A trajectory reconstruction algorithm for PEPT tracer particles

Abstract

The present invention discloses a trajectory reconstruction algorithm for PEPT tracer particles. The algorithm performs frame division and positioning processing on line of response (LoRs) data captured by a PEPT detector, and performs overlapping segmentation of the data through a sliding window method to improve the utilization rate of the LoRs data, thereby increasing the positioning frequency of the PEPT tracer particles. At the same time, the center points of the shortest segments of two non-planar straight lines are introduced into the positioning process as the approximate positions of the lines of response (LoRs) emitted by two positron annihilations, so that the positioning process is closer to the actual physical process and has a higher positioning frequency of the PEPT tracer particles.

Description

Technical Field

[0001] The invention belongs to the technical field of multiphase flow measurement, and in particular relates to a trajectory reconstruction algorithm for a PEPT tracing example. Background Art

[0002] PEPT (Positron Emission Particle Tracer) technology is a novel, non-destructive, and non-perturbative measurement technique for complex multiphase flows in industrial processes. It is capable of imaging the three-dimensional dynamics of various liquid, powder, and particle systems. The basic principle of PEPT is to detect the position of radioactive tracer particles using 3D gamma-photon imaging. Because the radionuclides within the tracer particles are extremely unstable, positron emission and positron annihilation events are highly likely to occur. Simultaneously, gamma rays are radiated from the tracer particles and captured by the detector. The PEPT tracer particle positioning algorithm then converts the captured gamma-ray data into tracer particle position data. Therefore, PEPT technology can measure the motion trajectory of tracer particles. Further dynamic analysis can obtain physical parameters such as the three-dimensional velocity field, turbulence field, density field, and dispersion of the PEPT tracer particles. PEPT can be applied to the study of systems and flow phenomena across a wide range of scales, geometries, and physical states.

[0003] Among them, PEPT tracer particle trajectory reconstruction is the core step of PEPT technology. It converts the gamma-ray data (also known as the line of response, LoR) captured by the PEPT detector into the trajectory of the tracer particle. Therefore, the PEPT tracer particle trajectory reconstruction algorithm must first frame the LoRs data stream and then convert a single frame of LoRs data into a tracer particle spatial position. In theory, ignoring the distance the tracer particle moves in a very short period of time, each line of response (LoR) mathematically corresponds to a spatial straight line passing through the tracer particle position, and the intersection of two ideal straight lines (LoRs) is the spatial position of the tracer particle. However, due to the influence of scattering noise, environmental noise, and other factors, the vast majority of LoRs are skew lines and cannot intersect at a single point in space. Therefore, dozens or hundreds of LoRs are usually used to determine the spatial position of a PEPT tracer particle to ensure that a single frame of LoRs data contains sufficient valid data.

[0004] Currently, the main algorithms for reconstructing PEPT tracer particle trajectories include the Birmingham algorithm, the line density algorithm, and the clustering algorithm. These algorithms generally use a direct segmentation method, where each frame of segmented data is concatenated end to end to form the original data stream. This results in low utilization of LoRs data, which in turn leads to a low frequency of PEPT tracer particle positioning. Furthermore, the Birmingham algorithm simplifies the single-frame PEPT positioning problem to finding a point in space that minimizes the sum of its distances to all straight lines, also known as the minimum distance point. The line density algorithm and clustering algorithm convert single-frame LoRs data into the distribution of straight lines in a three-dimensional grid space, then approximate locations with high line density as the tracer particle locations. These methods simplify the positioning process without considering the actual physical process of positron annihilation. Summary of the Invention

[0005] In view of the above problems, the present invention aims to provide a trajectory reconstruction algorithm for PEPT tracing examples.

[0006] The specific technical solutions are as follows:

[0007] A trajectory reconstruction algorithm for a PEPT tracing example includes the following steps:

[0008] Step 1: Read the LoRs (Lines of Response) data stream collected by the PEPT detector, where the data format corresponding to each LoR is [t, x A ,y A , z A , x B ,y B , z B ], where t represents the data acquisition time of the LoR, x A ,y A , z A and x B ,y B , z B Represent the coordinates of the space where points A and B are located, and calculate the sampling rate N of LoRs data s =N all / t all , in Hz, where N all , t all Respectively represent the total number of LoRs data and the total acquisition time, in seconds;

[0009] Step 2: Based on the PEPT measurement conditions, input the estimated effective LoRs ratio f, which represents the proportion of effective data in all LoRs data, generally set in the range of 20% to 60%; estimate the single-frame LoRs sample length Where Δ is the detector's inherent resolution, expressed in mm, and v is the estimated tracer particle velocity, expressed in m / s. Setting the frame sequence's moving step k (the sample window moving step per frame) determines the data overlap area during subsequent data segmentation. Generally, smaller k values ​​lead to higher LoRs utilization, meaning a higher frequency of PEPT tracer particle localization. However, infinitely decreasing k will also result in a large amount of redundancy in the positioning data and a large amount of computational complexity. Typically, k is set to (0.1–0.5)w.

