Dataset denoising processing method based on empirical mode decomposition algorithm

Abstract

The invention discloses a data set denoising processing method based on an empirical mode decomposition algorithm, and the method comprises the following steps: S1, data selection: obtaining an operation monitoring data set of a proton exchange membrane fuel cell, the data set at least comprising an output voltage signal; s2, degradation index determination: performing correlation analysis on the data set, and screening out an output voltage signal which is strongly and negatively correlated with the service life of the proton exchange membrane fuel cell as a performance degradation core index; s3, data sampling simplification: sampling the output voltage signals in the step S2 at equal time intervals to obtain a simplified voltage time sequence; s4, empirical mode adaptive decomposition: performing empirical mode decomposition on the simplified voltage time sequence to obtain a plurality of intrinsic mode function components and a residual component; s5, noise component elimination: eliminating high-frequency noise components from the plurality of intrinsic mode function components; and S6, signal reconstruction: superposing the residual intrinsic mode function component after elimination with the residual component, and reconstructing to obtain a denoised voltage degradation signal. According to the EMD-based denoising processing method, accurate extraction of real degradation features is realized through data screening, simplification, adaptive decomposition and noise elimination.

Description

A Dataset Denoising Method Based on Empirical Mode Decomposition Algorithm Technical Field

[0001] This invention relates to the field of proton exchange membrane fuel cell data preprocessing technology, specifically to a dataset denoising method based on empirical mode decomposition algorithm. Background Technology

[0002] As a clean and renewable energy technology, the operation monitoring data of proton exchange membrane fuel cells (PEMFC) is the core basis for analyzing the performance degradation of the fuel cell stack. At present, the PEMFC operation dataset has the following key problems: (1) Data dimensional redundancy and ambiguity of core indicators: PEMFC monitoring data contains more than 24 parameters such as output voltage, current, hydrogen flow rate, and temperature. Most parameters have weak correlation with performance degradation and are difficult to be directly used for feature extraction; (2) Significant noise interference in the original data: The original output voltage data contains a large amount of noise and voltage spikes caused by monitoring equipment errors and external environmental disturbances. If not processed, it will cover up the real degradation trend; (3) Large data scale leads to heavy computational burden: The original voltage data has more than 140,000 sampling points. The fluctuation of adjacent data is very small. Direct processing will occupy a lot of computing resources and reduce data processing efficiency; (4) Poor adaptability of traditional denoising methods: Traditional methods such as wavelet analysis require preset basis functions. The selection of basis functions directly affects the denoising effect and cannot adaptively process the non-stationary and nonlinear characteristics of PEMFC voltage data, making it difficult to achieve accurate separation of noise and real signal. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies, such as low accuracy and poor reliability in extracting performance degradation features of PEMFCs due to data redundancy, noise interference, computational complexity, and poor adaptability of traditional denoising methods. This invention provides an adaptive and efficient PEMFC dataset denoising method that can automatically identify core degradation indicators, significantly reduce data size to alleviate computational burden, and accurately remove noise to extract true and smooth performance degradation trends, providing a high-quality data foundation for subsequent stack health status analysis and lifetime prediction.

[0004] To achieve the above objectives, this invention provides a dataset denoising method based on empirical mode decomposition (EMD) algorithm, comprising the following steps: Step S1, Data selection: Obtaining a proton exchange membrane fuel cell (PEMFC) operation monitoring dataset, wherein the dataset contains at least an output voltage signal; Step S2, Degradation index determination: Performing correlation analysis on the dataset, and selecting the output voltage signal that is strongly negatively correlated with the lifespan of the PEMFC as the core performance degradation index; Step S3, Data sampling simplification: Sampling the output voltage signal obtained in Step S2 at equal time intervals to obtain a simplified voltage time series; Step S4, Empirical mode adaptive decomposition: Performing empirical mode decomposition on the simplified voltage time series to obtain several intrinsic mode function components and a residual component, comprising: Step S4.1: Let the original output voltage signal be \(x(t)\), where t is the running time, and find All local maxima ( ) and local minimum points ( ), where i and j are the indices of extreme points; Step S4.2: Construct the upper envelope using a cubic spline interpolation function. and lower envelope ,satisfy (1-1) Step S4.3: Calculate the average value of the upper and lower envelopes: (1-2) Step S4.4: Calculate the intermediate signal: (1-3) Step S4.5: Iterative sieving: Judgment Does it meet the two conditions of the IMF: a) the number of local extrema is equal to or differs from the number of zeros by at most 1 within the time history; b) the average of the envelopes of local maxima and local minima at any time is 0; if not, then... For the new "original signal", repeat steps S4.2-S4.4. The intermediate signal for the k-th iteration is: (1-4) until Satisfying the intrinsic mode function component conditions, let be denoted as . For the first eigenmode function component Step S4.6: Calculate the first residual component: (1-5) Step S4.7: Repeat steps S4.1 to S4.6, to... For the new processing object, the second intrinsic mode function component is obtained by decomposition. and the second residual component After n iterations, when the residual component The decomposition stops when the function becomes monotonic, and the final result is: (1-6); Step S5, noise component removal: remove high-frequency noise components from the plurality of intrinsic mode function components; Step S6, signal reconstruction: superimpose the remaining intrinsic mode function components after removal with the residual components to reconstruct the denoised voltage degradation signal. (1-7).

