral entropy value of the time-frequency spectrum is calculated to quantify the concentration degree distribution characteristics of the vibration energy of each frequency band. The waveform curvature feature projection value is extracted based on the time-frequency spectrum, and the local curvature change of the transient waveform is represented by the second derivative operation. The Otsu method is used to adaptively segment the curvature feature projection value to dynamically determine the boundary coordinate interval of the transient impact waveform. In the marked boundary interval, the cubic Hermite interpolation function is called to fit the vibration signal waveform to locate the extreme value point coordinates of the acceleration response. The Monte Carlo repeated sampling is performed on the extreme value point coordinate set to calculate the spatial distribution probability density function, and the feature point coordinate sequence with a confidence interval is output.

[0036] Time-frequency feature extraction: the short-time Fourier transform converts the non-stationary signal into a time-frequency domain representation, and the spectral entropy value calculation objectively reflects the frequency band energy distribution characteristics, providing input basis for subsequent algorithms.

[0037] Boundary detection mechanism: the waveform curvature feature projection value quantifies the degree of signal shape mutation, and the Otsu method adaptively determines the threshold to overcome the adaptability limitations of fixed threshold to complex vibration environment.

[0038] Extreme value positioning method: the cubic Hermite interpolation maintains the continuity of the waveform high-order derivative within the boundary interval, avoiding the extreme value point deviation caused by the smoothing algorithm.

[0039] Confidence evaluation: the Monte Carlo repeated sampling establishes the probability distribution model of the extreme value point coordinates, and the confidence interval index quantifies the reliability of the feature extraction result.

[0040] The spectral entropy value input step 3 algorithm scheduling decision, and the feature point coordinate sequence with a confidence interval provides basic data for step 4 trajectory simulation. The whole process maintains the true shape of the vibration signal in the transient impact boundary through the non-smoothing processing mechanism, solves the rectification error calculation distortion problem caused by the smoothing operation of the existing method. The collaborative design of boundary detection and extreme value positioning effectively preserves the physical response characteristics of high-frequency transient components.

[0041] Specifically, the accelerometer vibration rectification error analysis method described in the application, step 3 comprises: An algorithm and feature mapping rule table is established, and the following corresponding relationship is defined: steady-state sinusoidal vibration corresponds to the Levenberg-Marquardt method, impact response corresponds to the simulated annealing algorithm, and wideband random vibration corresponds to the particle swarm optimization; Receive the confidence interval attribute and frequency band distribution characteristic data of the feature point coordinate sequence; Perform cosine similarity matching on the confidence interval attribute and frequency band distribution characteristic data of the feature point coordinate sequence and the rule table, and output the optimized algorithm combination; Call the optimized algorithm combination to process the feature point coordinate sequence, fit the local curvature feature by the Levenberg-Marquardt method, and extract the average value of the trend component; Search for the maximum value sequence of the envelope contour by the simulated annealing algorithm; Locate the minimum value of the non-stationary interval by the particle swarm optimization, and output the local statistical data set of the maximum value sequence of the envelope and the minimum value of the non-stationary interval.

[0042] An algorithm and feature mapping rule table is established, and the following corresponding relationship is defined: steady-state sinusoidal vibration corresponds to the Levenberg-Marquardt method, impact response corresponds to the simulated annealing algorithm, and wideband random vibration corresponds to the particle swarm optimization. Receive the confidence interval attribute and frequency band distribution characteristic data of the feature point coordinate sequence output by step 2, the confidence interval attribute represents the reliability degree of the feature point coordinate, and the frequency band distribution characteristic data reflects the concentration characteristics of the vibration energy in the frequency spectrum dimension. Perform cosine similarity calculation on the confidence interval attribute and frequency band distribution characteristic data and the rule table, quantify the matching degree of the input features and the preset vibration mode, and output the optimized algorithm combination call sequence. Call the determined algorithm combination to cooperatively process the feature point coordinate sequence: the Levenberg-Marquardt method performs nonlinear least squares fitting on the coordinate sequence to extract the average value of the trend component of the vibration signal; the simulated annealing algorithm performs global optimization search in the envelope space to locate the maximum value sequence; and the particle swarm optimization performs parallel optimization in the non-stationary interval to identify the minimum value distribution. Output the partition parameter set including the local average value, the maximum value sequence, and the minimum value, as the input basis of the error correction model.

[0043] Rule table construction: based on the matching relationship between the vibration mode and the algorithm characteristics, the mapping rule is established, the gradient optimization method is used to capture the trend feature for steady-state vibration, the heuristic search is used to locate the extreme value for impact response, and the swarm intelligence optimization is used to process random components for wideband vibration.

[0044] Feature data reception: the confidence interval attribute inherits the Monte Carlo sampling result of step 2, and the frequency band distribution characteristic is derived from the spectral entropy calculation of step 2, which constitutes the decision basis for dynamic scheduling.

[0045] Similarity matching: cosine similarity calculation compares the feature data vector with the preset mode of the rule table, quantifies the matching degree, and outputs the algorithm call priority sequence.

[0046] Collaborative processing mechanism: The three algorithms divide the work according to the mapping relationship. The Levenberg-Marquardt method fits the local curvature, the simulated annealing algorithm searches the envelope contour, and the particle swarm optimization locates the non-stationary interval.

