Singular Value Decomposition Method Research Articles

An aeromagnetic denoising-decomposition-3D inversion approach for mineral exploration

Reduction of aeromagnetic noise and extraction of mineralization-related residual anomalies are critical for aeromagnetic data processing in mineral exploration. This study introduced a multifractal singular value decomposition (MSVD) method to remove the noise and improved the bi-dimensional empirical mode decomposition (BEMD) algorithm to extract residual magnetic anomalies. It is shown that MSVD and improved BEMD could effectively reduce the noise and extract residual magnetic anomalies. Then, a wavenumber–domain iterative approach is applied in 3D imaging of magnetic anomalies and gradients with depth constraints, which is a rapid tool for qualitative and quantitative interpretation of magnetic data and is suitable for rapidly imaging large-scale data. The 3D inversion result is verified by four geological sections along the regional tectonic directions and some drilling holes on the deposits. It is revealed that this proposed approach is practical and effective in dealing with aeromagnetic data interpretation and inversion for mineral exploration.

An Improved Sap Flow Prediction Model Based on CNN-GRU-BiLSTM and Factor Analysis of Historical Environmental Variables

Sap flow is widely used to estimate the transpiration and water consumption of canopies and to manage water resources. In this paper, an improved time series prediction model was proposed by integrating three basic networks—CNN, GRU and BiLSTM—to assess sap flow with historical environment variables. A dataset with 17,569 records of each, including 9 environment variables and 1 sap flow, was applied from a public database of SAPFLUXNET. After normalization, the environment variables were analyzed and composed with the factor analysis method. After the CNN-GRU-BiLSTM structure was designed, N records of three main factors were computed from environment variables, which were measured at N previous moments, and the sap flow was measured at the current moment, and they were applied for each training, validation, and testing cycle. To improve and compare the CNN-GRU-BiLSTM-based model, nine other models, using the methods of multiple linear regression, support vector regression, random forest, LSTM, GRU, BiLSTM, CNN-GRU, CNN-BiLSTM, and CNN-GRU-LSTM, were constructed in this study, respectively. Results show that the performance of the CNN-GRU-BiLSTM-based model has more accuracy than the other nine models we built in this paper, with the mean absolute error, mean squared error, mean absolute percentage error, and coefficient of determination (R2) being 0.0410, 0.0029, 0.2708 and 0.9329, respectively. Furthermore, for a comparison of the descending dimension method of factor analysis, principal component analysis (PCA) and singular value decomposition (SVD) methods were applied and compared, respectively. Results show that the performance of the factor analysis-based model is better than the PCA- or SVD-based model, with the R2 results of the factor analysis-based model being higher than the PCA- and SVD-based models by 5.06% and 10.63%, respectively. This study indicates that the CNN-GRU-BiLSTM-based sap flow prediction model established with a factor analysis of historical environmental variables has optimistic applications for analyzing the transpiration of trees and evaluating water consumption.

Vectorization of a Thread-Parallel Jacobi Singular Value Decomposition Method

The eigenvalue decomposition (EVD) of (a batch of) Hermitian matrices of order two has a role in many numerical algorithms, of which the one-sided Jacobi method for the singular value decomposition (SVD) is the prime example. In this paper the batched EVD is vectorized, with a vector-friendly data layout and the AVX-512 SIMD instructions of Intel CPUs, alongside other key components of a real and a complex OpenMP-parallel Jacobi-type SVD method, inspired by the sequential xGESVJ routines from LAPACK. These vectorized building blocks should be portable to other platforms that support similar vector operations. Unconditional numerical reproducibility is guaranteed for the batched EVD, sequential or threaded, and for the column transformations, that are, like the scaled dot-products, presently sequential but can be threaded if nested parallelism is desired. No avoidable overflow of the results can occur with the proposed EVD or the whole SVD. The measured accuracy of the proposed EVD often surpasses that of the xLAEV2 routines from LAPACK. While the batched EVD outperforms the matching sequence of xLAEV2 calls, speedup of the parallel SVD is modest but can be improved and is already beneficial with enough threads. Regardless of their number, the proposed SVD method gives identical results, but of somewhat lower accuracy than xGESVJ.

