A machine learning based master drift chamber overlapped waveform resolution method

Abstract

The application discloses a kind of main drift chamber overlap waveform resolution methods based on machine learning, obtain the digitized alias waveform data of main drift chamber MDC output;The waveform data obtained is preprocessed;The waveform data after pre-processing is input into convolutional neural network model, and the local time sequence features and multi-peak structure features in waveform are extracted by multi-layer convolution structure;The parameters of the case in the overlap waveform are predicted, and the time and charge information corresponding to each case are output, and the energy values corresponding to different cases are calculated by combining total energy;According to the parameter prediction result, the charge and time information of each case in the overlap waveform are resolved, and the resolution result is visually verified.The method can solve the problem of signal waveform accumulation and time overlap of main drift chamber under high counting rate condition, improve the extraction accuracy of time and charge information of overlapping signal, and enhance the recognition ability of readout electronics system to complex cases.

Description

Technical Field

[0001] This invention relates to the field of high-energy physics, and in particular to a method for resolving overlapping waveforms in a master drift chamber based on machine learning. Background Technology

[0002] The main drift chamber (MDC) is a widely used gas detector in high-energy physics experiments. Its readout electronics system is responsible for acquiring and processing the signals generated by charged particles, extracting key information such as time and charge, and providing data support for track reconstruction, particle identification, and triggering systems. As high-energy physics experiments move towards higher brightness and higher count rates, the main drift chamber faces severe waveform stacking and signal overlap problems under high count rate conditions. Waveform resolution has become one of the key technologies in readout electronics.

[0003] In existing main drift chamber studies, systems like BESIII operate at relatively low count rates, resulting in a low probability of signal overlap and thus typically eliminating the need for specialized waveform resolution algorithms. However, in the design conditions of next-generation high-luminosity colliders such as the Super Tau-Charm Facility, the main drift chamber count rate is significantly increased, leading to waveform stacking in most cases. The arrival time of the second waveform often precedes the end time of the first, making it difficult for traditional threshold discrimination, peak detection, and simple fitting methods to effectively extract the time and charge information of the signal.

[0004] Furthermore, the output signal of the main drift chamber typically exhibits a pronounced multi-peak structure and a long duration, with significant differences in waveform morphology between different events. Under high count rate conditions, traditional waveform fitting methods based on fixed models are difficult to apply to the resolution of complex overlapping waveforms. Therefore, it is urgent to investigate a method suitable for resolving complex overlapping waveforms under high count rate conditions to improve the extraction accuracy of time and charge information by the main drift chamber readout electronics system.

[0005] In view of this, the present invention is hereby proposed. Summary of the Invention

[0006] The purpose of this invention is to provide a machine learning-based method for resolving overlapping waveforms in the master drift chamber, thereby addressing the aforementioned technical problems in the prior art. The method described in this invention can solve the problems of signal waveform stacking and time overlap in the master drift chamber under high count rate conditions, improve the accuracy of extracting time and charge information from overlapping signals, and enhance the readout electronics system's ability to identify complex events.

[0007] The objective of this invention is achieved through the following technical solution: A machine learning-based method for resolving overlapping waveforms in a master drift chamber, the method comprising: Step 1: Obtain the digital aliased waveform data output from the main drift chamber MDC and construct the aliased waveform dataset; Step 2: Preprocess the waveform data obtained in Step 1, including sample normalization length processing, waveform total energy calculation, time delay normalization, and Tensor format conversion; Step 3: Input the preprocessed waveform data into the convolutional neural network model, and extract the local temporal features and multi-peak structure features in the waveform through a multi-layer convolutional structure to establish an overlapping waveform feature representation; Step 4: Based on the convolutional neural network model in Step 3, perform parameter prediction on the events in the overlapping waveform, output the time and charge information corresponding to each event, and calculate the energy value corresponding to different events by combining the total energy. The example is a single waveform data acquisition; the parameters include energy ratio and time delay parameters. The convolutional neural network model predicts the energy ratio of the first instance in the overlapping waveform and the time delay parameter between overlapping pulses through a fully connected layer; based on the predicted energy ratio and the total energy of the waveform, the energy value corresponding to the second instance is calculated. Step 5: Based on the parameter prediction results obtained in Step 4, distinguish the charge and time information of each event in the overlapping waveform, and perform visualization verification of the resolution results.

