An Efficient Local Radial Basis Function Method for Image Segmentation Based on the Chan-Vese Model

In this paper,we consider the Chan–Vese(C-V)model for image segmentation and obtain its numerical solution accurately and efficiently.For this purpose,we present a local radial basis function method based on a Gaussian kernel(GA-LRBF)for spatial discretization.Compared to the standard radial basis functionmethod,this approach consumes less CPU time and maintains good stability because it uses only a small subset of points in the whole computational domain.Additionally,since the Gaussian function has the property of dimensional separation,the GA-LRBF method is suitable for dealing with isotropic images.Finally,a numerical scheme that couples GA-LRBF with the fourth-order Runge–Kutta method is applied to the C-V model,and a comparison of some numerical results demonstrates that this scheme achieves much more reliable image segmentation.

Gaussian Kernel Based SVR Model for Short-Term Photovoltaic MPP Power Prediction

Predicting the power obtained at the output of the photovoltaic(PV)system is fundamental for the optimum use of the PV system.However,it varies at different times of the day depending on intermittent and nonlinear environmen-tal conditions including solar irradiation,temperature and the wind speed,Short-term power prediction is vital in PV systems to reconcile generation and demand in terms of the cost and capacity of the reserve.In this study,a Gaussian kernel based Support Vector Regression(SVR)prediction model using multiple input variables is proposed for estimating the maximum power obtained from using per-turb observation method in the different irradiation and the different temperatures for a short-term in the DC-DC boost converter at the PV system.The performance of the kernel-based prediction model depends on the availability of a suitable ker-nel function that matches the learning objective,since an unsuitable kernel func-tion or hyper parameter tuning results in significantly poor performance.In this study for thefirst time in the literature both maximum power is obtained at max-imum power point and short-term maximum power estimation is made.While evaluating the performance of the suggested model,the PV power data simulated at variable irradiations and variable temperatures for one day in the PV system simulated in MATLAB were used.The maximum power obtained from the simu-lated system at maximum irradiance was 852.6 W.The accuracy and the perfor-mance evaluation of suggested forecasting model were identified utilizing the computing error statistics such as root mean square error(RMSE)and mean square error(MSE)values.MSE and RMSE rates which obtained were 4.5566*10-04 and 0.0213 using ANN model.MSE and RMSE rates which obtained were 13.0000*10-04 and 0.0362 using SWD-FFNN model.Using SVR model,1.1548*10-05 MSE and 0.0034 RMSE rates were obtained.In the short-term maximum power prediction,SVR gave higher prediction performance according to ANN and SWD-FFNN.

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds, the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases, we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.

Study of formation boundary and dip attribute extraction based on edge detection technology

In the seismic profile interpretation process,as the seismic data are big and the small geological features are difficult to identify,improvement of the efficiency is needed. In this study,structure tensor method in computer image edge detection processing is applied into the 2D seismic profile. Coherent attribute is used to extract formation edge. At the same time,extracting the eigenvalues and eigenvectors to calculate the seismic geometric properties which include dip and apparent dip,automatic identification is achieved. Testing the Gaussian kernel function with synthetic models and comparing the coherent attribute and dip attribute extraction results before and after,the conclusion that Gaussian filter can remove the random noise is obtained.

A Kernel-Based Nonlinear Representor with Application to Eigenface Classification

This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple technique, it is applied to eigenface classification. Experimental results on the ORL face database show that it improves performance by around 6 points, in classification rate, over the Euclidean distance classifier.

Design of a Tree Ring Structure Analysis System to Estimate the Accurate Age of Tree Species in Sri Lanka

Determination of an age in a particular tree species can be considered as a vital factor in forest management.In this research we have introduced a novel scheme to determine the accurate age of the tree species in Sri Lanka.This is initially developed for the tree species called‘Hora’(Dipterocarpus zeylanicus)in wet zone of Sri Lanka.Here the core samples are extracted and further analyzed by means of the different image processing techniques such as Gaussian kernel blurring,use of Sobel filters,double threshold analysis,Hough line tran sformation and etc.The operations such as rescaling,slicing and measuring are also used in line with image processing techniques to achieve the desired results.Ultimately a Graphical user interface(GUI)is developed to cater for the user requirements in a user friendly environment.It has been found that the average growth ring identification accuracy of the proposed system is 93%and the overall average accuracy of detecting the age is 81%.Ultimately the proposed system will provide an insight and contributes to the forestry related activities and researches in Sri Lanka.

Pedestrian wind flow prediction using spatial-frequency generative adversarial network

Pedestrian wind flow is a critical factor in designing livable residential environments under growing complex urban conditions.Predicting pedestrian wind flow during the early design stages is essential but currently suffers from inefficiencies in numerical simulations.Deep learning,particularly generative adversarial networks(GAN),has been increasingly adopted as an alternative method to provide efficient prediction of pedestrian wind flow.However,existing GAN-based wind flow prediction schemes have limitations due to the lack of considering the spatial and frequency characteristics of wind flow images.This study proposes a novel approach termed SFGAN,which embeds spatial and frequency characteristics to enhance pedestrian wind flow prediction.In the spatial domain,Gaussian blur is employed to decompose wind flow into components containing wind speed and distinguished flow edges,which are used as the embedded spatial characteristics.Detailed information of wind flow is obtained through discrete wavelet transformation and used as the embedded frequency characteristics.These spatial and frequency characteristics of wind flow are jointly utilized to enforce consistency between the predicted wind flow and ground truth during the training phase,thereby leading to enhanced predictions.Experimental results demonstrate that SFGAN clearly improves wind flow prediction,reducing Wind_MAE,Wind_RMSE and the Fréchet Inception Distance(FID)score by 5.35%,6.52%and 12.30%,compared to the previous best method,respectively.We also analyze the effectiveness of incorporating the spatial and frequency characteristics of wind flow in predicting pedestrian wind flow.SFGAN reduces errors in predicting wind flow at large error intervals and performs well in wake regions and regions surrounding buildings.The enhanced predictions provide a better understanding of performance variability,bringing insights at the early design stage to improve pedestrian wind comfort.The proposed spatial-frequency loss term is general and can be flexibly integrated with other generative models to enhance performance with only a slight computational cost.

