Classical Decomposition Research Articles

Predictive accuracy of time series models applied to economic data: the European countries retail trade

Modeling and accurately forecasting trend and seasonal patterns of a time series is a crucial activity in economics. The main propose of this study is to evaluate and compare the performance of three traditional forecasting methods, namely the ARIMA models and their extensions, the classical decomposition time series associated with multiple linear regression models with correlated errors, and the Holt–Winters method. These methodologies are applied to retail time series from seven different European countries that present strong trend and seasonal fluctuations. In general, the results indicate that all the forecasting models somehow follow the seasonal pattern exhibited in the data. Based on mean squared error (MSE), root mean squared error (RMSE), mean absolute percentage error (MAPE), mean absolute scaled error (MASE) and U-Theil statistic, the results demonstrate the superiority of the ARIMA model over the other two forecasting approaches. Holt–Winters method also produces accurate forecasts, so it is considered a viable alternative to ARIMA. The performance of the forecasting methods in terms of coverage rates matches the results for accuracy measures.

Reduced-order variational mode decomposition to reveal transient and non-stationary dynamics in fluid flows

A novel data-driven modal analysis method, reduced-order variational mode decomposition (RVMD), is proposed, inspired by the Hilbert–Huang transform and variational mode decomposition (VMD), to resolve transient or statistically non-stationary flow dynamics. First, the form of RVMD modes (referred to as an ‘elementary low-order dynamic process’, ELD) is constructed by combining low-order representation and the idea of intrinsic mode function, which enables the computed modes to characterize the non-stationary properties of space–time fluid flows. Then, the RVMD algorithm is designed based on VMD to achieve a low-redundant adaptive extraction of ELDs in flow data, with the modes computed by solving an elaborate optimization problem. Further, a combination of RVMD and Hilbert spectral analysis leads to a modal-based time-frequency analysis framework in the Hilbert view, providing a potentially powerful tool to discover, quantify and analyse the transient and non-stationary dynamics in complex flow problems. To provide a comprehensive evaluation, the computational cost and parameter dependence of RVMD are discussed, as well as the relations between RVMD and some classic modal decomposition methods. Finally, the virtues and utility of RVMD and the modal-based time-frequency analysis framework are well demonstrated via two canonical problems: the transient cylinder wake and the planar supersonic screeching jet.

Variance of age-specific log incidence decomposition (VALID): a unifying model of measured and unmeasured genetic and non-genetic risks.

The extent to which known and unknown factors explain how much people of the same age differ in disease risk is fundamental to epidemiology. Risk factors can be correlated in relatives, so familial aspects of risk (genetic and non-genetic) must be considered. We present a unifying model (VALID) for variance in risk, with risk defined as log(incidence) or logit(cumulative incidence). Consider a normally distributed risk score with incidence increasing exponentially as the risk increases. VALID's building block is variance in risk, Δ2, where Δ = log(OPERA) is the difference in mean between cases and controls and OPERA is the odds ratio per standard deviation. A risk score correlated r between a pair of relatives generates a familial odds ratio of exp(rΔ2). Familial risk ratios, therefore, can be converted into variance components of risk, extending Fisher's classic decomposition of familial variation to binary traits. Under VALID, there is a natural upper limit to variance in risk caused by genetic factors, determined by the familial odds ratio for genetically identical twin pairs, but not to variation caused by non-genetic factors. For female breast cancer, VALID quantified how much variance in riskis explained-at different ages-by known and unknown major genes and polygenes, non-genomic risk factors correlated in relatives, and known individual-specific factors. VALID has shown that, while substantial genetic risk factors have been discovered, much is unknown about genetic and familial aspects of breast cancer risk especially for young women, and little is known about individual-specific variance in risk.

