A Real-time Tracking Method for System Response Function

Abstract

The present invention discloses a method for real-time tracking of a system response function. Since the system function is a time-varying random process and has high-order complexity, it is difficult to accurately describe with a typical mathematical model, and the global state of the system cannot be characterized by a certain instantaneous state. Therefore, it is necessary to perform real-time tracking of the system function. By continuously adding new information to the waveform space family, the waveform space family is updated and grown in a timely manner. In the continuous iterative update process, the optimal system response function and transfer function with the characteristics of "globality", "real-time", "accuracy" and "smoothness" are searched out, laying a solid foundation for the real-time correction of subsequent pulse shaping algorithms and the accurate identification of shaped pulses, and greatly improving the accuracy of energy spectrum measurement.

Description

Technical Field

[0001] The present invention relates to a method for real-time tracking of a system response function. Background Art

[0002] The front-end analog system of a nuclear radiation detector is jointly composed of a detector, a preamplifier, a C-R / R-C network, an amplifier circuit, and other conditioning circuits. Due to the fact that the charge collection time of the detector varies, and the cascaded RC networks of the resistor-capacitor feedback preamplifier connected to the detector, the cascaded RC networks, the cascaded CR-RC networks of the switch reset preamplifier, and the composition methods of other signal conditioning circuits are diverse (for example, different numbers of cascaded RC or CR are selected), the system has extremely high complexity in terms of circuit, manifested in the diversity of the forms of its output pulse signals and the complexity of the waveforms, that is, manifested in the complex high-order nature of the system function in the S domain. When the front-end analog system is affected by test conditions and ambient temperature and humidity, the parameters of its electronic components (such as the amplification factor and spectral response of a photomultiplier tube, the photon yield of a scintillator, the amplification factor of a linear pulse amplifier, etc.) will fluctuate and change over time, resulting in fluctuations, drifts, and distortions in the output pulse waveforms.

[0003] From the above analysis, it can be seen that the system function is a time-varying random process with high-order complexity, which is difficult to accurately describe with a typical mathematical model, and the global state of the system cannot be characterized by a certain instantaneous state. It is necessary to track the system function in real time. By performing real-time analysis on the waveform of the pulse signal output by the front-end analog system of the nuclear radiation detector, an optimal response function and transfer function with the characteristics of "globality", "real-time", "accuracy", and "smoothness" can be obtained in real time, laying a solid foundation for the real-time correction of subsequent pulse shaping algorithms and the accurate identification of shaped pulses, and greatly improving the accuracy of energy spectrum measurement. Summary of the Invention

[0004] The purpose of the present invention is to disclose a method for real-time tracking of a system response function, which is used to perform real-time analysis on the waveform of the pulse signal output by the front-end analog system of a nuclear radiation detector to achieve real-time tracking of the system response function and transfer function. The response function and transfer function obtained by this method are optimal functions with the characteristics of "globality", "real-time", "accuracy", and "smoothness", laying a solid foundation for the real-time correction of subsequent pulse shaping algorithms and the accurate identification of shaped pulses, and greatly improving the accuracy of energy spectrum measurement.

[0005] The real-time tracking of the response function of the front-end analog system of the nuclear radiation detector in the present invention is achieved through the following steps ① to ⑤.

[0006] Step ① Select M single-pulse waveform samples, unify the dimensions, and obtain the basic waveform space H1 after unit normalization.

[0007] The single pulse waveform samples here refer to complete pulses that are separated from each other and have no overlap.

[0008] Step ② In the basic waveform space H1, find the projection of the observed waveform x1 and shadow waveform vector

[0009] Step ③ The newly observed waveform x i Shadow Wave Vector As new information, it is added to the waveform space H i In this paper, a new waveform space H is derived. i+1 , through continuous iterative updates to achieve the growth of the waveform space family H.

[0010] Step ④ Waveform projection in the above steps The method of obtaining is implemented as follows A to C:

[0011] A. Design performance indicators Find the minimum value that satisfies the performance index

[0012] So sought It is called the optimal projection vector based on the waveform space family H(i), which is x1,x2,…,x i In the waveform space H1, H2, ..., H i The common projections on these waveform spaces H1, H2, ..., H i A manifestation of ethnicity.

