Layered progressive ppg signal generation method for data augmentation

By constructing a hierarchical progressive PPG signal generation method, we can build modules for heartbeat, cycle, and rhythm. Combined with progressive training and diffusion models, we can solve the problem of inconsistent PPG signal generation in existing technologies, generate high-quality PPG signals, and improve the performance of downstream tasks.

CN122271985APending Publication Date: 2026-06-26ZHEJIANG UNIV

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
ZHEJIANG UNIV
Filing Date
2026-05-12
Publication Date
2026-06-26

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Abstract

This invention discloses a hierarchical progressive PPG signal generation method for data augmentation, comprising: acquiring and preprocessing the original PPG dataset to obtain cardiac cycle segments; constructing a hierarchical progressive PPG signal generation model, which includes a cardiac layer module, a cycle layer module, and a rhythm layer module, respectively used to model the local waveform morphology of a single cardiac cycle, the short-time structure composed of multiple consecutive cardiac beats, and the global rhythm changes over a long time scale; training the hierarchical progressive PPG signal generation model using a progressive training strategy, training each layer module sequentially from local to global and from short sequences to long sequences; and generating a synthesized PPG signal based on the trained model. The hierarchical progressive PPG signal generation method for data augmentation provided by this invention can effectively generate interpretable, high-quality PPG signals in the absence of real, high-quality labeled PPG signals, thereby improving the capabilities of the PPG base model.
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Description

Technical Field

[0001] This invention belongs to the field of biological signal processing and artificial intelligence, and specifically relates to a hierarchical progressive PPG signal generation method for data augmentation. Background Technology

[0002] Photoplethysmography (PPG) is a physiological signal that reflects changes in blood volume in the human body through optical means. It is widely used in cardiovascular disease screening, physiological state monitoring, and wearable health devices. With the increasing application of deep learning technology in the field of medical signal analysis, tasks such as disease classification and health assessment based on PPG signals are becoming increasingly reliant on large-scale, high-quality labeled data.

[0003] However, in practical applications, the acquisition of high-quality PPG data is often limited by factors such as high collection costs, difficulty in annotation, and significant individual differences among subjects, resulting in a limited amount of data available for model training. To alleviate these problems, researchers have attempted to expand PPG datasets through data augmentation or signal generation techniques to improve the generalization performance of models for downstream tasks.

[0004] Existing PPG signal generation methods mostly model the complete time series directly, without fully considering the distinct physiological structural features and multi-timescale characteristics of PPG signals. On the one hand, PPG signals exhibit stable cardiac morphological structures at the local level; on the other hand, they show periodic changes and rhythmic characteristics at longer timescales. Ignoring these hierarchical structures can easily lead to a lack of physiological rationality in the generated signal's local morphology or global rhythm, thus affecting the usability of the generated signal.

[0005] Furthermore, as the length of the generated sequence increases, directly modeling long-term PPG signals often faces problems such as training instability and difficulty in capturing long-range dependencies, resulting in morphological distortion or rhythm drift in the generated results. Existing methods typically lack training mechanisms that learn progressively for different time scales, making it difficult to simultaneously ensure both local waveform consistency and global rhythm consistency.

[0006] Therefore, there is an urgent need for a method that can fully utilize the physiological prior information of PPG signals and achieve high-quality long sequence generation through reasonable training strategies, so as to effectively serve PPG data augmentation and related downstream tasks while ensuring the physiological consistency of the generated signals. Summary of the Invention

[0007] This invention provides a hierarchical progressive PPG signal generation method for data augmentation to solve the aforementioned technical problems, specifically adopting the following technical solution:

[0008] A hierarchical progressive PPG signal generation method for data augmentation includes the following steps:

[0009] The original PPG dataset was obtained and preprocessed to obtain cardiac cycle segments.

[0010] A hierarchical progressive PPG signal generation model is constructed, which includes a heartbeat layer module, a period layer module, and a rhythm layer module, which are used to model the local waveform morphology of a single heartbeat cycle, the short-time structure composed of multiple consecutive heartbeats, and the global rhythm changes over a long time scale, respectively.

