Singular Value Decomposition Method Research Articles

Control method for determining feasible pre-stresses of cable-struts structure

The structural stiffness of a cable-struts structure is dependent on its feasible pre-stresses. The search for the pre-stresses is an inverse problem, and classical approaches for this problem include the singular value decomposition (SVD) method. Driven by the need for more efficient methods, this study proposes a control method to search for feasible pre-stresses of cable-struts structures. First, we formulate the governing equation for cable-struts structures under pre-stresses and external loads. Then, we apply feedback control and use a proportional–integral–derivative (PID) controller to solve for the feasible pre-stresses based on the condition of zero structural displacements. To verify the proposed method, the study selects a Geiger dome, a Kiewitt dome and a honeycomb-type cable dome under three different loading conditions, and compares the present results against those from literature. The comparison shows that the developed control method can efficiently and accurately determine the feasible pre-stresses under external loads. The relative errors in the pre-stresses determined using the PID controller and using another two methods (singular value decomposition and iterative method) are less than 0.020% and 0.015% for the Geiger dome and the honeycomb-type dome, respectively. This study contributes to developing efficient methods for design of cable-struts structures under complex service loads.

Design of Plane Wave Generator Based on Strong Robust Inverse Radiation Problem Solving Method

In this manuscript, we reconsider the amplitude and phase combination of the plane-wave generator (PWG) from an electromagnetic field inverse radiation perspective and further propose a new method based on the Gauss-Newton inversion (GNI) to perform the inverse design of PWG. Furthermore, the wideband antenna pattern is applied in the transfer function and makes the inversion results closer to the engineering implementation. Compared with the traditional least-squares method (LSM) and singular value decomposition (SVD) method, the proposed method owns the merits of less amplitude range of the input source and stronger robustness.

SOTT: Greedy Approximation of a Tensor as a Sum of Tensor Trains

In the present work, a method is proposed in order to compute an approximation of a given tensor as a sum of Tensor Trains (TTs), where the order of the variates and the values of the ranks can vary from one term to the other in an adaptive way. The numerical scheme is based on a greedy algorithm and an adaptation of the TT-SVD method. The proposed approach can also be used in order to compute an approximation of a tensor in a Canonical Polyadic format (CP), as an alternative to standard algorithms like Alternating Linear Squares (ALS) or Alternating Singular Value Decomposition (ASVD) methods. Some numerical experiments are proposed, in which the proposed method is compared to ALS and ASVD methods for the construction of a CP approximation of a given tensor and performs particularly well for high-order tensors. The interest of approximating a tensor as a sum of Tensor Trains is illustrated in several numerical test cases.

Missing Data Imputation in GNSS Monitoring Time Series Using Temporal and Spatial Hankel Matrix Factorization

GNSS time series for static reference stations record the deformation of monitored targets. However, missing data are very common in GNSS monitoring time series because of receiver crashes, power failures, etc. In this paper, we propose a Temporal and Spatial Hankel Matrix Factorization (TSHMF) method that can simultaneously consider the temporal correlation of a single time series and the spatial correlation among different stations. Moreover, the method is verified using real-world regional 10-year period monitoring GNSS coordinate time series. The Mean Absolute Error (MAE) and Root-Mean-Square Error (RMSE) are calculated to compare the performance of TSHMF with benchmark methods, which include the time-mean, station-mean, K-nearest neighbor, and singular value decomposition methods. The results show that the TSHMF method can reduce the MAE range from 32.03% to 12.98% and the RMSE range from 21.58% to 10.36%, proving the effectiveness of the proposed method.

Double layer local contrast measure and multi-directional gradient comparison for small infrared target detection

