Local Decomposition Research Articles

Fault location for overhead and cable hybrid transmission line in VSC-HVDC system

Because the traditional fault location method cannot be applied to overhead and cable hybrid transmission line in the VSC-HVDC system, this paper proposes a novel fault location method, which primarily uses the principle of first determining the fault segment and then locating the fault point in the fault segment. Two voltage symbolic functions are defined, and the fault segment is determined according to the different numerical combinations of the two voltage symbolic functions. Through combining adaptive characteristic scale decomposition with improved general local frequency decomposition to adaptively extract the fault characteristic component, the intra-segment location equation is established based on the characteristic component to locate the fault point. The simulation results verify that the proposed method can accurately locate the fault point for the overhead and cable hybrid transmission line in the VSC-HVDC system.

An Innovative Hourly Water Demand Forecasting Preprocessing Framework with Local Outlier Correction and Adaptive Decomposition Techniques

Accurate forecasting of hourly water demand is essential for effective and sustainable operation, and the cost-effective management of water distribution networks. Unlike monthly or yearly water demand, hourly water demand has more fluctuations and is easily affected by short-term abnormal events. An effective preprocessing method is needed to capture the hourly water demand patterns and eliminate the interference of abnormal data. In this study, an innovative preprocessing framework, including a novel local outlier detection and correction method Isolation Forest (IF), an adaptive signal decomposition technique Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and basic forecasting models have been developed. In order to compare a promising deep learning method Gated Recurrent Unit (GRU) as a basic forecasting model with the conventional forecasting models, Support Vector Regression (SVR) and Artificial Neural Network (ANN) have been used. The results show that the proposed hybrid method can utilize the complementary advantages of the preprocessing methods to improve the accuracy of the forecasting models. The root-mean-square error of the SVR, ANN, and GRU models has been reduced by 57.5%, 27.8%, and 30.0%, respectively. Further, the GRU-based models developed in this study are superior to the other models, and the IF-CEEMDAN-GRU model has the highest accuracy. Hence, it is promising that this preprocessing framework can improve the performance of the water demand forecasting models.

An improved local characteristic-scale decomposition to restrict end effects, mode mixing and its application to extract incipient bearing fault signal

Empirical mode decomposition (EMD) adaptively decomposes a signal into a linear combination of waveforms embedded in the signal and has been successfully applied to many engineering areas including mechanical fault diagnosis. Local characteristic-scale decomposition (LCD) defines a new baseline signal and then conducts the sifting process to achieve decomposition. LCD utilizes the inherent instantaneous amplitude/frequency/phase information and morphological features of signals leading to a set of powerful adaptive signal filters. However, LCD suffers from the problems of end effects and mode mixing inheriting from the sifting process. This paper proposes an improved LCD (ILCD) method to reduce the two problems. First, the equivalent filter and equivalent impulse response of LCD are analyzed and compared with EMD and intrinsic time-scale decomposition (ITD). Furthermore, the ILCD deals with the problem of end effects based on support vector regression (SVR) boundary condition processing method and resolves the problem of mode mixing using complementary partial noise assisted method (CPNAM). Simulation case studies are used to verify the improvements of the proposed method. Finally, the ILCD is applied to extract bearing fault signals for an experimental bearing under variable speed condition and a practice case of wind power bearing. The analysis results from the applications demonstrate that the proposed algorithm is effective and robust in extracting incipient bearing fault signals.

Quantification of Noncovalent Interactions in Azide-Pnictogen, -Chalcogen, and -Halogen Contacts.

The noncovalent interactions between azides and oxygen‐containing moieties are investigated through a computational study based on experimental findings. The targeted synthesis of organic compounds with close intramolecular azide–oxygen contacts yielded six new representatives, for which X‐ray structures were determined. Two of those compounds were investigated with respect to their potential conformations in the gas phase and a possible significantly shorter azide–oxygen contact. Furthermore, a set of 44 high‐quality, gas‐phase computational model systems with intermolecular azide–pnictogen (N, P, As, Sb), –chalcogen (O, S, Se, Te), and –halogen (F, Cl, Br, I) contacts are compiled and investigated through semiempirical quantum mechanical methods, density functional approximations, and wave function theory. A local energy decomposition (LED) analysis is applied to study the nature of the noncovalent interaction. The special role of electrostatic and London dispersion interactions is discussed in detail. London dispersion is identified as a dominant factor of the azide–donor interaction with mean London dispersion energy‐interaction energy ratios of 1.3. Electrostatic contributions enhance the azide–donor coordination motif. The association energies range from −1.00 to −5.5 kcal mol−1.

