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.

Comparison Between Radial Basis Function Neural Network and Regression Model for Estimation of Rice Biophysical Parameters Using Remote Sensing

The radial basis function （RBF） emerged as a variant of artificial neural network. Generalized regression neural network （GRNN） is one type of RBF, and its principal advantages are that it can quickly learn and rapidly converge to the optimal regression surface with large number of data sets. Hyperspectral reflectance （350 to 2500 nm） data were recorded at two different rice sites in two experiment fields with two cultivars, three nitrogen treatments and one plant density （45 plants m^-2）. Stepwise multivariable regression model （SMR） and RBF were used to compare their predictability for the leaf area index （LAI） and green leaf chlorophyll density （GLCD） of rice based on reflectance （R） and its three different transformations, the first derivative reflectance （D1）, the second derivative reflectance （D2） and the log-transformed reflectance （LOG）. GRNN based on D1 was the best model for the prediction of rice LAI and CLCD. The relationships between different transformations of reflectance and rice parameters could be further improved when RBF was employed. Owing to its strong capacity for nonlinear mapping and good robustness, GRNN could maximize the sensitivity to chlorophyll content using D1. It is concluded that RBF may provide a useful exploratory and predictive tool for the estimation of rice biophysical parameters.

High mobility channel estimation method based on improved basis expansion model

In this paper, the problem of high mobility channel estimation in the Long-Term Evolution for Railway (LTE-R) communication system is investigated. By using a Basis Expansion Model (BEM), the channel impulse response is modeled as the sum of several basis functions multiplied by coefficients. By estimating the basis function coefficients, the fast time-varying channel can be approximated. In order to reduce the estimation error resulting from the high frequency basis function, the Generalized Complex Exponential BEM (GCE-BEM) is modified to form an Improved GCE-BEM (IGCE-BEM) by adding a correction coefficient to the basis function. Moreover, an Improved Baseline Tilting (IBT) method is proposed to reduce the Gibbs effect. In addition, linear interpolation, Gauss interpolation, and three-order Hermite interpolation are adopted to obtain the channel impulse response at non pilot locations based on the channel estimation results at pilot positions. The simulation results show that the IGCE-BEM outperforms the CE-BEM and GCE-BEM in terms of the Normalized Mean Squared Error (NMSE). The IB T method is better than the BT method in reducing the Gibbs effect. In addition, combined with the IBT, the IGCE-BEM also has low NMSE under high moving speed and high noise power. The performance of the threeorder Hermite interpolation method is higher than that of the linear interpolation and Gauss interpolation approaches.

A Gravity Forward Modeling Method based on Multiquadric Radial Basis Function

It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.

Deep learning-based time-varying channel estimation with basis expansion model for MIMO-OFDM system

For high-speed mobile MIMO-OFDM system,a low-complexity deep learning(DL) based timevarying channel estimation scheme is proposed.To reduce the number of estimated parameters,the basis expansion model(BEM) is employed to model the time-varying channel,which converts the channel estimation into the estimation of the basis coefficient.Specifically,the initial basis coefficients are firstly used to train the neural network in an offline manner,and then the high-precision channel estimation can be obtained by small number of inputs.Moreover,the linear minimum mean square error(LMMSE) estimated channel is considered for the loss function in training phase,which makes the proposed method more practical.Simulation results show that the proposed method has a better performance and lower computational complexity compared with the available schemes,and it is robust to the fast time-varying channel in the high-speed mobile scenarios.

CMAC BASED NONLINEAR PROCESS CONTROL SYSTEMS,PART I : CMAC WITH GENERAL BASIS FUNCTIONS FOR MODELLING

ＣＭＡＣＢＡＳＥＤＮＯＮＬＩＮＥＡＲＰＲＯＣＥＳＳＣＯＮＴＲＯＬＳＹＳＴＥＭＳ，ＰＡＲＴＩ：ＣＭＡＣＷＩＴＨＧＥＮＥＲＡＬＢＡＳＩＳＦＵＮＣＴＩＯＮＳＦＯＲＭＯＤ－ＥＬＬＩＮＧＤｕａｎＰｅｉｙｏｎｇ（段培永）ＬｉＣｈｅｎｇｄｏｎｇ（李成东）ＳｈａｏＨ...

