A method for sparse adaptive reconstruction based on dynamic adjustment and binary search

Abstract

The application discloses a dynamic adjustment and dichotomy search sparse adaptive reconstruction method. The method obtains compressed observation values by constructing a random Gaussian observation matrix, and uses a discrete wavelet transform to perform sparse representation on an original signal. In the iterative reconstruction process, a dynamic scaling factor guided cumulative energy proportion atom dynamic adjustment mechanism is first introduced, and a dichotomy search strategy is introduced to realize efficient sparse estimation. The method successfully creates a power quality disturbance signal reconstruction scheme which has sparse adaptivity, fast convergence and high noise robustness. Compared with OMP, original SAMP and other methods, the method can reduce the iteration number by 60%-80%, improve the reconstruction signal-to-noise ratio by 8-12 dB, and reduce the root mean square error by 10%-25%. The method has higher robustness and real-time performance in power quality disturbance signal reconstruction, and is suitable for compressed sampling, edge computing and high-speed signal reconstruction in a power quality monitoring system.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and compressed sensing technology, specifically relating to a sparse adaptive reconstruction method based on dynamic adjustment and binary search, which is suitable for rapid reconstruction and edge computing scenarios of power quality disturbance signals in power systems. Background Technology

[0002] With the continuous expansion of power systems and the rapid integration of various power electronic devices and renewable energy installations, power quality issues have become increasingly prominent in modern power grids. Multiple disturbance signals coexist, including harmonics, interharmonics, voltage flicker, voltage sags, voltage swells, voltage interruptions, voltage gaps, and voltage oscillations, exhibiting non-stationarity, transient nature, and complex and variable characteristics. This places higher demands on the data acquisition, transmission, and signal reconstruction capabilities of power quality monitoring systems. Traditional monitoring methods, based on the Nyquist sampling theorem, require a sampling frequency at least twice the highest signal frequency, resulting in massive amounts of sampled data and high storage and transmission costs, making it difficult to meet the application requirements of distributed monitoring, edge computing, and wireless sensing systems. How to reduce the sampling rate and data transmission volume while ensuring reconstruction accuracy has become a critical issue that urgently needs to be addressed in the field of power quality monitoring.

[0003] Compressed sensing technology provides an effective way to solve the above problems. This theory utilizes the sparsity of signals in a specific transform domain to achieve signal acquisition and reconstruction at rates far lower than the Nyquist sampling rate. In the compressed sensing framework, the performance of the reconstruction algorithm directly determines the quality of the final signal recovery. Among existing reconstruction algorithms, Orthogonal Matching Pursuit (OMP) and Compressed Sample Matching Pursuit (CoSaMP) are two classic greedy iterative algorithms that gradually identify the support set of the signal through iteration. OMP selects the atom most strongly correlated with the current residual in each iteration and updates the residual through orthogonal projection. It has high computational efficiency, but requires prior knowledge of the signal sparsity. However, the sparsity of actual power quality disturbance signals changes dynamically with the type of disturbance and operating conditions, making accurate acquisition difficult. CoSaMP improves convergence speed by selecting multiple atoms each time and supplementing with pruning operations. It also relies on prior information about sparsity; when the sparsity estimation is inaccurate, the reconstruction accuracy will significantly decrease.

[0004] The Sparse Adaptive Matching Pursuit (SAMP) algorithm overcomes the dependence on prior sparsity to some extent. This algorithm employs a phased incremental growth strategy, gradually expanding the support set size with a fixed step size until the residual convergence condition is met, thereby achieving adaptive estimation of unknown sparsity. However, when SAMP is applied to power quality disturbance signals with abrupt changes, spectral leakage and noise interference can cause the residuals to fail to converge below a preset threshold. Even if the main frequency components are accurately extracted, the residuals remain at a high level, leading the algorithm to erroneously continue expanding the support set, resulting in a severe overestimation of sparsity. As the support set size increases, the complexity of matrix operations rises significantly, and the computation time increases substantially. Simultaneously, the introduction of redundant atoms leads to overfitting, degrading the quality of the reconstructed signal, particularly when recovering key features such as sag depth and phase transitions. Existing techniques use fixed iteration counts or manually set sparsity upper limits for forced termination, but these methods cannot adapt to different types of disturbance signals, making it difficult to guarantee reconstruction accuracy while also compromising computational efficiency. Therefore, there is an urgent need for a compressed sensing reconstruction method that can reliably determine the reconstruction termination in environments with spectral leakage and noise interference without relying on sparsity priors.

