A method for extracting valid information of time parameters of railway signal relay

Abstract

The application discloses a method for extracting effective information of time parameters of railway signal relays, which comprises the following steps: arranging all time parameter sequences obtained through electric parameter experiments, and performing data preprocessing on the parameter sequences; decomposing the time parameter sequences obtained after data preprocessing into components capable of representing different information; performing autocorrelation function solving on all the components to obtain autocorrelation function images of the components, and determining signal-to-noise demarcation points according to the autocorrelation function images; performing wavelet threshold denoising processing on the components containing noise, and then reconstructing the processed IMF components, the IMF components not denoised and residual components to obtain parameter sequences after denoising, and extracting effective information of the parameters from the parameter sequences after denoising. The application can adaptively perform denoising on the time parameter sequences, and the improved wavelet threshold denoising method is used for denoising processing, so that the superiority of the method for denoising the time parameters of railway relays to extract effective information of the parameters is embodied.

Description

Technical Field

[0001] This invention relates to a signal relay detection technology, specifically a method for effectively extracting time parameters of railway signal relays. Background Technology

[0002] Railway signal relays are key equipment for achieving control objectives, signal transmission, and circuit isolation, playing an important role in the railway system. Their reliability affects the stability and safety of the entire system, so it is essential to effectively analyze the parameters of railway signal relays.

[0003] The timing parameters of a relay are an important indicator reflecting its operating characteristics and reliability. Effective analysis of these parameters not only helps in understanding the failure mechanism of the relay but also provides crucial data support for performance analysis and lifespan prediction. Therefore, data preprocessing of the timing parameters is essential. Furthermore, the control system of the electromagnetic relay low-level operation test equipment is subject to environmental noise interference during actual operation, making the selection of filtering and noise reduction methods paramount in data preprocessing.

[0004] Currently, the commonly used method for noise reduction of relay time parameters is wavelet threshold denoising. Wavelet denoising can reduce high-frequency noise interference, and at the same time, it can better preserve the original signal characteristics, thus having the functions of feature extraction and low-pass filtering. Figure 1 This is a flowchart of wavelet thresholding denoising. However, wavelet thresholding denoising is more effective for signals with high signal-to-noise ratios. When the signal-to-noise ratio is low, in noise-dominated regions, the search for wavelet basis is only used to describe the noise, which is not conducive to denoising.

[0005] The time parameters obtained through electrical life testing include: activation time, pull-in time, release time, normally open overtravel time, normally closed overtravel time, pull-in free movement time, and release free movement time. Changes in these time parameters reflect changes in the relay's operating state. However, due to errors in the testing system itself and the influence of the testing environment, the relay electrical parameters collected by the test platform will be subject to some contamination. Noise will affect the final test results, necessitating reasonable noise reduction of the time parameters of railway signal relays to extract effective information.

[0006] Therefore, how to reasonably reduce the noise of the time parameters of railway signal relays in order to extract the effective information of the parameters has become one of the problems that urgently need to be solved by those skilled in the art. Summary of the Invention

[0007] In view of the shortcomings of existing technologies, such as the inability to effectively extract time parameters of railway signal relays, the present invention aims to provide a method for effectively extracting time parameters of railway signal relays.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0009] This invention provides a method for extracting effective information of railway signal relay timing parameters, comprising the following steps:

[0010] 1) Organize all time parameter sequences obtained from the electrical parameter experiments and perform data preprocessing on the parameter sequences;

[0011] 2) Decompose the time parameter series obtained after data preprocessing into components that can represent different information;

[0012] 3) Solve for the autocorrelation function of all components to obtain the autocorrelation function image of each component, and determine the signal-to-noise boundary point based on the autocorrelation function image;

[0013] 4) Perform wavelet threshold denoising on the noisy components, and then reconstruct the denoised IMF components with the undenoised IMF components and residual components to obtain the denoised parameter sequence, from which the effective information of the parameters is extracted.

[0014] In step 2), the time parameter sequence obtained after data preprocessing is decomposed into components that can represent different information, specifically:

[0015] 201) Extract the extreme values ​​of the original time parameter sequence x(t) and fit them into a curve max1[x(t)] tangent to the maximum value and a curve min1[x(t)] tangent to the minimum value.

