Local Decomposition Research Articles

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Hexahedral (hex) meshing is a long studied topic in geometry processing with many challenging associated problems. Hex meshes vary from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges be adjacent to four hexes each. Edges failing this criteria are singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. Hex meshes with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. With this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

Multivariate complex modulation model decomposition and its application to gear fault diagnosis

The single-channel vibration signal of gears contains limited information, and it is easily affected by the transmission path. Therefore, multi-channel signals should be used for fault diagnosis because multi-channel gear signals usually contain richer and more comprehensive information about the equipment status. But the existing single-channel signal processing methods are not applicable to multi-channel signals, and each of the existing multi-channel signal processing methods has its own limitations. Therefore, this study proposes a new multi-channel signal processing method called multivariate complex modulation model decomposition (MCMMD), by which multi-channel signals can be decomposed accurately and adaptively at the same time. The core of the method is to iteratively update the model parameters by combining all channel signals to acquire the pattern alignment property. The decomposition performance is analyzed first. Then MCMMD is applied to simulation and experimental multi-channel gear fault signals. For comparison, ensemble empirical mode decomposition (EEMD), multivariate empirical mode decomposition (MEMD), multivariate variational mode decomposition (MVMD), multivariate local characteristic-scale decomposition (MLCD), and completely adaptive projection MLCD (CAPMLCD) are presented as well. The results show that the decomposition accuracy and robustness of MCMMD are better than those of the other methods compared. Therefore, MCMMD is an accurate and effective multi-channel signal processing method.

Gas Pipeline Leakage Detection Method Based on IUPLCD and GS-TBSVM

To improve the identification accuracy of gas pipeline leakage and reduce the false alarm rate, a pipeline leakage detection method based on improved uniform-phase local characteristic-scale decomposition (IUPLCD) and grid search algorithm-optimized twin-bounded support vector machine (GS-TBSVM) was proposed. First, the signal was decomposed into several intrinsic scale components (ISC) by the UPLCD algorithm. Then, the signal reconstruction process of UPLCD was optimized and improved according to the energy and standard deviation of the amplitude of each ISC, the ISC components dominated by the signal were selected for signal reconstruction, and the denoised signal was obtained. Finally, the TBSVM was optimized using a grid search algorithm, and a GS-TBSVM model for pipeline leakage identification was constructed. The input of the GS-TBSVM model was the data processed by the IUPLCD algorithm, and the output was the real-time working conditions of the gas pipeline. The experimental results show that IUPLCD can effectively filter the noise in the signal and GS-TBSVM can accurately judge the working conditions of the gas pipeline, with a maximum identification accuracy of 98.4%.

Evaluating satellite‐ and reanalysis‐based precipitation products over the Qinghai‐Tibetan Plateau in the perspective of a new error‐index system

AbstractThe necessity of evaluating satellite‐ and reanalysis‐based precipitation products as optional proxies of precipitation observations is widely understood. Four typical satellite‐ or reanalysis‐based precipitation products from TRMM, CPC, CMFD and ERA5‐Land datasets were evaluated at temporal and spatial scales using a new error‐index system method across the Qinghai‐Tibetan Plateau (QTP) from 1979 to 2018. The error‐index system consisted of 10 indices, which were classified into two categories, that is, the comprehensive error indices and error component indices. A local error decomposition scheme suitable for the QTP was built according to the simulation test. Results showed the datasets except ERA5‐Land performed better at monthly scale than that at daily scale generally, though significant differences were found among the products. Particularly, CMFD achieved the highest accuracy in estimating monthly and daily precipitation, followed by CPC, while TRMM performed similarly to ERA5‐Land. It was estimated that over one fifth of the precipitation were falsely recorded in the four products. Approximately over 15% of daily precipitation were overestimated or underestimated with an accumulated extent reaching up to 60 mm per month in summer. Spatial results indicated that large deviations were found in the southeast QTP, which were derived from a significant underestimation. Besides, a large proportion of false and missing estimation of precipitation events were witnessed in the northeast river basins. Through the comparison, CMFD and CPC had reduced all error components except HNB in both magnitude and the ratio. And the datasets tended to overestimate the slight precipitation and underestimate the heavy rainfall. And the products did not eliminate the large deviations in the southeast and north QTP. The assessment results reported here will provide some valuable feedbacks for the improvement of these products.

