Wavelet Neural Network Based on NARMA-L2 Model for Prediction of Thermal Characteristics in a Fe

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小波神经网络在手写数字识别中研究与应用

ｌ引言
字符识别技术是模式识别领域研究的热点问题，目的是利用计算机对印刷或手写字符进行自动识别和分类。数字识别是字符识别领域的一个重要分支，在邮件自动分拣、银行票据处理、财务账单处理等方面有很高的应用价值。目前，手写数字识别的方法主要有：模板匹配法、逻辑推理法、模糊判别法和神经网络法等。现行的识别技术存在误识率高、识别速度慢等问题，因此，设计速度快、精度高的数字识别
系统是努力的目标。
再对（ｔ）进行伸缩与平移变换，可以得到小波基函数。
（
式中，ａ为尺度伸缩因子，ｂ为时间平移因子，ａ，ｂ∈Ｒ，
ａ≠ ０。
小波分析中所用到的小波函数具有多样性，常用的小波函数有Ｈａ小波、Ｍｏｅ小波、Ｍｘｃｎ小波（ｒｒｒｔｅｉａ简称Ｍａｒｒ小波）ａｂｃｉｓ波（、Ｄｕｅｈｅ小简称ｄｂ小波）等，在此设计中选用Ｍｏｌ小波函数作为神经网络隐层的激励函数。ｒｔｅ
神经网络技术是人工智能研究领域的一个重要分支，它
具有自组织、自学习、分布式存储和并行处理等特点，广泛应用在模式识别、自动控制和专家系统等方面。对数字识别技术详细研究的基础上，提出将小波神经网络应用于手写数字识别技术中，克服了传统ＢＰ算法容易陷入局部极小点和收敛速度慢等缺点，提高了识别速度和识别率。

一种基于NARMAX模型的小波神经网络构造和实现

关键词：波神经网络；ＡＭＡ小ＮＲＸ模型；双正交小波
中图分类号：Ｐ８Ｔ１２文献标志码：Ａ
目前小波和神经网络结合的主要途径是辅助式结合和嵌套式结合．小波与神经网络的辅助式结合有两种方式：种是用神经网络求小波系数或参数，如Ｄｕｍａ一例ａｇｎ用神经网络求出Ｇｂｒａｏ小波最优系数；一种另
摘要：出了一种基于ＮＲＸ模型的小波神经网络结构确定和权系数估计算法．提ＡＭＡ采用ＮＲＸ模型ＡＭＡ
和双正交小波函数来构造小波神经网络，别人脸图像，验结果表明用本文构造的小波神经网络能提高识别正确识实率和识别速度．
Ｓ一｛（） … ，１忌一１２忌，，２尼一咒） … ；Ｎ（） … ，Ｎ（１忌，Ｊ（）；（） … Ｉ（２；Ｉ忌，Ｉ走一ｎ；（一１，，（一ｅ１；；Ｎ）０Ｏ（一ｍ），中项数为： —Ｎ４∑ ＋∑ ．Ｍｋ）… ＭＭ）则Ｓ的Ｐ－
的小波神经网络构造方法，采用双正交小波［，它运用到人脸图像识别中，１将］取得了很好的效果．
１小波神经网络的结构确定和权系数估计算法
３小波神经网络结构包括输入层、层隐含层和输出层，设计时需要考虑隐层小波基个数的确定和初始权值的设置．１图为小波神经网络的拓扑结构．设网络任一节点的激励函数为双正交小波函数 … （，为紧支撑的，于任一 ∈ Ｕ，志一）且对（

高精度自适应小波神经网络人工智能方法探索

高精度自适应小波神经网络人工智能方法探索高精度自适应小波神经网络是一种基于小波变换和人工神经网络结合的人工智能方法，广泛应用于信号处理、图像识别、数据分析等领域。

