Resolution and sensitivity - Implementation of RPT technique for high velocity system

Radioactive Particle Tracking (RPT) and Benchmarking for High Velocity Conditions

2.3 Implementation of RPT technique for high velocity system

2.3.2 Resolution and sensitivity

Resolution and sensitivity are calculated for different detector arrangements for the current experimental setup. The arrangement, which provides maximum resolution and sensitivity, is used for further studies to achieve maximum accuracy. Figure 2.14 shows the resolution and sensitivity plots. Resolution is around 2 mm at the axis of the belt where tracer particle

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D2 D5

1020 mm y

0 z ^D7 ^D10 ^D12

60 mm 130 mm

218 mm 220 mm

Ø 102 mm

Motor-I Motor-II

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almost no attenuation. Hence, counts recorded on detectors only depend on the distance between tracer particle and detector and solid angle formed by tracer particle on detector crystal. Therefore, the change in count with distance



^{dC dz}^/



is low and hence a larger resolution is observed compared to the resolution, which will be observed in the presence of attenuation. Therefore, it can be concluded that these experiments are performed in severe condition and one will achieve better results in case of actual RPT experiments.

Figure 2.14 Resolution and sensitivity of the accuracy experiment 2.3.3 Results and discussions

Stationary bias

The ability of RPT measurement to accurately locate the position of the tracer particle is majorly affected due to the statistical nature of gamma emission, accuracy of reconstruction algorithm and data acquisition frequency. Upadhyay (2010) has studied the effect of

reconstruction algorithms on position reconstruction of the stationary tracer particle.

However, the effect of data acquisition frequency on the ability of RPT measurement to locate the stationary position of the tracer particle has not been studied. Therefore, in the current work, with the same detector arrangement, the effect of data acquisition frequency on the ability of the RPT technique to locate the position of stationary tracer particle is studied. Experiments are performed by keeping the tracer particle at different positions distributed along the length of the belt. For each location data are acquired with different frequencies for long time (500 events/data points for each location at each frequency). To account the error due to statistical fluctuation, each event is treated as different data point and position of tracer particle is reconstructed by using the counts recorded on each detector for these individual events. This exercise is repeated at different positions and for different acquisition frequencies. It is to be noted that all these stationary positions, where accuracy of RPT measurement is tested, are not included in training of reconstruction algorithm.

Figure 2.15 shows the reconstructed position of tracer particles at different locations for different data acquisition frequency. It is observed that for all the locations, deviation in reconstructed particle position increases with the increase in data acquisition frequency.

Gamma emission and detection is a Poisson distribution process. The count recorded on detector is an integral of the count (area under the curve) between the time differences

 

^^t

for which data is acquired. The probability of this integral count predicting the mean of the Poisson distribution increases with the increase in data acquisition time. Thus, with decreasing data acquisition frequency, error reduces. Table 2.4 shows the standard error obtained in position reconstruction at different frequency for different locations. It clearly shows that standard error in position reconstruction decreases with decrease in data acquisition frequency.

Figure 2.15 Stationary bias

Table 2.4 Standard error in position reconstruction for stationary tracer position

Position RMS error in position (mm)

100 Hz 83 Hz 50 Hz 33 Hz 20 Hz

600 2.6514 2.4645 1.7158 1.9824 1.6522

700 2.5071 2.4029 1.7589 1.5716 1.2609

750 2.7085 2.5079 1.8439 1.6124 1.4422

800 2.3164 2.2108 1.7314 1.4463 1.1180

850 2.4694 2.2436 1.7251 1.5073 1.1225

Dynamic bias

As previously explained, the dynamic condition of the tracer increases uncertainty (Figure 2.12). To quantify the error due to dynamic bias, experiments are conducted for different acquisition frequency and different velocity (given in Table 2.4). In these experiments

particle is in a dynamic condition. Hence, it is necessary to determine the accuracy of RPT experiments in terms of position reconstruction and velocity measurement. However, it is difficult to measure the actual position of the tracer particle with an independent measurement when the particle is moving. Hence, displacement is compared instead of the position of the tracer particle. To compare the displacement, error in displacement



ma



is plotted where the actual displacement

 

a is calculated through tachometer reading. Figure 2.16a shows the PDF of error in displacement for 0.85 m/s velocity of the tracer particle at different data acquisition frequencies. PDF is comprised of displacement calculated at all the locations under investigated length. Results show that standard deviation of the error in displacement increases with decrease in data acquisition frequency.

It should be noted that error observed in these experiments is a combined effect of error due to statistical fluctuation, reconstruction and dynamic bias. Though it is difficult in current methodology to decouple the error caused due to stationary bias and dynamic bias, but it has been observed that error in dynamic condition has always been higher than error in a stationary condition. Further, it has been already established that the error due to stationary bias approximately remains same for a particular data acquisition frequency.

Hence, the error above the stationary bias (mentioned in Table 2.4) for a particular data acquisition frequency can be seen as a contribution of dynamic bias, which reduces with increase in data acquisition frequency. Therefore, from these results it can be concluded that higher data acquisition frequency minimizes the error, in measured displacement, caused due to dynamic bias.

Instantaneous velocity in RPT experiment is calculated by time differencing of two successive particle positions



^{ }^x^/ ^t



. Figure 2.16b shows the PDF of instantaneous velocity calculated through RPT measurement. The red line shows the velocity

measurement by a high precision tachometer and  v shows the mean velocity calculated through RPT experiments. Similar to displacement, PDF of instantaneous velocity is comprised of velocity calculated at all the locations under investigated length. Results indicate that though the error in displacement increases, the standard deviation of velocity prediction (calculated by using the mean velocity measured by tachometer) decreases with decrease in data acquisition frequency, Therefore, velocity prediction is better for lower data acquisition frequency compared to the higher data acquisition frequency. This is mainly because of  x/ t, which is used to calculate the velocity. Though the error in displacement is low at higher frequency, relatively lower value of t escalates the error in velocity measurement. Hence, acquiring the data at higher frequency to minimize the effect of dynamic bias, as suggested in literature, is not of much help particularly for velocity measurement. Therefore, one has to trade-off between accuracy in position reconstruction and accuracy in velocity measurement.

Figure 2.16a PDF of error in displacement at different acquisition frequency for tracer particle velocity of 0.85 m/s