[0016] 202) The mean curve of the original time parameter sequence x(t) is:

[0017] 203) Separate the mean curve from the original time parameter sequence x(t) to obtain a new data sequence with low frequencies removed, i.e., h1(t) = x(t) - m1(t);

[0018] 204) Repeat steps 201) to 203) k times until the mean of the curves max1[x(t)] and min1[x(t)], which define the local maxima and minima of the sequence, is zero, thus obtaining the first-order intrinsic mode component: IMF1(t) = h 1k (t)=h 1(k-1) (t)-m 1k (t), where t is the number of relay actions, IMF(t) is the first-order intrinsic mode component, and h 1k (t) represents the k-th new data sequence after removing low frequencies, m 1k (t) is the mean curve that makes the mean of curves max1[x(t)] and min1[x(t)] zero;

[0019] 205) Separate the first-order intrinsic mode component IMF1 from the original time parameter sequence x(t) to obtain a difference data sequence r1(t) with high-frequency components removed. Repeat steps 201) to 204) to obtain other IMF components r2(t) = r1(t) - IMF2(t), ..., r m (t)=r m-1 (t)-IMF m (t);

[0020] 206) The original time parameter sequence x(t) is expressed as follows after decomposition:

[0021]

[0022] Among them, IMF p Let r be the p-th IMF component, m be the total number of IMF components, and r be the number of IMF components. m (t) represents the average trend of the remaining components and sequence after decomposition. Each IMF component corresponds to a different feature scale and the component frequency gradually decreases.

[0023] In step 3), the autocorrelation function is calculated for all components to obtain the autocorrelation function image of each component. The signal-to-noise boundary point is then determined based on the autocorrelation function image. Specifically:

[0024] 301) Determine the correlation between the IMF components at two different numbers of actions:

[0025]

[0026] Where t1 and t2 represent the different number of times the relay operates, n is the total number of times the relay operates, x(t1) and x(t2) represent the parameter values ​​when the number of operations is t2, and R x (t1,t2) represents the correlation of the IMF components with respect to the number of actions in t1 and t2.

[0027] 302) Based on the attenuation characteristics of the autocorrelation function image, extract R x Calculate the ratio of the relevance information between the first 5% and the last 5% of (t1, t2):

[0028]

[0029] Where n is the total number of relay actions, R x (i) represents the i-th function value of the autocorrelation function, k q is the correlation information ratio of the q-th IMF component.

[0030] 303) The following formula is used to measure mutation status:

[0031]

[0032] To determine the boundary between noise and useful components, the average of the correlation information ratios between the q-th IMF component and its two preceding components is compared. When h q A point that is significantly greater than the average of the first two correlation information values ​​is considered a breakout point.

[0033] In step 4), the wavelet threshold is determined through the following steps:

[0034] 401) Perform linear fitting on the autocorrelation function of the first two components;

[0035] 402) Calculate the relevance information ratio of the current IMF component;

[0036] 403) Calculate the standard error of the correlation information ratio of the first two IMF components;

[0037] 404) The threshold is the correlation ratio of the current IMF component plus three times the mean error. When the actual value exceeds this threshold, it is considered a sign of "significant over-limit".

[0038] The present invention has the following beneficial effects and advantages:

[0039] 1. This invention decomposes a time parameter sequence into components that represent different information, analyzes each component separately, selects the components that need to be denoised, and can adaptively denoise the time parameter sequence; it uses an improved wavelet threshold denoising method for denoising, demonstrating the superiority of this method for denoising railway relay time parameters to extract effective information from the parameters.

[0040] 2. This invention uses different time parameters and different sample numbers for processing, which clearly demonstrates the advantages of this invention, namely, it can perform noise reduction processing on data of unlimited quantity and unlimited parameters in order to extract effective information of the parameters. Attached Figure Description

[0041] Figure 1 A flowchart for wavelet thresholding denoising;

[0042] Figure 2 This is a flowchart illustrating the overall process of the method for extracting effective information from the timing parameters of railway signal relays according to the present invention.

