Pulsar time data denoising method based on machine learning LSTM algorithm

Abstract

The invention discloses a pulsar time data denoising method based on a machine learning LSTM algorithm, and the method comprises the steps: extracting a first original pulse arrival time sequence from the obtained first original timing observation data of a millisecond pulsar; obtaining a first timing residual sequence between pulsar time PT and earth time TT based on the first original pulse arrival time sequence and a preset pulsar timing model; inputting the preprocessed first timing residual error sequence into a trained long short-term memory (LSTM) model to obtain a first noise sequence in the preprocessed first timing residual error sequence; performing first noise sequence removal on the first timing residual sequence to obtain a purified timing residual sequence; and pulsar time signals meeting a preset precision index are obtained through the purified timing residual sequence.

Description

Technical Field

[0001] This invention relates to the field of time and frequency technology, and relates to, but is not limited to, a pulsar time data denoising method based on the machine learning LSTM algorithm. Background Technology

[0002] The currently used International Atomic Time (IAT) is the recognized most accurate time and frequency standard and the most widely used time scale. However, because ATT is derived from atomic clocks, its reliability is not very high. Pulsars in the Milky Way, with their extremely fast and stable millisecond-level rotation speeds, are strictly constrained by the law of conservation of angular momentum and are unaffected by human factors. Therefore, a pulsar time system has been constructed, which shows significant application potential in time reference maintenance and navigation positioning, and is expected to become an important supplement or even a replacement for the existing atomic time system. The accuracy of pulsar time directly affects its feasibility and reliability in the above applications. However, the pulse arrival time series obtained from actual observations are often affected by various noises. These noises mask the inherent timing stability of millisecond pulsars, severely limiting further improvements in pulsar time accuracy. This has become a key bottleneck that urgently needs to be overcome in the process of transforming this technology from theoretical research to engineering applications.

[0003] Related technologies mainly rely on physical model-driven strategies, such as using polynomial fitting to separate deterministic and random components in timing noise, or performing parameter estimation and model selection within a Bayesian framework. However, these methods have two drawbacks. First, they are highly dependent on pre-defined noise models, while the sources of noise in actual observations are complex and diverse, making it difficult to accurately describe them using a single parameterized model. Second, the choice of the order in polynomial fitting is highly subjective, which can easily lead to overfitting or underfitting, while complex Bayesian methods face problems such as high computational costs and uncertain convergence.

[0004] Therefore, how to accurately and efficiently perform noise reduction to extract pure pulsar time signals has become an urgent problem to be solved. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a pulsar time data denoising method based on the machine learning LSTM algorithm, which at least solves the problem that related technologies cannot accurately and efficiently denoise to extract pure pulsar time signals.

[0006] According to a first aspect of the present invention, a pulsar time data denoising method based on the machine learning LSTM algorithm is provided, comprising: The first raw pulse arrival time sequence is extracted from the first raw timing observation data of the acquired millisecond pulsar, and the first timing residual sequence between pulsar time PT and Earth time TT is obtained based on the first raw pulse arrival time sequence and the preset pulsar timing model. The preprocessed first timing residual sequence is input into the trained Long Short-Term Memory (LSTM) model to obtain the first noise sequence in the preprocessed first timing residual sequence. The first timing residual sequence is subjected to the first noise sequence removal to obtain the purified timing residual sequence; and the pulsar timing signal that meets the preset accuracy index is obtained through the purified timing residual sequence.

[0007] According to a second aspect of the present invention, an electronic device is provided, comprising: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other via the communication bus; the memory is used to store at least one executable instruction, wherein the executable instruction causes the processor to perform an operation corresponding to the method described in the first aspect.

