Improved SVMD and SOBI combined bridge dynamic strain signal adaptive noise reduction method

Abstract

The invention discloses an improved SVMD combined SOBI bridge dynamic strain signal adaptive noise reduction method, which comprises the steps of obtaining an original signal of bridge dynamic strain through a strain sensor, improving an SVMD algorithm by taking kurtosis and a decomposition error as stopping criteria, and further decomposing the original signal; classifying the intrinsic mode function components through a K-means clustering algorithm so as to reconstruct a noise component signal and an initial noise reduction signal; constructing a three-channel hybrid observation matrix containing an original signal, a noise component signal and an initial noise reduction signal; performing blind source separation on the hybrid observation matrix by using an SOBI algorithm, and estimating to obtain a separated source signal and a hybrid matrix; noise components are identified based on kurtosis clustering, signals are reconstructed after frequency points are set to be zero, and high-precision noise reduction is achieved. According to the method, a deep collaborative architecture is constructed by introducing an adaptive decomposition mechanism, intelligent clustering recognition and accurate reconstruction are adopted, and efficient suppression of noise and high-fidelity retention of signal features are realized.

Description

Technical Field

[0001] This invention belongs to the fields of bridge engineering and intelligent algorithm technology, and relates to an improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI. Background Technology

[0002] To ensure the safe operation of bridges and prevent serious accidents, condition assessment and health monitoring of bridge structures are crucial. In bridge health monitoring, dynamic strain response is a key indicator for evaluating structural health and load-bearing capacity. Accurate acquisition and analysis of dynamic strain signals can effectively identify structural damage evolution, fatigue accumulation, and changes in dynamic characteristics. However, in practical engineering applications, most sensors are affected by factors such as electromagnetic interference, instrument noise, wind-induced vibration, and traffic excitation. Noise often overlaps with the actual structural response in the frequency domain, severely interfering with the extraction and identification of useful information and limiting the reliability of monitoring data and the accuracy of subsequent analysis. Therefore, employing reasonable and efficient algorithms for data denoising has become one of the important issues in bridge health monitoring data processing.

[0003] To improve signal quality, various noise reduction methods are widely used in bridge dynamic strain data processing. Traditional denoising algorithms, such as Fourier transform denoising based on frequency domain analysis, Wiener filtering based on minimum mean square error, and median filtering suitable for impulse noise, have the advantages of intuitive principles, simple calculation, and good real-time performance. However, they are essentially linear or quasi-linear processing methods, heavily relying on the assumption of the separability of signal and noise in the frequency domain. In actual bridge monitoring environments, noise sources are complex (including environmental electromagnetic interference, instrument thermal noise, wind-induced vibration, and traffic excitation transmission), and often severely overlap with the actual structural response in the frequency band. This results in limited denoising effectiveness of these methods, often blurring or losing subtle fault features and dynamic response details in the signal while suppressing noise. Similarly, wavelet transform denoising methods improve the processing performance of non-stationary signals to some extent by introducing time-frequency localization capabilities. However, its denoising effect still depends on the reasonable selection of wavelet basis functions, threshold rules and decomposition levels. Furthermore, it is not very adaptable to non-Gaussian noise and non-uniform noise in the signal, and is prone to artificial oscillations or distortion when the signal-to-noise ratio is low.

[0004] To overcome the limitations of traditional methods, Empirical Mode Decomposition (EMD) and its improved forms, such as Ensemble Empirical Mode Decomposition (EEMD), have been introduced into the field of engineering signal processing. These methods decompose data based on its own time-scale characteristics, without requiring pre-defined basis functions, and exhibit significant advantages in processing non-stationary and nonlinear signals. However, EMD methods are not designed for denoising, and their significant mode aliasing problem severely affects the physical meaning of the decomposition and the reliability of subsequent processing. Although researchers have attempted to combine EMD / EEMD with wavelet thresholding, correlation filtering, and other techniques to form hybrid denoising strategies, achieving results in certain specific applications, mode aliasing still makes it difficult to completely separate useful signal features from noise at the mode level, leading to information loss or incomplete denoising. The introduction of Variational Mode Decomposition (VMD) marks a significant advancement in adaptive signal decomposition. VMD constructs and solves variational optimization problems to adaptively determine the center frequency and bandwidth of each mode, achieving quasi-orthogonal mode separation and effectively suppressing mode aliasing. Denoising methods based on Virtual Mode Decomposition (VMD) typically utilize their decomposition capabilities to break down signals into a series of narrow-band intrinsic mode functions (IMFs). They then distinguish between noise-dominant and signal-dominant IMFs based on certain criteria, and reconstruct the signals after filtering or screening to achieve denoising. These methods have demonstrated superior accuracy and robustness compared to EMD methods in fields such as structural deformation monitoring and mechanical vibration analysis. However, the performance of VMD largely depends on the pre-setting of two key parameters: the penalty factor and the number of mode decompositions. In practical applications, these parameters are often determined empirically or through trial and error, lacking an adaptive selection mechanism suitable for different signal characteristics and noise backgrounds, which greatly limits its application potential in automated and intelligent monitoring systems.

[0005] Although the above methods improve signal processing capabilities to some extent, they still have the following significant limitations in practical applications of bridge dynamic strain monitoring: (1) The adaptive capability of mode decomposition parameters is weak and the noise resistance is insufficient: The performance of traditional VMD algorithms depends heavily on preset parameters. Faced with the characteristics of dynamic changes in the signal-to-noise ratio and significant non-stationary characteristics of bridge dynamic strain signals, fixed parameter settings and a single stopping criterion are difficult to achieve optimal decomposition, thus affecting the accuracy and reliability of subsequent processing stages.