[0011] The hierarchical progressive PPG signal generation model is trained using a progressive training strategy, with each layer module trained sequentially from local to global and from short sequences to long sequences.

[0012] Synthetic PPG signals are generated based on the trained model for data augmentation.

[0013] Furthermore, the preprocessing includes:

[0014] Denoising the PPG signal to eliminate motion artifacts and high-frequency noise;

[0015] The amplitude of the denoised signal is normalized to reduce the difference in signal amplitude between different individuals;

[0016] The heartbeat detection algorithm is used to segment the cycle and extract individual heartbeat cycle segments.

[0017] Furthermore, the hierarchical progressive PPG signal generation model incorporates a large language model to generate multi-level signal descriptions, wherein:

[0018] The cardiac layer module takes the PPG waveform of a single cardiac cycle as input, extracts local morphological features, and uses text template combinations to generate cardiac layer descriptions of 5, 10, and 15 cardiac cycles to describe the physiological structure of a single heartbeat.

[0019] The cycle layer module combines multiple consecutive heartbeat layer representations to form cycle layer inputs with lengths of 5, 10, and 15 cycles, generating cycle layer descriptions to express structured physiological information at short timescales.

[0020] The rhythm layer module fuses the period layer descriptions of 5, 10, and 15 cycle lengths with the original PPG signal and its corresponding disease label or physiological state label to generate a rhythm layer description to characterize the overall rhythm change features and its relationship with the disease state.

[0021] Furthermore, each module first extracts the feature representation of its own layer, and then uses a large language model to generate the corresponding semantic description. The cardiac layer description, periodic layer description, and rhythm layer description together constitute a semantic conditional representation of the multi-scale physiological characteristics of PPG signals, which is used to guide the subsequent signal generation process.

[0022] Furthermore, the progressive training strategy includes:

[0023] The heartbeat layer module, periodic layer module, and rhythm layer module are trained sequentially according to the hierarchical order, so that the model gradually transitions from learning local waveform morphology to learning global rhythm pattern.

[0024] During the training process at the same level, training data of 5, 10, and 15 periods are introduced in order of increasing period length, so that the model can learn temporal dependencies from simple to complex.

[0025] Furthermore, the progressive training strategy follows a learning sequence from local to global in scale dimension and from short to long in time dimension, where the scale set S={b,c,r} represents the cardiac layer, cycle layer, and rhythm layer, respectively, and the cycle length set T={5,10,15} represents the number of consecutive cycles used to construct training segments; in any training step, from the corresponding data subset... Sampling small batches of samples And optimize the unified generation objective function:

[0026]

[0027] in, The generation loss function is instantiated from the selected backbone network; the overall training course follows a preset order from easy to difficult, so that the model gradually transitions from local morphological learning to global rhythm learning, and gradually expands from short-term dependency learning to long-term dependency learning.

[0028] Furthermore, the synthesis of PPG signals is generated based on the trained model, specifically including: using at least one of the cardiac layer description, periodic layer description, and rhythm layer description as conditional information to guide the diffusion model to generate PPG signals consistent with the conditions during the stepwise denoising generation process, thereby achieving joint control of the local morphological features, short-time structure, and long-time rhythm features of the PPG signal.

[0029] Furthermore, the diffusion model adopts a continuous dynamics or flow matching form, representing the generation of PPG waveforms as a continuous evolution process driven by a learnable vector field at normalized time t∈[0,1]:

[0030]

[0031] Where P represents the hierarchical conditions extracted and fused from three scales: heartbeat, period, and rhythm; during training, these conditions are obtained by analyzing noisy samples. Compared with real samples Construct intermediate states and minimize the loss of physiological transition consistency:

[0032] .

[0033] Furthermore, the data augmentation includes:

[0034] Synthetic PPG signals are combined with the original PPG data to form an extended dataset, or to replace part of the original data, for training downstream disease classification models or physiological state recognition models, in order to improve the robustness and generalization ability of the models.

[0035] Furthermore, corresponding loss function weights are set during the training process of the heartbeat layer, cycle layer, and rhythm layer. The model as a whole is optimized using the Adam optimizer. The learning rate, loss weights, and cycle length-related hyperparameters required for each training stage are determined by grid search on the validation set.

