Iterative Decomposition Research Articles

An Iterative Nonconformal Domain Decomposition Surface Integral Equation Method for Scattering Analysis of PEC Objects

Domain decomposition methods (DDMs) can effectively solve electromagnetic scattering problems induced by multiscale perfectly electrically conducting (PEC) objects. However, boundary conditions between adjacent subdomains usually need to be carefully treated, especially when nonconformal meshes exist. To mitigate this issue, an iterative nonconformal domain decomposition surface integral equation (IDD-SIE) formulation is proposed. Each subdomain is independently solved with scattering fields generated from other subdomains as additional excitations. The continuity of current densities across touching interfaces is guaranteed by iteratively solving coupled fields among subdomains. Therefore, troublesome boundary transmission conditions can be avoided and nonconformal meshes are intrinsically supported. Numerical results show that the proposed IDD-SIE formulation is accurate and efficient, and has excellent convergent properties in terms of iteration numbers.

Well-controlled versus poorly controlled diabetes in patients with obesity: differences in MRI-evaluated pancreatic fat content.

Patients with obesity and poorly controlled type 2 diabetes (T2D) are at high risk of diabetic complications. This study aimed to determine the associations of visceral adipose tissue (VAT), hepatic proton-density fat fraction (PDFF), and pancreatic PDFF with poor glycemic control in patients with obesity and T2D and to evaluate the metabolic effect of bariatric surgery in patients with obesity and poorly controlled diabetes. In this retrospective cross-sectional study, from July 2019 to March 2021, 151 consecutive obese patients with new-onset T2D (n=28), well-controlled T2D (n=17), poorly controlled T2D (n=32), prediabetes (n=20), or normal glucose tolerance (NGT; n=54) were included. A total of 18 patients with poorly controlled T2D were evaluated before and 12 months after bariatric surgery, and 18 non-obese healthy individuals served as controls. VAT, hepatic PDFF, and pancreatic PDFF were quantified by magnetic resonance imaging (MRI) using a chemical shift-encoded sequence [iterative decomposition of water and fat with echo asymmetry and least-squares estimation quantitation (IDEAL-IQ)]. Univariate analysis and multivariate regression analysis were performed. There were significant differences in VAT, hepatic PDFF, and all pancreatic PDFF between the new-onset T2D, prediabetes, and NGT groups (all P<0.05). Pancreatic tail PDFF was significantly higher in the poorly controlled T2D group than in the well-controlled T2D group (P=0.001). In the multivariate analysis, only pancreatic tail PDFF was significantly associated with increased odds of poor glycemic control [odds ratio (OR) =2.09; 95% confidence interval (CI): 1.11-3.94; P=0.022]. The glycated hemoglobin (HbA1c), hepatic PDFF, and pancreatic PDFF significantly decreased (all P<0.01) after bariatric surgery, and the values were statistically similar to those observed in the non-obese healthy controls. Increased fat in the pancreatic tail is strongly associated with poor glycemic control in patients with obesity and T2D. Bariatric surgery is an effective therapy for poorly controlled diabetes and obesity, which improves glycemic control and decreases ectopic fat deposits.

Structural Damping Ratio Identification through Iterative Frequency Domain Decomposition

The frequency domain decomposition method (FDD) is a commonly used method to identify structural modal parameters and analyze the structural dynamic performance. Although FDD has a high identification accuracy in natural frequencies and mode shapes, damping ratios cannot be identified accurately. The logarithmic decay method to identify the damping ratio in FDD needs the transformation from a narrow frequency band to the time domain, which leads to the loss of the corresponding mode outside the narrow band and add other modes in the narrow band. In this paper, an iterative frequency domain decomposition method (iFDD) is proposed to identify the structural damping ratio in frequency domain. Firstly, the natural frequencies and mode shapes are obtained by the FDD method, and the damping ratios during this identification process are assumed to be unknowns. Then, the natural frequencies, mode shapes, and unknowns are substituted into the output power spectrum formula to construct nonlinear equations. The damping ratios are obtained by solving the equations using iterative optimization methods. Finally, a numerical example and benchmark model are employed to validate the effectiveness of the proposed method. The results showed that the proposed iFDD method can identify the damping ratio precisely in the frequency domain, which is better than the traditional FDD performance.

