Multiple arrhythmia signal classification methods

Abstract

This invention discloses various methods for classifying cardiac arrhythmia signals, belonging to the technical field of cardiac arrhythmia signal classification methods. Accurate classification of cardiac arrhythmias is of great significance for disease diagnosis and clinical treatment. However, traditional detection methods are often affected by various factors when handling multiple cardiac arrhythmias, such as signal non-stationarity caused by arrhythmias, feature non-specificity, artifacts, and noise, making it difficult to meet the required classification accuracy and efficiency. Therefore, this paper proposes a power normalized cepstral coefficient (SPNCC) method based on singular spectral analysis (SSA) to extract key features from photoplethysmography (PPG) signals and reduce the impact of noise. A deep learning classification model is constructed by combining convolutional neural networks and bidirectional long short-term memory networks (CNN-BiLSTM) to achieve accurate identification of multiple cardiac arrhythmias.

Description

Technical Field

[0001] This invention relates to a method for classifying cardiac arrhythmia signals, and more particularly to a variety of cardiac arrhythmia signal classification methods, belonging to the technical field of cardiac arrhythmia signal classification methods. Background Technology

[0002] Traditional diagnosis of arrhythmias relies mainly on manual analysis by clinicians. This method is highly dependent on the doctor's experience and expertise, and suffers from high subjectivity and low efficiency.

[0003] To improve diagnostic efficiency, researchers have introduced automated signal processing techniques, such as Fast Fourier Transform, Principal Component Analysis, and Wavelet Transform, to extract spectral features and key features.

[0004] Building on this, support vector machines and random forest machine learning algorithms have also been applied to classification tasks to improve automated recognition capabilities.

[0005] In recent years, with the development of deep learning technology, convolutional neural networks, recurrent neural networks, and long short-term memory networks have begun to be applied to the classification of arrhythmia signals due to their superior performance in feature extraction, temporal modeling, and long-term dependency capture, respectively. Deep learning models can automatically learn features, reduce the reliance on manual feature extraction, and significantly improve the accuracy and efficiency of classification.

[0006] However, the nonspecificity, non-stationarity, and noise interference of arrhythmia signals still pose challenges to existing methods. Therefore, developing more robust feature extraction methods and efficient classification methods has become a current research focus. Summary of the Invention

[0007] The main objective of this invention is to provide various methods for classifying arrhythmia signals.

[0008] The objective of this invention can be achieved by adopting the following technical solution:

[0009] A classification method for various cardiac arrhythmia signals includes the following steps:

[0010] Step 1: Preprocess the arrhythmia signal using the SPNCC preprocessing method;

[0011] Step 2: Transfer the preprocessed data to the CNN-BILSTM structure model for data processing;

[0012] Step 3: Transmit the data processed in Step 2 to the multidimensional performance index evaluation standard model for arrhythmia signal classification.

[0013] Preferably, the SPNCC preprocessing method in step one includes the following steps:

[0014] By selecting an appropriate window length L to lag the original time series, the trajectory matrix M1 is obtained.

[0015] Calculate the covariance matrix M1 of the trajectory matrix covariance matrix C.

[0016]

[0017] M1=U∑V T ;

[0018] The characteristic triples U∑V are obtained by performing eigenvalue decomposition C on the covariance matrix. T The eigenvalues ​​and their corresponding eigenvectors are sorted by size to obtain {λ1>λ2>…>λ L ≥0}{V1,V2,…,V n};

[0019] in singular values And the eigenvector V i It is a singular vector.

[0020] Each singular value obtained from the decomposition is reconstructed individually to transform it back into the trajectory matrix M2. Then, the anti-angle averaging method is used to convert the trajectory matrix into a sequence form, thus obtaining n components.

[0021] Correlation analysis is performed on the obtained components to assess the consistency between each component and the original PPG records. The formula for calculating the coherence coefficient is as follows:

[0022]

[0023] Where Sig represents the original PPG record, and the required component is selected according to a pre-set threshold (the initial threshold is 0.9, which can be further adjusted according to the experiment).

[0024] imf i It is a time series obtained by reconstructing the original sequence through feature vectors and then performing diagonal averaging, and selecting the required components according to a pre-set threshold;

[0025] cov represents the calculation of covariance, and Var represents the calculation of variance.