Infrared small target detection is one of the key technologies in the search and track (IRST) based on infrared imaging equipment. At present, the performance of small target detection based on single frame infrared image is directly related to the accuracy of subsequent target tracking, so it has been studied a lot. However, the existing small target detection algorithms have certain limitations in detection accuracy and real-time performance, especially when the contrast between the target and the background area is not high or the background is complex, especially in the complex sea or sky background, due to the influence of a large amount of noise and clutter in the background, the existing infrared small target detection algorithms have a high false alarm rate. To solve the above problems, this paper proposes a small target detection algorithm based on weighted double layer local contrast and multi-directional gradient map, which realizes the accurate detection of small targets from two aspects of targets’ local contrast and gradient. Firstly, we design an improved two layer local contrast measurement architecture, and use the weighted mean method to better represent the gray value of the local window; Secondly, a local contrast comparison method based on target and background is proposed to enhance the intensity of small targets and suppress some background clutter; Then, the multi-directional gradient map is used to further suppress the noise so as to improve the contrast between the target and the background. At the same time, singular value decomposition (SVD) method is used to extract the main features including small targets, which can effectively suppress the small texture interference around the targets in the background without losing the target intensity; Finally, an adaptive threshold method is used to separate small targets from their background. Experimental results show that compared with the existing algorithms, the proposed detection algorithm can effectively reduce the false alarm rate in different complex scenes, and the computational efficiency is improved compared with some multi-scale small target detection methods. At the same time, the signal to clutter ratio (SCR), background suppression factor (BSF) and receiver operating characteristic (ROC) curve are also better than these existing state of the art algorithms, which can display good robustness.

Secrecy sum rate maximization for a MIMO-NOMA uplink transmission in 6G networks

Non-orthogonal multiple access (NOMA), as a well-qualified candidate for sixth-generation (6G) mobile networks, has been attracting remarkable research interests due to high spectral efficiency and massive connectivity. The aim of this study is to maximize the secrecy sum rate (SSR) for a multiple-input multiple-output (MIMO)-NOMA uplink network under the maximum total transmit power and quality of service (QoS) constraints. Thanks to the generalized singular value decomposition method, the SSR of NOMA is compared with conventional orthogonal multiple access and other baseline algorithms in different MIMO scenarios. Due to the subtractive and non-convex nature of the SSR problem, the first-order Taylor approximation is exploited to transform the original problem into a suboptimal concave problem. Simulation results are provided and compared with some other benchmarks to evaluate the efficacy of the proposed method.

New results on stabilization for neutral type descriptor hybrid systems with time-varying delays

This paper revisits the issue of the stabilization for neutral type descriptor hybrid systems (NTDHSs) with time-varying delays. By a novel Lyapunov–Krasovskii functional (LKF) we constructed, a mode dependent and delay dependent criterion is acquired for the unforced NTDHSs to be stochastically admissible. On the basis of the criterion, a mode dependent state feedback controller (SFC) is designed such that the resulting closed-loop system is regular, impulse free and stochastically stable. By singular-value decomposition method, sufficient conditions are established via strict linear matrix inequality (LMI). And the gain of the SFC can be derived. It is worth noting that our results generalize the corresponding results published in latest literatures to some degree. The superiority and validity of our methods are displayed via two numerical examples.

A medical radar system for non-contact vital sign monitoring and clinical performance evaluation in hospitalized older patients

Medical radar plays an important role in non-contact vital sign monitoring. However, radar is sensitive and susceptible to noise that deteriorates signal quality, making its application unstable in medical practice settings. Previous studies have focused on detecting vital signs from radar output, but mainly used high-quality signals in laboratory settings. Therefore, signal quality evaluation to maintain good-quality signals for processing is crucial for radar applications. This paper presents a vital sign monitoring system using medical radar that automatically evaluates signal quality to eliminate unsatisfactory signals using the support-vector machine and to extract heartbeat and respiration signals using the singular value decomposition method. To evaluate the system performance, we tested it on 10 healthy subjects and compared the obtained vital signs with those measured using a contact-type ECG device and a respiration belt. Two evaluation steps were conducted. First, we measured 10 subjects for evaluating the signal quality in a laboratory setting. The results showed that the accuracy for each subject archive was 93.2%–100%. Second, we extracted vital signs including respiration rate (RR) and the heart rate (HR) following signal quality classification. The results showed RR and HR deviation from 0 to 1 bpm, and 0 to 4 bpm, respectively. Moreover, the system was applied in a real medical practice setting for continuously monitoring the bedside of hospitalized older patients at a hospital.

Hierarchical Amplitude-Aware Permutation Entropy-Based Fault Feature Extraction Method for Rolling Bearings.

