Dynamic classification-based few-sample pulse waveform identification method

Abstract

The invention discloses a few-sample pulse waveform identification method based on dynamic classification. Firstly, a similarity matrix is designed based on a function component, and a feature vector is obtained through mapping; then, designing a discrimination method based on quadratic programming optimization, and realizing rapid classification and identification based on a small number of optimal samples; and finally, a method based on dynamic adjustment is adopted, and pulse waveform dynamic classification and identification during type dynamic change are realized. After accurate classification, subsequent digital waveform forming, waveform parameter identification and other methods can be dynamically developed based on categories, the high sensitivity to dynamic changes of pulse orders and waveform categories is overcome, and finally, a guarantee is provided for the accuracy of radioactive measurement under complex dynamic conditions.

Description

Technical Field

[0001] The invention relates to a small number of sample pulse waveform recognition method based on dynamic classification. Background Art

[0002] In radioactive measurement, the front-end analog system of the detector is composed of detectors, preamplifiers, CR / RC networks, amplifier circuits, and conditioning circuits. The front-end analog system is composed of complex and diverse methods; therefore, the waveform of the pulse signal output by the system may show diversity and waveform complexity, which is manifested as different orders in the s domain, that is, the number of components contained in each pulse and the composition fraction of the components are also different. For example, in a complex radioactive environment (for example, when multiple rays coexist), multiple types of detectors are required for coordinated measurement, and the measured pulse signal waveform may show complexity and diversity.

[0003] The complex and diverse pulses output by the front-end analog system have different orders of mathematical models (some may be infinitely high), that is, the number of components contained in a single pulse and the composition fractions of the components are also different; 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, the corresponding algorithm must be designed based on the order of the pulse signal model and the specific parameters of each component, otherwise it will lead to reduced accuracy or even failure of energy spectrum measurement. For example, in the case of misjudgment of the pulse signal order, the shaping method based on the mathematical model will cause the top of the trapezoidal shaping to be distorted due to coefficient mismatch, which will ultimately lead to reduced accuracy of the acquired pulse amplitude and energy spectrum.

[0004] In view of the dynamic changes in pulse waveform types, for example, when multiple detectors are used to measure radiation scenes with multiple rays and multiple order waveform shapes at the same time, it is necessary to dynamically classify the pulses (for example, classification based on order or waveform characteristics), and then use the corresponding shaping and identification methods to ensure the accuracy of the acquired pulse waveform amplitude and other information and energy spectrum. The present invention adopts a small sample pulse waveform recognition method based on dynamic classification, and dynamically classifies pulses in the case of changes in pulse waveform types, so as to facilitate the subsequent qualitative and quantitative analysis of pulses and adopt corresponding matching algorithms, and ultimately provide guarantees for accurate radioactivity measurement, while greatly reducing the sample size used for recognition training and improving the calculation speed. Summary of the invention

[0005] The purpose of the present invention is to disclose a small-sample pulse waveform recognition method based on dynamic classification, which dynamically classifies the complex and diverse pulse waveforms output by the front-end analog system of a nuclear radiation detector, so as to facilitate the subsequent digital waveform shaping and waveform parameter recognition methods to be carried out based on the dynamic changes of the categories, overcome the high sensitivity of the waveform shaping and parameter recognition methods to the dynamic changes of the pulse order and pulse waveform type, and ultimately provide a guarantee for the accuracy of radioactivity measurement (for example, energy spectrum measurement) under complex conditions, while greatly reducing the amount of samples used for recognition training and improving the calculation speed.

[0006] The present invention relates to a method for identifying a few-sample pulse waveform based on dynamic classification, which is carried out by the following steps: ① achieved.

[0007] Step ① Assume that there are M types of pulse waveforms, and write the S-domain and time-domain expressions for each type.

[0008] Step ② Calculate the characteristic vector of the pulse waveform sample, which can be achieved by following steps (1) to (3). The pulse waveform sample is Indicates that its eigenvector is X;

[0009] (1) Obtain the similarity matrix H of the pulse waveform components;

[0010] (2) Obtaining the pulse waveform In the function component matrix Projection inside ;

[0011] (3) Based on the similarity matrix H and projection , find the pulse waveform The eigenvector X.

[0012] Step 3: Use the training set Class and The feature vector of the class sample, for the unknown sample Perform rough classification and recognition (i.e., rough recognition as Class or Class), implement it according to the following steps 3S1~3S3:

[0013] Step 3S1: design an objective function with constraints and obtain the optimal parameters of the objective function;

[0014] Step 3S2: Obtain the discriminant function ;

[0015] Step 3S3 Roughly classify the unknown samples to be classified and identified: ,but Belong to Class, and correct ;otherwise, Belong to Class, and correct .like , then correct , and return to step 3S1 to continue execution; otherwise, go to step ④.

