Pulse waveform identification and forming method based on dynamic space series decomposition

Abstract

The invention discloses a pulse waveform identification and forming method based on dynamic space series decomposition. Aiming at the difficulty in identifying and forming high-order, complex and fluctuating analog pulse signals, the order of a model, the number of primary functions and parameters are adaptively and dynamically adjusted to search a matched function space, the types of the primary functions are flexibly selected, complex pulses are represented in the form of series, the number of components in the series and the parameters of each component can be dynamically adjusted according to precision requirements, and the accuracy of the signals is improved. Complex waveform forming is converted into simple finite term series component forming, forming calculation becomes accurate, convenient and fast, and forming normalization and energy spectrum measurement accuracy are ensured.

Description

Technical Field

[0001] The invention relates to a pulse waveform recognition and shaping method based on dynamic space series decomposition. Background Art

[0002] The front-end analog system of the nuclear radiation detector is composed of the detector, preamplifier, CR / RC network, amplifier circuit and conditioning circuit designed to adapt to specific radiation scenarios. When these circuit links are numerous and the composition is complex and diverse, the pulse signal output by the system has the characteristics of diversity and complex waveform, that is, it is complex and high-order. In addition, when the detection system is affected by the test conditions and the ambient temperature and humidity, the parameters of its electronic components (such as the amplification factor of the photomultiplier tube and its spectral response, the photon yield of the scintillator, the amplification factor of the linear pulse amplifier, etc.) will fluctuate and change over time, resulting in the output pulse waveform still having volatility, drift and distortion. In fact, the complexity, diversity, volatility, drift and distortion of the output pulses of the front-end analog system are manifested as follows: the mathematical model of the pulse signal is of a high order (possibly infinitely high), the order of the model often changes and is difficult to accurately know, and the form of the model often fluctuates; therefore, when the pulse signal is subsequently digitized and waveform-shaped (for example, standard Gaussian, quasi-Gaussian SK, trapezoidal, bullet-shaped and other emerging shaping methods, etc.) to obtain the pulse amplitude, due to the high-order complexity, volatility and uncertainty of the pulse signal model, it is difficult to design a digital waveform shaping algorithm or to ensure the standardization of the pulse after shaping, which in turn leads to a reduction in the accuracy of the energy spectrum measurement or even failure. In summary, in order to accurately digitize high-order, complex, fluctuating and distorted analog pulse signals, it is particularly important to know the accurate physical model of the pulse signal before shaping; however, it is difficult to use a matching waveform fitting method to obtain an accurate model of the pulse signal without knowing the order and model form of the pulse signal; especially when the waveform order changes and the model form fluctuates, it is even more difficult to find an adaptive model to meet the waveform shaping needs. Therefore, it is necessary to develop a new and effective method that can adaptively adjust the order, form and parameters of the model according to the complex characteristics of the pulse signal, establish a dynamically changing mathematical model for the pulse waveform, and then achieve the purpose of accurate identification of the pulse signal and subsequent accurate digital shaping, and ultimately provide a guarantee for the accurate measurement of the energy spectrum. The present invention adopts a pulse waveform recognition and shaping method based on dynamic spatial series decomposition to solve the above problems. Summary of the invention

[0003] The purpose of the present invention is to disclose a pulse waveform recognition and shaping method based on dynamic spatial series decomposition, which is used to establish a dynamic adaptive mathematical model for the high-order, complex, and diverse pulse signal waveforms output by the front-end analog system of a nuclear radiation detector, that is, the order, form and parameters of the model can be adaptively adjusted, thereby achieving the purpose of accurate recognition of the pulse signal and subsequent accurate digital shaping, and ultimately providing a guarantee for the accurate measurement of the energy spectrum.

[0004] The present invention relates to a pulse waveform recognition and shaping method based on dynamic space series decomposition, which is realized through the following steps ① to ④.

