Basis Function Method Research Articles

Adaptive identification method of new energy grid operation risk based on linear decision function

The current conventional risk identification method of new energy grid operation mainly achieves risk identification by mining equipment status information, which leads to poor identification effect due to the lack of effective extraction of abnormal data features. In this regard, a linear decision function-based adaptive risk identification method for new energy grid operation is proposed. The data flow model is constructed by combining the linear decision function, and the features of interval abnormal data and fluctuating abnormal data are extracted. A sliding window model is constructed, and the unsupervised model is used to realize the effective update of new energy grid operation data. In the experiments, the proposed method is verified for recognition accuracy. The experimental results show that when the proposed method is used to identify the risk of grid operation, the effective data mis-deletion rate of the algorithm is low and has a more desirable identification effect.

Assessment of radial basis function method with thin plate spline kernel for evaluable precipitable water vapor interpolation from GPS observations over state of California, USA

Assessment of radial basis function method with thin plate spline kernel for evaluable precipitable water vapor interpolation from GPS observations over state of California, USA

A semiparametric spatio‐temporal model of crop yield trend and its implication to insurance rating

AbstractWe demonstrate the benefit of spatial smoothing for crop trend estimation with a deterministic spatio‐temporal trend model. The proposed model is semiparametric, where the parametric temporal trend is modeled with a two‐knot spline function for forecasting robustness, and the nonparametric spatially‐varying coefficients are modeled by the radial basis function method for flexibility. To select the smoothing parameter of our trend model, we propose a forward validation criterion tailored to meet the forecasting nature of rating crop insurance. This criterion is based on a rolling regression approach that adds one year of data at a time for validation. We also propose a new criterion for model comparison using relative mean squared error in forecasting insurance payouts. Our empirical results show that the proposed trend model is more efficient and capable of identifying profitable insurance policies than two competing models in most state‐crop combinations.

Multivariate uncertainty analysis of fracture problems through model order reduction accelerated SBFEM

An efficient Monte Carlo simulation (MCS) method that analyses the influences of multivariate uncertain parameters on the response of cracked structures is proposed. The scaled boundary finite element method (SBFEM) is used to solve the static and dynamic crack propagation problems and obtain a full-order snapshot model. The combination of a proper orthogonal decomposition with model order reduction and a radial basis function is used to achieve accelerated stochastic analysis based on MC simulations. The proper orthogonal decomposition-radial basis function (POD-RBF) method is more difficult to use directly for multivariate problems. Thus, we proposed an efficient operation suitable for multiple input variables. In crack propagation simulations, an optimized polygon meshing algorithm is used. Numerical results show that the proposed method can stochastically analyse multidimensional input variables and effectively obtain the responses of cracked structures, which verifies the effectiveness of the POD-RBF method.

Laminar Rayleigh–Benard convection in a closed square field with meshless radial basis function method

Abstract Research on natural convection is exciting in some experimental and numerical cases, especially in rectangular cavities with relatively low heat dissipation and thermal control systems with low cost, reliability, and ease of use. The present study will use the meshless radial basis function method to solve the velocity formulation of the Navier–Stokes equations by varying some nominal Rayleigh numbers of 104, 105, and 106. The numerical accuracy is compared with the previous research. The advantages of the meshless method are that it does not require a structured mesh and does not require inter-nodal connectivity. The results show that the temperature pattern is identical to the previous research. The calculations have been done for three different Rayleigh numbers of 104, 105, and 106 for 151 × 151 nodes. The variations of the Ra number will affect the isothermal, velocity contours, and Nusselt number.

Numerical Analysis of Seepage in Steady and Transient Flow State by the Radial Basis Function Method

Numerical Analysis of Seepage in Steady and Transient Flow State by the Radial Basis Function Method

Enhancing CBFM With Adaptive Frequency Sampling for Wideband Scattering From Objects Buried in Layered Media

An adaptive frequency sampling (AFS) strategy is proposed in conjunction with characteristic basis function method (CBFM) to investigate the problem of wide-band scattering from objects buried in layered media. Conventionally, the CBFM is implemented to reduce the solution time at a single frequency. However, wide-band analysis of the above problem is still time consuming when a large number of frequency samples (FSs) are employed with uniform sampling. To mitigate this issue and improve efficiency, the AFS algorithm is proposed to select FSs with a reduced number via an iterative process based on error-estimators. The vector fitting (VF) algorithm is used to derive the rational model, which allows to generate the scattered fields in the band efficiently. The key feature of the proposed AFS is it minimizes the number of the FSs and guarantees the convergence of the solution simultaneously. Numerical results demonstrate that the number of required samples is significantly reduced without compromising the accuracy of the solution.

