Singular Value Decomposition Method Research Articles

Surface crack detection on selective laser melting printed Inconel 718 using a laser generated ultrasound technique and phase space reconstruction

Abstract In the field of metallic additive manufacturing, Selective Laser Melting (SLM) has become a predominant technology due to its advantages of short production cycles, high precision, and low cost. It is frequently employed in the production of complex parts. This paper proposes the use of a scanning laser line source, in conjunction with the singular value decomposition method, to reconstruct phase space and identify surface cracks in SLM specimens. The scanning laser line source addresses the limitations of a single line source, which is often unable to accurately detect tiny cracks. By comparing experimental and simulation data, the results demonstrate that the scanning laser line source can effectively compensate for some of the detection deficiencies of a single line source.

Regularization methods for the inverse initial value problem for the time-fractional diffusion equation with robin boundary condition ★ ★ The project is supported by Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX23_2549) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20190578).

In the article, we focus on the inverse initial value problem for the time-fractional diffusion equation with robin boundary condition on a cylindrical symmetric field. The ill-posedness of this problem is proved. We introduce the modified Landweber iteration method(MLIM), the Truncated singular value decomposition(TSVD) method for solving it and propose a new regularization method, named as the TSVD-modified Landweber iteration method(TMLIM). The error estimates between the exact solution and the regularized approximate solution are presented by using two regularization parameter selection rules. Finally, numerical examples are provided to demonstrate the effectiveness and feasibility of the regularization methods.

Generating Extremely Low-Dimensional Representation of Subsurface Earth Models using Vector Quantization and Deep Autoencoder

Geological model compression is crucial for making large and complex models more manageable. By reducing the size of these models, compression techniques enable efficient storage, enhance computational efficiency, making it feasible to perform complex simulations and analyses in a shorter time. This is particularly important in applications such as reservoir management, groundwater hydrology, and geological carbon storage, where large geomodels with millions of grid cells are common. This study presents a comprehensive overview of previous work on geomodel compression and introduces several autoencoder-based deep-learning architectures for low-dimensional representation of modified Brugge-field geomodels. The compression and reconstruction efficiencies of autoencoders (AE), variational autoencoders (VAE), vector-quantized variational autoencoders (VQ-VAE), and vector-quantized variational autoencoders2 (VQ-VAE2) were tested and compared to the traditional singular value decomposition (SVD) method. Results show that the deep-learning-based approaches significantly outperform SVD, achieving higher compression ratios while maintaining or even exceeding the reconstruction quality. Notably, VQ-VAE2 achieves the highest compression ratio of 667:1 with a structural similarity index metric (SSIM) of 0.92, far surpassing the 10:1 compression ratio of SVD with a SSIM of 0.9. The result of this work shows that, unlike traditional approaches, which often rely on linear transformations and can struggle to capture complex, non-linear relationships within geological data, VQ-VAE's use of vector quantization helps in preserving high-resolution details and enhances the model's ability to generalize across varying geological complexities.

Spatial Spectrum Estimation of Weak Scattering Wave Signal in Range-Doppler Domain

How to enhance the desired signal with low signal-to-noise ratio (SNR) is a difficult problem in the estimation process of the direction-of-arrival (DOA) of the target scattering wave signal. In this paper, the feasibility of spatial spectrum estimation in the Range-Doppler (RD) domain is analyzed in principle, and the SNR gain expression of weak scattering wave signal is derived when constructing multi-snapshots virtual array data. On this basis, the mutual eigenvector singular value decomposition (MESVD) method based on RD domain mode excitation is proposed, which can robustly and effectively estimate the direction of the coherent weak signals. Simulation experiments verify that the RD domain spectral estimation method has the ability to simultaneously obtain the direction of multiple weak target scattering waves, and the direction-finding accuracy can reach the Cramer–Rao bound (CRB) of conventional spectral estimation method. The results of Monte Carlo experiments show that the root-mean-square-error (RMSE) of azimuth estimation of RD domain spatial spectrum estimation method is 5.76° lower than that of a conventional multiple signal classification (MUSIC) method. In addition, the practicability of the proposed method is demonstrated by comparing the DOA estimation results of a set of real data with Automatic Dependent Surveillance-Broadcast (ADS-B) data.

