A cooperative radial basis function method for variable-fidelity surrogate modeling

By coupling the low-fidelity (LF) model with the high-fidelity (HF) samples, the variable-fidelity model (VFM) offers an efficient way to overcome the expensive computing challenge in multidisciplinary design optimization (MDO). In this paper, a cooperative radial basis function (Co-RBF) method for the VFM is proposed by modifying the basis function of RBF. The RBF method is constructed on the HF samples, while the Co-RBF method incorporates the entire information of the LF model with the HF samples. In Co-RBF, the LF model is regard as a basis function of Co-RBF and the HF samples are utilized to compute the Co-RBF model coefficients. Two numerical functions and three engineering problems are adopted to verify the proposed Co-RBF method. The predictive results of Co-RBF are compared with those of RBF and Co-Kriging, which show that the Co-RBF method improves the efficiency, accuracy and robustness of the existing VFMs.     

基于LS-SVM的石油期货价格预测研究

建立了基于最小二乘支持向量机的石油期货价格预测模型。应用该模型对纽约商品交易市场的两种石油期货价格数据进行了预测,并将预测结果与RBF神经网络的预测结果进行了比较。研究结果表明最小二乘支持向量机预测模型具有较高的拟合和预测精度,明显优于RBF神经网络预测模型。     

确定RBF神经网络隐层节点数的最大矩阵元法

针对基于训练样本输入信息进行非监督聚类来确定RBF神经网络隐层节点数的方法存在利用信息不充分的缺陷,该文提出了一种新的确定RBF神经网络隐层节点数的方法。利用训练样本输入输出全部信息建立样本间的相似矩阵,然后采用最大矩阵元法来确定RBF神经网络隐层节点数。实验仿真表明,该方法是有效的。     

柴油发动机气缸压力和燃烧始点的辨识

在柴油发动机气缸压力的识别过程中，针对缸盖振动信噪比较低的问题，提出了对RBF网络训练样本进行时域统计平均降噪的方法，同时在对燃烧始点的辨识中应用了Kaiser差分器。时域统计平均有效提高了信号的信噪比，对柴油发动机气缸压力的恢复获得了很好的结果；Kaiser差分器有效提高了对燃烧始点的辨识。通过实践证明，该计算方法可以有效地从柴油发动机缸盖振动信号恢复气缸压力，并进一步辩识燃烧始点。     

一种基于分级RBF网络的车牌字符识别方法

提出了一种基于分级RBF神经网络的车牌字符识别方法,采用两级RBF神经网络结构,由一级网络识别后,根据识别结果和置信度,建立识别分布图,进行二级网络设计,确定了12个二级子网。RBF网络中自动确定隐层神经元数,无需实验调整。用大量样本对系统进行测试,车牌整体识别率达到了85.4%,通过对比性研究,验证了该方法的有效性和先进性。     

Reformulated radial basis neural networks trained by gradientdescent

This paper presents an axiomatic approach for constructing radial basis function (RBF) neural networks. This approach results in a broad variety of admissible RBF models, including those employing Gaussian RBFs. The form of the RBFs is determined by a generator function. New RBF models can be developed according to the proposed approach by selecting generator functions other than exponential ones, which lead to Gaussian RBFs. This paper also proposes a supervised learning algorithm based on gradient descent for training reformulated RBF neural networks constructed using the proposed approach. A sensitivity analysis of the proposed algorithm relates the properties of RBFs with the convergence of gradient descent learning. Experiments involving a variety of reformulated RBF networks generated by linear and exponential generator functions indicate that gradient descent learning is simple, easily implementable, and produces RBF networks that perform considerably better than conventional RBF models trained by existing algorithms     

自构造RBF神经网络及其参数优化

径向基函数神经网络的构造需要确定每个RBF的中心、宽度和数目。该文利用改进的聚类算法自动构造RBFN,考虑样本的类别属性,根据样本分布自动计算RBF的中心和宽度,并确定RBF的数目。所有的网络参数采用非线性优化算法来优化。通过IRIS分类问题和混沌时间序列预测评价自构建RBFN的性能,验证参数优化效果。结果表明,自构造RBFN不但能够自动确定网络结构,而且具有良好的模式分类和函数逼近能力。通过对网络参数的非线性优化,该算法明显改善了网络性能。     

An ART-based construction of RBF networks

Radial basis function (RBF) networks are widely used for modeling a function from given input-output patterns. However, two difficulties are involved with traditional RBF (TRBF) networks: The initial configuration of an RBF network needs to be determined by a trial-and-error method, and the performance suffers when the desired output has abrupt changes or constant values in certain intervals. We propose a novel approach to over. come these difficulties. New kernel functions are used for hidden nodes, and the number of nodes is determined automatically by an adaptive resonance theory (ART)-like algorithm. Parameters and weights are initialized appropriately, and then tuned and adjusted by the gradient-descent method to improve the performance of the network. Experimental results have shown that the RBF networks constructed by our method have a smaller number of nodes, a faster learning speed, and a smaller approximation error than the networks produced by other methods.     

RBF神经网络在遥感影像分类中的应用研究

用RBF神经网络进行遥感影像分类，在网络结构设计上使RBF层与输出层的节点数都等于所要分类的类别数。用Kohonen聚类算法确定RBF中心的时候，用训练样本的均值作为初始中心，并在RBF宽度进行求取的时候进行了改进，以避免内存溢出。所设计的RBF神经网络分类模型具有结构简单、算法简洁的优点。实验结果表明，该方法用于遥感影像分类取得了较高的分类精度，具有实际应用价值。     

径向基网络中样本属性的贡献因子研究

通常对径向基(radial basis function,RBF)神经网络的改进大多是注重隐藏节点选取、大规模数据学习速率和函数组织形式,忽视了初始输入样本自身间的结构信息。研究发现,输入样本的不同属性对分类能力影响的程度也不同,即每个属性应该有自己的分类权重。在对样本归一化预处理后,研究了不同属性在分类时的贡献因子,提出了新的算法模型CFRBF(contribution factors RBF),用贡献因子来描述样本各个属性的重要性。选用了蛋白质二级预测问题来验证模型,传统的二级预测是将样本直接输入网络,仅仅依靠海明距离来分类,丢失大量信息。针对设计的新模型,使用了一种新的组织形式来解决预测问题。实验证明,采用新的组织形式后网络性能明显提高,而用CFRBF算法后其精度再次提高。同时通过贡献因子可以揭示看似无规律的蛋白质序列之间氨基酸构态影响关系,而且还能给出样本不同属性的分类重要性。