A pile foundation signal processing method and system based on RIME-VMD

Abstract

The application relates to a pile foundation signal processing method based on RIME-VMD, which comprises the following steps: acquiring a pile foundation detection signal, constructing a physical-statistical composite fitness function, performing iterative optimization on the pile foundation detection signal based on RIME to obtain an optimal parameter combination of a decomposition layer number and a penalty factor of VMD and a variational mode decomposition model; configuring the variational mode decomposition model based on the optimal parameter combination, performing variational mode decomposition on the pile foundation detection signal to obtain a plurality of intrinsic mode function (IMF) components; performing clustering scoring based on the intrinsic mode function (IMF) components to obtain a primary denoising reconstructed signal; and calculating the pile foundation defect space depth and the total length of the pile body based on the primary denoising reconstructed signal. The frost and ice optimization algorithm is used to optimize the parameters of the variational mode decomposition algorithm, so that the optimal decomposition layer number and the penalty factor are automatically obtained, the pile foundation detection data processing automation is realized, and the problems of inaccurate manual parameter setting and easy falling into local optimization are solved.

Description

Technical Field

[0001] This invention relates to the field of pile foundation detection signal processing technology, specifically to a pile foundation signal processing method and system based on RIME-VMD. Background Technology

[0002] Pile integrity testing is a crucial method for assessing the quality of bridges, high-rise buildings, and various large structures. Currently, the low-strain reflection wave method, also known as dynamic testing, is widely used. By analyzing the propagation and reflection patterns of impact pulses within the pile, it enables the location of pile defects and the verification of pile length. However, in existing bridge pile foundation testing or pile foundation monitoring in complex geological environments, the measured signals are affected by environmental complexity. Effective reflection information is often masked by high-frequency noise or low-frequency environmental vibration signals, making it extremely difficult to distinguish the effective signal from background noise. To address this challenge, variational mode decomposition (VMD) technology, which processes non-stationary signals, has become an effective approach.

[0003] In related technologies, while variational mode decomposition (VMD) can effectively suppress mode aliasing in empirical mode decomposition (EMD) and decouple complex signals into multi-order intrinsic mode functions (EMFs), its practical application still faces significant technical bottlenecks. Specifically, the selection of VMD parameters, such as the number of decomposition layers and the penalty factor, is highly dependent on human experience. When processing pile foundation signals with strong transient impact characteristics, blindly setting parameters can easily lead the algorithm into local optima, resulting in the false filtering of effective reflected wave characteristics or the generation of spurious components. If VMD parameters are optimized solely based on pure data statistics (such as envelope entropy), it is easy to extract spurious mode components that are mathematically orthogonal but belong to "pseudo-responses" in the physical propagation of stress waves, which can easily lead to misjudgment or missed judgment. Summary of the Invention

[0004] This application provides a pile foundation signal processing method and system based on RIME-VMD, which solves the technical problem in related technologies that VMD parameters are highly dependent on human experience or that pure data statistical optimization parameters are prone to misjudgment or omission.

[0005] This application provides a pile foundation signal processing method based on RIME-VMD, which includes the following steps: Step S1: Obtain the pile foundation detection signal, construct the physical-statistical composite fitness function, and iteratively optimize the pile foundation detection signal based on the RIME frost optimization algorithm to obtain the optimal parameter combination of the number of decomposition layers and the penalty factor of the variational mode decomposition algorithm VMD, and the variational mode decomposition model. Step S2: Configure the variational mode decomposition model based on the optimal parameter combination, and perform variational mode decomposition on the pile foundation detection signal to obtain several orders of intrinsic mode function (IMF) components; Step S3: Perform clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal; Step S4: Calculate the spatial depth of pile foundation defects and the total length of pile body based on the first denoised reconstruction signal.

[0006] In one implementation, the physical-statistical composite fitness function is expressed as: ; in, The first in the population Composite fitness evaluation score of each intrinsic mode function component; Let be the envelope entropy of this component; This is the absolute value of the Pearson correlation coefficient between this component and the pile foundation detection signal; This represents the kurtosis of the component. The residual is a one-dimensional dynamic. and These are the global minimum and global maximum values ​​of the physical residuals generated by all candidate solutions in the current frost optimization algorithm iteration population, respectively. As a weighting factor; and All are preset constants.

[0007] In one implementation, the one-dimensional dynamic residual Expressed as: ; in, This represents the total number of discrete sampling points. Sampling time point; For this component in time The time-domain amplitude; and These are the first-order and second-order time differences of the component, respectively; The center angular frequency of this component; The viscous damping coefficient of the soil layer around the pile, as a function of time. A changing stepwise piecewise function.

[0008] In one implementation, step S1 involves acquiring pile foundation detection signals, constructing a physical-statistical composite fitness function, and iteratively optimizing the pile foundation detection signals based on the RIME (Ripple-Induced Icy) optimization algorithm to obtain the optimal parameter combination of the number of decomposition layers and the penalty factor for the Variational Mode Decomposition (VMD) algorithm. The Variational Mode Decomposition model includes: Step S11: Initialize the initial frost particle population of the RIME frost optimization algorithm and the number of decomposition layers to be optimized in the VMD variational mode decomposition algorithm. With penalty factor Parameter combination Defined as the position coordinates of each frost particle in the initial frost particle population; Step S12: Based on the parameter combination corresponding to each frost particle in the initial frost particle population, decompose and calculate the acquired pile foundation detection signal to obtain several intrinsic mode function (IMF) components; construct a physical-statistical composite fitness function to obtain the physical-statistical composite fitness evaluation score corresponding to the component, and take the minimum score as the current optimal fitness of the optimal frost particle. Step S13: Based on the current iteration number Set the maximum number of iterations. Determine the current iteration number based on the current optimal fitness. Has the maximum number of iterations been reached? ; If not reached, update the current iteration count. And repeat step S13 in a loop; If the target has been reached, then the frost particle position coordinates corresponding to the current optimal fitness mapping are taken as the final frost particle, and the VMD parameters corresponding to the final frost particle are combined. As the optimal combination of parameters.