Resolving the intricate role of climate in litter decomposition.

With approximately 60 Pg of carbon (C) released as CO2 annually, the decomposition of dead organic matter feeds the major terrestrial global CO2 flux to the atmosphere. Macroclimate control over this critical C flux facilitates the parametrization of the C cycle in Earth system models and the understanding of climate change effects on the global C balance. Yet, the long-standing paradigm of climate control was recently challenged by the so far underestimated environmental heterogeneity at local scales, questioning the conceptual framework of thousands of decomposition studies and accuracy of current predictive models. Using three complementary decomposition experiments at a European scale, we showed that macroclimate and litter characteristics largely control plant litter decomposition, reaffirming the role of macroclimate as an integrative decomposition driver through direct environmental control and by influencing co-evolving local plant and decomposer communities. Neglecting this latter indirect effect, commonly used standard litter types overrated micro-environmental control and failed to predict local decomposition of plot-specific litter. Our data help clarify a key question on the regulation of the global C cycle by identifying the relative role of control factors over decomposition and the scales at which they matter and by highlighting sources of confusion in the literature.

Validity of Whitham's modulation equations for dissipative systems with a conservation law: Phase dynamics in a generalized Ginzburg-Landau system

It is well-established that Whitham's modulation equations approximate the dynamics of slowly varying periodic wave trains in dispersive systems. We are interested in its validity in dissipative systems with a conservation law. The prototype example for such a system is the generalized Ginzburg-Landau system that arises as a universal amplitude system for the description of a Turing-Hopf bifurcation in spatially extended pattern-forming systems with neutrally stable long modes. In this paper we prove rigorous error estimates between the approximation obtained through Whitham's modulation equations and true solutions to this Ginzburg-Landau system. Our proof relies on analytic smoothing, Cauchy-Kovalevskaya theory, energy estimates in Gevrey spaces, and a local decomposition in Fourier space, which separates center from stable modes and uncovers a (semi)derivative in front of the relevant nonlinear terms.

Secure State Estimation against Sparse Attacks on a Time-varying Set of Sensors

This paper studies the problem of secure state estimation of a linear time-invariant (LTI) system with bounded noise in the presence of sparse attacks on an unknown, time-varying set of sensors. At each time, the attacker has the freedom to choose an arbitrary set of no more than p sensors and manipulate their measurements without restraint. To this end, we propose a secure state estimation scheme and guarantee a bounded estimation error irrespective of the attack signals subject to 2p-sparse observability and a mild, technical assumption that the system matrix has no degenerate eigenvalues. The proposed scheme comprises a design of decentralized observers for each sensor based on the local observable subspace decomposition. At each time step, the local estimates of sensors are fused by a median operator to obtain a secure estimation, which is then followed by a local detection-and-resetting process of the decentralized observers. The estimation error is shown to be upper-bounded by a constant which is determined only by the system parameters and noise magnitudes. Moreover, we design the detector threshold to ensure that the benign sensors never trigger the detector. The efficacy of the proposed algorithm is demonstrated by its application on a benchmark example of IEEE 14-bus system. We show that our proposed scheme can effectively tolerate sparse attacks on an unknown set of sensors, ensuring a bounded estimation error and effectively detecting and resetting the attacked sensors.

