Hankel Singular Value Decomposition Research Articles

Precision Heart Rate Estimation Using a PPG Sensor Patch Equipped with New Algorithms of Pre-Quality Checking and Hankel Decomposition.

A new method for accurately estimating heart rates based on a single photoplethysmography (PPG) signal and accelerations is proposed in this study, considering motion artifacts due to subjects' hand motions and walking. The method comprises two sub-algorithms: pre-quality checking and motion artifact removal (MAR) via Hankel decomposition. PPGs and accelerations were collected using a wearable device equipped with a PPG sensor patch and a 3-axis accelerometer. The motion artifacts caused by hand movements and walking were effectively mitigated by the two aforementioned sub-algorithms. The first sub-algorithm utilized a new quality-assessment criterion to identify highly noise-contaminated PPG signals and exclude them from subsequent processing. The second sub-algorithm employed the Hankel matrix and singular value decomposition (SVD) to effectively identify, decompose, and remove motion artifacts. Experimental data collected during hand-moving and walking were considered for evaluation. The performance of the proposed algorithms was assessed using the datasets from the IEEE Signal Processing Cup 2015. The obtained results demonstrated an average error of merely 0.7345 ± 8.1129 beats per minute (bpm) and a mean absolute error of 1.86 bpm for walking, making it the second most accurate method to date that employs a single PPG and a 3-axis accelerometer. The proposed method also achieved the best accuracy of 3.78 bpm in mean absolute errors among all previously reported studies for hand-moving scenarios.

Anomaly detection of complex magnetic measurements using structured Hankel low-rank modeling and singular value decomposition.

The magnetic anomalies generated by the ferromagnetic targets are usually buried within uncontrollable interference sources, such as the power frequency and random noises. In particular, the variability of the geomagnetic field and the low signal-to-noise ratio (SNR) of the magnetic anomalies cannot be avoided. In this paper, to improve the performance of magnetic anomaly detection (MAD) with a low SNR, we propose a novel structured low-rank (SLR) decomposition-based MAD method. In addition, a new framework based on the SLR and singular value decomposition (SVD) is constructed, dubbed SLR-SVD, and the corresponding working principle and implemented strategy are elaborated. Through comparing the SLR-SVD with two state-of-the-art methods, including principal component analysis and SVD, the results demonstrate that the proposed SLR-SVD can not only suppress the noise sufficiently, i.e., improving 55.26% approximately of the SNR, but also retain more boundary information of magnetic anomalies, i.e., decreasing approximately 68.05% of the mean squared error and improving approximately 28.47% of the structural similarity index.

A novel series arc fault detection method for photovoltaic system based on multi-input neural network

There is a risk of fire caused by series arc failure in the operation of photovoltaic (PV) system. Therefore, it is required to discuss a solution for rapid arc fault detection. To address the series arc fault (SAF) detection under different working conditions, a method based on squeeze-and-excitation (SE)-inception multi-input convolutional neural network (MICNN) is proposed. Firstly, normalization and Hankel-singular value decomposition algorithm are used to denoise the current, which effectively avoid the influence of switching frequency on the subsequent diagnostic accuracy. Subsequently, the filtered time-domain signal and the frequency-domain signal after Fourier transform are input into a variant one-dimensional convolutional neural network (1D-CNN) model for training and testing. The proposed model is characterized by transforming the traditional CNN into MICNN, and introducing the inception network with spatial scaling function and the SE network structure with channel attention mechanism. Extensive simulations are performed to evaluate the efficacy with a desirable result of 97.48%, which is superior to traditional methods such as CNN, wavelet decomposition, and mathematical statistics. The proposed method can not only detect arc faults occurring in different locations, but also resist the disturbance of dynamic shading, maximum power point tracking (MPPT), strong wind, etc. In addition, this model achieved satisfactory results in three cases of long line fault, single series and array ageing.

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.

