Carbon data prediction method and system of data form perception loss based on Parseval theorem

Abstract

The invention discloses a carbon data prediction method and system for data form perception loss based on the Parseval theorem, and belongs to the field of carbon data prediction.The method comprises the following steps that original TCCON site data is preprocessed to obtain preprocessed data; fourier transform and key feature extraction are carried out on the preprocessed data to obtain frequency domain features; constructing an atmospheric carbon data prediction model, and adjusting energy distribution based on frequency domain characteristics to obtain adjusted frequency domain data; lag offset detection and adjustment optimization are carried out based on the adjusted frequency domain data and the preprocessed data to obtain adjusted lag offset parameters; constructing a joint loss function based on the adjusted lag offset parameter and the adjusted frequency domain data; training an atmospheric carbon data prediction model based on the joint loss function and the preprocessed data to obtain a trained atmospheric carbon data prediction model; and inputting new atmospheric carbon data to be predicted into the trained atmospheric carbon data prediction model to obtain a prediction result of the atmospheric carbon data.

Description

Technical Field

[0001] The present invention belongs to the technical field of carbon data prediction, and in particular relates to a carbon data prediction method and system based on data morphology perception loss of Parseval theorem. Background Art

[0002] In the field of time series prediction, the complex pattern changes and dynamic characteristics of signals place higher demands on model performance. Traditional time series methods mostly focus on modeling time domain characteristics, but these methods often seem powerless when dealing with the frequency domain characteristics and overall morphological changes of complex dynamic signals. Especially in applications such as atmospheric carbon concentration prediction, signals contain diverse frequency components and sudden change characteristics, which are difficult to capture with a single time domain characteristic.

[0003] In the field of atmospheric carbon concentration prediction, the TCCON (Total Carbon Column Observing Network) dataset has become an important data source. TCCON monitors the carbon column concentration in the atmosphere through ground observation stations around the world, providing accurate data for studying the temporal and spatial distribution of atmospheric carbon concentration. These data contain a variety of meteorological and environmental variables, which can reflect the changing trend of carbon concentration over time. The TCCON dataset is characterized by a high degree of temporal sequence and dynamic changes between data, and due to the different influences of climatic conditions and human activities in different regions of the world, the pattern of carbon concentration changes is complex and uncertain. Therefore, it is difficult to fully capture the changing pattern of carbon concentration using traditional time domain methods, especially in the face of frequent and drastic changes. Therefore, there is an urgent need for a carbon data prediction system. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a carbon data prediction system based on data morphology perception loss of Parseval's theorem to solve the problems existing in the above prior art.

[0005] To achieve the above object, the present invention provides a carbon data prediction method based on Parseval's theorem and data morphology-aware loss, comprising the following steps:

[0006] Preprocessing the original TCCON site data to obtain preprocessed data; wherein the preprocessed data includes prediction data and verification data;

[0007] Performing Fourier transform on the preprocessed data to obtain frequency domain data;

[0008] Extracting key features from the frequency domain data to obtain frequency domain features;

[0009] Constructing an atmospheric carbon data prediction model, and adjusting the energy distribution based on the frequency domain characteristics to obtain adjusted frequency domain data;

[0010] Performing hysteresis offset detection and adjustment optimization based on the adjusted frequency domain data and the preprocessed data to obtain adjusted hysteresis offset parameters;

[0011] constructing a joint loss function based on the adjusted lag offset parameter and the adjusted frequency domain data;

[0012] Training the atmospheric carbon data prediction model based on the joint loss function and the preprocessed data to obtain a trained atmospheric carbon data prediction model;

[0013] The new atmospheric carbon data to be predicted is input into the trained atmospheric carbon data prediction model to obtain the prediction result of the atmospheric carbon data.

[0014] Optionally, the process of preprocessing the original TCCON site data includes:

[0015] The original TCCON site data were subjected to missing value interpolation, fixed interval sampling, outlier removal and regularization to obtain preprocessed data.

[0016] Optionally, the process of performing Fourier transform on the preprocessed data to obtain frequency domain data includes:

[0017] Aligning the predicted data and the verification data by timestamp to obtain aligned data;

[0018] Unifying the data dimensions of the prediction data and the verification data in the aligned data to obtain dimension-unified data;

[0019] Performing Fourier transform on the dimensionally unified data to obtain frequency domain data.

[0020] Optionally, the process of extracting the frequency domain features includes calculating the energy distribution of the signal at different frequencies by Fourier transform;

[0021] The process of calculating the energy distribution of the signal at different frequencies includes:

[0022] The frequency domain signal corresponding to the frequency domain data is obtained by Fourier transform;

[0023] Calculating the amplitude and phase information of each frequency component based on the frequency domain signal;

[0024] The energy of each frequency component is calculated based on the amplitude and phase information of each frequency component, and the energy distribution is obtained based on the energies of several frequency components.

[0025] Optionally, the process of adjusting the energy distribution based on the frequency domain features includes: introducing a morphological perception optimization mechanism based on Parseval's theorem into a loss function to obtain Parseval's morphological perception loss, and adjusting the frequency domain energy feedback response to the time domain signal morphological features based on the Parseval's morphological perception loss.

[0026] Optionally, the process of obtaining the adjusted hysteresis offset parameter comprises:

[0027] Obtaining a predicted value based on the atmospheric carbon data prediction model;

[0028] Identify potential lag effects by calculating the correlation between predicted and true values;

[0029] Correlation analysis was performed at different lag steps to estimate the lag amount;

[0030] The lag step length is introduced into the loss function to obtain the lag offset loss. Based on the lag offset loss, the response of the atmospheric carbon data prediction model at different time steps is adjusted to capture the lag effect between the true value and the predicted value, and the adjusted lag offset parameter is determined.

[0031] Optionally, the process of constructing the joint loss function includes: weighting and synthesizing the lag offset loss and the Parseval morphological perception loss to form a joint loss function.

