Noise characteristic checking formula adaptive wavelet denoising method for PEPT track data

Abstract

This invention discloses an adaptive wavelet denoising method for noise characteristic verification of PEPT trajectory data. The method first performs statistical analysis on the PEPT trajectory data under static conditions to obtain its noise characteristics. Then, it uses an adaptive wavelet denoising method to obtain the denoised PEPT trajectory and noise data. It then verifies whether the statistical characteristics of the filtered noise data conform to the noise characteristics under static conditions. Based on the verification results, the denoising parameters are dynamically adjusted for iterative feedback until the verification conditions for noise characteristics are met, at which point the method stops. This method uses "filtered components conforming to noise characteristics" as the convergence criterion, providing an objective statistical verification basis for denoising quality. It can effectively filter out as much noise data as possible from the PEPT trajectory without excessively smoothing out the real high-frequency motion. Moreover, it does not rely on the prior motion model of the tracer particles, thus having stronger universality.

Description

Technical Field

[0001] This invention belongs to the field of multiphase flow measurement technology, specifically relating to an adaptive wavelet denoising method for noise characteristic verification of PEPT trajectory data. Background Technology

[0002] PEPT (Positron Emission Particle Tracing) technology is a novel, non-destructive measurement method suitable for multiphase flow analysis in industrial processes. By introducing PEPT tracer particles into a multiphase flow system, it enables visualization and imaging of the three-dimensional dynamic behavior of liquids, powders, and particles. Because PEPT tracer particles contain unstable radionuclides, they continuously undergo positron emission and positron-electron annihilation processes, releasing pairs of gamma rays at their locations. These gamma-ray pairs are captured by surrounding PEPT detectors and then converted into a time-varying sequence of PEPT measurement locations using a dedicated PEPT particle localization algorithm; this is known as PEPT trajectory data (the data format for each location is...). It boasts millimeter-level positioning accuracy and kHz-level positioning frequency. Based on this trajectory data, further dynamic calculations of the tracer particles can be performed to obtain key physical parameters such as the three-dimensional velocity field, turbulence field, and acceleration field of each phase in complex multiphase flow systems. PEPT technology can adapt to systems of different scales, geometries, and physical states, and is widely used in the study of various complex multiphase flow phenomena and processes, especially in achieving effective three-dimensional dynamic measurements within non-transparent or dense devices.

[0003] In the field of fluid measurement, the flow parameters tracking the entire motion of a tracer particle are described by Lagrangian, while the flow parameters at a fixed point in space are described by Eulerian. Engineering analysis focuses more on the latter (such as velocity fields, turbulence fields, and acceleration fields). The first step in solving tracer particle dynamics is to perform numerical difference on the PEPT trajectory data to obtain the instantaneous velocity of the tracer particle, and then perform numerical difference on the instantaneous velocity data to obtain the instantaneous acceleration. These flow parameters are all described by Lagrangian, i.e. The second step involves using grid averaging to statistically integrate the data into the velocity and acceleration fields of the tracer particles in three-dimensional space. Simultaneously, by statistically analyzing velocity perturbations within any grid, the turbulent field in three-dimensional space can be calculated. These flow parameters are all described by Eulerian parameters. Due to millimeter-level positioning errors in the PEPT trajectory data, the numerical difference process in the aforementioned dynamic solution introduces error propagation and amplification effects, significantly amplifying the measurement errors of instantaneous velocity and acceleration described by Lagrange, making it difficult to meet the requirements of high-precision quantitative analysis. Although grid averaging in the second step can smooth out the influence of random errors to some extent, it is still difficult to achieve high-precision measurement of parameters such as the turbulent and acceleration fields described by Eulerian parameters. Therefore, filtering the PEPT trajectory data before dynamic solution is a necessary means to suppress subsequent error propagation and improve parameter accuracy.

