A multi-layer optimized mapping pulse waveform classification method

Abstract

The application discloses a kind of multi-layer optimization mapping pulse waveform classification methods.First, according to waveform feature, establish normalized orthogonal function set;Then, the feature vector after mapping of all samples in function space in pulse waveform training set is solved;Then, twice projection (i.e nonlinear projection and optimal direction linear projection) is carried out to feature vector, to obtain critical decision point;Finally, unknown waveform is identified based on critical decision point to obtain its final destination class.This method classifies complex and diverse pulse waveforms, facilitating subsequent digital waveform shaping methods and waveform parameter identification methods based on categories, overcoming the high sensitivity of waveform shaping and parameter identification methods to pulse order and waveform complexity, ultimately providing protection for accurate measurement of energy spectrum under complex conditions.

Description

Technical Field

[0001] This invention relates to a pulse waveform classification method with multi-layer optimized mapping. Background Technology

[0002] The front-end simulation system of a nuclear radiation detector consists of a detector, preamplifier, CR / RC network, amplifier circuit, and conditioning circuit. The configuration of the front-end simulation system is complex and varied. Therefore, the output pulse signal waveform may exhibit diversity and complexity, manifesting as different orders in the s-domain, meaning that the number of components and the composition of each component differ. For example, in complex radioactive environments (e.g., where multiple types of radiation coexist), multiple types of detectors need to be used in conjunction for measurement, and the measured pulse signal waveform may exhibit complexity and diversity. Because the pulses output by the front-end analog system are complex and diverse, their mathematical models have varying orders (some may be infinitely high), meaning the number of components and their constituent fractions differ in a single pulse. Therefore, when subsequently performing digital waveform shaping on the pulse signal (e.g., standard Gaussian, quasi-Gaussian SK, trapezoidal, bullet-shaped, and other emerging shaping methods) to obtain the pulse amplitude, it is essential to design corresponding algorithms based on the order of the pulse signal model and the specific parameters of each component. Otherwise, the accuracy of the energy spectrum measurement will decrease or even fail. For example, in the case of pulse signal order misjudgment, the shaping method based on the mathematical model may result in a distortion at the top of the trapezoidal shape due to coefficient mismatch, ultimately leading to a decrease in the accuracy of the obtained pulse amplitude and energy spectrum. In radiometric measurements, when pulse waveforms exhibit multiple orders and shapes (e.g., in radiation scenarios involving multiple detectors measuring various types of radiation), it is essential to classify the pulses (e.g., based on order or waveform characteristics) and then employ corresponding shaping and identification methods to ensure the accuracy of the acquired pulse waveform amplitude and energy spectrum information. This invention employs a multi-layer optimized mapping pulse waveform classification method to categorize pulses in cases with multiple waveform types. This facilitates subsequent qualitative and quantitative analysis of the pulses using appropriate matching algorithms, ultimately ensuring accurate radiometric measurements. Summary of the Invention

[0003] The purpose of this invention is to disclose a multi-layer optimized mapping pulse waveform classification method, which classifies the complex and diverse pulse waveforms output by the front-end simulation system of a nuclear radiation detector. This facilitates subsequent digital waveform shaping and waveform parameter identification methods based on the categories, overcoming the high sensitivity of waveform shaping and parameter identification methods to pulse order and waveform complexity and diversity. Ultimately, this provides a guarantee for the accuracy of radioactive measurements (e.g., energy spectrum measurements) under complex conditions.

[0004] This invention relates to a pulse waveform classification method based on multi-layer optimized mapping, which is achieved through the following steps ① to ④.

[0005] Step ①: Design M basis functions and obtain the normalized orthogonal function set. The function space spanned by the orthogonal function set is denoted as H. M .

[0006] Step ② Calculate all samples x in the pulse waveform training set. i (t)(a≤t≤b) in function space H M The eigenvector X within i The set of feature vectors of the l-th and j-th samples is denoted as A. lj Initialize l = 2 and j = 1; and define an L-dimensional array NumClass, initialized to 0.