[0032] The present invention also provides a carbon data prediction system based on Parseval's theorem data morphology perception loss, which is used to implement a carbon data prediction method based on Parseval's theorem data morphology perception loss, the system comprising: a data preprocessing module, a data time-frequency conversion module, a frequency domain feature calculation and extraction module, a frequency domain energy adjustment feedback module, a hysteresis offset detection and adjustment optimization module, a hysteresis offset parameter loss and Parseval's morphology perception loss fusion module, a model training optimization module and a carbon data prediction module;

[0033] The data preprocessing module is used to preprocess the original TCCON site data to obtain preprocessed data; the preprocessed data includes prediction data and verification data;

[0034] The data time-frequency conversion module is used to perform Fourier transform on the prediction data and the verification data;

[0035] The frequency domain feature calculation and extraction module is used to extract the frequency domain features of the prediction data and the verification data after Fourier transformation, and obtain the energy distribution of the prediction data and the verification data at different frequencies through Fourier transformation calculation;

[0036] The frequency domain energy adjustment feedback module is used to form Parseval morphological perception loss and respond the frequency domain energy adjustment feedback to the time domain signal morphological characteristics;

[0037] The hysteresis offset detection and adjustment optimization module is used to identify potential hysteresis effects by calculating the correlation between the predicted value and the true value;

[0038] The hysteresis offset parameter loss and Parseval morphological perception loss fusion module is used to weight the hysteresis offset loss and the Parseval morphological perception loss to synthesize a joint loss function;

[0039] The model training optimization module is used to train the atmospheric carbon data prediction model based on the joint loss function;

[0040] The carbon data prediction module is used to perform data prediction on the acquired carbon concentration data to be predicted based on the trained atmospheric carbon data prediction model to obtain the prediction result of the atmospheric carbon data.

[0041] Compared with the prior art, the present invention has the following advantages and technical effects:

[0042] The carbon data prediction method based on Parseval's theorem and data morphology-aware loss proposed in this paper significantly improves the accuracy and efficiency of atmospheric carbon data prediction through a series of innovative steps. First, by preprocessing the original TCCON site data, the data is divided into prediction data and verification data, providing a structured data foundation for model training and verification. Then, the preprocessed data is converted to the frequency domain using Fourier transform, and key features are extracted to capture the periodicity and trend information in the data, enhancing the model's understanding of the inherent laws of the data.

[0043] By adjusting the energy distribution of frequency domain data, the model can pay more attention to the features that have a greater impact on the prediction results, thereby improving the accuracy of the prediction. Hysteresis offset detection and adjustment optimization further refine the model parameters, allowing the model to better adapt to the time series characteristics of the data. The construction of the joint loss function effectively combines frequency domain and time domain information, providing a more comprehensive optimization target for model training.

[0044] Finally, the atmospheric carbon data prediction model obtained through training can accurately predict new atmospheric carbon data to be predicted, providing strong technical support for carbon emission monitoring and management. This method not only improves the accuracy of prediction, but also enhances the robustness of the model to outliers and noise through data morphology perception loss, making the prediction results more stable and reliable. The present invention has important application value and broad market prospects in the field of carbon data prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0046] Figure 1 This is a flow chart of a carbon data prediction method based on data morphology perception loss of Parseval's theorem according to an embodiment of the present invention;

[0047] Figure 2 This is a structural diagram of a carbon data prediction system based on Parseval theorem data form perception loss according to an embodiment of the present invention;

[0048] Figure 3 This is a schematic diagram of frequency domain energy adjustment based on the Parseval principle according to an embodiment of the present invention;

[0049] Figure 4 This is an effect diagram of the data morphology-aware loss function of Parseval's theorem in an embodiment of the present invention;

[0050] Figure 5 Monitoring of shape perception and hysteresis sensitivity loss and overall loss changes during model training in an embodiment of the present invention;

[0051] Figure 6 The system prediction experimental form perception loss of the embodiment of the present invention is used to compare and visualize the prediction results before and after. DETAILED DESCRIPTION

[0052] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0053] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0054] Embodiment 1

[0055] Parseval's theorem provides a theoretical tool to feed back frequency domain energy balance to time domain characteristics, providing a new research perspective for optimizing signal morphology perception. By analyzing the energy distribution of the signal in the frequency domain, it is not only possible to describe high-frequency changes more accurately, but also to enhance the ability to capture overall trends. This method shows significant advantages in modeling complex non-stationary signals, especially in the face of extreme values ​​and dynamic changes in signals, which can improve the robustness and accuracy of the prediction model.

[0056] In recent years, with the combination of frequency domain analysis and deep learning, researchers have designed a variety of model optimization methods based on frequency domain energy perception. By introducing frequency domain characteristics into the loss function, the model can more keenly perceive the morphological characteristics of the signal, thereby achieving the coordinated optimization of global trend prediction and local fluctuation capture of time series. This method shows broad application prospects in the modeling of complex dynamic systems such as atmospheric science, financial markets and energy monitoring.

[0057] Combining the analysis of frequency domain energy with Parseval's theorem helps to optimize the prediction model of carbon data and improve its perception of abnormal fluctuations. To this end, the present invention provides a carbon data prediction method based on Parseval's theorem data morphology perception loss, including: preprocessing the original TCCON site data to obtain preprocessed data; wherein the preprocessed data includes prediction data and verification data; Fourier transforming the preprocessed data to obtain frequency domain data; extracting key features from the frequency domain data to obtain frequency domain features; constructing an atmospheric carbon data prediction model, adjusting the energy distribution based on the frequency domain features to obtain adjusted frequency domain data; performing hysteresis offset detection and adjustment optimization based on the adjusted frequency domain data and the preprocessed data to obtain adjusted hysteresis offset parameters; constructing a joint loss function based on the adjusted hysteresis offset parameters and the adjusted frequency domain data; training the atmospheric carbon data prediction model based on the joint loss function and the preprocessed data to obtain a trained atmospheric carbon data prediction model; inputting new atmospheric carbon data to be predicted into the trained atmospheric carbon data prediction model to obtain the prediction result of atmospheric carbon data.