[0016] Step ④ If , reset and , return to step ③ and continue the loop execution; otherwise, the array The sequence number corresponding to the largest element in is The final category of is the maximum value, then the pulse waveform Attribution kind.

[0017] Step ⑤ When the types of pulse waveforms increase, the parameters in the above steps ① and ② are modified as follows.

[0018] In summary, through steps ① to ⑤, a small number of sample pulse waveform recognition method based on dynamic classification is adopted to realize the classification and recognition of pulse waveforms with dynamically changing types.

[0019] The beneficial effects of the present invention are:

[0020] In view of the dynamic changes in pulse waveform types, for example, when multiple detectors are used to measure radiation scenarios with multiple rays and multiple order waveform shapes at the same time, it is necessary to dynamically classify the pulses (for example, classification based on order or waveform characteristics) and then use corresponding shaping and identification methods to ensure the accuracy of the acquired pulse waveform amplitude and energy spectrum information.

[0021] The present invention adopts a small number of sample pulse waveform recognition method based on dynamic classification to dynamically classify pulses in the case of multiple types of pulse waveforms. The beneficial effects of this method are: (1) based on the function components contained in various pulse waveforms in the pulse data set, a similarity matrix is ​​designed, and waveform mapping is performed based on the similarity matrix to obtain a feature vector, thereby effectively extracting the pulse waveform feature information; (2) the continuous infinite-dimensional time domain waveform is converted into a finite-dimensional feature vector, and at the same time, the "inconspicuous difference" between pulse waveforms in the time domain is converted into an "obvious difference" of the feature vector, thereby facilitating the accurate separability of pulse waveforms; (3) a discrimination method based on quadratic programming optimization is designed to achieve the accuracy of the pulse waveform recognition based on a small number of optimal samples. Classification and recognition not only ensures recognition accuracy but also reduces the amount of calculation; (4) The characteristic vector of the pulse waveform is nonlinearly mapped so that the similarities and differences between samples are highly reflected, laying a solid foundation for the accurate identification of the pulse waveform type; (5) A method based on dynamic adjustment is adopted to accurately classify the complex and changing pulse waveform, which facilitates the subsequent digital waveform shaping and waveform parameter identification methods to be dynamically carried out based on the category, and then the corresponding matching algorithm is adopted for the qualitative and quantitative analysis of the pulse, overcoming the high sensitivity of waveform shaping and parameter identification methods to the dynamic changes of pulse order and waveform type, and finally providing a guarantee for the accuracy of radioactivity measurement (for example, energy spectrum measurement) under complex conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0025] 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.

[0026] The present invention relates to a method for identifying a few-sample pulse waveform based on dynamic classification, which is carried out by the following steps: ① ⑤Achieved.

[0027] Step ① Assume that there are M types of pulse waveforms, and the S-domain expression of each type is as shown in formula (1):

[0028] (1)

[0029] in, The S-domain expression representing the m-th type of waveform; , , and represents the coefficients of the S-domain expression of the m-th type of waveform, and All are real numbers.

[0030] The mth type of waveform contains components, and the time domain expressions corresponding to each component are:

[0031] (2)

[0032] Step ② Calculate the characteristic vector of the pulse waveform sample, which can be achieved by following steps (1) to (3). The pulse waveform sample is Indicates that its eigenvector is X;

[0033] (1) Obtain the similarity matrix H of the pulse waveform components:

[0034] (3)

[0035] The "T" in H represents transposition, and its submatrix expression is shown in formula (4);

[0036] (4)

[0037] in, Each element of is as follows:

[0038] (5)

[0039] The parameters in formula (5) refer to formulas (1) and (2);

[0040] At the same time, H is expressed as:

[0041] (6)

[0042] In formula (6)

[0043] (7)

[0044] H uses the function component matrix It is expressed as:

[0045] (8)

[0046] The matrix in formula (8) as follows:

[0047] (9)

[0048] (2) Obtaining the pulse waveform In the function component matrix Projection inside , according to the following formulas (10)~(13):

[0049] (10)

[0050] (11)

[0051] (12)

[0052] (13)

[0053] (3) Based on the similarity matrix H and projection , find the pulse waveform The feature vector X is implemented as follows A and B:

[0054] A. The pulse waveform The approximate expression using eigenvectors and function component sequences is as follows:

[0055] (14)

[0056] Where X is evaluated in step B, and .

