Singular Value Decomposition Method Research Articles

Multi-innovation adaptive Kalman filter algorithm for estimating the SOC of lithium-ion batteries based on singular value decomposition and Schmidt orthogonal transformation

The state of charge (SOC) of lithium battery is a key parameter for effective management of battery management systems (BMS). To address the problems of low precision, complex computation and poor robustness of traditional charging state estimation methods, an enhanced algorithm based on Unscented Kalman filter (UKF) is proposed. The singular value decomposition (SVD) method is adopted to ensure the normal operation of the Unscented Kalman Filter (UKF) algorithm even when the matrix P lacks positive semi-definiteness from a mathematical perspective. This enhancement significantly improves the theoretical robustness of UKF. Schmidt orthogonal transformation is concurrently used to reduce the computational complexity in the sampling point selection process, and the multi-innovation theory is combined with adaptive noise control to further improve the accuracy of SOC estimation. The algorithm is validated using the Urban Dynamometer Driving Schedule (UDDS) condition. The simulation results are excited using Singular value decomposition-multi-innovation adaptive Schmidt orthogonal unscented Kalman filter method (SVD-MIASOUKF). 0.95 % and 1.29 % of maximum errors are obtained at 25 °C and −10 °C, while the maximum errors are 2.46 %–2.99 % using SVD-UKF and UKF. The proposed approach shows faster convergence speed and higher estimation accuracy in comparison to traditional algorithms.

Multiscale Damage Identification Method of Beam-Type Structures Based on Node Curvature

This paper proposes a multiscale damage identification method for beam-type structures based on node curvature. Firstly, based on the assumption that micro-damage has little effect on stress redistribution and the basic relationship between structural bending moment and curvature, combined with the denoising function of wavelet analysis, the linear matrix equation before and after node curvature damage is solved using the singular value decomposition (SVD) method. Then, the theoretical feasibility of this method is verified with laboratory tests of a simply supported beam. Finally, the damage sensitivity and noise resistance of this method are verified using field measurements of a beam bridge. The results show that the nodal curvature serves as an indicator parameter for damage identification in beam-type structures, enabling the precise localization of damage within these structures. When utilizing a multiscale finite element model for analysis, the nodal curvature enhances the ability to identify both the location and severity of damage within small-scale elements. Furthermore, this method can provide a reference for the damage identification and health monitoring of other types of bridges.

GNSS-assisted optimal alignment method for low-cost SINS motion of vehicle

Abstract To improve the alignment accuracy and environmental applicability of the micro-electromechanical system (MEMS)-based strapdown inertial navigation system (SINS), this study proposes a global navigation satellite system (GNSS)-assisted multi-vector determination of the attitude optimal indirect coarse alignment. Using the inertial information output from the inertial measurement unit and the velocity information from the GNSS, a simplified velocity observation vector is constructed and the velocity lever arm stemming from the mounting position inconsistencies of the GNSS and SINS is fed back into the velocity of the carrier system. When constructing the observation vectors, the integration interval is shortened by reconstructing the two-vector integration formula for reducing the cumulative error of the inertial device. The attitude matrix problem is defined as the Wahba problem, which is solved using the singular value decomposition method. Based on the relationship between gyro zero bias and misalignment angle, the corresponding state and measurement equations are designed. Furthermore, owing to the measurement noise uncertainty, the adaptive traceless Kalman filtering algorithm is introduced to realize the effective adaptation processing of the measurement noise. More accurate attitude matrix estimates are obtained by continuously correcting the carrier system transformation matrix. The running car experiment results show that the proposed method exhibits higher alignment accuracy and environmental applicability than the current MEMS strapdown inertial navigation coarse alignment method and the traditional optimization-based alignment method.

Parameter identification of rock mass in the time domain

A time domain rock mass parameter identification method considering the Rayleigh damping is proposed in this paper. Starting with a set of initial parameter values, the algorithm solves the finite-element (FE) equations updating the parameters in each iterative step until the result converges to a local optimum. Numerical FE analysis, displacement sensitivity analysis, and the truncated singular value decomposition method are integrated into the solution algorithm for parameter identification. The technique introduced is verified in numerical studies with in-situ experiments of rock mass structures. Our results show that the approach, compared with conventional methods, can reduce ambiguities caused by inadequate data and provide more accurate insights into the subsurface for rock mass quality evaluation.