In order to detect the incipient fault of rolling bearings and to effectively identify fault characteristics, based on amplitude-aware permutation entropy (AAPE), an enhanced method named hierarchical amplitude-aware permutation entropy (HAAPE) is proposed in this paper to solve complex time series in a new dynamic change analysis. Firstly, hierarchical analysis and AAPE are combined to excavate multilevel fault information, both low-frequency and high-frequency components of the abnormal bearing vibration signal. Secondly, from the experimental analysis, it is found that HAAPE is sensitive to the early failure of rolling bearings, which makes it suitable to evaluate the performance degradation of a bearing in its run-to-failure life cycle. Finally, a fault feature selection strategy based on HAAPE is put forward to select the bearing fault characteristics after the application of the least common multiple in singular value decomposition (LCM-SVD) method to the fault vibration signal. Moreover, several other entropy-based methods are also introduced for a comparative analysis of the experimental data, and the results demonstrate that HAAPE can extract fault features more effectively and with a higher accuracy.

Monitoring multistage multivariate therapeutic processes using risk‐adjusted model‐based group multivariate EWMA control chart

AbstractThere exist multitude of therapeutic processes and the results are commonly observed during various dependent steps. For studying such processes that are referred to as multistage therapeutic processes, two concepts are of particular importance; risk adjustment and cascade property. To monitor such processes, a variety of control charts including model‐based control charts are used. In order to design model‐based control charts, analysts must first recognize a suitable model to identify the multistage processes by considering process risks and cascade property. Based on the identified model, the control charts can be proposed. In this study, a risk‐adjusted time‐variant linear state space model is introduced. Afterward, the model order and its parameters are estimated based on Hankel singular value decomposition (HSVD) and prediction error minimization (PEM) methods. Then, the group multivariate exponentially weighted moving average (GMEWMA) control chart is used to monitor a multistage multivariate therapeutic process. To evaluate the performance of the model‐based control chart, a simulation study as well as a two‐stage thyroid cancer surgery was used. Results show that the proposed control chart performs well for predicting and monitoring of multistage multivariate therapeutic processes in real world.

Addressing dynamics in radio frequency tomography

Tomographic imaging of a dynamic scene is addressed for the first time in this article. The effect of dynamics of the imaged object is studied for some deformation scenarios using the conventional truncated singular value decomposition (TSVD) method, which is applied in numerous static inverse scattering problems, together with variational data assimilation (DA) methods including three-dimensional variational (3D-VAR) and four-dimensional variational (4D-VAR) techniques. Results show that the DA frameworks outperform the TSVD method, which assumes the scene static, especially for objects with higher contrast. Also, it is seen that applying the conventional TSVD method makes the image blurred and distorts it for high-speed dynamic changes, particularly when the contrast is increased. However, the proposed DA methods seem to be robust against large deformation distortions and can still detect the object.

Strain accuracy enhancement of stereo digital image correlation for object deformation with large rotations

We propose a full-field stereo digital image correlation (DIC) strain measurement method to overcome the poor accuracy while measuring the deformation under large rotations. Such a drawback comes from the failure to consider rotation movements of the deformed objects when calculating their strain values. To address this, we first used a DIC matching algorithm combined with a rotated subset and feature point detection to obtain displacement fields. By employing a singular value decomposition method, we can then calculate rotation matrices of the strain windows before and after deformations. Finally, to eliminate the strain errors caused by rotation, we introduced the rotation matrices into the classical pointwise least squares DIC strain calculation method. Both numerical simulations and experiments are performed, and the accuracy and effectiveness of the proposed method are confirmed by the experimental results.

Robust Max-Min Energy Efficiency for RIS-Aided HetNets With Distortion Noises

The energy efficiency (EE) of femtocells is always limited by the surrounding radio environments in heterogeneous networks (HetNets), such as walls and obstacles. In this paper, we propose to deploy reconfigurable intelligent surfaces (RISs) to improve the EE of femtocells. However, perfect channel state information is more difficult to obtain due to the passive characteristics of RISs and non-cooperative relationship between different tiers. Besides, the low-cost transceivers and reflecting units suffer nontrivial hardware impairments (HWIs) due to the hardware limitations of practical systems. To this end, we investigate a realistic robust beamforming design based on max-min fairness for an RIS-aided HetNet under channel uncertainties and residual HWIs. The joint optimization of transmit beamforming vectors of femto base stations (FBSs) and the phase-shift matrices of RISs is formulated as a non-convex problem to maximize the minimum EE of the femtocell subject to the constraints of the maximum transmit power of FBSs, the quality of service of users, and unit modulus phase-shift constraints of RISs. We develop an iterative block coordinate descent-based algorithm which exploits the semi-definite relaxation, the S-procedure, and the singular value decomposition method. Simulation results reveal that the proposed algorithm outperforms existing algorithms in terms of fairness, EE, and outage probability.