The Criticality Problem for the Anisotropic Scattering with Two Discrete Eigenvalues

In a recent study, the eigenvalue numbers of Case eigenfunctions were investigated for the situation of anisotropic scattering. The results of this study is applied to the criticality problem. The investigation is performed with two different methods: the singular value decomposition (SVD) method and the H N method. The former was recently improved using the SVD to solve the matrix of the problem, and the latter is based on the usage of the Case method for proper boundary conditions. We have two different eigenvalues for the given number of secondary neutrons and the scattering parameter. Either these eigenvalues are both complex, or one is complex and one is real. The investigation is to show the effect of the second eigenvalues over the critical thickness values.

Behaviour Analysis of Modeling and Model Evaluating Methods in System Identification for a Multiprocess Station

Systems are designed to perform specific task by giving certain input which produces the required output in an orderly manner known as process. The input, output, and the state variables should be known that will help in interacting with the system. The relation between these variables can be brought out by building a model that resembles or expresses the original performance of the system. The parameters of the model are estimated using the least squares approximation, maximum likelihood, maximum log-likelihood, and Bayesian parameter estimation methods by utilizing the experimental data from the multiprocess station. The selected parameters are converted to nine different transfer function models that represent the given dynamic system. The models framed are analyzed by the criterion curve technique using seven criterion functions evaluating the fitness of the model. Order of the model is found from Hankel matrix representation methods such as singular value decomposition and determinant method. Response of the models is compared with the original response to choose the best fit model by calculating ISE standard. All the above methods are used to model the system without physical and theoretical laws which is known as system identification.

Influence of Spring Precipitation over Maritime Continent and Western North Pacific on the Evolution and Prediction of El Niño–Southern Oscillation

Previous studies suggested that spring precipitation over the tropical western Pacific Ocean can influence the development of El Niño–Southern Oscillation (ENSO). To identify crucial precipitation patterns for post-spring ENSO evolution, a singular value decomposition (SVD) method was applied to spring precipitation and sea surface temperature (SST) anomalies, and three precipitation and ENSO types were obtained with each highlighting precipitation over the Maritime Continent (MC) or western north Pacific (WNP). High MC spring precipitation corresponds to the slow decay of a multi-year La Niña event. Low MC spring precipitation is associated with a rapid El Niño-to-La Niña transition. High WNP spring precipitation is related to positive north Pacific meridional mode and induces the El Niño initiation. Among the three ENSO types, ocean current and heat content behave differently. Based on these spring precipitation and oceanic factors, a statistical model was established aimed at predicting winter ENSO state. Compared to a full dynamical model, this model exhibits higher prediction skills in the winter ENSO phase and amplitude for the period of 1980–2022. The explained total variance of the winter Niño-3.4 index increases from 43% to 75%, while the root-mean-squared error decreases from 0.82 °C to 0.53 °C. The practical utility and limitations of this model are also discussed.

A novel lidar signal denoising method based on variational mode decomposition optimized using whale algorithm

Original lidar return signals are covered by high levels of noise that seriously affect the accuracy of subsequent data processing and inversion. Therefore, it is important to separate the effective signal from the returned signal with noise interference. In this paper, an efficient denoising method based on the variational mode decomposition (VMD) algorithm optimized using the global search strategy-based whale algorithm and the total variational stationary wavelet transform (GSWOA-VMD-SWTTV) is proposed, and this method is applied to denoising of lidar return signals. First, the global search strategy-based whale optimization algorithm (GSWOA) is used to acquire the optimal parameters of the VMD algorithm adaptively, and the lidar return signal is then decomposed by global search strategy-based whale optimization algorithm (GSWOA)-VMD. The effective modal components are then determined using the cross-correlation coefficient method from the decomposed modal components, and total variation stationary wavelet denoising is performed on each effective mode. Finally, the effective modes are reconstructed to obtain a clean lidar return signal. Moreover, to provide further verification of the effectiveness of the proposed method, it is compared with the ensemble empirical mode decomposition (EEMD) method, the complete EEMD with adaptive noise (CEEMDAN) method, the singular value decomposition (SVD) method, and the wavelet threshold method under sunny, cloudy, and dusty weather conditions. The experimental results demonstrate the superior noise reduction performance of the proposed algorithm, which can filter out strong noise from the signal while retaining the complete signal details without distortion; additionally, the proposed method has the highest signal-to-noise ratio and lowest mean square error.

