An adjacent IMF adaptive merging method based on multi-index similarity discrimination
Patent Information
- Application Number
- CN202610980982.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-02
- Publication Date
- 2026-09-22
AI Technical Summary
[0009]因此，现有技术仍缺少一种面向相邻IMF或相邻IMF组的自适应合并方法
[0028]1）本发明能够有效减少主体振荡结构被多个相邻IMF割裂表示的问题，提高模态表示的完整性：现有方法通常在模态分解后直接选择单个IMF或固定序号IMF进行分析，但短时、非平稳、多尺度叠置复合数字信号中的同一主体振荡结构可能在分解过程中被拆分到多个相邻IMF分量中。本发明通过相邻IMF多指标相似性判别与合并重构，将属于同一主体振荡结构的相邻IMF重新组合为候选模态，从而克服了现有方法中模态分散造成的分析对象不完整问题。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of digital signal processing technology, and in particular to an adaptive merging method for adjacent IMFs based on multi-index similarity discrimination. Background Technology
[0002] In the field of digital signal processing, methods such as Fourier spectrum analysis, short-time Fourier transform, wavelet transform, and Hilbert instantaneous frequency analysis are commonly used to extract the frequency features of signals. These methods can describe signal features from aspects such as overall frequency composition, local time-frequency distribution, or instantaneous frequency changes. However, for short-time, non-stationary, multi-component composite digital signals, they are still easily affected by factors such as time windows, basis function selection, phase abrupt changes, low-amplitude points, and the superposition of multiple components, resulting in unstable frequency feature extraction results.
[0003] To improve the adaptive analysis capability of non-stationary signals, Empirical Mode Decomposition (EMD) and its improved methods are widely used in multi-scale oscillatory signal processing. EMD can adaptively decompose the original signal into several Intrinsic Mode Functions (IMF) components without pre-setting fixed basis functions. However, traditional EMD is susceptible to local extrema and signal perturbations, and may produce mode aliasing problems. To overcome these shortcomings, Ensemble Empirical Mode Decomposition (EEMD) improves the mode aliasing problem to some extent by adding white noise to the original signal and performing EMD decomposition multiple times and then averaging the results. However, EEMD may still suffer from residual auxiliary noise, inconsistent numbers of modes obtained from different trials, and reconstruction errors.
[0004] In existing technologies, the short-time composite digital signal to be processed is first subjected to mode decomposition to obtain multiple IMF components. Then, based on the IMF index, energy level, dominant frequency range, correlation coefficient, or human experience, one or more IMF components are selected as the objects of subsequent feature analysis. This type of method can separate the multi-scale oscillatory components in the original signal to a certain extent, but it still has the following problems in practical applications.
[0005] First, the IMF indices obtained from mode decomposition primarily reflect the mode arrangement order during the adaptive decomposition process, and do not necessarily correspond to fixed frequency bands or fixed physical meanings. For different samples, even if the signals have similar main oscillation structures, their corresponding principal components may appear in different IMF indices. Therefore, directly selecting analysis objects according to fixed IMF indices can easily lead to inconsistencies in mode selection criteria between different samples.
[0006] Secondly, for short-time, non-stationary, multi-scale superimposed composite digital signals, the same main oscillation structure may be split into multiple adjacent IMF components during the decomposition process. This phenomenon is called mode dispersion. If only a single IMF component is used as the analysis object, the waveform structure and energy contribution of the same main oscillation may be fragmented, causing the subsequent feature extraction results to be affected by mode dispersion.
[0007] Furthermore, existing methods for selecting or processing IMFs often rely on a single indicator, such as energy, dominant frequency, or correlation, making it difficult to simultaneously constrain the consistency of adjacent IMFs in terms of frequency level, time-domain waveform, spectral shape, and effective energy contribution. When adjacent IMFs actually belong to the same dominant oscillatory response, judging by a single indicator is prone to problems such as misselection, omission, or over-retention of dispersed modes.
[0008] Furthermore, existing methods typically process IMF components by filtering, screening, or reconstructing individual IMFs, lacking a systematic mechanism for determining the relationships between adjacent IMFs. For cases where multiple consecutive IMFs exhibit similarity, existing technologies also fail to provide an effective iterative merging solution.
[0009] Therefore, existing technologies still lack an adaptive merging method for adjacent IMFs or groups of adjacent IMFs. This method should be able to jointly assess the frequency proximity, waveform similarity, spectral similarity, and energy contribution between adjacent IMFs after mode decomposition such as CEEMDAN, and merge and reconstruct them when similarity conditions are met, thereby forming a more complete and stable set of candidate modes. Summary of the Invention
[0010] The purpose of this invention is to overcome the shortcomings of existing technologies by determining whether adjacent IMFs or groups of adjacent IMFs belong to the same main oscillation structure through multi-index similarity discrimination, and to merge and reconstruct them when conditions are met. This reduces the impact of the main oscillation being represented by adjacent IMFs in a dispersed manner, and improves the consistency and reliability of the mode construction results of short-time composite digital signals. It provides an adaptive merging method for adjacent IMFs based on multi-index similarity discrimination. This method can be applied to the mode reconstruction and feature analysis process of short-time, non-stationary, multi-scale superimposed composite digital signals such as seismic digital signals, mechanical equipment vibration signals, speech signals, and biomedical signals.