Shedding light on the physical nature of ion pair interactions involving carba-closo-dodecaborate anions. Insights from computation.

closo-Carboranes are structures that have been studied for many decades due to their vast applicability in medicine, catalysis, and energy storage. In order to go deeper into the physics behind the interactions of oppositely charged ions, which have potential applications in electrical energy storage and conversion devices, the present work aims to shed light on the physical nature of the interactions involving (R-CB11H11-, R = H, F, CH3, CF3) and Mq+ = Li+, Na+, Mg2+, Zn2+ ions. The bonding situations are evaluated in light of both canonical Kohn-Sham energy decomposition, EDA-NOCV, and local energy decomposition, LED, analyses. Electron and hole transports are also evaluated through charge transfer integrals. The findings reveal that such complexes present not only more significant electrostatic, but also non-negligible orbital contributions. Both energy decomposition analyses EDA-NOCV and DLPNO-LED confirm that the strength of ionic pair interactions (R-CB11H11- ↔ Mq+) is much more dependent on the nature of the cation employed than on the substituent R used. The results also reveal that charge transfers are not significant in such interacting systems.

Analysis of the energy justice in natural gas distribution with Multiscale Geographically Weighted Regression (MGWR)

Energy justice is violated when particular customers and locations are excluded from a variety of urban energy service distribution. This study explores energy justice in terms of natural gas distribution by providing empirical evidence from 356 neighborhoods of Izmir Metropolitan Area (IMA). The aim is to reveal driving factors of natural gas investment and the spatial reflections of the relationships between investment, and socio-economic and physical characteristics. A global regression model, OLS, and two local spatial regression models, GWR and MGWR, are conducted. Population, income, employment and disadvantaged areas are the significant determinants of natural gas investments. Due to the presence of spatial autocorrelation in OLS residuals, GWR and MGWR are utilized to account for spatial variation in the response variable. Local models are superior to the global model according to AICc values, which are 607.3, 586.7, and 558.5, in OLS, GWR, and MGWR, respectively. MGWR further improves the overall fit with higher R-sq and lower AICc values. The local R-sq values indicate at least 70% variability is explained in 85% of the study area in MGWR, and in 73% of IMA in GWR. Parameters are slightly overestimated in GWR at the mean level. None of the local models are subject to multicollinearity according to local condition numbers, but local variance decomposition proportions indicate the effects of multicollinearity in some observations. Spatial modeling of investments helps to demonstrate local variations of energy injustice and to develop site-specific policies. Population and employment are related to potential customers, which lead to higher investments. Income depends on purchasing power, and there are economic barriers that need to be regulated through subsidies and incentives for the low-income households. Awareness raising policies can also be developed to better inform households about energy alternatives. Disadvantaged areas, either declared as urban transformation areas or currently under urban transformation, lack the natural gas service in general, while the investments can be considered in those areas along with the new development plans.

Geometric Invariants for a Class of Submodules of Analytic Hilbert Modules Via the Sheaf Model

Let \(\Omega \subseteq {\mathbb {C}}^m\) be a bounded connected open set and \({\mathcal {H}} \subseteq {\mathcal {O}}(\Omega )\) be an analytic Hilbert module, i.e., the Hilbert space \({\mathcal {H}}\) possesses a reproducing kernel K, the polynomial ring \(\mathbb C[{\varvec{z}}]\subseteq {\mathcal {H}}\) is dense and the point-wise multiplication induced by \(p\in {\mathbb {C}}[{\varvec{z}}]\) is bounded on \({\mathcal {H}}\). We fix an ideal \({\mathcal {I}} \subseteq {\mathbb {C}}[{\varvec{z}}]\) generated by \(p_1,\ldots ,p_t\) and let \([{\mathcal {I}}]\) denote the completion of \({\mathcal {I}}\) in \(\mathcal H\). The sheaf \({\mathcal {S}}^{\mathcal {H}}\) associated to analytic Hilbert module \({\mathcal {H}}\) is the sheaf \({\mathcal {O}}(\Omega )\) of holomorphic functions on \(\Omega \) and hence is free. However, the subsheaf \({\mathcal {S}}^{\mathcal [{\mathcal {I}}]}\) associated to \([{\mathcal {I}}]\) is coherent and not necessarily locally free. Building on the earlier work of Biswas, Misra and Putinar (Journal fr die reine und angewandte Mathematik (Crelles Journal) 662:165–204, 2012), we prescribe a hermitian structure for a coherent sheaf and use it to find tractable invariants. Moreover, we prove that if the zero set \(V_{[{\mathcal {I}}]}\) is a submanifold of codimension t, then there is a unique local decomposition for the kernel \(K_{[{\mathcal {I}}]}\) along the zero set that serves as a holomorphic frame for a vector bundle on \(V_{[{\mathcal {I}}]}\). The complex geometric invariants of this vector bundle are also unitary invariants for the submodule \([{\mathcal {I}}] \subseteq {\mathcal {H}}\).