[0008] According to a third aspect of the present invention, a computer storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0009] According to the scheme provided in the embodiments of the present invention, a first original pulse arrival time sequence is extracted from the first original timing observation data of the acquired millisecond pulsar, and a first timing residual sequence between pulsar time PT and Earth time TT is obtained based on the first original pulse arrival time sequence and a preset pulsar timing model; the preprocessed first timing residual sequence is input into a trained LSTM model to obtain a first noise sequence in the preprocessed first timing residual sequence; the first noise sequence is removed from the first timing residual sequence to obtain a purified timing residual sequence; and the pulsar time signal that meets the preset accuracy index is obtained through the purified timing residual sequence. In this process, on the one hand, the timing noise of pulsars often has long-scale correlation, and the unique gating mechanism of the LSTM model enables it to effectively memorize and utilize the dependencies between distant time points in the sequence, thereby more accurately predicting and separating noise. Moreover, the LSTM model can automatically learn the complex and nonlinear characteristics of noise from the data, making it more universal and robust to various types of noise. On the other hand, by inputting the preprocessed first timing residual sequence into the trained LSTM model, the LSTM model can output the corresponding noise sequence. The noise reduction process is very fast, greatly reducing manual intervention and subjective judgment. In summary, the above method can accurately and efficiently perform noise reduction to extract clean pulsar timing signals. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. 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, wherein: Figure 1 A flowchart illustrating a pulsar time-lapse data denoising method based on the machine learning LSTM algorithm provided in an embodiment of the present invention; Figure 2 A comparison chart of the denoising effect of a test set provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, not all embodiments. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0012] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0013] It should be noted that the terms "first, second, and third" used in the embodiments of the present invention are only used to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first, second, and third" can be interchanged in a specific order or sequence where permitted, so that the embodiments of the present invention described herein can be implemented in an order other than that illustrated or described herein.

[0014] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which these embodiments of the invention pertain. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0015] Explanation of parameters appearing in the text: Pulsar Time (PT), Terrestrial Time (TT), Long Short-Term Memory (LSTM) model, and Root Mean Square (RMS).

[0016] Figure 1 This is a flowchart illustrating a pulsar time-time data denoising method based on the machine learning LSTM algorithm provided in an embodiment of the present invention. The pulsar time-time data denoising method based on the machine learning LSTM algorithm provided in this embodiment of the present invention can be executed by an electronic device, such as a computer or server.

[0017] like Figure 1 As shown, a pulsar time data denoising method based on the machine learning LSTM algorithm includes: S101. Extract the first original pulse arrival time sequence from the first original timing observation data of the acquired millisecond pulsar, and obtain the first timing residual sequence between pulsar time PT and Earth time TT based on the first original pulse arrival time sequence and the preset pulsar timing model.

[0018] In embodiments of the present invention, the raw timing observation data refers to the unprocessed raw signal records received by the telescope during pulsar timing observations. This typically includes information such as reception time, frequency, signal strength, and instrument status. The raw pulse arrival time series is a series of pulse signals that actually arrive at Earth after preliminary processing from the raw observation data, such as template matching and pulse profile fitting. The current or latest first raw timing observation data of the millisecond pulsar is acquired, and the first raw pulse arrival time series is extracted from this data. The preset pulsar timing model can be a timing model set in the TEMPO2 software. The first raw pulse arrival time series is input into the TEMPO2 software, and the first timing residual sequence between pulsar time PT and Earth time TT is calculated using the set pulsar timing model.

[0019] The first timing residual sequence includes each time point and the timing residual corresponding to that time point.

[0020] For example, the raw timing observation data of the millisecond pulsar PSRJ0437-4715 can be obtained through a radio telescope pulsar timing observation system, and the raw pulse arrival time can be further extracted.

[0021] S102. Input the preprocessed first timing residual sequence into the trained Long Short-Term Memory (LSTM) model to obtain the first noise sequence in the preprocessed first timing residual sequence.

[0022] In an embodiment of the present invention, the first timing residual sequence is cleaned, including handling possible missing values ​​and removing obviously invalid or outlier values ​​caused by observational interference. Subsequently, the cleaned first timing residual sequence is filtered to ensure that the data type is numerical. Finally, it is further normalized to scale it to a range of 0 to 1 suitable for training the neural network model, resulting in the preprocessed first timing residual sequence.

[0023] Furthermore, the first timing residual sequence contains various noises introduced by factors such as the interstellar medium and measurement errors. The preprocessed first timing residual sequence is input into the trained LSTM model. The trained LSTM model can predict various noises in the first timing residual sequence, and finally obtain the first noise sequence in the first timing residual sequence.

[0024] S103. Perform first noise removal on the first timing residual sequence to obtain a purified timing residual sequence; and obtain a pulsar timing signal that meets the preset accuracy index through the purified timing residual sequence.

[0025] In an embodiment of the present invention, the first noise sequence can be denormalized to obtain a processed first noise sequence. Then, the processed first noise sequence is removed from the first timing residual sequence to obtain a purified timing residual sequence that does not contain noise. The theoretical pulse arrival time calculated by the preset pulsar timing model is obtained. The purified timing residual sequence is added to the calculated theoretical pulse arrival time to obtain a high-precision and high-stability pulsar timing signal that meets the preset accuracy index.