Data-Driven Compression of Electron-Phonon Interactions

First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon (e−ph) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For e−ph interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress e−ph interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to e−ph interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of e−ph interactions. Furthermore, they accelerate state-of-the-art first-principles e−ph calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of e−ph interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter. Published by the American Physical Society 2024

Digital Image Watermarking

Digital watermarking has become an essential method for encrypting multimedia files by adding undetectable data. In this work, we present a novel approach to digital watermarking that makes use of the Singular Value Decomposition (SVD) and Discrete Wavelet Transform (DWT) methods. By combining these methods, robustness against different types of attacks can be achieved while preserving excellent perceptual quality. Our approach ensures resilience and invisibility by embedding the watermark in the singular values that are obtained from the decomposition of DWT subbands. The outcomes of the experiments show that the suggested strategy is more efficient and effective than the current techniques when it comes to maintaining image quality and being resistant to common image processing threats.

Iterative removal of sources to model the turbulent electromotive force

ABSTRACT We describe a novel method to compute the components of dynamo tensors from direct magnetohydrodynamic (MHD) simulations. Our method relies upon an extension and generalization of the standard Högbom CLEAN algorithm widely used in radio astronomy to systematically remove the impact of the strongest beams on to the corresponding image. This generalization, called the Iterative Removal of Sources (IROS) method, has been adopted here to model the turbulent electromotive force (EMF) in terms of the mean magnetic fields and currents. Analogous to the CLEAN algorithm, IROS treats the time series of the mean magnetic field and current as beams that convolve with the dynamo coefficients which are treated as (clean) images to produce the EMF time series (the dirty image). We apply this method to MHD simulations of galactic dynamos, to which we have previously employed other methods of computing dynamo coefficients such as the test-field method, the regression method, as well as local and non-local versions of the singular value decomposition (SVD) method. We show that our new method reliably recovers the dynamo coefficients from the MHD simulations. It also allows priors on the dynamo coefficients to be incorporated easily during the inversion, unlike in earlier methods. Moreover, using synthetic data, we demonstrate that it may serve as a viable post-processing tool in determining the dynamo coefficients, even when the power of additive noise to the EMF is twice as much the actual EMF.

Convex set-oriented singular value decomposition with bounded uncertainties

Singular value decomposition (SVD) has played a crucial role in mathematics and applied mathematics, particularly in the field of practical engineering technology, which is almost indispensable in these fields. However, incomplete information caused by uncertainties from multiple sources and fluctuations in inherent properties during engineering practice can seriously interfere with obtaining singular values. Based on the convex set uncertainty theory, a novel convex set-oriented singular value decomposition (CSSVD) is proposed to overcome the limitations of using the nominal SVD method. The CSSVD aims to accurately and efficiently calculate the uncertainty bounds of singular values and vectors through the bounds and correlations of initial uncertainty parameters. Traditional probability methods rely on a sufficient sample size, and when the sample size is insufficient, accurate results cannot be obtained. However, the CSSVD method is based on set theory and can still demonstrate excellent performance in scenarios with small samples. This study investigates the detailed derivation steps of the proposed CSSVD method, taking into consideration properties such as normalization, orthogonality, and Monte Carlo simulation (MCS) to verify the accurate bounds of convex sets. The proposed method is finally applied to several numerical examples to demonstrate its superiority. This includes verifying singular values and vectors, handling high-order matrices, matrices with close singular values, and rectangular matrices. An application of image denoising is also used to evaluate the effectiveness of the proposed method.