[0009] In one implementation, step S3, performing clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal, includes: Step S31: Extract the multidimensional feature parameters of each intrinsic mode function (IMF) component to construct a high-dimensional feature matrix, and divide each IMF component into several candidate clusters based on a clustering algorithm; Step S32: Calculate the comprehensive score of each candidate cluster according to the preset cluster integrity scoring criteria, calculate the average score of all the candidate clusters as the dynamic reconstruction threshold, and take the candidate clusters with a comprehensive score greater than or equal to the dynamic reconstruction threshold as the target clusters. Step S33: Extract the intrinsic mode function (IMF) components contained in all the target clusters, and perform time-domain linear accumulation to obtain a first-order denoised reconstructed signal.

[0010] In one implementation, the expression for the preset cluster integrity scoring criterion is: ; in, For the first Cluster integrity score of each candidate cluster; This represents the total number of intrinsic mode components contained within the candidate cluster; The first in this candidate cluster The absolute value of the Pearson correlation coefficient between each component and the pile foundation detection signal; The first in this candidate cluster The kurtosis value of each component; The first in this candidate cluster The energy percentage of each component; and All of these are preset normalized weighting coefficients.

[0011] In one embodiment, step S4, calculating the spatial depth of pile foundation defects and the total length of the pile body based on the first denoised reconstruction signal, includes: Step S41: Perform adaptive non-uniform smoothing processing on the first denoised and reconstructed signal based on the local differential gradient algorithm; Step S42: Perform time-varying exponential gain compensation on the processed first denoised reconstructed signal to obtain the final enhanced signal; Step S43: Calculate the spatial depth of the pile foundation defect and the total length of the pile body based on the final enhanced signal.

[0012] In one embodiment, step S41, performing adaptive non-uniform smoothing processing on the first-order denoised reconstructed signal based on the local differential gradient algorithm, includes: Step S411: Calculate the local differential gradient of the first denoised reconstructed signal based on the local differential gradient algorithm; Step S412: Establish a dynamic smoothing weight factor allocation mechanism based on the local differential gradient and set the gradient threshold; When the local differential gradient is greater than a set gradient threshold, the smoothing weight factor is reduced. Increase the smoothing weight factor when the local differential gradient is less than or equal to the gradient threshold; Step S413: Perform non-uniform smoothing processing on the first denoised reconstructed signal based on the updated smoothing weight factor.

[0013] In one embodiment, step S43, calculating the spatial depth of pile foundation defects and the total length of the pile body based on the final enhanced signal, includes: Peak finding is performed on the time-domain curve of the final enhanced signal; The stress wave reflection times corresponding to the maximum and minimum peaks are extracted separately, and the spatial depth of pile foundation defects and the total length of the pile body are calculated by combining the stress wave propagation velocity.

[0014] This application also provides a pile foundation signal processing system based on RIME-VMD, which applies the pile foundation signal processing method based on RIME-VMD as described in any of the above claims, and includes: The optimal parameter combination calculation module is configured to: acquire pile foundation detection signals, construct a physical-statistical composite fitness function, and iteratively optimize the pile foundation detection signals based on the RIME frost optimization algorithm to obtain the optimal parameter combination of the decomposition level and penalty factor of the Variational Mode Decomposition (VMD) algorithm, and the Variational Mode Decomposition (VMD) model. The IMF component calculation module is configured to: configure the variational mode decomposition model based on the optimal parameter combination, and perform variational mode decomposition on the pile foundation detection signal to obtain several orders of intrinsic mode function (IMF) components; The clustering scoring module is configured to perform clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal. The signal calculation module is configured to calculate the spatial depth of pile foundation defects and the total length of the pile body based on the first denoised and reconstructed signal.

[0015] The beneficial effects of the technical solutions provided in this application include: This application provides a pile foundation signal processing method based on RIME-VMD. It constructs a physical-statistical composite fitness function and uses the frost-ice optimization algorithm to intelligently optimize the key parameters of the variational mode decomposition algorithm (VMD), thereby automatically obtaining the optimal number of decomposition layers and penalty factor. Then, by performing variational mode decomposition and clustering scoring on the pile foundation detection signal, a denoised and reconstructed signal is obtained, and the spatial depth of pile foundation defects and the total length of the pile body are calculated. This automates the processing of pile foundation detection data, eliminates the subjective influence of manual parameter adjustment and interpretation in related technologies, and solves the problems of inaccurate manual parameter setting and easy getting trapped in local optima. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the steps for pile foundation signal processing based on RIME-VMD in one embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of pile foundation detection signals in one embodiment of the present invention.

[0019] Figure 3 This is a schematic diagram of the RIME convergence curve in one embodiment of the present invention.

[0020] Figure 4 This is a schematic diagram of VMD decomposition in one embodiment of the present invention.

[0021] Figure 5 This is a schematic diagram of cluster scoring in one embodiment of the present invention.

[0022] Figure 6 This is a schematic diagram of time-varying gain in one embodiment of the present invention.

[0023] Figure 7 This is a comparative schematic diagram of signal processing in one embodiment of the present invention. Detailed Implementation

[0024] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0025] This application provides a pile foundation signal processing method based on RIME-VMD, which can solve the technical problem in related technologies that VMD parameters are highly dependent on human experience or that pure data statistical optimization parameters are prone to misjudgment or omission.

[0026] like Figure 1 As shown, Figure 1 This is a flowchart of the steps for pile foundation signal processing based on RIME-VMD in one embodiment of the present invention.