[0005] Step ① Design M functions as the function space H M The basis function and the correlation matrix L of the basis function are obtained M In practical applications, the type of basis function may be determined according to needs and waveform characteristics, and it is not necessary to select the same type as the basis function in this step.

[0006] Step ② Find the measured pulse waveform x(k) (k = 1, ..., N) in the function space H M Projection inside Based on the correlation matrix L M and projection And in the function space H M Search for similar functions of x(k) in

[0007] Step ③ Calculate the pulse waveform x(k) and similar waveforms The error E M , according to the error E M The size and function space H M Dimension M; follow the steps below 3S 1 ~3S 2 accomplish:

[0008] Step 3S 1 :Calculate the pulse waveform x(k) and similar waveform The error E M .

[0009] Step 3S 2 There are three cases: A, B, and C:

[0010] Case A: If E M >E 0 , and M <M 0 , expand the function space to H M+1 , and given in the function space H M+1 Search for similar functions of x(k) in The recursive algorithm, E 0 and M0 are the upper limit of error and the upper limit of dimension respectively; let M=M+1 and return to step ③ to continue.

[0011] Case B: If E M >E 0 , and M ≥ M 0 , for M 0 and τ, and return to step ① to continue.

[0012] Case C: If E M ≤E 0 , proceed to step ④.

[0013] Step ④: The waveform similarity function obtained in the above steps Find the z-domain expression And the shaping algorithm of the measured pulse waveform x is given.

[0014] In summary, through steps ① to ④, a dynamically changing basis function is used to form a function space, the pulse waveform x output by the detection system is projected into the function space, and the similar function (or similar waveform) of the pulse waveform x in the function space is searched based on the projection vector. Reconstruct the pulse waveform x in series form within the error tolerance range; finally, based on the similarity function (or similar waveform) The shaping algorithm of the pulse waveform x is obtained by using the series components of the pulse waveform.

[0015] The beneficial effects of the present invention are: When the front-end analog system of a nuclear radiation detector is designed to adapt to specific radiation scenarios, the circuit links are numerous and the configuration is complex and diverse, the pulse signal output by the system has the characteristics of diversity and waveform complexity, that is, it is complex and high-order. In addition, when the detection system is affected by test conditions and environmental temperature and humidity, the parameters of its electronic components will fluctuate and change over time, resulting in the output pulse waveform still having volatility, drift and distortion. The front-end analog system based on the above situation has the characteristics of high order (possibly infinitely high) in its output of complex, diverse, fluctuating, drifting and distorted pulse signals, the mathematical model of which has the characteristics of constant change in order and fluctuation in model form. For such complex pulse signals, when subsequent digital waveform shaping is performed to obtain the pulse amplitude, it will be difficult to design the digital waveform shaping algorithm or to ensure the standardization of the pulse after shaping, which will lead to reduced accuracy or even failure of energy spectrum measurement. In summary, in order to accurately digitize high-order, complex, fluctuating and distorted analog pulse signals, it is particularly important to know the accurate physical model of the pulse signal before shaping; however, it is difficult to use a matching waveform fitting method to obtain an accurate model of the pulse signal without knowing the order and model form of the pulse signal; especially when the waveform order changes and the model form fluctuates, it is even more difficult to find an adaptive model to meet the waveform shaping needs. To this end, the present invention adopts a pulse waveform recognition and shaping method based on dynamic spatial series decomposition to solve the above problems. The beneficial effects of this method are: (1) according to the complex characteristics of the pulse signal, the order of the model can be adaptively adjusted dynamically; (2) according to the fluctuation characteristics of the pulse signal, the number and parameters of the basis functions can be adaptively adjusted dynamically to search for the function space that matches the pulse waveform; (3) according to the waveform characteristics of the pulse signal, the type of basis function suitable for the specific situation can be flexibly selected; (4) in mathematical expression, the complex pulse is represented in the form of a series, and the parameters and number of components of each component in the series expression can be dynamically adjusted according to the accuracy requirements; (5) it achieves: accurate mathematical expression of complex, high-order, fluctuating and even distorted pulse signals, overcomes the problem of non-standard and inaccurate shaping pulses caused by the mismatch between the mathematical model of the pulse waveform and the subsequent shaping algorithm, and transforms the complex waveform shaping into a simple shaping of finite series components, making the shaping calculation accurate, convenient and fast, ensuring the standardization of the shaping and the accuracy of the energy spectrum measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0017] The following is a detailed description of an embodiment of the present invention in conjunction with the accompanying drawings. This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and process are given, but the protection scope of the present invention is not limited to the following embodiment.