[0036] The advantage of this invention is that the hierarchical progressive PPG signal generation method for data augmentation provided can effectively generate interpretable high-quality PPG signals in the absence of real high-quality labeled PPG signals, thereby improving the capabilities of the PPG base model. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a schematic diagram of the hierarchical progressive PPG signal generation method for data augmentation according to this application;

[0039] Figure 2 This is the PPG signal diagram generated by the present invention;

[0040] Figure 3 This is a comparison of the t-SNE distribution of the generated signal and the real signal, as well as the distributions of Heart Rate, RMSSD, and SDNN. Detailed Implementation

[0041] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0042] like Figure 1 The diagram illustrates a hierarchical progressive PPG signal generation method for data augmentation according to this application, comprising the following steps: S1: Obtaining and preprocessing the original PPG dataset to obtain cardiac cycle segments. S2: Constructing a hierarchical progressive PPG signal generation model, which includes a cardiac layer module, a cycle layer module, and a rhythm layer module, respectively used to model the local waveform morphology of a single cardiac cycle, the short-time structure composed of multiple consecutive cardiac beats, and the global rhythm changes over long time scales. S3: Training the hierarchical progressive PPG signal generation model using a progressive training strategy, training each layer module sequentially from local to global and from short sequences to long sequences. S4: Generating synthetic PPG signals based on the trained model for data augmentation. This hierarchical progressive PPG signal generation method for data augmentation can effectively generate interpretable, high-quality PPG signals in the absence of real, high-quality labeled PPG signals, thereby improving the capabilities of the PPG base model. The specific steps are described in detail below.

[0043] For step S1: Obtain the original PPG dataset and preprocess it to obtain cardiac cycle segments.

[0044] Understandably, the dataset can come from public databases or be obtained through wearable devices.

[0045] In embodiments of this application, preprocessing includes:

[0046] The PPG signal is denoised to eliminate motion artifacts and high-frequency noise.

[0047] The amplitude of the denoised signal is normalized to reduce the difference in signal amplitude between different individuals.

[0048] Periodic segmentation is performed based on a heartbeat detection algorithm to extract individual heartbeat cycle segments. Specifically, the start and end positions of each heartbeat cycle are determined using the heartbeat detection algorithm, thereby dividing the continuous PPG signal into several single heartbeat cycle segments. Formulatically, let the original waveform corresponding to a single heartbeat cycle be represented as... The place of public notice shall be set up by The cardiac layer sample consisting of consecutive cardiac cycles is represented as follows: ,in This indicates the beat-scale. The period length is used in this implementation method. At least 5, 10, and 15 should be selected, as this waveform represents the smallest physiological unit for subsequent hierarchical modeling.

[0049] After segmenting the cardiac cycle, various training samples are constructed based on different time scales. Multiple adjacent cardiac cycles are sequentially concatenated to form a cycle layer sample. Formulatically, let... A periodic layer sample consisting of consecutive heartbeat cycles is represented as follows: ,in Indicates a cycle-scale layer. Let be the period length, used to represent short-sequence structures of different lengths. Simultaneously, rhythmic layer samples are constructed on longer time scales and associated with corresponding disease labels or physiological state labels. Formulatically, let the rhythmic layer sample be represented as... ,in This represents the rhythm-scale, a sample used to characterize overall rhythmic changes over long time scales.

[0050] For step S2: Construct a hierarchical progressive PPG signal generation model. The hierarchical progressive PPG signal generation model includes a heartbeat layer module, a period layer module, and a rhythm layer module, which are used to model the local waveform morphology of a single heartbeat cycle, the short-time structure composed of multiple consecutive heartbeats, and the global rhythm changes over a long time scale, respectively.