[0005] Therefore, there is an urgent need for a compressed sensing reconstruction method that can reliably determine the reconstruction termination in environments with spectral leakage and noise interference without relying on sparsity priors, so as to improve the stability and practicality of power quality disturbance signal reconstruction. Summary of the Invention

[0006] The technical problem this application aims to solve is as follows: addressing the technical shortcomings of existing compressed sensing reconstruction algorithms in power quality disturbance signal processing, specifically including the fact that orthogonal matching pursuit and compressed sampling matching pursuit require prior knowledge of signal sparsity, which is difficult to obtain accurately in practice; sparseness adaptive matching pursuit uses a fixed step-size linear search strategy, resulting in slow convergence; and problems such as sparsity overestimation, iterative redundancy, decreased reconstruction accuracy, and insufficient robustness easily occur under spectral leakage and noise interference environments. This application proposes a power quality disturbance signal reconstruction method that can achieve fast sparsity estimation, effectively suppress the effects of noise and spectral leakage, reduce the number of iterations, and improve reconstruction accuracy and noise resistance without relying on sparsity priors.

[0007] To address the aforementioned technical issues, this application proposes a reconstruction method based on Dynamic Scaling Factor and Binary Search Sparse Adaptive Matching Pursuit (DSFBSAMP). This method organically combines a dynamic adjustment atom selection mechanism with a binary search strategy to construct an efficient and robust reconstruction framework. Specifically, the dynamic adjustment mechanism for the cumulative energy ratio atom dynamically determines the number of pre-selected atoms in each iteration based on the projected distribution of the residual energy, effectively suppressing pseudo-correlated atoms introduced by noise and spectral leakage, thus enhancing the algorithm's anti-interference capability. The binary search strategy replaces the linear step search of the traditional SAMP, reducing the number of iterations for sparsity estimation from linear to logarithmic, significantly improving convergence efficiency. Furthermore, this method uses the residual change as the update criterion for the binary search interval and combines it with the residual norm termination condition to achieve precise termination of the iteration process. This method includes the following steps:

[0008] S101 collects raw power quality disturbance signals including harmonics, interharmonics, voltage flicker, voltage interruption, voltage oscillation, voltage sag, voltage spike, and voltage rise. And construct a discrete time-domain sampling sequence of length N;

[0009] S102, Selecting the Compressed Sensing Sparse Transform Basis and random Gaussian observation matrix ;

[0010] S103, reconstruction begins using dynamic adjustment and binary search sparsity adaptive matching pursuit, the algorithm initializes the residuals. Support set index set Candidate set The binary search method has a lower bound of L=0, an upper bound of R=M, an intermediate value of K=M / 2, and a number of iterations. =1, iteration termination threshold Binary search decision threshold e, dynamic scaling factor Scaling factor increment ;

[0011] S104, Determine the current estimated sparsity using binary search. Calculate the atomic correlation vector Based on dynamic scaling factor The preselected atom set is determined according to the cumulative energy ratio criterion. Merge support sets and Obtain candidate set Calculate the inner product of the observation matrix submatrix corresponding to the candidate set and the observation vector y, and select the indices corresponding to the K largest inner products to update the support set. Calculate the reconstruction coefficients for the current iteration and update the residuals. ;

[0012] S105, Calculate the residual change between two adjacent iterations. ;

[0013] S106, Residual change calculated based on S105 To guide the binary search interval update and iteration termination determination, if If L > R, then the iteration is terminated and the algorithm jumps to S107; otherwise, if Then update the upper bound R=K and update the dynamic scaling factor. Otherwise, update the lower bound L=K; iteration count k=k+1, jump to S104;

[0014] S107 outputs the final reconstructed original signal. .