[0047] The average value extracted by the Levenberg-Marquardt method is input into the mechanical dynamics model in step 4. The sequence of maximum and minimum values ​​drives the virtual shaker simulation. The partition parameter set provides a statistical basis for error quantization and reconstruction in step 5, while the frequency band distribution characteristic data is used to update the rule table weights in step 10. The dynamic scheduling mechanism overcomes the adaptability limitations of fixed algorithms to complex vibration environments and avoids the distortion of statistical characteristics caused by smoothing operations.

[0048] Specifically, the accelerometer vibration rectification error analysis method of the present invention, step 4 includes: In the mechanical dynamics model, the virtual vibration table is driven by using the maximum value and minimum value data in the partition parameter set to generate first trajectory data, wherein the first trajectory data represents a simulation result of the mechanical dynamics model; Injecting vibration environment interference noise into the control model to reconstruct the theoretical output current signal and generate second trajectory data, the second trajectory data representing the reconstructed signal of the control model; A dynamic time warping algorithm is executed on the first trajectory data and the second trajectory data to align the motion trajectories to obtain an aligned dual path, a root mean square error value of the aligned dual path is calculated, and an error correction coefficient matrix is ​​output.

[0049] The partition parameter set output from step 3 is loaded into the mechanical dynamics model. The maximum and minimum data are extracted to drive the multibody dynamics equations of the virtual vibration table, generating first trajectory data reflecting the actual response of the mechanical system. The vibration environment interference noise component collected in step 1 is injected into the control model, and the output current signal is reconstructed based on the accelerometer's theoretical transfer function to generate second trajectory data representing the ideal sensor response. A dynamic time warping algorithm is applied to the first and second trajectory data. A nonlinear time axis transformation eliminates the time domain scale difference between the physical response and the theoretical model, achieving spatial alignment of the dual-path motion trajectories and outputting the time-synchronized aligned dual paths. The displacement deviation of the corresponding spatial coordinate points of the aligned dual paths is calculated. The statistical characteristics of the trajectory offset are calculated using the root mean square error formula, and an error correction coefficient matrix is ​​output to characterize the distribution of system errors.

[0050] Physical response simulation mechanism: The maximum sequence and minimum value of the partition parameter set are input into the multi-degree-of-freedom dynamic equation to drive the virtual vibration table to generate a motion trajectory including nonlinear damping effects.

[0051] Theoretical benchmark construction method: The control model superimposes the original vibration noise and applies the ideal mathematical model of the sensor to construct a theoretical trajectory benchmark without error interference.

[0052] Spatiotemporal synchronization processing: The dynamic time warping algorithm adaptively stretches the time axis to solve the phase offset problem between the simulation trajectory and the theoretical trajectory caused by system delay.

[0053] Error quantification process: After spatial alignment, the dual-path coordinates are subjected to point-by-point difference calculation, and the root mean square error is integrated with statistical features to generate a correction coefficient matrix.

[0054] The maximum and minimum data are derived from the partition parameter set in step 3, and the error correction coefficient matrix is ​​input into the weighted reconstruction process in step 5. The dual-path verification mechanism overcomes the error propagation flaws of single-path analysis by comparing the physical system response with the ideal mathematical model. The dynamic time warping algorithm addresses the nonuniform deformation of nonstationary vibration signals along the time axis, ensuring the spatial comparability of the error correction coefficient matrix. The root mean square error calculation of the aligned dual paths provides a spatial domain basis for vibration rectification error quantification.

[0055] Specifically, the accelerometer vibration rectification error analysis method of the present invention, step 5 includes: Perform weighted processing on the original non-stationary vibration data set in step 1 and the error correction coefficient matrix; Perform Gaussian process regression on the weighted data to compensate for system deviation and reconstruct the quantized value of vibration rectification error; The ring topology self-organizing map network is called to perform cluster analysis on the vibration rectification error quantization value. When the proportion of abnormal vibration modes in the clustering results exceeds the preset threshold, the weight update instruction is transmitted to the knowledge base in step 3 and the parameter reset instruction is transmitted to step 2.

[0056] The original non-stationary vibration dataset output from step 1 and the error correction coefficient matrix generated in step 4 are weighted and fused, achieving spatial domain correction of the vibration data through matrix dot multiplication. Gaussian process regression modeling is performed on the weighted data to compensate for the inherent bias and nonlinear distortion components of the sensor system and reconstruct the quantized vibration rectification error. A ring-topology self-organizing map neural network is used to load the error quantization dataset and perform unsupervised clustering analysis to identify error distribution patterns. When the proportion of abnormal vibration patterns in the clustering results exceeds a preset threshold, a knowledge base weight update instruction is generated and transmitted to the knowledge base module in step 3. Simultaneously, a feature point detection parameter reset instruction is generated and transmitted to the feature extraction module in step 2.

[0057] Data correction mechanism: The original non-stationary vibration data set is weighted element-wise with the error correction coefficient matrix, which is derived from the dual-path error verification results in step 4 and corrects the spatial offset component of the vibration signal.

[0058] System bias compensation: Gaussian process regression establishes a nonlinear mapping relationship to compensate for the influence of sensor inherent system error on the total flow rate, and outputs an error quantization value with clear physical meaning.

[0059] Intelligent clustering analysis: the ring topology self-organizing mapping network organizes error data according to the neighborhood competition mechanism, and outputs a cluster pattern distribution map to identify abnormal vibration response.

[0060] Feedback instruction generation: the abnormal mode proportion triggers cross-module instruction transmission, the knowledge base weight update instruction optimizes the step 3 algorithm scheduling rule, and the parameter reset instruction triggers the step 2 feature extraction process to reinitialize.