[0051] Specifically, in the model building phase, a hierarchical progressive PPG signal generation model, HP3G, was constructed based on the aforementioned multi-scale samples. This model is divided into modules according to the physiological organization of PPG signals: a periodic layer module and a rhythmic layer module. A large language model is introduced to describe and generate signal representations at different levels. Specifically, for the cardiac layer samples… The system extracts feature information reflecting the morphological structure of the cardiac cycle and inputs it into the description generation module to generate a cardiac layer description. This description is used to characterize the local waveform morphology of a single heartbeat. For periodic layer samples... A periodic layer representation is constructed to describe the morphological changes and local rhythmic features between multiple consecutive heartbeats, and the corresponding periodic layer description is generated. For rhythm layer samples By fusing periodic layer descriptions, raw PPG waveform information, and disease or state labels, a rhythm layer description is generated. This is used to express overall rhythmic patterns over long time scales and their association with disease states. The above description... , and This constitutes a semantic conditional representation of the multi-scale physiological characteristics of PPG signals.

[0052] Specifically, the cardiac layer module takes the PPG waveform of a single cardiac cycle as input, extracts local morphological features, and uses text template combinations to generate cardiac layer descriptions of 5, 10, and 15 cardiac cycles to describe the physiological structure of a single heartbeat.

[0053] The cycle layer module combines multiple consecutive cardiac beat layer representations to form cycle layer inputs of 5, 10, and 15 cycles in length, generating cycle layer descriptions to express structured physiological information at short timescales.

[0054] The rhythm layer module fuses the period layer descriptions of 5, 10, and 15 cycle lengths with the original PPG signal and its corresponding disease label or physiological state label to generate a rhythm layer description to characterize the overall rhythm change features and its relationship with the disease state.

[0055] In the embodiments of this application, each layer module first extracts the feature representation of its own layer, and then uses a large language model to generate the corresponding semantic description. The cardiac layer description, periodic layer description and rhythm layer description together constitute the semantic conditional representation of the multi-scale physiological characteristics of PPG signals, which is used to guide the subsequent signal generation process.

[0056] For step S3: The hierarchical progressive PPG signal generation model is trained using a progressive training strategy, and each layer module is trained sequentially from local to global and from short sequences to long sequences.

[0057] In embodiments of this application, the progressive training strategy includes:

[0058] The cardiac rhythm layer module, periodic rhythm layer module, and rhythmic rhythm layer module are trained sequentially according to hierarchical order, allowing the model to gradually transition from learning local waveform morphology to learning global rhythmic patterns. During the training process at the same level, training data with period lengths of 5, 10, and 15 are introduced in order of increasing period length, allowing the model to gradually learn temporal dependencies from simple to complex.

[0059] Specifically, during the model training phase, a progressive training strategy was employed to optimize HP3G. The training process began with the cardiac layer, allowing the model to prioritize learning the stable morphological structure of a single cardiac cycle. Subsequently, samples from the periodic and rhythmic layers were gradually introduced, enabling the model to learn short-term structures and long-term rhythmic patterns based on its existing knowledge of local morphological features. Simultaneously, during the training of the periodic and rhythmic layers, training samples were introduced progressively in order of cycle length, from shortest to longest. The periodic or rhythmic layer samples are used for training, and then the samples are introduced sequentially. and The training strategy uses a variety of samples to allow the model to gradually learn temporal dependencies from simple to complex. This ensures that the model has stable local modeling capabilities before learning long-term structures, which helps improve the overall stability of the training.

[0060] In the embodiments of this application, the progressive training strategy follows a course learning sequence from local to global in scale dimension and from short to long in time dimension, where the scale set S={b,c,r} represents the cardiac layer, periodic layer, and rhythmic layer, respectively, and the period length set T={5,10,15} represents the number of consecutive periods used to construct training segments. In any training step, from the corresponding data subset... Sampling small batches of samples And optimize the unified generation objective function:

[0061]

[0062] in, The generation loss function is instantiated from the selected backbone network. The overall training course follows a preset order from easy to difficult, gradually transitioning the model from local morphological learning to global rhythmic learning, and gradually expanding from short-term dependency learning to long-term dependency learning.

[0063] In the embodiments of this application, corresponding loss function weights are set during the training process of the heartbeat layer, cycle layer and rhythm layer. The model as a whole is optimized using the Adam optimizer. The learning rate, loss weights and cycle length related hyperparameters required for training at each stage are determined by grid search on the validation set.

[0064] For step S4: Generate a synthetic PPG signal based on the trained model for data augmentation.