Spectral Decompositions Arising from Atzmon’s Hyperinvariant Subspace Theorem

By means of a weaker functional model, we prove the existence of non-trivial closed hyperinvariant subspaces for linear bounded operators generalizing, in particular, a classical theorem of Atzmon and revealing the spectral nature of the hyperinvariant subspaces involved. As an application, we show non-trivial spectral subspaces for Bishop operators on $$L^p[0,1)$$ , $$1\le p<\infty $$ , as long as they satisfy Atzmon’s Theorem, providing, in turns, a local spectral decomposition.

Mixed GMsFEM for linear poroelasticity problems in heterogeneous porous media

Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome this computational challenge, various multiscale methods are developed. In this paper, we consider a class of linear poroelasticity problems in high contrast heterogeneous porous media, and develop a mixed generalized multiscale finite element method (GMsFEM) to obtain a fast computational method. Our aim is to develop a multiscale method that is robust with respect to the heterogeneities and contrast of the media, and gives a mass conservative fluid velocity field. We will construct decoupled multiscale basis functions for the elastic displacement as well as fluid velocity. Our multiscale basis functions are local. The construction is based on some suitable choices of local snapshot spaces and local spectral decomposition, with the goal of extracting dominant modes of the solutions. For the pressure, we will use piecewise constant approximation. We will present several numerical examples to illustrate the performance of our method. Our results indicate that the proposed method is able to give accurate numerical solutions with a small degree of freedoms.

Multibaseline InSAR Layover Detection Based on Local Frequency and Eigenvalue

Layover detection has long been the focus of attention for interferometric synthetic aperture radar (InSAR) data processing. As for the existing layover detection methods, most of them are applied to single-baseline scenarios. Since multibaseline InSAR provides more image samples, the performance of layover detection can be further improved. In this article, a joint detection method of layover is proposed on the basis of local frequency and eigenvalue of multibaseline InSAR. To obtain a precise local frequency, maximum likelihood estimation is performed for flattened interferometric phase fusion and removing the reference terrain phase is chosen to ensure the proportionality of flattened phase to the baseline length. Adaptive image selection based on coherence is proposed to obtain a distinct eigenvalue. Then, the joint detection method is elaborated on. Based on the results of local frequency estimation and eigenvalue decomposition, precise thresholds are set for joint detection, and joint judgment is made by combining the layover detected by local frequency, the layover detected by eigenvalue, and the thresholds. Finally, the proposed method is validated through comparative experiments on simulated data and real data. Both theoretical analysis and experimental results show the feasibility and superiority of the proposed method.

A Temperature Compensation Approach for Dual-Mass MEMS Gyroscope Based on PE-LCD and ANFIS

Because the dual-mass MEMS gyroscope's output is greatly influenced by temperature, which can lead to errors that cannot be ignored. To solve this problem, a novel compensation method is proposed: a parallel processing algorithm, which integrates the Permutation entropy (PE), Local Characteristic-scale Decomposition (LCD) and Adaptive network-based fuzzy inference system (ANFIS). Firstly, LCD is used to decompose the output which contains temperature noises and drifts into a trend component and several intrinsic scale components (ISC), according to autocorrelation and complexity, three different categories will be obtained by PE: pure noise output, mixed output, and drift output. The different processes are as follows, the noise output is discarded, the mixed output is filtered by SG (Savitzky-Golay filter), then dual ANFIS is applied. Since the drift output completely reflects the temperature characteristics, the degree of non-linearity is high, the ANFIS with complex rules is used for processing. And the mixed output is composed of intermediate layer modes, containing a relatively small amount of temperature characteristics, simple rule ANFIS is adopted for processing. Finally, the signal is reconstructed. After that, the temperature error experiment is carried out, the result shows the method can effectively eliminate the error and compensate for the drift, it has a fast convergence speed and good effect, and has the advantage of good compensation efficiency.