[0006] (2) The algorithm's collaborative mechanism is superficial, and noise suppression is incomplete: Existing denoising strategies are relatively simple and lack sufficient collaboration. For example, after the initial decomposition, some IMFs are directly selected for reconstruction or input into SOBI, failing to fully consider the problem that noise and signal components still have coupling residues after the initial separation. In addition, the noise components separated from SOBI are often directly discarded, which can easily cause effective signal loss or reconstruction distortion due to the estimation bias of the mixing matrix or the correlation between components, making it impossible to achieve deep denoising and high-fidelity recovery.

[0007] (3) Low level of intelligence in signal and noise component identification: Existing methods mostly rely on manually set thresholds (such as energy ratio, correlation coefficient, etc.) to distinguish noise from dominant signal components, lacking an adaptive discrimination mechanism. When signal characteristics change or the noise environment is complex, the classification results are unreliable, which can easily lead to noise residue or excessive signal deletion, affecting the accuracy of the noise reduction results.

[0008] Due to the limitations mentioned above, existing methods still fall short in terms of improving signal-to-noise ratio, reducing root mean square error, and maintaining waveform fidelity when processing low signal-to-noise ratio and non-stationary bridge dynamic strain signals, making it difficult to meet the increasingly demanding data quality requirements of structural health monitoring. Summary of the Invention

[0009] To address the aforementioned issues, this invention provides an improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI. By introducing an adaptive decomposition mechanism, constructing a deep collaborative architecture, and employing intelligent clustering identification and precise reconstruction strategies, it achieves efficient noise suppression and high-fidelity preservation of signal features.

[0010] The technical solution adopted in this invention is an improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI, comprising the following steps: S1, the original signal f(t) of the dynamic strain of the bridge is obtained through strain sensors. The original signal f(t) includes the dynamic response of the structure and the background noise of the environment. S2 improves the SVMD algorithm by using kurtosis and decomposition error as stopping criteria, and then decomposes the original signal f(t) to extract... The intrinsic mode functions are calculated, and the kurtosis value of each intrinsic mode function component is used as the feature vector; where the SVMD algorithm is a successive variational mode decomposition. S3. Based on the feature vector, a feature space is constructed. The intrinsic mode function components are classified by the K-means clustering algorithm to obtain the noise-dominant mode subset and the information-dominant mode subset, thereby reconstructing the noise component signal f1(t) and the initial noise-reduced signal f2(t) and completing the initial noise separation. S4. Construct a three-channel hybrid observation matrix X(t) = [f(t), f1(t), f2(t)] containing the original signal f(t), the noise component signal f1(t), and the initial denoised signal f2(t). T The SOBI algorithm is used to perform blind source separation on the mixed observation matrix X(t), and the separated source signals are estimated. and the mixing matrix A; S5, for the separated source signal The normalized kurtosis value of each component is calculated; the K-means clustering algorithm is reused to identify the noise-dominant source component; the identified noise component is zeroed at its frequency point to suppress broadband noise; a subset of effective information components is retained, and the estimated mixing matrix A is used for reverse reconstruction to obtain the final high-precision denoised signal.

[0011] Furthermore, S2 includes the following steps: S21, the original signal f(t) can be decomposed into two types of signals, namely the k-th order modal component. and residual signal ; Residual signal Including the sum of first mode and undecomposed parts ; The i-th modal component is one of the sub-signal components obtained after decomposing the original signal f(t); S22, Construct constraints; Modal compactness constraints: (1) In the formula: It is the center frequency of the k-th mode. It is a convolution operator; Represents the k-th modal component bandwidth energy; It is the instantaneous rate of change of the signal; Here, t is the impulse function; t is the time variable; j represents the imaginary unit. Spectral Separability Constraint: Selecting an appropriate filter to achieve residual signal With the k-th modal component The spectral overlap should be minimized, and the frequency response of the suitable filter should be... for: (2) The established constraints are: (3) In the formula: The impulse response of the filter is given by equation (2); The residual signal was measured. In the filter Energy within the passband; Indicates frequency, Indicates the center frequency; Indicates the bandwidth control factor; Modal confusion avoidance constraints: using constraints with and The frequency response of the filter that minimizes the constraint of overlapping frequencies. for: (4) The established minimization constraints are: (5) In the formula: The impulse response of the filter in equation (4); The k-th modal signal was measured. The sum of energy within the passband of the filter for the first k-1 modes; S23 employs the VMD algorithm, transforming the constrained problem of S22 into an unconstrained problem by constructing an augmented Lagrangian function, and then using the alternating direction multiplier method to iteratively minimize it. In each iteration of SVMD, the k-th modal component is updated. With center frequency Continue until the set stopping criteria are met.

[0012] Furthermore, the stopping criterion in S2 is a joint judgment based on the kurtosis threshold and the reconstruction error threshold, and the kurtosis value is calculated using equation (6): (6) In the formula: μ is the i-th modal component The mean, σ is The standard deviation; K represents the kurtosis value, and E represents the mathematical expectation operator.

[0013] Furthermore, the normalized reconstruction error is calculated using equation (7): (7) This represents the normalized reconstruction error.

[0014] Furthermore, in step S3, all intrinsic mode function components belonging to the noise-dominant mode subset in the clustering results are summed in the time domain to reconstruct the noise component signal f1(t); all intrinsic mode function components belonging to the information component dominant mode subset in the clustering results are summed in the time domain to reconstruct the initial denoised signal f2(t).

