Low-strain detection waveform analysis method integrating time-frequency feature extraction

Abstract

This invention relates to a low-strain detection waveform analysis method based on time-frequency feature extraction. The method involves segmenting the acquired low-strain waveform signal along the time axis, detecting the energy change rate and start time of each time segment, and filtering out signal segments significantly different from background noise to form a local feature signal set. The method analyzes the occurrence interval, duration, and energy change trend of each feature signal to identify related signals belonging to the same potential damage process, generating a time correlation chain. Based on the time correlation chain and multi-frequency features, the method performs a consistency analysis on the performance of each feature across different time-frequency dimensions, retaining signals that are stable in both time and frequency, and eliminating isolated anomalies that occasionally stand out in a single domain, thus obtaining a reliable feature set for low-strain detection. The method tracks the time and frequency changes of these reliable features, and based on the evolution of features at different stages, determines the occurrence and development of low-strain damage and outputs the detection results.

Description

Technical Field

[0001] This invention relates to a low-strain detection waveform analysis method, specifically a low-strain detection waveform analysis method that integrates time-frequency feature extraction. Background Technology

[0002] For example, Chinese patent CN119352583A, "A Method and System for Intelligent Low-Strain Detection and Analysis of Pile Foundations," currently employs a fusion time-frequency feature extraction method in low-strain detection waveform analysis, which still has several shortcomings and drawbacks. Specifically, these shortcomings manifest in the following ways: First, existing technologies primarily rely on comparing the design pile foundation parameters in a cloud database with data from sensing devices to determine whether a complex calculation process is triggered, thereby simplifying the processing complexity in some working conditions. While this approach helps improve efficiency, its core detection mechanism still focuses on mapping and comparing known design information, i.e., performing quality inference in scenarios with reference benchmarks. However, in actual engineering, pile foundations often face non-standardized designs or local structural changes, making it difficult for design parameters to accurately reflect the essential characteristics of the measured waveform, thus affecting the effectiveness of the system's judgment. Furthermore, this scheme emphasizes the consistency of multi-sensor results as a trigger condition for analysis simplification, but it does not provide detailed analysis methods for weak signal scenarios such as low amplitude, short period, and complex coupling, which can easily lead to misjudgment or missed judgment of weak precursor signals.

[0003] Secondly, in terms of joint time-frequency feature extraction, existing technologies tend to rely on image recognition of existing signals (such as waveform image size measurement) and vibration propagation model fitting to determine frequency levels, failing to establish a time-frequency dynamic structure perception framework oriented towards the actual signal evolution laws. However, under complex geological or tectonic conditions, the frequency component changes of signals typically exhibit nonlinear, non-stationary, and cross-scale behavior. Analysis based on single frequency extraction and propagation velocity models cannot accurately identify asynchronously occurring and co-evolving potential damage chains. This approach lacks in-depth modeling of the multi-band energy coupling characteristics in time series, especially in the trend analysis of high-frequency perturbations evolving to low frequencies, failing to form an effective identification mechanism and thus lacking sensitivity to frequency transfer responses induced by early microcracks. Furthermore, existing technologies do not systematically consider the enhancing effect of waveform structural features on anomaly identification. Although their solutions propose a low-strain detection and analysis model based on model training for result matching, they lack structural-level modeling and consistency verification mechanisms for the internal morphology of waveforms (such as peak-valley structure, continuity, and periodicity). Especially when the damage is still in its early stages, the waveform exhibits intermittent, latent disturbance characteristics under high noise background. If multi-dimensional joint indicators such as waveform principal component structure alignment, offset trend synergistic analysis, and spectral energy focusing dynamics are not introduced, relying solely on the comparison of frequency and pile length values ​​may result in pseudo-consistent results with structural mismatch but matching parameters, thereby misleading the system's judgment.

[0004] Furthermore, current methods neglect the crucial role of the temporal evolution of frequency response in assessing risk levels. Focusing solely on the difference between the design pile length and the response pile length ignores the immense value of feature coupling in the frequency-time-structure three-dimensional space for early identification, resulting in poor differentiation between non-evolving risks and continuously evolving damage. Finally, while emphasizing the automatic judgment characteristics of model training and matching processes, these methods lack proactive feature extraction and dynamic adaptation mechanisms in scenarios with complex data sources, uneven noise distribution, and significant signal-to-noise ratio variations. This makes them prone to overfitting known models and failing in new scenarios. Summary of the Invention

[0005] The purpose of this invention is to provide a low-strain detection waveform analysis method that integrates time-frequency feature extraction, thereby addressing some of the drawbacks and shortcomings pointed out in the background art.

[0006] The present invention addresses the aforementioned technical problems by employing the following technical solution: a low-strain detection waveform analysis method integrating time-frequency feature extraction, comprising: segmenting the acquired low-strain waveform signal on the time axis, detecting the energy change rate and start time of each time segment, filtering out signal segments that are significantly different from the background noise, and forming a local feature signal set; arranging the local feature signals in chronological order, analyzing the occurrence interval, duration, and energy change trend of each feature signal, identifying related signals belonging to the same potential damage process, and generating a time correlation chain; Local signals corresponding to the time correlation chain are extracted from multiple frequency bands, the correlation of energy changes between different frequency bands is analyzed, and low-amplitude signal features that appear synchronously or influence each other in multiple frequency bands are identified. Based on the time correlation chain and multi-frequency band features, the consistency of the performance of each feature under different time and frequency dimensions is analyzed, signals that are stable in both time and frequency are retained, and isolated anomalies that occasionally stand out in a single domain are eliminated to obtain a reliable feature set for low strain detection. The system tracks the changing trends of the reliable features in time and frequency, identifies the feature transfer and amplification process from high frequency to low frequency, and judges the occurrence and development of low strain damage and outputs the detection results based on the evolution law of features at different stages.

[0007] Furthermore, before the segmentation process, the original low-strain waveform signal is pre-scanned for amplitude change rate, and non-equal length segmentation intervals are set according to the trend of amplitude slope change within different segments; during the detection of energy change rate, short-period signals that conform to the combination of low persistence and high transition amplitude are preferentially identified and extracted as local abnormal subsequences; the cross-correlation coefficient between preceding and following segments is introduced as a noise elimination factor, and signals that are not continuous with the waveform of adjacent segments are retained as independent abnormal features.