[0015] Optionally, the detailed steps of S102 include:

[0016] Considering the good sparsity of power quality perturbations under discrete wavelet transform basis, discrete wavelet transform basis is adopted as the sparse transform basis for power quality perturbations. The power quality disturbance signal of length N Convert to sparse coefficient vector Then, a random Gaussian observation matrix was used. Compressed observations yielded measured values. .

[0017] Optionally, the detailed steps of S103 include:

[0018] The iteration termination threshold The initial value is set to Dynamic scaling factor =0.1, scaling factor increment .

[0019] Optionally, the detailed steps of S104 include:

[0020] Calculate the atomic correlation vector Sort s in descending order, select the smallest integer n such that the accumulated energy of the first n atoms exceeds u times the total energy, and construct a pre-selected atom set using the indices of the n atoms. The reconstruction coefficients corresponding to the candidate set are calculated using least squares. Select the K largest coefficients from the indexes to update the support set. The reconstruction coefficients of the current iteration are calculated using least squares. and update the residuals. .

[0021] The DSFBSAMP method proposed in this application has the following advantages compared with traditional OMP, CoSaMP, and SAMP:

[0022] 1. Effectively Avoiding Sparsity Overestimation: This application employs a binary search strategy instead of the fixed-step linear search of traditional SAMP. The change in residual is used as the update criterion for the binary search interval. When the change in residual is less than a threshold, the upper bound of the search is tightened in a timely manner, effectively preventing the sparsity estimate from exceeding the true value. Simultaneously, the dynamic adjustment mechanism for the cumulative energy ratio atoms can accurately screen effective atoms under spectral leakage and noise interference, preventing redundant atoms from entering the support set. This fundamentally solves the sparsity overestimation problem caused by spectral leakage in traditional SAMP.

[0023] 2. Significantly improve computational efficiency: This application adopts a binary search strategy, which reduces the number of iterations for sparsity estimation from linear to logarithmic order, greatly reducing computation time, significantly improving the computational efficiency of the algorithm, and shortening the overall time required for reconstruction.

[0024] 3. Improved Reconstruction Accuracy: This application utilizes a dynamic scaling factor-guided cumulative energy ratio atom dynamic adjustment mechanism to dynamically select atoms with strong correlation to the residual, effectively suppressing spurious correlated atoms introduced by noise and spectral leakage. Under different noise conditions, the signal-to-noise ratio (RSNR) of the reconstructed signal is significantly improved, and the root mean square error (RMSE) is significantly reduced, with particularly significant advantages in non-stationary disturbances and spectral leakage scenarios.

[0025] 4. Enhanced noise robustness: This application employs a dynamic adjustment mechanism, which can dynamically adjust the stringency of atomic screening according to the residual evolution. It can effectively distinguish between real signal components and noise interference in a strong noise environment, making the algorithm suitable for high-noise application environments in actual power grids. Attached Figure Description

[0026] Figure 1 This is an overall flowchart of a SAMP reconstruction method based on dynamic adjustment and binary search as described in an embodiment of this application.

[0027] Figure 2 This is a schematic diagram illustrating the relationship between the residual norm change and the number of iterations in an embodiment of this application.

[0028] Figure 3 Let e ​​represent the impact of RSNR and computational cost. Here, e is the binary search decision threshold of this application.