System Matrix Reconstruction Algorithm for Thermoacoustic Imaging With Magnetic Nanoparticles Based on Acoustic Reciprocity Theorem.

According to the acoustic reciprocity theorem (ART), we propose a system matrix reconstruction algorithm of thermoacoustic imaging for magnetic nanoparticles (MNPs) by a single-pulse magnetic field. In both cases of inhomogeneous and homogeneous acoustic velocity, we respectively derive the linear equation between the sound pressure detection value and the distribution of MNPs. The image reconstruction problem is converted to an inverse matrix solution by using the truncated singular value decomposition (TSVD) method. In forward problem, the calculated forward results are consistent with the simulated thermoacoustic signal signals. In inverse problem, we build the two-dimensional breast cancer model. The TSVD method based on the ART faithfully reflects the distribution of abnormal tissue labeled by the MNPs. In the experiment, the biological sample injected with the MNPs is used as the imaging target. The reconstructed image well reflects the cross-sectional images of the MNPs area. The TSVD method based on the ART takes into account energy attenuation and inhomogeneous acoustic velocity, and use a non-focused broadband ultrasonic transducer as the receiver to obtain a larger imaging field-of-view (FOV). By comparing the image metrics, we prove that the algorithm is superior to the traditional time reversal method. The TSVD method based on the ART can better suppress noise, which is expected to reduce the cost by reducing the number of detectors. It is of great significance for future clinical applications.

Numerical and experimental study on acoustic tomographic reconstruction of flow field

This paper reports the acoustic vector tomography (AVT) method to reconstruct the airflow as a vector field. In order to increase the efficiency of reconstruction process, proposed radial basis functions approximate the flow velocity components. Tikhonov-Gaussian regularization combined with Generalized Singular Value Decomposition method and modified L-curve are introduced to solve the ill-posed problem and select the optimal regularization parameters. The feasibility and validity of the method are verified by numerical simulation and experiment. The numerical results confirmed the effectiveness of the proposed method with higher accuracy, better anti-noise capability and shorter consuming time compared with other reconstruction methods. Besides, a physical experiment is performed for further testing. We measured the incident flow and vortex field using the proposed acoustic method. The results show that the tendency and data of the acoustical reconstructed flow field are consistent with the strip display and anemometer results. The relative errors of most measurement points are under 15% and our proposed acoustic method is effective in practical velocity field measurement.

Research on the surface crack detection of specimen manufactured by selective laser melting based on local singular value decomposition method

SLM (selective laser melting) is an important additive manufacturing technology. Parts with complex structures can be produced by SLM, so surface cracks and other defects within SLM parts are difficult to be identified by traditional nondestructive testing techniques. In this paper, laser ultrasonic technology is proposed to identify the surface crack of SLM specimen. Because of the anisotropy and residual stress of the specimen, the time signal is strongly interfered with by noise, which makes the identification and location of the crack difficult. To solve this problem, the phase space was reconstructed from the time signal and analyzed by the local singular value decomposition method. According to the result of the experiment, this method can reveal the variation of the phase space and has a good effect on the identification and location of the surface crack whose depth is larger than 1 mm.

A novel linear stability analysis method for plane Couette flow considering rarefaction effects