[0008] Furthermore, after arranging the local feature signals in chronological order, a cross-segment causal relationship map is constructed by detecting the delayed response structure between local segments to identify potential damage activity chains that are discontinuous but have consistent behavior. In the case of multiple similar feature signals within the same time period, a signal overlap threshold is set. If the signal peak window overlap rate is higher than the set value, it is marked as a time-domain collaborative abnormal chain group and assigned a high-risk level.

[0009] Furthermore, during the multi-band extraction process, high-frequency abrupt change points of the signal in the corresponding time correlation chain are retrieved and used as the initial frequency index; the energy correlation between different frequency bands includes determining whether they constitute a frequency response synergy based on amplitude statistics and the degree of consistency of periodic waveform patterns.

[0010] Furthermore, when analyzing the consistency of each characteristic signal across different time-frequency dimensions, a feature expression sparsity index is constructed to preferentially retain signal groups that appear in different forms across multiple frequency bands but have consistent structural trends. For signals that exhibit short-term instability but have consistent overall trends across multiple scales, a time-frequency dynamic compensation mechanism is used to correct and incorporate them into the reliable feature set.

[0011] Furthermore, when tracking the temporal evolution trend of the reliable features, the increasing frequency of detection is used as a non-amplitude criterion for early damage occurrence, for strain precursor identification; the feature transfer process from high frequency to low frequency is marked by the downward shift of the time series center position, and when multiple features show a shift trend at the same time, the damage evolution identification mechanism is triggered; the determination result of low strain damage is based on the phased intensity comparison of the signal distribution in the reliable feature set. If the early signal group is stronger than the later group as a whole, the system marks it as a non-continuously evolving risk to distinguish transient strain behavior; In continuously monitored strain signals, if multiple high-frequency features show a continuous trend of shifting to lower frequencies over time, it can be regarded as one of the signs of early damage evolution. This trend is achieved by observing the change in the center of gravity of the time series. The increasing frequency pattern of feature occurrence is used as a criterion for early non-steady-state disturbances, which is suitable for the identification of precursors in environments with small disturbances or low signal-to-noise ratios. A function is introduced to express the trend of concentration change and the centroid of frequency of the characteristic signal: in: For representative moments The dynamic evolution response function of the reliable characteristics; The total number of features involved in the identification; For the first Each feature at time The normalized frequency value; The interference regulation factor controls the intensity of characteristic time-dependent diffusion suppression. The characteristic peak diffusion suppression rate constant; Features The location of the maximum response time is used to locate the principal components of the features; To enhance the perception of low-amplitude fluctuations, higher-order variations are introduced to adjust the parameters for nonlinear response. when A sustained decline occurred over a period of time, exhibiting multiple characteristics. The backward synchronization trend triggers the damage evolution identification mechanism in the system; if the early period (e.g.) )of The overall mean was significantly higher than in the later period ( If the risk is not continuously evolving, it is considered a transient strain behavior rather than a continuously evolving damage; the overall system uses nonlinear trend judgment and signal distribution change criterion to form a multi-layer identification mechanism; function The derivation process includes: Firstly, considering that the early characteristics of low-strain damage often exhibit a gradual shift from high to low frequencies, it is necessary to construct a response function that can comprehensively describe the dynamics of multiple feature frequency distributions. Let the normalized frequency of each feature be... The initial form can then be written as This format only reflects the average level of the overall frequency and cannot reflect the clustering and lag of features over time. To introduce time evolution sensitivity, the influence of each feature is weighted, and the weights are designed as follows: The exponent term Used to characterize features at center time Local clustering in the vicinity, parameters Controlling the convergence rate of this aggregation, and As a regulatory factor, it determines the contribution of this local inhibition to the overall trend; In this way, when the main response at a certain characteristic frequency deviates... At longer distances, its contribution to the overall response function is weakened, ensuring the model's high sensitivity to early significant shifts. Secondly, to enhance the ability to sense low-amplitude signal disturbances and avoid distortion of traditional linear weighting under transient fluctuations, a nonlinear higher-order oscillation factor is introduced into the weighting frequency term. This term controls the steepness of the periodic response through a cubic time offset, amplifying minute frequency jumps in the function value; where This determines the strength of nonlinear amplification. When features shift synchronously in time, the nonlinear terms of different features will resonate synergistically, leading to... A sudden, rapid downward shift or fluctuation occurs; ultimately, by coupling the aforementioned time-sensitive weights with the nonlinear perturbation response to the frequency distribution, the formula is obtained. This formula can comprehensively characterize the three-dimensional evolution of early damage features: frequency convergence (through...). It has the characteristics of time offset (through weighting terms) and transient enhancement (through higher-order nonlinear factors), so it is more sensitive to the stage changes in the distribution of precursor signals than the traditional amplitude criteria, and is especially suitable for the early identification and risk classification of low-strain damage.

[0012] Furthermore, the detection of the increasing frequency pattern includes: constructing a time series density map for each reliable feature in different detection periods; if the density center continuously shifts forward in time, it is determined to be an active precursor feature; the criterion for increasing frequency also includes statistical analysis of the growth acceleration between frequency increases; when the growth rate increases period by period, it is marked as an accelerated strain precursor.

[0013] Furthermore, during the process of detecting the downward shift of the time series center of the feature transfer, a signal morphology structure alignment condition is added. If the feature waveforms before and after the transfer maintain the same main structure, the confidence level of the transfer trend is increased by one level. When multiple features simultaneously exhibit a shift trend, a shift synchronization coefficient matrix within the time band is established. If the main diagonal elements in the matrix have a positive continuous slope, it is determined that the systemic damage evolution process has been initiated.

[0014] Furthermore, the structural alignment conditions include using the number of peaks and valleys, relative positions, and durations of the waveforms before and after the transfer as structural feature comparison factors. Only when all three indicators are consistent is it determined that the main structure is consistent. When additional structural variations are detected in the waveform after the transfer but the overall center shifts downward, it is determined whether it is a false consistency caused by external disturbance by comparing the overlapping area weights of the main components of the waveform.