[0061] The original non-stationary vibration data set comes from step 1, the error correction coefficient matrix inherits the output result of step 4, and the reconstructed quantization value is input into the inclination detection model of step 6. The knowledge base weight update instruction acts on the dynamic scheduling rule of step 3, and the parameter reset instruction drives the feature extraction module of step 2 to update the detection threshold. The ring topology structure enhances the neighborhood correlation of clustering analysis, and the abnormal vibration pattern recognition mechanism solves the blind area problem of existing methods to compound interference. The double-path design of feedback instruction realizes the cooperative optimization of algorithm parameters and feature extraction.

[0062] Specifically, the accelerometer vibration rectification error analysis method disclosed by the application comprises the following steps: When receiving the feature point detection parameter reset instruction, execute the following sequence to empty the currently cached feature point coordinate sequence; Load the original non-stationary vibration data set from step 1, and recalculate the Otsu adaptive threshold based on the reloaded data set; Pause the optimization algorithm combination scheduling of step 3 until step 2 outputs the updated feature point coordinate sequence, which is generated by step 2 based on the reloaded data set.

[0063] After receiving the parameter reset instruction transmitted by step 5, empty the currently cached feature point coordinate sequence storage area to eliminate the interference of historical data on the analysis process. Load the original non-stationary vibration data set with absolute time scale from the original data storage module of step 1 as the input source of feature extraction. Based on the reloaded data set, perform waveform curvature feature projection value calculation, and dynamically update the adaptive threshold parameter of transient shock waveform boundary detection using the Otsu method. Pause the calling operation of the optimization algorithm combination of the dynamic scheduling mechanism of step 3, and maintain the knowledge base scheduling module in a waiting state. After waiting for step 2 to complete the feature extraction process based on the reloaded data set and output the updated feature point coordinate sequence, restore the optimization algorithm combination scheduling function of step 3.

[0064] Command response mechanism: The parameter reset command triggers the data clearing operation, interrupting the current analysis process and entering the reset state.

[0065] Data retrospective loading: Recall the original non-stationary vibration data set from step 1 and restore the initial input conditions for characteristic analysis.

[0066] Dynamic threshold update: The waveform curvature feature projection value is recalculated based on the new data set, and the Otsu method is applied to generate a boundary detection threshold that adapts to the current vibration environment.

[0067] Process synchronization control: Pause the scheduling function of step 3 to avoid mixed processing of new and old data, and wait for step 2 to output the updated sequence before resuming the subsequent process.

[0068] The parameter reset instruction originates from the cluster analysis results of step 5. The reloaded dataset inherits the original data features from step 1. The Otsu method's adaptive threshold update mechanism maintains consistent terminology with the boundary detection method of step 2. The scheduling function of step 3 is restored after the feature point coordinate sequence is output. A pause mechanism prevents the knowledge base scheduling module from processing unupdated feature data, maintaining the timing correctness of the analysis process. The threshold recalculation process uses the same waveform curvature feature projection value calculation method as step 2 to ensure the consistency of the technical logic.

[0069] Specifically, the accelerometer vibration rectification error analysis method of the present invention, step 6 further includes: The vibration rectification error quantization value is implanted into the finite element model to calculate the theoretical inclination angle and output the theoretical angle data; The actual displacement data of the vibration table is obtained through the laser interferometer; Calculate the actual angle data by performing coordinate transformation based on the actual displacement data; The least square method is used to fit the deviation curve between theoretical angle data and actual angle data; Extract the amplitude fluctuation parameters and frequency domain distribution parameters of the deviation curve; The fluctuation parameter and distribution parameter are substituted into the dynamic threshold function to judge the convergence. When the output value of the function exceeds the set threshold, a retraining trigger pulse is generated.

[0070] The quantized value of the vibration rectification error reconstructed in step 5 is embedded in the finite element model. The theoretical inclination change of the accelerometer's sensitive structure is calculated using the stress-strain relationship, and the theoretical angle data is output. A laser interferometer is used to collect spatial displacement data of the vibration table surface in real time, recording the actual motion trajectory. Based on the actual displacement data obtained by the laser interferometer, a three-dimensional coordinate transformation is performed to calculate the actual inclination data of the accelerometer mounting base. The least squares method is used to fit the deviation curve between the theoretical and actual angle data, and a model for the distribution of angle deviation over time is established. The amplitude fluctuation parameters of the deviation curve are extracted to characterize the angle offset amplitude, and the frequency domain distribution parameters are extracted to describe the spectral characteristics of the deviation signal. The amplitude fluctuation parameters and frequency domain distribution parameters are input into the dynamic threshold function, and the convergence criterion is output through multi-parameter fusion calculation. When the output value of the dynamic threshold function exceeds the set threshold, a retraining trigger pulse signal is generated to initiate the neural network weight update process.

[0071] Theoretical modeling method: The finite element model is loaded with the quantized value of the vibration rectification error, and the theoretical inclination angle output is calculated based on the mechanical properties of the material.

[0072] Experimental data acquisition: Laser interferometer directly measures the displacement data of the vibration table and provides a benchmark for the actual motion trajectory.

[0073] Spatial coordinate solution: Three-dimensional coordinate transformation converts displacement data into inclination information, keeping it consistent with the spatial reference of the theoretical model.

[0074] Deviation quantification modeling: Least squares fitting is used to establish a time series model of theoretical-actual angle deviation.