Communication signal detection based on high-order cumulants time-frequency analysis: on the application of deep learning YOLOV5 network

The detection of communication signals in heterogeneous electromagnetic environments currently relies primarily on a one-dimensional statistical feature threshold method. However, this approach is highly sensitive to dynamic changes in the environment, fluctuations in signal-to-noise ratios, and complex noise. To address these limitations, this paper proposes a novel time-frequency diagram based on high-order accumulation for signal detection. Traditional time-frequency diagrams suffer from poor noise suppression ability and unclear features. However, higher-order cumulants can effectively overcome these shortcomings. Currently, methods based on higher-order cumulants are typically limited to one-dimensional signals. Yet, two-dimensional time-frequency signal diagrams can represent a broader array of features. This paper employs higher-order accumulation to extract time-frequency features from the received signal, thereby transforming the conventional radio detection problem into an image recognition challenge. By merging the advantages of higher-order accumulations and time-frequency diagrams, we propose the use of higher-order accumulation time-frequency diagrams for signal detection. Extensive experimental simulations demonstrate that the proposed time-frequency diagram exhibits strong anti-noise performance and effectively suppresses frequency bias from multiple perspectives. The performance of the Higher-Order Cumulant-Time Frequency (HOC-TF) indicated lower Root Mean Square Error (RMSE) compared with the Short-Time Fourier Transform-Time Frequency (STFT-TF) and Wavelet Transform-Time Frequency (WT-TF). Additionally, compared to the STFT-TF and WT-TF methodologies, the novel time-frequency diagram introduced demonstrates superior stability using the Singular Value Decomposition (SVD) method. Moreover, by combining the new time-frequency diagram with the deep learning YOLOV5 network, signal detection and modulation identification of communication signals can be achieved.

Self-Equilibrium Analysis and Minimal Mass Design of Tensegrity Prism Units

Abstract This paper provides a specific analysis strategy for tensegrity prism units with different complexities and connectivity. Through the nodal coordinate matrix and connectivity matrix, we can establish the equilibrium equation of the structure in the self-equilibrium state, and the equilibrium matrix can be obtained. The Singular Value Decomposition (SVD) method can find the self-equilibrium configuration. The torsional angle formula between the upper and bottom surfaces of the prismatic tensegrity structure, which includes complexity and connectivity, can be obtained through the SVD form-finding method. According to the torsional angle formula of the self-equilibrium configuration, we carry out the mechanical analysis of the single node, and the force density relationship between elements is gained. As one of the standards, the mass is used to evaluate the light structure. This paper also studied the minimal mass of the self-equilibrium tensegrity structure with the same complexity in different connectivity and got the minimal mass calculation formula. A six-bar tensegrity prism unit is investigated in this paper, which shows the feasibility of systematic analysis of prismatic structures. This paper provides a theoretical reference for prismatic tensegrity units.

Three-dimensional deformation measurement techniques in space multi-physical fields based on digital image correlation

Aiming at the three-dimensional deformation measurement requirement of the high-stability structure of spacecraft in space multi-physical fields, a comprehensive instrument protection device in a vacuum high-low temperature environment is developed using ultra-low temperature anti-condensation and vacuum heat insulation technology. This ensures that the digital image correlation (DIC) measurement camera always remains in a constant temperature and pressure environment and can stably exert its original efficiency in space multi-physical field environments. Subsequently, a path-dependent DIC method based on a graphics processing unit computing parallel acceleration is proposed by combining a pre-interpolation strategy and integrated image technology, which realizes high-precision matching of digital images before and after deformation in a spatial multi-physical field environment and improves the computing efficiency. To address the problem that a common reference point may deform significantly in a space environment with a large temperature change, which leads to inaccurate system accuracy, combined with a random sampling consistency algorithm and singular value decomposition method, the optimal registration of the coordinate system and the solution of deformation were realized by setting the threshold of the reference point margin screening. Finally, a three-dimensional deformation measurement system in high- and low-temperature vacuum environments was built, and the three-dimensional deformation measurement of the satellite antenna in high- and low-temperature vacuum environments was verified, which proves the effectiveness and accuracy of the above method.