Motor bearing fault diagnosis based on local characteristic-scale decomposition and support vector optimized by sine cosine algorithm

When the motor bearing fails, the nonlinear and unstable characteristics of the vibration signal will lead to a low fault identification accuracy. This paper proposes a fault diagnosis method for motor bearings based on local characteristic-scale decomposition (LCD) and sine-cosine algorithm to optimize support vector machine. In this paper, the LCD algorithm is used to decompose the vibration signal, and screened out the effective intrinsic scale components (ISC) component. Then, Sample Entropy and Permutation Entropy are extracted from the filtered components. For the selection of parameters c and g of SVM, this paper introduces the sine and cosine optimization algorithm (SCA) for position update optimization, and builds an SVM model to obtain a classification model for motor bearing faults after training on the data set. After importing the remaining test data set into the classification model for testing, the fault classification accuracy results of the motor bearing can be obtained. The results of the simulation experiments show that the recognition rate of motor bearing faults based on LCD and SCA-SVM is 98.75%.

Effects of leaf quality and colonization time on the abundance of bacteria in an experimental design

Small rivers, henceforth streams, depend on organic matter (nutrients and energy) from riparian vegetation. The quality of such allochthonous debris is determinant for the transformation of organic matter compounds, where the bacterial community has a crucial role in the final decomposition of the substrate. During bacterial colonization, debris with higher concentration of nutrients (more palatable) is prioritized, which accelerates the process. This study investigated the effects of leaf palatability of two native trees on bacterial colonization (abundance) over time, through a laboratory experiment that lasted 60 days. Values of C, N, P, C:N, C:P, polyphenols, tannins, lignin, lignin:N and leaf toughness of both species were compared. Bacterial abundance was higher in species with higher nitrogen values, although they had higher leaf toughness and more polyphenols, which differs from studies indicating that high leaf toughness represents low nutritional quality. The colonization time did not influence bacterial abundance. Therefore, processes degrading riparian vegetation and reducing nutritional quality can affect local decomposition, decreasing bacterial abundance.

Local characteristic decomposition based central-upwind scheme

We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the studied systems come from the complicated wave structures, such as shocks, rarefactions and contact discontinuities, arising even for smooth initial conditions. In order to reduce the diffusion in the original central-upwind schemes, we use a local characteristic decomposition procedure to develop a new class of central-upwind schemes. We apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics to illustrate the performance on a variety of examples. The obtained numerical results clearly demonstrate that the proposed new schemes outperform the original central-upwind schemes.

London Dispersion Stabilizes Chloro-Substituted cis-Double Bonds

AbstractWe present a combined experimental and computational study on the thermodynamic stability of cis- and trans-alkenes substituted with dispersion energy donor (DED) groups. To investigate the role of noncovalent interactions on equilibrium of cis- and trans-alkenes we utilized hydrochlorination reactions. While the general assumption is that increasing steric bulk favors the trans-alkene, we observe an equilibrium shift towards the more crowded cis-alkene with increasing substituent size. With the aim to quantify noncovalent interactions, we performed a double mutant cycle to experimentally gauge the attractive potential of bulky substituents. Additionally, we utilized local energy decomposition analysis at the DLPNO-CCSD(T)/def2-TZVP level of theory. We found LD interactions and Pauli exchange repulsion to be the most dominant components to influence cis- and trans-alkene equilibria.