Symplectic period mode decomposition method and its application in fault diagnosis of rolling bearing

The rolling bearing fault signals are accompanied with the specific periodic impulse components in case of fault. Due to the background noise, the periodic impulse component is extremely weak and difficult to be extracted. The periodic segment matrix (PSM) has excellent singular value aggregation property and can accurately separate the periodic impulse components from the signal. Based on this, a symplectic period mode decomposition (SPMD) method is proposed. Firstly, the singular value squared difference ratio (SVSDR) spectrum is defined, and the embedded dimension of PSM is determined. Then, the symplectic geometry component matrix is obtained by symplectic geometry similarity transformation, and the first symplectic geometry period component (SPC) is obtained by periodic impact intensity (PII). Finally, the spectral L2/L1 norm (SNL2/L1) index is used as the termination condition, and the iterative decomposition is terminated when the SNL2/L1 of the residual signal decreases. The emulation and experimental signals results indicate that the SPMD method can extract periodic impulse components accurately and is an effective rolling bearing fault diagnosis method.

Quantitative analysis of heavy metals in soil by X-ray fluorescence with improved variable selection strategy and bayesian optimized support vector regression

As a sensitive analytical technique, x-ray fluorescence (XRF) has received increasing attention in elemental analysis applications. In this paper, XRF technique coupled with improved variable selection strategy and bayesian optimized support vector regression was proposed for predicting heavy metals in the soil. First of all, an iterative variational mode decomposition (VMD) framework was provided to tackle continuous background interference in the XRF spectra of soil. The corrected spectra were then utilized for quantitative analysis of heavy metals. Aiming to implement accurate heavy metal prediction, we resorted to support vector regression (SVR) to establish the non-linear model. Combined with Bayesian optimization algorithm, the bayesian optimized SVR (BO-SVR) with optimal hyperparameters was obtained. However, severe collinearity between input variables can affect the accuracy and stability of the model. Towards this, the research utilized sensitivity analysis as the variable selection approach prior to BO-SVR prediction of XRF data sets. The experimental results revealed that BO-SVR assisted with VMD and sensitivity analysis yielded the best model outcome. Moreover, considerable contributions were observed by employing sensitivity analysis. It showed Rp2 of 0.9472 (for Cu), 0.7534 (for As), 0.9374 (for Zn), and 0.9283 (for Pb), and RMSEP of 58.0472 (for Cu), 16.5271 (for As), 63.2069 (for Zn) and 64.0662 (for Pb) without using variable selection technique. Resorting to sensitivity analysis, the Rp2 of Cu, As, Zn and Pb achieved 0.9918, 0.9526, 0.9611 and 0.9541, respectively and the RMSEP of Cu, As, Zn and Pb achieved 22.8803, 11.6868, 38.8753 and 32.9387, respectively. The results of this study clearly illustrated that the proposed model is an effective method for the analysis of heavy metals in soil.

Interrupted-sampling repeater jamming suppression based on iterative decomposition

Interrupted-sampling repeater jamming (ISRJ) is a type of intra-pulse coherent interference. The classical ISRJ model has constraints on forwarding strategies. We generalize the classical ISRJ model. The entire ISRJ is viewed as the sum of multiple sub-interference signals corresponding to different sampling sequences. Based on the general model, an iterative decomposition method is proposed. The received signal is decomposed into several sub-signals. In each iteration, the processes of extraction, estimation, smoothing, identification and cancellation are finished. First, the signal sample corresponding to the current target is extracted. Then we use the amplitude information of the main peak to establish the objective function. The sample points that contribute to the amplitude are selected during optimization and the corresponding sampling sequence can be estimated. Finally, the attribution of the current target is determined by the characteristic value, and the corresponding sub-signal is eliminated from the original echo. The processes are repeated until all sub-signals are eliminated. Simulation experiments show that the proposed method has excellent recognition and suppression performance for direct forwarding, repeated forwarding, and periodic forwarding ISRJ.

An asymptotic resolution of a conjecture of Szemerédi and Petruska

Consider a 3-uniform hypergraph of order n with clique number k such that the intersection of all its k-cliques is empty. Szemerédi and Petruska proved n≤8m2+3m, for fixed m=n−k, and they conjectured the sharp bound n≤(m+22). This problem is known to be equivalent to determining the maximum order of a τ-critical 3-uniform hypergraph with transversal number m (details may also be found in a companion paper by Kézdy and Lehel).The best known bound, n≤34m2+m+1, was obtained by Tuza using the machinery of τ-critical hypergraphs. Here we propose an alternative approach, a combination of the iterative decomposition process introduced by Szemerédi and Petruska with the skew version of Bollobás's theorem on set pair systems. The new approach improves the bound to n≤(m+22)+O(m5/3), resolving the conjecture asymptotically.

