Count rate meter with a time constant using adaptive digital signal processing
Introduction
Fluctuations of the results of processing of signals from radiation detectors in order to obtain the mean count rate are caused by random variations of the spacing between successive input pulses even in a steady state (Knoll, 1999). This property of both analog and digital rate meters is present irrespective of which measurement principle, time constant or preset count is applied. The properties of preset count algorithms have been analyzed in detail (Arandjelović et al., 1998) by applying classical methods of analysis. The improvements as regards statistical fluctuations by modifying spacings between input pulses (Arandjelović et al., 2002) have been implemented in practice (Žigić et al., 2003, Žigić et al., 2004, Šaponjić et al., 2003). The corresponding analyses of time constant algorithms have also been reported (Arandjelović and Koturović, 1997, Arandjelović and Koturović, 1998, Koturović and Arandjelović, 1995).
No attempts have been made so far to apply adaptive digital signal-processing methods in the analysis and design of digital rate meters even though some indications of the equivalence of FIR and IIR filters and some of digital rate meter algorithms have been reported (Fehlau, 1993, Milić et al., 1998).
The purpose of this paper is to present the application of digital filters (Antoniou, 1979) and adaptive digital signal processing (Haykin, 1986) methods to the design of digital systems for calculation of the mean count rate.
Two methods for improving the performance of classical time constant algorithms are proposed. The reason for introducing the two new methods proposed are: to shorten the time constant for higher stationary pulse input rates, to enable a specified and controllable error when the mean count rate remains within certain predefined limits from its true value, and provide a fast response to rapid changes of the mean count rate beyond the defined limits, by using an adaptive digital signal processor realizable in hardware or in software as a modern, powerful and flexible solution.
The first method starts with a longer time constant of 10 s assuming stationary pulse input rates corresponding to background radiation levels and then uses an adaptation algorithm to adjust the duration of the time constant interval if the mean count rate is changed. The second method starts with a shorter time constant of 1 s, being immediately prepared to react to sudden changes of the mean count rate, but switches to a longer time constant interval of 10 s if stationary pulse input rates corresponding to background radiation levels are maintained.
Both methods use an optimized detection algorithm to sense the change of the mean count rate, an adaptive low-pass filter to implement mean count rate error control by controllable suppression of fluctuations and an optimized algorithm of adaptation of time constant interval based on the current value of the mean count rate. The relative standard deviation defined as the ratio of the standard deviation of the mean count rate and the mean count rate is used as the performance criterion for the selection of the optimum parameter values. Optimum values are those that minimize the relative standard deviation. The methods differ in the strategy of execution of the algorithm for adaptation of the time constant interval. In the first method, the time constant interval adaptation algorithm is executed after the low-pass filters. This allows to obtain shorter time constant intervals for higher stationary pulse input rates. The second method executes the adaptation algorithm before the low-pass filters, which enables sensing of rapid changes in the average rate before the fluctuations’ suppression is carried out.
Both methods were investigated using a self-designed software package. The practical applications of the methods were as follows: the first method was implemented in a newly developed hand-held digital gamma rate meter and the second method was implemented in a newly developed modified version of the digital portable beta and gamma rate meter. The second method was also implemented in the stationary gamma monitoring system installed at the gates of the Institute of Nuclear Sciences “VINČA”.
Section snippets
Problem description
The stochastic nature of pulse arrivals suggests that the fluctuations from the average number of pulse arrivals shown in a pulse counter within a fixed time interval (time constant) will also represent a random process. Should the fluctuations obey a normal distribution then the standard deviation could represent the appropriate measure of the mean count rate error.
It would be appropriate to find a convenient low-pass signal processing to suppress the fluctuations of the mean count rate. In
The statistics of the fluctuations from the average number of pulse arrivals
The signals of pulse arrivals generated by pulse counters, such as GM tubes, represent a random process. Time intervals between adjacent pulses for a Poisson random process are given by Knoll (1999)where r is the mean count rate, t is the time interval and is the distribution function for time intervals between adjacent pulses. The fluctuations of the number of pulses from the mean during the time constant interval will form a random process. Therefore, the standard
Signal processing for fluctuations’ suppression
The most salient features of count rate meters are their accuracy in calculation of the mean count rate and their response time to the fast changes of the mean count rate. The first requirement concerning accuracy results in the need to have one or more rate meter parameters whose adjustments would maintain the fluctuations within defined limits. This calls for very narrow bandwidth low-pass filtering. The second requirement is in direct opposition to the first requirement since it requires a
The realized time constant methods
The methods using adaptive digital signal processing pertain to background radiation-level measurements with possible sudden radiation-level variations. It is supposed to provide accurate measurements of the mean count rate with a predefined count rate fluctuation of 5–10% in the stationary conditions, and a guaranteed maximum 1 s response time for a sudden increase of the count rate from the background level. The range of the radiation levels considered in the present paper is from 0.2 to 100
Conclusions
By applying adaptive signal-processing tools, two methods for improving the classical time constant rate meters were presented. The two new methods were proposed with the aim of: shortening the time constant for higher stationary pulse input rates, to make it possible to specify and control the error when the mean count rate remains within certain predefined limits from its true value, and to enable a fast response to rapid changes of the mean count rate beyond the defined limits, by using an
References (13)
Digital Filters: Analysis and Design
(1979)- et al.
The optimum dynamic parameters of digital rate meter algorithms
Rev. Sci. Instrum.
(1997) - et al.
The optimum dynamics of preset count digital rate meter algorithms
Rev. Sci. Instrum.
(1998) - et al.
The dynamic properties of the preset count digital rate meter algorithms
Rev. Sci. Instrum.
(1998) - et al.
A software method for suppressing statistical fluctuations in preset count digital rate meter algorithms
IEEE Trans. Nucl. Sci.
(2002) Comparing a recursive digital filter with the moving-average and sequential probability-ratio detection methods for SNM portal monitors
IEEE Trans. Nucl. Sci.
(1993)