Optimized principal component analysis for camera spectral sensitivity estimation.

This paper describes the use of a weighted principal component analysis (PCA) method for camera spectral sensitivity estimation. A comprehensive set of spectral sensitivities of 111 cameras was collected from four publicly available databases. It was proposed to weight the spectral sensitivities in the database according to the similarities with those of the test camera. The similarity was evaluated by the reciprocal predicted errors of camera responses. Thus, a set of dynamic principal components was generated from the weighted spectral sensitivity database and served as the basis functions to estimate spectral sensitivities. The test stimuli included self-luminous colors from a multi-channel LED system and reflective colors from a color chart. The proposed method was tested in both the simulated and practical experiments, and the results were compared with the classical PCA method, three commonly used basis function methods (Fourier, polynomial, and radial bases), and a regularization method. It was demonstrated that the proposed method significantly improved the accuracy of spectral sensitivity estimation.

Mass spectra of bottom-charm baryons

In this paper, we investigate the mass spectra of bottom-charm baryons systematically, where the relativistic quark model and the infinitesimally shifted Gaussian basis function method are employed. Our calculation shows that the [Formula: see text]-mode appears lower in energy than the other excited modes. According to this feature, the allowed quantum states are selected and a systematic study of the mass spectra for [Formula: see text] ([Formula: see text]) and [Formula: see text] ([Formula: see text]) families is performed. The root mean square radii and quark radial probability density distributions of these baryons are analyzed as well. Next, the Regge trajectories in the [Formula: see text] plane are successfully constructed based on the mass spectra. At last, we present the structures of the mass spectra, and analyze the difficulty and opportunity in searching for the ground states of bottom-charm baryons in experiment.

A continuum model for dislocation climb

Dislocation climb plays an important role in understanding plastic deformation of metallic materials at high temperature. In this paper, we present a continuum formulation for dislocation climb velocity based on densities of dislocations. The obtained continuum formulation is an accurate approximation of the Green’s function-based discrete dislocation dynamics method (Gu et al., 2015). The continuum dislocation climb formulation has the advantage of accounting for both the long-range effect of vacancy bulk diffusion and that of the Peach–Koehler climb force, and the two long-range effects are canceled into a short-range effect (integral with fast-decaying kernel) and in some special cases, a completely local effect. This significantly simplifies the calculation in the Green’s function-based discrete dislocation dynamics method, in which a linear system has to be solved over the entire system for the long-range effect of vacancy diffusion and the long-range Peach–Koehler climb force has to be calculated. This obtained continuum dislocation climb velocity can be applied in any available continuum dislocation dynamics frameworks. We also present numerical validations for this continuum climb velocity and simulation examples for implementation in continuum dislocation dynamics frameworks.

Scaled Consensus of Exponentially Unstable Networked Systems With Time-Varying Input Delay

This work studies the scaled consensus problems of exponentially unstable networked systems with time-varying input delays. First, a distributed consensus algorithm is designed under the truncated predictor feedback technique. Then, a delay bound is evaluated by utilizing the Lyapunov function-based method. Moreover, the consensus can be guaranteed when the upper bound of the time-varying input delay is no more than the delay bound. Furthermore, the relation between the delay bound and the network synchronizability is established. In other words, better network synchronizability implies a bigger delay bound. Finally, in the simulation examples, the feasibility of the theoretical results is verified, and the actual delay bounds are evaluated.