A biobjective capacitated vehicle routing problem using metaheuristic ILS and decomposition

Vehicle routing problems (VRPs) have usually been studied with a single objective function defined by the distances associated with the routing of vehicles. The central problem is to design a set of routes to meet the demands of customers at minimum cost. However, in real life, it is necessary to take into account other objective functions, such as social functions, which consider, for example, the drivers' workload balance. This has led to growth in both the formulation of multiobjective models and exact and approximate solution techniques. In this article, to verify the quality of the results, first, a mathematical model is proposed that takes into account both economic and work balance objectives simultaneously and is solved using an exact method based on the decomposition approach. This method is used to compare the accuracy of the proposed approximate method in test cases of medium mathematical complexity. Second, an approximate method based on the Iterated Local Search (ILS) metaheuristic and Decomposition (ILS/D) is proposed to solve the biobjective Capacitated VRP (bi-CVRP) using test cases of medium and high mathematical complexity. Finally, the nondominated sorting genetic algorithm (NSGA-II) approximate method is implemented to compare both medium- and high-complexity test cases with a benchmark. The obtained results show that ILS/D is a promising technique for solving VRPs with a multiobjective approach.

Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions

In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove that the proposed multiscale method achieves nearly exponential convergence in the approximation error with respect to the computational degrees of freedom. Our strategy is to perform an energy orthogonal decomposition of the solution space into a coarse scale component comprising $a$-harmonic functions in each element of the mesh, and a fine scale component named the bubble part that can be computed locally and efficiently. The coarse scale component depends entirely on function values on edges. Our approximation on each edge is made in the Lions--Magenes space $H_{00}^{1/2}(e)$, which we will demonstrate to be a natural and powerful choice. We construct edge basis functions using local oversampling and singular value decomposition. When local information of the right-hand side is adaptively incorporated into the edge basis functions, we prove a nearly exponential convergence rate of the approximation error. Numerical experiments validate and extend our theoretical analysis; in particular, we observe no obvious degradation in accuracy for high-contrast media problems.

Corrosion Inhibition of Aluminium in Gas and Acid Media by Some Chalcone-Based N-(3-Aminopropyl)Imidazoles: TD-DFT-Based FMO, Conceptual DFT, QTAIM and EDA Studies

The efficacy and mode of action of five chalcone-based imidazole derivatives as corrosion inhibitors of aluminium metal in gas-phase and acidic medium have been investigated herein via quantum chemical calculations. Dispersion-corrected DFT (DFT-D3) and time-dependent DFT (TD-DFT) calculations were performed at PBE0/def2-TZVP//PBEh-3c and CAM-B3LYP/def2- TZVP levels of theory, respectively. Conceptual DFT, the quantum theory of atoms-in-molecules (QTAIM) and local energy decomposition (LED) analyses have been performed. The LED analysis was performed at the coupled-cluster singles and doubles with perturbative triples (CCSD(T))/def2-SVP level of theory. Frontier molecular orbital energy gaps calculated using the TD-DFT method are found to lie in the range 3.574 - 4.444 eV, indicative of good adsorption and corrosion inhibition efficacies of the investigated molecules. The interactions between aluminium and the inhibitor molecules studied are found to be energetically favorable, owing to negative computed interaction energy values. Furthermore, QTAIM analysis revealed metal-carbon, metal-oxygen and metal-nitrogen interactions in the inhibitor-aluminium complexes, which are predominantly electrostatic in character, according to LED analysis results. Calculated proton affinities (PAs) have revealed the anticorrosion potentials of the investigated inhibitors in acidic medium, with a noticeable dependency on temperature within the range 273.15 - 343.15 K.

A new approach for local cutting force modeling enabling the transfer between different milling conditions and tool geometries

The modeling of modern high performance machining with intermittent cut and varying effective cutting parameters requires a flexible local cutting force prediction. Due to complex tool geometries and varying cutting conditions without a rigid reference system new approaches for the local cutting force decomposition are applied, investigated and compared. The force decompositions are based on the separation of the effective cutting speed into normal and tangential components to adequately consider the locally acting mechanisms. Regression models based on the effective cutting parameters are defined to compare and validate the local force decomposition. A high feed peripheral milling experiment with specific cutting force measurement is presented to develop the regression models. An extensive cutting force database for AISI 5115 is created by tool geometry and process control variable variations. The effective cutting conditions are calculated through geometric penetration simulation. Considering the tool deflection in the simulation achieves a high regression accuracy even with low chip thicknesses. This is especially important for the cutting force prediction of finishing processes. The resulting regression cutting force models and force decompositions are rated based on the applicability to different tool geometries, like a ball end mill.