[0065] In the embodiments of this application, the generation of synthetic PPG signals based on the trained model specifically includes: using at least one of the cardiac layer description, periodic layer description and rhythm layer description as conditional information to guide the diffusion model to generate PPG signals consistent with the conditions during the gradual denoising generation process, thereby achieving joint control of the local morphological features, short-term structure and long-term rhythm features of the PPG signal.

[0066] Specifically, in the generation stage, a conditional diffusion model is used to generate the PPG signal. Formulatly, the true target signal is assumed to be... During the forward diffusion process, an intermediate state is obtained by gradually adding Gaussian noise. ,in This indicates the number of diffusion steps. During the reverse generation process, the model predicts the noise component and progressively denoises it based on conditional information at each diffusion step. This conditional information includes at least a cardiac layer description. Periodic layer description and rhythm layer description One or a combination of the above conditions. By introducing the above conditional information into the diffusion denoising process, the generated result is guided to maintain consistency with the corresponding conditions in terms of local morphology, short-term structure, and long-term rhythm, thereby generating a synthetic PPG signal with high physiological rationality.

[0067] In the embodiments of this application, the diffusion model adopts a continuous dynamics or flow matching form, representing the generation of PPG waveforms as a continuous evolution process driven by a learnable vector field over normalized time t∈[0,1]:

[0068]

[0069] Where P represents the hierarchical conditions extracted and fused from semantic / conditional data at three scales: heart rate, period, and rhythm. During training, these conditions are obtained from noisy samples. Compared with real samples Construct intermediate states and minimize the loss of physiological transition consistency:

[0070] .

[0071] In embodiments of this application, data enhancement includes:

[0072] Synthetic PPG signals are combined with the original PPG data to form an expanded dataset, or partially replace the original data, for training downstream disease classification models or physiological state recognition models, thereby improving the robustness and generalization ability of the models. This method expands the data scale without requiring additional real PPG data collection and enhances the robustness and generalization ability of downstream disease classification or physiological state recognition models on the test set.

[0073] The dataset is divided into training, testing, and validation sets according to a certain ratio. Models are built using different hyperparameter combinations and input into the training set samples. The models are trained by minimizing the loss function using the Adam optimizer, and their performance is validated on the validation set. After selecting the optimal hyperparameter combination on the validation set, the corresponding model is tested on the testing set to obtain the final performance result of the proposed method.

[0074] Specifically, taking this experimental dataset as an example, a total of 18,295 patients' PPG signal data were collected from two public datasets (vitalDB and MIMIC-III) and one private dataset (Lexin). Using the current state-of-the-art PPG basic model PaPaGei, and comparing it with the most advanced existing data augmentation methods, Table 1 shows that the PPG signals generated by this invention are of better quality and can better help the PPG basic model improve the performance of downstream tasks.

[0075] Table 1. Performance comparison between the current method and the most advanced data augmentation methods.

[0076]

[0077] pass Figure 2 and Figure 3 As can be seen, the PPG signal generated by this invention can more realistically reflect the physiological characteristics of PPG signals, and the generated result is closer to the real PPG signal and more consistent with the characteristics of the real signal.

[0078] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the present invention in any way, and all technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A layered progressive PPG signal generation method for data augmentation, characterized in that, Includes the following steps: The original PPG dataset was obtained and preprocessed to obtain cardiac cycle segments. A hierarchical progressive PPG signal generation model is constructed, which includes a heartbeat layer module, a period layer module, and a rhythm layer module, which are used to model the local waveform morphology of a single heartbeat cycle, the short-time structure composed of multiple consecutive heartbeats, and the global rhythm changes over a long time scale, respectively. The hierarchical progressive PPG signal generation model is trained using a progressive training strategy, with each layer module trained sequentially from local to global and from short sequences to long sequences. Synthetic PPG signals are generated based on the trained model for data augmentation.

2. The hierarchical progressive PPG signal generation method for data augmentation according to claim 1, characterized in that, The preprocessing includes: Denoising the PPG signal to eliminate motion artifacts and high-frequency noise; The amplitude of the denoised signal is normalized to reduce the difference in signal amplitude between different individuals; Based on the heartbeat detection algorithm, the cycle is segmented to extract individual heartbeat cycle segments.