[0013] B. Find the optimal projection vector of the adjacent space family H(i-1) and H(i) and The relationship is about to i-1 Shadow Wave Vector Add to the space family H(i-1), grow a new space family H(i), and H(i) and contains the new information x i The waveform set X(i) is used to find the optimal projection of H(i)

[0014] C. Find the optimal projection of H(i) The recursive process is implemented as follows (a) to (c):

[0015] (a) Setting the initial value use and x1=[x1(1)x1(2)...x1(N)] T express

[0016] (b) Replace the most original vector in the waveform space H1 with as a new vector to obtain the waveform space H2, and use the waveform spaces H1, H2, x1, x2, and to represent

[0017] (c) Replace the most original vectors in H1, H2, …, H with i-1 as new vectors respectively to obtain the waveform spaces H2, H3, …, H i , and combine x1, x2, …, x i-1 and to obtain

[0018] Step ⑤ avoids the infinite growth of the space family H(i), limits the maximum space capacity, modifies the iterative equation; and searches in real time for the projection vector with a relatively stable state Combine the shadow vectors to obtain the best response waveform of the detection system in the current time period, and obtain the best transfer function.

[0019] Through steps ① to ⑤, the real-time tracking of the response function and transfer function of the detection system is completed. The obtained response function and transfer function have the characteristic of real-time, providing a solid guarantee for the real-time correction of the subsequent pulse shaping algorithm, the accurate identification of the shaped pulse, and even the accurate acquisition of the nuclear energy spectrum.

[0020] Taking the trapezoidal shaping of the pulse waveform as an example, it shows how to update the trapezoidal shaping algorithm with the response function and transfer function obtained in real time.

[0021] The beneficial effects of the present invention are as follows:

[0022] Due to the influence of the test conditions and environment on the front-end analog system of the nuclear radiation detector and the fluctuations and changes of the parameters of its own circuit components over time, the pulse waveform output by it has volatility, high-order complexity, drift, and distortion. In terms of the system function, it is: the system function is a time-varying random process, with high-order complexity, difficult to accurately describe with a typical mathematical model, and unable to characterize the global state of the system with a certain instantaneous state, and it is necessary to track the system function in real time.

[0023] A method for real-time tracking of the detector system response function and transfer function, which adds continuous new information to the waveform space family, enabling the waveform space family to be updated and grown in a timely manner. The obtained response function and transfer function are the optimal functions with the characteristics of "globality", "real-time", "accuracy" and "smoothness". This fully considers the following aspects: The system parameter fluctuations caused by test conditions and the environment during the measurement process are a slow process with time correlation before and after, and have the characteristics of "real-time change" and "smooth change"; The system function has the characteristics of random volatility and high-order complexity; The volatility of the system function indicates that its so-called "optimal" and "accurate" should be "global" "optimal" and "accurate" in the sense of probability. This lays a solid foundation for the real-time correction of subsequent pulse shaping algorithms and the accurate identification of shaped pulses, and can greatly improve the accuracy of energy spectrum measurement. Brief Description of the Drawings

[0024] Figure 1 It is a flowchart of the method of the present invention. Detailed Implementation Manner

[0025] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. These embodiments are implemented on the premise of the technical solution of the present invention, and detailed implementation manners and processes are given. However, the protection scope of the present invention is not limited to the following embodiments.

[0026] The present invention relates to a method for real-time tracking of a system response function, which is realized through the following steps ① to ⑤ and is used for real-time tracking of the response function of the detector front-end analog system.

[0027] Step ① Select M single-pulse waveform samples, unify the dimensions, and obtain the basic waveform space H1 after unit normalization

[0028] Suppose the selected M single-pulse waveform samples are Each waveform sample has N sampling values, as follows:

[0029]

[0030] Here, the single-pulse waveform sample refers to a complete pulse that is separated from each other and has no overlap.