Bridge Frequency Scanning Using the Contact-Point Response of an Instrumented 3D Vehicle: Theory and Numerical Simulation

Scanning the bridge’s frequencies from the passing vehicle’s vibration data has been frequently investigated recently. However, in previous studies, vehicles were typically simplified to quarter- or half-car models, and apparent disparity could be observed between the models and real vehicles. To make the vehicle model more practical, in this study, a 3D vehicle model is built to extract the bridge’s frequencies from vehicle vibrations. For the first time, equations for calculating the contact-point (CP) response of the 3D vehicle model are derived with tire damping. Furthermore, residual CP responses between front and rear wheels are utilized to eliminate the inverse effects of road roughness, making the bridge frequencies outstanding in the frequency domain. The robustness of the proposed method is tested under different influence factors, and two possible measurement errors are as follows: the sensor position and axle distance when applying the proposed method in engineering. Results show that the proposed method performs stably under the influence of different road roughness classes and tire damping. Bridge frequencies can be identified when the vehicle is travelling at a highway speed (108 km/h in this study). Environmental noises can submerge the bridge’s high-order frequencies but have little influence on the low-frequency range. High bridge damping will restrain the transmission of bridge vibration to the vehicle, making high-order bridge frequencies less visible. In addition, the errors introduced by a vehicle body sensor position can be eliminated when calculating the CP responses for tires, thus will not influence bridge frequency identification. To avoid possible errors induced by manual measurement of the axle distance, a novel cross-correlation function-based method is employed, which is verified effective and practical for calculating residual CP responses.

Investigating patterns of air pollution in metropolises using remote sensing and neural networks during the COVID-19 pandemic

The purpose of this study is to determine the amount of air pollution in Tehran, Isfahan, Semnan, Mashhad, Golestan, and Shiraz during the Corona era and before. For this purpose, Sentinel satellite images were used to investigate the concentration of Methane (CH4), Carbon Monoxide (CO), Carbon Dioxide (CO2), Nitrogen Dioxide (NO2), Ozone (O3), Sulfur Dioxide (SO2), aerosol pollutants in In the era before and during Corona. Furthermore, greenhouse effect-prone areas were determined in this study. In the following, the state of air inversion in the studied area was determined by taking the temperature on the surface of the earth and in the upper atmosphere, as well as the wind speed into account. In this research, the prediction of air temperature for the year 2040 was conducted using the Markov and Cellular Automaton (CA)-Markov methods, considering the impact of air pollution on the air temperature of metropolises. Additionally, the Radial Basis Function (RBF) and Multilayer Perceptron (MLP) methods have been developed to determine the relationship between pollutants, areas prone to air inversions, and temperature values. According to the results, pollution caused by pollutants has decreased in the Corona era. According to the results, there is more pollution in Tehran and Isfahan metropolises. In addition, the results showed that air inversions in Tehran is the highest. Additionally, the results showed a high correlation between temperature and pollution levels (R2 = 0.87). Thermal indices in the studied area indicate that Isfahan and Tehran, with high values of Surface Urban Heat Island (SUHI) and being in the 6th class of thermal comfort (Urban Thermal Field Variance Index (UTFVI)), are affected by thermal pollution. The results showed that parts of southern Tehran province, southern Semnan and northeastern Isfahan will have higher temperatures in 2040 (class 5 and 6). Finally, the results of the neural network method showed that the MLP method with R2 = 0.90 is more accurate than the RBF method in predicting pollution amounts. This study significantly contributes by introducing innovative advancements through the application of RBF and MLP methods to assess air pollution levels during the COVID-19 and pre-pandemic periods, while also investigating the intricate relationships among greenhouse gases, air inversion, air temperature, and pollutant indices within the atmosphere. The utilization of these methods notably enhances the accuracy and reliability of pollution predictions, amplifying the originality and significance of this research.

An Efficient Reliability Analysis Method Based on the Improved Radial Basis Function Neural Network

Abstract This paper develops an efficient reliability analysis method based on the improved radial basis function neural network (RBFNN) to increase the accuracy and efficiency of structural reliability analysis. To solve the problems of low computational accuracy and efficiency of the RBFNN, an improved RBFNN method is developed by transferring the sampling center of Latin hypercube sampling (LHS) from the mean values of random variables to the most probable point (MPP) in the sampling step. Then, the particle swarm optimization algorithm is adopted to optimize the shape parameters of RBFNN, and the RBFNN model is assessed by the cross-validation method for subsequent reliability analysis using Monte Carlo simulation (MCS). Four numerical examples are investigated to demonstrate the correctness and effectiveness of the proposed method. To compare the computational accuracy and efficiency of the proposed method, the traditional radial basis function method, hybrid radial basis neural network method, first-order reliability method (FORM), second-order reliability method (SORM), and MCS method are applied to solve each example. All the results demonstrate that the proposed method has higher accuracy and efficiency for structural reliability analysis. Importantly, one practical example of an industrial robot is provided here, which demonstrates that the developed method also has good applicability and effectiveness for complex engineering problems.