[0057] B. Find the pulse waveform The eigenvector X is obtained by following the steps below:

[0058] First, write the sum of squared errors J:

[0059] (15)

[0060] And find the partial derivative:

[0061] (16)

[0062] Combination , H and projection The expression of further leads to formulas (17)~(19);

[0063] (17)

[0064] (18)

[0065] (19)

[0066] in is the inverse matrix of H, Further expressed as:

[0067] (20)

[0068] Then, obtain The eigenvector X is as follows:

[0069] (twenty one)

[0070] Suppose the mth ( ) The category of the sample is express, The number of class samples is ,but:

[0071] (twenty two)

[0072] The characteristic vector of the pth sample in the class sample is recorded as:

[0073] (twenty three)

[0074] For the execution of subsequent steps, initialize m=2 and j=1; and define the M-dimensional array as , and initialized to 0.

[0075] Step 3: Use the training set Class and The feature vector of the class sample, for the unknown sample Perform rough classification and recognition (i.e., rough recognition as Class or Class), implement it according to the following steps 3S1~3S3:

[0076] Step 3S1 Design an objective function with constraints and find the optimal parameters of the objective function as follows:

[0077] First, the following quadratic programming equation is designed as the objective function:

[0078] (twenty four)

[0079] in , , , U is dimensional vector; represents the inner product; represents the two-norm; It represents a nonlinear mapping relationship, which is explained in the subsequent formula (33) and is not listed here. The specific expression of does not affect the subsequent derivation process.

[0080] Then, the partial derivative of R is taken as follows:

[0081] (25)

[0082] Right now (26)

[0083] Substitute the above formula (26) into (24) and use Substituting R, we get: (27)

[0084] Further obtain the objective function with constraints as follows:

[0085] (28)

[0086] in

[0087] (29)

[0088] Assume that in formula (28) Maximum The corresponding optimal vector is , expressed as follows:

[0089] (30)

[0090] in ;

[0091] Get the optimal solution of vector U as follows:

[0092] (31)

[0093] From vector Randomly select a non-zero element from the elements of , and its corresponding eigenvector (when i>m) or (when (time) is recorded as X i , and obtain the optimal solution for parameter c as follows:

[0094] (32)

[0095] The nonlinear mapping here The relationship expressed by the following formula (33) is satisfied:

[0096] (33)

[0097] Step 3S2: Obtain the discriminant function as follows:

[0098] (34)

[0099] in , and as follows:

[0100] (35)

[0101] Step 3S3: The unknown samples to be classified and identified Perform a rough classification (i.e., roughly identify Class or class), follow the steps (1) to (3):

[0102] (1) Seek The eigenvector of , as shown in formula (36),

[0103] (36)

[0104] in .

[0105] (2) The feature vector Substituting into the discriminant function (34), we get :

[0106] (37)

[0107] in and The expression is as follows:

[0108] (38)

[0109] (3) Based on feature vector , for unknown samples Perform two-category discrimination, that is Identify as Class or Class, as follows:

[0110] like ,but Belong to Class, and correct ;otherwise, Belong to Class, and correct .

[0111] like , then correct , and return to step 3S1 to continue execution; otherwise, go to step ④.

[0112] Step ④ If , reset and , return to step ③ and continue the loop execution; otherwise, the array The sequence number corresponding to the largest element in is The final category of is the maximum value, then the pulse waveform Attribution kind.

[0113] Step ⑤ When the number of pulse waveforms increases, the parameters in steps ① and ② above are modified as follows:

[0114] (1) The newly added function component is denoted as , the function component matrix is ​​modified to :

[0115] (39)

[0116] (40)

[0117] (2) The pulse waveform x(t) in the function component matrix The projection correction inside is , the similarity matrix H is modified to :

[0118] (41)

[0119] (42)

[0120] (43)

[0121] (3) The characteristic vector X of the pulse waveform x(t) is modified to :

[0122] (44)

[0123] (45)

[0124] And the following relationship holds:

[0125] (46)

[0126] (4) Eigenvector The recursive algorithm is shown in formula (47):

[0127] (47)

[0128] in, ;

[0129] If there is more than one newly added function component, let , , , , continue to make corrections according to steps (1) to (4).

[0130] In summary, through steps ① to ⑤, a few-sample pulse waveform recognition method based on dynamic classification is adopted to achieve classification and recognition of pulse waveforms with dynamically changing types.

[0131] As described above, a small number of sample pulse waveform recognition methods based on dynamic classification dynamically classify the complex and diverse pulse waveforms output by the front-end analog system of a nuclear radiation detector, making it easier for subsequent digital waveform shaping and waveform parameter recognition methods to be carried out based on the dynamic changes of categories. This overcomes the high sensitivity of waveform shaping and parameter recognition methods to the dynamic changes of pulse orders and pulse waveform types, and ultimately provides a guarantee for the accuracy of radioactivity measurements (for example, energy spectrum measurements) under complex conditions. At the same time, it greatly reduces the amount of samples used for recognition training and improves the calculation speed.

[0132] In the above-mentioned embodiment of the present invention, a method for identifying a small number of pulse waveforms based on dynamic classification is described in detail, but it should be noted that the above is only one embodiment of the present invention. When other forms of classification and recognition involve 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 scope of protection of the present invention.