[0010] Step 3: Calculate the shortest segment length d0 and the segment center point (x0, y0, z0) of each pair of LoRs (non-coplanar straight lines) between the fth LoR and the k LoRs before and after it. At this time, each LoR data corresponds to 2k shortest line segments and their center points. The unit of d0 is m.

[0011] Step 4: Based on the sliding window method, the LoRs sequence data is framed and w LoRs and their corresponding shortest line segments and center points (2kw) are obtained in each frame. The average acquisition time of the LoRs data in this frame is calculated as the timestamp t′ of the data in this frame. i , unit is s;

[0012] Step 5: Before performing PEPT tracer particle positioning on a single frame of data, remove the center points of the shortest line segments outside the detector field of view and where the length of the shortest line segment is greater than 2R to eliminate the influence of some environmental noise, where R is the equivalent radius of the detection field of view, in meters.

[0013] Step 6: Group the remaining shortest line center points into a point group, use the least squares method to fit the centroid of the point group, and calculate the distance d from the center points of all remaining shortest line segments to the centroid j , unit is m.

[0014] Step 7: Calculate the RMS of all distances And D use Remove the farthest position (d j >D use ) of the shortest segment center point, the number of remaining valid shortest segment center points is N use .

[0015] Step 8: Return to step 6 and re-execute steps 6 and 7 until the remaining effective shortest segment center points account for N use / 2kw is not higher than the preset ratio f.

[0016] Step 9: Output the time and position [t′, x′, y′, z′] of the PEPT tracer particle in the current frame, and enter the next frame to perform the calculation in a loop starting from step 5.

[0017] Step 10: After all frames are calculated, the complete motion trajectory of the PEPT tracer particles is output.

[0018] The beneficial effects of the present invention are:

[0019] The present invention provides a trajectory reconstruction algorithm for a PEPT tracer example, the positioning process of which is closer to the positron annihilation physical process and has a higher PEPT tracer particle positioning frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Schematic diagram of LoRs data segmentation based on the sliding window method;

[0021] Figure 2 Detailed flow chart of the present invention. DETAILED DESCRIPTION

[0022] The present invention will be further described below with reference to the accompanying drawings, but the protection scope of the present invention is not limited thereto.

[0023] like Figure 2 As shown in FIG, a trajectory reconstruction algorithm for a PEPT tracing example includes the following steps:

[0024] Step 1: Read the LoRs data stream collected by the PEPT detector, where the data format corresponding to each LoR is [t, x A ,y A , z A , x B ,y B , z B ], where t represents the data acquisition time of the LoR, x A ,y A , z A and x B ,y B , z B Represent the coordinates of the space where points A and B are located, and calculate the sampling rate N of LoRs data s =N al1 / t all , where N a11 , t all Respectively represent the total number of LoRs data and the total collection time;

[0025] Step 2: Based on the PEPT measurement conditions, input the estimated effective LoRs ratio f, which represents the proportion of effective data in all LoRs data, generally set in the range of 20% to 60%; estimate the single-frame LoRs sample length w is the number of samples in a single frame, where Δ is the intrinsic resolution of the detector and v is the estimated speed of the tracer particles. Setting the moving step k of the frame sequence determines the data overlapping area during subsequent data segmentation. Generally, a smaller k value will lead to a higher utilization rate of LoRs, that is, a higher frequency of PEPT tracer particle positioning. However, infinitely reducing the value of k will also lead to a large amount of redundancy in the positioning data and a huge amount of calculation. Usually, k is selected from (0.1 to 0.5)w.

[0026] Step 3: Calculate the shortest segment length d0 and the segment center point (x0, y0, z0) of each pair of LoRs (non-coplanar straight lines) between the i-th LoR and its preceding and following k LoRs. At this time, each LoR data corresponds to 2k shortest segments and their center points.

[0027] Step 4: Based on the sliding window method, the LoRs sequence data is framed and w LoRs and their corresponding shortest line segments and center points (2kw) are obtained in each frame. The average acquisition time of the LoRs data in this frame is calculated as the timestamp t′ of the data in this frame. i , specifically Figure 1 shown.

[0028] Step 5: Before performing PEPT tracer particle positioning on a single frame of data, remove the center point of the shortest line segment outside the detector field of view to eliminate the influence of some environmental noise.

