极小点

BP算法存在局部极小点，收敛速度慢等缺点。

BP algorithm has its local minima and its slow training speed .

目的对BP学习算法中存在的大量局部极小点以及收敛速度慢问题进行研究并提出相应的改进方案。

Aim To study the standard BP algorithms local minima and learning speed problems and propose the scheme for improvement .

针对普通BP算法存在的收敛速度慢以及容易陷入局部极小点等问题，提出了一种改进的BP算法，应用该算法对空调系统传感器故障进行诊断。

An improved BP algorithm was presented and applied it to sensor fault diagnosis of air-conditioning unit .

BP人工神经网络模型被认为是最适宜于样本分类的模型，而传统的标准BP算法存在着诸如训练速度慢、易陷入局部极小点等问题，针对这些问题，文中给出了改进的方法。

The artificial neural network model of BP is considered to be the most suitable method for the model classification .

然而也存在一些致命的缺点（如容易陷入局部极小点），通过遗传算法（GA）与BP网络结合，可以有效地解决该问题。

The problems such as trapping into the local minimum are solved by combining GA and BP neural network .

BP算法的最大缺陷之一，是易于陷入局部极小点。

One of the main weak points of BP algorithm is that the optimal procedure is easily stacked into local minimum value .

且控制器的算法采用的是优化的BP算法，可以避免网络陷入局部极小点，也可以加快网络的训练速度。

Moreover , improved BP algorithm in controller can make study speed of network faster and can eliminate the disadvantages of BP network .

求解Lipschitz型规划全局极小点的改进的填充函数法

A modified filled function method for solving Lipschitz programming problems

利用遗传算法来避免BP算法的局部极小点，从而达到均方根误差全局最小点，也解决了BP算法的收敛慢的问题；

This algorithm could avoid the local minimum point , and achieve the minimum point of RMS error so as to solve the problem of slow restraint .

本文从理论上探讨用向量p-范数（1≤p≤2）度量数据逼近项和正则项的所得目标泛函极小点的唯一性。

We discuss the uniqueness of minimum point of objective functional obtained by using l_p - norm ( 1 ≤ p ≤ 2 ) to measure data approximation item and regularization item in theory .

对传统BP神经网络收敛速度慢且容易陷入局部极小点等缺陷进行改造；采用了改进型的神经网络进行字符识别。

Defects are improved that BP neural network convergences traditional slow and easy dives into local minimum points . Improved neural network is proposed to recognize license character .

但BP网络是基于梯度的方法确定权值，而梯度下降法本身就很容易受到局部极小点的影响。

But BP network is based on the gradient method to determine the weights , and the gradient descents are inherently vulnerable to the effects of local minima .

诊断结果表明，采用RBF这种新型的网络结构，进行柴油机燃油系统故障诊断，可以从根本上避免网络陷入局部极小点和收敛速度慢的问题，从而准确快速地诊断故障。

Diagnosis results show that RBF network can fundamentally overcome the problems of converge to the local minimum point and low convergence rate .

在已有研究的基础上，针对标准BP学习算法收敛速度慢、存在局部极小点等缺点，探索了一种改进的BP算法。

Based on the discussion of disadvantages of the present BP algorithm and study of improvement methods propounded by other people , the paper explores a new improved BP algorithm .

作为一种新的机器学习方法，SVM能较好地解决小样本、非线性、高维数和局部极小点等实际问题。

As a new machine learning method , SVM can solve the small sample , nonlinear , high dimension and local minima , the actual problem .

该方法弥补了传统的BP神经网络收敛速度慢，易陷入局部极小点等缺陷。

The method remedies the defects of the traditional BP neural networks such as restraining on calculating speed slowly and falling into the partly extreme minimum value easily and so on .

将混沌机制引入常规BP算法，利用混沌机制固有的全局游动，逃出权值优化过程中存在的局部极小点，解决了网络训练易陷入局部极小点的问题。

Chaotic mechanism is introduced to normal BP algorithm , and the problem of local limit value for network is solved using global moving characteristic of chaotic mechanism is weight optimization .