[0015] Furthermore, in step S3, a feature space is constructed based on the feature vectors, and the intrinsic mode function components are classified using the K-means clustering algorithm, including the following steps: S31, Initialization: Take the dataset consisting of kurtosis values ​​calculated from each component after SVMD decomposition as input, and randomly select two kurtosis values ​​from this dataset as the initial cluster centers of the K-means algorithm; S32, Assign sample points: Calculate the Euclidean distance between each sample point and each cluster center, and assign the sample point to the cluster containing the nearest cluster center; S33, Update cluster centers: Calculate the mean of all sample points in each cluster and use it as the new cluster center; S34, repeat S322 and S33 until the cluster centers no longer change or the predetermined number of iterations is reached; S35, Output: Two clusters are obtained in the end, each containing a set of sample points, thus obtaining two clear classification results, namely the noise-dominant mode subset and the information-dominant mode subset.

[0016] Furthermore, S4 includes the following steps: S41, the mixed observation matrix X(t) is whitened to eliminate the instantaneous correlation between its components; the whitened signal Z(t) is obtained by solving the whitening matrix W: (8) S42, Set a set of fixed delays , j represents the index of the different time delay points used to calculate the covariance matrix; calculate the whitened signal Z(t) at each time delay. The sampling covariance matrix under : (9) E is calculated using equation (6); Indicates the whitening signal at time point The value is used to capture the correlation of the signal at different time points; express transpose, and The relationship between them is matrix multiplication; S43, the covariance matrix obtained from S42 Perform a joint approximate diagonalization algorithm to obtain an orthogonal matrix U; S44, after obtaining the orthogonal matrix U, calculate the separated source signals. and the original hybrid matrix , W + Whitening matrix W The pseudo-inverse matrix.

[0017] Furthermore, S5 is reverse reconstructed using equation (10): (10) In the formula: The reconstructed observation signal vector, To be The vector is formed by retaining the source signal components and setting the rest to zero; B is the inverse of the mixing matrix A.

[0018] The beneficial effects of this invention are: (1) Significantly improved signal decomposition accuracy and adaptive capability: In view of the problem that traditional methods such as VMD are difficult to determine the number of modes and are prone to over-decomposition or under-decomposition in strong noise environment, this invention introduces a dual stopping criterion based on kurtosis detection and energy conservation principle into SVMD, combining the prior knowledge of noise with the completeness requirements of signal decomposition, so that the algorithm can autonomously judge the decomposition process, adaptively determine the optimal number of modes and effectively suppress noise over-decomposition. This improvement not only effectively suppresses the mode mixing and over-decomposition phenomenon caused by noise, but also significantly improves the extraction accuracy and robustness of useful components in non-stationary and nonlinear bridge dynamic strain signals.

[0019] (2) Two-level collaborative architecture achieves deeper noise suppression: Traditional methods often rely on single decomposition or filtering methods, which are limited in performance under complex noise backgrounds. This invention constructs an improved two-level noise reduction mechanism that combines SVMD and SOBI. First, coarse separation (initial noise separation) is achieved through SVMD. Then, a three-channel hybrid observation matrix of the original signal, noise components, and initial screening signal is constructed to provide multi-dimensional input for SOBI. Then, SOBI is used to perform blind source separation on the aliased observation signal to achieve secondary deep noise reduction. After outputting the source signal component set, the dominant noise frequency is set to zero (preserving effective information of the edge frequency band), which effectively solves the problem of coupling between residual noise and real signal components in the initial separation. This achieves more thorough noise suppression and higher-fidelity signal reconstruction. Through secondary noise suppression and signal reconstruction, a systematic collaborative noise reduction process is formed.

[0020] (3) Efficient and intelligent identification of noise-signal components: Existing methods often rely on manually set threshold indicators, which makes it difficult to robustly distinguish between noise and effective components. This invention proposes a kurtosis-based double K-means clustering strategy, which performs feature clustering at the modal layer (IMF components after SVMD decomposition) and the source signal layer after SOBI separation, respectively. By making full use of multi-dimensional statistical characteristics, it achieves adaptive and high-precision separation of noise and information components, greatly reducing the need for manual intervention and improving the applicability of the algorithm in complex working conditions.

[0021] (4) Noise suppression and signal structure integrity preservation: In view of the problem that broadband interference may remain in the noise components after SOBI separation, this invention does not use traditional filtering or direct elimination methods, but innovatively adopts the processing method of frequency point zeroing combined with anti-mixing reconstruction. Under the premise of preserving useful frequency band information to the maximum extent, noise is suppressed, thereby significantly improving the signal-to-noise ratio and waveform fidelity of the output signal and avoiding distortion of useful components or introduction of secondary distortion. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a flowchart of an embodiment of the present invention based on an improved SVMD combined with SOBI noise reduction algorithm.

[0024] Figure 2 This is a block diagram illustrating the principle of the SOBI algorithm in an embodiment of the present invention.

[0025] Figure 3 This is a schematic diagram illustrating the principle of the Kmeans algorithm in an embodiment of the present invention.

[0026] Figure 4 The simulated signal for dynamic strain simulation in this embodiment of the invention is shown in (a), where (a) is the signal after noise addition and (b) is the corresponding spectrum.

[0027] Figure 5 The diagram shows the decomposition effect of the improved SVMD algorithm according to an embodiment of the present invention; where (a) is the SVMD decomposition and (b) is the corresponding spectrum diagram.

[0028] Figure 6 This is the IMF classification result of K-means in the embodiment of the present invention.

[0029] Figure 7 This is the hybrid observation matrix of this invention embodiment; where (a) is the signal retained after processing, (b) is the noise signal after processing, and (c) is the original signal.

[0030] Figure 8 This is the source signal component set of the embodiment of the present invention; wherein (a) is the first SOBI demixing component, (b) is the second SOBI demixing component, and (c) is the third SOBI demixing component.