[0029] Figure 4Performance analysis of various methods under different compression ratios (CR). Among them, (a) shows the relationship between different compression ratios and RSNR; (b) shows the relationship between different compression ratios and RMSE. Detailed Implementation

[0030] A sparse adaptive reconstruction method based on dynamic adjustment and binary search is specifically implemented as follows:

[0031] S101 collects raw power quality disturbance signals including harmonics, interharmonics, voltage flicker, voltage interruption, voltage oscillation, voltage sag, voltage spike, and voltage rise. And construct a discrete time-domain sampling sequence of length N;

[0032] S102, Selecting the Compressed Sensing Sparse Transform Basis and random Gaussian observation matrix ;

[0033] S103, reconstruction begins using dynamic adjustment and binary search sparsity adaptive matching pursuit, the algorithm initializes the residuals. Support set index set Candidate set The binary search method has a lower bound of L=0, an upper bound of R=M, an intermediate value of K=M / 2, and a number of iterations. =1, iteration termination threshold Binary search decision threshold e, dynamic scaling factor Scaling factor increment ;

[0034] S104, Determine the current estimated sparsity using binary search. Calculate the atomic correlation vector Based on dynamic scaling factor The preselected atom set is determined according to the cumulative energy ratio criterion. Merge support sets and Obtain candidate set Calculate the inner product of the observation matrix submatrix corresponding to the candidate set and the observation vector y, and select the indices corresponding to the K largest inner products to update the support set. Calculate the reconstruction coefficients for the current iteration and update the residuals. ;

[0035] S105, Calculate the residual change between two adjacent iterations. ;

[0036] S106, Residual change calculated based on S105 To guide the binary search interval update and iteration termination determination, if If L > R, then the iteration is terminated and the algorithm jumps to S107; otherwise, if Then update the upper bound R=K and update the dynamic scaling factor. Otherwise, update the lower bound L=K; iteration count k=k+1, jump to S104;

[0037] S107 outputs the final reconstructed original signal. .

[0038] The core innovation of this application lies in using the residual change to guide the binary search interval update, and using "residual norm" and "interval convergence" as the criteria for iterative termination. Its rationale can be demonstrated through… Figure 2 and Figure 3 prove.

[0039] Figure 2 This diagram illustrates the relationship between the residual norm change and the number of iterations. It shows the curve of the residual norm changing with the number of iterations when reconstructing a voltage oscillation signal using the traditional SAMP algorithm. When the estimated sparsity is close to the true sparsity K=116, the residual norm decreases rapidly; however, once the sparsity exceeds the true value, the change in the residual norm tends to level off. This phenomenon indicates that the residual change... It can serve as an effective indicator for judging whether the sparsity estimate exceeds the true value, and provides a theoretical basis for the use of residual change to guide the binary search interval update in this application.

[0040] Figure 3 This illustrates the impact of the proposed decision threshold e on RSNR and computational cost, where e is the binary search decision threshold. As shown in the figure, the binary search decision threshold e... The study examines the trade-off between reconstruction signal-to-noise ratio and computation time when the value of e varies within the range of 1. Experimental results show that the algorithm achieves the optimal balance between reconstruction accuracy and computational efficiency when e=0.05. This result validates the rationality of the threshold e=0.05 set in this application, ensuring that the residual change criterion can accurately guide the update of the search interval.

[0041] To verify the effectiveness of the DSFBSAMP method proposed in this application, simulation experiments were conducted in the MATLAB environment. The experimental settings are as follows: fundamental frequency... =50Hz, sampling frequency =12.8kHz, the length of each sampled signal is N=2560, and the compression length is fixed at M=256. The reconstruction performance is quantitatively evaluated using two commonly used metrics: RSNR, RMSE, and CR. The specific calculation formulas are as follows:

[0042]

[0043]

[0044]

[0045] In the formula, and These are the original signal and the estimated signal after denoising, respectively.

[0046] This application compares the reconstruction performance of four algorithms—OMP, SAMP, CoSaMP, and DSFBSAMP—under noise-free conditions. The evaluation metrics include estimated RSNR, RMSE, and average computation time. The specific results are shown in Table 1 below.