3. The hierarchical progressive PPG signal generation method for data augmentation according to claim 1, characterized in that, The hierarchical progressive PPG signal generation model introduces a large language model to generate multi-level signal descriptions, wherein: The cardiac layer module takes the PPG waveform of a single cardiac cycle as input, extracts local morphological features, and uses text template combinations to generate cardiac layer descriptions of 5, 10, and 15 cardiac cycles to describe the physiological structure of a single heartbeat. The cycle layer module combines multiple consecutive heartbeat layer representations to form cycle layer inputs with lengths of 5, 10, and 15 cycles, generating cycle layer descriptions to express structured physiological information at short timescales. The rhythm layer module fuses the period layer descriptions of 5, 10, and 15 cycle lengths with the original PPG signal and its corresponding disease label or physiological state label to generate a rhythm layer description to characterize the overall rhythm change features and its relationship with the disease state.

4. The hierarchical progressive PPG signal generation method for data augmentation according to claim 3, characterized in that, Each module first extracts the feature representation of its own layer, and then uses a large language model to generate the corresponding semantic description. The cardiac layer description, periodic layer description and rhythm layer description together constitute the semantic conditional representation of the multi-scale physiological characteristics of PPG signals, which is used to guide the subsequent signal generation process.

5. The hierarchical progressive PPG signal generation method for data augmentation according to claim 4, characterized in that, The progressive training strategy includes: The heartbeat layer module, periodic layer module, and rhythm layer module are trained sequentially according to the hierarchical order, so that the model gradually transitions from learning local waveform morphology to learning global rhythm pattern. During the training process at the same level, training data of 5, 10, and 15 periods are introduced in order of increasing period length, so that the model can learn temporal dependencies from simple to complex.

6. The hierarchical progressive PPG signal generation method for data augmentation according to claim 5, characterized in that, The progressive training strategy is performed according to a curriculum learning order from local to global in the scale dimension and from short to long in the time dimension, wherein the scale set S={b, c, r} respectively represents a heartbeat layer, a period layer and a rhythm layer, and the period length set T={5, 10, 15} represents a number of continuous periods used for constructing a training segment; in any training step, a corresponding data subset Sampling small batch samples ), and optimizing a unified generation objective function: wherein, is a generative loss function instantiated by the selected generative backbone network; the overall training curriculum follows a pre-set order from easy to difficult, making the model gradually transition from local pattern learning to global rhythm learning, and gradually expand from short-time dependency learning to long-time dependency learning.

7. The hierarchical progressive PPG signal generation method for data augmentation according to claim 3, characterized in that, The synthesis of PPG signals based on the trained model specifically includes: using at least one of cardiac layer description, periodic layer description and rhythm layer description as conditional information to guide the diffusion model to generate PPG signals consistent with the conditions during the stepwise denoising generation process, thereby achieving joint control of the local morphological features, short-term structure and long-term rhythm features of the PPG signal.

8. The hierarchical progressive PPG signal generation method for data augmentation according to claim 7, characterized in that, The diffusion model adopts a continuous dynamics or flow matching form, representing the generation of PPG waveforms as a continuous evolution process driven by a learnable vector field at normalized time t∈[0,1]. Wherein P represents the hierarchical conditions extracted and fused by the three semantic / conditions of heart beat, cycle, and rhythm; during training, the intermediate state is constructed between the noise sample and the real sample and the physiological transfer consistency loss is minimized: 。 9. The hierarchical progressive PPG signal generation method for data augmentation according to claim 1, characterized in that, The data augmentation includes: Synthetic PPG signals are combined with the original PPG data to form an extended dataset, or to replace part of the original data, for training downstream disease classification models or physiological state recognition models, in order to improve the robustness and generalization ability of the models.

10. The hierarchical progressive PPG signal generation method for data augmentation according to claim 1, characterized in that, During the training of the heartbeat layer, cycle layer, and rhythm layer, corresponding loss function weights were set respectively. The model as a whole was optimized using the Adam optimizer. The learning rate, loss weights, and cycle length-related hyperparameters required for each training stage were determined by grid search on the validation set.