Smooth Coefficients Research Articles

Permanent magnet synchronous motor demagnetization fault diagnosis based on PCA-ISSA-PNN

Aiming at the demagnetization fault problem of the permanent magnet synchronous motor (PMSM), a demagnetization fault diagnosis method based on the combination of the principal component analysis (PCA) algorithm, the improved sparrow search algorithm (ISSA), and the probabilistic neural network (PNN) algorithm is proposed. First, the principal components of phase currents are extracted using PCA. Second, ISSA is used to optimize the smoothing coefficients of the PNN algorithm, and the optimized PNN algorithm is combined with PCA to obtain the PCA-ISSA-PNN fault diagnosis model. Finally, the established fault diagnosis model was tested using the current data collected from the experiments and compared with the fault diagnosis indexes and optimization performance of the conventional PNN, PCA-PNN, PCA-GA (genetic algorithm)-PNN, PCA-DA (dragonfly algorithm)-PNN, PCA-GTO (artificial gorilla troop optimizer)-PNN, PCA-AHA-PNN, and PCA-SSA-PNN. The test results show that the fault diagnosis accuracy of PCA-ISSA-PNN reaches 95.83%, and the fault diagnosis indexes are significantly higher than those of PNN, PCA-PNN, PCA-GA-PNN, and PCA-DA-PNN; its optimization performance is also significantly better than that of PCA-GTO-PNN, PCA-AHA-PNN, and PCA-SSA-PNN, which verifies the accuracy and efficiency of the proposed method.

Economic impacts of tourism demand on the European food and accommodation industry

Sustainability strategies have become central topics in the literature on tourism development, given the significant increase in tourism demand in Europe. This study examines the economic (cost) impact of increased tourism demand on the European Food and Accommodation Industry. We employed three distinct models — pooled linear regression, flexible nonparametric, and semiparametric smooth coefficients — using data spanning European countries from 2005 to 2020. Our findings reveal the heterogeneous impacts of tourist arrivals and length of stay on costs. Although the direct effects were predominantly positive, the indirect effects were found to be negative, resulting in a minor overall negative effect on the average. Furthermore, we found that the proportion of domestic tourists has a notable impact on costs, revealing that higher proportions are linked to lower direct costs but higher indirect costs on average. These findings provide valuable insights for industry stakeholders and policymakers alike.

An improved immersed boundary method for turbulent flow simulations on Cartesian grids: extension of a global geometric approach for thin boundary layers and strong flow incidence

This paper presents further improvements to the immersed boundary method introduced in [1]. The proposed developments take place during the pre- and post-processing stages of the simulation workflow and aim to further increase the accuracy of the approach for steady-state simulations of high Reynolds number turbulent flows around aerodynamic geometries facing strong incidence. To this end, the location of the forcing points is further optimized prior to simulation, with an adaptive and local modeling height that accounts for the evolution of the turbulent boundary layer thickness, especially at the leading edge. In addition, the direct extrapolation of the pressure solution at the wall is replaced by first- and second-order reconstructions using the normal pressure gradients interpolated at a new set of image points. This second approach is used only in post-processing, after the simulation, and prevents the degradation of the wall pressure in the presence of strong curvatures or thin boundary layers. These developments have been validated by simulating subsonic turbulent flows around the NACA0012 profile, 2D multi-element airfoil (2DMEA), and HL-CRM half-plane at significant angles of attack. Smooth and accurate skin pressure and friction coefficients are observed, in excellent agreement with body fitted wall-resolved solutions, even for coarser Cartesian meshes. Better drag and lift coefficients calculated by direct near-field integrations are obtained, along with accurate predictions of the near-wall flow physics throughout the turbulent boundary layer.

Energy storage peak-shaving demand prediction based on an improved neural network with hidden layers

Abstract The result shows that the BP neural network has a very low convergent speed for load prediction, which leads to local optimization. This paper presents a modified GA for the optimization of the threshold value, the initial weight, and the addition of the smoothing coefficient. In addition, it improves the BP neural network’s adaptive learning speed and further improves the efficiency of the search. The proposed model is characterized by high convergent speed and global space retrieval capability. To validate the validity of the modified GA-BP model, the prediction of power load in some regions is made. Compared with the BP neural network forecast algorithm, this method has better performance in terms of prediction accuracy and takes less time in terms of prediction time than the BP neural network. In parallel, the realization of multiple sources of electricity from wind, solar, and heat storage is an important way to deal with large-scale new grid connections. Starting from an improvement in the efficiency of wind and PV generation, it is also possible to build a joint optimization scheduling model for wind, solar, and heat storage. The purpose of taking the minimum net load fluctuation is for optimization. Taking the typical output day of user scenarios as the optimization scenario, the scheduling strategies of wind power, PV, thermal units, and energy storage systems are introduced and simulated on the platform. It is proved that the proposed model can decrease the reduction ratio and the peak and valley load.