[0004] Currently, the main methods for denoising PEPT trajectory data include: moving average filtering, least squares fitting, and Kalman filtering. Moving average filtering reduces noise by averaging adjacent data points, but it can overly smooth out the actual motion trajectory and cannot effectively distinguish between high-frequency noise and real high-frequency motion (such as sharp turns and collisions). Least squares fitting fits the trajectory using a polynomial within a local window, but it is highly dependent on the polynomial model, making it difficult to apply to different nonlinear motions, and it is sensitive to outliers. Kalman filtering estimates the trajectory optimally based on the motion model and noise statistics, but it is also highly dependent on the motion model. Each of these methods has its own applicable conditions, making it difficult to achieve good filtering results for PEPT trajectory data with various motion processes. Therefore, there is an urgent need to research a universal PEPT trajectory data filtering method. Summary of the Invention

[0005] The purpose of this invention is to propose an adaptive wavelet denoising method for noise characteristic verification of PEPT trajectory data. This method first performs statistical analysis on the PEPT trajectory data under static conditions to obtain its noise characteristics. Then, it uses an adaptive wavelet denoising method to obtain the denoised PEPT trajectory and noise data. It then verifies whether the statistical characteristics of the filtered noise data conform to the noise characteristics under static conditions. Based on the verification results, the denoising parameters are dynamically adjusted for iterative feedback until the verification conditions for noise characteristics are met, at which point the method stops. This method uses "filtered components conforming to noise characteristics" as the convergence criterion, providing an objective statistical verification basis for denoising quality. It can effectively filter out as much noise data as possible from the PEPT trajectory without excessively smoothing out real high-frequency motion (such as sharp turns, collisions, etc.). Moreover, it does not rely on the prior motion model of the tracer particles, thus having stronger universality.

[0006] The technical solution adopted in this invention is an adaptive wavelet denoising method for noise characteristic verification of PEPT trajectory data, comprising:

[0007] S1, Statistical analysis of the noise distribution characteristics of PEPT trajectory data measured under static conditions; S2, PEPT dynamic trajectory data resampling; S3, perform wavelet decomposition on the PEPT dynamic trajectory of each axis; S4, Set initial denoising parameters, including the base threshold. and threshold decay coefficient ; S5, calculate the adaptive threshold for each layer of wavelet denoising, and perform adaptive wavelet threshold denoising. S6, reconstruct the noise-free PEPT trajectory; S7, calculate and statistically analyze the filtered noise; S8, check whether the statistical characteristics of noise filtering for each axis meet the noise characteristics under static conditions; If S9 is not satisfied, then the basic threshold is adjusted iteratively. and threshold decay coefficient Then re-execute S5-S8 until the test condition of S8 is met; S10: If the test condition of S8 is met, then output noise-free PEPT trajectory data.

[0008] Furthermore, in S1, the PEPT trajectory data measured under static conditions is represented as the sum of the noise-free PEPT trajectory and the noise, i.e. ,in , and These represent the original noisy PEPT trajectory data, the noise-free PEPT trajectory data, and the noisy data in the original PEPT trajectory, respectively. These represent the trajectory components of the noise-free PEPT trajectory on the x, y, and z axes, respectively. These represent the noise components on the x, y, and z axes of the original PEPT trajectory, respectively.

[0009] In S1, the distribution fit goodness test method is used to perform statistical analysis on the PEPT trajectory noise throughout the measurement time to obtain the distribution characteristics of the PEPT trajectory data noise.

[0010] Furthermore, in S2, the PEPT dynamic trajectory data is read and resampled using interpolation to convert it into uniform time intervals. The position sequence.

[0011] Furthermore, in S3, a Chebyshev wavelet basis is selected, and an L-level wavelet decomposition is performed on the PEPT trajectory time series of each axis to obtain the wavelet coefficients of each group, including approximation coefficients. and detail coefficient , … .

[0012] Furthermore, in S4, a basic threshold is set. ,in , These represent the noise standard deviations in the x, y, and z axes, respectively, and the threshold attenuation factor. It is a constant.

[0013] Furthermore, in S5, an adaptive threshold is calculated for each layer of wavelet denoising. ,in This represents the denoising threshold for the wavelet coefficients of the j-th layer. Then, for each axis and each layer, the detail coefficients that are less than the corresponding threshold are... The wavelet coefficients are set to zero, while the rest are retained to obtain the denoised detail coefficients. , … .

[0014] Furthermore, in S6, for the reconstruction of the PEPT trajectory on each axis, the denoised approximation coefficients are used. and detail coefficient , … Perform inverse discrete wavelet transform to reconstruct the denoised position sequence. .