[0007] Step ③ uses ω from the training set l With ω j The sample in function space H M The feature vectors in the data are used to perform a rough classification and identification of the unknown sample x′(t) (a≤t≤b) based on a nonlinear projection method (i.e., roughly identify it as ω). l Class or ω j (Class), implement according to the following steps 3S1~3S4: Step 3S1: Calculate ω l The feature vectors of sample class A lj The average value of the nonlinear mapping in Step 3S2: Calculate ω j The feature vectors of sample class A lj The average value of the nonlinear mapping in Step 3S3: Find ω l Class and ω j Two types of critical decision points w0; Step 3S4 involves roughly classifying the unknown sample x′(t) (a≤t≤b) to be classified (i.e., roughly identifying it as ω). l Class or ω j (Class), proceed as follows (1) to (3): (1) Find x′(t) (a≤t≤b) in the function space H M The eigenvector X′ within; (2) Place the eigenvector X′ in set A lj After performing a nonlinear mapping, in the optimal direction The projection value y is obtained by projecting it again: (3) Based on the projection value y of the feature vector X′, perform binary discrimination on the unknown sample x′(t), that is, classify x′(t) as ω. l Class or ω j Classes, in the following way: If y > w0, then x′(t) belongs to ω l Classify and correct NumClass(l) = NumClass(l) + 1; otherwise, x′(t) belongs to ω. j The class is modified, and NumClass(j) = NumClass(j) + 1 is corrected. If j < l-1, then correct j = j+1 and return to step 3S1 to continue execution; otherwise, proceed to step ④.

[0008] Step ④ If l < L, reset l = l + 1 and j = 1, and return to step ③ to continue the loop; otherwise, take the index corresponding to the largest element in the array NumClass as the final class of x′(t). For example, if NumClass(k) is the maximum value, then the pulse waveform x′(t) is assigned to ω. k kind.

[0009] In summary, through steps ① to ④, a multi-layer optimized mapping pulse waveform classification method was adopted to classify complex and diverse pulse waveforms.

[0010] The beneficial effects of this invention are: In radiometric measurements, when pulse waveforms exhibit multiple orders and shapes (e.g., in radiation scenarios involving multiple detectors and various types of rays), it is essential to categorize the pulses (e.g., based on order or waveform characteristics) and then employ corresponding shaping and identification methods to ensure the accuracy of the acquired pulse waveform amplitude and energy spectrum information. This invention employs a multi-layer optimized mapping pulse waveform classification method to categorize pulses in cases where multiple types of pulse waveforms exist. The beneficial effects of this method are: (1) Designing a matching orthogonal normalization function set based on the characteristics of various pulse waveforms in the pulse dataset, and obtaining feature vectors by mapping the waveforms based on the function set, effectively extracting pulse waveform feature information; (2) Transforming high-dimensional time-domain waveform features into finite-dimensional feature vectors, and simultaneously transforming the "insignificant differences" between pulse waveforms in the time domain into "significant differences" in feature vectors, facilitating accurate separation of pulse waveforms; (3) Performing nonlinear projection on the feature vectors of pulse waveforms, realizing... (3) Further separation between the feature vectors of various types of pulse waveforms was achieved, laying a solid foundation for accurate identification of pulse waveform types; (4) The feature vectors after nonlinear mapping were projected again in the optimal direction, ensuring accurate identification of pulse waveform types; (5) After accurately classifying complex and diverse pulse waveforms, it is convenient for subsequent digital waveform shaping and waveform parameter identification methods to be carried out based on categories, and then corresponding matching algorithms are adopted for qualitative and quantitative analysis of pulses, overcoming the high sensitivity of waveform shaping and parameter identification methods to pulse order and waveform complexity and diversity, and finally providing a guarantee for the accuracy of radioactive measurement (e.g., energy spectrum measurement) under complex conditions. Attached Figure Description

[0011] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0012] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. These embodiments are implemented based on the technical solution of the present invention and provide detailed implementation methods and processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0013] This invention relates to a pulse waveform classification method based on multi-layer optimized mapping, which is achieved through the following steps ① to ④.

[0014] Step ①: Design M basis functions and obtain the normalized orthogonal function set, as follows: (1) to (2)

[0015] (1) Taking pulse waveform classification and recognition with s-domain expression as shown in formula (1) and poles being real numbers as an example, the designed basis functions are f1(t), f2(t), f3(t), ..., f M (t); The number of basis functions is M, and the expression of each basis function is shown in formula (2): Where the parameter τ m M is set automatically based on the characteristics of the pulse waveform.

[0016] (2) Obtain the normalized orthogonal function set according to the following formulas (3) to (6): Right now: In formula (3) φ k (t) is calculated according to the following formula (5), <f m (t),φ k (t)> is calculated according to the following formula (6); From φ1(t),φ2(t),φ3(t),...,φ M (t) forms a normalized orthogonal function set, and the function space spanned by it is denoted as H. M .