[0015] Furthermore, in the determination of the offset trend of multiple features, if the offset direction of any feature is opposite to that of most features, then the feature is temporarily removed from the calculation of the synchronization coefficient matrix. In the synchronization coefficient matrix, in addition to the main diagonal, the positive offset cumulative value of the upper triangular region is also analyzed. If its trend is consistent with the main diagonal, then the confirmation level of the systemic damage evolution is strengthened.

[0016] The beneficial effects of this invention: The low-strain detection waveform analysis method proposed in this invention, which integrates time-frequency feature extraction, significantly improves the sensitivity and discrimination accuracy of weak anomalous signals by processing the low-strain waveform signal into non-equal-length segments on the time axis and combining multi-dimensional criteria such as energy change rate, frequency synchronization, and waveform structure consistency. This method overcomes the limitations of traditional methods that rely on a single amplitude threshold or frequency domain energy determination, and can accurately screen out local anomalous feature signals and construct time correlation chains in high-noise interference and non-continuous strain scenarios. It is particularly suitable for complex detection environments where early damage signals exhibit short-period, low-amplitude, and discontinuous characteristics.

[0017] By integrating energy correlation analysis and structural consistency tracking mechanisms across multiple sub-bands in the frequency domain, this invention enables dynamic identification of high-frequency to low-frequency feature transfer processes. Furthermore, by combining multi-source evolution indicators such as time series center shift, offset synchronization coefficient matrix, and frequency increment patterns, it effectively determines damage development trends and their stage-specific risk levels. Compared to existing technologies, this method exhibits stronger robustness and diagnostic foresight in the field of low-strain detection, particularly demonstrating significant advantages in identifying potential hidden defects, assessing non-continuous evolutionary risks, and distinguishing precursory strain behaviors. This provides more practical technical support for structural health monitoring and early warning. Attached Figure Description

[0018] Figure 1 This is the main flowchart of the low-strain detection method that integrates time-frequency feature extraction according to the present invention.

[0019] Figure 2 This is a simplified functional relationship diagram for low-strain detection waveform analysis in this invention.

[0020] Figure 3 This is a flowchart illustrating the evolution trend analysis of low-strain damage characteristics in this invention.

[0021] Figure 4 This is a schematic diagram of the low-strain anomaly detection and multi-frequency collaborative analysis process in Embodiment 1 of the present invention.

[0022] Figure 5 This is a flowchart of the time-frequency evolution of low-strain characteristics of pile foundation and the determination of systemic damage in Embodiment 2 of the present invention. Detailed Implementation

[0023] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0024] Combined with appendix Figure 1This invention integrates a low-strain detection waveform analysis method based on time-frequency feature extraction. It acquires the original waveform signal generated by the structural response using a low-strain detection device. This signal contains background noise and possible strain-induced reflection signals. To improve the ability to identify weak anomalies, the original signal is segmented along the time axis. The segmentation method can be based on the local amplitude change rate of the waveform, using non-uniform length divisions. Locations with significant energy abrupt changes or sudden slope increases are preferentially set as segment boundaries, thus obtaining multiple time segments. For each time segment, the energy change rate and the starting time of the change are calculated. Segments with change rates exceeding the background statistical fluctuation threshold are extracted. Simultaneously, the cross-correlation between consecutive segments is used as an auxiliary condition to exclude normal responses with strong continuity, thereby retaining... Segments exhibiting significant differences in temporal distribution, waveform morphology, or energy abrupt changes are designated as local feature signals. These local feature signals are arranged according to their temporal order within the original signal to construct an initial feature sequence. Furthermore, the time intervals, durations, and relative energy trends between each feature are calculated. Based on this, features exhibiting regularity in intervals, consistent trends, and energy correlations are categorized and identified, identifying several feature segments belonging to the same potential damage induction process. By establishing their sequential relationships and interaction paths, a temporal correlation chain is formed. This temporal correlation chain serves as the foundational data structure for subsequent time-frequency joint analysis and damage evolution assessment, thereby providing more accurate and robust analytical support for anomaly identification, feature tracking, and early structural damage warning in low-strain signals.

[0025] After constructing the time correlation chain based on time domain segmentation and energy screening, multi-scale feature extraction and correlation analysis are further carried out in the frequency domain. Specifically, for the time segments corresponding to each local signal in the identified time correlation chain, its frequency domain components are extracted sequentially in multiple frequency bands. These multiple frequency bands can be preset equally spaced sub-bands or non-uniform frequency bands dynamically adjusted according to the signal spectrum structure to capture the weak response of low-strain reflection signals in different frequency ranges. Based on this, the energy change trend of local signals in each frequency band is analyzed, and indicators such as energy correlation coefficient, phase delay, and spectral crossover between each frequency band are calculated to determine whether there are low-amplitude signal features that occur synchronously or influence each other in multiple frequency bands. If certain multi-frequency synchronization or energy coupling characteristics are met, they are marked as frequency domain cooperative signal features. Furthermore, based on the aforementioned time correlation chain and the extracted multi-frequency band signal group, a consistency analysis is performed on the performance of each signal in the time and frequency dimensions, including but not limited to its energy. By considering stability, structural similarity, and continuity of response patterns, signal features exhibiting persistence, trend consistency, and noise robustness across both time and frequency dimensions are retained, while isolated anomalies that only occasionally stand out in one dimension are eliminated, thus constructing a reliable feature set for low-strain detection. Subsequently, the evolution trend of this reliable feature set is tracked, focusing on identifying density changes on the time axis and the evolution trend of the center frequency on the frequency axis. When a characteristic frequency is detected to shift orderly from the high-frequency band to the low-frequency band, with gradually increasing energy, this trend is used as a marker of the damage evolving from the initial local perturbation to the macroscopic evolution stage. Furthermore, by analyzing the evolution paths and differences in manifestations of features at each stage, a staged map of low-strain damage is constructed to determine whether it belongs to a reversible perturbation type, a continuously developing type, or a critical transition type damage process. Finally, the detection results, including risk level, evolution status, and damage trend direction, are output to achieve accurate interpretation of the structural response signal under low-strain excitation and interpretable identification of early anomalies.