Monitoring method and application of transition process with nonstationary conditions based on stability factor partitioning and RSFA

It is common for the working conditions to change with time in actual industrial processes. However, the transition modes of complex industrial processes under different working conditions often have various degrees of dynamic nonstationarity, which makes the traditional process monitoring model based on the stationarity assumption ineffective. In this paper, a Recursive Slow Feature Analysis method based on Stability Factor Partitioning (SFP-RSFA) is proposed for fine process monitoring of transition modes under dynamic nonstationarity characteristics. First, we calculate the stability factor according to the different stationarity characteristics of the production process variables. Then, K-means clustering is carried out according to the stability factor of each variable, and the stability factor of the cluster center is mapped to the interval [0,1] as the smoothing coefficient of the exponential weighted moving average (EWMA), which is applied to each data subblock respectively to highlight the steady-state and dynamic characteristics of the monitoring data subblock. In the online monitoring stage, the monitored data are fed into the subblock recursive slow feature analysis (RSFA) monitoring model. Finally, a comprehensive statistic method is proposed to integrate the subblock monitoring statistics. The Tennessee Eastman (TE) process and actual cement clinker production process were tested and compared with existing RPCA, RCA and RSFA methods. The effectiveness and superiority of the proposed method in the problem of nonstationary transition mode process monitoring are verified.

Random noise attenuation of 3D multicomponent seismic data using a fast adaptive prediction filter

Random noise in seismic records affects the accuracy of effective signal identification, making it difficult for subsequent seismic data processing, imaging, and interpretation. Therefore, random noise attenuation has always been an important step in seismic data processing, especially for 3D data. In recent years, multicomponent exploration has been developed rapidly. However, the common method for processing multicomponent data is to process each component separately resulting in the correlation between multicomponent data being neglected. For 3D multicomponent data, we develop a multicomponent adaptive prediction filter (MAPF) based on noncausal regularized nonstationary autoregressive models to implement random noise attenuation in the t- x- y domain. The MAPF for multicomponent signals can be used to identify the potential correlations and differences between each pair of components, providing not only a robust analysis of the individual components but also effective information about the consistency and differences between each component with more information and constraints compared with traditional 1C prediction. Moreover, it can obtain smooth nonstationary prediction coefficients by solving the least-squares problem with shaping regularization. The example results demonstrate that the MAPF method is superior to the traditional adaptive prediction filtering method. Furthermore, because the multicomponent method requires more coefficients and takes a longer time to predict than the 1C method, we further develop a fast MAPF (FMAPF) combining the data pooling and coefficient reconstruction strategies. The example results demonstrate that the FMAPF method is effective at denoising and greatly improves computational efficiency. The method comes with a slight decrease in computational accuracy.

An adaptive harmonic polynomial cell method for three-dimensional fully nonlinear wave-structure interaction with immersed boundaries

To accurately simulate wave-structure interaction based on fully nonlinear potential flow theory, a three-dimensional (3 D) high-order immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method is proposed. Both the free surface and body surface are immersed in background octree cells that are adaptively refined near the boundaries of interest, thereby dramatically reducing computational costs without loss of accuracy. We also propose an easy-to-implement IB strategy to deal with possible instabilities in the time-domain solution arising from the intersection of Dirichlet–Neumann boundaries. For a linearized problem of wave-wall interaction, a matrix-based stability analysis is performed, providing mathematical support for the robustness of the proposed IB strategy. In contrast to the two-dimensional HPC method, compressed cells are found to offer superior stability compared to stretched cells in the vertical direction, while equal mesh aspect ratio in the horizontal plane is superior. Cubic octree cells are, however, still preferred in practice. The free surface is primarily described by a set of massless background wave markers; however, to address the challenges of IB methods in tracking the free surface evolution near the structure, additional body-fitted wave markers are introduced close to the waterline. The information exchange between these two sets of wave markers is realized by radial basis function (RBF) interpolation. While standard RBF schemes have grid-size-dependent filtering performance, we propose a normalized RBF scheme, which is then optimized in terms of the number of neighboring nodes, a smoothing coefficient and the basis functions. Excellent accuracy properties of the proposed 3 D IB-AHPC method are demonstrated by studying fully nonlinear wave propagation. The method is further applied to study relevant fully nonlinear wave-structure interaction problems, including sloshing in 3 D rectangular tanks and wave diffraction of a bottom-mounted cylinder in regular waves. Satisfactory agreement is demonstrated with existing experimental and numerical results, suggesting that the proposed 3 D IB-AHPC method is a promising potential-flow method in marine hydrodynamics.