[0058] like Figure 1 As shown, this embodiment provides a carbon data prediction method based on Parseval's theorem with data morphology-aware loss, including the following steps:

[0059] Step S1, preprocessing the TCCON site data including missing value interpolation, fixed interval sampling, outlier removal and regularization;

[0060] S11. Missing value interpolation: In the data preprocessing step, cubic spline interpolation is used to interpolate missing values. Specifically, for each missing data point, the information of the adjacent data points before and after it is used to fit the changing trend of the data through the cubic spline function to generate a smooth curve to fill the missing value. This method can avoid the limitations of linear interpolation and provide smoother and more accurate interpolation results. It is suitable for processing missing values ​​in time series data, especially when the data fluctuates greatly, and can effectively avoid the accumulation of errors caused by interpolation.

[0061] Cubic spline interpolation is a method commonly used to process missing values ​​in time series data. Unlike linear interpolation, cubic spline interpolation can generate a smooth curve to avoid data mutations and is suitable for situations where data fluctuations are large. The specific implementation of this embodiment includes the following steps:

[0062] (1) Select neighboring data points: For each missing data point x ti , select the known data points x before and after it ti-1 and x ti+1 .

[0063] (2) Fitting cubic polynomial: Interpolate the adjacent data points through the cubic spline function. The form of the cubic spline function is:

[0064] S(x)=a i x 3 +b i x 2 +c i x+d i

[0065] Among them, a i , b i , c i , d i is the coefficient to be determined.

[0066] (3) Calculate the coefficients: These coefficients are calculated by solving the system of equations using the values ​​of the known data points and the boundary conditions.

[0067] (4) Generate interpolation: Use the calculated coefficients to interpolate the missing value x ti .

[0068] S12, Fixed interval sampling (hours): Fixed interval sampling is performed on TCCON station data, and all timestamp data are standardized to a sampling interval of once per hour. By adjusting the timestamps of the original data, consistency and uniformity between time points in the data set are ensured, thereby avoiding analysis bias caused by irregular time intervals and ensuring that the data structure can be unified in subsequent data processing and modeling.

[0069] Timestamp standardization: In time series data, especially data collected from different sensors, timestamps may be irregular. Therefore, before modeling the TCCON site data, its timestamps need to be standardized to ensure that the time intervals of the data set are consistent. The specific implementation of this embodiment includes the following steps:

[0070] (1) Timestamp unification: All original timestamps are adjusted to a uniform time interval, such as sampling once every hour.

[0071] (2) Formula: Assume that the timestamps are t1, t2, ..., t n , by adjusting the timestamp t of the original data i To meet the hourly requirement, generate a new time series:

[0072] t′ i =t1+i×Δt,Δt=1hour.

[0073] S13. Outlier removal: Use an outlier detection method based on statistical analysis to remove outliers in the data. Specifically, the IQR (interquartile range) method is used to identify and remove extreme data points that deviate significantly from the normal distribution. For each data point, first calculate its quartile range (Q1, Q3) and its IQR = Q3-Q1. If the data point exceeds Q1-1.5*IQR or Q3+1.5*IQR, it is considered an outlier and is removed.

[0074] IQR (interquartile range) method and Z-score: In time series data, outliers are often caused by sensor failure, environmental interference or data entry errors. These outliers can be effectively identified and removed through statistical analysis methods. The specific implementation of this embodiment includes the following steps:

[0075] (1) Calculate the first quartile Q1 and the third quartile Q3 of the data, where:

[0076] Q1=25th percentile, Q3=75th percentile

[0077] (2) Calculate the interquartile range: IQR = Q3-Q1

[0078] (3) Calculate the upper and lower bounds:

[0079] Lower bound=Q1-1.5xIQR, Upper bound=Q3+1.5xIQR

[0080] (4) Any data points outside these limits are considered outliers and are removed.

[0081] S14, Regularization: Regularize the processed data to eliminate the impact of different feature dimension differences on model training. Use the Z-score standardization method to calculate the mean and standard deviation of each feature, and convert each feature value into a deviation value under its standard deviation unit, so that the mean of all features is 0 and the standard deviation is 1. Accelerate the model training process and improve the convergence of the model, avoiding instability in the model training process caused by inconsistent dimensions.

[0082] Z-score standardization: In order to avoid model training instability due to different dimensions between different features, all features need to be standardized. The specific implementation of this embodiment includes the following steps:

[0083] (1) Calculate the mean and standard deviation: Calculate the mean μi and standard deviation σi for each feature Xi.

[0084] (2) Standardization: Use the Z-score standardization method to convert each feature Xi into a deviation value in standard deviation units:

[0085]

[0086] After this processing, the mean of each feature is 0 and the standard deviation is 1.

[0087] (3) Apply regularization: Perform subsequent training process on standardized data.

[0088] Step S2: During the model training process, Fourier transform the prediction data and verification data to complete the conversion from time domain to frequency domain;

[0089] S21. Matching predicted data with verification data: Align and match the predicted data with the verification data to ensure that they have the same time range and data dimension, and that the data points correspond one to one. Through timestamp alignment and preprocessing, the time consistency of the predicted data and the verification data is ensured, thereby providing accurate input for the subsequent Fourier transform. As a specific implementation method of this embodiment, the following steps are included: aligning the predicted data and the verification data by timestamp to obtain aligned data; unifying the data dimensions of the predicted data and the verification data in the aligned data to obtain dimension-unified data; and performing Fourier transform on the dimension-unified data to obtain frequency domain data.

[0090] (1) Timestamp alignment: For the predicted data {X pred ,t} and verification data {X val ,t}, timestamp matching is performed to ensure that each data point t has the same time range between the two.