Following the stability analysis method in classic fluid dynamics, a linear stability equation (LSE) suitable for rarefied flows is derived based on the Bhatnagar–Gross–Krook (BGK) equation. The global method and singular value decomposition method are used for modal and non-modal analysis, respectively. This approach is validated by results obtained from Navier–Stokes (NS) equations. The modal analysis shows that LSEs based on NS equations (NS-LSEs) begin to fail when the Knudsen number ($Kn$) increases past$\sim$0.01, regardless of whether a slip model is used. When$Kn\geq 0.01$, the growth rate of the least stable mode is generally underestimated by the NS-LSEs. Under a fixed wavenumber, the pattern (travelling or standing wave) of the least stable mode changes with$Kn$; when the mode presents the same pattern, the growth rate decreases almost linearly with increasing$Kn$; otherwise, rarefaction effects may not stabilize the flow. The characteristic lengths of the different modes are different, and the single-scale classic stability analysis method cannot predict multiple modes accurately, even when combined with a slip model and even for continuum flow. However, non-modal analysis shows that this error does not affect the transient growth because modes with small growth rates offer little contribution to the transient growth. In rarefied flow, as long as the Mach number ($Ma$) is large enough, transient growth will occur in some wavenumber ranges. The rarefaction effect plays a stabilizing role in transient growth. The NS-LSEs-based method always overestimates the maximum transient growth.

Bistatic Sea Clutter Suppression Method Based on Compressed Sensing Optimization

In order to reduce the sea clutter interference in the detection of sea surface targets, we propose a bistatic sea clutter suppression method based on compressed sensing optimization in this paper. The proposed method mitigates the interference effect by reconstructing and cancelling out the sea clutter. Since the fixed sparse base is not always completely applicable for the sparse representation of sea clutter, we propose a sparse base optimization algorithm based on transfer learning to convert the fixed sparse base into an adaptive one. Moreover, we introduce a sensing matrix optimization algorithm to decrease the cross-correlation coefficient between the measurement matrix and the sparse base matrix, which can enhance the signal reconstruction quality. Finally, we use the orthogonal matching pursuit algorithm to reconstruct the sea clutter and employ the reconstructed results to cancel and suppress the sea clutter. The simulation results demonstrate that the proposed method outperforms the traditional methods such as the root time-domain cancellation method and the singular value decomposition method (SVD). Therefore, the proposed method has great practical significance for the detection of bistatic sea surface targets.

Research on Joint Beamforming of High-Speed Railway Millimeter-wave MIMO Communication with Reconfigurable Intelligent Surface

The advantage of a reconfigurable intelligent surface (RIS) is that it optimizes the wireless signal transmission environment. It can ameliorate the high loss of high-speed railway (HSR) millimeter-wave (mmWave) communications and increase signal strength by coherently superimposing signals at the receiving end through an appropriate beamforming design. In this paper, an mmWave multiple-input multiple-output communication system for HSR is discussed. The channel modeling takes into account the Doppler effect and the properties of mmWave channels. Aiming at the problem of high coupling of optimization variables, the singular value decomposition method is utilized to decouple them and to achieve the optimal active beamforming design. The original optimization problem is then rewritten into a more manageable form through a sequence of transformations. In order to overcome the restrictions imposed by non-convex constraints, the optimal RIS phase shift is directly calculated using the Riemann gradient descent (RGD) method. In this paper, spectral efficiency (SE) is taken as the optimization objective. Considering the fast time-varying environment of HSR, a step size selection scheme with easier convergence is adopted in the RGD method to complete the joint beamforming design. The numerical simulations demonstrate that the proposed solution outperforms the semi-definite relaxation scheme and the RIS-free auxiliary scheme in terms of SE performance and computational complexity.

Damage quantification in composite laminates based on sparsity-difference estimation of the normal time–frequency representation

Damage index (DI) is of vital importance for the health monitoring of composite structures. However, most of the existing DI construction methods cannot reveal the rich information hidden in Lamb waves, such as the time-varying characteristics of the signal amplitude and phase, and thus cannot well characterize the evolutionary trend of damage. To address this limitation, this study proposes a novel DI construction method for damage identification in composite structures. The normal time–frequency transform is first applied to obtain the unbiased time–frequency distribution of the received Lamb wave signal, and then the singular value decomposition method is used to obtain the singular value sequence of the two-dimensional time–frequency matrix to characterize its matrix sparsity. Next, the dynamic time warping method is used to measure the distance between singular value sequences of the current and baseline signals. A quantitative DI is finally defined using these distances. Two experimental studies are utilized to validate the effectiveness of the proposed method. Results show that the proposed method can reveal the rich information hidden in the Lamb wave signals and has better trend-matching performance in fitting the actual damage propagation trend than traditional methods.