Series Arc Fault Detection of Grid-Connected PV System via SVD Denoising and IEWT-TWSVM

Series arc fault (SAF) is one of the most harmful faults during the operation of photovoltaic (PV) systems. It is a challenging task to find SAFs promptly for avoiding the PV fire. Aiming at the SAFs under different operating conditions, a novel detection algorithm by combining the Hankel singular value decomposition (Hankel-SVD) denoising method and the improved empirical wavelet transform–twin support vector machine (IEWT-TWSVM) is proposed. The Hankel-SVD algorithm is used to denoise the dc-bus current, which alleviates the influence of switching frequency and irrelevant background noise effectively. Then, the denoised current is decomposed by the IEWT, and the composite multiscale permutation entropy of each frequency band is input into the TWSVM classifier of the salp swarm optimization for completing the fault detection. The proposed algorithm not only can detect SAFs at various fault locations, but also resist dynamic shading, inverter startup, strong wind, and other interference phenomena. Moreover, the detection performance due to the arc transient process, a long-line fault, a single string array fault, a multiply string array fault, and different sampling rates of this model is verified in this study, and the corresponding results are relatively ideal. Experimental results show that the detection accuracy of the proposed method is as high as 98.10% for the measured data, which is more superior than other methods, such as wavelet decomposition, empirical mode decomposition, statistics methods including mean, standard deviation, and entropy.

Method for fast lipid reconstruction and removal processing in 1 H MRSI of the brain.

To develop a new rapid spatial filtering method for lipid removal, fast lipid reconstruction and removal processing (FLIP), which selectively isolates and removes interfering lipid signals from outside the brain in a full-FOV 2D MRSI and whole-brain 3D echo planar spectroscopic imaging (EPSI). FLIP uses regularized least-squares regression based on spatial prior information from MRI to selectively remove lipid signals originating from the scalp and measure the brain metabolite signals with minimum cross contamination. FLIP is a noniterative approach, thus allowing a rapid processing speed, and uses only spatial information without any spectral priors. The performance of FLIP was compared with the Papoulis-Gerchberg algorithm (PGA), Hankel singular value decomposition (HSVD), and fast image reconstruction with L2 regularization (L2). FLIP in both 2D and 3D MRSI resulted in consistent metabolite quantification in a greater number of voxels with less concentration variation than other algorithms, demonstrating effective and robust lipid-removal performance. The percentage of voxels that met quality criteria with FLIP, PGA, HSVD, and L2 processing were 90%, 57%, 29%, and 42% in 2D MRSI, and 80%, 75%, 76%, and 74% in 3D EPSI, respectively. The quantification results of full-FOV MRSI using FLIP were comparable to those of volume-localized MRSI, while allowing significantly increased spatial coverage. FLIP performed the fastest in 2D MRSI. FLIP is a new lipid-removal algorithm that promises fast and effective lipid removal with improved volume coverage in MRSI.

Kernel Function Definition Completion for Time–Domain State–Space Representations of Radiation Forces: Application to the Hankel Singular Value Decomposition

This paper focuses on the formulation of state–space representations of radiation forces for marine structures using Hankel Singular Value Decomposition (HSVD), a method used to obtain a state–space realization from a Hankel matrix, with the classical definition of the kernel function and its new definition given in this paper. The first part shows the influence of a term commonly neglected and the resulting improvement by taking this term into account. The second part will focus on the feedthrough matrix to understand why some models have none and why some others, such as HSVD, have one. An exact definition of the kernel function will be given underlying its discontinuity and its causality. This study also shows the interest of extrapolating hydrodynamic coefficients before approaching radiation forces by a state–space model.

Model-Based Monitoring of Patient Response to Staged Thyroidectomy

The goal of this study is to develop a model-based control chart for monitoring patient behavior in a staged thyroidectomy considering risk factors and clinical prescription. prospectively collected data are gathered from thyroid surgery unit of a hospital located in Tehran, Iran for 80 staged thyroidectomy patients discharged from 2009 to 2013. A risk adjusted state space model is developed based on the staged thyroidectomy. Variables to be included in the model are determined as a part of the model building process. Performance criteria, clinical prescription and patient risk factors are three variable components for the model. The appropriate risk factors are directly involved in the model and no scoring system is used for the model construction. Model identification is performed in two steps; model order selection and parameter estimation. In the first step, Hankel singular value decomposition (HSVD) is used for detecting the model order and in the second step, unknown parameters are estimated by the prediction error minimization (PEM) method. For monitoring patient responses, a group individual (GI) control chart is introduced and applied to a real-world problem. Results indicate that the suggested control chart can monitor the staged thyroidectomy patient’s behavior with an acceptable accuracy. Also, computer aided diagnosis (CAD) systems can be developed based on the proposed identification and monitoring method.