[0075] Feature parameter extraction: Amplitude fluctuation parameters reflect static offset, and frequency domain distribution parameters characterize dynamic error characteristics.

[0076] Convergence decision mechanism: The dynamic threshold function integrates time-frequency features to output convergence criteria, triggering pulse signals to drive system optimization.

[0077] The theoretical angle data is derived from the error quantization value obtained in step 5, while the actual displacement data is obtained from the vibration table test environment. The amplitude fluctuation parameters and frequency domain distribution parameters of the deviation curve are extracted using the same method as in step 8. The output of the dynamic threshold function triggers neural network initialization in step 9. The entire process, through dual validation through theoretical modeling and experimental verification, addresses the transmission distortion problem of vibration rectification errors in inclination angle detection. The generation conditions of the retraining trigger pulse and the threshold set by the dynamic threshold function form a closed decision loop, ensuring reliable system convergence.

[0078] Specifically, the accelerometer vibration rectification error analysis method of the present invention, step 6 further includes: The dynamic threshold function receives the amplitude fluctuation parameter and the frequency domain distribution parameter, and outputs the convergence criterion by calculating the function value including the frequency, amplitude and the logarithm of the vibration energy; When the retraining trigger pulse arrives, the weight matrix of the self-organizing map neural network is cleared and the structural parameters are initialized; The initialized neural network re-receives the vibration rectification error quantization value reconstructed in step 5 to perform cluster analysis.

[0079] The dynamic threshold function receives the amplitude fluctuation parameters and frequency domain distribution parameters extracted in step 6. The amplitude fluctuation parameters characterize the amplitude variation characteristics of the angular deviation, and the frequency domain distribution parameters describe the spectral energy distribution of the deviation signal. The function performs multi-dimensional calculations by fusing frequency components, amplitude characteristics, and vibration energy logarithmic terms, and outputs a quantitative convergence criterion indicator. When the retraining trigger pulse signal generated in step 6 arrives, the weight matrix data stored in the self-organizing map neural network in step 5 is cleared, and the topological structure parameters of the neurons are initialized. The initialized self-organizing map neural network reloads the vibration rectification error quantization value data set reconstructed in step 5 and executes the updated error distribution clustering analysis process.

[0080] Criterion generation mechanism: A dynamic threshold function integrates the time-domain amplitude fluctuation and frequency-domain energy distribution parameters, and outputs a convergence criterion to quantify system stability.

[0081] Network reset operation: The retraining trigger pulse drives the neural network weight matrix back to zero, and the structural parameters are initialized to restore the initial learning state.

[0082] Closed-loop learning process: After initialization, the network reprocesses the quantized value of the vibration rectification error and updates the cluster analysis results.

[0083] The trigger pulse originates from the convergence determination phase in step 6, and the weight matrix clearing operation targets the self-organizing map neural network in step 5. The re-received quantized value of the vibration rectification error originates from the reconstructed output in step 5, ensuring consistency between technical terminology and data source. This entire process uses a dynamic threshold to trigger a neural network reset, addressing clustering model mismatch issues caused by changes in error distribution. After initialization, cluster analysis updates the abnormal pattern recognition results, which are fed back to the instruction generation phase in step 5, forming a closed-loop cross-module optimization loop.

[0084] Specifically, the accelerometer vibration rectification error analysis method of the present invention, step 6 further includes: Generate dynamic scheduling priority data based on the feature point coordinate sequence and perform sorting operations on the algorithm combinations in the knowledge base; The clustering results are used to extract waveform curvature feature correction parameters and update the Otsu method adaptive threshold calculation parameters; According to the convergence criterion output by the dynamic threshold function, the weight distribution ratio in the rule table is reconstructed, and the weight distribution ratio in the replacement algorithm and feature mapping rule table is replaced; The updated rule table drives the cosine similarity matching process in step 3, forming a feedback control loop for the cross-step error analysis process.

[0085] Dynamic scheduling priority data is generated based on the feature point coordinate sequence output in step 2. By calculating weighted scores based on confidence interval attributes and frequency band distribution characteristics, a ranking operation is performed on the Levenberg-Marquardt method, simulated annealing algorithm, and particle swarm optimization combination in the knowledge base. Waveform curvature feature correction parameters are extracted from the clustering results in step 5. The mapping relationship between abnormal vibration modes and curvature features is analyzed to update the Otsu method adaptive threshold calculation parameters in step 2. The weight distribution ratios in the reconstruction rule table are output using the convergence criteria in step 6, replacing the weight distribution ratios for steady-state sinusoidal vibration, impulse response, and broadband random vibration in the algorithm and feature mapping rule table in step 3. The updated algorithm and feature mapping rule table drives the cosine similarity matching process in step 3, forming a cross-step error analysis process feedback control loop covering feature extraction in step 2, algorithm scheduling in step 3, cluster analysis in step 5, and verification in step 6.

[0086] Dynamic scheduling mechanism: The confidence interval attributes and frequency band distribution characteristics of the feature point coordinate sequence are input into the priority calculation model to generate an algorithm call sequence list and optimize the execution priority sorting of the three algorithms in the knowledge base.

[0087] Feature parameter update: An association model is established between the abnormal vibration modes in the clustering results and the waveform curvature characteristics. The output correction parameters dynamically adjust the boundary detection threshold of the Otsu method in step 2 to enhance the environmental adaptability of transient shock identification.