[0031] Unit-normalize the waveform to obtain the basic waveform space H1:

[0032]

[0033] In formula (2) Obtained from the following formula:

[0034]

[0035]

[0036] Waveform Consisting of N sampling values where i = 1, …, M; in formula (3) Denotes The sum of all sampling values of the waveform

[0037] Step ② In the basic waveform space H1, obtain the projection of the observed waveform x1 and the shadow waveform vector

[0038] Let the first observed waveform vector be x1 = [x1(1) x1(2)... x1(N)] T , and its projection in the basic waveform space H1 is:[[]]

[0039]

[0040] Are the projection components of x1 on respectively.

[0041] The shadow waveform vector of x1 in the H1 space is:[[]]

[0042]

[0043] Step ③ Use the shadow waveform vector i of the newly observed waveform x as new information and add it to the waveform space H i to derive a new waveform space H i+1 , and realize the growth of the waveform space family H by continuous iterative update, which is implemented according to the following methods A and B:[[]]

[0044] A. When 1 ≤ i ≤ M:[[]]

[0045] Use the shadow waveform vector of x1 in the H1 space as a new vector to replace the most original vector in H1 to form a waveform space H2 containing new information :[[]]

[0046]

[0047] Use the shadow waveform vector of x2 in the H2 space as a new vector to replace the most original vector in H2 to form a waveform space H3 containing new information :[[]]

[0048]

[0049] And so on, use x i in H iShadow waveform vector of the space Replace H with the new vector i The most primitive vector in To form a waveform space H containing innovation where i+1 where is the projection of x i onto H i The method for obtaining is described later The waveform spaces formed above are listed as follows

[0050] The waveform spaces formed above are listed as follows

[0051]

[0052] B. When i > M

[0053] Use x i in H i The shadow waveform vector of the space Replace the j-th vector in H i with the new vector which is actually the most primitive waveform vector in H i To form a waveform space H containing innovation where the relationship between i and j is as follows i+1 where i, j have the following relationship

[0054] i = nM + j, 1 ≤ j ≤ M, n ≥ 1 (10)

[0055] where i, j, and n are all integers

[0056] The waveform spaces formed above are listed as follows

[0057]

[0058] The newly observed waveform x i 、x i The shadow waveform vectors of x on the waveform space H i The projection of x x i onto H i and the relationship between the waveform space family H(i) are summarized as follows The relationship between the newly observed waveform x

[0059]

[0060]

[0061]

[0062] where H(i) is the i adjacent waveform spaces H1, H2, …, H iThe waveform space family is composed of X(i) and X(i) is the observed waveform x1, x2,…, x i A collection of .

[0063] Step ④ Waveform projection in the above steps The method for obtaining is implemented as follows A to C:

[0064] A. Design performance indicators As follows, we find the minimum value of the performance index.

[0065]

[0066] Find partial derivatives:

[0067]

[0068] make It turns out that:

[0069] So sought It is called the optimal projection vector based on the waveform space family H(i), which is x1,x2,…,x i In the waveform space H1, H2, ..., H i The common projections on these waveform spaces H1, H2, ..., H i A manifestation of ethnicity.

[0070] B. Find the optimal projection vector of the adjacent space family H(i-1) and H(i) and The relationship is about to i-1 Shadow Wave Vector Add to the space family H(i-1), grow a new space family H(i), and H(i) and contains the new information x i The waveform set X(i) is used to find the optimal projection of H(i) The derivation is as follows:

[0071] C. Find the optimal projection of H(i) The recursive process is implemented as follows (a) to (c):

[0072] (a) Set the initial value:

[0073]

[0074] Respectively and x1=[x1(1)x1(2)...x1(N)] T Just substitute it into the above formula;

[0075] (b) (b) Obtaining:

[0076] Using as the new vector to replace the most original vector in H1 to obtain H2, and then obtaining the waveform set X(2) and the waveform space family H(2) according to formula (14), and further obtaining:

[0077]

[0078] (c) (c) Obtaining:

[0079] According to step ③, using as the new vector to replace the most original vectors in H1, H2,..., H i-1 to obtain the waveform spaces H2, H3,..., H i , and combining them according to (14) to obtain the waveform space family H(i), and further obtaining:

[0080]

[0081] Step ⑤ avoids the infinite growth of the space family H(i), limits the maximum space capacity, and modifies the iterative equation; and searches for the projection vectors with relatively stable states in real time Combining the shadow vectors to obtain the optimal response waveform of the detection system in the current time period, and obtaining the optimal transfer function, which is realized according to the following links A and B:

[0082] A. Avoid the infinite growth of the space family H(i), limit the maximum space capacity, and modify the iterative equation

[0083] Set the upper limit of the capacity of the waveform spaces contained in the space family to I (I > M), that is, when the number of waveform spaces contained in the space family after multiple growths is I, re-use the waveform space H I+1 as the first space, and grow a new space family based on it; for this purpose, modify the iterative equation as follows:

[0084]

[0085] During the growth process of the space family, use the waveform x kI+q in the space H kI+q shadow waveform vector as the new vector to replace the j-th vector in H kI+q which is actually the most original vector in H to form a waveform space H kI+q containing new information , where q and j have the following relationship: kI+q+1 ​

[0086] kI + q = nM + j, 1 ≤ j ≤ M, n ≥ 1, q ≤ i (23)

[0087] where i, j, q, and n are all positive integers.

[0088] B. Search for the projection vector with a relatively stable state in real time For the shadow vector Combine them to obtain the optimal response waveform of the detection system at the current time period, and obtain the optimal transfer function

[0089] The continuous innovation x i Add it to the waveform space family and perform continuous iterative update of the projection vector During this process, search for the projection vector with a relatively stable state The method is as follows:

[0090] Set L, σ (where L is a positive integer, 0 < σ < 0.1). When there are L consecutive Satisfying the following formula (24), it is determined that Is in a relatively stable state, and obtain the waveform according to formula (26) As the optimal response function waveform of the detection system at the current time period.

[0091]

[0092]

[0093]

[0094]

[0095] Obtain the z-domain expression of the waveform :

[0096]

[0097] Is the optimal transfer function H opt (z) of the detection system at the current time period; the time-domain expression of the waveform Is the optimal response function h opt (n) of the detection system at the current time period, and the expression is as follows:

[0098]

[0099] where δ(n - k) is the unit function sequence.

[0100] The real-time tracking of the response function and transfer function of the detection system is completed through steps ① to ⑤. The obtained response function and transfer function are characterized by real-time performance, providing a solid guarantee for the real-time correction of the subsequent pulse shaping algorithm and the accurate identification of the shaped pulse.

[0101] Taking the trapezoidal shaping of the pulse waveform as an example, the following illustrates how to update the trapezoidal shaping algorithm using the real-time obtained response function h opt (n) and transfer function H opt (z).

[0102] Given the rise time t a of the trapezoidal pulse, the sum t b of the rise time and flat-top time of the trapezoidal pulse, and the width t c of the trapezoidal pulse, its z-domain expression is as follows:

[0103]

[0104] In formula (30), A0 is the flat-top amplitude of the trapezoidal pulse, Y(z) represents the z-transform of the trapezoidal pulse, n a = t a / T s , n b = t b / T s , n c = t c / T s , T S is the sampling period.

[0105] Then, the current trapezoidal shaping algorithm is corrected in real time as follows:

[0106]

[0107] H T (z) is the z-domain expression of the trapezoidal shaping algorithm, h T (0) = 0, and truncation processing is performed on H T (z):

[0108]

[0109] n c See formula (30).

[0110] For the measured pulse waveform x′, the pulse after trapezoidal shaping is:

[0111]

[0112] Y(k) is the time-domain expression of the pulse after trapezoidal shaping.

[0113] In summary, by performing steps ① to ⑤, the response function and transfer function of the detection system are obtained in real time, and the obtained response function and transfer function are used for real-time correction of pulse shaping, avoiding the distortion of the shaped pulse waveform caused by fluctuations in the parameters of the detection system, and providing guarantee for the accurate acquisition of nuclear energy spectra.