Structural and Crack Parameter Identification on Structures Using Observer Kalman Filter Identification/Eigen System Realization Algorithm

Structural and crack parameters in a continuous mass model are identified using Observer Kalman filter Identification (OKID) and Eigen Realization Algorithm (ERA). Markov parameters are extracted from the input and out responses from which the state space model of the structural system is determined using Hankel matrix and singular value decomposition by Eigen Realization algorithm. The structural parameters are identified from the state space model. This method is applied to a lumped mass system and a cantilever which are excited with a harmonic excitation at its free end and the acceleration responses at all nodes are measured. The stiffness and damping parameters are identified from the extracted matrices using Newton-Raphson method on the structure. Later, cracks are introduced in the cantilever and all structural parameters are assumed as known priori, the unknown crack parameters such as normalized crack depth and its location are identified using OKID/ERA. The parameters extracted by using this algorithm are compared with other structural identification methods available in the literature. The main advantage of this algorithm is good accuracy of identified structural parameters.

A Novel Data-Driven Magnetic Resonance Spectroscopy Signal Analysis Framework to Quantify Metabolite Concentration

Developing tools for precise quantification of brain metabolites using magnetic resonance spectroscopy (MRS) is an active area of research with broad application in non-invasive neurodegenerative disease studies. The tools are mainly developed based on black box (data-driven), or basis sets approaches. In this study, we offer a multi-stage framework that integrates data-driven and basis sets methods. We first use truncated Hankel singular value decomposition (HSVD) to decompose free induction decay (FID) signals into single tone FIDs, as the data-driven stage. Subsequently, single tone FIDs are clustered into basis sets while using initialized K-means with prior knowledge of the metabolites, as the basis set stage. The generated basis sets are fitted with the magnetic resonance (MR) spectra while using a linear constrained least square, and then the metabolite concentration is calculated. Prior to using our proposed multi-stage approach, a sequence of preprocessing blocks: water peak removal, phase correction, and baseline correction (developed in house) are used.

Model reduction for Model Predictive Control of district and communal heating systems within cooperative energy systems

The benefits of applying advanced control approaches such as Model Predictive Control to the building energy domain are well understood. Furthermore, to facilitate the decarbonisation of the sector, district heating, communal heating and heat pumps are set to become more common, leading to a greater need to employ advanced approaches to enable flexible integration with the power grid whereby buildings can provide flexibility services to mitigate grid stress. The development of models that are complex enough to capture the behaviour of large numbers of buildings without introducing excessive computational effort remains a challenge. In this paper, an approach is proposed in which model reduction techniques based on Hankel Singular Value Decomposition are applied in cooperation with state-of-the-art building energy modelling tools to produce models of large numbers of buildings that remain tractable within an MPC framework. The approach is demonstrated using a case study in which a MPC is developed for a 95-flat communal heating system. Centralised and decentralised approaches are considered, particularly in their respective ability to incorporate externally imposed constraints on the supply.

Tensor-Based Method for Residual Water Suppression in 1H Magnetic Resonance Spectroscopic Imaging.

Magnetic resonance spectroscopic imaging (MRSI) signals are often corrupted by residual water and artifacts. Residual water suppression plays an important role in accurate and efficient quantification of metabolites from MRSI. A tensor-based method for suppressing residual water is proposed. A third-order tensor is constructed by stacking the Löwner matrices corresponding to each MRSI voxel spectrum along the third mode. A canonical polyadic decomposition is applied on the tensor to extract the water component and to, subsequently, remove it from the original MRSI signals. The proposed method applied on both simulated and in-vivo MRSI signals showed good water suppression performance. The tensor-based Löwner method has better performance in suppressing residual water in MRSI signals as compared to the widely used subspace-based Hankel singular value decomposition method. A tensor method suppresses residual water simultaneously from all the voxels in the MRSI grid and helps in preventing the failure of the water suppression in single voxels.