[0088] Rule table reconstruction process: The convergence criterion analyzes the matching degree between the theoretical angle deviation and the actual data, generates a weight distribution ratio, updates the mapping weights of the three types of vibration modes and the algorithm in the rule table, and improves the effectiveness of the scheduling strategy.

[0089] Closed-loop control mechanism: The updated rule table re-drives the cosine similarity matching in step 3, forming a self-optimizing cycle for feature extraction, algorithm scheduling, cluster analysis, and convergence verification, continuously improving the accuracy of error analysis.

[0090] Input data inheritance: The dynamic scheduling priority data is derived from the feature point sequence in step 2. The waveform curvature feature correction parameters are inherited from the clustering results in step 5. The weight distribution ratio is generated based on the convergence criterion in step 6.

[0091] Cross-step linkage: Otsu's adaptive threshold update directly affects the boundary detection in step 2, rule table reconstruction controls the algorithm scheduling in step 3, and the cosine similarity matching result affects the clustering input in step 5.

[0092] The present invention enhances the adaptability of knowledge base scheduling through dynamic priority sorting; waveform curvature feature correction parameters improve the accuracy of transient boundary detection; rule table weight reconstruction optimizes the matching efficiency of vibration mode and algorithm; four-step closed-loop control realizes the self-correction function of the error analysis process, eliminating the error transmission and amplification problem caused by fixed parameters in existing methods.

[0093] The technical solution of the present invention solves the technical problem of signal distortion introduced by smoothing operation in the processing of non-stationary vibration signals, and is mainly achieved through the following logical path. In the data acquisition and preprocessing stage, step 1 receives the original current signals of multiple accelerometers, uses time stamp synchronization to align the channel data, and outputs the original non-stationary vibration data set that retains the high-frequency components to avoid any weakening of the high-frequency transient components by smoothing operations. Step 2 performs short-time Fourier transform based on the data set to identify the frequency band in which the vibration energy is concentrated, combines the Zernike moment algorithm to detect the boundary of the transient impact waveform, and fits the extreme envelope by Hermite interpolation within the marked interval. This method maintains the continuity of the high-order derivatives of the waveform, directly locates the extreme points without relying on averaging processing, and outputs a sequence of feature point coordinates with confidence, eliminating the risk of extreme point offset caused by smoothing.

[0094] During the feature optimization and error modeling phase, step 3 dynamically schedules a combination of optimization algorithms from the knowledge base based on the confidence level and frequency band distribution characteristics of the feature point coordinate sequence. The Levenberg-Marquardt method fits local curvature features to extract the average value of the trend component, a simulated annealing algorithm searches for the maximum sequence of envelope profiles, and particle swarm optimization locates the minimum value of the non-stationary interval. Multiple algorithms collaborate to output a partitioned parameter set, thus avoiding the lack of adaptability of fixed algorithms to non-stationary signals. Step 4 inputs the partitioned parameter set into the mechanical dynamics model to generate the first trajectory data. Simultaneously, vibration environment interference noise is injected into the control model to reconstruct the second trajectory data. The dual-path motion trajectories are aligned using a dynamic time warping algorithm, and the root mean square error is calculated to output the error correction coefficient matrix. The dual-path verification mechanism directly quantifies the difference between the physical response and the theoretical model, eliminating the error transmission of single-path analysis.

[0095] During the error verification and closed-loop feedback phase, step 5 uses the error correction coefficient matrix to reconstruct the quantized value of the vibration rectification error. This is then fed into a self-organizing map neural network for cluster analysis. When the proportion of abnormal vibration modes exceeds a threshold, a parameter reset instruction is output. The cluster identification mechanism directly responds to actual vibration feature changes. Step 6 feeds the quantized value into the inclination angle detection model to calculate the theoretical angle deviation. The amplitude fluctuation parameters and frequency domain distribution parameters of the deviation curve are extracted using shaker test data. Convergence is determined using a dynamic threshold function. When the deviation exceeds the threshold, neural network retraining is triggered and the error reconstruction process returns. Simultaneously, step 10 forms a cross-step feedback control loop. Dynamic scheduling priority data is generated based on the feature point coordinate sequence to update the algorithm ranking. The clustering results extract waveform curvature feature correction parameters to update the boundary detection threshold. Based on the convergence criteria output by the dynamic threshold function, the weight distribution ratio in the rule table is reconstructed, driving the cosine similarity matching process to continuously optimize feature extraction accuracy. The entire technical process achieves a vibration rectification error calculation result that closely matches the actual physical response by preserving high-frequency components, employing a non-smooth feature extraction algorithm, a dynamic scheduling mechanism, dual-path verification, and closed-loop feedback.

[0096] In the accelerometer vibration rectification error analysis scenario, the present invention uses a vibration table to generate a multi-axis composite vibration environment, including steady-state sinusoidal, transient impact, and broadband random vibration components. Multiple accelerometers are mounted on a dedicated vibration fixture, and their output current signals are transmitted to a processing system via parallel data channels.

[0097] During step 1, the vibration tooling's A / D conversion module acquires raw current signals at a sampling rate of at least 1 MHz, generating parallel data streams. A GPS-disciplined clock source stamps each data channel with nanosecond absolute timestamps, eliminating inter-channel time asynchrony. Transmission line impedance matching is performed on the timestamped data to suppress signal reflection interference. The multi-channel data is integrated to generate a raw, non-stationary vibration dataset with an absolute time stamp, preserving high-frequency transient components above 2 kHz.