[0011] The objective of this invention is achieved through the following technical solution: an adaptive merging method for adjacent IMFs based on multi-index similarity discrimination, comprising the following steps:
[0012] Step 1: Acquire the short-time composite digital signal to be processed;
[0013] Step 2: Decompose the short-time composite digital signal using the mode decomposition method to obtain multiple IMF components;
[0014] Step 3: Calculate the instantaneous frequency of each IMF component, and extract the dominant frequency, median instantaneous frequency, energy, waveform correlation and spectral characteristics of each IMF component;
[0015] Step 4: Initialize IMF groups, with each IMF component forming a separate IMF group, and only perform subsequent merging judgments on adjacent IMF groups;
[0016] Step 5: Perform multi-index similarity discrimination on adjacent IMF groups, calculate the relative difference of the dominant frequency, the relative difference of the median instantaneous frequency, the correlation coefficient of the time-domain waveform, the spectral similarity, and the combined energy ratio between adjacent modes corresponding to adjacent IMF groups, and determine whether adjacent IMF groups belong to the same main oscillation structure.
[0017] Step 6: Determine whether adjacent modes simultaneously satisfy multiple merging conditions; if they are simultaneously satisfied, then treat the adjacent IMF groups corresponding to the adjacent modes as similar split components of the same main oscillation structure and perform merging.
[0018] Step 7: Merge adjacent IMF groups corresponding to adjacent modes that meet the merging conditions into a new IMF group, merge the index sets of adjacent IMF groups, add the IMF components corresponding to adjacent IMF groups to reconstruct the merged mode, and update the IMF group set;
[0019] Step 8: For the updated IMF group set, repeat the similarity judgment and merging reconstruction process of adjacent IMF groups until there are no adjacent IMF groups that meet the merging conditions. Finally, a candidate mode set that maintains the original IMF order and does not overlap is obtained and output.
[0020] Preferably, the mode decomposition method is the CEEMDAN decomposition method, which extracts each mode by adding adaptive auxiliary noise step by step and updating the residuals. In the ensemble averaging process, positive and negative paired auxiliary noise is added so that the random noise cancels each other out during the ensemble averaging process.
[0021] Preferably, the mode decomposition method is the EMD or EEMD mode decomposition method.
[0022] Preferably, in step three, a Hilbert transform is performed on each IMF component to construct an analytical signal, obtaining the instantaneous amplitude and instantaneous phase, and then the instantaneous frequency is obtained; the dominant frequency is the frequency corresponding to the main energy peak of the mode, and the median instantaneous frequency is the median of the instantaneous frequencies.
[0023] Preferably, the merging conditions include: the relative difference of the main frequency is less than or equal to the main frequency difference threshold, the correlation coefficient of the time-domain waveform is greater than or equal to the correlation coefficient threshold of the time-domain waveform or the spectral similarity is greater than or equal to the spectral similarity threshold, the relative difference of the median instantaneous frequency is less than or equal to the median frequency difference threshold, and the combined energy ratio is greater than or equal to the energy ratio threshold.
[0024] Preferably, step eight employs an iterative merging mechanism. When multiple consecutive IMF groups are pairwise similar, they are first merged sequentially. The merged new IMF group is then compared with the next adjacent IMF group. If all merging conditions are still met, the next merging is performed.
[0025] Preferably, the short-time composite digital signal is a local reflection seismic wavelet signal, mechanical equipment vibration signal, voice signal, electrocardiogram signal, electroencephalogram signal, radar signal, sonar signal, or ultrasonic detection signal from the seismic digital signal.
[0026] Preferably, the candidate mode set is further used for tasks such as dominant mode recognition, frequency feature extraction, signal classification, anomaly detection, or digital signal analysis.
[0027] The beneficial effects of this invention are:
[0028] 1) This invention effectively reduces the problem of the main oscillation structure being fragmented by multiple adjacent IMFs, improving the completeness of modal representation: Existing methods typically select a single IMF or a fixed-order IMF for analysis after modal decomposition. However, the same main oscillation structure in short-time, non-stationary, multi-scale superimposed composite digital signals may be split into multiple adjacent IMF components during the decomposition process. This invention, through multi-index similarity discrimination and merging reconstruction of adjacent IMFs, recombines adjacent IMFs belonging to the same main oscillation structure into candidate modes, thereby overcoming the problem of incomplete analysis objects caused by modal dispersion in existing methods.
[0029] 2) This invention does not rely on fixed IMF indices, but rather performs adaptive judgment based on multiple indicator characteristics between adjacent IMFs, improving the consistency of candidate mode construction among different samples: Existing methods select analysis objects according to fixed IMF indices, and even if signals have similar main oscillation structures, their corresponding main components may appear in different IMF indices, causing inconsistencies in mode selection criteria among different samples. This invention performs adaptive merging through joint discrimination of multiple indicators such as frequency proximity, waveform similarity, spectral consistency, and energy contribution between adjacent IMFs, without relying on fixed IMF indices, effectively reducing the risk of misselection and omission caused by fixed IMF selection or single indicator judgment.