[0031] Figure 9 This is a noise reduction effect diagram of an embodiment of the present invention.

[0032] Figure 10 These are dynamic strain signals collected on-site in embodiments of the present invention; wherein (a) is a working condition with a speed of 90 km / h, (b) is a working condition with a speed of 100 km / h, (c) is a working condition with a speed of 110 km / h, and (d) is a working condition with a speed of 120 km / h.

[0033] Figure 11These are comparison diagrams of dynamic strain signals before and after denoising in an embodiment of the present invention; where (a) is the working condition with a speed of 90km / h, (b) is the working condition with a speed of 100km / h, (c) is the working condition with a speed of 110km / h, and (d) is the working condition with a speed of 120km / h. Detailed Implementation

[0034] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0035] Example An improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI, such as... Figure 1 As shown, it includes the following steps: S1. The original dynamic strain signal f(t) of the bridge is obtained using a strain sensor. This signal contains the dynamic response of the structure and the background noise of the environment.

[0036] S2, the improved SVMD algorithm is applied to decompose the original signal f(t) and extract... There are 10 intrinsic mode functions (IMFs). The kurtosis value of each IMF component is calculated as an eigenvector.

[0037] VMD Algorithm Basics: Variational mode decomposition is a method for solving variational problems based on the concepts of classical Wiener filtering, Hilbert transform, and frequency mixing. It can be written as a constrained optimization problem as follows: (1) In the formula: f(t) is the original signal; u k This represents the k-th modal component (IMF), i.e., the sub-signal obtained after decomposition; Here, k represents the center frequency of each modal component, and k is the number of iterations. This indicates a constraint condition, specifying that the sum of the decomposed signals must equal the original signal; It is the partial derivative with respect to time t (physically meaning the instantaneous rate of change of the signal); t is the time variable; j represents the imaginary unit ( In signal processing, it is often used for frequency domain representation.

[0038] with u k The physical meanings are the same, the difference being that t in parentheses emphasizes that the signal is a function of time (continuous domain representation); in discrete implementations, t may be replaced by the sampling index n, but the physical meaning remains unchanged.

[0039] Let be the impact function, and its expression is: (2) Introducing a secondary penalty factor The augmented Lagrange function, together with the constrained variational problem, solves the aforementioned variational problem, transforming it into an unconstrained variational problem, thus forming the extended Lagrange function expression: (3) In the formula: As a secondary penalty factor, through To adjust the completeness of the variational mode decomposition method; This is the input signal.

[0040] λ(t) is the Lagrange multiplier function, a continuous-time function used to enforce constraints. During optimization, it acts as a "penalty weight," ensuring that the sum of the decomposed modes matches the original signal. Physically, it represents the adjustment amount for the degree of constraint violation in the time domain. {λ} denotes the set of Lagrange multipliers.

[0041] L represents the Lagrangian function. Represents the square of the L2 norm; The inner product operation is represented by the inner product of the Lagrange multiplier and the constraint condition, which is used to strengthen the constraint.

[0042] Therefore, the optimal solution of the constrained variational model can be obtained: (4) (5) This indicates that the k-th modal component is at frequency The updated value at that point corresponds to iteration step n+1; The Fourier transform of the original signal f represents the overall frequency content of the signal in the frequency domain; This indicates that the i-th modal component is at frequency The current estimate at (during iteration); Represent the Lagrange multipliers in the frequency domain; This represents the frequency value in the frequency domain; physically, it represents the frequency components of a signal and is a fundamental variable in frequency domain analysis. In the formula, Used to evaluate the values ​​of a mode at different frequencies; This represents the updated value of the center frequency of the k-th mode at iteration step n+1; This represents the current estimate of the k-th modal component at the frequency (during iteration).

[0043] Considering the inherent nonstationarity and nonlinearity of actual bridge dynamic strain signals, this embodiment of the invention uses successive variational mode decomposition (SVMD) to decompose the signal. Compared with variational mode decomposition (VMD) which decouples all frequency components at once, SVMD iteratively extracts intrinsic mode functions in frequency order. A dual stopping criterion based on kurtosis detection and energy conservation principles is introduced into SVMD.

[0044] Suppose that the original signal f(t) can be decomposed into two types of signals, namely the k-th order mode component. and residual signal .

[0045] (6) where: residual signal The sum of k-1 order modes and undecomposed parts .

[0046] It represents the i-th (order) mode component, which is one of the sub-signal components obtained after decomposing the original signal f(t); This is a general representation, representing modal components of any order; Specifically refers to the k-th modal component.

[0047] To ensure the above relationship holds, the following constraints must be satisfied: (1) Modal compactness constraint: Each mode is compact near its center frequency, therefore, it can be achieved by minimizing the constraint, which is: (7) In the formula: It is the center frequency of the k-th mode. It is a convolution operator. Represents the k-th modal component The bandwidth energy is calculated using the Alternating Directional Multiplier Method (ADMM) iteratively. In each iteration, the modal components are updated. and center frequency The value of J1 is gradually reduced. This process ensures that each modal component gradually converges to near its center frequency, achieving adaptive decomposition of the signal, as shown in Equation (13).

[0048] (2) Spectral separation constraint: Implemented by selecting a suitable filter. and The spectral overlap should be minimized. To ensure this constraint can be stably achieved, a suitable filter was selected, and its frequency response... for: (8) This represents the bandwidth control factor.

[0049] The established constraints are: (9) In the formula: The impulse response (in time domain representation) of the filter in equation (8) corresponds to the frequency response. .

[0050] The residual signal was measured. In the filter Energy within the passband. Minimize. This helps ensure that the residual signal does not contain mode-related frequency components, thereby promoting spectral separation and making the decomposed modes purer.