[0098] Step 2: Perform a short-time Fourier transform on the original data set, setting the window length to 1 / 8 of the vibration fundamental period. Generate a time-frequency spectrum and calculate the spectral entropy. Calculate the waveform curvature feature projection based on the time-frequency spectrum. Dynamically segment the curvature feature map using the Otsu method, and output the boundary coordinates of the transient impact waveform. Within the boundary interval, use the Hermite interpolation function three times to fit the extreme envelope and locate the spatial coordinates of the extreme points. Calculate the confidence interval of the extreme points through 1000 Monte Carlo resampling, and output a feature point coordinate sequence with a confidence level of ≥95%.

[0099] Step 3: Establish an algorithm and feature mapping rule table, defining the Levenberg-Marquardt method for steady-state sinusoidal vibration, the simulated annealing algorithm for impulse response, and particle swarm optimization for broadband random vibration. Receive the confidence interval attributes and frequency band distribution feature vectors of the feature point sequence. Perform cosine similarity matching between the feature vector and the rule table, setting the similarity threshold to 0.85, and output the optimization algorithm combination. Invoke the combination for collaborative processing: The Levenberg-Marquardt method is used to fit local curvature to extract the average value of the trend component; the simulated annealing algorithm searches for the envelope maximum at a cooling rate of 0.01°C; and the particle swarm optimization algorithm locates the minimum value of the non-stationary interval using a swarm of 50 particles. Output is a partition parameter set consisting of the average value, maximum value sequence, and minimum value.

[0100] Step 4: Load the partition parameter set into the mechanical dynamics model and drive the virtual vibration table to generate the first trajectory data. The control model injects the vibration noise collected in step 1 and reconstructs the theoretical current signal to generate the second trajectory data. A dynamic time warping algorithm is applied to the two trajectories, setting the warping path bending cost coefficient to 0.5. After aligning the motion trajectories, the root mean square error (RMS) is calculated and the error correction coefficient matrix is ​​output.

[0101] Step 5: The original data set and the error correction coefficient matrix are weighted using the Hadamard product. System deviations are compensated for using Gaussian process regression, and the Matan covariance function is used as the kernel function to reconstruct the quantized vibration rectification error. A ring-topology self-organizing map (with an initial neighborhood radius of 0.3) is used to perform cluster analysis. When the proportion of abnormal vibration modes exceeds 15%, a weight update instruction is sent to the knowledge base, and a parameter reset instruction is sent to the feature extraction module.

[0102] Step 6: Quantized vibration rectification error values ​​are embedded in the finite element model to calculate theoretical inclination angle data. A laser interferometer collects vibration table displacement data at a resolution of 0.1 μm, and coordinate transformation is used to calculate the actual inclination angle. The least squares method is used to fit the theoretical-actual angle deviation curve, extracting amplitude fluctuation parameters and frequency domain distribution parameters. A dynamic threshold function (weight coefficients α = 0.6, β = 0.4) outputs the convergence criterion, and a retraining trigger pulse is generated when the threshold is exceeded.

[0103] Closed-loop control execution: The algorithm scheduling priority is generated based on the confidence level of the feature point sequence, and the knowledge base call order is updated. Waveform curvature feature correction parameters are extracted from the clustering results to adjust the Otsu detection threshold in step 2. Based on the convergence criteria output by the dynamic threshold function, the weight distribution ratio in the rule table is reconstructed (steady-state vibration weight +0.2, impulse response weight -0.1), driving the cosine similarity matching process in step 3.

[0104] By retaining high-frequency components and extracting non-smooth features, the extreme point offset caused by existing smoothing operations is eliminated; the dual-path verification mechanism solves the error transmission problem of a single model; the dynamic scheduling algorithm improves adaptability to complex vibration environments; and cross-step feedback control realizes the coordinated optimization of boundary detection thresholds, algorithm weights, and clustering parameters, thereby reducing the deviation between the rectification error calculation results and the physical response.

[0105] AD conversion in this context refers to analog-to-digital conversion. An analog-to-digital converter discretizes a continuous analog signal into a digital signal for processing by a digital system. The AD conversion module in the vibration tooling is responsible for collecting the analog current signal output by the accelerometer and converting it into a parallel digital data stream.

[0106] The GPS Disciplined Clock Source is a high-precision time synchronization technology that uses GPS satellite signals to calibrate the local clock, providing microsecond-level absolute timestamps for multi-channel data, ensuring time consistency in vibration data collection.

[0107] Zernike moments are an image moment algorithm based on orthogonal polynomials. They are used to extract the geometric features of vibration waveforms and detect the contours and boundary features of transient shock waveforms by calculating the moment invariants of image projections.

[0108] Hermite interpolation is a polynomial interpolation method. Cubic Hermite interpolation not only fits a smooth curve through known data points but also utilizes first-order derivative information at the nodes. This makes it suitable for accurately fitting the envelope of extreme points in vibration signals.

[0109] STFT stands for Short-Time Fourier Transform. It processes non-stationary signals by windowing and segmenting them, generating a time-frequency spectrum of the signal's frequency components over time. This spectrum is used to analyze the frequency band distribution characteristics of vibration energy.

[0110] The Monte Carlo method is a numerical calculation method based on random sampling. Monte Carlo repeated sampling uses random simulation to perform probability statistics on the coordinates of extreme points, calculate their confidence intervals, and evaluate the statistical reliability of feature point detection results.