[0027] This embodiment provides a pile foundation signal processing method based on RIME-VMD, which includes the following steps: Step S1: Obtain pile foundation detection signals, construct a physical-statistical composite fitness function, and iteratively optimize the pile foundation detection signals based on the RIME (Rome-In-Frost) optimization algorithm to obtain the optimal parameter combination of the number of decomposition layers and the penalty factor of the Variational Mode Decomposition (VMD) algorithm, and the Variational Mode Decomposition (VMD) model. Step S2: Configure the variational mode decomposition model based on the optimal parameter combination, and perform variational mode decomposition on the pile foundation detection signal to obtain several orders of intrinsic mode function (IMF) components; Step S3: Perform clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal; Step S4: Calculate the spatial depth of pile foundation defects and the total length of the pile body based on the first denoised and reconstructed signal.

[0028] The RIME frost optimization algorithm provides an intelligent adaptive solution mechanism. By simulating the growth patterns of soft and hard frost in the natural frost formation process, the algorithm can efficiently perform global exploration and local development in a complex solution space, automatically locking in the optimal decomposition parameters.

[0029] This embodiment provides a pile foundation signal processing method based on RIME-VMD. It constructs a physical-statistical composite fitness function and uses the frost-ice optimization algorithm to intelligently optimize the key parameters of the variational mode decomposition algorithm (VMD), thereby automatically obtaining the optimal number of decomposition layers and penalty factor. Then, by performing variational mode decomposition and clustering scoring on the pile foundation detection signal, a denoised and reconstructed signal is obtained, and the spatial depth of pile foundation defects and the total length of the pile body are calculated. This automates the processing of pile foundation detection data, eliminates the subjective influence of manual parameter adjustment and interpretation in related technologies, and solves the problems of inaccurate manual parameter setting and easy getting trapped in local optima.

[0030] The following provides a detailed explanation of each step.

[0031] In one embodiment, in step S1, the physical-statistical composite fitness function is expressed as: ; in, The first in the population Composite fitness evaluation score of each intrinsic mode function component; Let be the envelope entropy of this component; This is the absolute value of the Pearson correlation coefficient between this component and the pile foundation detection signal; This represents the kurtosis of the component. The residual is a one-dimensional dynamic. and These are the global minimum and global maximum values ​​of the physical residuals generated by all candidate solutions in the current frost optimization algorithm iteration population, respectively. As a weighting factor; and All of these are preset constants, which are minimum values ​​set to ensure that the denominator is not zero and will not affect the actual calculation.

[0032] In one embodiment, one-dimensional dynamic residual Expressed as: ; in, This represents the total number of discrete sampling points. Sampling time point; For this component in time The time-domain amplitude; and These are the first-order and second-order time differences of the component, respectively; The center angular frequency of this component.

[0033] The viscous damping coefficient of the soil layer around the pile, as a function of time. The changing step-piece function is expressed as: ; in, For the first The empirical viscosity damping coefficient of the soil layer is extracted from the geological survey report.

[0034] To accurately characterize the non-uniform energy dissipation characteristics of stress waves propagating in layered foundations, a step-type time-varying damping function is used for the viscous damping coefficient of the soil around the pile. Its construction method is as follows: Based on the propagation velocity of stress waves in the pile body Depth of interface with each soil layer Through the formula: Calculate the reflection time nodes corresponding to each soil layer; Based on the time node, the constant damping coefficient is extended into a step vector that is piecewise assigned according to the discrete time step. , making In the time interval The value within is always equal to the first The viscous damping coefficient of the soil layer; Time-varying damping function Substitute the absolute value of the local physical residual From the calculation formula, the above-mentioned modified residual calculation formula is obtained.

[0035] Through the above scheme, when constructing the physical-statistical composite fitness function of the frost-ice optimization algorithm, it not only integrates the data-driven statistical feature term constraints of kurtosis, envelope entropy, and correlation coefficient, but also strongly couples the physical consistency residual constraint term based on the one-dimensional wave dynamics equation of the pile-soil system. In particular, it uses the "one-dimensional wave dynamics equation residual," representing the true propagation mechanism of elastic waves, as a penalty term, nested into the composite fitness function to perform physical consistency constraint. The dual-driven optimization based on propagation laws and data statistical characteristics facilitates the comprehensive consideration of signal envelope entropy, kurtosis, and correlation during the optimization process. This constrains the parameter optimization process with physical laws, improves the signal decoupling purity under complex interference, and avoids the extraction of spurious modal components that are mathematically orthogonal but belong to "pseudo-responses" in the physical propagation of stress waves, as in traditional pure data-driven optimization.

[0036] In one embodiment, step S1 involves acquiring pile foundation detection signals, constructing a physical-statistical composite fitness function, and iteratively optimizing the pile foundation detection signals based on the RIME (Rinse-In-Time) optimization algorithm to obtain the optimal parameter combination of the decomposition level and penalty factor of the Variational Mode Decomposition (VMD) algorithm. The Variational Mode Decomposition model includes: Step S11: Set the maximum number of iterations for the algorithm. The initial frost particle population of the RIME frost optimization algorithm is randomly initialized, and the number of decomposition layers to be optimized in the VMD variational mode decomposition algorithm is determined. With penalty factor Continuous parameter combination Defined as the coordinates of the positions of each frost particle in the initial frost particle population.

[0037] The position coordinates of each frost particle in the initial frost particle population are represented as a set of candidate parameter combinations. In the optimization iteration process of the RIME algorithm, particle position updates are performed by simulating the soft frost penetration exploration and hard frost encapsulation development mechanism in the natural frost formation process.

[0038] Step S12: Based on the parameter combination corresponding to the coordinates of each frost particle in the initial frost particle population, decompose and calculate the acquired pile foundation detection signal to obtain several intrinsic mode functions (IMF) components under the current particle parameters; construct a physical-statistical composite fitness function to obtain the physical-statistical composite fitness evaluation score corresponding to each IMF component, and extract the minimum fitness evaluation score in the entire population as the current optimal fitness of the optimal frost particle.