Research on Noise Reduction Method of Pressure Pulsation Signal of Draft Tube of Hydropower Unit Based on ALIF‐SVD

Aiming at the problem that it is difficult to extract the characteristics of the draft tube pressure fluctuation signal under the background of strong noise, this study proposes a dual noise reduction method based on adaptive local iterative filtering (ALIF) and singular value decomposition (SVD). First, perform ALIF decomposition of the signal to be decomposed to obtain a series of IMF components, calculate the sample entropy of each component, select some IMF components to reconstruct according to the set sample entropy threshold, and then perform SVD decomposition on the reconstructed signal, and according to the location of the singular value difference spectrum mutation point, the appropriate number of reconstructions is selected for reconstruction, so as to achieve the double noise reduction effect. The ALIF‐SVD dual noise reduction method proposed in this study is compared with the single ALIF, EMD, and EMD‐SVD dual noise reduction method through simulation, and the correlation coefficient, signal‐to‐noise ratio, and mean square error are used to evaluate the noise reduction. It is found that the ALIF‐SVD dual noise reduction method avoids the phenomenon of modal aliasing in the decomposition process, effectively removes the noise, and can retain the useful information of the original signal, and the noise reduction effect is better. A unit of a hydropower station in China is further selected as the research object, and its draft tube pressure fluctuation data were analyzed for noise reduction. It was found that this method can accurately extract the signal characteristics under strong noise background, so as to determine the type of pressure fluctuation of the unit, which is helpful to improve the fault recognition rate of hydraulic turbines. And it provides some technical support for the safe and stable operation of hydropower units and the promotion of condition‐based maintenance strategy and improves the intelligent level of hydropower station operation management.

Mechanical Model of Methane Hydrate Self-Preservation in a Gaseous Medium

The distinctive features of methane hydrate decomposition in gaseous and water media under the conditions of thermobaric phase instability of methane hydrates are considered. In the course of preceding field observations it has been established that methane hydrate decomposes significantly more rapidly in the water medium as compared with the gaseous methane medium. The basic idea consists in the fact that methane hydrate decomposition takes place inside methane hydrate fractures in which there are decomposition nuclei. Deceleration of methane hydrate decomposition is caused by the formation of ice plugs in the local zones of methane hydrate decomposition, namely, in the fractures. An ice plug is formed as a result of local methane hydrate decomposition into gas and water and intense heat consumption. In the process of freezing, water forms the plug and thereby blocks methane hydrate decomposition in the fracture. Relatively low heat conduction of gaseous methane protects the ice plugs against rapid melting.

Partial discharge signal denoising method based on frequency spectrum clustering and local mean decomposition

Suppressing the background noise of partial discharge (PD) is one of the key issues for accurately diagnosing the state of electrical equipment insulation. To solve this problem, this study proposes a new denoising method based on frequency spectrum clustering and local mean value decomposition. First, the K-means clustering is employed on the frequency spectrum to pick out narrow-band interference frequencies. Next, the PD signal with white noise is decomposed by local mean decomposition into different product function components, and the components contain more information about time–frequency than the intrinsic mode functions originated from empirical mode decomposition. Besides, the adaptive threshold is utilised to eliminate white noise in the components. Finally, the denoised PD signal is synthesised by these denoised components. The proposed method and three traditional methods are applied to simulated and field-detected noisy PD signals, respectively. The results of the evaluation indicators confirm that the proposed method is better than the existing PD denoising methods.