[0008] Compared with existing technologies, the method provided by this invention introduces a deep learning-based digital waveform resolution scheme, which is different from traditional threshold or template fitting methods. It enhances the ability to process complex overlapping signals under high count rate conditions and provides important technical support for high-precision time measurement and event identification in high-energy physics experiments. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 A schematic diagram of the process for resolving overlapping waveforms in the master drift chamber based on machine learning, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of the Convolutional Neural Network (CNN) model constructed according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the overlapping waveform in the main drift chamber according to an embodiment of the present invention. Detailed Implementation

[0011] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them, and do not constitute a limitation on the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0012] First, the following explanations are provided for the terms that may be used in this article: The term "and / or" means that either or both can be achieved simultaneously. For example, X and / or Y means that it includes both "X" or "Y" as well as the three cases of "X and Y".

[0013] The terms "comprising," "including," "containing," "having," or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, including a technical feature element (such as raw material, component, ingredient, carrier, dosage form, material, size, part, component, mechanism, device, step, process, method, reaction conditions, processing conditions, parameter, algorithm, signal, data, product or article of manufacture, etc.) should be interpreted as including not only the expressly listed technical feature element, but also other technical feature elements that are not expressly listed and are well-known in the art.

[0014] The term "composed of" excludes any technical features not expressly listed. When used in a claim, it closes the claim to exclude all technical features other than those expressly listed, except for associated conventional impurities. If the term appears only in a clause of a claim, it limits the claim to the elements expressly listed in that clause; elements recited in other clauses are not excluded from the overall claim.

[0015] The technical solution provided by this invention will be described in detail below. Contents not described in detail in the embodiments of this invention belong to prior art known to those skilled in the art. For example... Figure 1 The diagram shows a flowchart of a machine learning-based main drift chamber overlapping waveform resolution method provided in an embodiment of the present invention. The method includes: Step 1: Obtain the digital aliased waveform data output from the main drift chamber MDC and construct the aliased waveform dataset; In this step, since waveform accumulation and pulse overlap are prone to occur in the main drift chamber under high count rate conditions, a waveform digitization sampling scheme is adopted to acquire the detector output signal at high speed, thereby obtaining digital waveform data containing time and charge information.

[0016] Specifically, the readout electronics system amplifies and shapes the analog signal output by the detector, and then samples the waveform through a high-speed analog-to-digital converter (ADC) to obtain the digital waveform data of the main drift chamber MDC. The digitized waveform data includes an aliased waveform data file output from the main drift chamber and a corresponding tag information file; the aliased waveform data file is used to record the sampled waveform, and the tag information file is used to record the actual energy and time parameters corresponding to each event.

[0017] Step 2: Preprocess the waveform data obtained in Step 1, including sample normalization length processing, waveform total energy calculation, time delay normalization, and Tensor format conversion; In this step, in order to improve the stability of subsequent neural network training and inference, it is necessary to preprocess the acquired waveform data.

[0018] In the specific implementation, the preprocessing process is as follows: First, the input waveform is standardized in length, specifically by truncating the input waveform to a fixed length so that all waveforms contain 1024 data points. Then, the total waveform energy is calculated based on the waveform sampling values, and the inter-pulse delay parameter is normalized. The energy calculation formula is as follows: ; in, t represents the total energy of the waveform; t represents time; t1 represents the start time of the waveform; t2 represents the end time of the waveform; E() represents the waveform function; Finally, the normalized waveform data is converted into Tensor form and used as input to the convolutional neural network model, as follows: Let the first Waveform samples After fixed-length processing and normalization, it becomes: ; in, The number of sampling points contained in each waveform sample; For the first The waveform at the ... Normalized sampled values ​​at each sampling point; For the real number field; waveform sample Convert to Tensor form The process is represented as: ; in, This represents Tensor transformation and dimension reconstruction operations; This indicates the number of channels in the waveform data; When inputting N waveform samples at a time, the waveform samples are stacked along the batch dimension to obtain a batch input Tensor. , is represented as: ; Where N is the number of waveform samples in the batch; Stack() represents the tensor stacking operation, which combines multiple waveform samples into a single input tensor along the new batch dimension.