[0026] Combined with appendix Figure 2To address the characteristics of target signals in low-strain detection, which typically exhibit short periods, weak amplitudes, high abrupt changes, and are often submerged by background noise, a waveform analysis method based on fused time-frequency feature extraction is proposed. Specifically, before segmenting the original low-strain waveform signal, a pre-scanning process of the amplitude change rate is performed on the entire original waveform. This step involves calculating the amplitude slope and analyzing its changing trend by sliding along the entire time axis to identify potential fluctuation characteristic change regions within the signal. Instead of using equal-length segmentation, a dynamic non-equal-length segmentation interval is set based on the non-uniformity of the amplitude slope change, especially prioritizing segment boundaries at slope abrupt changes to form a structurally sensitive preliminary segmentation. Next, in the energy change rate detection process, a dual-criteria mechanism is introduced: for each time segment, not only is its local energy change rate calculated, but also... Duration characteristics are prioritized to identify signal segments with short durations but significant amplitude transitions. These segments are identified as short-period anomalous signals with a combination of low duration and high amplitude transitions, and are extracted as local anomalous subsequences for subsequent analysis. To further improve the purity of anomalous signal extraction, the cross-correlation coefficient between preceding and following segments is introduced as a noise exclusion factor. By calculating the correlation between the current segment and its preceding and following adjacent segments in waveform structure, if significant waveform breaks or morphological discontinuities are found between the current segment and its adjacent segments (i.e., the cross-correlation coefficient is below a set threshold), the segment is identified as an independent anomalous response signal unrelated to environmental fluctuations and is marked as potential damage characterization information with independent characteristics. Conversely, if the current segment shows a continuous trend with the preceding and following signals, it is judged to be a normal structural response and is excluded.

[0027] After completing the time-domain segmentation and extraction of local feature signals from the low-strain waveform, the local feature signals are further arranged according to their natural order on the time axis. Based on this order, the delay relationship between the response structures of the segments is identified. Cross-correlation analysis and signal peak position difference calculation are performed on each pair of adjacent or non-adjacent local feature segments to determine whether there is a traceable time delay structure between their responses. If the delay structure exhibits relatively stable time-shift characteristics, accompanied by continuity in energy trend direction or waveform shape, a directional connection relationship between segments is established. Based on this, a cross-segment causal relationship map is constructed. This map uses nodes to represent local feature signals and edges to represent delay coupling relationships with potential causal connections. It can identify anomalous signals that are discontinuous in time but highly consistent in physical response behavior. This method extracts potential damage activity chains whose temporal sequence is elongated due to structural defect propagation or wave velocity variations, but whose behavior remains coherent. Furthermore, to avoid fragment redundancy caused by the overlap of multiple spatially adjacent or signal sources, the analysis also considers the evaluation of the peak time window overlap if multiple similar local characteristic signals exist within the same time period. A sliding time window is set, and the overlap rate of multiple signal peaks within this window is statistically analyzed. If the overlap rate is higher than a preset threshold, it indicates the existence of a coordinated response phenomenon within this time period, i.e., multiple anomalous fragments are triggered simultaneously within a similar time frame, exhibiting significant structural resonance or systemic disturbance characteristics. Such signal groups are labeled as time-domain coordinated anomalous chain groups and assigned a higher risk level than ordinary anomalous chains to reflect their higher damage evolution potential and early warning importance.

[0028] When extending the frequency domain features of the established time-domain correlation chain, spectral analysis is performed on each local signal segment within the correlation chain, with particular attention paid to high-frequency abrupt changes exhibiting significant local variations in the frequency domain. These abrupt changes can be obtained by calculating the first derivative of the signal spectrum or the energy density gradient, and their location typically corresponds to the instantaneous high-frequency response excited by local strain perturbations. These high-frequency abrupt changes are used as initial frequency indices to define the starting point for feature extraction in each frequency band. Based on this, the analysis is progressively extended upwards and downwards to construct a multi-band analysis range, ensuring coverage of the full-cycle features of the potential frequency response chain. Subsequently, during this multi-band extraction process, the signal energy in each frequency band is quantified. Statistical analysis is used to form a cross-frequency band amplitude distribution sequence, and energy correlation indicators such as Pearson correlation coefficient and energy synchronicity ratio are calculated to assess the amplitude coordination between different frequency bands. In addition to energy indicators, consistency analysis of periodic waveform patterns is further introduced. By comparing the waveform period, symmetry, and main structural repetition of each frequency band, the degree of overlap in waveform morphology and whether the evolution trend direction is consistent are quantified. If local signal groups with similar periodic characteristics, similar response patterns and synchronous energy fluctuations appear simultaneously in multiple frequency bands, the group of signals is identified as a frequency response coordination body, which is considered to reflect the multi-scale manifestation of the same damage behavior in the frequency domain.

[0029] In the process of consistency analysis of the performance of various characteristic signals in different time-frequency dimensions, in order to enhance the ability to identify atypical but trend-stable signals, a feature expression sparsity index is constructed. This index is calculated by statistically analyzing the number of times the same signal appears in different frequency bands, the dispersion of its performance pattern, and the similarity of its structural trends. Essentially, it is used to measure the signal's expression coverage and morphological consistency in multiple frequency dimensions. When a signal exhibits morphological changes or local instability in some frequency bands, if its overall structural trend remains consistent and it repeatedly appears in multiple frequency bands, it indicates that it has cross-frequency stable evolutionary characteristics. Therefore, guided by this sparsity index, those signals that appear in multiple frequency bands are preferentially retained. Although the signals appear in different forms, they have a consistent overall structural trend, thus avoiding the misremoval of effective features due to differences in surface morphology. Furthermore, for signals that exhibit short-term instability in a specific time window or frequency scale, if their overall trend remains consistent with other stable signals in a wider scale space, they are identified as quasi-stable features affected by transient interference. To avoid misclassifying such signals as anomalies or noise, the system introduces a time-frequency dynamic compensation mechanism. That is, by comparing the deviation between the morphological reconstruction value of the signal in adjacent frequency bands and time periods and the average evolution trajectory, if the deviation is within an acceptable range, the unstable segment is morphologically compensated and corrected, and the corrected signal is re-included in the reliable feature set.