[0026] By calculating the coherence coefficient and filtering with the corresponding threshold, x suitable components are finally obtained, and these x components are arranged into a matrix of size x×L.

[0027] Preferably, SPNCC feature extraction is performed on the feature matrix composed of the components, specifically including the following steps:

[0028] Calculate P using the following formula. i Power spectrum of (ω):

[0029]

[0030] The power estimate P i (ω) Input to a gamma-pass filter for filtering. The time-domain impulse response of the gamma-pass filter is:

[0031] G(t)=αt n-1 e -2πωt cos(2πf0t+φ), (t>0);

[0032] Where α is a scaling factor used to adjust the response strength of the filter, t is the time-domain input variable of the filter, f0 is the center frequency of the filter, which determines the main frequency response of the filter to the input signal, φ is the phase offset of the filter, also known as phase rotation, which controls the phase of the filter response, ω is the filter bandwidth, and n is the filter order.

[0033] After filtering the signal using a gamma-pass filter, the power spectrum of the filtered signal will be normalized. The normalization process uses the following formula:

[0034]

[0035] Among them, POW n The value is obtained from the gamma-pass filter, μ[ω] is the average power, and ω is the frequency. g This reflects the spectrum after the filtering process;

[0036] Finally, the normalized power spectrum is subjected to nonlinear processing:

[0037]

[0038] Where θ is the exponential factor, 0 < θ < 1;

[0039] The SPNCC eigenvalues ​​are the obtained feature matrix;

[0040] After obtaining the SPNCC feature matrix through the above processing, it is combined with the temporal features and input into the CNN-BILSTM-Attention structure model for training.

[0041] Preferably, the CNN-BILSTM-Attention structure model specifically includes an input layer composed of multiple data augmentation modules, including random addition of Gaussian noise, signal scaling and cropping, time shifting, and signal inversion;

[0042] CNN layer: includes multiple convolutional layers and pooling layers. The convolutional layer learns multiple different convolutional kernels simultaneously. Each convolutional kernel extracts features from different aspects of the data, selects the important features, and obtains the output data Output1. Then, the pooling layer performs dimensionality reduction on the data, retains the most significant features, removes invalid features, and obtains the output data Output2.

[0043] BILSTM layer: It contains two independent LSTM layers, one for information acquisition in the forward time step and the other for information acquisition in the backward time step. These two LSTM layers are independent of each other, and each has its own hidden state and cell state. The forward LSTM starts processing data from the beginning of the sequence, while the backward LSTM starts processing data from the end of the sequence.

[0044] ATTENTION layer: Contains multiple independent attention heads from different angles, which map temporal features to different sub-representation spaces to guide the model to learn the correlation information of different sub-representation spaces to obtain richer representations;

[0045] Output layer: Consists of Dropout layer and full connected layer. Dropout reduces the model's dependence on specific neurons by randomly dropping some neurons, thus making the model more robust. Full connected outputs the final classification result and regression value.

[0046] The preferred training and signal transmission processes of the CNN-BILSTM-ATTENTION model are as follows:

[0047] Input the data used for training the CNN-BILSTM-ATTENTION model;

[0048] Reconstruct the original input data;

[0049] The optimal hyperparameters obtained using Bayesian optimization will be used to initialize the CNN-BILSTM-ATTENTION model;

[0050] The reconstructed signal is sequentially processed by CNN through multiple convolutional and pooling layers to obtain the CNN output Output-One.

[0051] OutPut-One passes through multiple hidden layers of BILSTM in sequence to obtain the output OutPut-Two of BILSTM;

[0052] OutPut-Two then performs CNN computation again through new convolutional and pooling layers to obtain the CNN output OutPut-Three;

[0053] OutPut-Three undergoes attention processing through a Multi-head Attention layer to obtain the output OutPut-Four;

[0054] OutPut-Four is finally processed by a fully connected layer to obtain the final result, and the predicted loss value is calculated.

[0055] Verify whether the final loss value triggers the early stopping mechanism; if so, save the trained model.

[0056] If not, return to step four and repeat the above process until the early stop condition is met.

[0057] Preferably, in step three, the misclassification cases for each category are extracted from the confusion matrix;

[0058] Calculate the misclassification rate for each category based on the number of misclassified samples and the total number of samples in each category:

[0059]

[0060] The weights are dynamically adjusted based on the false positive rate.