Improved Estimates of Host-Guest Interaction Energies for Endohedral Fullerenes Containing Rare Gas Atoms, Small Molecules, and Cations.

Endohedral fullerenes have evinced much interest from the fundamental and applications points of view. However, given the nature of the weak interaction between the guest species and the host cage in these confined systems, the interaction energy values obtained using various theoretical methods, and different basis sets vary over a wide range. For example, the reported interaction energy for the HF@C60 system ranges from -2.5 kcal/mol to -14.9 kcal/mol. In the present manuscript, we report reliable interaction energy values for different endohedral fullerenes (He@C60 , Ne@C60 , Ar@C60 , Kr@C60 , H2 @C60 , HF@C60 , H2 O@C60 , NH3 @C60 , CH4 @C60 , Li+ @C60 , Na+ @C60 , and K+ @C60 ) obtained using the domain-based local pair natural orbital coupled-cluster singles, doubles, and perturbative triples (DLPNO-CCSD(T)) method and the def2-TZVP basis set. We believe that these energy values could be considered as benchmark values, and the performance of other quantum chemical methods could be assessed accordingly. Local energy decomposition analysis within the DLPNO-CCSD(T) framework is used to estimate the electrostatic, exchange, and dispersion components of the interaction energy for some of the endohedral fullerenes.

Strength of Composite Columns Consists of Welded Double CF Sigma-Sections Filled with Concrete—An Experimental Study

In-filled tubes section is a very successful configuration for axially loaded members such as columns and struts. Steel shell tube filled with concrete has many advantages, such as eliminating the need for shuttering, reinforcement bars or ties besides increasing both flexural and axial capacities and enhancing the ductility. The main disadvantage of in-filled tubes is the need for a shell thick enough to prevent the local buckling and hence the local decomposition. Previous studies tried to solve this problem using intermediate stiffeners or shear connectors. This research presents another approach to solve this problem using double cold-formed sigma-sections (face to face) as steel shell tubes. Sixteen specimens with different lengths, cross section dimensions and shell thicknesses were tested under both concentric and eccentric compression loads. Ultimate capacities, lateral deformations and normal strains were recorded. The theoretical capacities were calculated using AISC-LRDF-94, EN-1994-04 and CSI-COL software considering full composite action, and the deviations from the experimental results were 24%, 24% and 13%, respectively.

Adaptive noise removal for biological Raman spectra with low SNR

Raman data with low signal-to-noise ratio (SNR) are often obtained in the process of rapid or low-power acquisition for biological samples. The noise removal out of a biological Raman spectrum is laborious owing to numerous and superimposed Raman peaks, and it often takes a lot of time to find the optimal preproceed parameters. In this study, an adaptive denoising method for biological Raman data has been proposed, using three comparisons and a quantitative prediction model to show its simplicity and effectiveness. In this work, we decomposed Raman spectra of human skin and rice leaf on Hilbert vibration decomposition (HVD) method, to obtain a series of initial values, for example as peak position, intensity and full width at half maximum (FWHM), then fitted Raman spectrum according the Vogit function until the indicator function F reached the minimum value. The SNR and the root mean square error（RMSE) of HVD denoised spectrum were 57.5864 dB and 0.0108, and were both better than those of preproceed data (35.1826 dB, 0.0337; 32.4120 dB, 0.0352; 38.0685 dB, 0.0226) by Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), and Local Complementary Ensemble Empirical Mode Decomposition (LCEMD), compared with adaptive denoising methods, EMD, EEMD and LCEEMD, the improved algorithm had the advantages of no modal aliasing, no noise residue and independence of normalized permutation entropy. Then HVD denoised data of rice leaf samples were compressed by principal component analysis (PCA) and used for chlorophyll content prediction model. The correlation coefficient and standard error for prediction set of HVD +PCA model were 0.856 and 5.38, and were also better than those of non-adaptive preproceed data models (Mobing Average Smoothing, Gaussian Filter Smoothing, Median Filter Smoothing, Savitzky-Golay Smoothing and Wavelet Transform Denoising). The final experimental comparison showed that the HVD denoising method can also be applied to the Raman spectrum noise removal of inorganic samples, but better performances had been shown in the noise removal of complex biological Raman spectra. Accurate denoising of biological Raman spectrum is of great significance for accurate quantitative prediction and qualitative analysis, and no prior setting of the preproceed parameters makes the HVD denoising method easy to operate.