Optimization-Based Three-Way Decisions With Interval-Valued Intuitionistic Fuzzy Information.

Due to the effectiveness and advantages of interval-valued intuitionistic fuzzy sets (IVIFSs) in evaluating uncertainty and risk, we introduce IVIFSs into loss functions of decision-theoretic rough sets (DTRSs) and propose an optimization-based approach to interval-valued intuitionistic fuzzy three-way decisions. First, based on the classical DTRSs and two previous optimization models, we construct a new concise linear programming model for simultaneously determining the threshold pair. Our model is mathematically equivalent to the DTRSs and the previous models under the Karush-Kuhn-Tucker (KKT) condition. Second, we extend the constructed model via the IVIFSs of loss functions and we discuss the relations between these loss functions based on a similarity measure function-based ranking method and a multiple score function-based ranking method for IVIFSs. Third, we develop our extended models via two ranking methods and we prove the existence and uniqueness of the optimal solution of the model. The optimization-based method, along with its algorithm for three-way decisions, is designed in an interval-valued intuitionistic fuzzy environment. Compared to the latest existing methods, our method has three advantages (see Advantages 1-3). Finally, an illustrative example is considered, and the advantages of our approach are demonstrated by this example.

Fault Detection in DC Microgrid: A Transient Monitoring Function-Based Method

This paper develops a transient monitoring function (TMF) based fault detection method for DC microgrids (DCMGs). In this method, the measured currents from one-end of the poles are firstly transformed into modal components. Then, the modal current is estimated using TMF concept. Afterward, the residual signal is defined as the absolute value of the difference between the modal and estimated currents. This signal has negligible fluctuations during the normal operation, while it experiences significant variations after fault occurrence. This feature is selected to reflect the fault incidence. To do so, the teager-kaiser energy operator (TKEO) is applied to the residual signal to amplify the changes, followed by a fault detection index (FDI). Comparing FDI with a threshold can reveal the fault. Furthermore, FDI can discriminate the faulty conditions in different operation modes of DCMG with a wide variation of fault conditions. To assess the developed scheme performance, a DCMG with different kinds of sources and loads is simulated in MATLAB/Simulink. The results confirm the quickness and the high accuracy of the proposed technique. Moreover, the method is validated in an experimental laboratory small-scale test bench. Finally, to demonstrate the superiority of the method, a comparative study with recent methods is presented.

Performance of Radial Basis Function and Group Method of Data Handling-type Neural-Networks in Flammability Characteristics Prediction of PMMA

Performance of Radial Basis Function and Group Method of Data Handling-type Neural-Networks in Flammability Characteristics Prediction of PMMA

Performance of atrial conduction velocity algorithms: a comparative in-silico study

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): British Heart Foundation Background Atrial conduction velocity is a key determinant of re-entry. Measurement of conduction velocity from electroanatomic mapping data is challenging due to sparsity, distribution, and uncertainty of measurements. Several mathematical methods have been proposed to address these challenges but their relative sensitivity to the typical uncertainty of clinical data is unknown. Furthermore, prior clinical studies utilising these algorithms provide conflicting results. Purpose To assess the performance of conduction velocity methods (triangulation, planar fitting, and radial basis function interpolation) for the calculation of atrial conduction velocity. Method Atrial activation was simulated with known conduction velocity using the monodomain model, Courtemanche cell model and atrial geometry derived from cardiac magnetic resonance imaging with mapped fibre orientations. The model was paced from the pulmonary veins, the mid coronary sinus, and the insertion of Bachmann's bundle. Reconstructed electroanatomic maps were used for conduction velocity calculation in OpenEP[1]. To test the robustness of algorithms to electrogram sampling density, simulated sampling densities were reduced from 16.45 to 8.43 points/cm2 (1950-1000 points/map). To test the robustness to uncertainty in local activation time assignment, random uniform noises with the maximum amplitude of ± 20ms was added to the local activation times from simulations. Mean squared velocity error was calculated using the differences between the ground truth and estimated conduction velocities. Result In electroanatomic maps recreated with high electrogram sampling density (16.45 points/cm2), planar fitting showed a slightly higher error compared to triangulation and the radial basis function methods (0.16 ± 0.03 m/s, 0.11 ± 0.01 m/s and 0.12 ± 0.03 m/s, respectively, P < 0.05). As mapping density was decreased, the relative performance of the planar fitting method increased and in low-density maps (13.5 to 8.43 points/cm2) the planar fitting method resulted in the lowest error. When local activation times were accurately assigned, all methods performed well. However, when uncertainty in local activation time assignment increased, conduction velocities calculated using planar fitting had a significantly lower error compared to those calculated with the triangulation and radial basis function methods (0.19 ± 0.03 m/s, 0.36 ± 0.04 and 0.29 ± 0.04 m/s, respectively, P < 0.05). Conclusion This study highlights the importance of spatial and temporal accuracy for the assessment of conduction velocity. At high electroanatomic mapping sampling densities (>16.9 points/cm2), all methods performed well. Below 13.5 points/cm2 (~1600 points per map), the planar fitting method outperformed the triangulation and radial basis function methods. The differential effects of clinical measurement uncertainty on the accuracy of each method may explain the conflicting results of prior studies.