Stochastic regional-based profit-maximizing hub location problem: A sustainable overview

Climate change is one of the most important concerns globally, and countries need to improve their transportation infrastructure to handle flows with the least air pollution. In specific cities and regions, carbon emissions may cause in future many issues for people and societies. Although transportation hubs are very helpful in the reduction of transportation costs, they may cause an increase in carbon emissions in some regions, leading to long-term environmental problems. In this study, a model is developed for the profit-maximizing hub location problem that incorporates three pillars of sustainability. The proposed model is not only designed to maximize profit but also to control carbon emissions using a carbon cap policy and to reduce differences in emissions between regions with consideration of population density. This scheme will lead to achieving a sustainable transportation network. A two-stage stochastic programming approach is employed to cope with demand uncertainty. An enhanced sampling based on the self-organizing map method was utilized to cluster scenarios that lead to dealing with small-sized problems. Furthermore, classical Benders decomposition, Pareto-optimal cut Benders decomposition, and L-shaped algorithms are employed to solve the proposed models more efficiently. The proposed models are analyzed using the well-known Turkish Network (TR) data set. Computational results demonstrate that the proposed models help to achieve sustainability. Factors of sustainability such as environmental and social can be achieved by slightly reducing the amount of profit in the economic factor. Furthermore, results show that the L-shaped algorithm with a multi-cut scheme outperforms the commercial solver, classical Benders decomposition, and Pareto-optimal cut Benders decomposition algorithms in large-size instances.

Iterative solution of spatial network models by subspace decomposition

We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be applied to a wide range of models, fulfilling a set of abstract assumptions. The proposed method builds on a classical subspace decomposition into a coarse subspace, realized as the restriction of a finite element space to the nodes of the spatial network, and localized subspaces with support on mesh stars. The main contribution of this work is the convergence analysis of the proposed method. The analysis translates results from finite element theory, including interpolation bounds, to the spatial network setting. A convergence rate of the PCG algorithm, only depending on global bounds of the operator and homogeneity, connectivity and locality constants of the network, is established. The theoretical results are confirmed by several numerical experiments.

Rolling bearing faults identification based on multiscale singular value

To solve the vulnerability of singular value denoising to the effective number of singular value orders and influence of Hankel matrix structure, the paper has proposed a multiscale singular value denoising algorithm (M-SVD). Meanwhile, in concerning that when a fault of bearing occurs, the fault feature information contained in vibration signal tends to be weak and complex, the M-SVD method is blended with variational mode decomposition (VMD) algorithm in identification. Firstly, when bearing faults occur, raw vibration acceleration signals are decomposed using the superiority of VMD algorithm for non-stationary signal; in addition, considering that with the larger difference between singular values of signal, feature information will be more obvious, the method takes advantage of sensibility of variance to signal intensity and proposes to constitute Hankel matrix based on variance feature of signal. During the construction of Hankel matrix, the method to determine effective length of variance sequence (optimal scale) has been brought forward by sample entropy which is able to precisely measure the regularity of signal and detect the weak change of signal. Furthermore, component signals are denoised in line with reconstructed Hankel matrix and the spectrum of signals denoised are selected to describe fault characteristic information and judge the failure types. For the sake of verification of the accuracy and effectiveness of proposed method, the paper has analyzed and verified the data of rolling bearing in 3 different failure types and 2 different installation positions of accelerometers. The comparative analysis with classical singular value difference spectrum (SVDS) and singular value median decomposition (SVMD) denoising has further proved that presented VMD combined M-SVD method can effectively restrain noise while retaining fault characteristic information of signal. Therefore, the identification for rolling bearing fault types can be implemented, accurately.

Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell’s equations with different wave numbers

In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step. The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process. To substantiate this proof of concept, we investigate a few subdomains in some numerical experiments with low frequencies. Therein the new approach is compared to a classical domain decomposition method. Moreover, we highlight current challenges of training and testing with different wave numbers and we provide information on the behaviour of the neural-network, such as convergence of the loss function, and different activation functions.