[0030] 3) This invention employs a multi-index joint criterion to simultaneously constrain the similarity of adjacent IMFs from multiple dimensions, significantly reducing the risk of erroneous merging: This invention simultaneously uses four indicators: main frequency difference, median frequency difference, waveform correlation, and spectral similarity. These four indicators describe the similarity of adjacent IMFs from different perspectives, such as main frequency, overall frequency level, time-domain waveform structure, and frequency-domain energy distribution, and have obvious complementary effects. The four indicators are related by a "simultaneous satisfaction" logic; merging is only performed when all four indicators reach their respective thresholds, avoiding erroneous merging caused by a single indicator or a majority of indicators being close.
[0031] 4) This invention employs an iterative merging mechanism, which can correctly handle the situation where multiple consecutive IMFs are pairwise similar, avoiding erroneous merging: When multiple consecutive IMFs exhibit adjacent similarity, this invention uses an iterative merging mechanism of "adjacency determination—pairwise merging—set update—feature recalculation—continued determination". Since adjacent similarity relationships are not necessarily transitive, the method of merging first and then recalculating features can avoid erroneous merging of modalities with different overall attributes due to local pairwise similarity, ensuring that each merging is performed after thorough verification.
[0032] 5) This invention can form a more stable and complete candidate mode set, providing more reliable input for subsequent digital signal analysis tasks: the merged candidate modes maintain the adjacent order and non-overlapping relationship of the IMF, while reducing the mode dispersion problem caused by excessive decomposition. This candidate mode set can be further used for subsequent digital signal analysis tasks such as dominant mode recognition, frequency feature extraction, signal classification, anomaly detection, or first arrival picking, providing input data with a more concentrated structure and clearer physical meaning for feature extraction and signal recognition.
[0033] 6) This invention has strong versatility and wide applicability: Besides being applied to the processing of local reflection seismic wavelets in digital seismic signals, it can also be applied to other digital signals with short-time, non-stationary, and multi-scale superimposed characteristics, such as vibration signals from mechanical equipment, speech signals, electrocardiogram signals, electroencephalogram signals, radar signals, sonar signals, or ultrasonic detection signals. Its core lies in the joint determination and selective merging of multiple features of adjacent modes obtained from decomposition, without relying on the physical parameters of specific signal types, thus possessing good prospects for cross-domain application.
[0034] 7) The necessity and effectiveness of this invention have been verified in actual seismic signal samples: In the test of local wavelet samples of actual seismic digital signals, 71 out of 90 local wavelet samples exhibited IMF merging-dominated characteristics, accounting for 78.9%. This statistical result indicates that the main oscillation is dispersed in adjacent IMFs, which is quite common in actual short-time composite seismic signals. The adaptive merging step of adjacent IMFs proposed in this invention is practically necessary and can effectively address the processing needs of this type of signal. Attached Figure Description
[0035] Figure 1 This is an overall flowchart of the present invention;
[0036] Figure 2 This is a schematic diagram of the original local seismic wavelet used in the algorithm example;
[0037] Figure 3 A schematic diagram showing the CEEMDAN decomposition and characteristic calculation results of a local seismic wavelet;
[0038] Figure 4 The results show the candidate modes and signal reconstructions after merging similar IMFs. Detailed Implementation
[0039] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0040] See Figures 1-4 This invention provides a technical solution: an adaptive merging method for adjacent IMFs based on multi-index similarity discrimination, comprising the following steps:
[0041] Step 1: Acquire the short-time composite digital signal to be processed;
[0042] Step 2: Decompose the short-time composite digital signal using the mode decomposition method to obtain multiple IMF components;
[0043] Step 3: Calculate the instantaneous frequency of each IMF component, and extract the dominant frequency, median instantaneous frequency, energy, waveform correlation and spectral characteristics of each IMF component;
[0044] Step 4: Initialize IMF groups, with each IMF component forming a separate IMF group, and only perform subsequent merging judgments on adjacent IMF groups;
[0045] Step 5: Perform multi-index similarity discrimination on adjacent IMF groups, calculate the relative difference of the dominant frequency, the relative difference of the median instantaneous frequency, the correlation coefficient of the time-domain waveform, the spectral similarity, and the combined energy ratio between adjacent modes corresponding to adjacent IMF groups, and determine whether adjacent IMF groups belong to the same main oscillation structure.
[0046] Step 6: Determine whether adjacent modes simultaneously satisfy multiple merging conditions; if they are simultaneously satisfied, then treat the adjacent IMF groups corresponding to the adjacent modes as similar split components of the same main oscillation structure and perform merging.
[0047] Step 7: Merge adjacent IMF groups corresponding to adjacent modes that meet the merging conditions into a new IMF group, merge the index sets of adjacent IMF groups, add the IMF components corresponding to adjacent IMF groups to reconstruct the merged mode, and update the IMF group set;
[0048] Step 8: For the updated IMF group set, repeat the similarity judgment and merging reconstruction process of adjacent IMF groups until there are no adjacent IMF groups that meet the merging conditions. Finally, a candidate mode set that maintains the original IMF order and does not overlap is obtained and output.