[0039] Specifically, the original time-domain signal of the low-strain reflected wave detection of the pile foundation is obtained. It can be used as a pile foundation detection signal; of course, further detrending and bandpass filtering preprocessing can be performed to obtain preprocessed detection signal sequence data, which can then be used as a pile foundation detection signal.

[0040] Step S13: Based on the current iteration number Set the maximum number of iterations. Determine the current iteration number based on the current optimal fitness. Has the maximum number of iterations been reached? ; If not reached, update the current iteration count. And repeat step S13 in a loop; If the target has been reached, then the frost particle position coordinates corresponding to the current optimal fitness mapping are taken as the final frost particle, and the VMD parameters corresponding to the final frost particle are combined. As the optimal parameter combination Step S13: Based on the current iteration number Set the maximum number of iterations. Determine the current iteration number based on the current optimal fitness. Has the maximum number of iterations been reached? include: Step S131: Based on the current iteration number With setting the maximum number of iterations Calculate the current adhesion coefficient of the initial frost particles. .

[0041] Specifically, the current adhesion coefficient The formula for switching between global exploration and local development using particle control is: .

[0042] Step S132: Generate the first random number and the second random number Determine the second random number. With current adhesion coefficient The order of magnitude.

[0043] If the second random number Greater than or equal to the current adhesion coefficient If so, update the current iteration count and jump to repeat step S13; If the second random number Less than the current adhesion coefficient Update the initial frost particle positions to obtain the updated frost particle population, and calculate the current normalized fitness value of the updated frost particle population.

[0044] Specifically, if the second random number Less than the current adhesion coefficient The position update mechanism of the frost-ice algorithm is used to update the spatial positions of all initial frost-ice particles to obtain an updated frost-ice particle population, and the optimal fitness corresponding to each frost-ice particle in the updated frost-ice particle population is re-obtained; further, based on the optimal fitness in the updated frost-ice particle population, the current normalized fitness value of the updated frost-ice particle population is calculated and confirmed.

[0045] The position update mechanism is as follows: the position of the particle population is updated by combining the characteristics of soft frost and hard frost. The position update formula is: ; in, For the updated version The particle in the first Wei's new position; This represents the position of the best particle in the current population. for Random numbers within; Used to control the direction of movement; Environmental factors; A random number used to control the distance from the particle center; and These represent the upper and lower bounds of the parameter optimization space, respectively.

[0046] Step S133: Generate a third random number Determine the third random number The magnitude of the current normalized fitness value.

[0047] If the third random number If the frost particle position is less than the current normalized fitness value, update the frost particle position a second time to obtain the latest frost particle population, and extract the latest best frost particle and its corresponding latest best fitness from the latest frost particle population. If the third random number If the value is greater than or equal to the current normalized fitness value, then update the current iteration number and jump to repeat steps S131 to S132.

[0048] Step S134: Determine the size of the latest optimal fitness and the current optimal fitness.

[0049] If the latest optimal fitness is greater than or equal to the current optimal fitness, then update the current iteration number and jump to repeat steps S131 to S133; otherwise, continue to step S135. Step S135: Replace the latest best fitness with the current best fitness and determine the current iteration number. Has the maximum number of iterations been reached? ; If not reached, update the current iteration count. And repeat steps S131 to S134 in a loop; If the target has been reached, then the frost particle position coordinates corresponding to the current optimal fitness mapping are taken as the final frost particle, and the VMD parameters corresponding to the final frost particle are combined. As the optimal combination of parameters.

[0050] Through the above scheme, a physical-statistical composite fitness function is constructed, integrating the residuals of the one-dimensional dynamic wave equation and the statistical characteristics of the data. Driven by this composite fitness function, the RIME algorithm is used to simulate the penetrating global exploration behavior of soft frost and the enveloping local development behavior of hard frost in nature. The minimum value is used to iteratively update the spatial position of the particle swarm. The iteration continues until the set maximum number of iterations is reached. When the time is reached, the algorithm stops and outputs the optimal particle position with the minimum global fitness value. This position coordinate corresponds to the optimal parameter combination—the target decomposition layer number—for the current specific pile foundation detection signal. With target penalty factor This method achieves adaptive global optimization of model parameters, ensuring the objectivity and physical correctness of subsequent signal decomposition. It avoids errors from manual parameter tuning and, through the constraint mechanism of the one-dimensional dynamic wave equation, accurately eliminates pseudo-modes that score high in pure data calculations but violate the actual stress wave propagation laws. The introduction of the one-dimensional dynamic wave equation makes the algorithm's optimization highly consistent with the physical propagation mechanism of stress waves in the pile, thus significantly improving the applicability and signal decoupling purity of this method in pile foundation testing.

[0051] Step S2: Configure the variational mode decomposition model based on the optimal parameter combination, and perform variational mode decomposition on the pile foundation detection signal to obtain several orders of intrinsic mode function (IMF) components.

[0052] The variational mode decomposition model is configured based on the optimal parameter combination obtained in step S1. The VMD solution process is constructed as a constrained variational problem, with the objective of minimizing the sum of the estimated bandwidths of each IMF: ; in, Characterization decomposition A set of intrinsic mode function components This is the set of central angular frequencies corresponding to each component; For the Dirichlet impulse function; The imaginary unit; symbol This is a convolution operation.

[0053] The constraints are: By introducing a secondary penalty factor With Lagrange multipliers The expression is transformed into an unconstrained augmented Lagrange functional, and the Alternating Direction Multiplier Method (ADMM) is used for iterative optimization to find the optimal solution. .

[0054] In one embodiment, step S3, performing clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal, includes: Step S31: Extract the multidimensional feature parameters of each intrinsic mode function (IMF) component to construct a high-dimensional feature matrix, and divide each IMF component into several candidate clusters based on a clustering algorithm.

[0055] Specifically, the multidimensional feature parameters include the center frequency, correlation coefficient, energy percentage, kurtosis, and envelope entropy of each intrinsic mode function (IMF) component. For example, extracting each component... The five-dimensional features are used to construct the feature matrix. The calculation formulas for each feature dimension are as follows: Center frequency Extract the dominant peak frequency of the amplitude spectrum: .