[0061]

[0062] Dynamic adjustment based on task objective weight allocation:

[0063]

[0064] Where Base is the initial weight, reflecting the basic preference of the task objective for the indicator;

[0065] ErrorFactorAcc is the average of the overall misclassification rate, which measures the overall classification accuracy of the model;

[0066] ErrorFactorRecall is the sum of the proportions of samples from each category that are misclassified as other categories, emphasizing the impact of misclassification on recall.

[0067] ErrorFactorPrecision is the sum of the proportions of samples misclassified as the target class for each category, emphasizing the impact of misclassification on precision.

[0068] α is a dynamic adjustment coefficient used to control the degree of influence of the misjudgment rate on the weight.

[0069] Preferably, the harmonic mean of all evaluation methods is calculated, including the accuracy, recall, F1 score, and precision of heart rate signal classification;

[0070]

[0071] Subsequently, the time exponent (T) was calculated. n ), representing a metric that is proportional to computation time.

[0072]

[0073] Wherein, the coefficient σ∈(0,1] represents the time proportion, which is determined according to the time sensitivity of the task; the higher the σ, the stronger the time sensitivity of the task.

[0074] σ is set to 0.2, while normalize(Time) refers to normalizing the computation time of all methods;

[0075] MDPI=T n ×H n ;

[0076] The time exponent is multiplied by the harmonic mean to provide a comprehensive evaluation of the computation time and accuracy of all methods.

[0077] Beneficial technical effects of the present invention:

[0078] This invention provides a multi-arrhythmia signal classification method to extract key features from photoplethysmography (PPG) signals and reduce the impact of noise. It combines a convolutional neural network and a bidirectional long short-term memory network (CNN-BiLSTM) to construct a deep learning classification model, achieving accurate identification of various arrhythmias. Experimental results show that this method achieves a classification accuracy of 99.6% on the MIT-BIH and MIMIC-III datasets, outperforming existing methods in multiple metrics (such as recall and F1 score). Furthermore, this paper introduces a comprehensive evaluation metric, T-Mean, which achieves an optimal balance between classification performance and computational efficiency. Therefore, the proposed SPNCC-CNN-BiLSTM method not only effectively solves the non-stationarity and noise problems of PPG signals but also significantly improves the classification accuracy and robustness of various arrhythmias, providing reliable support for intelligent healthcare and early disease screening. Attached Figure Description

[0079] Figure 1 This is a flowchart of the model training and testing process according to a preferred embodiment of the various arrhythmia signal classification methods of the present invention;

[0080] Figure 2 This is a schematic diagram of the CNN-BILSTM-ATTENTION model framework, which is a preferred embodiment of a preferred embodiment of the various arrhythmia signal classification methods of the present invention.

[0081] Figure 3This is a diagram illustrating the training process of a CNN-BILSTM-ATTENTION model according to a preferred embodiment of a preferred embodiment of the various arrhythmia signal classification methods of the present invention.

[0082] Figure 4 This is a flowchart of a preferred embodiment of a method for classifying various arrhythmia signals according to the present invention. Detailed Implementation

[0083] To enable those skilled in the art to understand the technical solution of the present invention more clearly, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0084] Includes the following steps:

[0085] Step 1: Preprocess the arrhythmia signal using the SPNCC preprocessing method;

[0086] Step 2: Transfer the preprocessed data to the CNN-BILSTM structure model for data processing;

[0087] Step 3: Transmit the data processed in Step 2 to the multidimensional performance index evaluation standard model for arrhythmia signal classification.

[0088] Preferably, the SPNCC preprocessing method in step one includes the following steps:

[0089] By selecting an appropriate window length L to lag the original time series, the trajectory matrix M1 is obtained.

[0090] Calculate the covariance matrix M1 of the trajectory matrix covariance matrix C.

[0091]

[0092] M1=U∑V T ;

[0093] The characteristic triples U∑V are obtained by performing eigenvalue decomposition C on the covariance matrix. T The eigenvalues ​​and their corresponding eigenvectors are sorted by size to obtain {λ1>λ2>…>λ L ≥0}{V1,V2,…,V n};in singular values And the eigenvector V i It is a singular vector.