Local Decomposition of Kalman Filters and its Application for Secure State Estimation

This article is concerned with the secure state estimation problem of a linear discrete-time Gaussian system in the presence of sparse integrity attacks. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {m}$</tex-math></inline-formula> sensors are deployed to monitor the state and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {p}$</tex-math></inline-formula> of them can potentially be compromised by an adversary, whose data can be arbitrarily manipulated by the attacker. We show that the optimal Kalman estimate can be decomposed as a weighted sum of local state estimates. Based on these local estimates, we propose a convex optimization based approach to generate a more secure state estimate. It is proved that our proposed estimator coincides with the Kalman estimator with a certain probability when all sensors are benign. Besides, we establish a sufficient condition under which the proposed estimator is stable against the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {(p,m)}$</tex-math></inline-formula> -sparse attack. A numerical example is provided to validate the secure state estimation scheme.

The positivity of local equivariant Hirzebruch class for toric varieties

The central object of investigation of this paper is the Hirzebruch class, a deformation of the Todd class, given by Hirzebruch (for smooth varieties) in his celebrated book "Topological Methods in Algebraic Geometry". The generalization for singular varieties is due to Brasselet-Sch\"urmann-Yokura. Following the work of Weber, we investigate its equivariant version for (possibly singular) toric varieties. The local decomposition of the Hirzebruch class to the fixed points of the torus action and a formula for the local class in terms of the defining fan are mentioned. After this review part, we prove the positivity of local Hirzebruch classes for all toric varieties, thus proving false the alleged counterexample given by Weber.

Unraveling individual host-guest interactions in molecular recognition from first principles quantum mechanics: Insights into the nature of nicotinic acetylcholine receptor agonist binding.

Drug binding to a protein target is governed by a complex pattern of noncovalent interactions between the ligand and the residues in the protein's binding pocket. Here we introduce a generally applicable, parameter-free, computational method that allows for the identification, quantification, and analysis of the key ligand-residue interactions responsible for molecular recognition. Our strategy relies on Local Energy Decomposition analysis at the "gold-standard" coupled cluster DLPNO-CCSD(T) level. In the study case shown in this paper, nicotine and imidacloprid binding to the nicotinic acetylcholine receptor, our approach provides new insights into how individual amino acids in the active site determine sensitivity and selectivity of the ligands, extending and refining classical pharmacophore hypotheses. By inference, the method is applicable to any kind of host/guest interactions with potential applications in industrial biocatalysis and protein engineering.

Preparation of superconducting RuGd-1222 single crystals by partial melting

Growth of single crystals of RuGd-1222 ((Gd,Ce)2Sr2RuCu2O10−δ) remains a major challenge, and previous studies have indicated that epitaxial thin films of these compounds exhibit deteriorated superconductivity. We have been working toward the synthesis of RuGd-1222 single crystals using the self-flux and partial melting techniques. In this paper, we report on the synthesis of RuGd-1222 single-crystal lumps by partial melting. The maximum size of a single crystal was approximately 80 μm in length, which is almost the same as that of our previous studies by self-flux method. Although these samples contained some impurity phases, the predominant phase was confirmed to be RuGd-1222. Furthermore, following optimization of the synthetic conditions, superconductivity with an onset transition temperature (Tc-onset) of 27 K was observed for a RuGd-1222 single-crystal lump prepared by partial melting. Local decomposition from RuGd-1222 plate-like crystals to RuGd-1212 single crystals was observed after prolonged sintering. The synthesis of single crystals of ruthenocuprates by partial melting is expected to contribute to an improved understanding of this class of magnetosuperconductors.

High-Resolution Anisotropic Prestack Kirchhoff Dynamic Focused Beam Migration

Kirchhoff beam migration is a kind of ray-based seismic imaging method boasting the advantages of both high efficiency and high accuracy. In this paper, anisotropic ray tracing will be applied to extend it to an anisotropic seismic imaging method. However, two problems exist in this method for imaging calculation: Firstly, the conventional local plane wave decomposition method has a low computational precision; secondly, the original beam propagator diverges quickly when the propagation distance increases. These two problems can both increase imaging noise, and finally reduce the resolution of the final imaging results. In this paper, the high-resolution anisotropic Kirchhoff dynamic focused beam migration is proposed to solve these two problems. Local plane wave decomposition method considered from the perspective of inversion is employed to obtain higher-quality slant stack data and dynamic focused beam propagator is adopted to control the divergence of beams. Both the anisotropic layer model and Hess model are adopted to test the imaging ability of the new method.