Robust fusion filter for networked uncertain descriptor systems with colored noise and cyber-attacks

The robust fusion filtering problem of multi-sensor networked uncertain descriptor systems (NUDSs) with colored noise, uncertain noise variances and cyber-attacks is investigated. During data transmission in unreliable communication networks, the data can be maliciously attacked by attackers. In other words, the local filters (LFs) may receive false data or may not receive data because of the cyber-attacks. By adopting the singular value decomposition (SVD) method, the original NUDSs can be converted into two reduced-order subsystems with uncertain correlated fictitious white noises, and the cyber-attacks are transformed into the fictitious noises. Cross-covariance matrices between local filtering errors are derived. The robust LFs are obtained according to the minimax robust estimation principle. Under the linear unbiased minimum variance criterion, three weighted fusion algorithms are applied to fuse the LFs. For all allowable uncertainties of noise variances and cyber-attacks, the minimal upper bounds of covariance matrices of the local and distributed fusion filters are guaranteed. The proof of their robustness is established through the minimax estimation principle and Lyapunov equation method. Finally, the correctness and effectiveness of the proposed algorithms are verified by a circuit system example.

Tool wear feature extraction in BTA deep hole drilling process based on maximum probability multi-synchrosqueezing transform of spindle current signal

Multi-synchrosqueezing transform (MSST) enhances the concentration of the time–frequency representation (TFR) of time-varying signals by introducing multi-instantaneous frequency (IF) estimation operator. However, the existence of estimation bias may lead to uncertainty in the discrete values of IF during computer computations, causing issues with non-reassigned points. In this paper, a maximum probability multi-synchrosqueezing transform (MPMSST) is proposed, which incorporates distribution probability during the discretization process of the IF, taking the frequency corresponding to the maximum distribution probability as the determined value of IF. Through verification with multi-component time-varying simulation signals, MPMSST not only effectively eliminates non-reassigned points but also accurately estimates the theoretical time–frequency curve. By applying MPMSST to analyze spindle motor current signals during deep hole machining, TFRs under different tool wear states are obtained. The singular value decomposition (SVD) method is utilized to extract the principal component of the TFR, and a tool wear state feature index is constructed based on the sum of squares of the first 10 singular values. The correlation coefficient and covariance between the proposed feature index and the tool wear curve are 0.835 and 5.704 respectively, indicating a good consistency of the index with tool wear changes, and a high sensitivity to variations in tool wear state.

Intelligent analysis and measurement of semicircular canal spatial attitude.

The primary aim of this investigation was to devise an intelligent approach for interpreting and measuring the spatial orientation of semicircular canals based on cranial MRI. The ultimate objective is to employ this intelligent method to construct a precise mathematical model that accurately represents the spatial orientation of the semicircular canals. Using a dataset of 115 cranial MRI scans, this study employed the nnDetection deep learning algorithm to perform automated segmentation of the semicircular canals and the eyeballs (left and right). The center points of each semicircular canal were organized into an ordered structure using point characteristic analysis. Subsequently, a point-by-point plane fit was performed along these centerlines, and the normal vector of the semicircular canals was computed using the singular value decomposition method and calibrated to a standard spatial coordinate system whose transverse planes were the top of the common crus and the bottom of the eyeballs. The nnDetection target recognition segmentation algorithm achieved Dice values of 0.9585 and 0.9663. The direction angles of the unit normal vectors for the left anterior, lateral, and posterior semicircular canal planes were [80.19°, 124.32°, 36.08°], [169.88°, 100.04°, 91.32°], and [79.33°, 130.63°, 137.4°], respectively. For the right side, the angles were [79.03°, 125.41°, 142.42°], [171.45°, 98.53°, 89.43°], and [80.12°, 132.42°, 44.11°], respectively. This study successfully achieved real-time automated understanding and measurement of the spatial orientation of semicircular canals, providing a solid foundation for personalized diagnosis and treatment optimization of vestibular diseases. It also establishes essential tools and a theoretical basis for future research into vestibular function and related diseases.

Evaluation of fluence-to-dose response function of neutron survey meter using singular value decomposition method

This paper presents the evaluation of the fluence-to-ambient dose equivalent response function (referred to as F2D response function) of the Aloka TPS-451C neutron dose equivalent rate meter (hereafter referred to as a neutron meter) based on a singular value decomposition (SVD) approach. Measurements of neutron ambient dose equivalent rates, Ḣ∗(10), using the neutron meter were conducted in various neutron standard fields of 241Am-Be source with different neutron fluence rate spectra. A series of Ḣ∗(10) values and corresponding neutron fluence rate spectra were used as the input data for unfolding the F2D response function of the neutron meter. To verify the SVD-based method, the fluence response functions of a well-known Bonner sphere spectrometer system were unfolded using the SVD method, and the results were compared with those provided in the IAEA technical report No. 403. The SVD method was then applied to determine the F2D response function of the Aloka TPS-451C neutron meter with the use of the ICRP-74 F2D response function and that predicted in a previous work as initial guesses. The consistency between initial guesses and the SVD unfolded F2D response function of the Aloka TPS-451C neutron meter implies the reliability of the SVD method for determining the response functions of neutron meters.