High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake

The Earth’s natural pulse electromagnetic field data consists typically of an underlying variation tendency of intensity and irregularities.The change tendency may be related to the occurrence of earthquake disasters.Forecasting of the underlying intensity trend plays an important role in the analysis of data and disaster monitoring.Combining chaos theory and the radial basis function neural network,this paper proposes a forecasting model of the chaotic radial basis function neural network to conduct underlying intensity trend forecasting by the Earth’s natural pulse electromagnetic field signal.The main strategy of this forecasting model is to obtain parameters as the basis for optimizing the radial basis function neural network and to forecast the reconstructed Earth’s natural pulse electromagnetic field data.In verification experiments,we employ the 3 and 6 days’data of two channels as training samples to forecast the 14 and 21-day Earth’s natural pulse electromagnetic field data respectively.According to the forecasting results and absolute error results,the chaotic radial basis function forecasting model can fit the fluctuation trend of the actual signal strength,effectively reduce the forecasting error compared with the traditional radial basis function model.Hence,this network may be useful for studying the characteristics of the Earth’s natural pulse electromagnetic field signal before a strong earthquake and we hope it can contribute to the electromagnetic anomaly monitoring before the earthquake.

ESTIMATION OF BASIS EXPANSION MODELS FOR DOUBLY SELECTIVE CHANNELS

By analyzing the relationship between Basis Expansion Model (BEM) and Doppler spectrum, this letter proposed a quasi-MMSE-based BEM estimation scheme for doubly selective channels. Based on the assumption that the basis coefficients are approximately independent and have the same variance for the same channel tap, the quasi-MMSE estimation shows approximately optimal performance and is robust to noise. Moreover, it can avoid a high Peak-to-Average Power Ratio (PAPR) by using continuous pilots. Performance of the proposed estimation scheme has been shown with computer simulations.

Triangular domain extension of algebraic trigonometricB′ezier-like basis

In computer aided geometric design （CAGD）, B′ezier-like bases receive more andmore considerations as new modeling tools in recent years. But those existing B′ezier-like basesare all defined over the rectangular domain. In this paper, we extend the algebraic trigono-metric B′ezier-like basis of order 4 to the triangular domain. The new basis functions definedover the triangular domain are proved to fulfill non-negativity, partition of unity, symmetry,boundary representation, linear independence and so on. We also prove some properties of thecorresponding B′ezier-like surfaces. Finally, some applications of the proposed basis are shown.

Synchronization of chaos using radial basis functions neural networks

The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.

Modeling Analysis on the Relationship between Fruit and Leaves Damaged by Basilepta melanopus Lefevre on Camellia oleifera Abel

[Objective] Camellia oleifera Abel is a typical woody oil plant in China and it has many functional components. Since it was first found in 1980, Basilepta melanopus Lefevre has become the pest with outbreak area, which makes the yield and quality of camellia seed oil suffer great losses. The aim was to provide refer- ences for the field damages and prediction of Basilepta melanopus Lefevre based on severity of damage and the actual need for prediction of B. melanopus. [Meth- ods] The investigation was carried out to study the average number of wormholes in damaged leaves, average number of fruit per branch and leaf damage rate caused by B. melanopus using point-survey systematically at Yong＇an Town of Changsha, Hunan Province from early May to middle June in 2014. Six functions were used to find the optimal model through fitting to calculate the threshold of mean wormhole number. [Results] The cubic equations had the best effects in fitting the 3 pairs of variables of average wormhole number and camellia fruit, camellia fruit and leaf damage rate, and wormhole number and leaf damage rate, and the variance analy- sis reached the extreme significant difference （P〈0.05）. [Conclusion] Based on these mathematical models, the threshold of wormhole number is 5.01 per leaf.