[0049] In this embodiment, the focus is on short-time, non-stationary, multi-scale superimposed composite digital signals, specifically applicable to local wavelet processing in seismic digital signals. The core idea is: after obtaining multiple IMF components through CEEMDAN decomposition, instead of directly selecting analysis objects according to fixed IMF indices, similarity judgment is performed on adjacent IMFs or adjacent IMF groups; when adjacent IMFs meet preset conditions in terms of frequency level, waveform structure, spectral morphology, and energy contribution, they are merged and reconstructed into the same candidate mode, thereby reducing the problem of the same main oscillation structure being fragmented by multiple adjacent IMFs.
[0050] The method of this invention can be executed by a computer device, processor, or signal processing program. Its input is a short-time composite digital signal to be processed, and its output is a set of candidate modes obtained after merging similar IMFs. The core process of this invention can be summarized as follows: First, the short-time, non-stationary composite digital signal is decomposed using CEEMDAN to obtain multiple IMFs arranged according to frequency scale; then, features such as frequency proximity, waveform similarity, spectral consistency, and energy relationship between adjacent IMFs are extracted; then, based on a multi-feature joint criterion, it is determined whether adjacent IMFs belong to similar oscillatory components, and adjacent IMFs that meet the conditions are merged; finally, the merged modes replace the original IMFs, the mode set is updated, and the judgment continues until no adjacent IMFs that meet the conditions are found.
[0051] The specific steps are as follows:
[0052] (a) Acquiring the short-time composite digital signal to be processed. Let the signal to be processed be:
[0053] ,in, This represents the signal amplitude at the nth sampling point, where N is the number of signal sampling points. For applications involving digital seismic signals, It can be a local seismic wavelet signal extracted from a single seismic record.
[0054] (ii) Ceemdan decomposition of short-time composite digital signals: for the input signal Performing CEEMDAN decomposition yields several IMF components (the order of the IMFs is the natural oscillation scale order output by the decomposition algorithm) and residual terms, expressed as follows:
[0055] in, Let J be the j-th IMF component, and J be the total number of IMF components. These are residual terms. This invention primarily focuses on similarity discrimination and merging of IMF components; residual terms do not participate in the merging process of adjacent IMFs.
[0056] (III) Calculate the instantaneous frequency and fundamental characteristics of each IMF component:
[0057] For each IMF component Perform a Hilbert transform to construct an analytic signal:
[0058] in, Represents the Hilbert transform. For instantaneous amplitude, Let be the instantaneous phase. The instantaneous frequency of the j-th IMF component can be expressed as:
[0059] The dominant frequency, median instantaneous frequency, energy, waveform correlation, and spectral characteristics of each IMF component or IMF group are further calculated for subsequent similarity judgment of adjacent IMFs.
[0060] (iv) Initializing IMF Groups: To avoid arbitrary combinations of non-adjacent IMFs, this invention only performs merging judgments on adjacent IMFs or adjacent IMF groups. Initially, each IMF component constitutes a separate IMF group:
[0061] Among them, G p This represents the index set of the p-th IMF group. Initially, the number of IMF groups is equal to the total number of IMF components.
[0062] For the current two adjacent IMF groups G p and G p+1 The corresponding modes are defined as follows:
[0063]
[0064] Where u(t) n ) and v(t) n ) represent the two adjacent modes to be compared.
[0065] (v) Multi-index similarity judgment of adjacent IMF groups: This invention judges whether adjacent IMF groups belong to the same main oscillation structure from four aspects: frequency proximity, time-domain waveform similarity, spectrum similarity and combined energy contribution.
[0066] First, let's set Indicates the dominant frequency of the mode. Let u(t) represent the median instantaneous frequency of the mode. Then, the adjacent modes u(t) n ) and v(t) n The relative difference in clock speed is defined as follows:
[0067]
[0068] The relative difference in median instantaneous frequency is defined as:
[0069]
[0070] in, To avoid extremely small positive numbers with a denominator of zero.
[0071] Secondly, the time-domain correlation coefficient is used to represent the waveform similarity of adjacent modes:
[0072]
[0073] in, and u(t) n ) and v(t) n The mean of ).
[0074] Secondly, amplitude spectrum cosine similarity is used to represent the spectral similarity of adjacent modes. Let U q and V q u(t) n ) and v(t) n The amplitude spectrum of ) is then:
[0075]
[0076] Finally, define the combined energy percentage of adjacent modes, and let the total energy of the IMF components be:
[0077]
[0078] Then adjacent modes u(t) n ) and v(t) n The combined energy ratio is as follows:
[0079]
[0080] This metric is used to prevent perturbation components with low energy contributions from being incorporated into candidate modes.
[0081] (vi) Determine whether to merge adjacent IMF groups based on preset conditions: when adjacent modes u(t) n ) and v(t) n When both conditions are met simultaneously, they are considered to have similar oscillation scales, similar waveform structures or spectral morphologies, and effective energy contributions, and can be regarded as similar decomposed components of the same main oscillation structure:
[0082]
[0083] in, and These thresholds are: the upper limit of the relative difference between the dominant frequencies of adjacent modes, the upper limit of the relative difference between the median instantaneous frequencies of adjacent modes, the lower limit of the correlation coefficient of the time-domain waveforms of adjacent modes, the lower limit of the similarity of the amplitude spectrum of adjacent modes, and the lower limit of the energy ratio of the combination of adjacent modes. These thresholds can be preset according to the specific signal type, sampling conditions and processing requirements, or a unified empirical threshold can be used in specific embodiments.