[0005] Optionally, in step S3, the equal time interval is 0.5h to 2h.

[0006] Optionally, in step S3, the equal time interval is 1 hour.

[0007] Optionally, in step S1, the dataset may further include output current, hydrogen flow rate, hydrogen inlet and outlet temperatures, and air humidity.

[0008] In step S4, the empirical mode adaptive decomposition specifically includes: Optionally, in step S4, the screening termination condition of the empirical mode decomposition is: the intrinsic mode function components obtained by decomposition satisfy that the number of extreme points and the number of zero points within the time history are equal or differ by less than or equal to 1, and the upper and lower envelopes are locally symmetrical about the time axis.

[0009] Optionally, in step S5, the screening criterion for the noise components is: based on the frequency distribution of the intrinsic mode function components, high-frequency intrinsic mode function components with frequencies higher than a preset threshold are removed.

[0010] Optionally, the preset threshold is determined based on the inherent timescale of voltage degradation in a proton exchange membrane fuel cell.

[0011] Optionally, after step S6, the method further includes denoising effect verification: calculating the root mean square error and mean absolute error of the voltage degradation signal before and after denoising to verify the denoising effect.

[0012] Optionally, the root mean square error is less than or equal to 0.0069, and the mean absolute error is less than or equal to 0.0048.

[0013] Compared with the prior art, the beneficial effects of the present invention include at least the following: The present invention utilizes the Empirical Mode Decomposition (EMD) algorithm to decompose the voltage data of the proton exchange membrane fuel cell according to its own scale, without the need to preset basis functions as in wavelet analysis. Therefore, it can automatically adapt to the non-stationary and nonlinear characteristics of the voltage of the proton exchange membrane fuel cell.

[0014] Based on empirical mode decomposition, high-frequency noise intrinsic mode function components are accurately identified and eliminated by frequency thresholding, and only low-frequency components and residual components representing the true degradation trend are retained for reconstruction, thereby protecting the effective signal to the maximum extent while removing noise.

[0015] This invention simplifies the data size from over 140,000 to 1,154 by sampling at equal time intervals, significantly reducing the computational burden while ensuring the integrity of the degradation trend. Attached Figure Description

[0016] Figure 1 is a simplified flowchart of the dataset denoising method based on the empirical mode decomposition algorithm of the present invention.

[0017] Figure 2 shows a portion of the proton exchange membrane fuel cell dataset of the present invention.

[0018] Figure 3 is a correlation matrix of variables in the PEMFC dataset of the present invention.

[0019] Figure 4 shows the output voltage data after EMD noise reduction according to the present invention. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] As shown in Figure 1, the core idea of ​​this invention is to achieve efficient denoising of the PEMFC dataset through a process of "data filtering - simplification - adaptive decomposition - noise removal - signal reconstruction". Specifically, the following steps are taken: A PEMFC operation monitoring dataset is obtained. This dataset originates from the publicly available FC1 dataset (or similar PEMFC experimental datasets) from the FCLAB laboratory, containing 24-dimensional monitoring parameters such as output voltage, output current, hydrogen flow rate, hydrogen inlet and outlet temperatures, and air humidity. A variable correlation matrix is ​​constructed using Person correlation analysis. The output voltage, which exhibits a strong negative correlation with PEMFC lifetime, is selected as the core indicator of performance degradation. Output voltage is readily available and directly reflects the degree of stack performance decay.

[0022] To address the computational burden caused by an excessive number of original voltage data sampling points, sampling is performed at equal time intervals based on the total stable operation time of PEMFC (e.g., 1154 hours). The sampling interval is determined according to the principle of "reducing computational burden + preserving degradation features," with 1 hour being the preferred sampling interval. This simplifies the original 143,862 sampling points to 1,154 effective sampling points, reducing the computational complexity of subsequent processing while ensuring data integrity.

[0023] The sampled voltage data is subjected to EMD decomposition. The specific process is as follows: (1) Find all local maxima and minima of the voltage signal; (2) Connect the maxima with cubic spline curves to form the upper envelope and connect the minima to form the lower envelope, ensuring that the upper and lower envelopes contain all data points; (3) Calculate the average value of the upper and lower envelopes, subtract the average value of the envelope from the original signal to obtain the intermediate signal; (4) Iteratively screen the intermediate signal until the two criteria for IMF components are met (the number of extreme points and zeros are equal or differ by 1, and the upper and lower envelopes are locally symmetrical), and obtain the first IMF component; (5) Remove the IMF component from the original signal, repeat the above process for the remaining signal until the remaining component is a monotonic function (residual component), and finally obtain several IMF components and 1 residual component.