Multi-TDOA Estimation and Source Direct Position Determination Based on Parallel Factor Analysis

In this paper, source localization exploiting time difference of arrival (TDOA) information is discussed, and a parallel factor (PARAFAC) analysis based method for multi-TDOA estimation and direct position determination (DPD) is proposed. Firstly, signals from the radiation source are received by multiple antennas through synchronous sensing. Then, the data from multiple antennas is fused by extracting the time delay matrix to construct a PARAFAC model. Thereafter, the time delay matrix is obtained by fast iterative decomposition using the trilinear alternating least square (TALS) algorithm. In the case of no multipath or weak multipath, where the typical scenario is the antennas being deployed on the airborne platform, the multi-TDOA estimation can be obtained simultaneously according to the time delay matrix to improve the processing speed. In the case of multipath, such as the antennas being located on the ground, the DPD cost function directly related to the source position can be established based on the time delay matrix, and the source position estimation can be achieved through grid search. Compared with other DPD methods, the proposed DPD method has better positioning performance and lower complexity. The effectiveness and superiority of the proposed methods are verified by both simulations and actual scenario tests.

Use of IDEAL-IQ in Quantifying Femoral Bone Marrow Involvement in Gaucher Disease.

To quantitatively measure femoral bone marrow involvement in patients with Gaucher disease (GD) by using fat fraction (FF) derived from the iterative decomposition of water and fat with echo asymmetry and least-squares estimation quantitation (IDEAL-IQ) technique. Bilateral femora of 23 patients with type 1 GD receiving low-dose imiglucerase treatment were prospectively scanned using structural magnetic resonance imaging sequences and an IDEAL-IQ sequence. Femoral bone marrow involvement was evaluated by both semiquantification (bone marrow burden [BMB] score based on magnetic resonance imaging structural images) and quantification (FF derived from IDEAL-IQ) methods. These patients were further divided into subgroups according to whether they underwent splenectomy or had bone complications. The interreader agreement of measurements and the correlation between FF and clinical status were statistically analyzed. In patients with GD, both BMB and FF evaluation of femora showed good interreader concordance (intraclass correlation coefficient = 0.98 and 0.99, respectively), and FF highly correlated with BMB score ( P < 0.001). The longer the duration of disease, the lower the FF ( P = 0.026). Femoral FF was lower in subgroups with splenectomy or bone complications than those without splenectomy or bone complications (0.47 ± 0.08 vs 0.60 ± 0.15, 0.51 ± 0.10 vs 0.61 ± 0.17, respectively, both P < 0.05). Femoral FF derived from IDEAL-IQ could be used to quantify femoral bone marrow involvement in patients with GD, and low bone marrow FF may predict worse outcomes of GD patients in this small-scale study.

Electrophysiological Correlates of Proactive Control and Binding Processes during Task Switching in Tourette Syndrome.

The occurrence of tics in Tourette syndrome (TS) has often been linked to impaired cognitive control, but empirical findings are still inconclusive. A recent view proposes that tics may be the result of an abnormally strong interrelation between perceptual processes and motor actions, commonly referred to as perception-action binding. The general aim of the present study was to examine proactive control and binding effects in the context of task switching in adult human patients with TS and matched healthy controls. A cued task switching paradigm was employed in 24 patients (18 male, 6 female) and 25 controls while recording electroencephalography (EEG). Residue iteration decomposition (RIDE) was applied to analyze cue-locked proactive cognitive control and target-locked binding processes. Behavioral task switching performance was unaltered in patients with TS. A cue-locked parietal switch positivity, reflecting proactive control processes involved in the reconfiguration of the new task did not differ between groups. Importantly, target-locked fronto-central (N2) and parietal (P3) modulations, reflecting binding processes between perception and action, differed between groups. Underlying neurophysiological processes were best depicted after temporal decomposition of the EEG signal. The present results argue for unaltered proactive control but altered perception-action binding processes in the context of task switching, supporting the view that the integration of perception and action is processed differently in patients TS. Future studies should further investigate the specific conditions under which binding may be altered in TS and the influence of top-down processes, such as proactive control, on bindings.