[0017] Step ② Calculate all samples x in the pulse waveform training set. i (t)(a≤t≤b) in function space H M The eigenvector X within i This can be achieved using the following formula (7): Where x i (t)(a≤t≤b) represents the i-th pulse waveform sample in the training set, with a total of N samples; the feature vector X i The elements are shown in formula (8); Where X i =[X i (1),X i (2),...,X i (M)],X i (m) is X i The m-th element; Suppose there are L classes of samples in the pulse waveform training set, and the class of the l-th (l=1,...,L) sample is denoted by ω. l It means that ω l The number of samples of each class is N. l ,but: ω l The feature vector of sample p in class sample is denoted as: The set of feature vectors of samples of class l and class j is denoted as A. lj ; To prepare for the execution of subsequent steps, initialize l=2 and j=1; and define the L-dimensional array as NumClass=[NumClass(1),NumClass(2),...,NumClass(L)], and initialize it to 0.

[0018] Step ③ uses ω from the training set l With ω j The sample in function space H M The feature vectors in the data are used to perform a rough classification and identification of the unknown sample x′(t) (a≤t≤b) based on a nonlinear projection method (i.e., roughly identify it as ω). l Class or ω j (Class), implement according to the following steps 3S1~3S4:

[0019] Step 3S1: Calculate ω l The feature vectors of sample class A lj The average value M of the nonlinear mapping in l : Where N′=N l +N j , It is an N′×1 matrix. Represents ω l All feature vectors of class samples in set A lj The average value after performing a nonlinear mapping on the q-th vector; here, the nonlinear mapping... As shown in formula (12).

[0020] Step 3S2: Calculate ω j The feature vectors of sample class A lj The average value of the nonlinear mapping in Where N′=N l +N j , It is an N′×1 matrix. Represents ω j All feature vectors of class samples in set A lj The average value after performing a nonlinear mapping on the q-th vector; here, the nonlinear mapping... As shown in formula (14).

[0021] Step 3S3: Find ω l Class and ωj The two critical decision points w0 of the class are given by the following formula (15); In formula (15) Calculate using the following formulas (16) to (17): in, For ω l The average vector after nonlinear mapping of sample In the optimal direction Projection on; For ω j The average vector after nonlinear mapping of sample In the optimal direction The projection on the surface. The optimal direction in formula (17) It is given by the following formula (18): In formula (18), I is the identity matrix, and υ is the matrix that makes B υ For positive definite matrices, T represents the matrix transpose, and D is an additional variable. l For N l ×N l A matrix whose elements are D j For N j ×N j A matrix whose elements are C l and C j As shown in formulas (19) and (20);

[0022] Step 3S4 involves roughly classifying the unknown sample x′(t) (a≤t≤b) to be classified (i.e., roughly identifying it as ω). l Class or ω j (Class), proceed as follows (1) to (3):

[0023] (1) Find x′(t) (a≤t≤b) in the function space H M The eigenvector X′ within the region is shown in formula (21). Where X′=[X′(1),X′(2),...,X′(M)], and X′(m) is the m-th element of X′.

[0024] (2) Place the eigenvector X′ in set A lj After performing a nonlinear mapping, in the optimal direction The projection value y is obtained by projecting it again: Where X q It is A lj The q-th vector in the set.

[0025] (3) Based on the projection value y of the feature vector X′, perform binary discrimination on the unknown sample x′(t), that is, classify x′(t) as ω. l Class or ω j Classes, in the following way: If y > w0, then x′(t) belongs to ω l Classify and correct NumClass(l) = NumClass(l) + 1; otherwise, x′(t) belongs to ω. j The class is modified, and NumClass(j) = NumClass(j) + 1 is corrected. If j < l-1, then correct j = j+1 and return to step 3S1 to continue execution; otherwise, proceed to step ④.

[0026] Step ④ If l < L, reset l = l + 1 and j = 1, and return to step ③ to continue the loop; otherwise, take the index corresponding to the largest element in the array NumClass = [NumClass(1), NumClass(2), ..., NumClass(L)] as the final class to which x′(t) belongs. For example, if NumClass(k) is the maximum value, then the pulse waveform x′(t) belongs to ω. k kind.

[0027] In summary, through steps ① to ④, a function space is constructed using dynamically changing basis functions. The pulse waveform x output by the detection system is projected into the function space, and similar functions (or similar waveforms) of the pulse waveform x in the function space are searched based on the projection vector. Within the allowable error range, the pulse waveform x is reconstructed in series form; finally, it is based on a similarity function (or similar waveform). An algorithm for obtaining the shaping of pulse waveform x by series components.