Block-wise recursive sliding variational mode decomposition method and its application on online separating of bridge vehicle-induced strain monitoring signals

A critical element of structural intelligence monitoring is to separate the vehicle-induced response from the original monitoring signal in real time. To separate the vehicle-induced strain components from the strain monitoring signals mixed with various load effects, an online recursive sliding variational mode decomposition method is proposed in this paper. A real-time online signal separation framework is first proposed; then four technical measures are taken to modify the classical variational mode decomposition (VMD) to address the problems of its time-consuming nature and unsuitable for online use. These measures include: by establishing the block recursive Fourier transform results between frames in the sliding, which significantly reducing calculation time and achieving the best balance between calculation efficiency and real-time performance; during iteration, the center frequency is initialized to avoid possible traps; the convergence criterion is tightened; displacement technology eliminates boundary effects during sliding. Simulations show that the proposed method has a better separation effect than VMD, and its operation speed is much higher than VMD, which meets the real-time requirements of online signal separation. Based on the real-time data collected by Daishan Second Bridge Health Monitoring System strain sensors, the proposed recursive sliding variational mode decomposition (RSVMD) realizes the online real-time separation of vehicle-induced strain signals, proving its capability and potential in actual bridge health monitoring.

Exploring the factors contributing to increase in facility child births in Bangladesh between 2004 and 2017–2018

BackgroundAlthough Bangladesh has gained rapid improvement in births at health facilities, yet far behind to achieve the SDG target. Assessing the contribution of factors in increased use of delivery at facilities are important to demonstrate. ObjectiveTo explore the determinants and their contribution in explaining increased use of facility child births in Bangladesh. ParticipantsReproductive-aged women (15–49 years) of Bangladesh. Methods and materialsWe used the latest five rounds (2004, 2007, 2011, 2014, 2017–2018) of Bangladesh Demographic and Health Surveys (BDHSs). The regression based classical decomposition approach has been used to explore the determinants and their contribution in explaining the increased use of facility child birth. ResultsA sample of 26,686 reproductive-aged women were included in the analysis, 32.90% (8780) from the urban and 67.10% (17,906) from the rural area. We observed a 2.4-fold increase in delivery at facilities from 2004 to 2017–2018, in rural areas it is more than three times higher than the urban areas. The change in mean delivery at facilities is about 1.8 whereas, the predicted change is 1.4. In our full sample model antenatal care visits contribute the largest predicted change of 22.3%, wealth and education contributes 17.3% and 15.3% respectively. For the rural area health indicator (prenatal doctor visit) is the largest drivers contributing 42.7% of the predicted change, hereafter education, demography and wealth. However, in urban area education and health contributed equally 32.0% of the change followed by demography (26.3%) and wealth (9.7%). Demographic variables (maternal BMI, birth order, age at marriage) contributing more than two-thirds (41.2%) of the predicted change in the model without the health variables. All models showed more than 60.0% predictive power. ConclusionHealth sector interventions should focus both coverage and quality of maternal health care services to sustain steady improvements in child birth facilities.

A hybrid projection/data-driven reduced order model for the Navier-Stokes equations with nonlinear filtering stabilization

We develop a Reduced Order Model (ROM) for the Navier-Stokes equations with nonlinear filtering stabilization. Our approach, that can be interpreted as a Large Eddy Simulation model, combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies in the use within the EFR algorithm of a nonlinear, deconvolution-based indicator function that identifies the regions of the domain where the flow needs regularization. The ROM we propose is a hybrid projection/data-driven strategy: a classical Proper Orthogonal Decomposition Galerkin projection approach for the reconstruction of the velocity and the pressure fields and a data-driven reduction method to approximate the indicator function used by the nonlinear differential filter. This data-driven technique is based on interpolation with Radial Basis Functions. We test the performance of our ROM approach on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0≤Re≤100. The accuracy of the ROM is assessed against results obtained with the full order model for velocity, pressure, indicator function and time evolution of the aerodynamics coefficients.