此外，还在HF／6-31G（d）水平下计算了6个过渡态和8个极小点的优化构型。

Also 8 minimum points and 6 transition state are optimized under HF / 6-31G ( d ) level .

贝叶斯正则化方法提高BP神经网络的泛化能力。在学习中使用了Bayes正则化算法，使得网络的推广能力得到提高，同时为了避免多层前向神经网络陷入局部极小点，使用了权值调整技术。

Bayes ' regularization raises the ability to extend of BP neural network . By using Bayes regularization method in learning , the networks have a better generalization ability .

充分利用RBF网络具有唯一最佳逼近和没有局部极小点的重要特征，对柴油机燃油系统进行故障诊断。

The RBF networks have unique best approximation and have no local minimum . Using these important features , fault diagnosis of diesel fuel system is carried out .

考虑到BP神经网络模型的收敛速度慢，目标函数存在局部极小点，隐含层数和隐节点数难以确定等缺点，本文采用增加动量项的改进BP模型。

Slow converging speed , the existence of a local minimum point in target function , the difficulty in determining the hidden layer number sand hiding nodes are all shortcomings of BP neural network models .

支持向量机（SVM）是近年来发展起来的机器学习的新方法，它较好地解决小样本、非线性、高维数、局部极小点等问题，具有更好的综合性能。

Support vector machine ( SVM ) is a novel machine learning method , which is useful for the problem as small sample , nonlinearity , high dimension and local minimization .

针对疲劳寿命服从Weibull分布时，研究了材料pSN曲线方程拟合的极大似然法，将求解方程参数的问题化为求多元非线性函数的极小点问题。

Maximum likelihood method for getting p_S_N curves when lifetime follows Weibull distribution is studyed in this paper . The parameters of the curves equation can be obtained by finding the minimum points of non-linear multiplex function .

针对自适应IR滤波器（AIRF）潜在的不稳定性和性能指标函数容易陷入局部极小点而导致性能下降等问题，本文将进化规划用于直接、并联、级联和格型结构的AIIRF的优化设计。

Adaptive IIR filtering ( AIIRF ) suffers from potential instability and converges to a local minimum of the objective function .

基于递阶遗传算法的BP神经网络可以改善传统BP神经网络训练速度慢，局部极小点的逃离和算法收敛速度慢的问题。

Based on hierarchical genetic algorithm of BP neural network can improve the traditional BP neural network . The traditional BP neural network training speed is slow , the local minimum points escape and algorithm of slow convergence speed .

将模拟退火算法应用于短期负荷预测领域，其特点是模型简单、运算效率高，并具有较好的全局最优性能，从而很好地克服了传统BP算法容易陷入局部极小点的缺陷。

The advantages of applying simulated annealing algorithm to short-term load forecast include less model complexity , high forecasting accuracy and global optimal property , which alleviate the tendency of traditional BP algorithm to be trapped in local minimum .

由于步长在迭代过程中自适应进行调整，使误差函数E在超曲面上的不同方向按照步长向极小点逼近，实现了对目标函数的优化。

Due to the adaptive adjustment of step length in the iteration process , error function E approaches the minimum point in different directions on the super curved surface in accordance with the step length to realize the optimization of goal function .

由于变压器故障时所能搜集到的特征向量有限，这对于需要大量训练样本的BP网络来说，网络的训练具有一定的局限性，存在局部极小点和过学习等问题。

As the eigenvectors that can be collected when the transformers fail to work are limited , the training of the network that requires a large number of the training samples has some limitations and problems of local minimum and devilishly learning .

BP算法因收敛速度慢、易于陷入局部极小值等缺点，使得对于较大的搜索空间、多峰值和不可微函数常常不能搜索到全局极小点，这些制约了BP网络在各个领域中的应用。

BP algorithm has weaknesses such as slow convergent speed and easy getting into local minimum , insurable to find global extreme value point for multi-modal and non-differential function in larger searching zone , which restrict neural network 's application in every field .

提出了一种新的标准：根据Ln（D/S）～A曲线，正确的因子数在曲线的第一个极小点，并且D

E. D new criterion is propsed : according to the ln ( D / S ) - A , curve , the real factor number lies at the first low extreme point where D