[0024] Effective components are selected based on the frequency characteristics of the IMF components: high-frequency IMF components mainly correspond to noise interference, while low-frequency IMF components and residual components reflect the true degradation trend of the PEMFC voltage. By setting a frequency threshold (determined based on the inherent time scale of PEMFC voltage degradation), high-frequency noise components are eliminated, while effective IMF components and residual components are retained. The effective components are then superimposed and reconstructed to obtain a smooth voltage degradation signal, thus completing the denoising process.

[0025] Root mean square error (RMSE) and mean absolute error (MAE) are used as evaluation metrics to compare the deviations of the signals before and after denoising from the actual degradation trend. The verification results must meet the following requirements: RMSE ≤ 0.0069 and MAE ≤ 0.0048 for the denoised signal, ensuring that noise is effectively removed and the actual degradation characteristics are not lost.

[0026] In some embodiments, the equal time interval is 0.5h to 2h. Preferably, the equal time interval is 1h.

[0027] In some embodiments, the empirical mode adaptive decomposition specifically includes: denoting the original output voltage signal as \(x(t)\), where t is the running time, and searching for... All local maxima ( ) and local minimum points ( ), where i and j are the indices of extreme points; Step S4.2: Construct the upper envelope using a cubic spline interpolation function. and lower envelope ,satisfy (1-1) Step S4.3: Calculate the average value of the upper and lower envelopes: (1-2) Step S4.4: Calculate the intermediate signal: (1-3) Step S4.5: Iterative sieving: Judgment Does it meet the two conditions of the IMF: a) the number of local extrema is equal to or differs from the number of zeros by at most 1 within the time history; b) the average of the envelopes of local maxima and local minima at any time is 0; if not, then... For the new "original signal", repeat steps S4.2-S4.4. The intermediate signal for the k-th iteration is: (1-4) until Satisfying the intrinsic mode function component conditions, let be denoted as . For the first eigenmode function component Step S4.6: Calculate the first residual component: (1-5) Step S4.7: Repeat steps S4.1 to S4.6, to... For the new processing object, the second intrinsic mode function component is obtained by decomposition. and the second residual component After n iterations, when the residual component The decomposition stops when the function becomes monotonic, and the final result is: (1-6).

[0028] Example: This example uses the FC1 dataset published by the French FCLAB laboratory at the IEEE PHM 2014 Data Challenge. The PEMFC operating conditions are: temperature 60℃, load current 70A, and relative humidity 50%. The dataset contains 24-dimensional monitoring parameters and a total of 143,862 sampling points of raw output voltage data.

[0029] Pearson correlation analysis was performed on the 24-dimensional data to construct a variable correlation matrix (as shown in Figure 2). The analysis results show that the absolute value of the correlation coefficient between output voltage and running time is the largest (strong negative correlation), thus determining output voltage as the core indicator of PEMFC performance degradation.

[0030] The stable operating time of PEMFC is 1154 hours. To balance the computational burden and data integrity, the sampling interval is set to 1 hour. 1154 valid sampling points are extracted from the original 143862 sampling points to form a simplified voltage time series.

[0031] EMD decomposition was performed on the sampled voltage sequence: (1) 326 local maxima and 324 local minima of the voltage signal were identified; (2) upper and lower envelopes were constructed by cubic spline curves to ensure that the envelopes completely contained all sampling points; (3) after 12 iterations of sieving, 8 IMF components (IMF1-IMF8) and 1 residual component (Res) were obtained, of which IMF1-IMF3 are high-frequency components, and IMF4-IMF8 and Res are low-frequency effective components; (4) the IMF components were verified to meet the judgment conditions: the difference between the number of extreme points and zero points is ≤1, and the local symmetry error of the upper and lower envelopes is ≤0.01V.

[0032] High-frequency noise components IMF1-IMF3 are removed, while IMF4-IMF8 and residual components Res are retained. These components are then superimposed and reconstructed to obtain the denoised voltage degradation signal. The fluctuation amplitude of the reconstructed signal is significantly reduced, and it smoothly reflects the voltage decay trend over time.

[0033] The performance indicators of the signals before and after denoising were calculated as follows: before denoising, RMSE=0.0237 and MAE=0.0198; after denoising, RMSE=0.0069 and MAE=0.0048, indicating a significant noise removal effect.