Arctic biogeochemical and optical properties of dissolved organic matter across river to sea gradients

Arctic landscapes are warming and becoming wetter due to changes in precipitation and the timing of snowmelt which consequently alters seasonal runoff and river discharge patterns. These changes in hydrology lead to increased mobilization and transport of terrestrial dissolved organic matter (DOM) to Arctic coastal seas where significant impacts on biogeochemical cycling can occur. Here, we present measurements of dissolved organic carbon (DOC) and chromophoric DOM (CDOM) in the Yukon River-to-Bering Sea system and two river plumes on the Alaska North Slope which flow into the Beaufort Sea. Our sampling characterized optical and biogeochemical properties of DOM during high and low river discharge periods for the Yukon River-Bering Sea system. The average DOC concentration at the multiple Yukon River mouths ranged from a high of 10.36 mg C L-1 during the ascending limb of the 2019 freshet (late May), 6.4 mg C L-1 during the descending limb of the 2019 freshet (late June), and a low of 3.86 mg C L-1 during low river discharge in August 2018. CDOM absorption coefficient at 412 nm (aCDOM(412)) averaged 8.23 m-1, 5.07 m-1, and 1.9 m-1, respectively. Several approaches to model DOC concentration based on its relationship with CDOM properties demonstrated cross-system seasonal and spatial robustness for these Arctic coastal systems despite spanning an order of magnitude decrease in DOC concentration from the lower Yukon River to the Northern Bering Sea as well as the North Slope systems. “Snapshot” fluxes of DOC and CDOM across the Yukon River Delta to Norton Sound were calculated from our measurements and modeled water fluxes forced with upstream USGS river gauge data. Our findings suggest that during high river flow, DOM reaches the delta largely unaltered by inputs or physical and biogeochemical processing and that the transformations of Yukon River DOM largely occur in the plume. However, during low summer discharge, multiple processes including local precipitation events, microbial decomposition, photochemistry, and likely others can alter the DOM properties within the lower Yukon River and Delta prior to flowing into Norton Sound.

Ogden material calibration via magnetic resonance cartography, parameter sensitivity and variational system identification.

Contemporary material characterization techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterization problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully three-dimensional displacement fields acquired in silicone elastomers with our recently developed magnetic resonance cartography (MR-u) technique on the order of greater than [Formula: see text], we leverage partial differential equation-constrained optimization as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric and discuss the implications for experimental design. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Completely adaptive projection multivariate local characteristic-scale decomposition and its application to gear fault diagnosis

Multichannel signal can be quickly and effectively decomposed using multivariate local characteristic-scale decomposition (MLCD). However, multi-channel signals acquired by sensors often have power imbalance characteristic, and MLCD uses uniform projection to estimate the baseline, which leads to inaccuracy of MLCD in decomposing such signals. Additionally, uniform projection introduces some projection vectors that can't precisely describe the multichannel signal, based on which, completely adaptive projection (CAP) is proposed in this paper. Completely adaptive projection multivariate local characteristic-scale decomposition (CAPMLCD) is developed on the basis of CAP. The simulation and experimental results show that CAPMLCD and MLCD perform better in terms of suppressing mode mixing, decomposition efficiency, and decomposition accuracy than multivariate empirical mode decomposition (MEMD) and adaptive projection intrinsically transformed multivariate empirical mode decomposition (APIT-MEMD). By comparing with MEMD, APIT-MEMD and MLCD, CAPMLCD has better decomposition accuracy and lower dependence on the number of projections.