[0084] (vii) Merge and reconstruct adjacent IMF groups that meet the conditions: If the current adjacent IMF group G p and G p+1 If the merging conditions are met, the index sets of the two will be merged into:
[0085]
[0086] The corresponding merged mode reconstruction is:
[0087]
[0088] It can also be written as:
[0089]
[0090] After merging, the original (p+1)th IMF group is deleted, and the IMF group number to its right is updated. The new merged group continues to be compared with its adjacent IMF groups to its right. If multiple adjacent IMF groups consecutively meet the similarity condition, they can continue to be merged to form a candidate mode containing multiple IMF components.
[0091] If the current adjacent IMF groups do not meet the merging conditions, the original IMF groups remain unchanged, and the next pair of adjacent IMF groups is determined.
[0092] (viii) Output the candidate mode set after iteration: Repeat the similarity judgment and merging reconstruction process of adjacent IMF groups until there are no adjacent IMF groups that meet the merging conditions. The final result is a set of IMF groups that maintain the original IMF order and do not overlap (i.e., the candidate mode set):
[0093] Where P is the number of candidate modes after merging, and .
[0094] The p-th candidate mode is defined as:
[0095]
[0096] If G p If it contains only one IMF component, then For a single IMF candidate mode; if G p If it contains multiple adjacent IMF components, then To merge and reconstruct candidate modes, the original IMF set is transformed into a candidate mode set.
[0097]
[0098] This invention achieves adaptive merging and candidate mode construction of adjacent IMFs through the above processing. This method does not rely on fixed IMF indices, nor does it select IMFs based on a single metric. Instead, it uses a multi-metric approach—frequency, waveform, spectrum, and energy—to jointly judge and reconstruct adjacent IMFs that may belong to the same main oscillation structure, thereby improving the integrity and stability of the short-time composite digital signal mode representation.
[0099] The definitions of the core discrimination parameters for merging adjacent IMFs during the calculation process are shown in Table 1:
[0100] Table 1
[0101]
[0102] The definitions of the input signal and sampling parameters are shown in Table 2:
[0103] Table 2
[0104]
[0105] The definitions of the parameters for CEEMDAN decomposition and IMF feature calculation are shown in Table 3:
[0106] Table 3
[0107]
[0108] The Hilbert transform and the definition of instantaneous frequency variables are shown in Table 4:
[0109] Table 4
[0110]
[0111] The definitions of the parameters for calculating the spectrum and frequency characteristics are shown in Table 5:
[0112] Table 5
[0113]
[0114] The parameters for merging adjacent IMFs are defined as shown in Table 6:
[0115] Table 6
[0116]
[0117] The definitions of IMF grouping, merging, and iteration variables are shown in Table 7:
[0118] Table 7
[0119]
[0120] In some embodiments, the mode decomposition method is the CEEMDAN decomposition method, which extracts each mode by adding adaptive auxiliary noise step by step and updating the residuals. In the ensemble averaging process, positive and negative paired auxiliary noise is added so that the random noise cancels each other out during the ensemble averaging process.
[0121] In this embodiment, the core idea of the present invention does not absolutely rely on the CEEMDAN decomposition method. The main role of CEEMDAN in this invention is to decompose short-time, non-stationary composite signals into multiple modal components arranged according to frequency scales, providing processing objects for subsequent multi-index discrimination and selective merging between adjacent modes. Therefore, as long as other decomposition methods can obtain multiple modal components with clear frequency scales and arrangement relationships, the subsequent discrimination and merging ideas of this invention can still be applied in principle.
[0122] This invention chooses CEEMDAN primarily because it offers better decomposition stability compared to traditional EMD and EEMD. Traditional EMD is susceptible to local extrema and signal perturbations, and may produce mode aliasing. While EEMD reduces mode aliasing by repeatedly adding white noise and performing ensemble averaging, it may still suffer from residual auxiliary noise, inconsistent mode counts across different trials, and reconstruction errors. CEEMDAN extracts modes at each order by progressively adding adaptive auxiliary noise and updating the residuals. This approach reduces mode aliasing while maintaining decomposition completeness, lowers reconstruction errors, and improves consistency between repeated decomposition results. In the specific implementation of this invention, positive and negative paired auxiliary noise can be added to cancel out random noise during ensemble averaging, further reducing noise residue and improving the stability and repeatability of the decomposition results.
[0123] While VMD can adaptively extract multiple modes with different center frequencies, it typically requires manually setting parameters such as the number of modes before decomposition. When the preset number of modes is inappropriate, under-decomposition or over-decomposition may occur, making it difficult to guarantee reasonable and consistent modal results for different signal samples. Therefore, this invention employs CEEMDAN, not because the subsequent merging idea can only be based on CEEMDAN, but because CEEMDAN can provide relatively stable, complete, and easily comparable modal decomposition results in current applications, making it a superior front-end decomposition method.