[0094] The singular values ​​are divided into x unconnected groups, representing different trends and periodic components, where x is the number of target components;

[0095] Reconstructing x unconnected groups yields a matrix of size x×K;

[0096] After performing SSA decomposition on the PPG records, each unique component and residual is obtained;

[0097] Correlation analysis was performed to assess the consistency between each component and the original PPG record. The formula for calculating the coherence coefficient is as follows:

[0098]

[0099] Where n represents the total number of components obtained;

[0100] Sig represents the raw PPG record, and the desired component is selected based on a pre-set threshold;

[0101] imf i It is a time series obtained by reconstructing the feature vectors and then averaging them diagonally, and the required components are selected according to a pre-set threshold.

[0102] cov represents the calculation of covariance, and Var represents the calculation of variance.

[0103] After SSA processing of the PPG records, these components are organized and represented by a feature matrix composed of these components.

[0104] Preferably, SPNCC feature extraction is performed on the feature matrix composed of the components, specifically including the following steps:

[0105] Calculate P using the following formula. i Power spectrum of (ω):

[0106]

[0107] The power estimate P i (ω) Input to a gamma-pass filter for filtering. The time-domain impulse response of the gamma-pass filter is:

[0108]

[0109] Where ω is the filter bandwidth and n is the filter order;

[0110] After filtering, the filter is normalized to a power spectrum using the following expression:

[0111]

[0112] Among them, POW n This is the value obtained from the gamma-pass filter, where μ[ω] is the average power;

[0113] Nonlinear processing: Performing power function nonlinear processing using expressions:

[0114]

[0115] Where θ is the exponential factor, 0 < θ < 1;

[0116] The SPNCC eigenvalues ​​are the obtained feature matrix;

[0117] After obtaining the SPNCC feature matrix through the above processing, it is combined with the temporal features and input into the CNN-BILSTM-Attention structure model for training.

[0118] Preferably, the CNN-BILSTM-Attention structure model specifically includes an input layer composed of multiple data augmentation modules, including random addition of Gaussian noise, signal scaling and cropping, time shifting, and signal inversion;

[0119] CNN layer: includes multiple convolutional layers and pooling layers. The convolutional layer learns multiple different convolutional kernels simultaneously. Each convolutional kernel extracts features from different aspects of the data, selects the important features, and obtains the output data Output1. Then, the pooling layer performs dimensionality reduction on the data, retains the most significant features, removes invalid features, and obtains the output data Output2.

[0120] BILSTM layer: It contains two independent LSTM layers, one for information acquisition in the forward time step and the other for information acquisition in the backward time step. These two LSTM layers are independent of each other, and each has its own hidden state and cell state. The forward LSTM starts processing data from the beginning of the sequence, while the backward LSTM starts processing data from the end of the sequence.

[0121] ATTENTION layer: Contains multiple independent attention heads from different angles, which map temporal features to different sub-representation spaces to guide the model to learn the correlation information of different sub-representation spaces to obtain richer representations;

[0122] Output layer: Consists of Dropout layer and full connected layer. Dropout reduces the model's dependence on specific neurons by randomly dropping some neurons, thus making the model more robust. Full connected outputs the final classification result and regression value.

[0123] The preferred training and signal transmission processes of the CNN-BILSTM-ATTENTION model are as follows:

[0124] Input the data used for training the CNN-BILSTM-ATTENTION model;

[0125] Reconstruct the original input data;

[0126] The optimal hyperparameters obtained using Bayesian optimization will be used to initialize the CNN-BILSTM-ATTENTION model;

[0127] The reconstructed signal is sequentially processed by CNN through multiple convolutional and pooling layers to obtain the CNN output Output-One.

[0128] OutPut-One passes through multiple hidden layers of BILSTM in sequence to obtain the output OutPut-Two of BILSTM;

[0129] OutPut-Two then performs CNN computation again through new convolutional and pooling layers to obtain the CNN output OutPut-Three;

[0130] OutPut-Three undergoes attention processing through a Multi-head Attention layer to obtain the output OutPut-Four;

[0131] OutPut-Four is finally processed by a fully connected layer to obtain the final result, and the predicted loss value is calculated.

[0132] Verify whether the final loss value triggers the early stopping mechanism; if so, save the trained model.

[0133] If not, return to step four and repeat the above process until the early stop condition is met.