[0030] Combined with appendix Figure 3To enhance the identification of low-amplitude, non-steady-state damage precursors when tracking the temporal evolution trend of reliable features, an analysis mechanism based on the increasing frequency pattern of feature occurrence is introduced. This mechanism, as a non-amplitude criterion, is effectively used for the identification of early strain precursors, especially suitable for complex environments where signal amplitude changes are not obvious or noise interference is strong. Specifically, in the continuously monitored low-strain waveform sequence, by statistically analyzing the time-frequency distribution trajectory of multiple features, if multiple high-frequency feature points are observed to continuously shift towards lower frequencies over time, and their distribution centers gradually move backward on the time axis, it is determined to be a trend of high-frequency features clustering towards lower frequencies. This trend is marked by the downward shift of the time series center position and serves as a prerequisite for potential damage evolution behavior. When multiple features simultaneously exhibit a significant frequency shift trend, the system further constructs a frequency centroid evolution function. This serves as the criterion for determining whether a damage evolution marker mechanism is triggered. The function is shown below: in, Indicates at time The dynamic response strength of each reliable feature; The total number of features being counted; For the first Each feature at time The normalized frequency value; This is a disturbance regulation factor used to control the intensity of the suppression of the overall trend by features far from the principal component response time; The characteristic peak diffusion suppression rate constant is used to adjust the sensitivity of the weights to time shift. Features Location of maximum response time; This is a nonlinear response adjustment parameter, which enhances the response capability to weak signal disturbances through a cubic nonlinear term; through this function, when... The main response time exhibits a sustained decline over a certain period and multiple characteristics. Moving backward, the system determines that the damage evolution process has been activated; furthermore, to distinguish between transient strain behavior and continuous evolutionary damage, this method compares the signal energy intensity at different stages. If in the early time period... Inside The average value was higher than that in the later period. The level of [a certain level] is then marked as a non-evolving risk; the construction process of the function reflects a multi-factor coupling approach, firstly based on [a certain level]. A framework for the overall frequency mean is obtained, but this framework cannot characterize the time shift and feature density distribution characteristics. Therefore, time-sensitive weights are introduced. The main response contribution of each feature is modulated; secondly, to enhance the model's response sensitivity to short-term disturbances, a nonlinear oscillation factor is superimposed on the weighted frequency term. By controlling the steepness of the oscillation with a cube power, a synergistic resonance effect is generated when multiple features are time-shifted, thereby enhancing the identification of potential damage feature chains; the final combination yields a complete... The expression, which can simultaneously describe frequency convergence, time offset and transient enhancement, significantly improves the system's accuracy in identifying early damage features in low signal-to-noise ratio backgrounds. It also constructs a multi-level judgment mechanism through evolution trend judgment and feature energy comparison to achieve highly reliable detection and risk level classification of low strain damage.

[0031] To improve the system's sensitivity to low-strain damage precursors during the identification of the temporal evolution trend of reliable features, a detection mechanism based on increasing frequency patterns is introduced. This detection includes two complementary criteria: First, for each signal identified as a reliable feature, a time-series density map is constructed over multiple consecutive detection periods. Specifically, the times when the signal appears in different detection windows are statistically analyzed as time distribution points, and the center position of its density distribution in each period is calculated. If the density center shows a stable forward (i.e., earlier) shift trend as the detection time window progresses, it indicates that the feature has [reliability / reliability] during its evolution. The system identifies the characteristics of gradually activating and responding in advance as "proactive precursor features," which indicate that the damage activity has entered an activated state but has not yet formed a significant amplitude disturbance. Secondly, based on the above, the system further statistically analyzes the acceleration information of frequency growth. Specifically, it tracks the maximum frequency of reliable features in each cycle, calculates the frequency increment during each cycle, and obtains the growth trend of these increment sequences. If the increment value itself shows a continuous increase, that is, it shows a gradual increase in the frequency growth rate, it indicates that the strain process has signs of accelerated evolution, and the system identifies it as an "accelerated strain precursor."

[0032] In detecting the downward shift of the time series center position during feature transfer, to improve the reliability of transfer determination and reduce misjudgments caused by occasional fluctuations, the system introduces an auxiliary criterion of signal morphological structure alignment. That is, while determining that the feature waveform undergoes a center shift in the time dimension, a similarity comparison is performed on the waveform structure before and after the transfer. This comparison is mainly based on the matching degree of the number of peaks and valleys, the relative position ratio, and the duration of the waveform. If all three structural features remain consistent within the set similarity tolerance range, the transfer behavior is considered to have structural continuity and behavioral consistency. Based on this, the confidence level of the original downward shift trend of the time center is increased by one level to enhance the recognition accuracy of actual damage processes rather than noise fluctuations. Furthermore, in When multiple reliable features simultaneously exhibit a shift trend, in order to assess whether it belongs to systemic damage evolution rather than isolated fluctuations, the system constructs a time-band shift synchronization coefficient matrix based on the feature time shift. Each element of this matrix represents the degree of shift correlation between two features within a certain detection window. The main diagonal elements represent the unidirectional shift slope of each feature as the time window progresses. When the value of the diagonal element is observed to show a continuous upward trend in the time series, i.e., a positive continuous slope pattern, it indicates that the shift direction and rate of multiple features are coordinated and the overall trend is consistent. This phenomenon is marked by the system as the "systemic damage evolution initiation" state, and the system will activate the subsequent high-risk processing mechanism and output early warning information.