[0124] From a technical perspective, the core of this invention is not the CEEMDAN algorithm itself, but rather the multi-feature comparison of adjacent modes obtained from the decomposition, the determination of whether they belong to similar oscillatory components based on joint criteria, and the selective merging and mode set update of adjacent modes that meet the conditions. Therefore, if CEEMDAN is simply replaced with EEMD, VMD, or other mode decomposition methods with the same function, while the subsequent discriminant index, joint determination logic, selective merging, and mode set update steps are substantially the same as those of this invention, from a technical standpoint, it constitutes an adoption of the core processing flow of this invention, rather than forming a completely different inventive concept.
[0125] In some embodiments, the mode decomposition method is an EMD or EEMD mode decomposition method.
[0126] In some embodiments, in step three, an analytical signal is constructed by performing a Hilbert transform on each IMF component to obtain the instantaneous amplitude and instantaneous phase, and then the instantaneous frequency is obtained; the dominant frequency is the frequency corresponding to the main energy peak of the mode, and the median instantaneous frequency is the median of the instantaneous frequencies.
[0127] In some embodiments, the merging conditions include: the relative difference of the main frequency is less than or equal to the main frequency difference threshold, the correlation coefficient of the time-domain waveform is greater than or equal to the correlation coefficient threshold of the time-domain waveform or the spectral similarity is greater than or equal to the spectral similarity threshold, the relative difference of the median instantaneous frequency is less than or equal to the median frequency difference threshold, and the combined energy ratio is greater than or equal to the energy ratio threshold.
[0128] In this embodiment, during the method design process, it was initially considered to use only a single frequency indicator, or to use fewer indicators such as "frequency difference plus waveform correlation" for judgment. Ultimately, four indicators were adopted: main frequency difference, median frequency difference, waveform correlation, and spectral similarity. This is mainly because these four indicators describe the similarity of adjacent IMFs from different perspectives and have obvious complementary effects.
[0129] The difference in dominant frequency reflects the main oscillation scale corresponding to the main energy peaks of the two IMFs, providing an intuitive assessment, but it is easily affected by local spectral peaks, noise, and multi-peak spectra. The difference in median frequency reflects the overall instantaneous frequency level of the IMF; compared to a single dominant frequency, it is more robust to local outliers and instantaneous fluctuations, and can be used to supplement dominant frequency determination. Waveform correlation reflects whether the waveform changes of the two IMFs are synchronized from a time-domain perspective, but it may be affected by phase shift, local amplitude changes, and window position. Spectral similarity, starting from the overall frequency domain structure, compares the energy distribution and frequency band composition of the two IMFs, avoiding erroneous merging based solely on a single representative frequency similarity, but it itself cannot reflect time-domain phase and waveform changes.
[0130] Therefore, using only one indicator can easily lead to erroneous merging due to the limitations of that indicator itself. For example, similar dominant frequencies do not necessarily mean consistent overall spectrum, and similar spectra do not necessarily mean synchronized time-domain waveforms. While using only two indicators can improve reliability, it may still miss information from other dimensions. The technical consideration of using four indicators in combination is to simultaneously constrain the dominant frequencies, overall frequency levels, time-domain waveform structures, and frequency-domain energy distributions of adjacent IMFs, reducing the risk of erroneously merging different oscillation components.
[0131] According to the currently adopted strict joint criteria, if any one of the four indicators fails to reach the corresponding threshold, the merger will not be executed. In other words, the four indicators are related by the logic of "simultaneous satisfaction," rather than by majority vote or weighted compensation.
[0132] The main consideration behind this design is to reduce the risk of erroneous merging. Four indicators constrain the main frequency, overall frequency level, time-domain waveform relationship, and frequency-domain structure of adjacent IMFs, respectively. If any one of these indicators is not met, it indicates that the two IMFs still have significant differences in at least one important dimension, and it cannot be fully confirmed that they belong to the same or similar oscillation components.
[0133] From a physical perspective, for example, if the main frequencies are similar but the spectral similarity is insufficient, it may indicate that the two IMFs only have similar main spectral peak positions, but differ in bandwidth, sidelobe structure, or energy distribution. If the frequency indicators and spectra are similar but the waveform correlation is insufficient, it may indicate that there are differences in phase relationship, local morphology, or temporal variation between the two. Directly merging them in this case may result in the incorrect combination of oscillatory components from different physical sources.
[0134] From a mathematical perspective, this criterion is equivalent to setting a joint acceptable region across four feature dimensions. Only when adjacent IMFs simultaneously fall within this region are they deemed mergingable. If any indicator exceeds the boundary, it means that the current similarity evidence is incomplete, thus adopting a conservative non-merging strategy.
[0135] This joint criterion can improve the reliability of the merger results and avoid erroneous mergers caused by a single indicator or a majority of indicators being close. For technical solutions that aim for stable and interpretable selective mergers, this conservative strategy is more suitable.
[0136] In some embodiments, step eight employs an iterative merging mechanism. When multiple consecutive IMF groups are pairwise similar, they are first merged sequentially. The merged new IMF group is then compared with the next adjacent IMF group. If all merging conditions are still met, the next merging is performed.