海域重力异常模型的多尺度分析

不同于传统的重力异常模型精度分析方法,本文以马里亚纳海沟区域(140°E—150°E,10°N—20°N)为例,利用DOG球面小波提取了DTU10、DTU17和SIO V32.1模型在不同波段内的重力异常信号,对模型间的差异进行了深入分析,并对基于径向基函数的不同深度、不同分辨率的多尺度分析进行了尝试。利用DOG球面小波对各模型多尺度分析的结果表明,随着尺度变小,模型间的差异在变大;DTU10、DTU17模型间的差异主要集中在10.9~43.6 km的波段内,分布在海岸、海沟、海底山附近,体现了Cryosat-2、Jason-1/GM观测数据和FES2014海潮模型的贡献;受模型构建方法不同、观测数据增多和波形重跟踪的影响,DTU17、SIO V32.1模型的差异大于DTU10、DTU17之间的差异。对传统径向基函数进行了改进,实现了多深度、多空间分辨率情况下径向基函数多尺度分析,结果略优于单一深度、单一空间分辨率径向基函数构建结果,有望应用于多源数据的重力场模型构建。

无模型自适应滑模控制的微波加热过程温度控制

微波加热模型具有无限维、非线性和时变等特点,导致控制器难于设计和实现。针对此问题,提出了一种适用于微波加热过程的无模型自适应滑模控制方法。首先,对微波加热过程传热数学模型进行分析,建立了微波加热过程输入功率与温度之间的全格式动态线性化数据模型。然后,根据该数据模型设计了无模型自适应滑模控制器,并给出了数据模型中相关未知时变参数和未知干扰的估计算法。最后,利用COMSOL和MATLAB进行仿真,仿真结果验证了所提控制方法的有效性。

混合情绪的测量:模型、方法与展望

混合情绪对个体的心理健康和目标追求具有重要的意义,由于测量方法等基础性研究的限制,其相关问题并未得到充分探讨。当前混合情绪的测量方法主要基于单变量、双变量和多变量三种模型,不同方法在操作性界定、测量工具和指标获得上存在各自的优势和适应性。未来研究应致力于完善混合情绪测量的理论基础;提高客观反应测量指标的特异性;建立适应混合情绪系统复杂性的测评体系;并关注混合情绪积极成分与消极成分的时间关系测量。

量子力学表示理论的一种实现

量子力学创立伊始,狄拉克就关注到了一般表示的问题,其后量子力学的发展又引入了福克态、相干态等表示。好的表示应能提供正交归一的完备基,同时又能给出问题的严格解析解或者允许方便地得到近似解,但这常常是做不到的。我们意识到此前得到的相干态正交化方法恰恰满足表示理论的一般性要求,且因为包含自由参数为构造归一化的完备正交基实际上提供了无限的选择,这样甚至在解决问题的过程中都可以灵活地选择不同的表示,从而带来计算量的大幅减小。通过对不同耦合强度下的近共振态Rabi模型最初10个能级的计算,并同关联的JC模型的结果相比较,验证了相干态正交化方法的有效性。

一种低复杂度的正交时频空系统接收机设计

正交时频空(OTFS)调制可以将时间和频率选择性信道转换为时延-多普勒(DD)域的非选择性信道,这为高速移动场景建立可靠的无线通信提供了解决方案。然而,在车联网等复杂的多散射场景下,信道存在严重的多普勒间干扰(IDI),这给OTFS接收机信号的准确解调带来了极大的挑战。针对上述问题,该文提出一种联合稀疏贝叶斯学习(SBL)和阻尼最小二乘最小残差(d-LSMR)的OTFS接收机设计。首先,根据OTFS时域和DD域的关系,采用基扩展模型(BEM)将信道估计问题转换为基系数恢复问题,精准估计包括多普勒采样点在内的DD域信道。然后,提出一种高效的转换算法将基系数转换为信道等效矩阵。其次,将信道估计中估计得到的噪声,用于d-LSMR均衡器中进行信道均衡,并利用DD域信道矩阵的稀疏性实现快速收敛。系统仿真结果表明,与目前代表性的OTFS接收机相比,该文所提方案实现了更好的误码率性能,同时降低了计算复杂度。