[0134] Preferably, in step three, the misclassification cases for each category are extracted from the confusion matrix;

[0135] Calculate the misclassification rate for each category based on the number of misclassified samples and the total number of samples in each category:

[0136]

[0137] The weights are dynamically adjusted based on the false positive rate.

[0138]

[0139] Dynamic adjustment based on task objective weight allocation:

[0140]

[0141] Where Base is the initial weight, reflecting the basic preference of the task objective for the indicator;

[0142] ErrorFactorAcc is the average of the overall misclassification rate, which measures the overall classification accuracy of the model;

[0143] ErrorFactorRecall is the sum of the proportions of samples from each category that are misclassified as other categories, emphasizing the impact of misclassification on recall.

[0144] ErrorFactorPrecision is the sum of the proportions of samples misclassified as the target class for each category, emphasizing the impact of misclassification on precision.

[0145] α is a dynamic adjustment coefficient used to control the degree of influence of the misjudgment rate on the weight.

[0146] Preferably, the harmonic mean of all evaluation methods is calculated, including the accuracy, recall, F1 score, and precision of heart rate signal classification;

[0147]

[0148] Subsequently, the time exponent (T) was calculated. n ), representing a metric that is proportional to computation time.

[0149]

[0150] Wherein, the coefficient σ∈(0,1] represents the time proportion, which is determined according to the time sensitivity of the task; the higher the σ, the stronger the time sensitivity of the task.

[0151] σ is set to 0.2, while normalize(Time) refers to normalizing the computation time of all methods;

[0152] MDPI=T n ×H n ;

[0153] The time exponent is multiplied by the harmonic mean to provide a comprehensive evaluation of the computation time and accuracy of all methods.

[0154] The above description is merely a further embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope disclosed in the present invention, based on the technical solution and concept of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method for classifying multiple arrhythmia signals, characterized in that: Includes the following steps: Step 1: Use the SPNCC preprocessing method to denoise and extract features from the arrhythmia signal; Step 2: Transfer the preprocessed data to the CNN-BILSTM structure model for data processing; Step 3: Transmit the data processed in Step 2 to the multidimensional performance index evaluation standard model for arrhythmia signal classification; Includes the following steps: Choose an appropriate window length By lag-relating the original time series, the trajectory matrix is ​​obtained. ; Calculate the covariance matrix of the trajectory matrix covariance matrix ; ； Eigenvalue decomposition of the covariance matrix Obtain the characteristic triplet And sort the eigenvalues ​​and corresponding eigenvectors by size to obtain ; in singular values , and eigenvectors These are singular vectors; Each singular value obtained from the decomposition is reconstructed individually to transform it back into a trajectory matrix. Then, the anti-angle averaging method is used to convert the trajectory matrix into a sequence form, thus obtaining n components; Correlation analysis is performed on the obtained components to assess the consistency between each component and the original PPG records. The formula for calculating the coherence coefficient is as follows: ； Where Sig represents the original PPG record, and the required component is selected according to a pre-set threshold; imf i It is a time series obtained by reconstructing the original sequence through feature vectors and then performing diagonal averaging, and selecting the required components according to a pre-set threshold; cov represents the calculation of covariance, and Var represents the calculation of variance. The final result is obtained by calculating the coherence coefficient and filtering using appropriate thresholds. A suitable portion, and the The components are arranged into a size of Matrix; After denoising the original time series, a corresponding matrix is ​​obtained. Feature extraction is then performed on this matrix, specifically SPNCC feature extraction on the feature matrix composed of its components. The specific steps include: Calculate using the following formula Power spectrum: ； Among them, IMF i For time series components IMF i The frequency domain representation obtained after Fourier transform, where T is the total duration of the signal; Power estimate The input is filtered by a gamma filter, and the time-domain impulse response of the gamma filter is: ； in, It is a scaling factor used to adjust the response intensity of the filter. t It is the time-domain input variable of the filter. The center frequency of the filter determines its primary frequency response to the input signal. It is the phase shift of the filter, also known as phase rotation, which controls the phase of the filter response. It is the filter bandwidth. It is the filter order; After filtering the signal using a gamma-pass filter, the power spectrum of the filtered signal will be normalized. The normalization process uses the following formula: ； in, The value is obtained from the gamma-pass filter. It is average power, frequency This reflects the spectrum after the filtering process; Finally, the normalized power spectrum is subjected to nonlinear processing: ； in, It is an exponential factor. ; The SPNCC eigenvalues ​​are the obtained feature matrix; After obtaining the SPNCC feature matrix through the above processing, it is input into the CNN-BILSTM-Attention structure model for training. The CNN-BILSTM-Attention architecture specifically includes an input layer composed of multiple data augmentation modules, including random addition of Gaussian noise, signal scaling and cropping, time shifting, and signal inversion. CNN layer: includes multiple convolutional layers and pooling layers; the convolutional layer learns multiple different convolutional kernels at the same time, each convolutional kernel extracts features from different aspects of the data, selects important feature data, and obtains output data OutPut1. Then, the pooling layer performs dimensionality reduction on the data, retains the most significant features, removes invalid features, and obtains output data Output2. BILSTM layer: It contains two independent LSTM layers, one for information acquisition in the forward time step and the other for information acquisition in the backward time step. These two LSTM layers are independent of each other, and each has its own hidden state and cell state. The forward LSTM starts processing data from the beginning of the sequence, while the backward LSTM starts processing data from the end of the sequence. ATTENTION layer: Contains multiple independent attention heads from different angles, which map temporal features to different sub-representation spaces to guide the model to learn the correlation information of different sub-representation spaces to obtain richer representations; Output layer: Consists of Dropout layer and full connected layer. Dropout reduces the model's dependence on specific neurons by randomly dropping some neurons, thus making the model more robust. Full connected outputs the final classification result and regression value.