[0019] Step 3: Input the preprocessed waveform data into the convolutional neural network model, and extract the local temporal features and multi-peak structure features in the waveform through a multi-layer convolutional structure to establish an overlapping waveform feature representation; In this step, such as Figure 2 The diagram shows the structure of the convolutional neural network model (CNN) constructed according to an embodiment of the present invention. The model is trained using simulation data. The convolutional neural network model adopts a multi-layer one-dimensional convolutional structure, and the input is preprocessed main drift chamber overlapping waveform data. First, local temporal features and multi-peak structure features in the main drift chamber waveform are extracted using a multi-layer one-dimensional convolutional structure. Let the first... The waveform sample at the ... The characteristics of the layer output are , Including local temporal features and multi-peak structure features; then the first The output of a one-dimensional convolutional layer is represented as: ; in, Indicates the first The waveform sample is processed by the first After processing by a one-dimensional convolutional layer, the convolutional feature value of the c-th output channel at the t-th position; express Layer Input feature values ​​in each channel; Indicates the convolution kernel weights; The parameter represents the bias parameter; r represents the position index within the convolution kernel. Indicates the kernel length; Indicates the convolution stride; express The number of channels in the layer feature; Indicates the input channel index; By using the sliding operation of convolutional kernels on the waveform time series, pulse peaks, rising edges, falling edges, and local amplitude variation features are extracted. As the number of convolutional layers increases, the receptive field of the network gradually expands, thereby further extracting multi-peak structural features such as the time interval between adjacent pulses, relative amplitude, number of peaks, and waveform overlap morphology. Subsequently, a nonlinear transformation is applied to the output of the convolutional layer using a nonlinear activation function to enhance the model's ability to express complex waveform features. The feature representation of the layer after nonlinear activation is as follows: ; in, This represents the characteristics after nonlinear activation; Represents a nonlinear activation function; By using a nonlinear activation function to set feature responses less than zero to zero and retain feature responses greater than or equal to zero, the ability of convolutional neural networks to express nonlinear waveform features is enhanced. After nonlinear activation, a pooling layer is used to locally filter and reduce the dimensionality of the activated features. When max pooling is used, the th... The output of each pooling layer is represented as follows: ; in, This represents the eigenvalues ​​obtained after pooling; Indicates the length of the pooling window; Indicates the pooling step size; max indicates taking the maximum value. Indicates the first The waveform sample at the ... After the layer undergoes nonlinear activation, the first In each channel, The eigenvalue at the location;

[0020] Pooling operations preserve features with strong responses in local regions, reduce the dimensionality of feature maps and the computational cost of subsequent networks, and improve the model's adaptability to changes in the local position of waveforms.

[0021] After multiple layers of one-dimensional convolution, nonlinear activation, and pooling, the feature representation of the overlapping waveform of the main drift chamber is obtained. Then, the multi-dimensional feature map output by the last feature extraction layer is unfolded into a one-dimensional feature vector. Let the convolutional neural network include L feature extraction layers, then the... The feature vector corresponding to each waveform sample is represented as follows: ; in, This represents the feature map output by the last feature extraction layer; Indicates feature expansion operation; This indicates the first number obtained after expansion. One-dimensional waveform feature vector corresponding to each waveform sample; Finally, the waveform feature vector The input is a fully connected layer, which establishes a mapping relationship between waveform features and target parameters. The output of the fully connected layer is represented as follows: ; in, This represents the weight matrix of the fully connected layer; This represents the bias vector of the fully connected layer; Indicates the first Predicted target parameters corresponding to the overlapping waveforms of the main drift chambers.