Estimation of both Nyquist zone index and code rate for BPSK radar signal intercepted by Nyquist folding receiver

Nyquist folding receiver (NYFR) can realize the wideband receiving with a small amount of equipment. As a tradeoff between the amount of equipment and the complexity of the signal processing, the NYFR output is usually a hybrid modulated signal. Therefore, it is necessary to investigate the parameter estimation method of the signal intercepted by the NYFR. Binary phase shift keying (BPSK) signal is a typical low probability of intercept radar signal and the authors focus on the parameter estimation of the BPSK radar signal intercepted by the NYFR. Firstly, matching component function is proposed to obtain Nyquist zone (NZ) index. Then, the Hankel-singular value decomposition (SVD) method is introduced to estimate the code rate of the BPSK signal. The efficacy of the Hankel-SVD method is proved in a mathematical way. Several numerical simulations demonstrate the merits of the proposed approach and finally, a brief investigation for case of the multiple BPSK signals intercepted by the NYFR is given. For NZ index estimation, the computational complexity of the matching component function is low and it has no need to use squaring process. In addition, the code rate estimation using the Hankel-SVD method is more accurate compared with the wavelet transform.

A GPU-Parallelized Eigen-Based Clutter Filter Framework for Ultrasound Color Flow Imaging.

Eigen-filters with attenuation response adapted to clutter statistics in color flow imaging (CFI) have shown improved flow detection sensitivity in the presence of tissue motion. Nevertheless, its practical adoption in clinical use is not straightforward due to the high computational cost for solving eigendecompositions. Here, we provide a pedagogical description of how a real-time computing framework for eigen-based clutter filtering can be developed through a single-instruction, multiple data (SIMD) computing approach that can be implemented on a graphical processing unit (GPU). Emphasis is placed on the single-ensemble-based eigen-filtering approach (Hankel singular value decomposition), since it is algorithmically compatible with GPU-based SIMD computing. The key algebraic principles and the corresponding SIMD algorithm are explained, and annotations on how such algorithm can be rationally implemented on the GPU are presented. Real-time efficacy of our framework was experimentally investigated on a single GPU device (GTX Titan X), and the computing throughput for varying scan depths and slow-time ensemble lengths was studied. Using our eigen-processing framework, real-time video-range throughput (24 frames/s) can be attained for CFI frames with full view in azimuth direction (128 scanlines), up to a scan depth of 5 cm ( λ pixel axial spacing) for slow-time ensemble length of 16 samples. The corresponding CFI image frames, with respect to the ones derived from non-adaptive polynomial regression clutter filtering, yielded enhanced flow detection sensitivity in vivo, as demonstrated in a carotid imaging case example. These findings indicate that the GPU-enabled eigen-based clutter filtering can improve CFI flow detection performance in real time.

Dynamic study of viscoelastic rotor: Reduction of higher order model using different techniques

Finite element formulation of general viscoelastic rotor reaches a higher order configuration due to the inherent material properties, resulting in a complicated system. The interest of this paper is the application of suitable reduction technique, which helps to rewrite the system equations with important coordinates. In order to understand the best methodology to reduce the higher order model, two different reduction techniques have been used: (i) Iterative Improved Reduction System, (ii) Balanced Realization System. In first case, an iterative algorithm is used to improve the transformation matrix by achieving convergence. Whereas, in second case, Hankel Singular Value Decomposition assures to predict the most controllable and observable states, which helps to reduce the system matrices accurately. The benefit of implementing these techniques is to tackle the problems caused due to skew-symmetric matrices that emanate for an addition of internal material damping and gyroscopic effects. The effectiveness of reduced model is well examined using various dynamic parameters. The agreement between reduced and original system predict the usefulness of this study.