[0033] Structural alignment conditions are an important constraint mechanism used to enhance the reliability of feature transfer trend judgment. They rigorously determine the consistency of waveform morphology before and after transfer, specifically including three structural feature comparison factors: First, the number of peaks and valleys, which counts the number of local extreme points (including peaks and valleys) in the same time window for both before and after transfer, serving as a basic indicator of waveform structural complexity; Second, relative position, which normalizes the positions of each peak and valley point to the corresponding waveform length ratio for alignment comparison, judging the stability of its spatial structure arrangement; Third, duration, which compares the duration of the two waveform segments on the overall time scale, ensuring that the transfer process does not introduce significant temporal stretching or compression. When all three indicators meet the set conditions... When the matching threshold (e.g., ±5% error range) is met, the system recognizes that the waveforms before and after the transfer have a consistent main structure, further enhancing the credibility of the transfer trend as a true feature evolution. In addition, if new peak-valley structures or local distortions are detected in the waveform after the transfer during actual monitoring, but the overall trend still shows a stable downward shift of the center position, the system will further extract the main component region of the waveform and calculate the signal energy weight ratio of the overlapping region of the main components. If the proportion of the overlapping part is higher than the set threshold (e.g., 80%), it is judged that the structural change is a non-primary behavior mode, that is, a pseudo-consistency phenomenon caused by environmental disturbances, measurement errors, etc. At this time, the system will reduce the weight of this feature in the final damage judgment or delay its entry into the damage chain analysis path.

[0034] To determine the offset trend of multiple reliable feature signals in the time dimension, the system first extracts the offset direction of the center time point of each feature within the continuous detection period, constructing an initial offset vector set. The system then forms the main offset direction benchmark by statistically analyzing the offset directions of the majority of features (e.g., more than 70% of features show a backward offset). When the offset direction of a feature is detected to be opposite to the main direction, for example, if the feature shows a significant advance offset or retreat trend within the same period, the system temporarily removes that feature from the subsequent synchronization coefficient matrix calculation to avoid the abnormal fluctuations of a few features affecting the overall evolution trend. To determine if interference is caused, when constructing the synchronization coefficient matrix within the time band, not only is the correlation of the degree of offset between each feature within the corresponding time window analyzed as the main diagonal element, but the cumulative value of all positive offset relationships in the upper triangular region of the matrix is ​​further extracted to characterize the level of synergy of synchronous offsets between multiple features. If it is found that the cumulative value shows a monotonically increasing trend in the same direction as the main diagonal over time, the system judges this as a strong consistent behavior of multiple features forming a collective evolutionary offset over time, thereby raising the confirmation level of the systemic damage evolution process by one level and marking it as a high-confidence evolutionary state.

[0035] Example 1: Combined with appendix Figure 4 In this embodiment, in a certain underground structure health monitoring project, a strain waveform acquisition device was used to continuously monitor the concrete pile foundation at a sampling frequency of 2000Hz, obtaining a 60-second low-strain raw signal data. First, the system pre-scanned the amplitude change rate of the raw waveform, calculated the average slope within each 1-second window, and performed non-equal-length segmentation processing on the signal according to its change trend. Taking the 17-18 second interval as an example, its average amplitude slope increased to 0.035 (unit normalized), which is more than 300% higher than the previous segment (16-17 seconds). The system set this interval as an independent analysis segment. Then, the energy change rate detection stage was entered. In this segment, the system identified multiple short-period high-transition signals with a duration of less than 0.3 seconds and a peak increase greater than 1.5 times the background energy. For example, the local anomalous subsequence located at 17.24 seconds had an energy mutation value of 2.6 times the background noise baseline and a duration of only 0.12 seconds. The system extracted it as a local anomalous feature and saved it.

[0036] After completing the analysis of all segments and extracting a total of 32 local anomalous subsequences, the system arranged them in chronological order and further detected the delayed response relationship between each feature segment. Within 0.9 seconds after the feature at 17.24 seconds, the system detected a second morphologically similar anomalous segment at 18.13 seconds. Through cross-correlation analysis, the delayed response of the two segments was 0.89 seconds, and the cross-correlation peak reached 0.76, forming a preliminary causal relationship pair. The system extended the entire sequence based on this relationship, constructing a potential damage activity chain containing 7 discontinuous anomalous segments between 22 and 29 seconds. To verify the anomalous clustering of this chain, the system statistically analyzed the peak window overlap rate of similar feature signals within the same time period. It found that the peak window overlap rate of 4 segments exceeded 0.65, exceeding the set threshold of 0.6. The system marked these as a temporal domain coordinated anomalous chain group and assigned a high-risk level based on the chain group density and response consistency.

[0037] After the system constructs a time correlation chain starting from 17.24 seconds based on time segment analysis, it enters the multi-band feature extraction stage. The system searches for high-frequency abrupt changes in this time correlation chain. Using a Short-Time Fourier Transform (STFT) window length of 256 and a step size of 32, it performs a spectral scan on the time period from 17.00 seconds to 19.00 seconds, identifying a momentary frequency rise abrupt change near 320Hz at 17.24 seconds. This abrupt change has an amplitude of 12dB and a duration of only 80ms. This abrupt change point is marked as the initial frequency index and used as the anchor point for subsequent multi-band analysis. Subsequently, in terms of frequency band division, the system divided the frequency range of 0–1000Hz into five sub-bands (0–200Hz, 200–400Hz, 400–600Hz, 600–800Hz, and 800–1000Hz). The energy distribution within the time windows corresponding to the aforementioned abrupt change points was analyzed, and the normalized mean amplitude of the signal in each band was calculated. It was found that significant energy increases occurred in the 400–600Hz and 200–400Hz bands between 17.24 and 17.32 seconds. The average amplitudes are 0.68 and 0.54, respectively, while the energy performance of other frequency bands is only below 0.12. The system compares and analyzes the fluctuation trends between these two frequency bands, and further introduces wavelet packet decomposition to obtain the main mode components of the corresponding periodic signals in each frequency band. By comparing the phase mode and the trend of the main frequency change through a sliding periodic window, it is found that the average phase difference between the main modes of the 200–400Hz and 400–600Hz frequency band signals is less than 20°, and the periodic deviation is less than 15%. Based on this, it is determined that the two form a frequency response synergy.