Induction Motor Noise Source Separation and Identification Based on Adaptive Scale-Space Mode Extraction

Separating induction motor noise sources can provide an important reference basis for induction motor condition detection, noise reduction treatment, and fault diagnosis. Induction motors have different types of noise sources that partially overlap, and most radiate outward through the housing, so it is difficult to separate these noise sources. Therefore, a single-channel induction motor noise source separation and identification method, based on adaptive scale-space modal extraction (ASSME) is proposed. Firstly, the adaptive scale-space mode extraction method is proposed by constructing the electromagnetic feature scale space and the adaptive penalty factor. The simulation results show that this method solves over-decomposition problems in the classical scale-space variational mode decomposition and the difficulty in balancing the harmonic and shock modes. Secondly, motor noise experiments are conducted to construct blind source separation multi-channel inputs using the adaptive scale-space modal extraction method, judging the validity of the modal components using correlation and the variance contribution rate. Finally, robust independent component analysis (RobustICA) is used to extract independent noise components and identify these noise sources by power spectral density and envelope analysis. The results show that the multi-channel input signals obtained by the proposed method are more accurate and practical than those obtained by other methods. The independent components extracted through this noise source separation method are: electromagnetic noise of different orders, aerodynamic noise, and switching frequency noise.

Enhanced Bruhat Decomposition and Morse Theory

AbstractMorse function is called strong if all its critical points have different critical values. Given such a function $f$ and a field $\mathbb{F}$ Barannikov constructed a pairing of some of the critical points of $f$, which is now also known as barcode. With every Barannikov pair (a.k.a. bar in the barcode), we naturally associate (up to sign) an element of $\mathbb{F} \setminus \{ 0 \}$; we call it Bruhat number. The paper is devoted to the study of these Bruhat numbers. We investigate several situations where the product of all the numbers (some being inversed) is independent of $f$ and interpret it as a Reidemeister torsion. We apply our results in the setting of one-parameter Morse theory by proving that generic path of functions must satisfy a certain equation mod 2 (this was initially proven in [ 2] under additional assumptions).On the linear-algebraic level, our constructions are served by the following variation of a classical Bruhat decomposition for $GL(\mathbb{F})$. A unitriangular matrix is an upper triangular one with 1s on the diagonal. Consider all rectangular matrices over $\mathbb{F}$ up to left and right multiplication by unitriangular ones. Enhanced Bruhat decomposition describes canonical representative in each equivalence class.

Degradation assessment of two silicon photovoltaic technologies under subtropical desert climate

<span lang="EN-US">The prediction of performance of photovoltaic technologies is crucial, not only to improve the reliability and durability of these technologies but also to increase the confidence of investors and consumers in them. The accurate calculation of the degradation rate D<sub>R </sub>(%) in real operating conditions under specific climatic stresses is, therefore, paramount. The present study provides a comparison of performance losses of two silicon PV technologies installed on the rooftop of the Higher School of Technology in Laâyoune-Morocco. The two systems are a polycristalline array (pc-Si: 1.82 kWp) and an amorphous array (a-Si: 1.55 KWp), which are grid connected. In the light of related performance gathered over three-year, the degradation rates of the two systems were estimated using four statistical methods under the open-source software R. The techniques engaged in this paper are: classical seasonal decomposition (CSD), holt-winters (HW), autoregressive integrated moving average (ARIMA), and seasonal and trend decomposition by LOESS (STL). The results obtained using those methods show that DR(%) varies between 0.39% and 0.99% for pc-Si and between 0.29% and 0.64% for a-Si. The analysis of degradation accuracy shows that STL and CSD techniques provide results with high accuracy than ARIMA and HW for the two systems. The present study adds to knowledge on PV degradation under the subtropical desert climate of Laâyoune.</span>

Drag Decomposition Using Partial-Pressure Fields: Ventus-3 and NASA Common Research Model