Digital Watermarking Using Hybrid Grasshopper Optimization Algorithm and Genetic Algorithm (HGOAGA)

The advancement of computer technology has raised significant issues with digital content piracy and copyright law. A popular method of protecting copyright and related uses is digital watermarking. Various algorithms have been developed to address the need for invisible performance and robustness in digital watermarking schemes. Here, we proposed a novel evolutionary algorithm, the hybrid Grass Hopper Optimization algorithm, and the Genetic algorithm (HGOAGA) for optimizing multiple scaling factors in the digital watermarking scheme in the frequency domain of hybrid Discrete Wavelet Transformation (DWT) and Singular Value Decomposition (SVD) method (hybrid DWT-SVD). The subcomponents of the image are determined by calculating the DWT of the cover image. The problem is determining the best scaling factor for watermarking after converting the subcomponent to the frequency domain using SVD. In HGOAGA, an optimal solution of multiple scaling factors is found after several iterations, starting with a set of randomly generated solutions. The advantages of GOA and GA are combined in the HGOAGA to balance exploration and exploitation functionalities. Furthermore, HGOAGA can converge quickly and escape local optima well. Some standard images were used in the MATLAB environment to test the proposed algorithm. The evaluation of the experiment was carried out using various metrics such as the Structural Similarity Index (SSIM), the Normalized Cross-Correlation (NCC), and the Peak Signal-to-Noise Ratio (PSNR). The experimental results of the tests showed a PSNR value of 51db for the proposed method compared to existing methods, and they are best suited to solving conflict problems between robustness and quality.

Damage identification method based on interval regularization theory

In the field of damage identification, traditional regularization methods neglect the impact of uncertainty factors on the selection of regularization parameters, leading to a decrease in the accuracy of damage identification. Therefore, this study proposes a damage identification based on interval truncated singular value decomposition (DI-ITSVD) method that considers the uncertainty in the selection of regularization parameter. This method treats model errors and measurement noise as interval uncertainties, and introduces the quantified uncertainties into the damage identification solutions through uncertainty propagation methods to determine the interval boundary. Uncertainty regularization parameters are selected to balance residuals and solutions using interval and generalized cross-validation methods. The key aspect of the proposed method in this paper is the integration of interval uncertainty propagation with the truncated singular value decomposition method to ensure the accuracy and stability of the damage identification equation solution. A numerical example of a 29-bar planar truss has been performed to test the effectiveness of the proposed method. The superiority of this method is verified by comparing the identification results with other improved truncated singular value decomposition methods. Finally, the practical application effect of the proposed method was also verified through an experimental work.

Effect of singular value decomposition on removing injection variability in 2D quantitative angiography: An in silico and in vitro phantoms study.