A Novel Automatic Probe-to-Pad Alignment Error Correction Approach

In wafer test, the probe mark center shall be close to the pad center as much as possible. But the traditional probe-to-pad alignment (PTPA) process cannot always meet the requirements. So a novel automatic error correction approach was developed in this paper to improve the PTPA process. The approach is based on a classic two dimension rigid motion model and enhanced by integrating an iteratively reweighted least squares algorithm. The singular value decomposition method is also used to seek the solutions. Using the probe mark and pad geometric information, it first best fits the probe mark centers to the targets, then it expands the minimum probe mark to pad edge clearance to the largest. The experiments proved its good feasibility, accuracy and efficiency.

Enhanced Invisibility and Robustness of Digital Image Watermarking Based on DWT-SVD.

The propagation of digital media over the Internet has helped improve digitization, which has given an excessive lead to copyright issues. Digital watermarking techniques have been applied to address copyright issues. In research, a system is being developed to handle veracious types of watermarked attacks, for obtaining extreme security and an adequate level of visibility and robustness. The discrete wave transform (DWT) and singular value decomposition (SVD) approaches were applied to analyze veracious types of attacks. The DWT method was used to embed the host image in four levels; this level was processed using the SVD method. The peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) were applied to measure the invisibility, and the normalization correlation (NC) was used to examine the robustness of watermarked images. The empirical results showed that the proposed DWT-SVD achieved superior accuracy in identifying the various attacks. The proposed DWT-SVD performance was confirmed during the training process, and the proposed system was shown to have high invisibility and robustness against various types of attacks on watermarked images. Finally, the results of the proposed system were compared to existing systems, and it was shown that DWT-SVD achieved better performance in terms of pixel-value modification attacks.

INVERS TERGENERALISASI MOORE PENROSE

The generalized inverse is a concept for determining the inverse of a singular matrix and and matrix which has the characteristic of the inverse matrix. There are several types of generalized inverse, one of which is the Moore-Penrose inverse. The matrix is called Moore Penrose inverse of a matrix if it satisfies the four penrose equations and is denoted by . Furthermore, if the matrix satisfies only the first two equations of the Moore-Penrose inverse and , then is called the group inverse of and is denoted by . The purpose of this research was to determine the group inverse of a non-diagonalizable square matrix using Jordan’s canonical form and Moore Penrose’s inverse of a singular matrix, also a non-square matrix using the Singular Value Decomposition (SVD) method. The results of this study are the sufficient condition for a matrix to have a group inverse, i.e., a matrix has an index of 1 if and only if the product of two matrices forming is a full rank factorization and is invertible. Whereas for a singular matrix and a non-square , the Moore-Penrose inverse can be determined using Singular Value Decomposition (SVD). Keywords: generalized matrix inverse, Moore Penrose inverse, group inverse, Jordan canonical form, Singular Value Decomposition.

Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Method

In recent years, as a simple and effective method of noise reduction, singular value decomposition (SVD) has been widely concerned and applied. The idea of SVD for denoising is mainly to remove singular components (SCs) with small singular value (SV), which ignores the weak signals buried in strong noise. Aiming to extract the weak signals in strong noise, this paper proposed a method of selecting SCs by the correntropy-induced metric (CIM). Then, the frequency components of characteristic signals can be found through cyclic correntropy spectrum (CCES) which is the extension of the correntropy (CE). The proposed method firstly merges the signals collected by the two channels, secondly uses the principal components analysis (PCA) method to reduce the dimensionality, thirdly uses the singular value decomposition method to decompose the signal, fourthly calculates the CIM value to determine the selected singular components for construction, and finally uses the cyclic correntropy spectrum displaying the characteristics of the reconstructed signal. The experimental results show that the proposed method has a good effect on feature extraction.