[0091] T1 and T2 represent the start time and end time of the time period respectively.

[0092] So that: predict data {X pred ,t} and verification data {X val ,t} are synchronized within the same time interval.

[0093] (2) Data dimensionality unification: Ensure that the dimensions of the prediction data and the verification data are consistent, that is, the number of variables at each time point is the same, to ensure that they can be matched one by one. If there is multivariate data, ensure that the multidimensional features of the prediction data and the verification data are consistent at each time step.

[0094] S22, data Fourier transform calculation: The original time domain data (prediction data and verification data) is converted to the frequency domain by Fourier transform, and the frequency domain features are extracted, including the amplitude and frequency distribution of the signal. Specifically, the fast Fourier transform (FFT) method is applied to process the time domain data to obtain its frequency domain representation. At the same time, the converted frequency domain data is normalized to ensure that different frequency components have a consistent scale in subsequent optimization, thereby facilitating the model to identify and optimize high-frequency and low-frequency signal features. The specific implementation method of this embodiment includes the following steps:

[0095] (1) Fourier transform: For each data point t (including prediction data and verification data), the fast Fourier transform (FFT) method is applied to convert the time domain data into the frequency domain.

[0096]

[0097] Among them, X(t) is the time domain data, X freq (f) is the frequency domain data, f is the frequency component, and T is the data length.

[0098] (2) Frequency domain feature extraction:

[0099] 1) Decompose the transformed frequency domain data into different frequency components, including low-frequency and high-frequency components.

[0100] 2) Extract the amplitude and phase information of each frequency component. The amplitude represents the energy of the frequency component, and the frequency represents the rate of change of the signal. Through frequency domain analysis, we can identify the signal characteristics at different frequencies, which helps to capture high-frequency fluctuations and low-frequency trends.

[0101] (3) Frequency domain data normalization: In order to ensure that different frequency components have consistent scales in subsequent optimization, we normalize the energy of each frequency component so that the contribution of each frequency is balanced in model optimization. The L2 norm is usually used for normalization:

[0102]

[0103] The frequency domain data processed in this way makes the energy of different frequency components more balanced, avoiding the phenomenon that high-frequency or low-frequency components excessively affect model training.

[0104] (4) Energy distribution of frequency components: Through frequency domain analysis, the energy distribution of each frequency component can be calculated. The energy proportion of each frequency component is usually measured by calculating the spectral density or power spectral density.

[0105] P(f)=|X freq (f)| 2

[0106] Where P(f) is the power spectral density at frequency f.

[0107] Step S3, extracting frequency domain features of the prediction data and the verification data, and calculating the energy distribution of the signal at different frequencies through Fourier transform;

[0108] S31, frequency domain feature extraction: extract the frequency components of the prediction data and verification data from the frequency domain data. In this step, the amplitude and phase information of each frequency component are first calculated by Fourier transform. Then, the energy of each frequency component is calculated, and the energy distribution is usually measured by the square of the amplitude of the frequency component. The purpose of this step is to obtain signal features at different frequencies and provide input for the subsequent Parseval morphological perception loss function. The specific implementation of this embodiment includes the following steps:

[0109] (1) Fourier transform: Fast Fourier transform (FFT) is used to convert time domain data X(t) into frequency domain data X(f), where f represents the frequency component.

[0110]

[0111] Where T is the data length and X(f) is the complex value of frequency f, which contains amplitude and phase information.

[0112] (2) Amplitude and phase extraction of frequency components: Extract the amplitude A(f) and phase φ(f) from the complex form X(f) output by FFT.

[0113] A(f)=|X(f)|,φ(f)=arg(X(f))

[0114] (3) Frequency component energy calculation: Calculate the energy of each frequency component, using the square of the amplitude as a measure of energy.

[0115] E(f)=A(f) 2

[0116] Wherein, E(f) represents the energy corresponding to frequency f.

[0117] (4) Energy distribution analysis: The energy of all frequency components is combined to form the power spectral density (PSD) of the signal to intuitively reflect the energy distribution of the signal at different frequencies.

[0118]

[0119] This normalization process ensures that the energy distribution has a consistent scale when used in the subsequent morphology-aware loss.

[0120] (5) Separation of high- and low-frequency features: Based on the frequency threshold (such as separating low-frequency and high-frequency signals), the frequency domain data is decomposed into low-frequency features X low (f) and high frequency features X high (f) for independent analysis of trend and tip extremes.

[0121] S32, calculation of energy gap between each frequency component of predicted data and verification data: For each frequency component, calculate the energy gap between predicted data and verification data. Compare the energy difference between predicted data and verification data at the same frequency to evaluate the performance difference of the model on different frequency components. This process can be quantified using energy error (such as absolute error or square error). This step captures the deviation between the prediction and actual data at different frequencies, and provides feedback information for subsequent optimization to help the model adjust the prediction ability in the frequency domain. The specific implementation method of this embodiment includes the following steps:

[0122] (1) Matching frequency components: ensuring prediction data and validation data X true (f k ) are aligned on the frequency axis.

[0123] f k ∈{f0,f1,...,f n}, With X true (f k )correspond

[0124] (2) Calculate the energy of the frequency component: For each frequency component f k , calculate the energy of the prediction data and the verification data respectively.

[0125] E true (f k )=|X true (f k )| 2

[0126] (3) Energy gap calculation: Compare the energy gap between the predicted data and the verification data at each frequency component and quantify it using absolute error or square error:

[0127]

[0128] (4) Energy gap distribution analysis: The energy gaps of all frequency components are combined to plot the energy error spectrum, which is used to intuitively evaluate the performance deviation of the model at different frequencies.

[0129] Energy error spectrum:

[0130] (5) Separation of high- and low-frequency errors: The frequency component is divided into high-frequency and low-frequency parts, and the high-frequency error ΔEhigh and the low-frequency error ΔElow are calculated respectively to distinguish the model's adaptability to trend signals (low frequency) and burst signals (high frequency).