2. The method for classifying various arrhythmia signals according to claim 1, characterized in that: The specific training process and signal transmission process of the CNN-BILSTM-ATTENTION model are as follows: Input the data used for training the CNN-BILSTM-ATTENTION model; Reconstruct the original input data; The optimal hyperparameters obtained using Bayesian optimization will be used to initialize the CNN-BILSTM-ATTENTION model; The reconstructed signal is sequentially processed by CNN through multiple convolutional and pooling layers to obtain the CNN output Output-One. OutPut-One passes through multiple hidden layers of BILSTM in sequence to obtain the output OutPut-Two of BILSTM; OutPut-Two then performs CNN computation again through new convolutional and pooling layers to obtain the CNN output OutPut-Three; OutPut-Three undergoes attention processing through a Multi-head Attention layer to obtain the output OutPut-Four; OutPut-Four is finally processed by a fully connected layer to obtain the final result, and the predicted loss value is calculated. Verify whether the final loss value triggers the early stopping mechanism; if so, save the trained model. If not, return to step four and repeat the above process until the early stop condition is met.

3. The method for classifying various arrhythmia signals according to claim 2, characterized in that: In step three, the misclassification cases for each category are extracted from the confusion matrix; Calculate the misclassification rate for each category based on the number of misclassified samples and the total number of samples in each category: ； The weights are dynamically adjusted based on the false positive rate. ； Dynamic adjustment based on task objective weight allocation: ； Where Base is the initial weight, reflecting the basic preference of the task objective for the indicator; ErrorFactorAcc is the average of the overall misclassification rate, which measures the overall classification accuracy of the model; ErrorFactorRecall is the sum of the proportions of samples from each category that are misclassified as other categories, emphasizing the impact of misclassification on recall. ErrorFactorPrecision is the sum of the proportions of samples misclassified as the target class for each category, emphasizing the impact of misclassification on precision. This is a dynamically adjustable coefficient used to control the impact of the misjudgment rate on the weights.

4. The method for classifying various arrhythmia signals according to claim 3, characterized in that: Calculate the harmonic mean of all evaluation methods, including the accuracy, recall, F1 score, and precision of heart rate signal classification; ； in For accuracy, For recall rate, For accuracy, These are preset weighted components; Subsequently, the time index was calculated. This represents a metric that is directly proportional to computation time. ； Among them, coefficient The time proportion represents the time required, which is determined based on the time sensitivity of the task. The higher the value, the stronger the time sensitivity of the task; Set to 0.2, while This refers to normalizing the computation time of all methods; ； The time exponent is multiplied by the harmonic mean to provide a comprehensive evaluation of the computation time and accuracy of all methods.

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