[0018] The present invention relates to a pulse waveform recognition and shaping method based on dynamic space series decomposition, which is realized through the following steps ① to ④.

[0019] Step ① Design M functions as basis functions, and the function space they span is denoted as H M , and find the correlation matrix L of the basis function M ; Follow the steps (1) to (2) below to achieve:

[0020] (1) The designed M basis functions are recorded as: Each basis function There are N sample values: Right now The sampling value expression is: The parameter τ is set by yourself; note: in practical applications, the type of basis function can be determined according to needs and waveform characteristics, and it is not necessary to choose the same type as the basis function in this step.

[0021] (2) Correlation matrix L of basis functions M for: L M The element expression in is shown in formula (4); In formula (4): i = 1, ..., M; j = 1, ..., M; L M Using the basis function matrix φ M It is expressed as: The basis function matrix φ in formula (5) M as follows: φ M The element expression in is shown in formula (7):

[0022] Step ② Find the measured pulse waveform x(k) (k = 1, ..., N) in the function space H M Projection inside And in the function space H M Search for similar functions of x(k) in Follow the steps (1) to (2) below to achieve:

[0023] (1) The pulse waveform x(k) in the function space H M Projection inside Calculate according to the following formulas (8) to (10): Right now: Where x = [x(1)x(2)…x(N)] T .

[0024] (2) Based on the correlation matrix L M and projection In the function space H M Search for similar functions of x(k) in Follow the steps A and B below to achieve:

[0025] A. Write similarity functions The expression because but It can be expressed by the following formula: in, called The weight vector of is obtained in step B; and

[0026] B. Find similarity function The weight vector To obtain similarity function First, write out x(k) and the similarity function The sum of squared errors J: And find the partial derivative: Combined with φ M , L M and projection The expression of further derives formulas (14) to (16); in YesL M The inverse matrix of Further expressed as: Then, we obtain the weight vector as follows: Finally, substituting equation (18) into equation (11), we obtain That is, x(k) in the function space H M Similar functions in Here the similarity function Also called the pulse waveform x(k) (k = 1, ..., N) in the function space H M Similar waveforms within.

[0027] Step ③ Calculate the pulse waveform x(k) and similar waveforms The error E M , according to the error E M The size and function space H M Dimension M; follow the steps below 3S 1 ~3S 2 accomplish:

[0028] Step 3S 1:Calculate the pulse waveform x(k) and similar waveform The error E M

[0029] Step 3S 2 It is implemented in three situations: A, B, and C:

[0030] Case A: If E M >E 0 , and M <M 0 , follow the steps (1) to (6) below to expand the function space to H M+1 , and given in the function space H M+1 Search for similar functions of x(k) in The recursive algorithm, E 0 and M 0 They are the upper limit of error and the upper limit of dimension respectively: (1) Add basis functions Depend on As a function space H M+1 The basis function of H M+1 The basis function matrix φ M+1 as follows: in, (2) Find the pulse waveform x(k) in the function space H M+1 Projection inside (3) Find the function space H M+1 The correlation matrix L M+1 : L M+1 The element expression in is shown in formula (24); In formula (24): i = 1,…,M+1; j = 1,…,M+1. L M+1 Further expressed as: (4) Constructing weight vector in, And the following relationship holds: (5) Find the weight vector The recursive algorithm of The calculation method of is shown in formulas (28) to (33): Further conclusion: make but Obtain The recursive formula is as follows: Then the similarity function The calculation method is as follows: (6) Let M=M+1 and return to step ③ to continue.