A simplified analysis method for long-span suspension bridges within the deck overlay retrofitting process from asphalt to UHPC

The steel-ultrahigh performance concrete (UHPC) lightweight composite deck (LWCD) is increasingly adopted by in-service steel bridges to address the fatigue cracking issue for orthotropic steel decks (OSDs) and the premature damage issue for asphalt overlays. While for in-service long-span suspension bridges that need to be retrofitted by LWCDs, the response of the UHPC layer in casting is complex. Within the UHPC casting process, the moment of the stiffening girder changes continuously as the self-weight of the stiffening girder changes in casting, and the change of moment will produce strains in the UHPC portion set earlier; in other words, the UHPC portion cast latter will produce strains in the UHPC portion cast earlier. If the resultant tensile strains are too high, the UHPC layer may crack within the casting process, which should be avoided. In this paper, a simplified analysis method, based on the linearized deflection theory, was proposed to rapidly obtain the response of long-span suspension bridges in retrofitting without significantly compromising the accuracy of the analysis results. A new solving method based on exponential functions was proposed, which is simpler than the commonly used hyperbolic function-based method. The proposed method was implemented as computer codes in Matlab and verified through two examples: a single-span suspension bridge and a three-span suspension bridge. The simplified analysis method was used to perform a detailed analysis for the Yichang Yangtze River Expressway Bridge (YYREB), a 960-m-long single-span suspension bridge in China, for which the existing asphalt overlay was replaced by an LWCD in 2021. In the analysis, three cast sequences were considered for the UHPC layer, i.e., from end to end, from mid-span to ends, and from ends to mid-span. It is revealed that the mid span-to-ends cast sequence produces the minimum tensile strain in UHPC, so the cracking risk of UHPC could be well controlled by using this casting method. Thus, the mid span-to-ends cast sequence was adopted by the YYREB within the deck overlay retrofitting process from asphalt to UHPC.

Electromagnetic Radiation Space Field Construction Collected along the Road Based on Layered Radial Basis Function

The electromagnetic radiation (EMR) data collected along a road have a largely empty region overall, while they have a linear distribution locally. Moreover, the traditional spatial interpolation method is not suitable for the electromagnetic radiation space field (EMR-SF) construction collected along the road. In this paper, a layered radial basis function (LRBF) method is proposed to generate the EMR-SF, which interpolates from outside to inside in a layered strategy. First, the regular grid points are constructed based on RBF within the range of sampling data and then are layered based on Ripley’s K function. Second, on the basis of layering, the EMR of grid points is generated layer by layer using the LRBF method. Finally, EMR-SF is constructed by using the sampling data and grid points. The LRBF method is applied to EMR data from an area of Yunnan Normal University in Kunming, China. The results show that the LRBF accuracy is higher than that of the ordinary kriging (OK) and inverse-distance-weighted (IDW) interpolation methods. The LRBF interpolation accuracy can be improved through the strategy of regular grid point construction and layering, and the EMR-SF constructed by LRBF is more realistic than OK and IDW.