Lagrange formula conjugate third order differential equation

The paper considers a boundary value problem for a third order with no smooth coefficients and pure derivatives. Odds. This is due to the fact to introduce the concept of the conjugate Green's function. It is very difficult to write the form of the conjugate differential operator corresponding to equation in the Lagrange sense. Therefore, in this work, without using strict conditions smoothness under the conditions and boundedness, an explicit form is found conjugate operator since the initial-boundary value problem for integral-differential equations has been studied based on the introduction special conjugate systems in the form of an integral-algebraic equations’ system. In this article, it can be said that Green's function is considered based on Lagrange's formula for the third-order differential equation with boundary conditions and its conjugate.

Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, III: singular coefficients

In this paper we continue the analysis of non-diagonalisable hyperbolic systems initiated in [25, 26]. Here we assume that the system has discontinuous coefficients or more in general distributional coefficients. Well-posedness is proven in the very weak sense for systems with singularities with respect to the space variable or the time variable. Consistency with the classical theory is proven in the case of smooth coefficients.

Superior Strength, Toughness, and Damage-Tolerance Observed in Microlattices of Aperiodic Unit Cells.

Characterized by periodic cellular unit cells, microlattices offer exceptional potential as lightweight and robust materials. However, their inherent periodicity poses the risk of catastrophic global failure. To address this limitation, a novel approach, that is to introduce microlattices composed of aperiodic unit cells inspired by Einstein's tile, where the orientation of cells never repeats in the same orientation is proposed. Experiments and simulations are conducted to validate the concept by comparing compressive responses of the aperiodic microlattices with those of common periodic microlattices. Indeed, the microlattices exhibit stable and progressive compressive deformation, contrasting with catastrophic fracture of periodic structures. At the same relative density, the microlattices outperform the periodic ones, exhibiting fracture strain, energy absorption, crushing stress efficiency, and smoothness coefficients at least 830%, 300%, 130%, and 160% higher, respectively. These improvements can be attributed to aperiodicity, where diverse failure thresholds exist locally due to varying strut angles and contact modes during compression. This effectively prevents both global fracture and abrupt stress drops. Furthermore, the aperiodic microlattice exhibits good damage tolerance with excellent deformation recoverability, retaining 76% ultimate stress post-recovery at 30% compressive strain. Overall, a novel concept of adopting aperiodic cell arrangements to achieve damage-tolerant microlattice metamaterials is presented.

A MULTIPOINT BOUNDARY VALUE PROBLEM IN TIME FOR A $2B$-PARABOLIC EQUATION WITH DEGENERACY

One of the most important issues in the general theory of differential equations with partial derivatives is establishing the solvability of boundary value problems. Among the boundary value problems for equations with partial derivatives, problems with nonlocal boundary conditions occupy an important place. Such interest in such problems is caused both by their rich practical application (the process of diffusion, moisture distortion in soils, plasma physics, etc.), and by the needs of the general theory of boundary value problems. A general multipoint boundary value problem for nonuniformly $2b$-parabolic equations with degeneracy is studied. The coefficients of parabolic equations and boundary conditions allow power degeneracy of arbitrary order in terms of time variable and spatial variables at some set of points. To solve the given multipoint boundary value problem, solutions of problems with smooth coefficients in Hölder spaces with the appropriate norm are studied. With the help of interpolation inequalities and a priori estimates, estimates of the solution of auxiliary problems and their derivatives in special Gelder spaces are established. Using the theorems of Ross and Archel, a convergent sequence is distinguished from the compact sequence of solutions of the auxiliary problems, the limiting value of which is the solution of the multipoint boundary value problem in time for the $2b$-parabolic equation with degeneracy. Estimates of the solution of the given problem are established in Hölder spaces with power-law weights. The order of the power weight is determined by the order of features of the coefficients of the equations and the boundary conditions. With certain restrictions on the right-hand side of the equation and boundary conditions, an integral image of the given problem is obtained.