Quantitative analysis of pelvic bone marrow fat using an MRI-based machine learning method for distinguishing aplastic anaemia from myelodysplastic syndromes

To determine the prospect of using machine learning with magnetic resonance imaging (MRI) to identify aplastic anaemia (AA) and myelodysplastic syndromes (MDS). This retrospective study included patients diagnosed with AA or MDS by pathological bone marrow biopsy, who underwent pelvic MRI with the iterative decomposition of water and fat with echo asymmetry and least-squares estimation quantitation (IDEAL-IQ) between December 2016 and August 2020. Based on values of right ilium fat fraction (FF) and radiomic features extracted from T1-weighted (T1W) and IDEAL-IQ images, three machine learning algorithms including linear discriminant analysis (LDA), logistic regression (LR), and support vector machine (SVM) were used to identify AA and MDS. A total of 77 patients were included in the study, including 37 men and 40 women, aged 20-84 years (median age 47 years). There were 21 patients with MDS (nine men and 12 women, aged 38-84 years, median age 55 years) and 56 patients with AA (28 men and 28 women, aged 20-69 years, median age 41 years). The ilium FF of patients with AA (mean±standard deviation [SD]: 79.23±15.04%) was determined to be significantly greater compared to MDS patients (mean±SD: 42.78±30.09%, p<0.001). Selecting from the machine learning models based on ilium FF, T1W imaging and IDEAL-IQ, the IDEAL-IQ-based SVM classifier model had the best predictive ability. The combination of machine learning and IDEAL-IQ technology may enable non-invasive and accurate identification of AA and MDS.

Redundancy allocation under state‐dependent distributional uncertainty of component lifetimes

In this paper, we consider a redundancy allocation problem in a series‐parallel system with uncertain component lifetimes of multiple states, which involves multitype components and mixed redundancy strategy. We develop a distributionally robust redundancy allocation model using state‐dependent ambiguity set, which describes the mean, expected cross‐deviation, and the support conditional on each state of the component lifetime distribution. Our structural analysis of the worst‐case system reliability function identifies a concave equivalent for the conditional worst‐case reliability function in each state and achieves an averaged finite piece‐wise affine representation for the overall worst‐case system reliability function, which enjoys valuable operational insights for reliability evaluation and scalable optimization of the redundancy designs. Furthermore, we analyze the reliability guarantees for the worst‐case reliability in optimality under possible misspecification of ambiguity‐set parameters, which admit the structure of “Reliability Target + Target Surplus + Estimated Elasticity,” and insightfully imply that the auxiliary dual variables obtained via solving the design problem can be regarded as the scale of elasticity. Computationally, the redundancy design problem can be linearized and reformulated as a mixed 0–1 second‐order cone program. Exploiting the above finite piece‐wise affine structure of the worst‐case reliability function, the design problem also admits a practical iterative decomposition scheme with finite convergence, which is more scalable especially for the possible situations of large number of states in practice. Finally, numerical experiments including a case with real‐life data of braking system components well justify the value of state information incorporated by our model in producing favorable cost‐effective redundancy designs for reliability operations.

CCPNet136: automated detection of schizophrenia using carbon chain pattern and iterative TQWT technique with EEG signals

Objective. Schizophrenia (SZ) is a severe, chronic psychiatric-cognitive disorder. The primary objective of this work is to present a handcrafted model using state-of-the-art technique to detect SZ accurately with EEG signals. Approach. In our proposed work, the features are generated using a histogram-based generator and an iterative decomposition model. The graph-based molecular structure of the carbon chain is employed to generate low-level features. Hence, the developed feature generation model is called the carbon chain pattern (CCP). An iterative tunable q-factor wavelet transform (ITQWT) technique is implemented in the feature extraction phase to generate various sub-bands of the EEG signal. The CCP was applied to the generated sub-bands to obtain several feature vectors. The clinically significant features were selected using iterative neighborhood component analysis (INCA). The selected features were then classified using the k nearest neighbor (kNN) with a 10-fold cross-validation strategy. Finally, the iterative weighted majority method was used to obtain the results in multiple channels. Main results. The presented CCP-ITQWT and INCA-based automated model achieved an accuracy of 95.84% and 99.20% using a single channel and majority voting method, respectively with kNN classifier. Significance. Our results highlight the success of the proposed CCP-ITQWT and INCA-based model in the automated detection of SZ using EEG signals.