[0131]

[0132] Step S4: Figure 3-Figure 4 As shown, a morphologically aware optimization mechanism based on Parseval's theorem is introduced into the loss function, by adjusting the frequency domain energy feedback response to the time domain signal morphological characteristics;

[0133] S41. Energy balance and feature adjustment: Apply Parseval's theorem to ensure that the total energy in the frequency domain is equal to the total energy of the time domain signal. In order to optimize the morphological characteristics of the signal, the energy is first adjusted in the frequency domain, mainly by redistributing the energy of different frequency bands. Specifically: in the frequency domain, by adjusting the energy ratio of high-frequency and low-frequency components, the high-frequency part of the signal is optimized to capture instantaneous changes or sudden fluctuations of the signal. The goal of this step is to adjust the spectrum of the signal to ensure that the various frequency components of the signal can better match the morphological characteristics of the target data during the reconstruction process. The specific implementation method of this embodiment includes the following steps:

[0134] (1) Total energy balance: according to Parseval's theorem;

[0135]

[0136] Among them, x[n] represents the time domain signal, and X[k] is the corresponding frequency domain signal. This formula ensures the equivalence of energy from the time domain to the frequency domain, providing a theoretical basis for spectrum optimization.

[0137] (2) Separation of high-frequency and low-frequency components:

[0138] In the frequency domain, the signal is separated into low-frequency and high-frequency components:

[0139] Low frequency component X low [k]: reflects the overall trend and long-term changes of the signal.

[0140] High frequency component X high [k]: Capture instantaneous changes and sudden fluctuations of the signal.

[0141] X[k]=X low [k]+Xhigh [k]

[0142] (3) Energy redistribution: Adjust the ratio of high-frequency and low-frequency energy to optimize morphological characteristics:

[0143] X′[k]=α·X low [k]+β·X high [k]

[0144] Among them, α and β are adjustable parameters used to balance the weights of high-frequency and low-frequency components.

[0145] (4) Frequency domain optimization feedback:

[0146] High-frequency optimization: Enhances the ability to capture sudden fluctuations in signals and emphasizes the significance of abnormal events.

[0147] Low-frequency optimization: Ensure that the overall trend remains smooth and avoid over-amplifying the impact of short-term fluctuations on the global pattern.

[0148] (5) Feedback to the time domain: The adjusted frequency domain signal is returned to the time domain through inverse Fourier transform:

[0149] x′[n]=IIFFT(X′[k])

[0150] Ensure that the optimized spectrum reflects a more accurate morphological feature match in the time domain.

[0151] S42, feedback of signal morphological features: After frequency domain adjustment, the optimization results are fed back to the time domain. This process converts the adjusted frequency domain signal back to the time domain through inverse Fourier transform, thereby adjusting the signal morphological features in the time domain. In this process, the model can recognize and respond to the morphological changes of the signal, especially the volatility changes in the high-frequency part. In this way, the optimized signal more accurately reflects the dynamic changes and trends of the actual signal, while reducing the impact of high-frequency noise or errors on model training. This feedback process enhances the morphological perception ability of the model, enabling the model to more accurately capture complex signal pattern changes. Specific implementation methods of this embodiment include:

[0152] (1) Inverse Fourier transform: Apply the inverse Fourier transform formula;

[0153]

[0154] Among them, X′[k] is the optimized frequency domain signal, and x′[n] is the adjustment signal fed back to the time domain. This step ensures that the frequency domain optimization has a direct impact on the time domain signal.

[0155] (2) Signal shape adjustment: In the time domain, the adjusted signal shape is closer to the real signal characteristics, which is specifically manifested as follows:

[0156] Enhanced high-frequency changes: Sudden changes and abnormal peaks are more accurately modeled and responded to.

[0157] Low-frequency trend smoothing: avoids the interference of short-term high-frequency fluctuations on the overall trend.

[0158] (3) Dynamic response to morphological changes: The model learns the optimized signal morphology through the training process, especially the instantaneous fluctuations in the high-frequency part, so that it can better adapt to the dynamic changes of the signal.

[0159] (4) Noise reduction and error suppression: The optimized signal is effectively reduced by balancing and adjusting the frequency domain, which effectively reduces the impact of high-frequency noise and avoids the error propagation to the time domain, thereby improving the overall fitting accuracy of the signal.

[0160] Step S5: Figure 5 As shown in Figure 1, a lag offset parameter optimization mechanism is introduced into the loss function to capture the lag effect between the predicted value and the true value.

[0161] S51. Lag offset detection: Identify potential lag effects by calculating the correlation between the predicted value and the true value. For each pair of predicted value and true value, correlation analysis is performed at different lag steps (δ), and the lag is estimated using a cross-correlation function or a rolling correlation calculation. This step can be dynamically calculated using a sliding window method, and the lag step (τ) is calculated for each time point and each pair of variables. In this way, the lag offset at each time point can be obtained as an input for optimization.

[0162] S52, hysteresis offset parameter introduction: The hysteresis step size (τ) obtained in step S51 is introduced into the loss function as a hysteresis offset parameter. This parameter is used to adjust the response of the prediction model at different time steps so that it can capture the hysteresis effect between the true value and the predicted value. The hysteresis offset parameter plays a regulatory role in the loss function, optimizing the prediction model to adapt to the dynamic changes of the hysteresis relationship in multivariate data. By introducing this optimization mechanism, the model can better identify and respond to dependencies caused by time delays.

[0163] The specific implementation of this embodiment includes:

[0164] (1) Correlation analysis: predicting the value and the true value Conduct correlation analysis with multiple lag step lengths δ;

[0165] Use the cross-correlation function (CCF) to calculate the correlation of the series under different lag conditions:

[0166]

[0167] δ: lag step size. are the means of the predicted and true values, respectively. The range of δ is controlled by [-Δ, Δ], where Δ is the maximum allowed lag range.

