CN115796095A - Pulse interpolation timing parameter optimization method based on genetic algorithm - Google Patents
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Abstract
The invention discloses a pulse interpolation timing parameter optimization method based on a genetic algorithm, which comprises the steps of randomly generating a certain number of candidate solution individuals, and constructing an initial candidate solution set { s }; randomly generating a set of pulse signals { V [ n ]]The pulse signal is a digital signal acquired at a fixed sampling rate, and the characteristic parameter comprises pulse amplitude V p And a rise time t r (ii) a Based on the generated pulse signal { V [ n ]]Calculating the fitness of each candidate solution individual in the candidate solution set { s } in sequence, and updating the candidate solution set; judging whether the set iteration times are reached, if so, selecting an optimal solution from the candidate solution set after the iteration is completed, and achieving the purpose of parameter optimization; otherwise, the iteration updating of the candidate solution is continued. The method can optimize and design parameters in the pulse interpolation timing method, realizes high time measurement precision under relatively low sampling rate, and has the advantages of pulse shape and amplitude variationHas good robustness.
Description
Technical Field
The invention relates to the technical field of high-precision time measurement, in particular to a pulse interpolation timing parameter optimization method based on a genetic algorithm.
Background
The high-precision time measurement has wide application in the fields of nuclear physics, particle physics experiments, nuclear medicine imaging and the like. For example, in Time-of-flight (ToF) Positron Emission Tomography (PET), extremely high pulse arrival Time measurement accuracy is required to achieve high spatial imaging resolution. The waveform digitization method acquires analog pulses output by a detector through a high-speed sampling technology, extracts time information carried by the pulses through a digital signal processing method, can obtain information in a full frequency band of the pulses compared with a traditional discrimination method combined with time-to-digital conversion, and can also obtain other interested information such as amplitude and shape of the pulses and the like besides extracting the time information based on the same digital signals.
At present, a waveform digitization method is widely researched internationally, but in order to achieve sufficiently high time measurement accuracy, a commonly used technical scheme adopts an extremely high sampling rate (> 5 GSps), and the high sampling rate causes problems such as high cost, high power consumption, and high data transmission and processing complexity. It is therefore desirable to investigate the temporal extraction method at relatively low sampling rates. Under the condition of a lower sampling rate, in order to reduce time measurement errors, generally, interpolation is carried out on digital signals obtained by acquisition, then the arrival time of pulses is obtained by methods such as digital threshold crossing discrimination and the like, and the interpolation process can be realized by an interpolation filter. In the practical application process, there are a plurality of parameters that affect the time measurement accuracy, including interpolation multiple, filter order, filter cut-off frequency, window function shape parameter, and threshold constant ratio.
In the prior art, a simple empirical method can be adopted for selecting the parameters, but the parameters easily fall into a local optimal solution, and the time precision is difficult to achieve sufficiently high; or use too high a filter order, which results in more computational resources.
Disclosure of Invention
The invention aims to provide a pulse interpolation timing parameter optimization method based on a genetic algorithm, which can optimize and design parameters in the pulse interpolation timing method, realizes high time measurement precision under relatively low sampling rate, and has good robustness on the shape and amplitude change of pulses.
The purpose of the invention is realized by the following technical scheme:
a method for pulse interpolation timing parameter optimization based on a genetic algorithm, the method comprising:
Each candidate solution comprises one-time selection of each parameter to be optimized, and the selected probability meets the uniform distribution in a certain range;
the parameters to be optimized comprise interpolation filter parameters and digital threshold crossing discrimination parameters; the interpolation filter parameters comprise interpolation multiple M, filter order N and filter cut-off frequency f c A window function shape parameter β; the digital threshold crossing discrimination parameter comprises a threshold constant ratio c f (ii) a Wherein M and N are discrete variables and f c Beta and c f Is a continuous variable;
The technical scheme provided by the invention shows that the method can optimize and design parameters in the pulse interpolation timing method, realizes high time measurement precision under a relatively low sampling rate, has good robustness on the shape and amplitude change of the pulse, has good effectiveness, universality and practicability, and is easy for hardware integration.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a pulse interpolation timing parameter optimization method based on a genetic algorithm according to an embodiment of the present invention.
Fig. 2 is a diagram of a reference PMT pulse waveform used in an embodiment of the present invention.