[0022] Step 4: Based on the convolutional neural network model in Step 3, perform parameter prediction on the events in the overlapping waveform, output the time and charge information corresponding to each event, and calculate the energy value corresponding to different events by combining the total energy. In this step, the example is a single waveform data acquisition; the parameters include energy ratio and time delay parameters. The convolutional neural network model predicts the energy ratio of the first instance in the overlapping waveform and the time delay parameter between overlapping pulses through a fully connected layer; based on the predicted energy ratio and the total energy of the waveform, the energy value corresponding to the second instance is calculated. In this model, a fully connected layer is used to predict the energy ratio corresponding to the first instance, and the corresponding formula is: ; in, and These represent the weight matrix and bias parameters of the fully connected layer for energy ratio prediction, respectively. This represents the Sigmoid activation function; This indicates the predicted energy proportion of the first event; Another fully connected layer is used to predict the time delay information between different pulses, and the corresponding formula is: ; in, and These represent the weight matrix and bias parameters of the fully connected layer for delay prediction, respectively. This represents the prediction delay parameter output by the model; Based on the predicted energy ratio and the total energy of the waveform, the energy value corresponding to the second event is calculated to separate the time and charge information of multiple events in the overlapping waveform. The calculation formula is as follows: ; ; in, The total energy of the waveform; This represents the energy value corresponding to the first case. This is the energy value corresponding to the second example.

[0023] The above operations can achieve accurate differentiation of complex overlapping waveforms.

[0024] Step 5: Based on the parameter prediction results obtained in Step 4, distinguish the charge and time information of each event in the overlapping waveform, and perform visualization verification of the resolution results.

[0025] In this step, such as Figure 3 The diagram shown is a schematic of the overlapping waveform of the main drift chamber according to an embodiment of the present invention. The energy parameters are predicted based on the output of the convolutional neural network model. (correspond Figure 3 The energy of the first waveform in the image (E1) and (correspond Figure 3 The energy E2 and time delay parameters of the second waveform in the data. and energy ratio parameters The resolution results of the overlapping waveforms in the main drift chamber were verified and visualized. Specifically: The predicted parameters , , and The model's resolution accuracy is evaluated by comparing the predicted value with the true label parameter corresponding to the sample and calculating the error between the predicted value and the true value. In specific implementation, the error can be calculated using mean square error (MSE) or root mean square error (RMSE). Those skilled in the art can also choose other error calculation methods according to actual needs.

[0026] Simultaneously, the aliased waveform, predicted values ​​of each parameter, actual values, and errors are visualized, and a frequency histogram of the error is drawn to verify the model's ability to distinguish the time and charge information of each event in the overlapping waveform.

[0027] In a specific implementation, the waveform resolution method described in this embodiment of the invention can be deployed on a Field-Programmable Gate Array (FPGA) hardware platform. By utilizing the parallel processing capability of the FPGA, the convolution operation and parameter prediction tasks can be parallelized, significantly reducing the waveform analysis time and enabling online real-time resolution of the main drift chamber signal under high count rate conditions.

[0028] It is worth noting that the contents not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

[0029] This invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the method.

[0030] This invention also provides a computer storage medium storing a plurality of instructions adapted for loading and executing the method by a processor.

[0031] In summary, the method described in the embodiments of the present invention has the following advantages: (1) To address the problem of multi-peak waveform overlap in the main drift chamber under high count rate conditions, a waveform resolution scheme based on convolutional neural network is introduced, which can fully extract the temporal and amplitude features in the waveform and achieve high-precision extraction of time and charge information in complex aliased waveforms. (2) In terms of algorithm design, deep learning methods are combined to model complex overlapping waveforms. Compared with traditional threshold discrimination or waveform fitting methods, it has stronger adaptability and robustness, and can effectively improve the signal resolution capability of the main drift chamber readout electronics system under high background and high count rate conditions. (3) The waveform resolution algorithm is deployed on the FPGA hardware platform to give full play to the advantages of hardware parallel computing. It can realize the online real-time processing of the overlapping waveforms in the main drift chamber, and improve the overall data processing efficiency and real-time performance of the system.