[0031] Case B: If E M >E 0 , and M ≥ M 0 , press the formula to M 0 and τ are corrected, M 0 =pM 0 τ=τ / p (34) Where p is an integer greater than 1; return to step ① and continue.

[0032] Case C: If E M ≤E 0 , proceed to step ④.

[0033] Step ④: The waveform similarity function obtained in the above steps Find the z-domain expression A shaping algorithm for the measured pulse waveform x is given and implemented according to the following steps (1) to (2).

[0034] (1) The similarity function is given by the following equation (35): The z-domain expression shown in formula (36) is obtained

[0035] (2) Using similarity function The shaping algorithm for the pulse waveform x is: Assume that the desired pulse waveform after shaping is y(k) and its z domain is Y(z), then the similarity function The z-domain algorithm H(z) for shaping the pulse waveform y(k) is: Take y(k) as an example of a trapezoidal pulse, and give the rise time t of the trapezoidal pulse a , the sum of the trapezoidal pulse rise time and the flat top time t b , and the width of the trapezoidal pulse t c , its z-domain expression is as follows: In formula (38), A 0 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; Similarity Function The z-domain algorithm H(z) for forming a trapezoidal pulse y(k) is: Truncate H(z): n c See formula (38), h(0)=0. The time domain recursive algorithm for trapezoidal shaping of the measured pulse waveform x is: Y x (k) is the time domain expression of the pulse after trapezoidal shaping of x.

[0036] In summary, through steps ① to ④, a dynamically changing basis function is used to form a function space, the pulse waveform x output by the detection system is projected into the function space, and the similar function (or similar waveform) of the pulse waveform x in the function space is searched based on the projection vector. Reconstruct the pulse waveform x in series form within the error tolerance range; finally, based on the similarity function (or similar waveform) The shaping algorithm of the pulse waveform x is obtained by using the series components of the pulse waveform.

[0037] As described above, the pulse waveform recognition and shaping method based on dynamic spatial series decomposition can dynamically and adaptively adjust the order of the model according to the complex characteristics of the pulse signal; can dynamically and adaptively adjust the number and parameters of the basis functions according to the fluctuation characteristics of the pulse signal to search for the function space that matches the pulse waveform; can flexibly select the type of basis function suitable for the specific situation according to the waveform characteristics of the pulse signal; in mathematical expression, the complex pulse is represented in the form of a series, and the parameters and number of components of each component in the series expression can be dynamically adjusted according to the accuracy requirements; can accurately mathematically express complex, high-order, fluctuating and even distorted pulse signals, and overcome the problem of irregular and inaccurate shaping pulses caused by the mismatch between the mathematical model of the pulse waveform and the subsequent shaping algorithm; transform the complex waveform shaping into the shaping of simple finite series components, making the shaping calculation accurate, convenient and fast. This lays a solid foundation for the accurate identification of the subsequent pulse after shaping, and can greatly improve the accuracy of energy spectrum measurement.