The development of partial-pressure field (PPF) theory (Schmitz, S “Drag Decomposition Using Partial-Pressure Fields in the Compressible Navier–Stokes Equations,” AIAA Journal, Vol. 57, No. 5, 2019, pp. 2030–2038) and the application of the concept to conditions relevant to commercial transport aircraft, operating in both the subsonic and transonic regimes (Hart, P. L., and Schmitz, S., “Drag Decomposition using Partial-Pressure Fields: ONERA M6 Wing,” AIAA Journal, Vol. 60, No. 5, 2022 pp. 2941–2951), have shown promise as complements to classical far-field methods. In the present work, a further comprehensive analysis of drag decomposition methods is applied to wing and aircraft configurations. First, the Ventus-3 sailplane wing case demonstrates the ability of PPFs to successfully deconstruct drag on industry-relevant cases including transition modeling and winglets. A quantitative comparison to classical aerodynamic theory and far-field methods supports PPF theory and provides additional insight to viscous–inviscid interaction by means of a viscous interactional aerodynamics term in PPF theory. Second, the NASA Common Research Model is simulated in transonic flow to showcase drag decomposition of full aircraft configurations where PPF applications are used to provide further insight into wave drag sources acting on the aircraft in comparison to classical far-field decomposition methods.

Interpretable deep dictionary learning for sound speed profiles with uncertainties.

Uncertainties abound in sound speed profiles (SSPs) measured/estimated by modern ocean observing systems, which impede the knowledge acquisition and downstream underwater applications. To reduce the SSP uncertainties and draw insights into specific ocean processes, an interpretable deep dictionary learning model is proposed to cater for uncertain SSP processing. In particular, two kinds of SSP uncertainties are considered: measurement errors, which generally exist in the form of Gaussian noises; and the disturbances/anomalies caused by potential ocean dynamics, which occur at some specific depths and durations. To learn the generative patterns of these uncertainties while maintaining the interpretability of the resulting deep model, the adopted scheme first unrolls the classical K-singular value decomposition algorithm into a neural network, and trains this neural network in a supervised learning manner. The training data and model initializations are judiciously designed to incorporate the environmental properties of ocean SSPs. Experimental results demonstrate the superior performance of the proposed method over the classical baseline in mitigating noise corruptions, detecting, and localizing SSP disturbances/anomalies.

The lines of descent of the present crisis

The neoliberal settlement has been comprehensively destabilised by the 2007 financial crisis, the imposition of austerity, growing social inequalities and the emergence of populism as a social force. This article explores why institutional opposition to this settlement has principally taken a nationalist form in Britain. It does so through a history of the present by tracing the labyrinthine lines of descent and the social forces and conflicts from which the contemporary moment emerged. In particular, I show how the conditions for the emergence of these nationalist projects were produced incrementally over time and through a series of interrelated social processes. These included the caesura of the 1970s and the shift from Fordist to flexible regimes of accumulation secured by extinguishing the educated hope generated by an increasingly multi-ethnic politics and language of class; the bipartisan commitment to neoliberalism; the racialisation of class through state multiculturalism; and the long-term failure to arrest the structural decline of non-urban localities caused by the technical decomposition of class. In this explanation, the 2007 financial crash and the continuing indifference of the political elites to the deepening injuries of class and locality constituted an accelerant placed on an already emergent crisis of representation helping to engineer a transformation in the political opportunity structure by opening a space for nationalist mobilising structures to fill the political vacuum.

On decomposition of left-right Atkinson linear relations and related classes

ABSTRACT In this paper, left Atkinson linear relations defined in a Banach space are considered. The behaviour of such notion in polynomials is studied and a spectral mapping theorem for the corresponding spectrum is deduced. Let denote any of the following classes: left (right) Atkinson, Fredholm, left (right) Weyl, Weyl, left (right) Browder, Browder linear relations. For a closed and everywhere defined linear relation we prove that under suitable conditions, where and is a bounded nilpotent operator if and only if admits a Kato-decomposition and 0 is not an interior point of the spectrum of As an application, some connections results between and are established, where denotes the Kato-decomposition spectrum of