[0051] (3) Modal confusion avoidance constraint: By minimizing the two criteria J1 and J2, it is possible to cause the k-th mode to mix with the first k-1 modes. Therefore, using the constraints with J1 and J2, we can avoid the k-th mode mixing with the first k-1 modes. and The frequency response of the filter that minimizes the constraint of overlapping frequencies. for: (10) It is a filter used for the k-th mode itself, whose frequency response is designed around the center frequency ω of the k-th mode. k The purpose is to extract or process the frequency components of the k-th mode.

[0052] It is a filter used for the first k-1 modes, but also around the center frequency ω of the k-th mode. k The design aims to suppress frequency components in the first k-1 modes that overlap with the k-th mode, thereby avoiding mode confusion.

[0053] The established minimization constraints are: (11) In the formula: Let be the impulse response of the filter in equation (10). The k-th modal signal was measured. The sum of energy within the passband of the filter for the first k-1 modes.

[0054] (4) Signal completeness constraint: The last constraint is to ensure that f(t) can be completely reconstructed from the unprocessed parts of the k modes and the signal: (12) After satisfying the above constraints, when k-1 modes are known, the k-th mode component can be expressed as a variational problem consisting of a combination of J1, J2, and J3, and its mathematical model is as follows: (13) In the formula: To balance the parameters of J1, J2, and J3. It is the k-th modal component to be determined; It is the center frequency of the k-th modal component; It is the residual signal, which is the remaining signal part containing other modes and noise after the k-th mode is decomposed.

[0055] Employing the VMD algorithm, the constrained problem is transformed into an unconstrained problem by constructing an augmented Lagrangian function, and the minimization problem is solved iteratively using the alternating direction multiplier method. In each iteration of SVMD, the modes are updated. Its center frequency Continue until the set stopping criteria are met.

[0056] Bridge dynamic strain signals are often accompanied by significant background noise. Traditional stopping criteria are difficult to distinguish between noise and effective signals and cannot guarantee the physical accuracy of the decomposition results. In order to improve the performance of SVMD decomposition, automatically determine the optimal number of modes and suppress noise over-decomposition, this embodiment introduces a dual stopping criterion based on the statistical characteristics of noise and the principle of energy conservation under the ADMM iterative framework. By coordinating the judgment of kurtosis threshold and reconstruction error threshold, an adaptive balance between noise suppression and feature preservation is achieved, which significantly improves the processing accuracy and robustness of bridge dynamic strain signals. The kurtosis value and normalized reconstruction error are calculated as shown in Equations (14) and (15).

[0057] (14) In the formula: μ is The mean, σ is The standard deviation.

[0058] K represents the kurtosis value, and E represents the mathematical expectation operator (i.e., statistical average), which is the average of all samples of a random signal in a probabilistic sense.

[0059] (15) This represents the normalized reconstruction error.

[0060] Equation (14) identifies the noise mode by using the statistical difference between the kurtosis of noise and the effective signal. Equation (15) verifies the completeness of the decomposition by the principle of energy conservation. The thresholds of the two are judged in concert, and the process stops only when the current mode is noise (K is close to the threshold) and the overall error is less than 1‰. This adaptively balances noise suppression and feature preservation, improving processing accuracy and robustness. It overcomes the contradiction between decomposition completeness (extracting all effective signals) and fidelity (avoiding noise being mistakenly analyzed as an effective mode).

[0061] S3. Based on the aforementioned kurtosis feature vectors, a feature space is constructed, and the K-means clustering algorithm is applied to classify the IMF components. Using Euclidean distance as the metric, the cluster centers are iteratively updated until convergence, yielding two clear classification results: dividing the IMFs into a noise-dominant mode subset and an information-dominant mode subset. All IMF components belonging to the noise-dominant mode subset in the clustering results are directly summed in the time domain to reconstruct the noise component signal f1(t); specifically, if this subset contains IMFs 1, 3, and 5, then... The superimposed signal f1(t) is the noise estimate initially separated from the original signal. Similarly, the initial denoised signal f2(t) is reconstructed by summing all IMF components belonging to the "information component dominant mode subset" in the clustering results in the time domain; if this subset contains IMFs 2 and 4, then... The superimposed signal f2(t) is the signal obtained after removing the IMF initially identified as noise, and retains the main structural response information, thus completing the initial noise reduction.

[0062] like Figure 3 As shown, the K-means algorithm is a distance-based clustering algorithm. It calculates the distance between the target dataset and the centroids of the clusters, and then partitions the data according to these distances, increasing intra-cluster similarity and decreasing inter-cluster similarity. The K-means algorithm process is as follows: (1) Initialization: The dataset consisting of kurtosis values ​​calculated from each component after decomposition of SVMD is used as input, and two kurtosis values ​​are randomly selected from this dataset as the initial cluster centers of the K-means algorithm.

[0063] (2) Assigning sample points: For each sample point, calculate its Euclidean distance to each cluster center and assign the sample point to the cluster containing the nearest cluster center; (3) Update cluster centers: For each cluster, calculate the mean of all its sample points and use the mean as the new cluster center; (4) Repeat steps 2 and 3 until the cluster centers no longer change or the predetermined number of iterations is reached; (5) Output results: Two clusters are finally obtained, each containing a set of sample points, thus obtaining two clear classification results, namely the noise-dominant mode subset and the information component-dominant mode subset.

[0064] S4. Construct a three-channel hybrid observation matrix X(t) = [f(t), f1(t), f2(t)] containing the original signal and its separated components. T The SOBI algorithm is used to perform blind source separation on the mixed observation matrix X(t), and the separated source signals are estimated. And the corresponding mixing matrix A.