Factor-augmented Model for Functional Data

We propose modeling raw functional data as a mixture of a smooth function and a high-dimensional factor component. The conventional approach to retrieving the smooth function from the raw data is through various smoothing techniques. However, the smoothing model is inadequate to recover the smooth curve or capture the data variation in some situations. These include cases where there is a large amount of measurement error, the smoothing basis functions are incorrectly identified, or the step jumps in the functional mean levels are neglected. A factor-augmented smoothing model is proposed to address these challenges, and an iterative numerical estimation approach is implemented in practice. Including the factor model component in the proposed method solves the aforementioned problems since a few common factors often drive the variation that cannot be captured by the smoothing model. Asymptotic theorems are also established to demonstrate the effects of including factor structures on the smoothing results. Specifically, we show that the smoothing coefficients projected on the complement space of the factor loading matrix are asymptotically normal. As a byproduct of independent interest, an estimator for the population covariance matrix of the raw data is presented based on the proposed model. Extensive simulation studies illustrate that these factor adjustments are essential in improving estimation accuracy and avoiding the curse of dimensionality. The superiority of our model is also shown in modeling Australian temperature data.

ON THE CORRECTNESS OF ONE CLASS OF FOURTH-ORDERSINGULAR DIFFERENTIAL EQUATIONS

The differential equation of fourth-order with variable smooth coefficients, given on the real axis, is investigated. The coefficients of the equation can be unbounded, and the sign of the potential (the lowest coefficient) is not defined. The case is considered that the intermediate term containing the second derivative of the desired function, as an operator, does not obey the operator of the equation. It is known that fourth-order differential equations with variable coefficients are used in various problems of mathematical physics. The simplest biharmonic equation with minor terms is important for its applications in the theory of elasticity, the mechanics of elastic plates and the slow flow of viscous liquids. However, it is a very special case of a general equation with variable coefficients. Some problems of stochastic analysis, oscillation theory, biology and mathematical finance lead to the equation we are studying. In addition, fourth–order singular differential equations are often used as regularizers in the study of lower-order equations, for example, reaction-diffusion equations. In the paper, sufficient solvability conditions of the equation and the maximal regularity inequality of a strong generalized solution are obtained. The restrictions are formulated in terms of the coefficients themselves and rather weak. They do not contain conditions for any derivatives of coefficients and represent relations between the orders of growth of coefficients of different orders at infinity. The weight estimation of the norms of a solution established by us allows us to additionally apply the methods of the theory of functional spaces to the study of further properties of the solution, for example, the approximation of its elements by finite-dimensional spaces.

Detection of Forest Disturbances with Different Intensities Using Landsat Time Series Based on Adaptive Exponentially Weighted Moving Average Charts

Forest disturbance detection is important for revealing ecological changes. Long-time series remote sensing analysis methods have emerged as the primary approach for detecting large-scale forest disturbances. Many of the existing change detection algorithms focus primarily on identifying high-intensity forest disturbances, such as harvesting and fires, with only a limited capacity to detect both high-intensity and low-intensity forest disturbances. This study proposes an online continuous change detection algorithm for the detection of multi-intensity forest disturbances such as forest harvest, fire, selective harvest, and insects. To initiate the proposed algorithm, the time series of the Normalized Difference Vegetation Index (NDVI) is fitted into a harmonic regression model, which is then followed by the computation of residuals. Next, the residual time series is entered into the adaptive exponentially weighted moving average (AEWMA) chart. This chart adaptively adjusts the smoothing coefficients to identify both high-intensity and low-intensity disturbances. When the chart value consistently deviates from the control limit, the forest pixel is classified as disturbed. With an overall spatial accuracy of 85.2%, including 86.1% producer’s accuracy and 84% user’s accuracy, along with a temporal accuracy of 96.7%, the algorithm enables precise and timely detection of forest disturbances with multiple intensities. This method provides a robust solution for detecting multi-intensity disturbances in forested regions.