[0026] Understandably, in the implementation of this invention, a first original pulse arrival time sequence is extracted from the first original timing observation data of the acquired millisecond pulsar, and a first timing residual sequence between pulsar time PT and Earth time TT is obtained based on the first original pulse arrival time sequence and a preset pulsar timing model. The preprocessed first timing residual sequence is input into a trained Long Short-Term Memory (LSTM) model to obtain a first noise sequence in the preprocessed first timing residual sequence. The first noise sequence is removed from the first timing residual sequence to obtain a purified timing residual sequence. The pulsar time signal that meets the preset accuracy index is obtained through the purified timing residual sequence. In this process, on the one hand, the timing noise of pulsars often has long-term scale correlation. The unique gating mechanism of the LSTM model enables it to effectively memorize and utilize the dependencies between distant time points in the sequence, thereby more accurately predicting and separating noise. Moreover, the LSTM model can automatically learn the complex and nonlinear characteristics of noise from the data, making it more universal and robust to various types of noise. On the other hand, by inputting the preprocessed first timing residual sequence into the trained LSTM model, the LSTM model can output the corresponding noise sequence. The noise reduction process is very fast, greatly reducing manual intervention and subjective judgment. In summary, the above method can efficiently and accurately perform noise reduction to extract clean pulsar timing signals.

[0027] In some embodiments of the present invention, the first timing residual sequence between pulsar time PT and Earth time TT obtained in S101 based on the first original pulse arrival time sequence and the preset pulsar timing model can be implemented through S1011 to S1012, as described in the following steps.

[0028] S1011. The first original pulse arrival time series is calibrated and corrected using the latest ephemeris parameters to obtain the corrected second original pulse arrival time series.

[0029] S1012. Compare the corrected pulse arrival time sequence with the preset pulsar timing model, and use the least squares method to fit the parameters until the first timing residual sequence is obtained.

[0030] In some embodiments of the present invention, the latest ephemeris parameters include, but are not limited to, the right ascension and declination, rotation frequency and first derivative, proper motion, parallax, dispersion, Faraday rotation and binary orbital parameters of the pulsar. The precise position of the Earth in the solar system is determined using the latest ephemeris parameters, and various delays are calculated from the position and pulsar direction. The corrected pulse arrival time sequence is obtained by subtracting various delays from the arrival time of the first original pulse.

[0031] Furthermore, the corrected pulse arrival time sequence is compared with the preset pulsar timing model, and the parameters of the preset pulsar timing model are fitted using the least squares method until convergence, thus obtaining the first timing residual sequence.

[0032] In some embodiments of the present invention, S102 can be implemented by S1021 to S1022, as described in the following steps.

[0033] S1021. Using a preset sliding window, the preprocessed first timing residual sequence is input into the first LSTM layer to obtain the first hidden state sequence at each time step. The remaining LSTM layers are then used to process the first hidden state sequence to obtain the context feature vector.

[0034] S1022. Obtain the first noise sequence in the preprocessed first timing residual sequence based on the context feature vector and multiple fully connected layers.

[0035] In some embodiments of the present invention, multiple LSTM layers are stacked in the LSTM model, with the number of LSTM layers being greater than or equal to two. The input layer, LSTM layer, fully connected layer, and output layer in the LSTM model are sequentially connected, with the number of fully connected layers being greater than or equal to two. LSTM1 is the first LSTM layer, containing 50 neurons, with return_sequences=True set to pass the complete output sequence to the next layer. LSTM2 is the second LSTM layer, containing 25 neurons. A continuous segment of length 10 is extracted from the preprocessed first timing residual sequence through a preset sliding window and input into the first LSTM layer of the LSTM model as a numerical tensor of shape (10, 1) to obtain the first hidden state sequence. (10, 1) represents a preprocessed first timing residual segment consisting of 10 time steps, with each time step containing a 1-dimensional timing residual feature. Then, the first hidden state sequence is processed sequentially through subsequent LSTM layers to finally obtain the context feature vector. Furthermore, the context feature vector is input into multiple fully connected layers, ultimately yielding the first noise sequence in the preprocessed first timing residual sequence.

[0036] In some embodiments of the present invention, the training process of the LSTM model can be implemented through S201 to S205, which will be described through the following steps.

[0037] S201. Obtain the second raw timing observation data of millisecond pulsars within a preset historical time period from the radio telescope observation database, and extract the arrival time series of the second raw pulses from the second raw timing observation data.

[0038] In some embodiments of the present invention, the radio telescope observation database stores raw timing observation data of multiple millisecond pulsars at different times. The second raw timing observation data of the millisecond pulsars within a preset historical time period is obtained from the radio telescope observation database. For example, the second raw timing observation data of the millisecond pulsar PSRJ0437-4715 for 19 years is obtained. Then, the arrival time series of the second raw pulse is extracted from the second raw timing observation data. This series contains multiple data points, such as 5302 data points.