[0065] Second-order blind identification (SOBI) is a typical blind source separation algorithm, and its principle block diagram is as follows: Figure 2 As shown, SOBI can effectively separate the source signal and its noise components from a mixed signal. Its advantage lies in the fact that it can estimate the source signal components using relatively few data points, and extract the original signal information completely while reducing noise interference, thus enabling further noise reduction of the signal.

[0066] For an n-dimensional statistically independent source signal, The m-dimensional observation signal is The transmission interference noise is .

[0067] In blind source separation, the source signal is the original, unmixed signal. This represents the first independent source signal component in the source signal vector, that is, the value of a specific source signal as a function of time t.

[0068] The observed signal is a mixed signal acquired through sensors or measuring devices, containing the combined effects of the source signal and noise. This represents the first observed signal component in the observed signal vector, i.e., the signal of one of the observed channels.

[0069] Noise can be caused by random errors during transmission or by environmental noise. This represents the value of the first noise component in the noise vector, i.e., the value of one of the noise signals as a function of time t.

[0070] The linear mixture model can be expressed as: (16) In the formula: A is called the mixing matrix, which represents the mixing transformation relationship from the source signal S(t) to the observed signal X(t) in the linear mixing model; the observed signal X(t) is the aforementioned mixing observation matrix. .

[0071] Blind source separation aims to find a separation matrix such that X(t) can be used to obtain an estimate of the source signal. : (17) In the formula: B is the (generalized) inverse matrix of A, which is the separation matrix.

[0072] For the blind source separation model described above, the steps for SOBI to perform blind source separation are as follows: (1) Calculate the whitening matrix W: Whiten the observed signal matrix X(t) to eliminate the instantaneous correlation between its components. The whitened signal Z(t) is obtained by solving the whitening matrix W (dimension n×m): (18) (2) Calculate the time delay covariance matrix Set a fixed delay. , j represents the index of different time delay points used to calculate the covariance matrix, and the whitened signal Z(t) is calculated at each time delay. The sampling covariance matrix under : (19) E is calculated using equation (14); Indicates the whitening signal at time point The value is used to capture the correlation of the signal at different time points. express transpose, Indicates whitening signal, and The relationship between them is matrix multiplication.

[0073] (3) Solve for the orthogonal matrix U by joint approximate diagonalization: For the covariance matrix obtained in step (2) Performing the joint approximate diagonalization algorithm yields an orthogonal matrix U that satisfies the following equation: It is a set of diagonal matrices.

[0074] (20) Equation (20) is a standard step in blind source separation (especially the SOBI algorithm) and is known in the art.

[0075] (4) Source signal separation estimation: After obtaining the orthogonal matrix U, the separated source signals can be calculated. : (twenty one) Further, the separation matrix can be obtained. and mixture matrix (W) +(This is the pseudo-inverse of the whitening matrix W).

[0076] S5. For the separated source signal component set S(t), calculate the normalized kurtosis value of each component. Apply the K-means algorithm again, and based on this feature, reuse the K-means clustering algorithm to identify the noise-dominant source components. Zero-frequency processing is performed on the identified noise components to suppress their broadband noise. A subset of effective information components is retained, and using the estimated mixing matrix A, an inverse mixing operation (reverse reconstruction) is performed to obtain the final high-precision denoised signal.

[0077] Solving the mixture matrix: removing Unwanted independent source signal components are reconstructed: (twenty two) In the formula: Xᵣ(t) is the reconstructed observation signal vector, ideally Xᵣ(t)=AS(t), Yᵣ(t) is the vector after retaining the source signal component in Y(t) and setting the rest to zero; B is the (generalized) inverse matrix of A.

[0078] To evaluate the denoising effect and applicability of the proposed method for acquiring bridge dynamic strain signals, the following steps were taken: First, a noisy dynamic strain signal consistent with the bridge structure was simulated using MATLAB. Second, the simulated signal was processed using a bridge dynamic strain denoising method based on an improved SVMD combined with SOBI. Finally, different denoising methods before the improvement were introduced and compared with the proposed method from a quantitative and intuitive perspective, verifying the effectiveness of the process.

[0079] To objectively evaluate the noise reduction performance of the proposed denoising algorithm for bridge dynamic strain signals, and considering that actual bridge dynamic strain signals generally exhibit nonlinear and non-stationary characteristics, and primarily display low-frequency multi-mode decaying oscillations under excitation, this embodiment constructs a nonlinear, non-stationary random signal model using the MATLAB platform to simulate the bridge dynamic strain signals. The mathematical expression is: (twenty three) In the formula: Q i Let be the amplitude of the i-th superimposed signal; O i t is the attenuation factor; i f is the delay time; i M is the main frequency; M is the number of superimposed signals.

[0080] Because real-world engineering environments contain a certain degree of noise interference, four sets of Gaussian white noise with signal-to-noise ratios (SNRs) of 5dB, 10dB, 15dB, and 20dB were randomly added to the simulated signal to make it closer to the actual acquired dynamic strain signal and enhance the algorithm's practicality. The dynamic strain simulation signal with a SNR of 5dB is shown below. Figure 4 (a) and (b).

[0081] The simulated signal was processed into 15 decomposition components using an improved SVMD algorithm, and the kurtosis value of each intrinsic mode component (IMF) was calculated. K-means was then used to automatically classify the IMFs into noise mode components and useful signal mode components, such as... Figure 5 In (a) and (b), and Figure 6 As shown.