[0111] The Levenberg-Marquardt method is a nonlinear least-squares optimization algorithm. By combining gradient descent and the Gauss-Newton method, it can quickly fit the local curvature characteristics of nonlinear curves and extract the trend component of the vibration signal.

[0112] The simulated annealing algorithm is a global optimization algorithm inspired by thermodynamics. It simulates the metal annealing process and gradually converges by controlling the temperature parameter. It is used to search for a sequence of global maxima in the envelope profile of a vibration signal.

[0113] PSO stands for particle swarm optimization. It simulates the social behavior of bird flocks, updating the search direction based on the historical optimal positions of individuals and the group, effectively locating the local minimum within the non-stationary range of the vibration signal.

[0114] DTW stands for Dynamic Time Warping. It eliminates phase differences between time series by nonlinearly stretching and compressing the time axis, achieving precise alignment between the mechanical simulation trajectory and the reconstructed signal trajectory.

[0115] RMSE stands for root mean square error. RMSE calculates the standard deviation of the aligned dual-path data points, quantifies the magnitude of the deviation between the simulated and theoretical trajectories, and generates an error correction coefficient matrix.

[0116] SOM stands for Self-Organizing Map Neural Network. It maps high-dimensional error data into a low-dimensional topological structure through competitive learning, enabling cluster analysis of vibration rectification error distribution and abnormal pattern recognition.

[0117] GPR stands for Gaussian Process Regression. As a non-parametric Bayesian regression method, GPR uses a kernel function to define covariance and perform systematic bias compensation and error reconstruction on weighted vibration data.

[0118] FEM stands for Finite Element Model. This model discretizes the physical system using mathematical approximations, embeds quantized vibration rectification errors, and calculates the theoretical inclination output of the accelerometer in a vibrating environment.

[0119] LSM stands for least squares method. It fits the deviation curve between theoretical and actual angle data by minimizing the residual sum of squares, extracting amplitude fluctuation parameters and frequency domain distribution parameters.

[0120] The dynamic threshold function is an adaptive decision algorithm that receives amplitude fluctuation parameters and frequency domain distribution parameters, and outputs a convergence criterion through multi-parameter weighted calculation to determine whether the system has reached the retraining condition.

[0121] Parallel data streaming is a data transmission format. It uses multi-channel synchronous transmission to achieve high-speed data exchange between the vibration tooling AD conversion module and the data processing unit, ensuring real-time signal acquisition.

[0122] Absolute time stamping is a time-stamping format that uses UTC time format to record the acquisition moment of each data point, forming a raw data matrix with a timestamp, providing a benchmark for subsequent spatiotemporal feature analysis.

[0123] A time-spectrogram is a representation of a joint time-frequency distribution. Generated by a short-time Fourier transform, it uses time as the horizontal axis and frequency as the vertical axis, with color depth representing energy intensity. It visually displays the distribution of vibration energy in the time-frequency domain.

[0124] A confidence interval is a statistical estimation format that represents the possible range of values ​​of feature point coordinates in the form of an interval. The confidence level is usually set to 95%, reflecting the statistical reliability of the detection results.

[0125] The error correction coefficient matrix is ​​a two-dimensional data table. The error correction coefficient matrix contains correction coefficients for each time point in the rows and channels in the columns. It is used to systematically compensate for vibration rectification errors.

[0126] The protocol field mapping table is a data structure that stores the correspondence between communication protocol fields and physical meanings in the form of key-value pairs. When the characteristic spectrum distribution offset exceeds 0.3, the mapping relationship is updated.

Claims

1. A method for analyzing accelerometer vibration rectification errors, characterized in that: include: Step 1: Receive the original current signals of multiple accelerometers under vibration excitation, align the channel data using time stamp synchronization, and output the original non-stationary vibration data set that retains the high-frequency components; Step 2: Based on the original non-stationary vibration data set, a short-time Fourier transform is performed to identify the frequency band where vibration energy is concentrated. The Zernike moment algorithm is used to detect the boundary of the transient impact waveform. The extreme envelope is fitted within the marked interval through Hermite interpolation, and a sequence of feature point coordinates with confidence is output. Step 3: Based on the confidence level and frequency band distribution characteristics of the feature point coordinate sequence, dynamically schedule the optimization algorithm combination in the knowledge base, call the scheduled algorithm combination to calculate and output the local statistical data set. The knowledge base includes the Levenberg-Marquardt method, simulated annealing algorithm, and particle swarm optimization. Step 4: Input the local statistical data set into the mechanical dynamics model to perform trajectory simulation, and simultaneously input the control model to reconstruct the signal output, compare the difference in positioning drift between the two paths, and generate the error correction coefficient matrix; Step 5: Use the error correction coefficient matrix to reconstruct the vibration rectification error quantization value, input it into the self-organizing map neural network to perform error distribution clustering, and when the clustering detects an abnormal pattern, it outputs the knowledge base update instruction and the feature point detection parameter reset instruction; Step 6: Import the quantized value of the vibration rectification error into the inclination detection model to calculate the theoretical angle deviation. Input the vibration table test data to verify the convergence. When the deviation exceeds the threshold, trigger the neural network retraining and return to the process of step 5 to reconstruct the quantized value of the vibration rectification error.

2. The accelerometer vibration rectification error analysis method according to claim 1, characterized in that: Step 1 includes: Receive parallel data stream from vibration tooling AD conversion module; Use GPS disciplined clock source to mark absolute timestamps for parallel data streams; Perform impedance matching on the timestamped data to suppress reflection interference; The processed data are integrated to generate a raw data matrix with absolute time scale.