SU‐F‐I‐23: 1H Magnetic Resonance Spectroscopy Baseline Correction WithSingular Value Decomposition Method

Purpose:Baseline distortions in NMR spectra are caused by the corruption of the first few data points in Free Induction Decay (FID) or originated from macromolecules and lipids. To study the Singular Value Decomposition (SVD) based baseline correction method.Methods:In‐house Singular Value Decomposition (SVD) program was developed with Matlab version 7.6 (Mathworks.com). Hankel SVD method (singular value decomposition of the acquired FID signal arranged in a Hankel matrix) is used to compute the signal poles and amplitude, and from them the signal frequencies and damping factors. The estimated FID signals are constructed from the quantification parameters; residue error spectrum was calculated by FFT of the difference of original FID and estimated FID. In order to study the baseline correction effect, known simulated FID with added noise to mimic known metabolites concentration was analyzed with SVD, quantification results were compared with known reference; then baseline distortion was introduced by removing the first 5 data points, after baseline corrected with SVD method, the quantification results were compared with original reference without baseline distortion.Known patient FID acquired with Siemens Verio 3T scanner was introduced baseline distortion by removing the first 3 data points, after baseline corrected with SVD method, corrected FID were compared with original results without baseline distortion.Results:Quantification results for simulated data were compared with reference, all within 10% deviation with SNR 20.For FID acquired with Siemens Verio 3T scanner, distorted FID and calculated baseline with SVD method was compared, the baseline matches the distortion well. Corrected FID were used for quantification, the quantification results match the corrected FID well.Conclusion:As demonstrated, SVD based baseline correction method can be used to correct the FID data point missing type of distortion, results are satisfactory for both simulated data and acquired patient data.

Hybrid Models Based on Singular Values and Autoregressive Methods for Multistep Ahead Forecasting of Traffic Accidents

The traffic accidents occurrence urges the intervention of researchers and society; the human losses and material damage could be abated with scientific studies focused on supporting prevention plans. In this paper prediction strategies based on singular values and autoregressive models are evaluated for multistep ahead traffic accidents forecasting. Three time series of injured people in traffic accidents collected in Santiago de Chile from 2000:1 to 2014:12 were used, which were previously classified by causes related to the behavior of drivers, passengers, or pedestrians and causes not related to the behavior as road deficiencies, mechanical failures, and undetermined causes. A simplified form of Singular Spectrum Analysis (SSA), combined with the autoregressive linear (AR) method, and a conventional Artificial Neural Network (ANN) are proposed. Additionally, equivalent models that combine Hankel Singular Value Decomposition (HSVD), AR, and ANN are evaluated. The comparative analysis shows that the hybrid models SSA-AR and SSA-ANN reach the highest accuracy with an averageMAPEof 1.5% and 1.9%, respectively, from 1- to 14-step ahead prediction. However, it was discovered that HSVD-AR shows a higher accuracy in the farthest horizons, from 12- to 14-step ahead prediction, which reaches an averageMAPEof 2.2%.

Non-stationary Clutter Rejection Based on Hankel-SVD for Ultrasound Color Flow Imaging

Effective rejection of the time-varying clutter originating from slowly moving vessels and surrounding tissues is very important for depicting hemodynamics in ultrasound color Doppler imaging. In this paper, a new adaptive clutter rejection method based on Hankel Singular Value Decomposition (Hankel-SVD) is presented for suppressing non-stationary clutter. In the proposed method, a Hankel data matrix is created for each slow-time ensemble. Then the orthogonal principle Hankel components can be obtained through the SVD of the Hankel data matrix. It achieves non-stationary clutter suppression by reconstructing the flow signal with only the high order principle Hankel components, which are estimated from the frequency content carried by the principle Hankel components. To assess its efficiency, the proposed Hankel-SVD based method is applied to synthetic slow-time data obtained from a Doppler flow model and carotid arterial complex baseband data acquired by a commercial ultrasound system (Sonix RP). The resulting flow and power images show that the proposed method outperforms the traditional IIR and polynomials regression filter in attenuation of high intense non-stationary clutter signal. It is also adaptive to highly spatially-varying tissue motion and can automatically select the order of the filter, which leads to improved distinguishing between blood and tissue regions compared to other eigen-based filters.