[0015] Furthermore, in S7, statistical model fitting and noise characteristic extraction are performed on the filtered noise components on each axis, including the kurtosis and skewness of the fitted Gaussian distribution.

[0016] Furthermore, the test condition for S8 is: the fitted model after filtering out noise components conforms to the noise model under static conditions, and the correlation between noise components is also consistent with that under static conditions.

[0017] The present invention also provides a noise characteristic verification adaptive wavelet denoising system for PEPT trajectory data, including a processor and a memory. The memory is used to store program instructions, and the processor is used to call the program instructions in the memory to execute the noise characteristic verification adaptive wavelet denoising method for PEPT trajectory data as described in the above technical solution.

[0018] The present invention provides an adaptive wavelet denoising method for noise characteristic verification of PEPT trajectory data. It uses "the filtered components conform to the noise characteristics" as the convergence criterion, which provides an objective statistical test basis for the denoising quality. It can effectively filter out as much noise data as possible in PEPT trajectory without excessively smoothing out real high-frequency motion (such as sharp turns, collisions, etc.). Moreover, it does not rely on the prior motion model of the tracer particles and has stronger universality. Attached Figure Description

[0019] Figure 1 This is a flowchart of an embodiment of the present invention.

[0020] Figure 2 This is an analysis of the noise characteristics of PEPT trajectory data in an embodiment of the present invention.

[0021] Figure 3 The following are PEPT motion trajectory analysis diagrams in this embodiment of the invention: (a) and (d): Comparison diagrams of the original and denoised PEPT trajectory components with the theoretical motion trajectory in the y and z directions. (b) and (e): Noise filtered out in the y and z directions. (c) and (f): Statistical distribution of the noise filtered out in the y and z directions.

[0022] Figure 4 In this embodiment of the invention, the velocity component analysis diagrams of the PEPT motion trajectory are shown in (a) and (c): comparison diagrams of the original and denoised PEPT measured velocity components with the theoretical motion velocity in the y and z directions. (b) and (d): velocity noise filtered out in the y and z directions.

[0023] Figure 5 The acceleration component analysis diagrams of the PEPT motion trajectory in this embodiment of the invention are shown in (a) and (c): comparison diagrams of the original and denoised PEPT measured acceleration components with the theoretical motion acceleration in the y and z directions. (b) and (d): acceleration noise filtered out in the y and z directions. Detailed Implementation

[0024] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0025] like Figure 1 As shown in the figure, this embodiment of the invention provides an adaptive wavelet denoising method for noise characteristic verification of PEPT trajectory data. The specific steps are as follows:

[0026] Step 1: Statistically analyze the noise distribution characteristics of PEPT trajectory data measured under static conditions. The PEPT trajectory data measured under static conditions is represented as the sum of the noise-free PEPT trajectory and the noise, i.e. ,in , and These represent the original noisy PEPT trajectory data, the noise-free PEPT trajectory data, and the noisy data in the original PEPT trajectory, respectively. These represent the trajectory components of the noise-free PEPT trajectory on the x, y, and z axes, respectively. These represent the noise components along the x, y, and z axes of the original PEPT trajectory, respectively. A goodness-of-fit test is used to evaluate the PEPT trajectory noise over the entire measurement time. Statistical analysis was performed to obtain the noise distribution characteristics of the PEPT trajectory data. For example... Figure 2 As shown, the PEPT trajectory points of a static tracer particle are concentrated around its actual location. Statistical analysis using the distribution goodness-of-fit test method reveals noise components on each axis of the trajectory points. They all conform to a Gaussian distribution and have a certain directionality.

[0027] Step 2: Resampling of PEPT dynamic trajectory data. Read the PEPT dynamic trajectory data. Then, it is resampled using interpolation to convert it into a uniform time interval. Position sequence ,in , This represents the total number of points in the PEPT trajectory.

[0028] Step 3: Perform wavelet decomposition on the PEPT dynamic trajectory for each axis. Since PEPT trajectories typically exhibit both local abrupt changes and continuous variations, a Chebyshev wavelet basis is chosen, and an L-level wavelet decomposition is performed on the time series of the PEPT trajectory for each axis to obtain the wavelet coefficients for each group, including approximation coefficients. and detail coefficient , … .