Diffraction Separation and Imaging Using an Improved Singular Value Decomposition Method

Faults, fractures, karst caves, and other small-scale geological targets are critical for carbonate oil and gas exploration. However, seismic responses of these small-scale geological targets are low-energy diffractions and it is difficult for traditional method to image them with high resolution. To identify these targets, the diffraction separation is a key technology. Based on the difference of diffractions and reflections in both kinematic and dynamic properties, the singular value decomposition (SVD) method can separate diffractions and reflections effectively. However, how to select the appropriate singular value sequence for diffractions and reflections is a key issue in the application. Based on the analysis of the singular value spectrum characteristics, we propose a second-order difference spectrum strategy to improve the SVD method. The improved SVD method can separate the diffractions and reflections with minimal error. It is stable when seismic data contain Gaussian noise. Reverse time migration (RTM) method is used in the diffraction imaging because it can keep the true shape of subsurface scatterers when diffractions information is complete. Synthetic examples demonstrate the effectiveness of this method.

Novel SVD integrated with GBDT based Virtual Sample Generation and Its Application in Soft Sensor

With the coming of the big data era, data-driven based modeling approaches have become the hot research topic in recent years. Unfortunately, due to the limitation of the actual process, the data is basically in a steady state and it is difficult to obtain enough high-quality data, which is defined as the small sample (SS) problem. Recently, to deal with the SS problem, a virtual sample generation (VSG) approach based on the distribution of the original data has been taken into account. In this paper, a VSG method based on singular value decomposition (SVD) feature decomposition and gradient boosting decision tree (GBDT) prediction model (SVD-GBDT) is proposed. In the proposed SVD-GBDT method, firstly, the distribution characteristics of the original data are used to extract the main features and expand the number of samples by using the SVD algorithm. Then the GBDT algorithm is used to find the virtual output of the virtual samples by the SVD method. Finally, SVD and GBDT are combined to complete the sample expansion (SVD-GBDT-VSG). In this paper, we choose the purified terephthalic acid (PTA) industrial process to verify the effectiveness of the proposed methodology. Simulation results show that compared with related methods, the proposed SVD-GBDT-VSG algorithm in this paper can achieve sample expansion well and at the same time can effectively improve the accuracy performance of soft measurement.

Correlation between the CT Perfusion Parameter Values and Response to Recanalization in Patients with Acute Ischemic Stroke.

CT perfusion (CTP) provides various hemodynamic parameters. However, it is unclear which CTP parameters are useful in predicting clinical outcome in patients with acute ischemic stroke (AIS). Between February 2019 and June 2021, patients with anterior circulation large-vessel occlusion who achieved successful recanalization within 8 hours after stroke onset were included. The relative CTP parameter values analyzed by the reformulated singular value decomposition (SVD) method in the affected middle cerebral artery territories compared to those in the unaffected side were calculated. In addition, the ischemic core volume (ICV) was evaluated using a Bayesian Vitrea. The final infarct volume (FIV) was assessed by 24-hour MRI. The correlation between these CTP-derived values and clinical outcome was assessed. Forty-two patients were analyzed. Among the CTP-related parameters, the ICV, relative cerebral blood volume (rCBV), and relative mean transit time (rMTT) showed a strong correlation with the FIV (ρ = 0.74, p <0.0001; ρ = -0.67, p <0.0001; and ρ = -0.66, p <0.0001, respectively). In multivariate analysis, rCBV, rMTT, and ICV were significantly associated with good functional outcome, which was defined as a modified Rankin Scale score ≤2 (OR, 6.87 [95% CI, 1.20-39.30], p = 0.0303; OR, 11.27 [95% CI, 0.97-130.94], p = 0.0269; and OR, 36.22 [95% CI, 2.78-471.18], p = 0.0061, respectively). Among the CTP parameters analyzed by the SVD deconvolution algorithms, rCBV and rMTT could be useful imaging predictors of response to recanalization in patients with AIS, and the performances of these variables were similar to that of the ICV calculated by the Bayesian Vitrea.