A new rapid positioning strategy for the impact-point using dynamic mode decomposition and time difference of arrival *

In outdoor shooting range experiments, locating the projectile impact point is typically done through manual search, which can be time-consuming and costly. To improve experimental efficiency and reduce costs, this paper proposes a new approach for localizing the impact point using the dynamic mode decomposition (DMD) extension method and time difference of arrival (TDOA) based on seismic waves. The DMD extension method is applied to one-dimensional seismic signals. Additionally, diagonal averaging is applied to recover the reconstructed matrix, which could achieve better noise reduction than conventional singular value decomposition and empirical mode decomposition methods. Numerical simulations are then conducted to analyze the impact point positioning model, resulting in an absolute location error within 20 m in a 1000 m square area. The work demonstrates that the joint positioning algorithm combining on DMD and TDOA achieves high positioning accuracy, making it a promising tool for future experiments on outdoor shooting ranges.

Deciphering Alloy Composition in Superconducting Single-Layer FeSe1-xSx on SrTiO3(001) Substrates by Machine Learning of STM/S Data.

Scanning tunneling microscopy (STM) is a powerful technique for imaging atomic structure and inferring information on local elemental composition, chemical bonding, and electronic excitations. However, a plain visual analysis of STM images can be challenging for such determination in multicomponent alloys, particularly beyond the diluted limit due to chemical disorder and electronic inhomogeneity. One viable solution is to use machine learning to analyze STM data and identify hidden patterns and correlations. Here, we apply this approach to determine the Se/S concentration in superconducting single-layer FeSe1-xSx alloys epitaxially grown on SrTiO3(001) substrates via molecular beam epitaxy. First, the K-means clustering method is applied to identify defect-related dI/dV tunneling spectra taken by current imaging tunneling spectroscopy. Then, the Se/S ratio is calculated by analyzing the remaining spectra based on the singular value decomposition method. Such analysis provides an efficient and reliable determination of alloy composition and further reveals the correlations of nanoscale chemical inhomogeneity to superconductivity in single-layer iron chalcogenide films.

Regularization Methods for Extracting Doppler Broadening From Hall Thruster Plasma

Extracting Doppler broadening from laser-induced fluorescence (LIF) measurements is essential for determining species temperature in the plasma. The fluorescence signal is a convolution of many broadening effects of which Doppler broadening is the most significant, but several others contribute as well: collisional (pressure) broadening (particle-to-particle interactions), natural lifetime broadening, and power broadening. The process that extracts Doppler broadening is an <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ill-posed</b> inverse problem. The regularization approach addresses the <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ill-posed</b> problem to ensure a unique and stable solution with the best possible accuracy. This study reported the Xe II temperature by applying truncated singular value decomposition (TSVD) and Tikhonov regularization (zeroth, first and second-order) methods for deconvolution of Doppler broadening. Tikhonov first-order and TSVD employing the generalized cross-validation (GCV) method provide accurate reconstruction within 2.0%–8.0% of the actual measurements.

The polarization filtering line spectrum extraction algorithm of underwater target signal

In order to increase the performance of underwater target line spectrum extraction, an adaptive polarization filtering line spectrum extraction method is researched in the paper. By using of the polarization characteristics of underwater target signals, the polarization characteristics of underwater target line spectrum signal is analyzed via singular value decomposition (SVD) method in frequency domain. Firstly, the line spectrum signal is presented by the eigenimage corresponding to the maximum singular value to increase the signal-to-noise ratio (SNR) of the signal. Then the polarization parameters are extracted according to the polarization characteristics of the line spectrum signals. And the line spectrum signal is filtered by constructing the polarization filtering function. The simulation results show that the output SNR of the proposed method are larger than that of conventional FFT analysis method when the SNR of the signal is larger than -9dB, and the detection probability of the proposed method is 100% when the SNR of the signal is -1 dB, while the detection probability of the conventional FFT analysis method is 27.73%. It shows that the proposed method provides a new approach for underwater line spectrum signal extraction techniques.