[0034] In summary, the present invention provides a dataset denoising method based on Empirical Mode Decomposition (EMD) algorithm, comprising the following steps: Step S1, Data Selection: Obtaining a proton exchange membrane fuel cell (PEMFC) operation monitoring dataset, wherein the dataset contains at least an output voltage signal; Step S2, Degradation Index Determination: Performing correlation analysis on the dataset to select the output voltage, which is strongly negatively correlated with the lifespan of the PEMFC, as the core performance degradation index; Step S3, Data Sampling Simplification: Sampling the output voltage signal at equal time intervals to obtain a simplified voltage time series; Step S4, Empirical Mode Adaptive Decomposition: Performing Empirical Mode Decomposition on the simplified voltage time series to obtain several intrinsic mode function (IMF) components and a residual component; Step S5, Noise Component Removal: Removing high-frequency noise components from the several IMF components; Step S6, Signal Reconstruction: Superimposing the remaining IMF components and the residual component to reconstruct the denoised voltage degradation signal. The EMD-based denoising method of the present invention achieves accurate extraction of true degradation characteristics through data screening, simplification, adaptive decomposition, and noise removal.

[0035] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A dataset denoising method based on the Empirical Mode Decomposition (EMD) algorithm, characterized in that, The process includes the following steps: Step S1, Data Selection: Obtain the operational monitoring dataset of the proton exchange membrane fuel cell, which at least includes the output voltage signal; Step S2, Degradation Indicator Determination: Perform correlation analysis on the dataset and select the output voltage signal that is strongly negatively correlated with the lifespan of the proton exchange membrane fuel cell as the core performance degradation indicator; Step S3, Data Sampling Simplification: Sample the output voltage signal selected in Step S2 at equal time intervals to obtain a simplified voltage time series; Step S4, Empirical Mode Adaptive Decomposition: Perform empirical mode decomposition on the simplified voltage time series to obtain several intrinsic mode function components and one residual component, including: Step S4.1: Let the original output voltage signal be \(x(t)\), where t is the operating time, and find All local maxima and local minimum points Where i and j are the indices of extreme points; Step S4.2: Construct the upper envelope using a cubic spline interpolation function. and lower envelope ,satisfy (1-1) Step S4.3: Calculate the average value of the upper and lower envelopes: (1-2) Step S4.4: Calculate the intermediate signal: (1-3) Step S4.5: Iterative sieving: Judgment Does it meet the two conditions of the IMF: a) the number of local extrema is equal to or differs from the number of zeros by at most 1 within the time history; b) the average of the envelopes of local maxima and local minima at any time is 0; if not, then... For the new "original signal", repeat steps S4.2-S4.

4. The intermediate signal for the k-th iteration is: (1-4) until Satisfying the intrinsic mode function component conditions, let be denoted as . The first eigenmode function component ； Step S4.6: Calculate the first residual component: (1-5) Step S4.7: Repeat steps S4.1 to S4.6, to... For the new processing object, the second intrinsic mode function component is obtained by decomposition. and the second residual component After n iterations, when the residual component The decomposition stops when the function becomes monotonic, and the final result is: (1-6); Step S5, noise component removal: remove high-frequency noise components from the plurality of intrinsic mode function components; Step S6, signal reconstruction: superimpose the remaining intrinsic mode function components after removal with the residual components to reconstruct the denoised voltage degradation signal. （1-7）。 2. The dataset denoising method as described in claim 1, characterized in that, In step S3, the equal time interval is 0.5h to 2h.

3. The dataset denoising method as described in claim 2, characterized in that, In step S3, the equal time interval is 1 hour.

4. The dataset denoising method as described in claim 1, characterized in that, In step S1, the dataset also includes output current, hydrogen flow rate, hydrogen inlet and outlet temperatures, and air humidity.

5. The dataset denoising method as described in claim 1, characterized in that, In step S4, the screening termination condition of the empirical mode decomposition is: the intrinsic mode function components obtained by decomposition satisfy that the number of extreme points and the number of zero points in the time history are equal or differ by less than or equal to 1, and the upper and lower envelopes are locally symmetrical about the time axis.

6. The dataset denoising method as described in claim 1, characterized in that, In step S5, the screening criterion for the noise components is: based on the frequency distribution of the intrinsic mode function components, high-frequency intrinsic mode function components with frequencies higher than a preset threshold are removed.

7. The dataset denoising method as described in claim 6, characterized in that, The preset threshold is determined based on the inherent timescale of voltage degradation in a proton exchange membrane fuel cell.

8. The dataset denoising method as described in claim 1, characterized in that, After step S6, the denoising effect is verified by calculating the root mean square error and mean absolute error of the voltage degradation signal before and after denoising to verify the denoising effect.

9. The dataset denoising method as described in claim 8, characterized in that, The root mean square error is less than or equal to 0.0069, and the mean absolute error is less than or equal to 0.0048.

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