An Abnormal Account Identification Method by Topology Feature Analysis for Blockchain-Based Transaction Network

Cryptocurrency, as one of the most successful applications of blockchain technology, has played a vital role in promoting the development of the digital economy. However, its anonymity, large scale of cryptographic transactions, and decentralization have also brought new challenges in identifying abnormal accounts and preventing abnormal transaction behaviors, such as money laundering, extortion, and market manipulation. Recently, some researchers have proposed efficient and accurate abnormal transaction detection based on machine learning. However, in reality, abnormal accounts and transactions are far less common than normal accounts and transactions, so it is difficult for the previous methods to detect abnormal accounts by training with such an imbalance in abnormal/normal accounts. To address the issues, in this paper, we propose a method for identifying abnormal accounts using topology analysis of cryptographic transactions. We consider the accounts and transactions in the blockchain as graph nodes and edges. Since the abnormal accounts may have special topology features, we extract topology features from the transaction graph. By analyzing the topology features of transactions, we discover that the high-dimensional sparse topology features can be compressed by using the singular value decomposition method for feature dimension reduction. Subsequently, we use the generative adversarial network to generate samples like abnormal accounts, which will be sent to the training dataset to produce an equilibrium of abnormal/normal accounts. Finally, we utilize several machine learning techniques to detect abnormal accounts in the blockchain. Our experimental results demonstrate that our method significantly improves the accuracy and recall rate for detecting abnormal accounts in blockchain compared with the state-of-the-art methods.

Innovative K-Means based machine learning method for determination of non-uniform image coordinate system in panoramic imaging: a case study with Ladybug2 camera.

Currently, the practical implementations of panoramic cameras range from vehicle navigation to space studies due to their 360-degree imaging capability in particular. In this variety of uses, it is possible to calculate three-dimensional coordinates from a panoramic image, especially using the Direct Linear Transformation (DLT) method. There are several types of omnidirectional cameras which can be classified mainly as central and non-central cameras for 360-degree imaging. The central omnidirectional cameras are those which satisfy the single-viewpoint characteristic. Multi-camera systems are usually developed for applications for which two-image stereo vision is not flexible enough to capture the environment surrounding a moving platform. Although the technology based on multi-view geometry is inexpensive, accessible, and highly customizable, multi-camera panoramic imaging systems pose a difficulty in obtaining a single projection center for the cameras. In this study, not only a defining method of the non-uniform image coordinate system is suggested by means of the K-Means algorithm for a single panoramic image, captured with a Ladybug2 panoramic camera in the panoramic calibration room but also the use of an elliptical panoramic projection coordinate system definition by Singular Value Decomposition (SVD) method in panoramic view. The results of the suggested method have been compared with the DLT algorithm for a single panoramic image which defined a conventional photogrammetric image coordinate system.

A novel approach to predictor selection among large-scale climate indices for seasonal rainfall forecasting in small catchments

ABSTRACT Utilizing identical climate indices as predictors for all climate divisions within large basins may result in unreliable rainfall forecasts at the sub-basin scale. This study aimed to develop a new approach to identify the most effective predictors among large-scale climate indices for seasonal rainfall forecasting in small areas. The proposed approach combines a selective singular value decomposition method (SSVD) with a non-linear sequential forward selection method (NLSFS). Applying the new algorithm for seasonal rainfall forecasting within two climate divisions in Karkheh basin, Iran, indicated that the climate indices identified by the SSVD differed between the study areas. The combination of these indices exhibited a correlation with seasonal rainfall approximately 11% higher than those derived from the SVD method. Moreover, NLSFS significantly enhanced the forecast accuracy compared to the frequently employed linear sequential forward selection (SFS) method, and the optimal predictors chosen by the two methods differed across all seasons.

Two‐Dimensional Hybrid Simulation of the Second‐Harmonic Generation of EMIC Waves in the Inner Magnetosphere

AbstractTwo‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation.

Reduced‐order observer‐based finite‐time control for one‐sided Lipschitz nonlinear switched singular systems

SummaryThe reduced‐order observer‐based finite‐time control problem for one‐sided Lipschitz nonlinear switched singular systems is addressed in this paper. First, the design method of the reduced‐order observer is given via state transformation. Then, based on the average dwell time (ADT) approach, some new sufficient conditions for regularity, impulse‐freeness, have a unique solution and finite‐time boundedness (FTB) of the dynamic augmented systems are obtained by exploring the reduced‐order observer‐based controller. Further, the lower finite‐time bound can be obtained by using singular value decomposition method. And the state feedback gain and the observer gain are computed by solving linear matrix inequalities (LMIs). Finally, the validity of the obtained method is illustrated by means of a numerical example and a DC motor system.