[0047]

[0048] Analysis of the data in Table 1 shows that for power grid harmonic signals without spectral leakage, traditional OMP, SAMP, CoSaMP, and DSFBSAMP can all achieve high-precision reconstruction. However, DSFBSAMP still has a significant advantage in reconstruction signal-to-noise ratio and root mean square error. The reconstruction signal-to-noise ratio of DSFBSAMP is 29.39 dB, higher than OMP's 26.98 dB, SAMP's 25.53 dB, and CoSaMP's 27.45 dB; its root mean square error is 0.0341, lower than the other three algorithms. However, for power quality disturbances with spectral leakage, such as interharmonics, voltage interruptions, voltage swells, voltage dips, pulses, oscillations, flicker, and voltage gaps, traditional OMP and CoSaMP exhibit severe performance degradation under certain disturbances. For example, under oscillating signals, the reconstruction signal-to-noise ratios (SNRs) of OMP and CoSaMP are only about 14.04 dB and 14.50 dB, respectively, with root mean square errors (RMSEs) as high as 0.1470 and 0.1395. Although SAMP is relatively stable (27.89 dB, 0.0305), its reconstruction SNR is still significantly lower than that of DSFBSAMP (32.82 dB, 0.0173). In contrast, the DSFBSAMP method proposed in this application, relying on a binary search strategy and an atomic selection mechanism guided by a dynamic scaling factor, maintains the highest reconstruction SNR and the lowest RMS error under all perturbation types. For example, in voltage interruption signal reconstruction, DSFBSAMP achieves a reconstruction signal-to-noise ratio of 40.19 dB, while OMP, SAMP, and CoSaMP achieve 29.79 dB, 28.19 dB, and 31.11 dB, respectively. Meanwhile, DSFBSAMP has a root mean square error of 0.0064, which is significantly better than the 0.0213, 0.0256, and 0.0183 of other algorithms.

[0049] Table 1 also lists the average running time of each algorithm, revealing the differences in computational efficiency. DSFBSAMP's computation time is slightly longer than OMP and CoSaMP, but significantly shorter than SAMP. For example, in voltage spur signals, DSFBSAMP takes 0.0530 seconds, OMP and CoSaMP take only 0.0308 seconds and 0.0729 seconds respectively, while SAMP takes 0.6458 seconds. Although DSFBSAMP's time is slightly longer than OMP and CoSaMP, its improvement in reconstruction accuracy is very significant. Compared to SAMP, DSFBSAMP reduces computation time by approximately 91% while improving the reconstruction signal-to-noise ratio by approximately 12 dB. This indicates that DSFBSAMP achieves an excellent balance between reconstruction accuracy and computational efficiency, making it highly suitable for practical applications requiring accurate and efficient power quality disturbance reconstruction.

[0050] To further evaluate the noise immunity performance of the DSFBSAMP algorithm in impulse noise environments, comparative experiments were conducted using harmonic PQD signals. Furthermore, the proposed method was compared with OMP, CoSaMP, and SAMP in terms of RSNR and RMSE. The relevant results are as follows: Figure 4 (a) and Figure 4 As shown in (b).

[0051] like Figure 4 As shown in (a), the RSNR of all methods generally improves with increasing CR, indicating that more compressed measurements are beneficial for signal recovery. Throughout the entire compression ratio range tested, DSFBSAMP consistently achieved the highest reconstruction SNR, demonstrating its superior reconstruction capability under both low and high compression ratios. In contrast, SAMP had the lowest reconstruction SNR in most cases, while OMP and CoSaMP performed moderately. These results demonstrate that the algorithm proposed in this application can more effectively utilize available measurement information during the reconstruction process.