[0032] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A method for resolving overlapping waveforms in a master drift chamber based on machine learning, characterized in that, The method includes: Step 1: Obtain the digital aliased waveform data output from the main drift chamber MDC and construct the aliased waveform dataset; Step 2: Preprocess the waveform data obtained in Step 1, including sample normalization length processing, waveform total energy calculation, time delay normalization, and Tensor format conversion; Step 3: Input the preprocessed waveform data into the convolutional neural network model, and extract the local temporal features and multi-peak structure features in the waveform through a multi-layer convolutional structure to establish an overlapping waveform feature representation; Step 4: Based on the convolutional neural network model in Step 3, perform parameter prediction on the events in the overlapping waveform, output the time and charge information corresponding to each event, and calculate the energy value corresponding to different events by combining the total energy. The example is a single waveform data acquisition; the parameters include energy ratio and time delay parameters. The convolutional neural network model predicts the energy ratio of the first instance in the overlapping waveform and the time delay parameter between overlapping pulses through a fully connected layer; based on the predicted energy ratio and the total energy of the waveform, the energy value corresponding to the second instance is calculated. Step 5: Based on the parameter prediction results obtained in Step 4, distinguish the charge and time information of each event in the overlapping waveform, and perform visualization verification of the resolution results.

2. The master drift chamber overlapping waveform resolution method based on machine learning according to claim 1, characterized in that, In step 1, the analog signal output by the detector is amplified and shaped using the readout electronics system, and then the waveform is sampled by a high-speed analog-to-digital converter to obtain the digital waveform data of the main drift chamber MDC. The digitized waveform data includes an aliased waveform data file output from the main drift chamber and a corresponding tag information file; the aliased waveform data file is used to record the sampled waveform, and the tag information file is used to record the actual energy and time parameters corresponding to each event.

3. The master drift chamber overlapping waveform resolution method based on machine learning according to claim 1, characterized in that, In step 2, the preprocessing process is as follows: First, the input waveform is standardized in length, specifically by truncating the input waveform to a fixed length so that all waveforms contain 1024 data points. Then, the total waveform energy is calculated based on the waveform sampling values, and the inter-pulse delay parameter is normalized. The energy calculation formula is as follows: ； in, t represents the total energy of the waveform; t represents time; t1 represents the start time of the waveform; t2 represents the end time of the waveform; E() represents the waveform function; Finally, the normalized waveform data is converted into Tensor form and used as input to the convolutional neural network model, as follows: Let the first Waveform samples After fixed-length processing and normalization, it becomes: ； in, The number of sampling points contained in each waveform sample; For the first The waveform at the ... Normalized sampled values ​​at each sampling point; For the real number field; waveform sample Convert to Tensor form The process is represented as: ； in, This represents Tensor transformation and dimension reconstruction operations; This indicates the number of channels in the waveform data; When inputting N waveform samples at a time, the waveform samples are stacked along the batch dimension to obtain a batch input Tensor. , represented as: ； Where N is the number of waveform samples in the batch; Stack() represents the tensor stacking operation.