Comparison of variational iteration and Adomian decomposition methods to solve growth, aggregation and aggregation-breakage equations

In this work, semi-analytical approaches such as the Adomian decomposition method (ADM), and variational iteration method (VIM) are examined to solve the aggregation, aggregation-breakage and pure growth equations in series forms. The analytical and truncated series solutions are compared for the number density and various moments. The solutions produced using ADM and VIM are mathematically equal in the pure growth case and provide closed-form solutions for constant growth rate. Additionally, Optimal variational iteration method (OVIM) is implemented to solve the growth and aggregation equations, which reduces the error compared to ADM and VIM to some extent but increases the computational cost. Furthermore, in this work, we provide the ADM and VIM formulations for the coupled aggregation-breakage model. Various test cases of each problem are taken to justify the efficiency and accuracy of the series approximated methods. These observations are shown numerically by comparing the finite term series solutions with the exact solutions of number density and moments.

Comparison of tropospheric delay correction methods for InSAR analysis using a mesoscale meteorological model: a case study from Japan

A major source of error in interferometric synthetic aperture radar (InSAR), used for mapping ground deformation, is the delay caused by changes in the propagation velocity of radar microwaves in the troposphere. Correcting this tropospheric delay noise using numerical weather models is common because of their global availability. Various correction methods and tools exist; selecting the most appropriate one by considering weather models, delay models, and delay calculation algorithms is essential for specific applications. We compared the performance of two tropospheric delay correction methods applied to Advanced Land Observing Satellite-2 (ALOS-2) data acquired over Japan, where the atmospheric field is complex with significant seasonal variation. We tested: (1) a method of delay integration along the slant radar line-of-sight (LOS) path using the mesoscale model (MSM) provided by the Japan Meteorological Agency and (2) the Generic Atmospheric Correction Online Service (GACOS) for InSAR, which estimates delay using the high-resolution forecast (HRES)-European Centre for Medium-Range Weather Forecasts (ECMWF) products along with an iterative decomposition approach. The results showed that the tropospheric delay correction using the slant-delay integration approach with MSM, which has a finer temporal and spatial resolution, performed slightly better than GACOS. We further found that the differences in the refractivity models would have limited significance, suggesting that the difference in performance mainly originates from differences in the numerical weather models being used. This study highlights the importance of using the best-available numerical weather model data for tropospheric delay calculations.Graphical

Parotid gland evaluation of menopausal women with xerostomia using the iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL-IQ) method of MRI: a pilot study.

This study aimed to analyze the quantitative fat fraction (FF) of the parotid gland in menopausal females with xerostomia using the iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL-IQ) method. A total 138 parotid glands of 69 menopausal females were enrolled in our study and participants were divided into normal group and xerostomia group. The xerostomia group was divided into those with or without Sjögren's syndrome. Participants underwent IDEAL-IQ sequences of MRI and the stimulated salivary flow test (s-SFR). The unpaired t-test was used to compare the FFs between the normal and xerostomia groups and between the subgroups with and without Sjögren's syndrome. The correlation between FF and s-SFR was analyzed by Pearson's correlation. Excellent intra- and interobserver agreement during the measurement of FFs by IDEAL-IQ method (ICC>0.99, respectively). FF value in the xerostomia group was statistically significantly higher than the value in the normal group (p < 0.05). Within the xerostomia group, the average FF value of females with Sjögren's syndrome was higher than that of females without Sjögren's syndrome. However, the difference was not statistically significant (p > 0.05). Within the xerostomia group, FF value correlated negatively with s-SFR (p < 0.05). The FF of the parotid gland was higher in the xerostomia group than in the normal group and FF value and s-SFR showed a negative correlation. Analyses of the FF using IDEAL-IQ in menopausal females can be helpful for the quantitative diagnosis of xerostomia.

Impact of physiological parameters on the parotid gland fat fraction in a normal population

Quantifying physiological fat tissue in the organs is important to further assess the organ’s pathologic status. This study aimed to investigate the impact of body mass index (BMI), age, and sex on the fat fraction of normal parotid glands. Patients undergoing magnetic resonance imaging (MRI) of iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL-IQ) due to non-salivary gland-related disease were reviewed. Clinical information of individual patients was categorized into groups based on BMI (under/normal/overweight), age (age I/age II/age III), and sex (female/male) and an inter-group comparison of the fat fraction values of both parotid glands was conducted. Overall, in the 626 parotid glands analyzed, the fat fraction of the gland was 35.80%. The mean fat fraction value increased with BMI (30.23%, 35.74%, and 46.61% in the underweight, normal and overweight groups, respectively [p < 0.01]) and age (32.42%, 36.20%, and 41.94% in the age I, II, and III groups, respectively [p < 0.01]). The fat content of normal parotid glands varies significantly depending on the body mass and age regardless of sex. Therefore, the patient’s age and body mass should be considered when evaluating fatty change in the parotid glands in imaging results.