[0056] Pearson correlation coefficient : Evaluation of the Each mode and the original preprocessed signal Waveform correlation: .

[0057] Energy percentage The formula for evaluating the proportion of a single component energy to the total energy of the original signal is as follows: .

[0058] kurtosis index Used to capture transient high-frequency impact pulses, the calculation formula is: .

[0059] Envelope Entropy Extracting the envelope using Hilbert transform The probability is then normalized, and the calculation formula is as follows: .

[0060] Calculation yields: ; By concatenating the above features, a high-dimensional feature matrix for adaptive clustering selection is constructed. , expressed as: ; The expanded matrix structure is as follows: .

[0061] In the formula, the number of rows in the matrix is ​​equal to the number of VMD decomposition layers.

[0062] Based on the agglomerative hierarchical clustering algorithm, the intrinsic mode functions (IMF) components are divided into several candidate clusters, including: dividing the feature matrix... After normalization, to avoid clustering oscillations in small sample spaces, a cohesive hierarchical clustering algorithm is used to calculate the Euclidean distance between each row vector. This is combined with an adaptive truncated dendrogram to classify modes with similar physical and statistical characteristics into candidate clusters, performing stable clustering. Specifically, IMFs with energy <0.1% are not included in the cluster. For the impact characteristics of pile foundation reflected waves, energy concentration is used to initially screen the decomposed components, followed by automatic clustering analysis using multidimensional feature indicators.

[0063] Step S32: Calculate the comprehensive score of each candidate cluster according to the preset cluster integrity scoring criteria, calculate the average score of all candidate clusters as the dynamic reconstruction threshold, and select the candidate clusters whose comprehensive score is greater than or equal to the dynamic reconstruction threshold as the target clusters.

[0064] Specifically, the underlying physical basis of this scoring criterion is that the target component representing the true defect reflection wave or pile bottom reflection wave not only needs to possess high physical energy, but also, due to severe defects such as diameter reduction and pile breakage causing phase reversal of the reflected wave, the effective defect component must have a high morphological fit with the original impact signal, and must also exhibit significant local pulse impact characteristics. After scoring all candidate clusters sequentially according to the preset cluster integrity scoring criterion, the average score of all current candidate clusters is calculated. And set a dynamic reconstruction threshold. To avoid the loss of multi-band information (such as high-frequency shallow defects and low-frequency deep pile bottom echoes) caused by single-cluster reconstruction, the system extracts all candidate clusters with a comprehensive score greater than or equal to the dynamic reconstruction threshold in parallel as the "target cluster".

[0065] Step S33: Extract the intrinsic mode function (IMF) components contained in all target clusters, and perform time-domain linear accumulation on a time-domain scale to obtain a primary denoised reconstructed signal that has removed a large number of pseudo-modes and background interference. .

[0066] The above scheme extracts multidimensional feature parameters of each intrinsic mode function (IMF) component to construct a feature matrix, and combines it with an agglomerative hierarchical clustering algorithm for adaptive partitioning of candidate clusters. By designing a comprehensive scoring criterion that integrates waveform-derived correlation and local impact abruptness, high-frequency environmental noise and low-frequency sensor drift interference are automatically separated, and the true reflection signal is accurately extracted from strong background noise. That is, the components containing the true defect reflection characteristics are extracted and superimposed in the time domain, reducing the reliance on manual selection and experience-based interpretation by inspection personnel in the data processing process, and avoiding the problem of missed or misjudged weak reflection signals due to the fact that the modal component screening criteria are mostly based on single indicators such as correlation coefficient or energy under complex working conditions.

[0067] In one embodiment, the expression for the preset cluster integrity scoring criterion is: ; in, For the first Cluster integrity score of each candidate cluster; This represents the total number of intrinsic mode components contained within the candidate cluster; The first in this candidate cluster The absolute value of the Pearson correlation coefficient between each component and the pile foundation detection signal; The first in this candidate cluster The kurtosis value of each component; The first in this candidate cluster The energy percentage of each component; and All of these are preset normalized weighting coefficients.

[0068] The above scheme provides a cluster integrity scoring criterion that integrates the consistency and mutability of features within a cluster.

[0069] In one embodiment, step S4, calculating the spatial depth of pile foundation defects and the total length of the pile body based on the first denoised reconstructed signal, includes: Step S41: Perform adaptive non-uniform smoothing processing on the first denoised and reconstructed signal based on the local differential gradient algorithm.

[0070] Step S42: Perform time-varying exponential gain compensation on the processed first-stage denoised reconstructed signal to obtain the final enhanced signal; Step S43: Calculate the spatial depth of pile foundation defects and the total length of the pile body based on the final enhanced signal.

[0071] In one embodiment, step S41, performing adaptive non-uniform smoothing processing on the first-order denoised reconstructed signal based on the local differential gradient algorithm, includes: Step S411: Calculate the local differential gradient of the denoised and reconstructed signal based on the local differential gradient algorithm.

[0072] Specifically, calculate the reconstructed signal Local differential gradient at each discrete time step : .

[0073] Step S412: Establish a dynamic smoothing weight factor allocation mechanism based on the local differential gradient and set the gradient threshold; Decrease the smoothing weight factor when the local differential gradient is greater than the set gradient threshold. Increase the smoothing weight factor when the local differential gradient is less than or equal to the gradient threshold.

[0074] Specifically, setting a reasonable gradient threshold : when When it is determined that there is a strong peak abrupt fluctuation in the time interval, the smoothing weight factor is actively reduced to "preserve the peak" in order to retain the peak sharpness, abrupt jump amplitude and phase accuracy of the impact signal to the greatest extent, and to prevent the effective signal from being over-smoothed and distorted.