[0018] In the above-mentioned embodiment of the present invention, the pulse waveform recognition and shaping method based on dynamic spatial series decomposition is described in detail, but it should be noted that the above is only one embodiment of the present invention. When the dynamic search and recognition method based on other types of basis functions involves the use of the method mentioned in this article, the present invention is still valid. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A pulse waveform recognition and shaping method based on dynamic spatial series decomposition, characterized in that: The waveform recognition and shaping of the pulse signal is achieved through the following steps ① to ④: Step ① Design M functions as basis functions, and the function space they span is denoted as H M , and find the correlation matrix L of the basis function M ; Follow the steps (1) to (2) below to achieve: (1) The designed M basis functions are recorded as: Each basis function There are N sample values: Right now The sampling value expression is: The parameter τ is set by yourself; (2) Correlation matrix L of basis functions M for: L M The element expression in is shown in formula (4); In formula (4): i = 1, ..., M; j = 1, ..., M; L M Using the basis function matrix φ M It is expressed as: The basis function matrix φ in formula (5) M as follows: φ M The element expression in is shown in formula (7): Step ② Find the measured pulse waveform x(k) (k = 1, ..., N) in the function space H M Projection inside And in the function space H M Search for similar functions of x(k) in Follow the steps (1) to (2) below to achieve: (1) The pulse waveform x(k) in the function space H M Projection inside Calculate according to the following formulas (8) to (10): Right now: Where x = [x(1)x(2)…x(N)] T ; (2) Based on the correlation matrix L M and projection In the function space H M Search for similar functions of x(k) in Follow the steps A and B below to achieve: A. Write similarity functions The expression because but It can be expressed by the following formula: in, called The weight vector of is obtained in step B; and B. Find similarity function The weight vector To obtain similarity function First, write out x(k) and the similarity function The sum of squared errors J: And find the partial derivative: Combined with φ M , L M and projection The expression of further derives formulas (14) to (16); in YesL M The inverse matrix of Further expressed as: Then, we obtain the weight vector as follows: Finally, substituting equation (18) into equation (11), we obtain That is, x(k) in the function space H M Similar functions in Here the similarity function Also called the pulse waveform x(k) (k = 1, ..., N) in the function space H M Similar waveforms within Step ③ Calculate the pulse waveform x(k) and similar waveform The error E M , according to the error E M The size and function space H M The dimension M is implemented as follows: Step 3S1: Calculate the pulse waveform x(k) and similar waveform The error E M Step 3S2 is executed in three cases: A, B, and C: Case A: If E M > E0 and M < M0, expand the function space to H according to the following steps (1) to (6) M+1 , and give the recurrence algorithm for searching the similar function of x(k) in the function space H M+1 . E0 and M0 are the error upper limit and the dimension upper limit respectively: ​ (1) Add basis functions Depend on As a function space H M+1 The basis function of H M+1 The basis function matrix φ M+1 as follows: in, (2) Find the pulse waveform x(k) in the function space H M+1 Projection inside (3) Find the function space H M+1 The correlation matrix L M+1 : L M+1 The element expression in is shown in formula (24); In formula (24): i = 1, ..., M + 1; j = 1, ..., M + 1; L M+1 Further expressed as: (4) Constructing weight vector in, And the following relationship holds: (5) Find the weight vector The recursive algorithm of The calculation method of is shown in formulas (28) to (33): Further conclusion: make but Obtain The recursive formula is as follows: Then the similarity function The calculation method is as follows: (6) Set M = M + 1 and return to step ③ to continue; Case B: If E M >E0, and M≥M0, M0 and τ are corrected as follows: M0=pM0 τ=τp (34) Where p is an integer greater than 1; return to step ① and continue; Case C: If E M ≤E0, proceed to step ④; Step ④: The waveform similarity function obtained in the above steps Find the z-domain expression The shaping algorithm of the measured pulse waveform x is given and implemented according to the following steps (1) to (2): (1) The similarity function is given by the following equation (35): The z-domain expression shown in formula (36) is obtained (2) Using similarity function The shaping algorithm for the pulse waveform x is: Assume that the desired pulse waveform after shaping is y(k) and its z domain is Y(z), then the similarity function The z-domain algorithm H(z) for shaping the pulse waveform y(k) is: Take y(k) as an example of a trapezoidal pulse, and give the rise time t of the trapezoidal pulse a , the sum of the trapezoidal pulse rise time and the flat top time t b , and the width of the trapezoidal pulse t c , its z-domain expression is as follows: In formula (38), 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; Similarity Function The z-domain algorithm H(z) for forming a trapezoidal pulse y(k) is: Truncate H(z): n c See formula (38), h(0) = 0; The time domain recursive algorithm for trapezoidal shaping of the measured pulse waveform x is: Y x (k) is the time domain expression of the pulse after the trapezoidal shaping of x.

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