Intraoperative 2D quantitative angiography (QA) for intracranial aneurysms (IAs) has accuracy challenges due to the variability of hand injections. Despite the success of singular value decomposition (SVD) algorithms in reducing biases in computed tomography perfusion (CTP), their application in 2D QA has not been extensively explored. This study seeks to bridge this gap by investigating the potential of SVD-based deconvolution methods in 2D QA, particularly in addressing the variability of injection durations. Building on the identified limitations in QA, the study aims to adapt SVD-based deconvolution techniques from CTP to QA for IAs. This adaptation seeks to capitalize on the high temporal resolution of QA, despite its two-dimensional nature, to enhance the consistency and accuracy of hemodynamic parameter assessment. The goal is to develop a method that can reliably assess hemodynamic conditions in IAs, independent of injection variables, for improved neurovascular diagnostics. The study included three internal carotid aneurysm (ICA) cases. Virtual angiograms were generated using computational fluid dynamics (CFD) for three physiologically relevant inlet velocities to simulate contrast media injection durations. Time-density curves (TDCs) were produced for both the inlet and aneurysm dome. Various SVD variants, including standard SVD (sSVD) with and without classical Tikhonov regularization, block-circulant SVD (bSVD), and oscillation index SVD (oSVD), were applied to virtual angiograms. The method was applied on virtual angiograms to recover the aneurysmal dome impulse response function (IRF) and extract flow related parameters such as Peak Height PHIRF, Area Under the Curve AUCIRF, and Mean transit time MTT. Next, correlations between QA parameters, injection duration, and inlet velocity were assessed for unconvolved and deconvolved data for all SVD methods. Additionally, we performed an in vitro study, to complement our in silico investigation. We generated a 2D DSA using a flow circuit design for a patient-specific internal carotid artery phantom. The DSA showcases factors like x-ray artifacts, noise, and patient motion. We evaluated QA parameters for the in vitro phantoms using different SVD variants and established correlations between QA parameters, injection duration, and velocity for unconvolved and deconvolved data. The different SVD algorithm variants showed strong correlations between flow and deconvolution-adjusted QA parameters. Furthermore, we found that SVD can effectively reduce QA parameter variability across various injection durations, enhancing the potential of QA analysis parameters in neurovascular disease diagnosis and treatment. Implementing SVD-based deconvolution techniques in QA analysis can enhance the precision and reliability of neurovascular diagnostics by effectively reducing the impact of injection duration on hemodynamic parameters.

A stable localized weak strong form radial basis function method for modelling variably saturated groundwater flow induced by pumping and injection

The unsaturated zone profoundly affects groundwater (GW) flow induced by pumping and injection due to the capillary forces. However, current radial basis function (RBF) numerical models for GW pumping and injection mostly ignore the unsaturated zone. To bridge this gap, we developed a new three-dimensional weak strong form RBF model in this study, called CCHE3D-GW-RBF. Flow processes were modelled by the mixed-form Richards equation which was iteratively solved by the modified Picard iteration. Soil-water characteristic curves were represented by the widely applicable formulas, the van Genuchten (1980) model. Differential operators were approximated by the localized Gaussian RBF, and the weighted singular value decomposition method was used to construct stable bases. The injection/pumping wells and the flux boundaries were handled by the weak formulation using Meshless Local Petrov Galerkin method, and the strong-form equation using the collocation RBF method was enforced on the other points. Good agreement was found between the simulation results from our numerical model and the well-accepted solutions in all three verification cases, demonstrating the accuracy and applicability of this model. In addition, a smaller RBF shape parameter was found to produce a more accurate modelling resulting, indicating the necessity of implementing stable bases for RBF models.

Numerical Calculation and Application for Crushing Rate and Fracture Conductivity of Combined Proppants

Proppant is one of the key materials for hydraulic fracturing. For special situations, such as middle-deep reservoirs and closure pressures ranging from 40 MPa to 60 MPa, using a single proppant cannot solve the contradiction between performance, which means crushing rate and fracture conductivity, and cost. However, using combined proppants is an economically effective method for hydraulic fracturing of such special reservoirs. Firstly, for different types, particle sizes, and proportions of combined proppants, various contact relationships between proppant particles are considered. The random phenomenon of proppant particle arrangement is described using the Monte Carlo method, and the deterministic phenomenon of proppant particles is processed using an optimization model, achieving computer simulation of the microscopic arrangement of proppant particles. Secondly, a mathematical model for the force analysis of combined proppant particles is established, and an improved singular value decomposition method is used for numerical solution. A computational model for the crushing rate and fracture conductivity of combined proppants is proposed. Thirdly, the numerical calculation results are compared and discussed with the test values, verifying the accuracy of the computational model. Finally, the application of combined proppants is discussed, and a model for optimizing the proportion of combined proppants is proposed. The onsite construction technology is introduced, and the cost and economic benefits of combined proppants are compared with those of all ceramic particles and excessive all-quartz sand. It is proved that combined proppants can balance performance and price, and are an economically effective method for hydraulic fracturing of special reservoirs. The research results can select the optimal proppant material and optimize the combination of different proppant types, which can help achieve cost reduction and efficiency increase in oil and gas development.