[0029] Step 4: Set initial denoising parameters. Based on the noise characteristics of the PEPT trajectory data under static conditions, set the initial denoising parameters and the base threshold. ,in , These represent the noise standard deviations in the x, y, and z axes, respectively, and the threshold attenuation factor. .

[0030] Step 5: Adaptive Wavelet Thresholding Denoising. Calculate the adaptive threshold used for each layer of wavelet denoising. ,in This represents the denoising threshold for the wavelet coefficients of the j-th layer. Then, for each axis and each layer, the detail coefficients that are less than the corresponding threshold are... The wavelet coefficients are set to zero, while the rest are retained to obtain the denoised detail coefficients. , … .

[0031] Step 6: Reconstruct the noise-free PEPT trajectory. Reconstruct the PEPT trajectory for each axis using the denoised approximation coefficients. and detail coefficient , … Perform inverse discrete wavelet transform to reconstruct the denoised position sequence. .

[0032] Step 7: Calculate and statistically analyze the filtered noise. The filtered noise can be obtained by subtracting the original trajectory sequence from the denoised trajectory sequence. Simultaneously, statistical model fitting and noise characteristic extraction are performed on the filtered noise components on each axis, such as fitting the kurtosis and skewness of a Gaussian distribution.

[0033] Step 8: Examine whether the statistical characteristics of noise filtering for each axis meet the noise characteristics under static conditions. The fitting model for the filtered noise components conforms to the noise model under static conditions, and the correlation between the noise components is also consistent with that under static conditions.

[0034] Step 9: If the condition is not met, iteratively adjust the base threshold. and threshold decay coefficient Then repeat steps five through eight until the test condition in step eight is met.

[0035] Step 10: If the verification conditions in step 8 are met, then output noise-free PEPT trajectory data.

[0036] The effects of this invention are illustrated below using specific experimental data:

[0037] A tracer particle is mounted on a uniformly rotating plate driven by a variable frequency motor, generating a theoretically uniform circular motion in the yz plane. The original PEPT trajectory is obtained through PEPT measurement.

[0038] After obtaining the denoised PEPT trajectory using the denoising method described in this invention, the denoised PEPT trajectory and the original PEPT trajectory in the y and z directions are compared with the theoretical motion trajectory, such as... Figure 3 As shown in (a) and (d) above, both the denoised PEPT trajectory and the original PEPT trajectory exhibit excellent consistency with the ideal motion trajectory. The corresponding filtered noise components are as follows: Figure 3 As shown in (b) and (e), the noise amplitude is about two orders of magnitude lower than the trajectory amplitude, indicating that this order of magnitude of noise contributes negligibly to the PEPT trajectory. Furthermore, as... Figure 3As shown in (c) and (f), the filtered noise components approximate a Gaussian distribution well, and their statistical properties are consistent with the previously estimated PEPT noise characteristics of static tracer particles.

[0039] By calculating the first and second derivatives of the ideal trajectory, the original PEPT trajectory, and the denoised PEPT trajectory of the tracer particle, the velocity and acceleration of the tracer particle can be obtained.

[0040] Figure 4 In Figures (a) and (c), the denoised and original PEPT-measured velocities are compared with the theoretical motion velocities. The velocity curve measured by the denoised PEPT is consistent with the theoretical velocity, while the velocity curve measured by the original PEPT, although generally consistent with the theoretical velocity trend, is accompanied by significant velocity noise disturbances. Figure 4 As shown in (b) and (d) in the figure, the velocity noise in the original PEPT measurement data is about half an order of magnitude of the theoretical velocity value, so this velocity error cannot be ignored in accurate velocity estimation.

[0041] Similarly, Figure 5 In Figures (a) and (c), the accelerations measured by the denoised and original PEPT were compared with the theoretical accelerations. The acceleration measured by the denoised PEPT matched the theoretical acceleration well, while the acceleration measured by the original PEPT deviated significantly from the theoretical value and showed severe oscillating noise. Figure 5 As shown in (b) and (d), the acceleration noise in the raw PEPT measurement data is about an order of magnitude higher than the theoretical acceleration, which can lead to serious misestimation in practical applications.