[0052] Figure 4 (b) The RMSE results further support the above observations. As the compression ratio increases, the reconstruction error of all methods generally decreases. DSFBSAMP maintains the lowest root mean square error across the entire compression ratio range, indicating higher reconstruction accuracy and lower distortion. In contrast, SAMP produces the largest error, while OMP and CoSaMP have moderate accuracy but are still inferior to DSFBSAMP. This performance improvement is attributed to the synergistic effect of the bisection search-based sparsity estimation and the dynamic atom selection mechanism.

[0053] In summary, this application proposes a DSFBSAMP reconstruction method for power quality disturbance signals. By employing a dynamically adjusted atom selection mechanism and a binary search strategy, it successfully solves the problems of sparsity overestimation, low computational efficiency, and poor noise resistance found in traditional algorithms such as SAMP in existing technologies. Furthermore, it exhibits excellent reconstruction capabilities even under impulse noise environments. Multiple simulation examples demonstrate that the proposed method outperforms existing technologies in terms of reconstruction accuracy, computational efficiency, and impulse noise resistance. It provides an efficient and reliable signal compression and reconstruction scheme for power quality monitoring, possessing significant practical value and broad application prospects.

Claims

1. A sparse adaptive reconstruction method based on dynamic adjustment and binary search, characterized in that, include: S101 collects raw power quality disturbance signals including harmonics, interharmonics, voltage flicker, voltage interruption, voltage oscillation, voltage sag, voltage spike, and voltage rise. And construct a discrete time-domain sampling sequence of length N; S102, Selecting the Compressed Sensing Sparse Transform Basis and random Gaussian observation matrix ; S103, reconstruction begins using dynamic adjustment and binary search sparsity adaptive matching pursuit, the algorithm initializes the residuals. Support set index set Candidate set The binary search method has a lower bound of L=0, an upper bound of R=M, an intermediate value of K=M / 2, and a number of iterations. =1, iteration termination threshold Binary search decision threshold e, dynamic scaling factor Scaling factor increment ; S104, Determine the current estimated sparsity using binary search. Calculate the atomic correlation vector Based on dynamic scaling factor The preselected atom set is determined according to the cumulative energy ratio criterion. Merge support sets and Obtain candidate set Calculate the inner product of the observation matrix submatrix corresponding to the candidate set and the observation vector y, and select the indices corresponding to the K largest inner products to update the support set. Calculate the reconstruction coefficients for the current iteration and update the residuals. ; S105, Calculate the residual change between two adjacent iterations. ; S106, Residual change calculated based on S105 To guide the binary search interval update and iteration termination determination, if If L > R, the iteration is terminated and the algorithm flow jumps to S107; Otherwise, if Then update the upper bound R=K and update the dynamic scaling factor. Otherwise, update the lower bound L=K; iteration count k=k+1, jump to S104; S107 outputs the final reconstructed original signal. .

2. The sparse adaptive reconstruction method based on dynamic adjustment and binary search according to claim 1, characterized in that, In step S102, considering that the power quality disturbance has good sparsity under the discrete wavelet transform basis, the discrete wavelet transform basis is used as the sparse transform basis for the power quality disturbance. The power quality disturbance signal of length N Convert to sparse coefficient vector Then, a random Gaussian observation matrix was used. Compressed observations yielded measured values. .

3. The sparse adaptive reconstruction method based on dynamic adjustment and binary search according to claim 1, characterized in that, In step S103, the iteration termination threshold The initial value is set to Dynamic scaling factor =0.1, scaling factor increment .

4. The sparse adaptive reconstruction method based on dynamic adjustment and binary search according to claim 1, characterized in that, In step S104, the atomic correlation vector is calculated. Arrange s in descending order, and select the smallest integer n such that the accumulated energy of the first n atoms exceeds the total energy. The preselected atom set is constructed by multiplying the indices of n atoms. The reconstruction coefficients corresponding to the candidate set are calculated using least squares. Select the K largest coefficients from the indexes to update the support set. The reconstruction coefficients of the current iteration are calculated using least squares. and update the residuals. .

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