[0028] As described above, a pulse waveform classification method based on a multi-layer optimized mapping is used to classify the complex and diverse pulse waveforms output by the front-end simulation system of a nuclear radiation detector. This facilitates subsequent digital waveform shaping and waveform parameter identification methods based on these categories, overcoming the high sensitivity of waveform shaping and parameter identification methods to pulse order and waveform complexity. Ultimately, this ensures the accuracy of radioactive measurements (e.g., energy spectrum measurements) under complex conditions.

[0029] In the above embodiments of the present invention, a pulse waveform classification method based on multi-layer optimized mapping has been described in detail. However, it should be noted that the above description is only one embodiment of the present invention. When other forms of classification and identification involve the use of the method proposed herein, the present invention is still effective. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A pulse waveform classification method with multi-layer optimized mapping, characterized in that, Classifying pulse signal waveforms involves the following steps ① ④ Achieved: Step ① Design M basis functions and obtain the normalized orthogonal function set, as follows: (1)~(2) (1) Using the s-domain expression as shown in formula (1), pulse waveforms with real poles are classified and identified. The designed basis functions are as follows: The number of basis functions is M, and the expression of each basis function is shown in formula (2): (1) (2) Where parameters And M is set automatically based on the characteristics of the pulse waveform; (2) Obtain the normalized orthogonal function set according to the following formulas (3) to (6): (3) Right now: (4) In formula (3) Calculate according to the following formula (5), Calculate according to the following formula (6); (5) (6) Depend on The normalized orthogonal function set constitutes the function space spanned by it, denoted as . ; Step 2: Calculate all samples within the pulse waveform training set. In function space eigenvectors within This can be achieved using the following formula (7): (7) in , where is the i-th pulse waveform sample in the training set, and the total number of samples is N; feature vector The elements are shown in formula (8); ； in , yes The m-th element; Suppose there are L classes of samples in the pulse waveform training set, and the class of the l-th sample is denoted by . express, , The number of samples of each class is ,but: (9) The feature vector of sample p in class sample is denoted as: (10) The set of feature vectors of samples of class l and class j is denoted as ; To prepare for subsequent steps, initialize l=2 and j=1; and define an L-dimensional array as... And initialized to 0; Step ③ Use the training set and Sample in function space The feature vectors in the data are used to perform analysis on unknown samples based on a nonlinear projection method. Roughly classify and identify as Class or The class is implemented according to the following steps 3S1~3S4: Step 3S1: Find The feature vectors of sample classes in the set The average value of the nonlinear mapping in : (11) in , for matrix, , express All feature vectors of a sample class in the set The average value after performing a nonlinear mapping on the q-th vector; here, the nonlinear mapping... As shown in formula (12); (12) Step 3S2 The feature vectors of sample classes in the set The average value of the nonlinear mapping in : (13) in , , for matrix, express All feature vectors of a sample class in the set The average value after performing a nonlinear mapping on the q-th vector; here, the nonlinear mapping... As shown in formula (14); (14) Step 3S3 Calculate Class and Two types of critical decision points According to the following formula (15); (15) In formula (15) , Calculate using the following formulas (16) to (17): (16) (17) in, for The average vector after nonlinear mapping of sample In the optimal direction Projection on; for The average vector after nonlinear mapping of sample In the optimal direction Projection on; The optimal direction in formula (17) It is given by the following formula (18): (18) In formula (18), I is the identity matrix. Is to make For positive definite matrices, there is an additional quantity, T, which denotes matrix transpose. for A matrix whose elements are ; for A matrix whose elements are ; and As shown in formulas (19) and (20); (19) (20) Step 3S4: Classify and identify the unknown samples. Roughly classify and identify as Class or Class, according to the following steps (1)~(3): (1) Find In function space eigenvectors within As shown in formula (21), (21) in , yes The m-th element; (2) The feature vector In the set After performing a nonlinear mapping, in the optimal direction The projection value y is obtained by projecting it again: (22) in yes The q-th vector in the set; (3) Based on feature vectors The projection value y for the unknown sample Perform binary discrimination, that is Distinguish as Class or Classes, in the following way: like ,but Belonging to Class, and correct ; otherwise, Belonging to Class, and correct ; like Then correct If the condition is met, return to step 3S1 to continue execution; otherwise, proceed to step ④. Step 4 If Reset and Return to step ③ and continue the loop; otherwise, convert the array... The index k of the largest element in the array corresponds to Class as The final classification.

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