[0168] (2) Sliding window dynamic calculation: Use the sliding window method to perform local lag analysis on time series data;

[0169] The time series is divided into subsequences of window length L.

[0170] Compute the lag step size within each subsequence:

[0171]

[0172] τ: The lag corresponding to the maximum correlation.

[0173] (3) Multivariate lag detection: Calculate the lag step size for each pair of variables i, j in the multivariate prediction task;

[0174]

[0175] τ ij [t] represents the lag between variables i and j at time point t.

[0176] (4) Lag optimization input: The lag step results are stored as a time series matrix and used as the input of the subsequent lag optimization module to adjust the alignment relationship of the prediction model.

[0177] S53. Lag offset optimization: Use the loss function optimized with the lag offset parameter to gradually adjust the model's predicted output by updating the parameters through gradient descent or other optimization algorithms. During the optimization process, the lag offset (τ) is dynamically adjusted to minimize the lag error between the predicted value and the true value. In this process, the model not only learns how to capture long-term dependencies, but also dynamically responds to short-term lag effects in the signal. The lag offset parameter is automatically updated at each training stage to always maintain the best adaptation to lag effects.

[0178] (1) Constructing the hysteresis shift optimization loss function

[0179] The lag optimization part of the loss function aligns the time of the predicted value (x^[t]) and the true value (x[t]) by considering the lag (τ):

[0180]

[0181] τ is the hysteresis offset parameter. N is the total amount of data. L lag Optimize loss for hysteresis.

[0182] (2) Dynamic lag parameter adjustment: In each training iteration, the lag offset parameter (τ) is dynamically updated through the following steps;

[0183] Calculate the current hysteresis error:

[0184]

[0185] Update the lag parameter using gradient descent:

[0186]

[0187] η: learning rate. Gradient of the lagged error with respect to the lagged offset parameter.

[0188] (3) Joint model parameter optimization: The hysteresis offset optimization is combined with the update of model parameters such as weights (W) and biases (b) to optimize the objective function as a whole;

[0189]

[0190] L base is the model base loss (such as MSE or cross entropy). α: lag loss weight.

[0191] (4) Iterative update: In each round of training, the lag loss (Llag) is calculated by forward propagation. Backward propagation updates the lag offset parameters and model parameters.

[0192] (5) Adaptive lag adjustment: As training progresses, the lag offset (τ) is dynamically adjusted based on the changing characteristics of the signal. In high-frequency signals or long-term dependency scenarios, the model can adapt to asynchronous dependencies.

[0193] S54. Hysteresis effect optimization feedback: During the training process, the prediction model that has been optimized for hysteresis offset will feed back the hysteresis adjustment to the entire prediction process. Specifically, the model will adjust its prediction value at each time step so that the output signal can be consistent with the hysteresis pattern of the actual data. This feedback mechanism ensures that the model can flexibly adjust its sensitivity to hysteresis relationships when dealing with multivariate time series data, and improve the prediction accuracy of the model under different hysteresis conditions.

[0194] (1) Lag-adjusted feedback mechanism: At each time step t, the model calculates the lag-adjusted forecast value based on the lag offset τ:

[0195]

[0196] Adjusted forecast value. τ: The lagged offset parameter for the current time step.

[0197] (2) Iterative optimization feedback: Lag optimization adjustments serve as feedback signals in each round of training to update the model’s predicted output and parameters.

[0198] Specific feedback formula:

[0199]

[0200] The amount by which the current prediction is adjusted. η: learning rate.

[0201] (3) Enhanced model adaptability: The adjusted prediction value affects the update of model parameters through back propagation, making the model dynamically adaptable when facing different lag steps.

[0202] This adjustment is repeatedly optimized until the predicted signal and the true signal are completely aligned in terms of lag characteristics.

[0203] (4) Dynamic adjustment mechanism: The model updates the lag parameters according to the dynamic changes of the lag pattern, so that it can flexibly respond to changes in different lag steps in the time series data.

[0204] For short-term lag effects, the model responds to sudden changes by making rapid adjustments; for long-term dependencies, the model gradually corrects the predicted trend.

[0205] (5) Improved prediction accuracy: Hysteresis feedback optimization ensures the alignment of the model output signal on the time axis while maintaining sensitivity to complex patterns. It helps to reduce the prediction error of the model under different hysteresis conditions and enhance the robustness and stability of the model.

[0206] Step S6, jointly constructing a Parseval morphological perception fusion loss function that introduces a hysteresis offset parameter;

[0207] S61. Merge the loss functions of lag shift and Parseval morphology perception: First, introduce the lag shift optimization and Parseval morphology perception mechanism into the framework of the loss function. Specifically, the Parseval morphology perception loss function focuses on the morphological change characteristics of the signal (such as periodicity, amplitude, and phase), while the lag shift parameter (τ) considers the lag relationship between the variables in the time series data. The goal of merging these two modules is to improve the prediction accuracy of time series data by optimizing the morphological characteristics and lag shift of the signal. In the loss function, the lag shift loss and the Parseval morphology perception loss are weighted and synthesized to achieve dual optimization of signal morphology and lag relationship.

[0208] (1) Loss function framework construction: Lag offset loss (L lag )

[0209]

[0210] Model predicted values. The true value after lag correction. τ ij : Hysteresis offset parameter.

[0211] Parseval shape perception loss (L shape )

[0212]

[0213] Predict the energy of a signal at frequency f. The energy of the actual signal at frequency f. The frequency domain energy is calculated using Parseval's theorem to ensure the consistency of the total energy in the frequency domain and the time domain.

[0214] (2) Joint loss function: Combining the above two losses, we get the joint loss function:

[0215]

[0216] α, β: weight parameters used to balance the contribution of lag shift and morphology perception. By setting different weights, it can be adjusted for different types of time series tasks to improve the adaptability of the model.