[0075] when When the interval is determined to be a relatively flat background area with no obvious reflection, the smoothing weight factor is actively increased to perform a stronger exponential smoothing process on the segment, thus deeply smoothing out the residual high-frequency spikes and background clutter.

[0076] Step S413: Perform non-uniform smoothing processing on the first denoised reconstructed signal based on the updated smoothing weight factor.

[0077] In one embodiment, step S42, performing time-varying exponential gain compensation on the processed first-stage denoised reconstructed signal to obtain the final enhanced signal, includes: The denoised and reconstructed signal after processing is reconstructed and then compensated. Compensation curve The calculation formula is: ; in, This is the gain compensation coefficient. For the sampling time point, This represents the total duration of the signal.

[0078] Despite a single denoising and reconstructing signal While high-purity noise reduction has been achieved, in engineering testing of deep overburden layers or ultra-long piles, the soil around the pile exhibits strong viscous hysteresis and frictional dissipation effects on high-frequency stress waves. In addition, the geometric damping caused by wavefront diffusion may lead to an exponential and severe attenuation of the echo signal energy propagating to deep defects or even the bottom of the pile.

[0079] The above scheme employs a cascaded strategy of "firstly, non-uniform adaptive smoothing based on local differential gradients, then introducing time-varying exponential gain compensation" to process the first-stage denoising and reconstructed signal. This strategy smooths background clutter while preserving the characteristics of the defect extreme peaks, and compensates for the geometric divergence and medium dissipation of stress waves based on the pile-soil damping attenuation law, amplifying weak echoes that attenuate with depth. While controlling the amplification of background noise, it avoids the problem of low positioning accuracy of deep defects and pile bottom interfaces caused by the swallowing of weak reflection peaks by residual minor noise, thus improving the recognition of weak echoes, or deep defects and pile bottom reflection signals, and ensuring high-precision quantitative positioning of quality defects and pile bottom interfaces throughout the entire pile length.

[0080] In one embodiment, step S43, calculating the spatial depth of pile foundation defects and the total length of the pile body based on the final enhanced signal, includes: Peak finding is performed on the time-domain curve of the final enhanced signal; The stress wave reflection times corresponding to the maximum and minimum peaks are extracted separately, and the spatial depth of pile foundation defects and the total length of the pile body are calculated by combining the stress wave propagation velocity.

[0081] Specifically, a bidirectional peak-finding algorithm is directly executed on the time-domain spectrum of the final enhanced signal. If a significant minimum peak (out-of-phase trough) is extracted, it is determined to be a defect that reduces wave impedance, such as a narrowed diameter or a broken pile. If a significant maximum peak (in-phase peak) is extracted, it is determined to be a diameter expansion or reflection from the bedrock at the pile bottom. Finally, the time nodes corresponding to each extreme point are extracted to calculate the specific depth of the defect and the pile bottom.

[0082] This application also provides a pile foundation signal processing system based on RIME-VMD, which applies the pile foundation signal processing method based on RIME-VMD described above, and includes: The optimal parameter combination calculation module is configured to: acquire pile foundation detection signals, construct a physical-statistical composite fitness function, and iteratively optimize the pile foundation detection signals based on the RIME frost optimization algorithm to obtain the optimal parameter combination of the decomposition level and penalty factor of the variational mode decomposition algorithm VMD, and the variational mode decomposition model. The IMF component calculation module is configured to: perform variational mode decomposition on the pile foundation detection signal based on the optimal parameter combination configuration variational mode decomposition model to obtain several orders of intrinsic mode function (IMF) components; The clustering scoring module is configured to perform clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal; The signal calculation module is configured to calculate the spatial depth of pile foundation defects and the total length of the pile body based on the first denoised and reconstructed signal.

[0083] The functions of each module have been explained in the preceding text and will not be repeated here.

[0084] The following provides a specific example for illustration.

[0085] This embodiment uses a C30 concrete cast-in-place pile from an actual engineering project as the test object. The pile under test is designed to be 10m long; it has a circular cap at the top, 0.8m high, and 0.3m x 0.2m x 0.2m wooden blocks as defects are placed 6m below the top of the pile. In the on-site dynamic testing operation, an accelerometer is attached to the pile body, the excitation point is set 1m from the top of the pile, and the accelerometer is located 2m below the excitation point. A nylon hammer is used as the excitation source, striking vertically downwards at the window of the pile body, and the original time-domain signal sequence of low-strain reflected wave detection is collected. .

[0086] This embodiment provides a pile foundation signal processing method based on RIME-VMD, which includes the following steps: Step S1: Obtain the pile foundation detection signal, construct the physical-statistical composite fitness function, and iteratively optimize the pile foundation detection signal based on the RIME frost optimization algorithm to obtain the optimal parameter combination of the number of decomposition layers and the penalty factor of the variational mode decomposition algorithm VMD, and the variational mode decomposition model.

[0087] like Figure 2 As shown, the original time-domain signal sequence of the low-strain reflected wave detection was acquired. Subsequently, due to the presence of low-frequency environmental vibration and high-frequency electromagnetic interference in the field environment, low-order polynomial fitting was used for de-trending processing, and a digital bandpass filter was used with the low-frequency cutoff frequency set to 10Hz and the high-frequency cutoff frequency set to 5000Hz to remove out-of-band interference, and the preprocessed detection signal sequence data was obtained as the pile foundation detection signal.

[0088] When constructing the physical-statistical composite fitness function for the frost-ice optimization algorithm, the population size and the number of iterations were set to 50; the specific results are shown in Table 1 and... Figure 3 As shown.

[0089] Table 1. Iterative optimization results of the RIME frost optimization algorithm

[0090] like Figure 3 As shown, the composite fitness score tends to stabilize after approximately 29 iterations as the number of iterations increases. The optimal combination of hyperparameters is: optimal number of decomposition layers. Optimal penalty factor .

[0091] Step S2: Configure the variational mode decomposition model based on the optimal parameter combination, and perform variational mode decomposition on the pile foundation detection signal to obtain several orders of intrinsic mode function (IMF) components.