[0029] Step 6: Group the remaining shortest line center points into a point group, use the least squares method to fit the centroid of the point group, and calculate the distance d from the center points of all remaining shortest line segments to the centroid j .

[0030] Step 7: Calculate the RMS of all distances And D use Remove the farthest position (d i >D use ) of the shortest segment center point, the number of remaining valid shortest segment center points is N use .

[0031] Step 8: Return to step 6 and re-execute steps 6 and 7 until the remaining effective shortest segment center points account for N use / 2kw is not higher than the preset ratio f.

[0032] Step 9: Output the time and position [t′, x′, y′, z′] of the PEPT tracer particle in the current frame, and enter the next frame to perform the calculation in a loop starting from step 5.

[0033] Step 10: After all frames are calculated, the complete motion trajectory of the PEPT tracer particles is output.

[0034] For example, for a typical PEPT detection system, the inherent resolution of the detector is Δ = 6 mm, the effective detection efficiency f is about 20%, and the number of response lines LoRs collected in 10 minutes is 60,000,000, so the average sampling rate of LoRs is N s =100kHz; PEPT tracer particles move within the detector field of view at a speed of 1m / s.

[0035] For the LoRs data collected by this typical detection system, the PEPT positioning frequency of the traditional positioning method (Birmingham algorithm) is about 250 times / second.

[0036] Using the positioning algorithm in the patent of this invention, according to the single frame LoRs data length estimation formula The value range of k is usually 0.1-0.5w. In this example, the average value k=0.25w≈48 is selected. For PEPT tracer particles, the number of The positioning frequency is about 8 times that of traditional methods.

Claims

1. A trajectory reconstruction algorithm for PEPT tracer particles, characterized in that: The steps include: Step 1: Read the LoRs data stream collected by the PEPT detector and calculate the sampling rate N of the LoRs data s , unit is Hz; Step 2: According to the measurement conditions of PEPT, the estimated effective LoRs ratio f is input, and the single-frame LoRs sample length w and the moving step k of the frame sequence are estimated; Step 3: Calculate the shortest segment length d0 and the segment center point (x0, y0, z0) of each pair of LoRs between the i-th LoR and its preceding and following k LoRs. At this time, each LoR data corresponds to 2k shortest segments and their center points. The unit of d0 is m. Step 4: Based on the sliding window method, the LoRs sequence data is framed and w LoRs and their corresponding shortest line segments and 2kw center points are obtained in each frame. The average acquisition time of the LoRs data in this frame is calculated as the timestamp t of the data in this frame. i ′ , unit is s; Step 5: Before performing PEPT tracer particle positioning on a single frame of data, remove the center points of the shortest line segments outside the detector field of view and corresponding to the shortest line segment length greater than 2R to eliminate the influence of some environmental noise, where R is the equivalent radius of the detection field of view, in meters; Step 6: Use the minimum multiplication method to fit the centroid of the remaining shortest line segment center point group, and calculate the distance d from all remaining center points to the centroid j , unit is m; Step 7: Take the root mean square of all distances and D use As a guideline, remove d j >D use The center point of the shortest line segment, the number of remaining valid shortest line segment centers is N use ; Step 8: Return to step 6 and re-execute steps 6 and 7 until the remaining effective shortest segment center points account for N use / 2kw is not higher than the preset ratio f; Step 9: Output the time and position of the PEPT tracer particle in the current frame [t ′ ,x ′ ,y ′ ,z ′ ] and enter the next frame and start the calculation loop from step 5; Step 10: After all frames are calculated, the complete motion trajectory of the PEPT tracer particles is output.

2. A PEPT tracer particle trajectory reconstruction algorithm according to claim 1, characterized in that: The data format of the LoRs data stream collected in the first step is [t,x A ,y A ,z A ,x B ,y B ,z B ], t represents the data acquisition time of LoR, x A ,y A ,z A and x B ,y B ,z B Respectively represent the coordinates of the space where points A and B are located; the sampling rate N s =N all / t all , where N all , t all Respectively represent the total number of LoRs data and the total acquisition time, in seconds.

3. A PEPT tracer particle trajectory reconstruction algorithm as claimed in claim 2, characterized in that: The length of LoRs samples in a single frame in the second step Where Δ is the intrinsic resolution of the detector in mm, v is the estimated velocity of the tracer particle in m / s, f is set to 20-60%, and k is selected to be 0.1-0.5w.

4. A PEPT tracer particle trajectory reconstruction algorithm as claimed in claim 3, characterized in that: The root mean square sum of all distances in step 7

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