3. The accelerometer vibration rectification error analysis method according to claim 2, characterized in that: Step 2 includes: Perform short-time Fourier transform on the original non-stationary vibration data set to generate a time-frequency spectrum and calculate the spectral entropy value to quantify the energy concentration of the frequency band; The waveform curvature feature projection value is calculated based on the time-frequency spectrum, and the transient shock waveform boundary is adaptively determined using the Otsu method. Call cubic Hermite interpolation to locate the extreme point coordinates in the boundary interval; Perform Monte Carlo repeated sampling on the extreme point coordinates to calculate the confidence interval and output a sequence of feature point coordinates with confidence intervals.

4. The accelerometer vibration rectification error analysis method according to claim 3, characterized in that: Step 3 includes: Establish an algorithm and feature mapping rule table and define the following correspondences: steady-state sinusoidal vibration corresponds to the Levenberg-Marquardt method, impulse response corresponds to the simulated annealing algorithm, and broadband random vibration corresponds to particle swarm optimization; Receiving confidence interval attributes and frequency band distribution characteristic data of a feature point coordinate sequence; Perform cosine similarity matching on the confidence interval attributes and frequency band distribution feature data of the feature point coordinate sequence and the rule table, and output the optimization algorithm combination; The optimization algorithm is used to process the feature point coordinate sequence, and the local curvature characteristics are fitted by the Levenberg-Marquardt method to extract the average value of the trend component. The maximum sequence of the envelope profile is searched by simulated annealing algorithm; The minimum value of the non-stationary interval is located through particle swarm optimization, and the envelope maximum value sequence and the local statistical data set of the minimum value of the non-stationary interval are output.

5. The accelerometer vibration rectification error analysis method according to claim 4, characterized in that: Step 4 includes: In the mechanical dynamics model, the virtual vibration table is driven by using the maximum value and minimum value data in the partition parameter set to generate first trajectory data, wherein the first trajectory data represents a simulation result of the mechanical dynamics model; Injecting vibration environment interference noise into the control model to reconstruct the theoretical output current signal and generate second trajectory data, the second trajectory data representing the reconstructed signal of the control model; A dynamic time warping algorithm is performed on the first trajectory data and the second trajectory data to align the motion trajectories to obtain an aligned dual path, a root mean square error value of the aligned dual path is calculated, and an error correction coefficient matrix is ​​output.

6. The accelerometer vibration rectification error analysis method according to claim 5, characterized in that: Step 5 includes: Perform weighted processing on the original non-stationary vibration data set in step 1 and the error correction coefficient matrix; Perform Gaussian process regression on the weighted data to compensate for system deviation and reconstruct the quantized value of vibration rectification error; The ring topology self-organizing map network is called to perform cluster analysis on the vibration rectification error quantization value. When the proportion of abnormal vibration modes in the clustering results exceeds the preset threshold, the weight update instruction is transmitted to the knowledge base in step 3 and the parameter reset instruction is transmitted to step 2.

7. The accelerometer vibration rectification error analysis method according to claim 6, characterized in that: Step 6 includes: When receiving the feature point detection parameter reset instruction, execute the following sequence to clear the currently cached feature point coordinate sequence; Reload the original non-stationary vibration data set from step 1 and recalculate the Otsu method adaptive threshold based on the reloaded data set; The optimization algorithm combination scheduling of step 3 is suspended until step 2 outputs the updated feature point coordinate sequence, which is generated by step 2 based on the reloaded dataset.

8. The accelerometer vibration rectification error analysis method according to claim 7, characterized in that: Step 6 also includes: The vibration rectification error quantization value is implanted into the finite element model to calculate the theoretical inclination angle and output the theoretical angle data; The actual displacement data of the vibration table is obtained through the laser interferometer; Calculate the actual angle data by performing coordinate transformation based on the actual displacement data; The least square method is used to fit the deviation curve between theoretical angle data and actual angle data; Extract the amplitude fluctuation parameters and frequency domain distribution parameters of the deviation curve; The fluctuation parameter and distribution parameter are substituted into the dynamic threshold function to judge the convergence. When the output value of the function exceeds the set threshold, a retraining trigger pulse is generated.

9. The accelerometer vibration rectification error analysis method according to claim 8, characterized in that: Step 6 also includes: The dynamic threshold function receives the amplitude fluctuation parameter and the frequency domain distribution parameter, and outputs the convergence criterion by calculating the function value including the frequency, amplitude and the logarithm of the vibration energy; When the retraining trigger pulse arrives, the weight matrix of the self-organizing map neural network is cleared and the structural parameters are initialized; The initialized neural network re-receives the vibration rectification error quantization value reconstructed in step 5 to perform cluster analysis.

10. The accelerometer vibration rectification error analysis method according to claim 9, characterized in that: Step 6 also includes: Generate dynamic scheduling priority data based on the feature point coordinate sequence and perform sorting operations on the algorithm combinations in the knowledge base; The clustering results are used to extract waveform curvature feature correction parameters and update the Otsu method adaptive threshold calculation parameters; According to the convergence criterion output by the dynamic threshold function, the weight distribution ratio in the rule table is reconstructed, and the weight distribution ratio in the replacement algorithm and feature mapping rule table is replaced; The updated rule table drives the cosine similarity matching process in step 3, forming a feedback control loop for the cross-step error analysis process.

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