[0042] The above results collectively demonstrate that the denoising scheme described in this method can effectively reduce noise in PEPT trajectories, especially for calculating higher-order motion parameters, thereby improving the reliability of PEPT trajectory analysis and its derived parameters in fluid mechanics applications.

[0043] On the other hand, embodiments of the present invention also provide a noise characteristic verification adaptive wavelet denoising system for PEPT trajectory data, including a processor and a memory. The memory is used to store program instructions, and the processor is used to call the program instructions in the memory to execute the noise characteristic verification adaptive wavelet denoising method for PEPT trajectory data as described in the above technical solution.

[0044] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data, characterized in that, include: S1, Statistical analysis of the noise distribution characteristics of PEPT trajectory data measured under static conditions; S2, PEPT dynamic trajectory data resampling; S3, perform wavelet decomposition on the PEPT dynamic trajectory of each axis; S4, Set initial denoising parameters, including the base threshold. and threshold decay coefficient ; S5, calculate the adaptive threshold for each layer of wavelet denoising, and perform adaptive wavelet threshold denoising. S6, reconstruct the noise-free PEPT trajectory; S7, calculate and statistically analyze the filtered noise; S8, check whether the statistical characteristics of noise filtering for each axis meet the noise characteristics under static conditions; If S9 is not satisfied, then the basic threshold is adjusted iteratively. and threshold decay coefficient Then re-execute S5-S8 until the test condition of S8 is met; S10: If the test condition of S8 is met, then output noise-free PEPT trajectory data.

2. The noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data as described in claim 1, characterized in that: In S1, the PEPT trajectory data measured under static conditions is represented as the sum of the noise-free PEPT trajectory and the noise, i.e. ,in , and These represent the original noisy PEPT trajectory data, the noise-free PEPT trajectory data, and the noisy data in the original PEPT trajectory, respectively. These represent the trajectory components of the noise-free PEPT trajectory on the x, y, and z axes, respectively. These represent the noise components on the x, y, and z axes of the original PEPT trajectory, respectively. In S1, the distribution fit goodness test method is used to perform statistical analysis on the PEPT trajectory noise throughout the measurement time to obtain the distribution characteristics of the PEPT trajectory data noise.

3. The noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data as described in claim 1, characterized in that: In S2, the PEPT dynamic trajectory data is read and resampled using interpolation to convert it into uniform time intervals. The position sequence.

4. The noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data as described in claim 1, characterized in that: In S3, a Chebyshev wavelet basis is selected, and L-level wavelet decomposition is performed on the PEPT trajectory time series of each axis to obtain the wavelet coefficients of each group, including approximation coefficients. and detail coefficient , … .

5. The noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data as described in claim 1, characterized in that: In S4, set the basic threshold. ,in , These represent the noise standard deviations in the x, y, and z axes, respectively, and the threshold attenuation factor. It is a constant.

6. The noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data as described in claim 1, characterized in that: In S5, the adaptive threshold for wavelet denoising at each layer is calculated. ,in This represents the denoising threshold for the wavelet coefficients of the j-th layer. Then, for each axis and each layer, the detail coefficients that are less than the corresponding threshold are... The wavelet coefficients are set to zero, while the rest are retained to obtain the denoised detail coefficients. , … .

7. The noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data as described in claim 6, characterized in that: In S6, the PEPT trajectory is reconstructed for each axis using denoised approximation coefficients. and detail coefficient , … Perform inverse discrete wavelet transform to reconstruct the denoised position sequence. .

8. The noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data as described in claim 1, characterized in that: In S7, statistical model fitting and noise characteristic extraction are performed on the filtered noise components on each axis, including the kurtosis and skewness of the fitted Gaussian distribution.

9. The noise characteristic verification-based adaptive wavelet denoising method for PEPT trajectory data as described in claim 1, characterized in that: The test condition in S8 is that the fitted model after filtering out noise components conforms to the noise model under static conditions, and the correlation between noise components is also consistent with that under static conditions.

10. An adaptive wavelet denoising system for noise characteristic verification of PEPT trajectory data, characterized in that: It includes a processor and a memory, the memory being used to store program instructions, and the processor being used to call the program instructions in the memory to execute the noise characteristic verification adaptive wavelet denoising method for PEPT trajectory data as described in any one of claims 1-9.

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