[0043] Figure 3 This is a flowchart illustrating the decomposition of the parameter sequence according to the present invention;

[0044] Figure 4A IMF1-IMF4 component images of the time series of 1 million pull-in actions;

[0045] Figure 4BIMF5-IMF8 component images of the time series of 1 million pull-in actions;

[0046] Figure 4C IMF9-IMF time series of 1 million action engagements 12 Component images;

[0047] Figure 4D IMF for 1 million pull-in time series of actions 13 -IMF 16 Component images;

[0048] Figure 4E IMF for 1 million pull-in time series of actions 17 -IMF 20 Component images;

[0049] Figure 4F Image of the residual component R of the time series of 1 million pull-in actions;

[0050] Figure 5A The autocorrelation function image of the IMF1-IMF4 components of the action 1 million times absorption time series;

[0051] Figure 5B Autocorrelation function image of the IMF5-IMF8 components of a time series of 1 million action absorptions;

[0052] Figure 5C IMF9-IMF time series of 1 million action engagements 12 The autocorrelation function graph of the component;

[0053] Figure 5D IMF for 1 million pull-in time series of actions 13 -IMF 16 The autocorrelation function graph of the component;

[0054] Figure 5E IMF for 1 million pull-in time series of actions 17 -IMF 20 The autocorrelation function graph of the component;

[0055] Figure 5F The autocorrelation function image of the residual component R of the time series of 1 million attracting actions;

[0056] Figure 6A Comparison chart before and after extracting effective information from the suction time series of 200,000 actions;

[0057] Figure 6B A comparison chart showing the extraction of effective information from the suction time series of 1 million actions before and after;

[0058] Figure 6C A comparison chart showing the extraction of effective information from the suction time series of 2 million actions before and after;

[0059] Figure 7A Comparison chart before and after extracting effective information from the dynamic overtravel time series of 200,000 actions;

[0060] Figure 7B A comparison chart showing the extraction of effective information from the dynamic overtravel time series of 1 million actions before and after;

[0061] Figure 7C A comparison chart showing the extraction of effective information from the dynamic overtravel time series of 2 million actions before and after. Detailed Implementation

[0062] The present invention will now be further described with reference to the accompanying drawings.

[0063] like Figure 2 As shown, the present invention provides a method for extracting effective information of railway signal relay timing parameters, comprising the following steps:

[0064] 1) Organize all time parameter sequences obtained from the electrical parameter experiments and perform data preprocessing on the parameter sequences;

[0065] 2) Decompose the time parameter series obtained after data preprocessing into components that can represent different information;

[0066] 3) Solve for the autocorrelation function of all components to obtain the autocorrelation function image of each component, and determine the signal-to-noise boundary point based on the autocorrelation function image;

[0067] 4) Perform wavelet threshold denoising on the noisy components, and then reconstruct the processed IMF components with the undenoised IMF components and residual components to obtain effective information on the time parameters.

[0068] In step 1), assuming there exists a time parameter sequence x(t) (x(t) is an n-row, 1-column one-dimensional column vector), outlier handling, mainly zero-value handling, is performed on each parameter sequence, replacing it with the mean of the five values ​​before and after it to complete the data. If x i (t)=0(x i (t) is the value of the i-th row of x(t), then let

[0069]

[0070] Where i = 1, 2, ..., n, the handling of missing values ​​and outliers is the same as the handling of zero values.

[0071] like Figure 3As shown, in step 2), the time parameter sequence obtained after data preprocessing is decomposed into components that can represent different information. The specific steps are as follows:

[0072] 201) Extract the extreme values ​​of the original time parameter sequence x(t) and fit them into a curve max1[x(t)] tangent to the maximum value and a curve min1[x(t)] tangent to the minimum value.

[0073] Identify the local maxima and minima of the parameter sequence x(t), connect the maxima to obtain the curve max1[x(t)] which is tangent to all maxima, and connect the minima to obtain the curve min1[x(t)] which is tangent to all minima.

[0074] 202) The mean curve of the original time parameter sequence x(t) is:

[0075] The mean value of the curve m1(t) is obtained by using the curves max1[x(t)] and min1[x(t)].

[0076] 203) Separate the mean curve from the original time parameter sequence x(t) to obtain a new data sequence with low frequencies removed, i.e., h1(t) = x(t) - m1(t);

[0077] 204) Repeat steps 201) to 203) k times until the mean of the curves max1[x(t)] and min1[x(t)], which define the local maxima and minima of the sequence, is zero, thus obtaining the first-order intrinsic mode component: IMF1(t) = h 1k (t)=h 1(k-1) (t)-m 1k (t), where t is the number of relay actions, IMF1(t) is the first-order intrinsic mode component, and h 1k (t) represents the k-th new data sequence after removing low frequencies, m 1k (t) is the mean curve that makes the mean of curves max1[x(t)] and min1[x(t)] zero.