该方法通过将小波变换和神经网络相结合，可以有效地提取数据的特征，较好地解决数据处理中的一些问题，同时具有高效、高精度、自适应等优点。

下面将对该方法进行详细讨论。

一、小波变换小波变换是一种时频分析方法，它可以将信号分解为不同尺度和频率的小波包，并将每个小波包的特征信息提取出来。

小波变换有以下两种类型：1. 连续小波变换（CWT）连续小波变换将信号与一个连续小波进行卷积，得到一系列连续的小波系数，不同的小波系数对应不同的尺度和频率。

离散小波变换将信号分解为不同尺度和频率的离散小波包，通过滤波和下采样操作，最终得到离散小波系数。

二、神经网络神经网络是一种模拟人脑神经元之间相互连接的计算模型，它能够通过学习经验来进行数据处理和分析。

神经网络由多个神经元组成，每个神经元接受来自其他神经元的输入，并根据输入计算输出。

神经网络训练的过程就是不断地调整神经元之间的连接权值，使网络可以更准确地进行预测和分类。

小波神经网络是将小波变换和神经网络相结合的方法，它将小波变换得到的特征作为神经网络的输入，利用神经网络的学习能力来构建模型并进行数据处理和预测。

小波神经网络的主要流程如下：1. 信号分解：将信号进行小波变换，得到多个小波系数。

2. 特征提取：将小波系数作为神经网络的输入，通过神经网络进行特征提取和数据降维。

3. 神经网络训练：利用已知的样本数据训练神经网络模型。

高精度自适应小波神经网络是对小波神经网络进行改进的方法，它通过引入自适应激活函数和粒子群优化算法来提高模型的精度和稳定性。

具体地，该方法将小波系数输入到神经元中，通过自适应激活函数计算输出，并利用粒子群优化算法动态调整神经元之间的连接权值。

优点：1. 可以有效地提取信号的特征，较好地解决信号处理中的一些问题。

小波变换与神经网络技术的滋养特征提取及识别应用

小波变换与神经网络技术的滋养特征提取及识别应用近年来，小波变换与神经网络技术已经在图像、音频、信号等领域广泛应用，特别是在特征提取和识别方面取得了许多重要进展。

本文将介绍小波变换和神经网络技术的原理及其在特征提取和识别中的应用。

一、小波变换原理小波变换是一种时间-频率分析方法，它将时域信号分解成不同尺度和不同频率的子信号，可以帮助我们更好地理解信号的局部特征。

在小波分析中，小波函数是一种长度有限的函数，它具有自相似性、局部化和可变性等特点。

小波变换的基本过程是将原始信号分解成一组小波系数，这些系数包含了信号在不同尺度上的特征信息，包括低频和高频成分。

其中，低频成分代表信号的整体趋势，高频成分反映了信号的局部细节。

二、神经网络技术原理神经网络是一种模拟人类神经系统运作的计算模型。

它由大量简单的单元组成，这些单元相互连接并通过学习来实现特定任务。

神经网络可以通过多次迭代来优化网络连接权重以及神经元的激活函数，从而得到更好的分类和识别效果。

在神经网络中，网络的输入层接收原始数据，隐含层和输出层则通过多层非线性变换将输入数据映射到具有特定意义的特征空间中。

神经网络的输出层通常表示分类或者识别结果。

三、小波变换与神经网络技术在特征提取中的应用小波变换和神经网络技术已经被广泛应用于图像、音频、信号等领域，特别是在特征提取和识别方面。

以下是一些典型应用案例：1.图像特征提取在图像处理中，小波变换可以将图像分解为不同的频率和尺度。

通过选取合适的小波函数和分解层数，可以提取出图像的不同特征，如边缘、纹理等。

这些特征可以被用于分类、识别和双目视觉等应用中。

神经网络可以通过卷积层和全连接层等深度学习结构学习这些特征，并将其映射到更高层次的特征空间中。

这些特征被广泛应用于计算机视觉任务，如图像分类、目标检测和物体识别等。

2.音频特征提取在音频处理中，小波变换可以将音频信号分解为不同频率的子信号。

这些子信号可以用于声音识别、语音合成、语音分析等应用。

小波变换与神经网络融合法在油页岩近红外光谱分析中的应用

其勘探开发也越来越受到全世界的重视【１］。油页岩含油率是指油页岩中页岩油所占的质量分数，是油页岩品位评价的关键参数，含油率越高，品位就越好［２］。
便携式近红外光谱技术可实现野外目标的现场检测，且不用粉碎样品，不使用化学试剂，不会对环境造成污染［３。Ｉ
页岩含油率检测，使用矿物与油的合成样品数据库，采用小波变换对样品原始光谱数据进行处理，提取近似系数形成ＡＮＮ输入矩阵，并通过比较原始数据ＡＮＮ模型与小波特征数据ＡＮＮ模型的建模速度与预测精度，寻找提高野外现场
富的油页岩等新型非常规能源，作为常规油气资源的替代，
然后再进行神经网络建模。为了验证有效性，利用３Ｏ个油页岩合成样品，从中随机选择２ｏ个用于训练，另外ｌｏ个用于预测，并分别使用全谱数据与小波特征数据进行了１ｏ次神经网络建模。结果表明，全谱数据建
模速度均值为５７０．３３ｓ，预测残差平方和及相关系数均值分别为０．００６０１２及０．８４３７５；而小波神经网络法
对应的以上均值为３．１５Ｓ，０．００２０４８及０．９５３１９。由此说明小波神经网络法优于全谱数据建模法，为油页
岩含油率的快速、高精度检测提供了一种新方法。关键词近红外光谱；小波变换；神经网络；油页岩；含油率