WE-C-116-12: Camer-Rao Lower Bound Analysis of 1H Magnetic Resonance Spectroscopic Imaging for Breast with Singular Value Decomposition, LCModel and QUEST

Purpose: LCModel and QUEST supply error estimate capability, however no standard basis available for unknown lipids mixture in breast. Singular Value Decomposition (SVD) with Linear Combination method was developed to implement desired CRLB function. The purpose of this study is to evaluate SVD, QUEST and LCModel quantification for breast MRSI with Camer-Rao Lower Bound (CRLB) analysis. Methods: Spectrum for 6 metabolite were simulated with Vespa (STEAM SVS, 3.0T, TE=42ms, TM=10ms), mixture spectrum was simulate with known ratio. jMRUI 4.0 (QUEST function) and LCModel 6.3 was used in the study, metabolite basis was generated from individually simulated data. In-house SVD was developed with Matlab 7.6 to combine Hankel SVD and Linear Combination method. The estimated FID signals are constructed from the quantification parameters, residue error spectrum was calculated by FFT of the difference of original FID and estimated FID. In order to study the CRLB, known simulated spectrum without noise was analyzed with SVD, QUEST and LCModel. Then introduce random noise, quantification residue was analyzed, and estimated parameters with CRLB were compared with results without noise. Sample patient breast MRSI data was collected with Siemens TrioTim (PRESS CSI, 3.0T, TE=80ms). Results: For simulated data, both Quest and LCModel can reliably quantify with SNR of 5 and signal as low as 17% of maximum; while SVD method can quantify with SNR of 10.Representative breast MRSI data were analyzed, LCModel residue error is 13.3% of original maximum and Cho CRLB is 56%; while SVD can achieve 3.7% and 3.6% respectively. Conclusions: For all methods, CRLB estimations increase with decrease the SNR. SVD is sensitive to noise, since it has no prior knowledge to reduce noise, if noise is larger than signal, fake peak can be introduced; while LCModel and QUEST can not quantify breast data well with limited simulated lipid basis.

TU‐G‐217A‐08: Camer‐Rao Lower Bound Analysis of 1H Magnetic Resonance Spectroscopic Imaging for Breast With Singular Value Decomposition Method and Linear Combination Method

Purpose: To study the Singular Value Decomposition (SVD) and Linear Combination (LC) quantification with Camer‐Rao Lower Bound (CRLB) analysis. Methods: In‐house Singular Value Decomposition (SVD) and LC program was developed with Matlab version 7.6 (Mathworks.com). Hankel SVD method (singular value decomposition of the acquired FID signal arranged in a Hankel matrix) is used to compute the signal poles and amplitude, and from them the signal frequencies and damping factors. In LC method, poles are generated from SVD analysis of averaged 10 FID, the amplitudes of the signal components were estimated by the least square method for individual FID signal. The estimated FID signals are constructed from the quantification parameters, residue error spectrum was calculated by FFT of the difference of original FID and estimated FID. In order to study the CR lower bound, known simulated spectrum without noise was analyzed with SVD and LC method. Then introduce random noise, quantification residue was analyzed, and estimated parameters with CRLB were compared with results without noise. Results: CRLB estimation is verified with the standard deviation calculation, CRLB is larger than and comparable to standard deviation. For small signal as low as 1.5% of maximum, SVD can detect at SNR 10, LC can handle SNR 5. For SNR 5, SVD can reliably detect signal like 12.5% of maximum. Typical patient data from breast tumor data was analyzed with SVD and LC methods too, results are reliable and consistent. Conclusions: CRLB estimation is verified with the standard deviation calculation. Both SVD and LC method can be used for human MRSI, the SVD method is sensitive to noise, since it has no prior knowledge to reduce noise; if noise is larger than signal, fake peak can be introduced. LC method combined with SVD generated poles can be exploited in MRSI with best results.