[0078] For nonstationary nonlinear parameter sequences, a single "filtering" process is insufficient to make the mean of the curves max1[x(t)] and min1[x(t)], which define the local maxima and minima, zero. In this case, the above operation needs to be repeated with h1(t) as the sequence to be processed, where h2(t) = h1(t) - m2(t). This process is repeated k times until h... k (t) satisfies the IMF condition, that is, the mean of the curves max1[x(t)] and min1[x(t)], which define the local maxima and minima of the sequence, is zero. 1k (t)=IMF1(t)

[0079] For the first intrinsic mode component (IMF component):

[0080] h 1k (t)=h 1(k-1) (t)-m 1k (t)

[0081] 205) Separate the first-order intrinsic mode component IMF1 from the original time parameter sequence x(t) to obtain a difference data sequence r1(t) with high-frequency components removed. Repeat steps 201) to 204) to obtain other IMF components r2(t) = r1(t) - IMF2(t), ..., r m (t)=r m-1 (t)-IMF m (t);

[0082] IMF1 is separated from the original time parameter sequence, and the remaining quantity r1(t) is used as a new sequence. Step (1) is executed iteratively. After the m-th iteration, m-1 remaining quantities are obtained. When r m The decomposition terminates when (t) approaches a monotonic function. The remaining quantities are respectively

[0083]

[0084] 206) The original time parameter sequence x(t) is expressed as follows after decomposition:

[0085]

[0086] Among them, IMF p Let r be the p-th IMF component, m be the total number of IMF components, and r be the number of IMF components. m (t) represents the average trend of the remaining components and sequence after decomposition. Each IMF component corresponds to a different feature scale and the component frequency gradually decreases.

[0087] In step 3), the autocorrelation function is calculated for all components to obtain the autocorrelation function image of each component. The signal-to-noise boundary point is then determined based on the autocorrelation function image. Specifically:

[0088] 301) Determine the correlation between IMF components at two different time points:

[0089]

[0090] Where t1 and t2 represent the different number of times the relay operates, n is the total number of times the relay operates, x(t1) and x(t2) represent the parameter values ​​when the number of operations is t2, and R x (t1,t2) represents the correlation of the IMF components with respect to the number of actions in t1 and t2.

[0091] 302) Based on the decay characteristics of the autocorrelation function, extract R x Calculate the ratio of the relevance information between the first 5% and the last 5% of (t1, t2):

[0092]

[0093] Where n is the total number of relay actions, R x (i) represents the i-th function value of the autocorrelation function, k q The relevance information ratio of the q-th IMF component;

[0094] 303) The following formula is used to measure mutation status:

[0095]

[0096] To determine the boundary between noise and useful components, the average of the correlation information ratios between the q-th IMF component and its two preceding components is compared. When h q A point that is significantly greater than the average of the first two correlation information values ​​is considered a breakout point.

[0097] To adaptively determine the boundary point, a straight line is first fitted to the first two data points to calculate the value after the current number of actions. Then, the mean error of the first two data points is calculated. The value after the current number of actions plus three times the mean error is used as the threshold. When the actual value exceeds this threshold, it is used as a sign of "significant over-limit".

[0098] In step 4), wavelet threshold denoising is performed on the noisy components. Then, the processed IMF components are reconstructed with the undenoised IMF components and residual components to obtain the denoised parameter sequence. The effective information of the parameters is extracted, as follows:

[0099] 401) Wavelet decomposition with noisy components

[0100] Based on the specific noisy components, a suitable wavelet basis and decomposition level N are selected. Then, the noisy signal is subjected to N-level wavelet decomposition to obtain the corresponding wavelet decomposition coefficients. The mathematical expression of the wavelet packet decomposition algorithm is as follows:

[0101]

[0102] in and is the wavelet packet coefficient; p is the transform coefficient; l is the decomposition level; q is the subband; a s-2l and b s-2l Take the derivatives of the filter coefficients;

[0103] 402) Threshold processing

[0104] The wavelet coefficients obtained from the decomposition are thresholded using an appropriate threshold function to denoise the detail coefficients. Wavelet thresholding methods are mainly divided into hard thresholding and soft thresholding. Hard thresholding can better preserve the local features of the signal, but its discontinuity can lead to significant noise near the threshold after denoising. To prevent signal distortion, this invention selects the hard thresholding method, the mathematical expression of which is:

[0105]

[0106] In the formula, α is a variable; β is a threshold.