基于SSA-RBF神经网络的煤自然发火预测模型

为解决传统煤自燃预测模型预测状态单一和预测精度不高的问题,提出基于麻雀搜索算法(SSA)优化的径向基(RBF)神经网络煤自然发火预测模型。首先,采用程序升温试验分析煤样指标气随温度的变化特征,将煤自然发火过程按煤温分为缓慢(80≤t_(i)<120℃)、加速(120≤t_(i)<160℃)和激烈(t_(i)≥160℃)3个氧化阶段,同时分析这3个阶段指标气与煤温的灰色关联度;其次通过不同维度测试函数检验粒子群算法(PSO)、灰狼算法(GWO)和SSA算法性能;最后利用6个矿区数据验证基于SSA-RBF神经网络的煤自燃预测模型的优越性。结果显示,缓慢氧化阶段CO/ΔO_(2)、CO、C_(2)H_(4)这3种指标气体与煤温的灰色关联系数最大;而加速氧化阶段C_(2)H_(4)/C_(2)H_(6)、CO/ΔO_(2)、CO_(2)/CO_(3)种指标与煤温的灰色关联系数最大。3种不同维度函数的测试结果表明:SSA与PSO、GWO相比具有更好的全局搜索能力和稳定性,其收敛速度更快;神经元数量为5个、迭代次数为300次时,SSA-RBF神经网络预测模型对缓慢氧化和加速氧化阶段的预测准确性分别达到了99%和93%。

智能汽车轨迹跟踪MPC-RBF-SMC协同控制策略研究

针对自动驾驶车辆行驶过程中模型失配以及外部环境干扰导致车辆轨迹跟踪环节精确性不高的问题,提出了一种结合车辆运动学模型预测控制(MPC)、径向基(RBF)神经网络和滑模控制(SMC)的轨迹跟踪控制策略。通过建立车辆运动学MPC模型计算当前状态车辆期望横摆角速度,并将其与实际横摆角速度的偏差输入RBF-SMC控制器,利用RBF快速逼近非线性模型的特点,结合滑模控制输出前轮转角,实现车辆的横向轨迹跟踪控制。仿真结果表明,与传统的控制器相比,该方法轨迹跟踪精度显著提高,并在不同行驶工况下表现出较好的鲁棒性。

一种基于径向基隐式曲面的地质三维建模方法

针对目前基于钻孔数据生成地质三维模型过程繁琐、算法复杂、中间数据庞大的弊端,本文使用钻孔点和径向基隐函数模型描述地层曲面,以多边形标量场提取曲面函数模型的等势面生成地质曲面进行可视化;再提取曲面的边框,根据网格大小长度提取边框的转折点数据;根据上下相邻两个地层曲面的边框转折点,绘制侧立面;合并侧立面与上下相邻两地质层曲面,生成地质三维模型。并使用郑州市高新区地质钻孔数据作为数据源进行实验,快速完整地生成了研究区的地质体三维模型。

面向数字孪生模型应用的油浸式变压器绕组温度POD-RBFLP降阶计算方法

了解油浸式电力变压器绕组的温度情况是保证其运行稳定性的关键,也是当前针对油浸式变压器数字孪生分析的必然需求。为了快速地获得变压器绕组的稳态温度,该文提出一种基于本征正交分解(proper orthogonal decomposition,POD)和包含线性多项式的径向基函数响应面法(radial basis function response surface method including linear polynomial,RBFLP)的降阶计算模型。首先,讨论POD方法的降阶特性,并设计一种基于留一法交叉验证的自适应获得快照矩阵方法,以提高计算精度及效率;其次,采用响应面方法建立POD模态系数与绕组工况的相关关系,旨在实现通过绕组工况快速获得POD模态系数,从而跳过对降阶模型的复杂非线性计算,进而高效重构绕组温度场。相关算例表明,该方法具有较好的计算精度和效率,在50组测试工况下,与全阶计算相比,误差不超过2.5 K,且总计算时间仅为1.45 s;最后,基于110 kV变压器绕组搭建温升试验平台,试验结果表明,降阶计算结果相较于试验结果,平均计算误差不超过2 K,且单步计算时间仅为0.03 s,相较于同等规模的全阶计算,计算效率有较大幅度地提升。