[0137] In this embodiment, when multiple consecutive IMFs exhibit adjacent similarity, the program first compares adjacent IMFs in frequency-scale order. If a pair of IMFs simultaneously meets the set joint criteria, the pair of IMFs is merged, and the original two IMFs are replaced with the merged new mode. Then, the dominant frequency, median frequency, waveform correlation, and spectral similarity of the new mode are recalculated, and it is compared with the new adjacent IMFs. If the merging conditions are still met, merging continues; if not, the current continuous merging stops, and other adjacent modes are evaluated until there are no adjacent combinations in the mode set that meet the conditions.
[0138] In principle, all originally pairwise similar IMFs should not be merged at once. This is because adjacent similarity relationships are not necessarily transitive. For example, if IMF1 is similar to IMF2, and IMF2 is similar to IMF3, it does not necessarily mean that IMF1 and IMF2, as a whole, will still satisfy all joint criteria with IMF3. Merging first and then recalculating features can avoid incorrectly merging modalities with different overall attributes due to local pairwise similarity.
[0139] Therefore, this invention employs an iterative merging mechanism, namely "adjacent determination—pairwise merging—set update—feature recalculation—continued determination," rather than merging all consecutive IMFs unconditionally at once. Only when the merged new mode and the next adjacent mode still satisfy all the criteria will multiple consecutive IMFs be finally merged into one mode.
[0140] In some embodiments, the short-time composite digital signal is a local reflection seismic wavelet signal, mechanical equipment vibration signal, voice signal, electrocardiogram signal, electroencephalogram signal, radar signal, sonar signal, or ultrasound detection signal from a seismic digital signal.
[0141] In this embodiment, the specific implementation is mainly applied to seismic digital signal processing, and the processing object is local seismic reflection signals or local seismic wavelets of the target layer. However, the core of this invention is to perform multi-feature joint determination and selective merging of adjacent IMFs obtained from CEEMDAN decomposition. This method does not rely on the physical parameters specific to seismic signals, and seismic digital signal processing is one of the main application scenarios.
[0142] Besides seismic digital signals, this invention can also be applied in principle to other digital signals with short-term, non-stationary, and multi-scale superposition characteristics, such as speech signals, electrocardiogram and electroencephalogram signals, mechanical vibration signals, radar or sonar signals, and ultrasonic detection signals. Their common characteristic is that after CEEMDAN decomposition, similar oscillatory components may be dispersed across multiple adjacent IMFs. This invention can selectively merge adjacent IMFs that meet certain conditions through multi-feature joint determination.
[0143] In some embodiments, the candidate mode set is further used for tasks such as dominant mode recognition, frequency feature extraction, signal classification, anomaly detection, or digital signal analysis.
[0144] The following is an algorithm example: To illustrate the specific processing procedure of the adaptive merging method for adjacent IMFs, a single-channel local seismic wavelet is selected as an example. This local wavelet contains 31 sampling points with a sampling interval of 2ms, corresponding to a sampling frequency of 500Hz. The original local seismic wavelet is as follows: Figure 2 As shown, its waveform consists of two main oscillation cycles, and there is a certain difference in the amplitude of the oscillations before and after.
[0145] First, the original local seismic wavelet Performing Ceemdan decomposition yields three IMF components. and and a final residual. ,Right now:
[0146]
[0147] CEEMDAN decomposition results and frequency characteristics of each IMF are as follows: Figure 3 As shown. The FFT dominant frequency of the original local wavelet is 31.25 Hz. The energies, average instantaneous frequencies, FFT dominant frequencies, and spectral centroids of the three IMFs are shown in Table 8.
[0148] Table 8
[0149]
[0150] After the CEEMDAN decomposition is completed, the three IMFs are initialized as independent IMF groups:
[0151]
[0152] Then, following the original IMF arrangement, adjacent IMF groups are merged from left to right. The merging criteria are:
[0153]
[0154] The program first compares IMF1 and IMF2. The relative difference in their dominant frequencies is 0, the relative difference in their median instantaneous frequencies is 0.13592, and their combined energy ratio is 0.91071, all meeting the corresponding threshold requirements. However, their absolute correlation coefficient is 0.67174, and their spectral similarity is 0.80636, both below the waveform or spectral similarity threshold. Therefore, IMF1 and IMF2 are not merged.
[0155] Then, IMF2 and IMF3 were compared. The relative difference in their dominant frequencies was 0, the relative difference in their median instantaneous frequencies was 0.10726, the absolute correlation coefficient was 0.89638, the spectral similarity was 0.93547, and the combined energy ratio was 0.99601. All of the above indicators satisfy Equation (4), therefore, IMF2 and IMF3 were determined to be similar adjacent modes and were merged and reconstructed. The specific discrimination results are shown in Table 9.
[0156] Table 9
[0157]
[0158] It should be noted that the relative differences in the main frequencies in Table 9 are calculated using an N-point FFT frequency grid within the merging program, while Figure 3 The FFT main frequency displayed is calculated by the plotting program using extended FFT points. Due to the different frequency resolutions of the two methods, the relative differences in main frequencies in the table should be based on the judgment results output by the merging program.