[0107] This invention uses Stein's unbiased estimator as the threshold criterion, with the threshold β being...

[0108]

[0109] 403) Signal Reconstruction

[0110] The denoised signal can be obtained by reconstructing the wavelet coefficients after thresholding; the mathematical expression of the reconstruction algorithm is as follows:

[0111]

[0112] In the formula μ l-2s and ν l-2s It is a set of orthogonal conjugate coefficients;

[0113] 404) for the noise-reduced components And component IMF that does not require noise reduction y+1 -IMF m Reconstructing the parameter sequence x with the remaining component R yields the parameter sequence from which the effective information is extracted. * (t).

[0114] When using the method of this invention, temperature and humidity are not limited, the types of parameters are not limited, and the number of railway signal relay samples is not limited.

[0115] In this embodiment, parameter data of 200,000, 1,000,000, and 2,000,000 cycles of dynamic overtravel time and pull-in time were selected for analysis. First, outlier processing was performed on the original data. Since these time parameters are measured during the operation of the relay, the time parameters are greater than zero. First, data less than or equal to zero were removed, and the average of the five values ​​before and after the zero value was taken to replace it, thus completing the data. The processing method for missing values ​​and outliers is the same as above.

[0116] Taking the pull-in time parameter after 1 million relay actions as an example, we first decompose the parameter sequence after removing outliers, obtaining 20 intrinsic mode function components and 1 residual component. The graphs of each component are shown below. Figures 4A-4FAs shown. Next, the autocorrelation function of the 20 intrinsic mode functions is solved, and the autocorrelation function graph of the IMF components is obtained (with the number of actions as the horizontal axis), as shown. Figures 5A-5F As shown, the autocorrelation function of the noise-dominated high-frequency components IMF1-IMF12 exhibits high-frequency oscillations. The longer the time interval, the less data there is, and the larger the oscillation amplitude. As the number of actions increases, it rapidly decreases to around 0, which is a typical noise autocorrelation function image. The eight components after IMF12 show a significant slowdown, indicating that the correlation among them becomes stronger, meaning the signal becomes stronger. Therefore, the first 12 components conform to the characteristics of random noise, indicating that the information in the first 12 components mainly contains random noise. Threshold denoising is applied to these 12 components, and the denoised components are reconstructed with the remaining eight components and the residual component R. A comparison of the parameter sequence image after extracting effective information with the original sequence image is shown in the figure. Figure 6B As shown.

[0117] The same method was used to process the attraction time series of 200,000 and 2,000,000 cycles, and the dynamic overrange time series of 200,000, 1,000,000, and 2,000,000 cycles, respectively. The results are as follows: Figure 6A , 6C As shown in 7A to 7C.

[0118] Next, in order to demonstrate the superiority of the present invention in noise reduction of railway signal relay time parameters, the SSIM index and SNR index are introduced to compare the noise reduction effect of the method used in the present invention with the wavelet threshold denoising method.

[0119] The structure of an image carries its most important information. Structural similarity (SSIM) interprets structural information from the perspective of image composition. Image structural information consists of three elements: brightness, contrast, and structure. The SSIM index ranges from [0,1], with higher indices indicating greater similarity between two images. SSIM can be modeled as follows:

[0120] SSIM(x, y) = [l(x, y)] ρ [c(x, y)] θ [s(x, y)] γ

[0121] in:

[0122]

[0123] Where x and y are the original data line graph and the filtered data line graph, respectively, l(x, y) is the brightness comparison function, c(x, y) is the contrast comparison function, s(x, y) is the structure contrast function, and c1, c2, and c3 are constants. μ x σ x The mean and standard deviation of the brightness of the original data line chart, μy σ y σ represents the mean and standard deviation of the brightness of the line graph of the filtered data. xy It represents the correlation between the original data line chart and the filtered data line chart.

[0124] The signal-to-noise ratio (SNR) of the timing parameters of railway signal relays is defined as follows: the higher the SNR, the better the noise reduction effect.