[0039] S202. Obtain the second timing residual sequence based on the arrival time sequence of the second original pulse, and divide the second timing residual sequence according to a preset ratio to obtain the training set and the test set.

[0040] In an embodiment of the present invention, following the same processing steps S1011 to S1012 described above, a second timing residual sequence is obtained based on the second original pulse arrival time sequence, and then the second timing residual sequence is divided according to a preset ratio, such as a 9:1 ratio, to obtain a training set and a test set.

[0041] S203. Use a preset sliding window to process the preprocessed training set to obtain multiple sets of data and corresponding labels. Each set of data contains continuous timing residual points.

[0042] In some embodiments of the present invention, a sliding window is used to process the preprocessed training set to obtain multiple sets of data (multiple sets of inputs). The length of the sliding window can be 10, and each set of inputs contains 10 consecutive timing residuals. The label is the real noise corresponding to each timing residual.

[0043] The process involves cleaning the split training set and then converting its data type. The cleaned training set is forcibly converted from other types (such as strings or integers) to floating-point numbers to ensure that subsequent numerical calculations will not result in errors due to type issues. Finally, the converted training set undergoes normalization. Extrema calculations are then performed on the converted training set to find the minimum and maximum values. Based on these minimum and maximum values, the data is linearly scaled to the [0,1] interval, resulting in the preprocessed training set. The subsequent test set also requires similar preprocessing steps, including data cleaning, data conversion, and data normalization.

[0044] A validation set can be partitioned from the training set to validate the trained LSTM model. During training, the LSTM model uses the Adam optimizer with an initial learning rate of 0.001, a batch size of 32, and 100 training epochs.

[0045] S204. Input multiple sets of data into the LSTM model to be trained in batches to obtain the predicted noise sequence, and calculate the loss using the preset loss function, the predicted noise sequence and the corresponding label.

[0046] S205. Adjust the parameters of the LSTM model to be trained using the loss function until the trained LSTM model is obtained.

[0047] In some embodiments of the present invention, a loss function is set, which can be a mean squared error loss function or an average error loss function. Multiple sets of data are input into the LSTM model to be trained in batches to obtain a predicted noise sequence. The predicted noise sequence and the label, i.e. the actual noise sequence, are then substituted into the set loss function to calculate the loss. The parameters of the LSTM model to be trained are adjusted using the loss until the training conditions are met, and the trained LSTM model is obtained.

[0048] Furthermore, after calculating the preset performance of the trained LSTM model, such as accuracy and error rate, if all performance metrics meet the preset performance accuracy, the trained LSTM model is tested using a test set. If the test results show that the trained LSTM model still meets the performance requirements, then the trained LSTM model is used as the final LSTM model. If the performance of the trained LSTM model does not meet the preset performance metrics, or the performance of the tested LSTM model does not meet the preset performance metrics, then the training and test sets are adjusted, and the LSTM model is continued to be trained and tested using the adjusted training and test sets until the final LSTM model is obtained.

[0049] The LSTM model also includes dropout layers. When training the LSTM model, the dropout rate of dropout layer 1 is set to 0.2, and the dropout rate of dropout layer 2 is also set to 0.2.

[0050] Figure 2 This is a comparison chart of the denoising effect of a test set provided in an embodiment of the present invention. The original pulse arrival times of 530 data points corresponding to the millisecond pulsar PSR J0437-4715, which were acquired but not used in model training, are used as the test set. Timing residuals are calculated based on the test set, processed accordingly, and then input into the trained LSTM model to obtain prediction noise. The prediction noise is then removed from the timing residuals to obtain the denoised timing residuals, i.e., the purified timing residuals. Figure 2 In the diagram, the red curve represents the timing residual before denoising, meaning the timing residual contains some noise; the green curve represents the timing residual after denoising. Figure 2As can be seen, on the one hand, the green curve is smoother overall than the red curve, and the peak value is lower, indicating that the LSTM model can effectively suppress noise in the timing residuals. On the other hand, after denoising by the LSTM model, the residual RMS decreased from 0.409 microseconds to 0.265 microseconds. In summary, this method can effectively remove noise contained in the timing residuals.

[0051] Reference Figure 3 The diagram shows a structural schematic of an electronic device according to an embodiment of the present invention. The specific embodiments of the present invention do not limit the specific implementation of the electronic device.