4. The master drift chamber overlapping waveform resolution method based on machine learning according to claim 1, characterized in that, In step 3, local temporal features and multi-peak structure features in the main drift chamber waveform are first extracted using a multi-layer one-dimensional convolutional structure. Let the first... The waveform sample at the ... The characteristics of the layer output are , Including local temporal features and multi-peak structure features; then the first The output of a one-dimensional convolutional layer is represented as: ； in, Indicates the first The waveform sample is processed by the first After processing by a one-dimensional convolutional layer, the convolutional feature value of the c-th output channel at the t-th position; express Layer Input feature values ​​in each channel; Indicates the convolution kernel weights; The parameter represents the bias parameter; r represents the position index within the convolution kernel. Indicates the kernel length; Indicates the convolution stride; express The number of channels in the layer feature; Indicates the input channel index; Subsequently, a nonlinear transformation is performed on the output of the convolutional layer using a nonlinear activation function. The feature representation of the layer after nonlinear activation is as follows: ； in, This represents the characteristics after nonlinear activation; Represents a non-linear activation function; The nonlinear activation function sets the feature responses less than zero to zero and retains the feature responses greater than or equal to zero. After nonlinear activation, pooling layers are used to locally filter and reduce the dimensionality of the activated features. When max pooling is used, the... The output of each pooling layer is represented as follows: ； in, This represents the eigenvalues ​​obtained after pooling; Indicates the length of the pooling window; Indicates the pooling step size; max indicates taking the maximum value. Indicates the first The waveform sample at the ... After the layer undergoes nonlinear activation, the first In each channel, The eigenvalue at the location.

5. The machine learning-based master drift chamber overlapping waveform resolution method according to claim 4, characterized in that, In step 3, after multiple layers of one-dimensional convolution, nonlinear activation, and pooling, the feature representation of the overlapping waveform of the main drift chamber is obtained. Then, the multi-dimensional feature map output by the last feature extraction layer is unfolded into a one-dimensional feature vector. Let the convolutional neural network include L feature extraction layers, then the... The feature vector corresponding to each waveform sample is represented as follows: ； in, This represents the feature map output by the last feature extraction layer; Indicates feature expansion operation; This indicates the first number obtained after expansion. One-dimensional waveform feature vector corresponding to each waveform sample; Finally, the waveform feature vector The input is a fully connected layer, which establishes a mapping relationship between waveform features and target parameters. The output of the fully connected layer is represented as follows: ； in, This represents the weight matrix of the fully connected layer; This represents the bias vector of the fully connected layer; Indicates the first Prediction results of target parameters corresponding to the overlapping waveforms of the main drift chambers.

6. The master drift chamber overlapping waveform resolution method based on machine learning according to claim 1, characterized in that, In step 4, a fully connected layer of the convolutional neural network model is used to predict the energy ratio corresponding to the first instance, and the corresponding formula is: ； in, and These represent the weight matrix and bias parameters of the fully connected layer for energy ratio prediction, respectively. This represents the Sigmoid activation function; This indicates the predicted energy proportion of the first event; Another fully connected layer is used to predict the time delay information between different pulses, and the corresponding formula is: ； in, and These represent the weight matrix and bias parameters of the fully connected layer for delay prediction, respectively. This represents the prediction delay parameter output by the model; Based on the predicted energy ratio and the total energy of the waveform, the energy value corresponding to the second event is calculated using the following formula: ； ； in, The total energy of the waveform; This represents the energy value corresponding to the first case. This is the energy value corresponding to the second example.

7. The master drift chamber overlapping waveform resolution method based on machine learning according to claim 1, characterized in that, In step 5, Energy parameters predicted based on the output of the convolutional neural network model and Delay parameters and energy ratio parameters The resolution results of the overlapping waveforms in the main drift chamber were verified and visualized. Specifically: The predicted parameters , , and The model's resolution accuracy is evaluated by comparing the predicted value with the true label parameter corresponding to the sample and calculating the error between the predicted value and the true value. Simultaneously, the aliased waveform, predicted values ​​of each parameter, actual values, and errors are visualized, and a frequency histogram of the error is drawn to verify the model's ability to distinguish the time and charge information of each event in the overlapping waveform.

8. The machine learning-based master drift chamber overlapping waveform resolution method according to claim 1, characterized in that, The method further includes: The waveform resolution method is deployed on the field-programmable gate array (FPGA) hardware platform to parallelize the convolution operation and parameter prediction tasks.

9. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to perform the method according to any one of claims 1 to 8.

10. A computer storage medium, characterized in that, The computer storage medium stores a plurality of instructions adapted for loading by a processor and executing the method of any one of claims 1 to 8.

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