[0217] (3) Target optimization: The optimization goal is to minimize the joint loss function L combined , optimizing the signal shape while capturing the hysteresis effect.

[0218] Joint optimization is achieved through gradient descent or other optimization algorithms:

[0219]

[0220] θ: model parameters. η: learning rate. Gradient of the joint loss with respect to the model parameters.

[0221] S62. Weighted adjustment of the various parts of the loss function: By setting the weight coefficients (α and β), the influence of the hysteresis offset and Parseval morphology perception parts in the total loss function can be controlled respectively. By adjusting these weights, the sensitivity of the model to the hysteresis effect and the adaptability to the signal morphology can be flexibly controlled.

[0222] (1) Weighted adjustment of the various parts of the loss function: When constructing the joint loss function of hysteresis shift and Parseval morphological perception, by introducing weight coefficients α and β, the hysteresis shift part (L lag ) and Parseval morphological perception part (L shape ) contributes to the total loss function. Specifically, the mechanism and goal of weight adjustment are as follows:

[0223] Joint loss function formula:

[0224]

[0225] Lag shift partial loss function. Morphological perception part loss function. α, β: weight coefficients used to control the influence of the two parts in the total loss.

[0226] The role of weight adjustment:

[0227] 1) Control lag sensitivity: The larger the value of α, the higher the proportion of the lag offset in the total loss function, and the more sensitive the model is to the lag relationship. It is suitable for time series data with significant lag relationships and strong dependencies between multiple variables.

[0228] 2) Enhanced morphological adaptability: The larger the value of β, the higher the proportion of the Parseval morphological perception part in the total loss function, and the stronger the model's adaptability to the signal morphology. It helps to capture the changes in the frequency components of complex signals, especially signals with high-frequency mutations and significant morphological characteristics.

[0229] 3) Flexible balance between the two parts: By adjusting the relative proportion of α and β, a dynamic balance between lag offset and signal morphology can be achieved. In different prediction tasks, the weight distribution can be reasonably adjusted to optimize the model performance according to the data characteristics (such as the significance of the lag relationship or the complexity of the signal morphology).

[0230] (2) Weight selection strategy:

[0231] Initial value setting: Usually the initial weight value is set according to the task requirements, for example, α=0.5, β=0.5, to ensure that the initial contributions of the two parts are equal.

[0232] Dynamic adjustment: During the training process, the weights are adjusted dynamically based on the loss convergence trend or the validation set performance indicators. α and β can be dynamically updated through optimization algorithms (such as automatic weight learning).

[0233] S63. Joint optimization and feedback mechanism of signal morphology and hysteresis relationship: During the model training optimization process, the jointly constructed loss function is updated and adjusted through back propagation. The feedback of the hysteresis offset parameter (τ) and the Parseval morphological perception mechanism continuously corrects the prediction results of the model to ensure that the output signal can accurately align the hysteresis relationship and maintain a high degree of fit to the signal morphology. The feedback mechanism ensures that the model can be dynamically adjusted to adapt to the hysteresis effects and signal pattern changes of different time scales. The specific implementation method of this embodiment includes the following steps:

[0234] (1) Lag offset update: By calculating the lag offset loss L lag, the model dynamically learns the lag step (τ) between each variable and adjusts the predicted value according to the lag to reduce the accumulation of lag errors.

[0235] (2) Frequency domain optimization feedback: using Parseval morphological perception loss L shape , the energy distribution of high-frequency and low-frequency components is adjusted in the frequency domain, and the optimization results are fed back to the time domain through inverse Fourier transform, thereby improving the fitting accuracy of the signal morphology.

[0236] (3) Joint weight update: The two parts of the loss are combined through weighting coefficients (α and β), and the weights are dynamically adjusted to ensure that the model has the best adaptability to the lag effects and signal morphology changes at different time scales.

[0237] Feedback mechanism function:

[0238] 1) Dynamic adjustment: During the training process, the joint loss function continuously corrects the model parameters through gradient descent so that it can adapt to the lag effects of different time scales.

[0239] 2) High fitting degree: ensure that the hysteresis relationship between the output signal and the real signal is consistent, and at the same time have a high-precision fitting of the signal shape.

[0240] 3) Improved robustness: Enhance the model’s robustness to complex pattern changes and effectively deal with uncertainties in multivariate time series.

[0241] Step S7, based on the Parseval shape perception loss function with the hysteresis offset parameter introduced on the real carbon data set of the TCCON site, an atmospheric carbon data prediction model is constructed and trained. As shown in Tables 1 and 2, during the training process, the total loss, shape perception loss, and hysteresis sensitive loss of the model all show a stable downward trend, indicating that the designed composite loss function can effectively guide the model to perform comprehensive optimization in terms of accuracy, shape matching, and hysteresis adjustment ability;

[0242] Table 1

[0243]

[0244]

[0245] Table 2

[0246]

[0247] Step S8: Use the trained atmospheric carbon data prediction model to process the acquired atmospheric carbon data to be predicted, and obtain the prediction result of the atmospheric carbon data, such as Figure 6 shown.

[0248] Embodiment 2

[0249] like Figure 2 As shown, in this embodiment, a carbon data prediction system based on data morphology perception loss of Parseval's theorem is provided, and the system includes: a data preprocessing module, a data time-frequency conversion module, a frequency domain feature calculation and extraction module, a frequency domain energy adjustment feedback module, a hysteresis offset detection and adjustment optimization module, a hysteresis offset parameter loss and Parseval morphology perception loss fusion module, a model training optimization module and a carbon data prediction module;

[0250] The data time-frequency conversion module is used to perform Fourier transform on the prediction data and verification data to complete the conversion from time domain to frequency domain of the prediction data and verification data;

[0251] The frequency domain feature calculation and extraction module is used to extract the frequency domain features of the prediction data and the verification data, and obtain the energy distribution of the prediction data and the verification data at different frequencies through Fourier transform calculation;

[0252] The frequency domain energy adjustment feedback module is used to introduce a morphology-aware optimization mechanism based on Parseval's theorem into the loss function, by adjusting the frequency domain energy feedback response to the time domain signal morphology characteristics;

[0253] The hysteresis shift detection and adjustment optimization module is used to identify potential hysteresis effects by calculating the correlation between the predicted value and the actual value;

[0254] The hysteresis offset parameter loss and Parseval morphology perception loss fusion module is used to weight and synthesize the hysteresis offset loss and Parseval morphology perception loss to achieve dual optimization of signal morphology and hysteresis relationship.