[0125]

[0126] In the formula, X signal X is the signal power of the railway signal relay time parameter. noise The power of the noise (original signal power - signal power after noise reduction).

[0127] When solving for the SSIM exponent, the image structure is mainly compared. Considering the influence of legends and coordinate axes, only the lines in the input line graph are retained for SSIM exponent calculation. The SNR and SSIM exponent results obtained using the method of this invention and the wavelet thresholding denoising method are shown in Table 1.

[0128] Table 1. Results of SNR and SSIM index calculation

[0129]

[0130] By solving the SSIM and SNR indices, it was found that the effective information extraction method of the present invention improved the signal-to-noise ratio and structural similarity index for different action numbers and different time parameter sequences. It can be seen that the method used in the present invention can better extract the effective information of the time parameters of railway signal relays.

Claims

1. A method for extracting valid information of time parameters of a railway signal relay, characterized in that Comprise the following steps: 1) collate all time parameter sequence obtained from electrical parameter experiment, data pretreatment is carried out to time parameter sequence; 2) the time parameter sequence obtained after data pretreatment is decomposed into IMF component capable of representing different information; 3) autocorrelation function solving is carried out to IMF component, the autocorrelation function image of IMF component is obtained, and the signal-to-noise demarcation point is determined according to the autocorrelation function image; 4) wavelet threshold denoising processing is carried out to the IMF component containing noise, then the IMF component after wavelet threshold denoising processing, each IMF component and residual component not being denoised are reconstructed, the parameter sequence after denoising is obtained, and the effective information of parameter is extracted; In step 3), autocorrelation function solving is carried out to IMF component, the autocorrelation function image of IMF component is obtained, and the signal-to-noise demarcation point is determined according to the autocorrelation function image, comprising the following steps: 301) Solving for the degree of correlation of the IMF components at two different motion counts ; ； Wherein, t and t+τ represent different action times of relay, x(t) and x(t+τ) represent parameter values when action times are t and t+τ respectively, and Rx(t, t+τ) is the correlation degree of IMF component when action times are t and t+τ; 302) According to the self-correlation function image attenuation characteristics, extract the ratio of the correlation degree information of the first 5% and the last 5%. ； Wherein, n is the total action times of the relay, τ is the time delay, representing the action times interval, is the total energy of the IMF component autocorrelation function, is rounded to the nearest integer, is rounded to the nearest integer, is the correlation degree information ratio of the qth IMF component; is rounded to the nearest integer, is rounded to the nearest integer. 303) the following formula is used to measure mutation condition: ； To determine the demarcation point between the noise IMF component and the useful IMF component, the correlation degree information ratio of the qth IMF component is compared with the average of the correlation degree information ratios of the two preceding components. When the correlation degree information ratio of the qth IMF component is significantly greater than the average of the correlation degree information ratios of the two preceding components, the qth IMF component is the demarcation point. When the correlation degree information ratio of the qth IMF component is significantly greater than the average of the correlation degree information ratios of the two preceding components, the qth IMF component is the demarcation point.

2. The method for extracting valid information of time parameters of a railway signal relay according to claim 1, characterized in that In step 2), the time parameter sequence obtained after data pretreatment is decomposed into IMF component capable of representing different information, comprising the following steps: 201) extracting the original time parameter sequence extremum, curve fitted tangent to the curve maximum and tangent to the curve minimum ; 202) original time parameter sequence The mean curve of ; 203) from the original time parameter sequence The mean curve is removed from the data sequence to obtain a new data sequence without low frequencies, i.e. ; 204) repeat steps 201)~203) the curve defined by the local maxima and minima of the sequence and the curve is zero, the first order intrinsic mode function (IMF) component is obtained: where t is the number of relay actions, is the first order intrinsic mode function (IMF) component, is the kth new data sequence with low frequency removed, is the mean curve for making the mean value of the curve and the curve zero; 205) from the original time parameter sequence separating the first intrinsic mode component IMF obtaining a difference data sequence without high frequency components repeating steps 201)~204) to obtain other IMF components , ; 206) original time parameter sequence After decomposition, it is expressed as: ； wherein, is the pth IMF component, m is the total number of intrinsic mode function components, is the residual IMF component, representing the IMF components and the mean trend of the sequence remaining after decomposition, each IMF component corresponds to a different characteristic scale and the component frequency gradually decreases.

Images