Fig. 3 is a time precision simulation verification diagram based on genetic algorithm parameter optimization according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments, and this does not limit the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The method is suitable for pulse signals output by detectors such as PMT/SiPM and the like, waveform digitization is completed through a sampling circuit, and after interpolation filtering is carried out in a digital domain, pulse arrival time extraction is completed through a digital threshold crossing discrimination method; the parameters of the interpolation filter and the digital threshold crossing discrimination are obtained by genetic algorithm simulation optimization. Fig. 1 is a schematic flow chart of a pulse interpolation timing parameter optimization method based on a genetic algorithm according to an embodiment of the present invention, where the method includes:
Each candidate solution comprises one-time selection of each parameter to be optimized, and the selected probability meets the uniform distribution in a certain range;
the parameters to be optimized comprise interpolation filter parameters and digital threshold crossing discrimination parameters; the interpolation filter parameters comprise interpolation multiple M, filter order N and filter cut-off frequency f c A window function shape parameter β; the digital threshold crossing discrimination parameters comprise threshold constant ratio c f (ii) a Wherein M and N are discrete variables and f c Beta and c f Is a continuous variable;
in addition, the number of the candidate solutions to be optimized is not only one, but the solution is optimized as a candidate solution set { s } as a whole.
For example, the number of candidate solutions in the set { s } of candidate solutions is set to 400; the selection range of the interpolation multiple M is 2, 4 or 8; the order N of the filter is set to be in direct proportion to M, and the coefficient is selected to be 6 to 10 times, for example, in the case of 8 times interpolation, the order N is 48 at minimum and 80 at maximum; filter cut-off frequency f c Set as inversely proportional to M, the coefficient being chosen to be between 0.05 and 1, e.g. in the case of 8-fold interpolation, the cut-off frequency f c The representation in the digital domain is at a minimum
Maximum, is
(ii) a The window function uses a Kaiser window, i.e. represented by the following formula:
wherein beta is a window function shape parameter, and the selection range is set to be between 1 and 20; i is 0 () is a zero order Bessel function of the first type;
threshold constant ratio c f For digital constant ratio timing, set between 0.3 and 0.9.
In this step, the randomness of the pulse signal is manifested in the following ways: sampling start point t 0 Of pulse amplitude V p Random, rise time t r And a noise amplitude V n [n]Random of (2);
amplitude of pulse V p And a rise time t r Is set according to the actual detector type, the noise amplitude V n [n]Referring to the noise settings of the actual front-end electronics hardware circuit;
for an analog pulse waveform V (t), the expression for generating a random digital pulse signal V [ n ] is as follows:
wherein T is a sampling period; v p0 Is the reference pulse amplitude; t is t r0 Is a reference rise time; t is t 0 Is a sampling starting point; v n [n]The value of n is a natural number.
For example, as shown in fig. 2, a reference PMT pulse waveform used in the embodiment of the present invention has a leading edge of about 4ns, a sampling rate of 500 MSps is selected to digitize the PMT pulse, and then a time extraction algorithm is used to obtain time information carried in the digitized pulse, where the reference pulse amplitude and time are the amplitude and time of the pulse waveform shown in fig. 2; the sampling period T is 2ns; range of variation of amplitude
Between 0.2 and 1; range of rise time variation
Between 0.9 and 1.8.
In addition, to ensure optimum results for pulse amplitude V p And a rise time t r Stability ofA set of pulse signals is randomly generated at the beginning of each iteration.
in this step, the fitness is determined by the particular solution candidate s (M, N, f) in the set { s } of solution candidates c , β, c f ) Corresponding time precision determination, namely the higher the precision is, the higher the individual fitness is;
the specific calculation process of the fitness comprises the following steps:
for the original pulse signal { V [ n ]]Each pulse of same amplitude V p And a rise time t r At the sampling start point t 0 Plus a fixed delay T d Selecting a random noise amplitude V n ’[n]Regenerating a set of delayed pulse signals { V } d [n]}；
Counting the original pulse signal { V [ n ]]And delayed pulse signal V d [n]Standard deviation RMS of the difference of arrival times of the two paths of pulse waveforms, wherein the fitness is the reciprocal of the RMS value; wherein, the arrival time of the pulse waveform is obtained by a digital constant ratio timing method;
selecting partial candidate solution individuals from the current candidate solution set { s } to become parents according to a certain probability;
generating filial generations from the parent through a certain crossing and mutation method, and sequentially calculating the fitness of the filial generation individuals;
and selecting candidate solution individuals with high fitness from the parent and the filial generation as a next generation candidate solution set { s }, thereby updating the candidate solution set.
For example, the number of pulse signals { V [ n ] } is 1000, the parent selection method is equal probability selection, and the probability of selecting each candidate solution is 80%.
The crossing method comprises the following steps: for each successive type variable, i.e. f c Beta and c f If the value of parent 1 is x 1 Parent 2 has a value of x 2 The values of the cross-generated offspring are respectively
And
(ii) a For discrete variables, i.e., M and N, children inherit the value of one of the parents.
The mutation method comprises the following steps: for each offspring that cross-breed, mutation occurred with 40% probability, and the mutation was a single point mutation, namely at (M, N, f) c , β, c f ) A variable is selected and a value is re-randomly selected from the set range.