Stochastic Economic Dispatch Considering the Dependence of Multiple Wind Farms Using Multivariate Gaussian Kernel Copula

Wind farms usually cluster in areas with abundant wind resources.Therefore,spatial dependence of wind speeds among nearby wind farms should be taken into account when modeling a power system with large-scale wind power penetration.This paper proposes a novel non-parametric copula method,multivariate Gaussian kernel copula(MGKC),to describe the dependence structure of wind speeds among multiple wind farms.Wind speed scenarios considering the dependence among different wind farms are sampled from the MGKC by the quasi-Monte Carlo(QMC)method,so as to solve the stochastic economic dispatch(SED)problem,for which an improved meanvariance(MV)model is established,which targets at minimizing the expectation and risk of fuel cost simultaneously.In this model,confidence interval is applied in the wind speed to obtain more practical dispatch solutions by excluding extreme scenarios,for which the quantile-copula is proposed to construct the confidence interval constraint.Simulation studies are carried out on a modified IEEE 30-bus power system with wind farms integrated in two areas,and the results prove the superiority of the MGKC in formulating the dependence among different wind farms and the superiority of the improved MV model based on quantilecopula in determining a better dispatch solution.

Non-iterative Cauchy kernel-based maximum correntropy cubature Kalman filter for non-Gaussian systems

This article addresses the nonlinear state estimation problem where the conventional Gaussian assumption is completely relaxed.Here,the uncertainties in process and measurements are assumed non-Gaussian,such that the maximum correntropy criterion(MCC)is chosen to replace the conventional minimum mean square error criterion.Furthermore,the MCC is realized using Gaussian as well as Cauchy kernels by defining an appropriate cost function.Simulation results demonstrate the superior estimation accuracy of the developed estimators for two nonlinear estimation problems.

Real-time comprehensive driving ability evaluation algorithm for intelligent assisted driving

To meet the needs of the human-machine co-driving decision problem in the intelligent assisted driving system for real-time comprehensive driving ability evaluation of drivers,this paper proposes a real-time comprehensive driving ability evaluation method that integrates driving skill,driving state,and driving style.Firstly,by analyzing the driving experiment data obtained based on the intelligent driving simulation platform(the experiment can effectively distinguish the driver's driving skills and avoid the interference of driving style),the feature values that significantly represent driving skills and driving state are selected,and the time correlation between driving state and driving skills is pointed out.Furthermore,the concept of relativity in comprehensive driving ability evaluation is further proposed.Under this concept,the natural driving trajectory dataset-HighD is used to establish the distribution map of feature values of the human driver group as the evaluation benchmark to realize the relative evaluation of driving skill and driving state.Similarly,HighD is used to establish a distribution map of human driver style feature values as an evaluation benchmark to achieve relative driving style evaluation.Finally,a comprehensive driving ability evaluation model with a“punishment”and“affirmation”mechanism is proposed.The experimental comparative analysis shows that the evaluation algorithm proposed in this paper can take into account the driver's driving skill,driving state,and driving style in the real-time comprehensive driving ability evaluation,and draw differential evaluation conclusions based on the“punishment”and“affirmation”mechanism model to achieve a comprehensive and objective evaluation of the driver's driving ability.It can meet the needs of human-machine shared driving decisions for driver's driving ability evaluation.

The Optimal Solution of Multi-kernel Regularization Learning

In regularized kernel methods, the solution of a learning problem is found by minimizing a functional consisting of a empirical risk and a regularization term. In this paper, we study the existence of optimal solution of multi-kernel regularization learning. First, we ameliorate a previous conclusion about this problem given by Micchelli and Pontil, and prove that the optimal solution exists whenever the kernel set is a compact set. Second, we consider this problem for Gaussian kernels with variance σ∈（0,∞）, and give some conditions under which the optimal solution exists.

SINS/GNSS integrated navigation system based on maximum versoria filter

In the missile-borne Strapdown Inertial Navigation System/Global Navigation Satellite System(SINS/GNSS)integrated navigation system,due to the factors such as the high dynamics,the signal blocking by obstacles,the signal intefereces,etc.,there always exist pulse interferences or measurement information interruptions in the satellite receiver,which make nonstationary measurement process.The traditional Kalman Filter(KF)can tackle the state estimation problem under Gaussian white noise,but its performance will be significantly reduced under nonGaussian noises.In order to deal with the non-Gaussian conditions in the actual missile-borne SINS/GNSS integrated navigation systems,a Maximum Versoria Criterion Extended Kalman Filter(MVC-EKF)algorithm is proposed based on the MVC and the idea of M-estimation,which assigns a smaller weight to the anomalous measurements so as to suppress the influence of anomalous measurements on the state estimation while maintaining a relatively low calculation cost.Finally,the integrated navigation simulation experiments prove the effectiveness and robustness of the proposed algorithm.