[0159] Based on the discrimination results, the index sets of IMF2 and IMF3 are merged into:
[0160]
[0161] Then, the corresponding IMF components are added together to obtain the merged candidate modes:
[0162]
[0163] Since IMF1 and IMF2 do not meet the merging criteria, IMF1 remains an independent candidate mode, i.e.:
[0164]
[0165] Therefore, the original three IMF components, after being merged from adjacent modes, form two candidate modes:
[0166]
[0167] Residual terms It does not participate in the merging. The signal reconstruction relationship after merging is as follows:
[0168]
[0169] The fused candidate modes and reconstruction results are as follows Figure 4 As shown.
[0170] The merging operation only changes the grouping and representation of the IMF, without altering the sum of each component and the residual term. Therefore, the overall reconstruction result of the signal remains consistent before and after merging. The relative reconstruction error in this example is:
[0171]
[0172] This demonstrates that the merging process did not disrupt the reconstruction consistency of the original local seismic wavelets. This example illustrates that the proposed method can distinguish between modes that are not suitable for merging and modes that can be considered as components of the same main oscillation, based on the frequency, waveform, spectrum, and energy characteristics of adjacent IMFs, and reconstruct adjacent IMFs that meet the conditions into candidate modes.
[0173] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.
Claims
1. An adaptive merging method for adjacent IMFs based on multi-index similarity discrimination, characterized in that: Includes the following steps: Step 1: Acquire the short-time composite digital signal to be processed; Step 2: Decompose the short-time composite digital signal using the mode decomposition method to obtain multiple IMF components; Step 3: Calculate the instantaneous frequency of each IMF component, and extract the dominant frequency, median instantaneous frequency, energy, waveform correlation and spectral characteristics of each IMF component; Step 4: Initialize IMF groups, with each IMF component forming a separate IMF group, and only perform subsequent merging judgments on adjacent IMF groups; Step 5: Perform multi-index similarity discrimination on adjacent IMF groups, calculate the relative difference of the dominant frequency, the relative difference of the median instantaneous frequency, the correlation coefficient of the time-domain waveform, the spectral similarity, and the combined energy ratio between adjacent modes corresponding to adjacent IMF groups, and determine whether adjacent IMF groups belong to the same main oscillation structure. Step 6: Determine whether adjacent modes simultaneously satisfy multiple merging conditions; If both conditions are met, then adjacent IMF groups corresponding to adjacent modes are regarded as similar split components of the same main oscillation structure and are merged. Step 7: Merge adjacent IMF groups corresponding to adjacent modes that meet the merging conditions into a new IMF group, merge the index sets of adjacent IMF groups, add the IMF components corresponding to adjacent IMF groups to reconstruct the merged mode, and update the IMF group set; Step 8: For the updated IMF group set, repeat the similarity judgment and merging reconstruction process of adjacent IMF groups until there are no adjacent IMF groups that meet the merging conditions. Finally, a candidate mode set that maintains the original IMF order and does not overlap is obtained and output.
2. The adaptive merging method for adjacent IMFs based on multi-index similarity discrimination according to claim 1, characterized in that: The mode decomposition method described is the CEEMDAN decomposition method, which extracts each mode by adding adaptive auxiliary noise at each order and updating the residuals. In the ensemble averaging process, positive and negative paired auxiliary noise is added so that the random noise cancels each other out during the ensemble averaging process.
3. The adaptive merging method for adjacent IMFs based on multi-index similarity discrimination according to claim 1, characterized in that: The mode decomposition method mentioned is the EMD or EEMD mode decomposition method.
4. The adaptive merging method for adjacent IMFs based on multi-index similarity discrimination according to claim 1, characterized in that: In step three, an analytical signal is constructed by performing a Hilbert transform on each IMF component to obtain the instantaneous amplitude and instantaneous phase, and then the instantaneous frequency is obtained; the dominant frequency is the frequency corresponding to the main energy peak of the mode, and the median instantaneous frequency is the median of the instantaneous frequencies.
5. The adaptive merging method for adjacent IMFs based on multi-index similarity discrimination according to claim 1, characterized in that: The merging conditions include: the relative difference of the main frequency is less than or equal to the main frequency difference threshold, the correlation coefficient of the time-domain waveform is greater than or equal to the correlation coefficient threshold of the time-domain waveform or the spectral similarity is greater than or equal to the spectral similarity threshold, the relative difference of the median instantaneous frequency is less than or equal to the median frequency difference threshold, and the combined energy ratio is greater than or equal to the energy ratio threshold.
6. The adaptive merging method for adjacent IMFs based on multi-index similarity discrimination according to claim 1, characterized in that: Step eight employs an iterative merging mechanism. When multiple consecutive IMF groups are pairwise similar, they are first merged sequentially. The merged new IMF group is then compared with the next adjacent IMF group. If all merging conditions are still met, the next merging is performed.
7. The adaptive merging method for adjacent IMFs based on multi-index similarity discrimination according to claim 1, characterized in that: The short-time composite digital signal mentioned above is a local reflection seismic wavelet signal, mechanical equipment vibration signal, voice signal, electrocardiogram signal, electroencephalogram signal, radar signal, sonar signal, or ultrasound detection signal from seismic digital signals.
8. The adaptive merging method for adjacent IMFs based on multi-index similarity discrimination according to any one of claims 1-7, characterized in that: The candidate mode set is further used for tasks such as dominant mode recognition, frequency feature extraction, signal classification, anomaly detection, or digital signal analysis.