[0114] As described above, the method for real-time tracking of the response function and transfer function of the detection system adds continuous new information to the waveform space family, enabling the waveform space family to be updated and grown in a timely manner. The obtained response function and transfer function are the optimal functions with the characteristics of "globality", "real-time", "accuracy", and "smoothness". This fully considers the following factors: the system parameter fluctuations caused by test conditions and the environment during the measurement process are a slow process with time correlation before and after, with the characteristics of "real-time change" and "smooth change"; the system function has the characteristics of random volatility and high-order complexity; the fluctuations of the system function indicate that its so-called "optimal" and "accurate" should be "global" "optimal" and "accurate" in the probabilistic sense. This lays a solid foundation for the real-time correction of subsequent pulse shaping algorithms and the accurate identification of shaped pulses, and can greatly improve the accuracy of energy spectrum measurement.

[0115] In the above embodiments of the present invention, the real-time tracking method for the response function and transfer function of the detection system has been described in detail. However, it should be noted that the above is only one embodiment of the present invention. When other types of system function identification and tracking methods involve using the methods described herein, the present invention is still valid. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A real-time tracking method for a system response function, characterized in that, The real-time tracking of the response function of the front-end analog system of a nuclear radiation detector is achieved through the following steps ① to ⑤: Step ①: Select M single-pulse waveform samples, unify the dimensions, and after normalization, obtain the basic waveform space H1, which is achieved as follows: Let the selected M single-pulse waveform samples be Each waveform sample has N sampling values as follows: The single-pulse waveform samples here refer to complete pulses that are separated from each other and have no overlap. Normalize the waveform to obtain the basic waveform space H1: In formula (2) Obtained from the following formula: Waveform consisting of N sampling values where i = 1, …, M; in formula (3) denotes the sum of all sampling values of the waveform Step ②, within the basic waveform space H1, obtain the projection of the observed waveform x1 and the shadow waveform vector which is implemented as follows: Let the first observed waveform vector be \(x_1 = [x_1(1)\ x_1(2)\...\ x_1(N)]\) T , and its projection onto the basis waveform space \(H_1\) is: They are respectively the projection components of x1 on ; The shadow waveform vector of x1 in the H1 space is: Step ③ adds the shadow waveform vector of the newly observed waveform x i as innovation to the waveform space H to derive a new waveform space H i . The growth of the waveform space family H is achieved by continuous iterative update and is implemented according to the following methods A and B: i+1 ​ A. When 1 ≤ i ≤ M: The shadow waveform vector of x1 in the H1 space Replace the most original vector in H1 with this new vector to form a waveform space H2 that contains new information : The shadow waveform vector of x2 in the H2 space Replace the most original vector in H2 with this new vector to form a waveform space H3 containing new information : And so on, using x i In H i The shadow waveform vector in the space As a new vector to replace the most primitive vector in H i To form a waveform space H containing innovation The method for obtaining is described later i+1 where is the projection of x i on H i ; The method for obtaining it is described later; The waveform spaces formed above are listed as follows: B. When i > M: Use x i In H i The shadow waveform vector in the space As a new vector to replace the j-th vector in H i Actually it is the most primitive waveform vector in H i To form a waveform space H containing innovations Where i and j have the following relationship: i+1 ​​ i = nM + j, 1 ≤ j ≤ M, n ≥ 1 (10) where i, j, and n are all integers; The waveform spaces formed above are listed as follows: Newly observed waveform x i , x i The shadow waveform vector on the waveform space H i And the relationship between the projection of x i On H i And the waveform space family H(i) is summarized as follows: And the relationship between the projection of where H(i) is a family of waveform spaces composed of i adjacent waveform spaces H1, H2, …, H i and X(i) is a set of observed waveforms x1, x2, …, x i . Waveform projection in step ④ among the above steps is obtained by the following steps A to C: A. Design performance indicators As follows, find the Find the partial derivative: Let It is obtained that: So sought It is called the optimal