Iteratively weighted least squares solution for universal 3D similarity transformation

The 3D similarity coordinate transformation is widely used to estimate the transformation parameters for measurement datum transformation. Accurate and reliable transformation parameters are crucial for accurate and reliable data integration. However, the accuracy of the transformation parameters can be significantly affected or even severely distorted when the observed coordinates are contaminated by gross errors. To address this problem, an advanced iteratively weighted least squares solution based on the weighted least squares is proposed. This solution utilizes the singular value decomposition method to obtain the rotation matrix and introduces a novel weight estimation approach based on Gaussian function. This approach enables the weight to be normalized and optimized iteratively. To verify the accuracy and reliability of the proposed algorithm, the root mean square errors from both true and pseudo-observed values are analyzed by simulation experiments. Furthermore, the results of simulated and empirical experiments show that the proposed algorithm can effectively reduce the influence of gross errors to obtain reliable measurement datum transformation parameters. It should be noted that the new algorithm can easily be extended to the 2D/3D affine and rigid transformation cases, such as image matching, point cloud registration, and absolute orientation of photogrammetry.

A robust attitude estimation algorithm for seabed inverted ultra-short baseline

The ultra-short baseline(USBL) is fixed upside down on the seafloor to position an autonomous underwater vehicle, which is the inverted ultra-short baseline (i-USBL). Three attitude angles between the i-USBL coordinate system and the navigation coordinate system will be produced when the USBL is installed on the seabed. Significant positioning error will occur if the USBL attitude is undefined. Besides, it also affects the accuracy of attitude angles estimation that the outliers produced when using USBL. In this paper, we propose a robust singular value decomposition (RSVD) method for estimating the attitude angles. Specifically, we develop an attitude calibration model based on the i-USBL positioning mode. The USBL attitude angles is solved using singular value decomposition (SVD) according to the least squares method. The new attitude angles are used to calculate the residuals of the coordinates at each measurement point. The residuals are used to calculate the weights of each point by the IGG III weighting function. The recalculation of attitude angles is performed by using up-to-date weights and SVD. The performance of SVD, the conventional Gaussian Newton iterative method (GN), and RSVD are compared in the simulations. The simulations show that the RSVD has high calibration accuracy and robustness.

Study on fractional vegetation cover dynamic in the Yellow River Basin, China from 1901 to 2100

Increasing climate change makes vegetation dynamic. At the same time, dynamic changes in vegetation not only have a feedback effect on climate change, but also affect the hydrological cycle process. Therefore, understanding the vegetation change and its response to climate change is a priority for predicting future climate change and studying the impact of vegetation change on the hydrological cycle. In this study, the Yellow River Basin in China is the study area. Based on the analysis of the evolution characteristics of meteorological elements and fractional vegetation cover (FVC), the delta downscaling Coupled Model Intercomparison Project Phase 6 (CMIP6) models are optimized. The empirical orthogonal function (EOF) and singular value decomposition (SVD) methods are used to investigate the impact of climate change on vegetation in the Yellow River Basin. The results show that: (1) in the four scenarios (SSP126, SSP245, SSP370, and SSP585), FVC in the Yellow River Basin from 2022 to 2100 shows an increasing trend, SSP370 (0.017 10a–1) &amp;gt; SSP126 (0.014 10a–1) &amp;gt; SSP245 (0.0087 10a–1) &amp;gt; SSP585 (0.0086 10a–1). Spatially, FVC in most regions of the Yellow River Basin show an increasing trend under the four scenarios, and the degraded areas are concentrated in a small part of the Yellow River headwaters. (2) There is a significant positive correlation between FVC and precipitation (Pre) and temperature (Tem) under four scenarios in the Yellow River Basin from 2022 to 2100. Under the same scenario, the annual average temperature can be considered as the dominant factor of FVC change in the Yellow River Basin. Under different scenarios, the impact of climate change on FVC under the high emission scenarios is greater than that under the low emission scenarios. This study will help to better understand the response of vegetation to climate change and provide a scientific basis for formulating ecological protection measures to cope with future climate change in the Yellow River Basin.