Claims

1. A method for identifying pulse waveforms with a small number of samples based on dynamic classification, characterized in that: Dynamic classification and recognition of pulse signal waveform is carried out through the following steps① ⑤Achieved: Step ① Assume that there are M types of pulse waveforms, and the S-domain expression of each type is as shown in formula (1): (1) in, The S-domain expression representing the m-th type of waveform; , , and represents the coefficients of the S-domain expression of the m-th type of waveform, and are all real numbers; The mth type of waveform contains components, and the time domain expressions corresponding to each component are: (2) Step ② Calculate the characteristic vector of the pulse waveform sample, which can be achieved by following steps (1) to (3). The pulse waveform sample is Indicates that its eigenvector is X; (1) Obtain the similarity matrix H of the pulse waveform components: (3) The "T" in H represents transposition, and its submatrix expression is shown in formula (4); (4) in, Each element of is as follows: (5) The parameters in formula (5) refer to formulas (1) and (2); At the same time, H is expressed as: (6) In formula (6) (7) H uses the function component matrix It is expressed as: (8) The matrix in formula (8) as follows: (9) (2) Obtaining the pulse waveform In the function component matrix Projection inside , according to the following formulas (10)~(13): (10) (11) (12) (13) (3) Based on the similarity matrix H and projection , find the pulse waveform The feature vector X is implemented as follows A and B: A. The pulse waveform The approximate expression using eigenvectors and function component sequences is as follows: (14) Where X is evaluated in step B, and ; B. Find the pulse waveform The eigenvector X is obtained by following the steps below: First, write the sum of squared errors J: (15) And find the partial derivative: (16) Combination , H and projection The expression of further leads to formulas (17)~(19); (17) (18) (19) in is the inverse matrix of H, Further expressed as: (20) Then, obtain The eigenvector X is as follows: (21) Suppose the mth ( ) The category of the sample is express, The number of class samples is ,but: (22) The characteristic vector of the pth sample in the class sample is recorded as: (23) For the execution of subsequent steps, initialize m=2 and j=1; and define the M-dimensional array as , and initialized to 0; Step 3: Use the training set Class and The feature vector of the class sample, for the unknown sample Perform rough classification and recognition (i.e., rough recognition as Class or Class), implement it according to the following steps 3S1~3S3: Step 3S1 Design an objective function with constraints and find the optimal parameters of the objective function as follows: First, the following quadratic programming equation is designed as the objective function: (24) in , , , U is dimensional vector; represents the inner product; represents the two-norm; represents a nonlinear mapping relationship, which is explained in the subsequent formula (33) and is not listed here. The specific expression of does not affect the subsequent derivation process; Then, the partial derivative of R is taken as follows: (25) Right now (26) Substitute the above formula (26) into (24) and use Substituting R, we get: (27) Further obtain the objective function with constraints as follows: (28) in (29) Assume that in formula (28) Maximum The corresponding optimal vector is , expressed as follows: (30) in ; Get the optimal solution of vector U as follows: (31) From vector Randomly select a non-zero element from the elements of , and its corresponding eigenvector (when i>m) or (when (time) is recorded as X i , and obtain the optimal solution for parameter c as follows: (32) The nonlinear mapping here The relationship expressed by the following formula (33) is satisfied: (33) Step 3S2: Obtain the discriminant function as follows: (34) in , and as follows: (35) Step 3S3: The unknown samples to be classified and identified Perform a rough classification (i.e., roughly identify Class or class), follow the steps (1) to (3): (1) Seek The eigenvector of , as shown in formula (36): (36) in ; (2) The feature vector Substituting into the discriminant function (34), we get : (37) in and The expression is as follows: (38) (3) Based on feature vector , for unknown samples Perform two-class discrimination, that is Identify as Class or Class, as follows: like ,but Belong to Class, and correct ;otherwise, Belong to Class, and correct ; like , then correct , and return to step 3S1 to continue execution; otherwise, go to step ④; Step ④ If , reset and , return to step ③ and continue the loop execution; otherwise, the array The sequence number corresponding to the largest element in is The final category of is the maximum value, then the pulse waveform Attribution kind; Step ⑤ When the number of pulse waveforms increases, the parameters in steps ① and ② above are modified as follows: (1) The newly added function component is denoted as , the function component matrix is ​​modified to : (39) (40) (2) The pulse waveform x(t) in the function component matrix The projection correction inside is , the similarity matrix H is modified to : (41) (42) (43) (3) The characteristic vector X of the pulse waveform x(t) is modified to : (44) (45) And the following relationship holds: (46) (4) Eigenvector The recursive algorithm is shown in formula (47): (47) in, ; If there is more than one newly added function component, let , , , , continue to make corrections according to steps (1) to (4).

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