A new method with C-means segmentation for non-uniform image coordinate system definition in panoramic imaging employing Ladybug2 camera

A panorama ensures a stunning wide-angle field of view up to 360° representation of a scene, exceeding the limits of a normal photograph. Panoramic cameras satisfy the single-viewpoint characteristic. There are several types of panoramic cameras for 360-degree imaging. Multi-camera panoramic imaging systems pose a difficulty in obtaining a single projection center for the cameras. In a variety of practical implementations of panoramic cameras, it is possible to calculate three-dimensional coordinates from a panoramic image, especially using the Direct Linear Transformation (DLT) method. In this study, not only a defining method of the non-uniform image coordinate system is presented by utilizing the C-Means algorithm for a single panoramic image, captured with a Ladybug2 panoramic camera in a panoramic calibration room but also the use of an elliptical panoramic projection coordinate system is defined by the Singular Value Decomposition method in a 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. It has been observed that the proposed method provides more accurate results for the 3D coordinate definition.

Life Table Prediction Using the Lee-Carter Model

<span lang="EN-US">Mortality is the state where all signs of life permanently, which can occur at any time after a person is born. Mortality data can be presented in the form of table called a mortality table, which is a table that provides an overview of the life of a population group starting from births at the same time and life of a population group that starts from birth at the same time and slowly decreases due to death. In actuarial studies, this table has a role as one of the important factors to determine the amount of premium costs and premium reserves, especially life insurance. Therefore, it is necessary for continuity in conducting research related to mortality tables. This research aims to forecast the death rate and the probability of death of the population in the future using the Lee-Carter model, which is a mortality forecasting model that combines a demographic model with a time series model. This mortality model shows that the logarithm of mortality rate is the sum of the parameters of the average general mortality rate by age and the multiplication of the trend parameter of mortality rate changes by age with the mortality index parameter. Forecasting process begins with estimating the parameters of the average mortality rate and the trend of mortality rate changes influenced by the mortality index parameter using the singular value decomposition (SVD) method. After that, the mortality index mortality index is forecasted using the ARIMA model and the results of this forecast are then reinserted into the Lee-Carter model to obtain death rate prediction. Based on the results of the mortality rate prediction, it can then be the prediction of the probability of death for the mortality table. The result of this research is a mortality table that contains predictions of the probability of death of the Indonesian population for both male and female gender using the Lee-Carter model from the year 2022 2026. Based on these results, it is concluded that the value of the probability of death for each year increases with increasing age.</span>

Cyclic tensor singular value decomposition with applications in low-rank high-order tensor recovery

The rapid advancements in emerging technologies have increased the demand for recovery tasks involving high-dimensional data with complex structures. Effectively utilizing tensor decomposition techniques to capture the low-rank structure of such data is crucial. Recently, the high-order t-SVD has demonstrated strong adaptability. However, this decomposition approach can only capture the low-rank correlation of two modes along other modes individually, while disregarding the structural correlation between different modes. In this paper, we propose a novel cyclic tensor singular value decomposition (CTSVD) method that effectively characterizes the low-rank structures of high-order tensors along all modes. Specifically, our method decomposes an order-N tensor into N factor tensors and one core tensor, connecting them using a defined mode-k tensor-tensor product (t-product). Building upon this, we establish the corresponding tensor rank and its convex relaxation. To address the issue of dimensional imbalance between adjacent modes in high-dimensional data, we propose and integrate a square reshaping strategy into the recovery models for tensor completion (TC) and tensor principal component analysis (TRPCA) tasks. Effective alternating direction method of multipliers (ADMM)-based algorithms are designed to these tasks. Extensive experiments on both synthetic and real data demonstrate that our methods outperform state-of-the-art approaches.

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.

A new method of noise reduction grounded on the Hankel matrix and its application in rubbing fault diagnosis

Abstract In processing signals with singular value decomposition (SVD), one of the keys lies in building an appropriate Hankel matrix from signals. To address the difficulty in extracting the feature information of rubbing faults between rotor and stator, by taking advantage of the nature of rubbing fault information closely related to the rotation period of equipment, a new method of SVD is presented based on the Hankel matrix built from the periodicity of a rotation machine. First, with the periodicity of the rub-impact fault as the basis, the interval step size between Hankel vectors was determined to self-adaptively build a Hankel matrix of signals. Second, the newly-built Hankel matrix was denoised through the singular value differential spectrum. Third, to reduce the loss of data as much as possible, a strategy was proposed to rebuild signals according to the first and last rows of denoised signals. Fourth, features of rubbing faults were extracted according to the frequency spectrum of reconstructed signals, and faults were identified. To verify the applicability and effectiveness of the presented algorithm, various types of simulation signals and tester signals from different states were incorporated. Meanwhile, the presented algorithm was compared with a variety of classical methods. The results prove that the proposed method can not only effectively constrain noise interference, but also highlight fault feature information and correctly identify rub-impact faults.

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 autoencoders 2 (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.