GNSS standard point positioning method based on spherical harmonic expansion of signal propagation path relating errors

The errors affecting standard point positioning mainly include the ionospheric delay error, tropospheric delay error, clock bias, and multipath effect. The errors are divided into two categories depending on the relation to the signal propagation path: errors related to the propagation path and errors unrelated to the propagation path. The ionospheric delay error, tropospheric delay error, and multipath effect are related to the satellite signal propagation path. Based on this characteristic, a new GPS standard point positioning algorithm based on spherical harmonic expansion (SPP-SH) is proposed, which uses spherical harmonic expansion to represent the errors related to the propagation path. We hope to continuously promote the further development of standard point positioning (SPP) by proposing this new algorithm and to further reduce the redundancy of SPP algorithms and improve the efficiency and reliability of the algorithms. The most important purpose of this manuscript is to validate the proposed SPP-SH algorithm based on GPS data provided by IGS stations. Pseudorange data of multiple continuous epochs are used to achieve a sequential sliding point positioning solution, and the truncated singular value decomposition and iteration method correcting characteristic values are used to solve the ill-conditioned equations in the SPP-SH algorithm. The SPP-SH algorithm is implemented and verified using IGS station data. The positioning accuracy of the SPP-SH algorithm for both dual-frequency data and single-frequency data is better than that of a traditional SPP algorithm. By analyzing the positioning results of the stations at different latitudes, when the spherical harmonic expansion is expanded to the same degree, the positioning accuracy in low latitude areas is poor because the station is seriously affected by factors such as the ionosphere and water vapor, while the positioning accuracy at high latitude stations is the best. The proposed SPP-SH algorithm is also realized in the kinematic scene based on the dual-frequency data collected dynamically. The kinematic data is collected by an Android phone which supports receiving dual-frequency GPS observations. To validate the reliability of the SPP-SH algorithm, two strategies are designed to validate the results, which proves that the newly proposed method can be used for positioning with low accuracy in kinematic conditions.

COLLABORATIVE FILTERING APPROACH: SKINCARE PRODUCT RECOMMENDATION USING SINGULAR VALUE DECOMPOSITION (SVD)

The recommendation system provides recommendations for something, be it goods, songs, or movies. The term system is not limited to a service system but concerns a model that can provide recommendations. With recent technological advances, many companies provide various skincare products because current generations are increasingly aware of self-care. With various choices, someone may experience confusion in determining the product they want to buy. Therefore, we need a system that can provide product recommendations run on any platform we use. The most common method for recommendation systems often comes with Collaborating Filtering (CF) where it relies on the past user and item dataset. The singular value decomposition (SVD) method uses a matrix factorization technique that predict the user's rating based on historical ratings. The measurement of the model's accuracy is the RMSE average of 1.01276, indicating that this value results from the best parameters. The results focus on showing skincare product recommendations to users sorted based on rating predictions.

Optimization of the magnetic diagnostics for plasma equilibrium reconstruction in EAST long-pulse operation

Plasma equilibrium is critical for experimental operation and data analysis in tokamaks. The number and location of magnetic diagnostics provide the magnetic field and flux information that influences the accuracy of the plasma equilibrium reconstruction. In this research, the truncated singular value decomposition method is applied to minimize the number of magnetic diagnostics for plasma equilibrium reconstruction based on Experimental Advanced Superconducting Tokamak existing magnetic diagnostics system. The reconstructed results with a reduced number of magnetic diagnostics are consistent with results obtained using full magnetic diagnostics by EFIT code. This implies that the approach of minimizing the number of magnetic diagnostics in reconstruction can reduce the demand for magnetic diagnostics while ensuring the accuracy of plasma equilibrium reconstruction with feasibility and reliability. Reduced magnetic diagnostics can increase tolerance for the absence of certain existing magnetic diagnostics and could be a reference for the redundancy design of magnetic diagnostics system in future fusion devices.