Multi-mitigation strategies in medical supplies for epidemic outbreaks

The outbreak of Coronavirus disease 2019 (COVID-19) highlights the importance of sufficient medical supplies stockpiling at the pre-event stage. In contrast, the potential disadvantages of maintaining adequate items at strategic locations (i.e., reserves) are considerable inventory-related costs. Unpredicted demand leads to a high degree of uncertainty. Efforts to mitigate the uncertainty should rely not only on prepositioning supplies at reserves but also on integrating various channels of medical materials. This paper proposes multi-mitigation strategies in medical supplies to ensure uninterrupted supply for hospitals and significant savings by introducing two-type suppliers, reserving and manufacturing suppliers. Thus, each hospital with uncertain demand is enabled to be served by various channels during pandemics: prepositioning in reserves, backups served by reserving suppliers, and medical commodities produced by manufacturing suppliers. Stochasticity is also incorporated into the raw materials available to produce. This research aims to develop an emergency response application that integrates preparedness action (reserve location, inventory level, and contract supplier's selection) with post-event operations (allocating medical materials from various channels). We formulate a two-stage stochastic mixed integer program to determine prepositioning strategy, including two-type suppliers' selection, and post-event allocation of multiple sources. A branch-and-Benders-cut method is developed for this problem and significantly outperforms both the classical Benders decomposition and Gurobi in the solution time. Different-sized test instances also verify the robustness of the proposed method. Based on a realistic and typical case study (inspired by the COVID-19 pandemic in Wuhan, China), significant savings, an increase in inventory utilization and an increase in demand fulfilment are obtained by our approach.

Adaptive POD-DEIM correction for Turing pattern approximation in reaction–diffusion PDE systems

Abstract We investigate a suitable application of Model Order Reduction (MOR) techniques for the numerical approximation of Turing patterns, that are stationary solutions of reaction–diffusion PDE (RD-PDE) systems. We show that solutions of surrogate models built by classical Proper Orthogonal Decomposition (POD) exhibit an unstable error behaviour over the dimension of the reduced space. To overcome this drawback, first of all, we propose a POD-DEIM technique with a correction term that includes missing information in the reduced models. To improve the computational efficiency, we propose an adaptive version of this algorithm in time that accounts for the peculiar dynamics of the RD-PDE in presence of Turing instability. We show the effectiveness of the proposed methods in terms of accuracy and computational cost for a selection of RD systems, i.e., FitzHugh–Nagumo, Schnakenberg and the morphochemical DIB models, with increasing degree of nonlinearity and more structured patterns.

Weighted singular value decomposition basis of Szegő kernel and its applications to signal reconstruction and denoising

For any circular analytic signal f+(eit)∈H2(T), if the sequence {ak}k=0∞ in the unit disc D satisfies the hyperbolic non-separability condition ∑k=0∞(1−|ak|)=∞, it is known that the first N+1 term approximation function based on the Takenaka–Malmquist system (SN+1f+)(eit)=∑k=0N〈f+(eit),Bk(eit)〉Bk(eit),can approximate the analytic signal f+(eit) in the L2-norm sense, where Bk(eit)=1−|ak|21−ak¯eit∏l=0k−1eit−al1−al¯eit, k∈N is the Takenaka–Malmquist system which can be seen as a generalization of Fourier series. We find that (SN+1f+)(eit) can also be represented by the standard basis, Lagrange basis and weighted SVD basis. Different bases have different merits. The standard basis is simple. The Lagrange basis has a neat and compact form, which is very convenient for theoretical analysis. With the Takenaka–Malmquist system, the first N+1 term approximation function (SN+1f+)(eit) is able to write in an iterative form. The Takenaka–Malmquist system has the advantage of inheritance, and the point ak∈D can be easily selected step by step through the greedy principle. In this paper, we focus our attention on the weighted SVD basis. We give some orthogonal properties of the weighted SVD basis. It demonstrates that any real signal f(eit)∈L2(T) can be precisely reconstructed within the given error range by the weighted SVD basis decomposition. The experimental results reveal that the algorithm based on weighted SVD basis is more stable and accurate. Furthermore, compared with classical Fourier decomposition and adaptive Fourier decomposition algorithms, the experimental results show that the weighted SVD basis decomposition is more insensitive to noise. This will provide a new method for signal denoising.