In this step, the number of iterations may be set as required, for example, the number of iterations is set to 100.
In specific implementation, after iteration is completed, time accuracy under a reference pulse waveform can be further verified, and the specific process is as follows:
dividing an input reference pulse waveform into two paths by adopting a line delay method, wherein one path is added with fixed delay and is respectively digitized; aiming at the digitized pulse waveform, calculating the arrival time of the pulse by adopting a digital constant ratio timing method, and counting the RMS of the difference between the arrival times of the two paths of pulse waveforms; the accuracy of a single channel being delayed RMS, taking into account that the measurements of the two channels are not correlated
(ii) a And respectively calculating single-channel precision under different delay amounts to verify the time precision performance.
Fig. 3 is a simulation verification diagram of time accuracy based on genetic algorithm parameter optimization according to an embodiment of the present invention, and it can be seen from fig. 3 that the method according to the present invention can achieve higher time measurement accuracy at a relatively low sampling rate.
It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.
In summary, the method provided by the embodiment of the present invention has the following advantages:
(1) The invention realizes high time measurement precision under relatively low sampling rate, and has good robustness to the shape and amplitude change of the pulse;
(2) The invention can optimize the order of the filter in the parameter iteration process, can reduce the resource consumption in hardware implementation, and has good effectiveness, universality and practicability.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims. The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Claims (4)
1. A pulse interpolation timing parameter optimization method based on a genetic algorithm is characterized by comprising the following steps:
step 1, randomly generating a certain number of candidate solution individuals, and constructing an initial candidate solution set which is expressed as { s (M, N, f) c , β, c f ) }; each candidate solution comprises one-time selection of each parameter to be optimized, and the selected probability meets the uniform distribution in a certain range; the parameters to be optimized comprise interpolation filter parameters and digital threshold crossing discrimination parameters; the parameters of the interpolation filter comprise interpolation multiple M, filter order N and filter cut-off frequency f c A window function shape parameter β; the digital threshold crossing discrimination parameter comprises a threshold constant ratio c f (ii) a Wherein M and N are discrete variables and f c Beta and c f Is a continuous variable;
step 2, randomly generating a group of pulse signals { V [ n ]]At a fixed sampling rateCollecting the obtained digital signal, the characteristic parameters including pulse amplitude V p And a rise time t r ；
Step 3, calculating the fitness of each candidate solution in the candidate solution set { s } in sequence based on the pulse signal { V [ n ] }generatedin the step 2, and updating the candidate solution set;
step 4, judging whether the set iteration times are reached, if so, selecting an optimal solution from the candidate solution set after the iteration is completed, and achieving the purpose of parameter optimization; otherwise, the iteration updating of the candidate solution is continued.
2. The pulse interpolation timing parameter optimization method based on genetic algorithm according to claim 1, wherein in step 2, the randomness of the pulse signal is represented by the following aspects: sampling start point t 0 Of pulse amplitude V p Random, rise time t r And a noise amplitude V n [n]Random of (2);
amplitude of pulse V p And a rise time t r Is set according to the actual detector type, and the noise amplitude V n [n]Referring to the noise settings of the actual front-end electronics hardware circuit;
for an analog pulse waveform V (t), the expression for generating a random digital pulse signal V [ n ] is as follows:
3. The genetic algorithm-based pulse interpolation timing parameter optimization method of claim 1, wherein in step 2, the optimization result is guaranteed to be V for pulse amplitude p And a rise time t r The set of pulse signals is randomly generated at the beginning of each iteration.
4. The method of claim 1, wherein in step 3, the fitness is determined by the specific solution candidates s (M, N, f) in the solution candidate set { s } c , β, c f ) Corresponding time precision determination, namely the higher the precision is, the higher the individual fitness is; the specific calculation process of the fitness comprises the following steps:
for the original pulse signal { V [ n ]]Each pulse of same magnitude V p And a rise time t r At the sampling start point t 0 Plus a fixed delay T d Selecting a random noise amplitude V n ’[n]Regenerating a set of delayed pulse signals { V } d [n]}；
Counting original pulse signal { V [ n ]]And delayed pulse signal V d [n]Standard deviation RMS of the difference of arrival times of the two paths of pulse waveforms, and the fitness is the reciprocal of the RMS value; wherein, the arrival time of the pulse waveform is obtained by a digital constant ratio timing method;
selecting partial candidate solution individuals from the current candidate solution set { s } to become parents according to a certain probability;
generating offspring from the parents through a certain crossing and mutation method, and sequentially calculating the fitness of the offspring individuals;
and selecting the candidate solution individuals with high fitness from the parent and the descendants as the next generation candidate solution set { s }, thereby updating the candidate solution set.
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