[0052] like Figure 3 As shown, the electronic device may include: a processor 502, a communications interface 504, a memory 506, and a communications bus 508.

[0053] in: The processor 502, communication interface 504, and memory 506 communicate with each other via communication bus 508.

[0054] Communication interface 504 is used to communicate with other electronic devices or servers.

[0055] The processor 502 is used to execute program 510, specifically the relevant steps in the above method embodiments.

[0056] Specifically, program 510 may include program code that includes computer operation instructions.

[0057] Processor 502 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention. The smart device may include one or more processors of the same type, such as one or more CPUs; or it may include processors of different types, such as one or more CPUs and one or more ASICs.

[0058] Memory 506 is used to store program 510. Memory 506 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0059] Specifically, program 510 can be used to cause processor 502 to perform the operations corresponding to the methods described in the above method embodiments.

[0060] The specific implementation of each step in program 510 can be found in the corresponding descriptions of the steps and units in the above method embodiments, and will not be repeated here. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the devices and modules described above can be referred to the corresponding process descriptions in the foregoing method embodiments, and will not be repeated here.

[0061] It should be noted that, depending on the implementation needs, the various components / steps described in the embodiments of the present invention can be broken down into more components / steps, or two or more components / steps or parts of the operation of components / steps can be combined into new components / steps to achieve the purpose of the embodiments of the present invention.

[0062] The methods described above according to embodiments of the present invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the methods described herein can be processed by software stored on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods described herein. Furthermore, when a general-purpose computer accesses code used to implement the methods shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for executing the methods shown herein.

[0063] Those skilled in the art will recognize that the units and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of the embodiments of the present invention.

[0064] The above embodiments are only used to illustrate the embodiments of the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the embodiments of the present invention. Therefore, all equivalent technical solutions also fall within the scope of the embodiments of the present invention, and the patent protection scope of the embodiments of the present invention should be defined by the claims.

Claims

1. A method for pulsar timing data denoising based on a machine learning LSTM algorithm, characterized in that, The application relates to a method for obtaining a millisecond pulsar time signal. The method comprises the following steps: extracting a first original pulse arrival time sequence from acquired first original timing observation data of a millisecond pulsar, and obtaining a first timing residual sequence between the pulsar time PT and the earth time TT based on the first original pulse arrival time sequence and a preset pulsar timing model; inputting the preprocessed first timing residual sequence into a trained long short-term memory (LSTM) model to obtain a first noise sequence in the preprocessed first timing residual sequence; 2. The method of claim 1, wherein, removing the first noise sequence from the first timing residual sequence to obtain a purified timing residual sequence, and obtaining a pulsar time signal meeting a preset accuracy index through the purified timing residual sequence. The method comprises the following steps: calibrating and correcting the first original pulse arrival time sequence by using the latest ephemeris parameters to obtain a corrected pulse arrival time sequence; 3. The method of claim 1, wherein, comparing the corrected pulse arrival time sequence with the preset pulsar timing model, and performing parameter fitting by using the least square method until the first timing residual sequence is obtained. The LSTM model is stacked with multiple LSTM layers, and the first LSTM layer is set as return_sequences=True. The method comprises the following steps: inputting the preprocessed first timing residual sequence into the first LSTM layer by using a preset sliding window to obtain a first hidden state sequence at each time step, and processing the first hidden state sequence by using the remaining LSTM layers to obtain a context feature vector; 4. To the method according to claim 1, characterized in that, obtaining the first noise sequence in the preprocessed first timing residual sequence based on the context feature vector and multiple fully connected layers.

5. The method according to any one of claims 1 to 4, characterized in that, The latest ephemeris parameters include but are not limited to the right ascension and declination of the pulsar, the rotation frequency and the first derivative, the proper motion, the parallax, the dispersion amount, the Faraday rotation amount and the binary orbit parameters. The trained LSTM model is obtained through the following training process: acquiring second original timing observation data of the millisecond pulsar in a preset historical time period from a radio telescope observation database, and extracting a second original pulse arrival time sequence from the second original timing observation data; obtaining a second timing residual sequence based on the second original pulse arrival time sequence, and dividing the second timing residual sequence into a training set and a test set according to a preset proportion; processing the preprocessed training set by using a preset sliding window to obtain multiple groups of data and corresponding labels, and each group of data contains continuous timing residual points; inputting the multiple groups of data into the LSTM model to be trained in batches to obtain a predicted noise sequence, and calculating a loss by using a preset loss function, the predicted noise sequence and the corresponding labels; adjusting the parameters of the LSTM model to be trained by using the loss until a trained LSTM model is obtained.

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