[0038] Entering the consistency analysis phase across different time-frequency dimensions, the system performs structural normalization on all frequency band features corresponding to time-related chains and introduces a feature expression sparsity index: in For signal feature vectors, To prevent the use of tiny positive numbers with a denominator of zero, comparisons revealed that the sparsity of the signal near 17.24 seconds in the 200–600 Hz frequency band was between 1.12 and 1.35, while other frequency bands showed greater fluctuations, reaching a maximum of 2.74, indicating a more concentrated expression of the main frequency band features. Combined with similarity morphology analysis, the system further evaluated the temporal consistency of these signals. It was found that although the 400–600 Hz band experienced local instability at 17.28 seconds, with an energy drop of up to 30%, this band quickly recovered at 17.31 seconds, forming a synchronous trend rebound with the other frequency bands. This phenomenon was identified by the system as a correctable feature of "short-term instability but consistent trend." The system applied a time-frequency dynamic compensation mechanism to interpolate and smoothly reconstruct the energy characteristics of the short-term instability segment, and after refitting, it was included in the reliable feature set. Ultimately, a total of 7 sets of multi-frequency consistent features were retained within this time period, serving as the basis for subsequent damage evolution identification.

[0039] Example 2: Combined with appendix Figure 5 In this embodiment, during a pile foundation structure health monitoring project, the raw low-strain signals collected by the sensors underwent preliminary preprocessing, resulting in the extraction of four sets of reliable feature signals, each representing the low-strain propagation response along different spatial paths. These features were observed during the monitoring period. The normalized frequency variations on are set as follows: , , , , These frequencies represent the gradual downward shift of the signal's main energy distribution center, simulating the evolution of the structure from initial high-frequency interference to low-frequency strain. The maximum response time for each corresponding feature is set to... The second reflects the response latency of this type of response. This is expressed by the formula: in , , The dynamic evolution function within the entire monitoring range can be calculated. As can be seen from the diagram, exist The continuous downward trend within the interval indicates that the frequency centroids of multiple characteristic signals are synchronously shifting to lower frequencies, and multiple characteristic response center times are appearing. The system will trigger the damage evolution recognition mechanism when the damage shifts backward.

[0040] To further assess whether it belongs to the non-persistent evolutionary risk category, the system... exist and Comparing two means, for example: Clearly, the overall average value of the early signal is significantly higher than that of the later stage, indicating that although the system shows signs of evolution, the signal subsequently decays, which is consistent with the characteristics of transient response. Therefore, the system will ultimately be judged as a risk type that does not continue to evolve.

[0041] The monitoring time range is Technicians further analyzed the four previously identified reliable feature signals to verify the presence of proactive precursors or accelerated strain evolution risk trends. In the actual signal processing, the system first divided each feature into five detection periods (2 seconds per period) and constructed a time-series density map of the frequency peak occurrence times within each period. For example, for the feature... Statistical analysis of the periodic dominant frequency distribution yielded the occurrence times of its dominant energy frequency in each period. By estimating the density center of this set of time values ​​(using a sliding window + Gaussian kernel density estimation), we can calculate its forward shift trend and find that its density centers are respectively The overall trend shows a forward shift, and the system marks this feature as an active precursor signal.

[0042] Next, we analyze whether it constitutes an acceleration precursor. The system further extracts the peak frequency increase of each cycle. For features The frequency changes are set sequentially as follows: Then its frequency increase is The frequency increase acceleration can be obtained as a second-order difference. The growth rate is constant and therefore marked as an accelerated strain precursor. When two or more characteristics simultaneously satisfy this type of accelerated growth characteristic, the system initiates further structural alignment verification.

[0043] During the structural alignment stage, the system confirms the morphological continuity of the signal by analyzing whether the number, relative position, and duration of peaks and valleys of the characteristic waveforms before and after the transfer are consistent. For example, for A comparison of the two waveform segments revealed that each segment had three peaks and valleys, with a duration of 0.6 seconds. The alignment rate of the main waveform was as high as 93%, thus satisfying the condition of consistency of the main structure and increasing the credibility level.

[0044] Finally, for all features exhibiting time-frequency shifts, the system constructs an intra-timeband offset synchronization coefficient matrix. , where matrix elements Representation of features and characteristics The synchronization of time centroids (e.g., measured by Spearman rank correlation or Pearson coefficient), for example, the 5 elements on the main diagonal of a matrix are... If the slope shows a continuous positive trend, the system is determined to be initiating systemic damage evolution and enters a high-risk warning state.

[0045] The system has identified a set of reliable characteristic signals suspected to be in the early stages of damage evolution. Among them Internally, multiple frequency features exhibit a downward shift in the spectral center. To confirm the authenticity of this evolutionary trend and eliminate the influence of occasional disturbances, the system is validated through examples based on structural alignment conditions and the synchronicity criterion of the offset trend.

[0046] First, the system analyzes the characteristic signals. and A comparative analysis of the waveform structure before and after the transition was conducted, and a structural feature vector was constructed using three indicators: the number of peaks and valleys, their relative time positions, and their durations. For example, exist The preceding waveform segment has three main peaks and valleys, whose relative positions are as follows: seconds, duration is And its in The subsequent transfer segment also exhibited three peaks and valleys, with relative position changes not exceeding ±5%, and a duration of [missing information]. The structural differences are within the preset tolerance range (10%), therefore they are determined to be consistent in terms of main structure. The same method is applied to... Analysis revealed that the number of peaks and troughs increased from three to four, with the addition of a secondary peak exhibiting slight fluctuations at the end. The system further extracted the overlapping regions between principal components (main peak duration > 30ms) and calculated the overlap ratio. The newly added energy weights were corrected, and the mutation was finally determined to be a "pseudo-consistency" caused by a slight external perturbation. Under the premise that the overall evolution trend remains unchanged, it can still be included in the reliable transfer.