[0082] After obtaining the IMF classification results, the signal is reconstructed to obtain the retained signal and noise signal. Combined with the original signal, a three-channel hybrid observation matrix containing the original signal and its separated components is constructed, such as... Figure 7 As shown in (a), (b), and (c), the SOBI algorithm is used to perform blind source separation on the mixing matrix, estimating the source signal component set. For the separated source signal component set, as shown... Figure 8 As shown in (a), (b), and (c), the K-means clustering algorithm is used to identify the noise-dominant source components. The identified noise components are then zeroed out at their frequencies to suppress broadband noise, resulting in a final high-precision denoised signal. Figure 9 As shown.

[0083] To further evaluate the advantages of the denoising effect of the method in the embodiments of the present invention, a quantitative analysis of the signal denoising is performed using two common signal denoising performance indicators: signal-to-noise ratio and root mean square error. (1) Signal-to-noise ratio (SNR) is usually the dimensionless ratio of the noise power contained in the signal power. The formula is as follows: (twenty four) (2) The formula for the root mean square error (RMSE) between the original signal and the denoised signal is as follows: (25) In the formula: Represents the original signal. This represents the denoised signal. This represents the number of sampling points.

[0084] The above two indicators are used to comprehensively evaluate the signal denoising effect. The higher the SNR value and the lower the RSME value of the denoised signal, the better the denoising effect. Four sets of noisy analog random signals with noise intensities of 5dB, 10dB, 15dB and 20dB were denoised using different denoising methods, and the evaluation index values ​​of the denoising methods were obtained, as shown in Table 1.

[0085] Table 1 Evaluation of Noise Reduction Effect for Different Intensities

[0086] A medium-low speed maglev line is currently in operation, but only during the daytime. Therefore, monitoring the dynamic strain variation at mid-span of the continuous beam bridge on this line can only be conducted at night during non-operational hours. The experiment was designed to have a maglev train pass over the continuous beam bridge at speeds of 90, 100, 110, and 120 km / h, corresponding to four different operating conditions. The Donghua DH3822 portable dynamic signal testing and analysis system was used to monitor the dynamic strain at mid-span of the continuous beam. Dynamic displacement data was collected a few seconds before the maglev train entered the bridge. Data collection was stopped a few seconds after the train passed the bridge and once the data stabilized, preparations were made for the next data collection. The data collection frequency was 200 Hz. The raw dynamic strain signals for the four operating conditions were obtained as follows: Figure 10 As shown in (a), (b), (c) and (d).

[0087] By observing the raw dynamic strain signals collected under various operating conditions, it was found that the signals were all mixed with noise interference, which would affect the judgment of their operating status. Therefore, it is necessary to perform noise reduction preprocessing on the dynamic strain signals.

[0088] The dynamic strain signal obtained after processing the original dynamic strain signal using the method of this embodiment is as follows: Figure 11 As shown in (a), (b), (c), and (d), the denoising effect diagrams clearly demonstrate that the denoising method of this invention can effectively remove various noises from the dynamic strain signal and has good adaptability to bridge dynamic strain signals at different vehicle speeds.

[0089] Because real-world dynamic strain signals are affected by complex factors, it is impossible to obtain a noise-free signal. Therefore, the signal-to-noise ratio (SNR) and root mean square error (RMSE) cannot be used to further evaluate the quality of signal denoising. Therefore, the following three evaluation metrics are adopted for the denoising quality of real-world dynamic strain signals: (1) Signal bias (BIAS) refers to the deviation between the original signal and the estimated signal after denoising, reflecting the overall trend of the denoising result being consistently higher or lower than the original signal.

[0090] (26) (2) Signal-to-Energy Ratio (SER) is a quantitative assessment from the perspective of energy, reflecting the similarity of energy before and after denoising.

[0091] (27) (3) Noise mode (NM) is also a quantitative assessment method from the perspective of energy.

[0092] (28) In the formula: Represents the original signal. This represents the denoised signal. This represents the number of sampling points.

[0093] Signal-to-energy ratio and noise modulus are two indicators considered from an energy perspective. The effectiveness of denoising the bridge dynamic strain signal is comprehensively evaluated using these three indicators. The original signal was denoised using SVMD, VMD, and the method described in this paper (an embodiment of the invention). The evaluation indicators for the denoised signal are shown in Table 2.

[0094] Table 2 Evaluation table of noise reduction effect under different working conditions

[0095] In Table 2, "-3.31e-17" represents -3.31 × 10 -17 .

[0096] From the perspective of signal image evaluation, signal deviation reflects the overall trend of the denoising result being consistently higher or lower than the original signal. The closer the value is to 0, the more accurate the estimation of the amplitude scale by the denoising algorithm is, indicating that there is no systematic amplification or reduction, and the denoised signal waveform best matches the original signal in terms of overall amplitude. Under the four operating conditions, the signal deviation value of the method in this embodiment is the lowest among the other methods, indicating that the denoising method in this embodiment retains more detailed information and the denoised signal is smoother.

[0097] From an energy perspective, the denoising effect was evaluated: the signal-to-energy ratios of the four denoising methods were all greater than 99.8%, indicating that only noise was removed; furthermore, noise was considered a low-probability event, therefore, a higher NM value was better. The noise moduli of the methods in this embodiment were 10.30, 11.15, 13.86, and 10.15, respectively, all higher than the other methods. Therefore, the method in this embodiment achieves the best denoising effect while preserving the details of the original signal.