[0255] The model optimization module is used to build and train the carbon data prediction model on TCCON carbon data based on the introduction of hysteresis offset parameters and Parseval morphological perception loss function;

[0256] The carbon data prediction module is used to use the trained carbon data prediction model to perform data prediction on the acquired carbon concentration data to be predicted, and obtain the prediction results of atmospheric carbon data.

[0257] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A carbon data prediction method based on data morphology-aware loss of Parseval's theorem, characterized in that: The following steps are involved: Preprocessing the original TCCON site data to obtain preprocessed data; wherein the preprocessed data includes prediction data and verification data; Performing Fourier transform on the preprocessed data to obtain frequency domain data; Extracting key features from the frequency domain data to obtain frequency domain features; Constructing an atmospheric carbon data prediction model, and adjusting the energy distribution based on the frequency domain characteristics to obtain adjusted frequency domain data; Performing hysteresis offset detection and adjustment optimization based on the adjusted frequency domain data and the preprocessed data to obtain adjusted hysteresis offset parameters; constructing a joint loss function based on the adjusted lag offset parameter and the adjusted frequency domain data; Training the atmospheric carbon data prediction model based on the joint loss function and the preprocessed data to obtain a trained atmospheric carbon data prediction model; The new atmospheric carbon data to be predicted is input into the trained atmospheric carbon data prediction model to obtain the prediction result of the atmospheric carbon data.

2. The method according to claim 1, characterized in that The process of preprocessing the original TCCON station data includes: The original TCCON site data were subjected to missing value interpolation, fixed interval sampling, outlier removal and regularization to obtain preprocessed data.

3. The method according to claim 1, characterized in that The process of performing Fourier transform on the preprocessed data to obtain frequency domain data includes: Aligning the predicted data and the verification data by timestamp to obtain aligned data; Unifying the data dimensions of the prediction data and the verification data in the aligned data to obtain dimension-unified data; Performing Fourier transform on the dimensionally unified data to obtain frequency domain data.

4. The method according to claim 3, characterized in that The process of extracting the frequency domain features includes calculating the energy distribution of the signal at different frequencies by Fourier transform; The process of calculating the energy distribution of the signal at different frequencies includes: The frequency domain signal corresponding to the frequency domain data is obtained by Fourier transform; Calculating the amplitude and phase information of each frequency component based on the frequency domain signal; The energy of each frequency component is calculated based on the amplitude and phase information of each frequency component, and the energy distribution is obtained based on the energies of several frequency components.

5. The method according to claim 4, characterized in that The process of adjusting the energy distribution based on the frequency domain features includes: introducing a morphological perception optimization mechanism based on Parseval's theorem into a loss function to obtain Parseval's morphological perception loss, and adjusting the frequency domain energy feedback response to the time domain signal morphological features based on the Parseval's morphological perception loss.

6. The method according to claim 5, characterized in that The process of obtaining the adjusted hysteresis offset parameters includes: Obtaining a predicted value based on the atmospheric carbon data prediction model; Identify potential lag effects by calculating the correlation between predicted and true values; Correlation analysis was performed at different lag steps to estimate the lag amount; The lag step length is introduced into the loss function to obtain the lag offset loss. Based on the lag offset loss, the response of the atmospheric carbon data prediction model at different time steps is adjusted to capture the lag effect between the true value and the predicted value, and the adjusted lag offset parameter is determined.

7. The method according to claim 6, characterized in that The process of constructing the joint loss function includes weighting and synthesizing the lag offset loss and the Parseval morphological perception loss to form a joint loss function.

8. A carbon data prediction system based on Parseval's theorem and data morphology-aware loss, characterized in that: The carbon data prediction method based on the data morphology perception loss of Parseval's theorem according to any one of claims 1 to 7 is used to implement the system, which includes: a data preprocessing module, a data time-frequency conversion module, a frequency domain feature calculation and extraction module, a frequency domain energy adjustment feedback module, a hysteresis offset detection and adjustment optimization module, a hysteresis offset parameter loss and Parseval morphology perception loss fusion module, a model training optimization module and a carbon data prediction module; The data preprocessing module is used to preprocess the original TCCON site data to obtain preprocessed data; the preprocessed data includes prediction data and verification data; The data time-frequency conversion module is used to perform Fourier transform on the prediction data and the verification data; The frequency domain feature calculation and extraction module is used to extract the frequency domain features of the prediction data and the verification data after Fourier transformation, and obtain the energy distribution of the prediction data and the verification data at different frequencies through Fourier transformation calculation; The frequency domain energy adjustment feedback module is used to form Parseval morphological perception loss and respond the frequency domain energy adjustment feedback to the time domain signal morphological characteristics; The hysteresis offset detection and adjustment optimization module is used to identify potential hysteresis effects by calculating the correlation between the predicted value and the true value; The hysteresis offset parameter loss and Parseval morphological perception loss fusion module is used to weight the hysteresis offset loss and the Parseval morphological perception loss to synthesize a joint loss function; The model training optimization module is used to train the atmospheric carbon data prediction model based on the joint loss function; The carbon data prediction module is used to perform data prediction on the acquired carbon concentration data to be predicted based on the trained atmospheric carbon data prediction model to obtain the prediction result of the atmospheric carbon data.

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