[0092] like Figure 4 As shown, the original signal is decoupled into 15th order intrinsic mode function (IMF) components.

[0093] Step S3: Perform clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal.

[0094] Multidimensional feature parameters of each intrinsic mode function (IMF) component were extracted to construct a high-dimensional feature matrix, and the results are shown in Table 2.

[0095] Table 2 Feature Parameter Table

[0096] Combination Figure 5 and Figure 6As shown, the automatically selected IMFs within the target cluster are extracted and linearly accumulated in the time domain to obtain a denoised and reconstructed signal. The process is as follows: The optimal number of decomposition levels is K=15; The optimal penalty factor Alpha = 26911.87; Optimal fitness = 0.354012; Physical constraint description: Physical residual penalty coefficient = 0.40; Automatically select IMF=[8 9 11 12 13 14]; Optimal Particle IMF Composite Score: [6.6647 3.9683 3.8857 5.9097 4.4357 4.5932 4.6857 1.4323 0.8691 0.354 1.1265 1.2769 1.2035 1.7432 8.6524].

[0097] Step S4: Calculate the spatial depth of pile foundation defects and the total length of the pile body based on the first denoised and reconstructed signal.

[0098] In this embodiment, a gain compensation coefficient is set. .like Figure 7 As shown, the enhancement process, which involves smoothing followed by compensation, multiplies the smoothed signal by the compensation curve. The resulting enhanced signal maintains the sharpness of the initial peak while exponentially amplifying the extremely difficult-to-identify weak deep reflections. The incident wave triggered by the nylon hammer strike was accurately captured at 15.3377s, and strong reflection peaks were successfully identified in the deep region at times of 15.3387s, 15.3389s, 15.3395s, and 15.3416s.

[0099] Calculate the travel time of stress waves: ; ; ; .

[0100] In this embodiment, the foundation pile is a C30 concrete bored cast-in-place pile, and the wave velocity calculation formula is as follows: , For longitudinal wave velocity, The elastic modulus of concrete. For concrete density, It is Poisson's ratio. (Based on research...) , Therefore, the calculation is as follows. The velocity is 4082 m / s, which is the one-dimensional elastic longitudinal wave propagation velocity of C30 concrete. Using 4082 m / s, the defect depth is calculated: ; in, For the pile length, The time difference between the reflected signal and the incident wave. This refers to the distance between the sensor at the top of the pile and the side wall of the pile.

[0101] Calculations showed that the distance between the first reflection point and the top of the pile was 2.041m, and its direction was opposite to the incident wave, indicating that this was a signal reflected from the pile cap. The actual distance between the sensor and the bottom of the pile cap was 2m, with an error of 2.05%.

[0102] The distance between the second reflection point and the top of the pile is 4.45m. Based on the original signal, it is determined that this is high-frequency interference from a large-diameter pile, which is not a characteristic signal.

[0103] The third reflection point is 5.67m away from the top of the pile and is in the same direction as the incident wave. It is determined that this is a defect reflection signal. The actual defect is located 5.85-6.15m below the top of the pile, with an error of 3.1%.

[0104] The fourth reflection point is 9.956m away from the pile top, and its direction is the same as the incident wave. Since this is a friction pile and the soil around the pile bottom is relatively soft, this is determined to be the signal at the pile bottom. The actual pile length is 10m, with an error of 0.4%.

[0105] This application utilizes the frost-ice optimization algorithm to adaptively optimize VMD decomposition parameters, comprehensively identifies impact components based on multi-dimensional features, and achieves fully automated processing of pile foundation signals with deep attenuation compensation through a unique compensation and smoothing mechanism. This enhances the scientific rigor and accuracy of pile foundation quality inspection. It significantly improves the accuracy of capturing weak features under complex interference environments, effectively eliminates strong background interference, and overcomes the problem of deep echo attenuation. It achieves fully automated, high-precision quantitative positioning of weak defects in pile foundations under complex working conditions, ensuring the accuracy of defect positioning across the entire pile length. This provides more reliable technical support for pile foundation defect identification, depth verification, and integrity assessment, and has extremely high engineering practical value.

[0106] It should be noted that the sequence numbers of the embodiments in this application are merely for descriptive purposes and do not represent the superiority or inferiority of the embodiments. The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not represent a sequential order, nor do they limit "first," "second," and "third" to different types.

[0107] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0108] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0109] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish the different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0110] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A pile foundation signal processing method based on RIME-VMD, characterized in that, It includes the following steps: Step S1: Obtain the pile foundation detection signal, construct the physical-statistical composite fitness function, and iteratively optimize the pile foundation detection signal based on the RIME frost optimization algorithm to obtain the optimal parameter combination of the number of decomposition layers and the penalty factor of the variational mode decomposition algorithm VMD, and the variational mode decomposition model. Step S2: Configure the variational mode decomposition model based on the optimal parameter combination, and perform variational mode decomposition on the pile foundation detection signal to obtain several orders of intrinsic mode function (IMF) components; Step S3: Perform clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal; Step S4: Calculate the spatial depth of pile foundation defects and the total length of pile body based on the first denoised reconstruction signal.

2. The pile foundation signal processing method based on RIME-VMD as described in claim 1, characterized in that, The physical-statistical composite fitness function is expressed as follows: ； in, The first in the population Composite fitness evaluation score of each intrinsic mode function component; Let be the envelope entropy of this component; This is the absolute value of the Pearson correlation coefficient between this component and the pile foundation detection signal; This represents the kurtosis of the component. The residual is a one-dimensional dynamic. and These are the global minimum and global maximum values ​​of the physical residuals generated by all candidate solutions in the current frost optimization algorithm iteration population, respectively. As a weighting factor; and All are preset constants.