[0098] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. An improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI, characterized in that, Includes the following steps: S1, the original signal f(t) of the dynamic strain of the bridge is obtained through strain sensors. The original signal f(t) includes the dynamic response of the structure and the background noise of the environment. S2 improves the SVMD algorithm by using kurtosis and decomposition error as stopping criteria, and then decomposes the original signal f(t) to extract... Each intrinsic mode function is used to calculate the kurtosis value of each intrinsic mode function component as an eigenvector; The SVMD algorithm is a successive variational mode decomposition. S3. Based on the feature vector, a feature space is constructed. The intrinsic mode function components are classified by the K-means clustering algorithm to obtain the noise-dominant mode subset and the information-dominant mode subset, thereby reconstructing the noise component signal f1(t) and the initial noise-reduced signal f2(t) and completing the initial noise separation. S4. Construct a three-channel hybrid observation matrix X(t) = [f(t), f1(t), f2(t)] containing the original signal f(t), the noise component signal f1(t), and the initial denoised signal f2(t). T The SOBI algorithm is used to perform blind source separation on the mixed observation matrix X(t), and the separated source signals are estimated. and the mixing matrix A; S5, for the separated source signal Calculate the normalized kurtosis value for each component; The K-means clustering algorithm is reused to identify the noise-dominant source components; the identified noise components are zeroed out at their frequencies to suppress broadband noise. By retaining a subset of effective information components and using the estimated mixing matrix A, reverse reconstruction is performed to obtain the final high-precision denoised signal.

2. The improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI as described in claim 1, characterized in that, S2 includes the following steps: S21, the original signal f(t) can be decomposed into two types of signals, namely the k-th order modal component. and residual signal ; Residual signal Including the sum of first mode and undecomposed parts ; The i-th modal component is one of the sub-signal components obtained after decomposing the original signal f(t); S22, Construct constraints; Modal compactness constraints: （1） In the formula: It is the center frequency of the k-th mode. It is a convolution operator; Represents the k-th modal component bandwidth energy; It is the instantaneous rate of change of the signal; Here, t is the impulse function; t is the time variable; j represents the imaginary unit. Spectral Separability Constraint: Selecting an appropriate filter to achieve residual signal With the k-th modal component The spectral overlap should be minimized, and the frequency response of the suitable filter should be... for: （2） The established constraints are: （3） In the formula: The impulse response of the filter is given by equation (2); The residual signal was measured. In the filter Energy within the passband; Indicates frequency, Indicates the center frequency; Indicates the bandwidth control factor; Modal confusion avoidance constraints: using constraints with and The frequency response of the filter that minimizes the constraint of overlapping frequencies. for: （4） The established minimization constraints are: （5） In the formula: The impulse response of the filter in equation (4); The k-th modal signal was measured. The sum of energy within the passband of the filter for the first k-1 modes; S23 transforms the constrained problem of S22 into an unconstrained problem by constructing an augmented Lagrangian function, and then uses the alternating direction multiplier method to iteratively solve for minimization; in each iteration of SVMD, the k-th modal component is updated. With center frequency Continue until the set stopping criteria are met.

3. The improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI as described in claim 2, characterized in that, The stopping criterion in S2 is a joint judgment based on the kurtosis threshold and the reconstruction error threshold. The kurtosis value is calculated using equation (6): （6） In the formula: μ is the i-th modal component The mean, σ is The standard deviation; K represents the kurtosis value, and E represents the mathematical expectation operator.

4. The improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI as described in claim 3, characterized in that, The normalized reconstruction error is calculated using equation (7): （7） This represents the normalized reconstruction error.

5. The improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI as described in claim 1, characterized in that, In step S3, all intrinsic mode function components belonging to the noise-dominant mode subset in the clustering results are summed in the time domain to reconstruct the noise component signal f1(t); all intrinsic mode function components belonging to the information component dominant mode subset in the clustering results are summed in the time domain to reconstruct the initial denoised signal f2(t).

6. The improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI as described in claim 1, characterized in that, In step S3, a feature space is constructed based on the feature vectors, and the intrinsic mode function components are classified using the K-means clustering algorithm, including the following steps: S31, Initialization: Take the dataset consisting of kurtosis values ​​calculated from each component after SVMD decomposition as input, and randomly select two kurtosis values ​​from this dataset as the initial cluster centers of the K-means algorithm; S32, Assign sample points: Calculate the Euclidean distance between each sample point and each cluster center, and assign the sample point to the cluster containing the nearest cluster center; S33, Update cluster centers: Calculate the mean of all sample points in each cluster and use it as the new cluster center; S34, repeat S322 and S33 until the cluster centers no longer change or the predetermined number of iterations is reached; S35, Output: Two clusters are obtained in the end, each containing a set of sample points, thus obtaining two clear classification results, namely the noise-dominant mode subset and the information-dominant mode subset.

7. The improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI as described in claim 1, characterized in that, S4 includes the following steps: S41, the mixed observation matrix X(t) is whitened to eliminate the instantaneous correlation between its components; the whitened signal Z(t) is obtained by solving the whitening matrix W: （8） S42, Set a set of fixed delays , j represents the index of the different time delay points used to calculate the covariance matrix; calculate the whitened signal Z(t) at each time delay. The sampling covariance matrix under : （9） E is calculated using equation (6); Indicates the whitening signal at time point The value is used to capture the correlation of the signal at different time points; express transpose, and The relationship between them is matrix multiplication; S43, the covariance matrix obtained from S42 Perform a joint approximate diagonalization algorithm to obtain an orthogonal matrix U; S44, after obtaining the orthogonal matrix U, calculate the separated source signals. and the original hybrid matrix ，W + Whitening matrix W The pseudo-inverse matrix.

8. The improved adaptive noise reduction method for bridge dynamic strain signals using SVMD combined with SOBI as described in claim 1, characterized in that, The S5 is reverse reconstructed using equation (10): （10） In the formula: The reconstructed observation signal vector, To be The vector is formed by retaining the source signal components and setting the rest to zero; B is the inverse of the mixing matrix A.

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