projection vector based on the waveform space family H(i), which is x1,x2,…,x i In the waveform space H1, H2, ..., H i The common projections on these waveform spaces H1, H2, ..., H i It is a manifestation of homogeneity; B. Obtain the optimal projection vector of adjacent space families H(i - 1) and H(i). and relationship, that is, add the shadow waveform vector of x i-1 to the space family H(i - 1) to grow a new space family H(i), and obtain the optimal projection of H(i) from H(i) and the waveform set X(i) containing the innovation x i as follows: The derivation is as follows: C. Obtain the optimal projection of H(i) The recursive process is implemented according to the following steps (a) to (c): (a) Set the initial value: Substitute and x1 = [x1(1) x1(2)... x1(N)] T into the above formula respectively; (b) Obtaining of: Take as the new vector to replace the most original vector in H1 to obtain H2, then obtain the waveform set X(2) and the waveform space family H(2) according to formula (14), and further obtain: (c) (c) obtaining: According to step ③, is used as a new vector to replace the most original vectors in H1, H2, …, H i-1 respectively, to obtain waveform spaces H2, H3, …, H i , and the waveform space family H(i) is obtained by combining according to (14), and further: Step ⑤ avoids the infinite growth of the spatial family H(i), limits the maximum spatial capacity, modifies the iterative equation; and searches in real time for a projection vector with a relatively stable state Combine the shadow vectors to obtain the optimal response waveform of the detection system in the current period, and obtain the optimal transfer function, which is implemented according to the following steps A and B: A. To avoid the infinite growth of the space family H(i), limit the maximum space capacity and modify the iterative equation Set the upper limit of the capacity of the waveform spaces contained in the space family to I (I > M), that is, when the number of waveform spaces contained in the space family reaches I after multiple growths, re-use the waveform space H I+1 as the first space and grow a new space family based on it; for this purpose, modify the iterative equation as follows: During the growth of the space family, using the waveform x kI+q In the space H kI+q The shadow waveform vector of As a new vector to replace the j-th vector in H kI+q Which is actually the most primitive vector in H To form a waveform space H containing new information kI+q Where q and j have the following relationship: The waveform space H kI+q+1 Where q, j have the following relationship: kI + q = nM + j, 1 ≤ j ≤ M, n ≥ 1, q ≤ i (23) where i, j, q, and n are all positive integers; B. Search for projection vectors with relatively stable states in real time For the shadow vector Combine them to obtain the optimal response waveform of the detection system in the current period and obtain the optimal transfer function Continuous innovation x i Add to the waveform space family and perform projection vectors Continuous iterative update, during which a projection vector with a relatively stable state is searched for The method is as follows: Set \(L\) and \(\sigma\) (where \(L\) is a positive integer and \(0 < \sigma < 0.1\)). When there are \(L\) consecutive satisfying the following formula (24), it is determined that is in a relatively stable state, and the waveform is obtained according to formula (26) as the best response function waveform of the detection system in the current period; Obtain the waveform z-domain expression of: is the optimal transfer function H opt (z) of the detection system in the current period; the waveform in the time domain is the optimal response function h opt (n) of the detection system in the current period, and the expression is as follows: where δ(n - k) is the unit function sequence; Through steps ① to ⑤, the real-time tracking of the response function and transfer function of the detection system is completed.

2. A real-time tracking method for a system response function, characterized in that, The update of the trapezoidal shaping algorithm using the response function and transfer function obtained in claim 1 is achieved as follows: The rise time t of the given trapezoidal pulse a , the sum t of the rise time and the flat-top time of the trapezoidal pulse b , and the width t of the trapezoidal pulse c , whose z-domain expression is as follows: In formula (30), A0 is the flat-top amplitude of the trapezoidal pulse, Y(z) represents the z-transform of the trapezoidal pulse, and n a = t a / T s , n b = t b / T s , n c = t c / T s , T S is the sampling period; Then, the current trapezoidal shaping algorithm is corrected in real time as follows: H T (z) is the z-domain expression of the trapezoidal shaping algorithm, h T (0) = 0. For H T (z), perform truncation processing: n c See formula (30); For the measured pulse waveform x′, the pulse after trapezoidal shaping is: Y(k) is the time-domain expression of the pulse after trapezoidal shaping.

Images