3. The pile foundation signal processing method based on RIME-VMD as described in claim 2, characterized in that, The one-dimensional dynamic residual Expressed as: ； in, This represents the total number of discrete sampling points. Sampling time point; For this component in time The time-domain amplitude; and These are the first-order and second-order time differences of the component, respectively; The center angular frequency of this component; The viscous damping coefficient of the soil layer around the pile, as a function of time. A changing stepwise piecewise function.

4. The pile foundation signal processing method based on RIME-VMD as described in claim 1, characterized in that, Step S1 involves acquiring pile foundation detection signals, constructing a physical-statistical composite fitness function, and iteratively optimizing the pile foundation detection signals based on the RIME (Rinse-In-Time) optimization algorithm to obtain the optimal parameter combination of the decomposition level and penalty factor of the Variational Mode Decomposition (VMD) algorithm. The Variational Mode Decomposition model includes: Step S11: Initialize the initial frost particle population of the RIME frost optimization algorithm and the number of decomposition layers to be optimized in the VMD variational mode decomposition algorithm. With penalty factor Parameter combination Defined as the position coordinates of each frost particle in the initial frost particle population; Step S12: Based on the parameter combination corresponding to each frost particle in the initial frost particle population, decompose and calculate the acquired pile foundation detection signal to obtain several intrinsic mode function (IMF) components; construct a physical-statistical composite fitness function to obtain the physical-statistical composite fitness evaluation score corresponding to the component, and take the minimum score as the current optimal fitness of the optimal frost particle. Step S13: Based on the current iteration number Set the maximum number of iterations. Determine the current iteration number based on the current optimal fitness. Has the maximum number of iterations been reached? ; If not reached, update the current iteration count. And repeat step S13 in a loop; If the target has been reached, then the frost particle position coordinates corresponding to the current optimal fitness mapping are taken as the final frost particle, and the VMD parameters corresponding to the final frost particle are combined. As the optimal combination of parameters.

5. The pile foundation signal processing method based on RIME-VMD as described in claim 1, characterized in that, Step S3, clustering and scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal, includes: Step S31: Extract the multidimensional feature parameters of each intrinsic mode function (IMF) component to construct a high-dimensional feature matrix, and divide each IMF component into several candidate clusters based on a clustering algorithm; Step S32: Calculate the comprehensive score of each candidate cluster according to the preset cluster integrity scoring criteria, calculate the average score of all the candidate clusters as the dynamic reconstruction threshold, and take the candidate clusters with a comprehensive score greater than or equal to the dynamic reconstruction threshold as the target clusters. Step S33: Extract the intrinsic mode function (IMF) components contained in all the target clusters, and perform time-domain linear accumulation to obtain a first-order denoised reconstructed signal.

6. The pile foundation signal processing method based on RIME-VMD as described in claim 5, characterized in that, The expression for the preset cluster integrity scoring criterion is: ； in, For the first Cluster integrity score of each candidate cluster; This represents the total number of intrinsic mode components contained within the candidate cluster; The first in this candidate cluster The absolute value of the Pearson correlation coefficient between each component and the pile foundation detection signal; The first in this candidate cluster The kurtosis value of each component; The first in this candidate cluster The energy percentage of each component; and All of these are preset normalized weighting coefficients.

7. The pile foundation signal processing method based on RIME-VMD as described in claim 1, characterized in that, Step S4, calculating the spatial depth of pile foundation defects and the total length of the pile body based on the first denoised and reconstructed signal, includes: Step S41: Perform adaptive non-uniform smoothing processing on the first denoised and reconstructed signal based on the local differential gradient algorithm; Step S42: Perform time-varying exponential gain compensation on the processed first denoised reconstructed signal to obtain the final enhanced signal; Step S43: Calculate the spatial depth of the pile foundation defect and the total length of the pile body based on the final enhanced signal.

8. The pile foundation signal processing method based on RIME-VMD as described in claim 7, characterized in that, Step S41, performing adaptive non-uniform smoothing processing on the first-order denoised reconstructed signal based on the local differential gradient algorithm, includes: Step S411: Calculate the local differential gradient of the first denoised reconstructed signal based on the local differential gradient algorithm; Step S412: Establish a dynamic smoothing weight factor allocation mechanism based on the local differential gradient and set the gradient threshold; When the local differential gradient is greater than a set gradient threshold, the smoothing weight factor is reduced. Increase the smoothing weight factor when the local differential gradient is less than or equal to the gradient threshold; Step S413: Perform non-uniform smoothing processing on the first denoised reconstructed signal based on the updated smoothing weight factor.

9. The pile foundation signal processing method based on RIME-VMD as described in claim 7, characterized in that, Step S43, calculating the spatial depth of pile foundation defects and the total length of the pile body based on the final enhanced signal, includes: Peak finding is performed on the time-domain curve of the final enhanced signal; The stress wave reflection times corresponding to the maximum and minimum peaks are extracted separately, and the spatial depth of pile foundation defects and the total length of the pile body are calculated by combining the stress wave propagation velocity.

10. A pile foundation signal processing system based on RIME-VMD, employing the pile foundation signal processing method based on RIME-VMD as described in any one of claims 1 to 9, characterized in that, It includes: The optimal parameter combination calculation module is configured to: acquire pile foundation detection signals, construct a physical-statistical composite fitness function, and iteratively optimize the pile foundation detection signals based on the RIME frost optimization algorithm to obtain the optimal parameter combination of the decomposition level and penalty factor of the Variational Mode Decomposition (VMD) algorithm, and the Variational Mode Decomposition (VMD) model. The IMF component calculation module is configured to: configure the variational mode decomposition model based on the optimal parameter combination, and perform variational mode decomposition on the pile foundation detection signal to obtain several orders of intrinsic mode function (IMF) components; The clustering scoring module is configured to perform clustering scoring based on the intrinsic mode function (IMF) components to obtain a first-order denoised reconstructed signal. The signal calculation module is configured to calculate the spatial depth of pile foundation defects and the total length of the pile body based on the first denoised and reconstructed signal.

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