Evaluation of the Use of Permeable Interlocking Concrete Pavement in Chile: Urban Infrastructure Solution for Adaptation and Mitigation against Climate Change

There is currently a context of climate change due to the way modern cities are developed, and they are made up mainly of impermeable surfaces and concrete buildings that change the hydrological cycle, causing (i) an increase in temperatures, (ii) the accumulation of stormwater on different surfaces, (iii) overflow in drainage systems, and (iv) the alteration of ventilation patterns, among others. This article presents a case study on the implementation of a permeable interlocking concrete paving (PICP) system, and it develops physical–mathematical modeling using software for the design of a parking lot that currently does not have adequate paving and urban drainage, resulting in sporadic flooding due to heavy rainfall in the city of Temuco, La Araucanía region, Chile. This article’s contribution highlights the application of new technology in Chile, discussing road infrastructure solutions based on sustainable urban drainage systems (SUDSs), which seek to implement feasible alternatives in urban sectors to improve human livelihood. The factors studied include structural and hydrological properties, along with the infiltration analysis of the system according to historical rainfall records in the area. This research concludes that the permeable pavement system with a drainage pipe and smooth roughness coefficient performs satisfactorily for an extreme hydrometeorological event corresponding to 140 mm considering 24 h of rainfall with a return period of 100 years equivalent to an inflow of 673 m3/day. Finally, the results indicate that, at least in the conditions of the city of Temuco, the use of permeable interlocking concrete pavement (PICP) proves to be a sustainable and feasible alternative to implementing measures of adaptation and mitigation against climate change, reducing the city’s flooding zones and allowing the irrigation of urban green areas.

Estimation in Semi-Varying Coefficient Heteroscedastic Instrumental Variable Models with Missing Responses

This paper studies the estimation problem for semi-varying coefficient heteroscedastic instrumental variable models with missing responses. First, we propose the adjusted estimators for unknown parameters and smooth functional coefficients utilizing the ordinary profile least square method and instrumental variable adjustment technique with complete data. Second, we present an adjusted estimator of the stochastic error variance by employing the Nadaraya–Watson kernel estimation technique. Third, we apply the inverse probability-weighted method and instrumental variable adjustment technique to construct the adaptive-weighted adjusted estimators for unknown parameters and smooth functional coefficients. The asymptotic properties of our proposed estimators are established under some regularity conditions. Finally, numerous simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed estimators.

Realizations and invariants of Lie algebras

Lie algebras of first-order differential operators with smooth coefficients are considered and their construction methods are reviewed. Obstacles preventing contractions of such operators are emphasized and a constructive procedure for parameterizations is proposed. A number of illustrative examples are considered.

Tunneling for a semi-classical magnetic Schrödinger operator with symmetries

We are interested in decay estimates of the ground state (or the low energy eigenstates), outside the potential wells, for a semi-classical Magnetic Schrödinger operator with smooth coefficients PA (x, hD x ) = (hD x − µA(x))2 + V (x) on L 2(R d ). We shall essentially consider the case where µ is large. This kind of estimates, in case of Schrödinger operator without a magnetic field, have been studied by Agmon [1], also in the case of a Riemannian manifold M. Agmon estimates hold true for any h, but are particularly useful in the limit h → 0 when studying tunneling.

A lightweight transformer and depthwise separable convolution model for remaining useful life prediction of turbofan engines

The degradation of turbofan engines under complex operating conditions makes it difficult to predict their remaining useful life (RUL), which affects aircraft maintenance efficiency and reliability. To maintain prediction accuracy while improving prediction speed under the limited computing power and memory resources of edge devices, a lightweight Transformer and depthwise separable convolutional neural network (DSCformer) prediction model has been proposed. In the proposed DSCformer method, a probsparse self-attention mechanism with convolutional transformation of the Value branch is developed to improve the efficiency of dot-product, and depthwise separable convolution is employed to extract local spatiotemporal features replace the decoder in Transformer. Additionally, the model’s ability to capture overall trends is improved by incorporating a scaling factor in the Bayesian optimization algorithm, which also accelerates the search for the smoothing coefficient. The evaluation on the C-MAPSS dataset shows that the proposed method achieves a root mean square error of 11.33 and 12.44, as well as scores of 634.22 and 947.35 for predicting FD002 and FD004, respectively, within a shorter training time. These results indicate that the proposed method outperforms state-of-the-art prediction methods under multiple operating conditions for aero engine RUL prediction.

Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case

In this article, we consider the asymptotic behaviour of the spectral function of Schrödinger operators on the real line. Let H: L^{2}(mathbb{R})to L^{2}(mathbb{R}) have the form \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ H:=-\\frac{d^{2}}{dx^{2}}+Q, $$\\end{document} where Q is a formally self-adjoint first order differential operator with smooth coefficients, bounded with all derivatives. We show that the kernel of the spectral projector, {1}_{(-infty ,rho ^{2}]}(H), has a complete asymptotic expansion in powers of ρ. This settles the 1-dimensional case of a conjecture made by the last two authors.