Quantification of lumbar vertebral fat deposition: Correlation with menopausal status, non-alcoholic fatty liver disease and subcutaneous adipose tissue.

To assess abdominal fat deposition and lumbar vertebra with iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL-IQ) and investigate their correlation with menopausal status. Two hundred forty women who underwent routine abdominal MRI and IDEAL-IQ between January 2016 and April 2021 were divided into two cohorts (first cohort: 120 pre- or postmenopausal women with severe fatty livers or without fatty livers; second cohort: 120 pre- or postmenopausal women who were obese or normal weight). The fat fraction (FF) values of the liver (FFliver) and lumbar vertebra (FFlumbar) in the first group and the FF values of subcutaneous adipose tissue (SAT) (FFSAT) and FFlumbar in the second group were measured and compared using IDEAL-IQ. Two hundred forty women were evaluated. FFlumbar was significantly higher in both pre- and postmenopausal women with severe fatty liver than in patients without fatty livers (premenopausal women: p < 0.001, postmenopausal women: p < 0.001). No significant difference in the FFlumbar was observed between obese patients and normal-weight patients among pre- and postmenopausal women (premenopausal women: p = 0.113, postmenopausal women: p = 0.092). Significantly greater lumbar fat deposition was observed in postmenopausal women than in premenopausal women with or without fatty liver and obesity (p < 0.001 for each group). A high correlation was detected between FFliver and FFlumbar in women with severe fatty liver (premenopausal women: r=0.76, p<0.01; postmenopausal women: r=0.82, p<0.01). Fat deposition in the vertebral marrow was significantly associated with liver fat deposition in postmenopausal women.

Tucker Decomposition Based on a Tensor Train of Coupled and Constrained CP Cores

Many real-life signal-based applications use the Tucker decomposition of a high dimensional/order tensor. A well-known problem with the Tucker model is that its number of entries increases exponentially with its order, a phenomenon known as the “curse of the dimensionality”. The Higher-Order Orthogonal Iteration (HOOI) and Higher-Order Singular Value Decomposition (HOSVD) are known as the gold standard for computing the range span of the factor matrices of a Tucker Decomposition but also suffer from the curse. In this paper, we propose a new methodology with a similar estimation accuracy as the HOSVD with non-exploding computational and storage costs. If the noise-free data follows a Tucker decomposition, the corresponding Tensor Train (TT) decomposition takes a remarkable specific structure. More precisely, we prove that for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -order Tucker tensor, the corresponding TT decomposition is constituted by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q-3$</tex-math></inline-formula> 3-order TT-core tensors that follow a Constrained Canonical Polyadic Decomposition. Using this new formulation and the coupling property between neighboring TT-cores, we propose a JIRAFE-type scheme for the Tucker decomposition, called TRIDENT. Our numerical simulations show that the proposed method offers a drastically reduced complexity compared to the HOSVD and HOOI while outperforming the Fast Multilinear Projection (FMP) method in terms of estimation accuracy.

Electromechanical Modes Identification Based on an Iterative Eigenvalue Decomposition of the Hankel Matrix

This paper proposes a novel strategy to precisely extract modal patterns from non-stationary multi-component signals associated with electromechanical oscillations in large-scale power systems. The strategy is composed of two stages: ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) a time-frequency representation (TFR) method; and ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) an energy-based operator. The former is equipped with a multivariate and iterative eigenvalue decomposition of the Hankel matrix (IEVDHM) that captures the swing dynamics as a mono-component signal criterion is fulfilled, meanwhile the latter instantaneously estimates the modal information (damping and frequency) through the discrete energy separation algorithm (DESA) that implements the discrete-time energy operators derived from the Teager-Kaiser energy operators (TKEO). The attained results and their comparisons with state-of-the-art techniques confirm the effectiveness and performance of the proposed strategy to demodulate synthetic, simulated and real oscillating signals, even under high noisy conditions, and to be a useful tool for off-line contingency analysis thanks to the capability of differentiating concurrent modes with close frequencies.