[0047] In establishing the feature offset synchronization judgment, the system extracts each feature in The direction of change of the frequency center position within the range is linearly fitted to the slope. Indicates the trend of deviation: such as , , , , Discovering features The offset direction is clearly opposite to that of the other four features (an upward trend), and the system will adjust accordingly based on the rules. The synchronization coefficient matrix construction is temporarily excluded. Subsequently, [the following is done / then...] Construct a synchronization coefficient matrix within a time period Furthermore, statistical analysis was performed on the cumulative positive offset values ​​of the upper triangular elements. Let the slope sequence of the main diagonal of the matrix be... It shows a positive upward trend; while the upper triangular elements, such as The sum of the offset values ​​is Consistent with the main trend, the system upgraded the confirmation level of the systemic damage evolution of the event from pending confirmation to confirmed, and recorded it as a Level II risk warning.

[0048] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A low-strain detection waveform analysis method integrating time-frequency feature extraction, characterized in that... include: The acquired low-strain waveform signal is segmented on the time axis, and the energy change rate and start time of each time segment are detected. Signal segments with energy change rates exceeding the background noise statistical fluctuation threshold are selected to form a local feature signal set. The local feature signals are arranged in chronological order, and the occurrence interval, duration and energy change trend of each feature signal are analyzed to identify related signals belonging to the same potential damage process and generate a time correlation chain. Local signals corresponding to the time correlation chain are extracted from multiple frequency bands, the correlation of energy changes between different frequency bands is analyzed, and signal features that appear synchronously or influence each other in multiple frequency bands are determined. Based on the time correlation chain and multi-frequency band features, the consistency analysis of the performance of each feature in different time and frequency dimensions is performed, signals that are stable in both time and frequency are retained, and isolated anomalies that stand out in a single domain are eliminated to obtain a reliable feature set for low strain detection. Track the changing trends of the reliable features in time and frequency, identify the feature transfer and amplification process from high frequency to low frequency, and determine the occurrence and development of low strain damage and output the detection results based on the evolution law of features at different stages. When tracking the temporal evolution trend of the reliable features, the increasing frequency of detection is used as a non-amplitude criterion for early damage occurrence and for strain precursor identification. The feature transfer process from high frequency to low frequency is marked by the downward shift of the center position of the time series. When multiple features show a shift trend at the same time, the damage evolution identification mechanism is triggered. The determination result of low strain damage is based on the phased intensity comparison of the signal distribution in the reliable feature set. If the early signal group is stronger than the later group, the system marks it as a non-continuously evolving risk to distinguish transient strain behavior. The detection of the increasing frequency of occurrence includes: constructing a time series density map for each reliable feature in different detection periods; if the density center continues to shift forward in time, it is determined to be an active precursor feature. The criteria for frequency increase also include statistical analysis of the growth acceleration between frequency increases, and when the growth rate increases period by period, it is marked as an accelerated strain precursor. During the detection of the downward shift of the time series center of the feature transfer, a signal morphology and structure alignment condition is added. If the feature waveforms before and after the transfer maintain the same main structure, the confidence level of the transfer trend is increased by one level. When multiple features simultaneously exhibit a shift trend, a shift synchronization coefficient matrix within the time band is established. If the main diagonal elements in the matrix have a positive continuous slope, it is determined that the systemic damage evolution process has been initiated.

2. The low-strain detection waveform analysis method based on fusion time-frequency feature extraction according to claim 1, characterized in that... Before segmentation, the original low-strain waveform signal is pre-scanned for amplitude change rate, and non-equal length segmentation intervals are set according to the trend of amplitude slope change within different segments. During the detection of energy change rate, short-period signals that meet the combination of low persistence and high transition amplitude are identified and extracted as local anomalous subsequences. Low persistence refers to a duration lower than a set time threshold, and high transition amplitude refers to a peak rise greater than a set multiple of the background energy. The cross-correlation coefficient between preceding and following segments is introduced as a noise elimination factor, and signals that are not continuous with the waveform of adjacent segments are retained as independent anomalous features.

3. The low-strain detection waveform analysis method based on fusion time-frequency feature extraction according to claim 1, characterized in that... After arranging the local feature signals in chronological order, a cross-segment causal relationship map is constructed by detecting the delayed response structure between local segments to identify potential damage activity chains that are discontinuous but have consistent behavior. In the case of multiple similar feature signals within the same time period, a signal overlap threshold is set. If the signal peak window overlap rate is higher than the set value, it is marked as a time-domain collaborative abnormal chain group and assigned a high-risk level.

4. The low-strain detection waveform analysis method based on fusion time-frequency feature extraction according to claim 1, characterized in that... During the multi-band extraction process, high-frequency abrupt change points of the signal in the corresponding time correlation chain are retrieved and used as the initial frequency index; the energy correlation between different frequency bands includes determining whether they constitute a frequency response synergy based on amplitude statistics and the consistency of periodic waveform patterns.

5. The low-strain detection waveform analysis method based on fusion time-frequency feature extraction according to claim 1, characterized in that... When analyzing the consistency of the characteristics of each signal across different time-frequency dimensions, a feature expression sparsity index is constructed to retain signal groups that appear in different forms across multiple frequency bands but have the same structural trend. For signals that experience local instability in a certain frequency band and then quickly recover and rebound synchronously with other frequency bands, a time-frequency dynamic compensation mechanism is used to correct and include them in the reliable feature set.

6. The low-strain detection waveform analysis method based on fusion time-frequency feature extraction according to claim 1, characterized in that... The structural alignment conditions include using the number of peaks and valleys, relative positions, and durations of the waveforms before and after the transfer as structural feature comparison factors. Only when all three indicators match simultaneously is the main structure considered consistent. When additional structural variations are detected in the waveform after the transfer but the downward shift trend of the center position remains unchanged, it is determined whether it is a false consistency caused by external disturbance by comparing the weights of the overlapping areas of the main components of the waveform.

7. The low-strain detection waveform analysis method based on fusion time-frequency feature extraction according to claim 1, characterized in that... In the determination of the offset trend of multiple features, if the offset direction of any feature is opposite to the main offset direction reference, then the feature is temporarily removed from the calculation of the synchronization coefficient matrix. In the synchronization coefficient matrix, in addition to the main diagonal, the positive offset cumulative value of the upper triangular region is also analyzed. If its trend is consistent with the main diagonal, then the confirmation level of systemic damage evolution is strengthened.

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