文献标识码：ＡＤＯＩ：１０．３９６４／］．ｉｓｓｎ．１０００ — ０５９３｛２０１３）０４ — ０９６８ — ０４

《神经网络与深度学习综述DeepLearning15May2014

Draft:Deep Learning in Neural Networks:An OverviewTechnical Report IDSIA-03-14/arXiv:1404.7828(v1.5)[cs.NE]J¨u rgen SchmidhuberThe Swiss AI Lab IDSIAIstituto Dalle Molle di Studi sull’Intelligenza ArtiﬁcialeUniversity of Lugano&SUPSIGalleria2,6928Manno-LuganoSwitzerland15May2014AbstractIn recent years,deep artiﬁcial neural networks(including recurrent ones)have won numerous con-tests in pattern recognition and machine learning.This historical survey compactly summarises relevantwork,much of it from the previous millennium.Shallow and deep learners are distinguished by thedepth of their credit assignment paths,which are chains of possibly learnable,causal links between ac-tions and effects.I review deep supervised learning(also recapitulating the history of backpropagation),unsupervised learning,reinforcement learning&evolutionary computation,and indirect search for shortprograms encoding deep and large networks.PDF of earlier draft(v1):http://www.idsia.ch/∼juergen/DeepLearning30April2014.pdfLATEX source:http://www.idsia.ch/∼juergen/DeepLearning30April2014.texComplete BIBTEXﬁle:http://www.idsia.ch/∼juergen/bib.bibPrefaceThis is the draft of an invited Deep Learning(DL)overview.One of its goals is to assign credit to those who contributed to the present state of the art.I acknowledge the limitations of attempting to achieve this goal.The DL research community itself may be viewed as a continually evolving,deep network of scientists who have inﬂuenced each other in complex ways.Starting from recent DL results,I tried to trace back the origins of relevant ideas through the past half century and beyond,sometimes using“local search”to follow citations of citations backwards in time.Since not all DL publications properly acknowledge earlier relevant work,additional global search strategies were employed,aided by consulting numerous neural network experts.As a result,the present draft mostly consists of references(about800entries so far).Nevertheless,through an expert selection bias I may have missed important work.A related bias was surely introduced by my special familiarity with the work of my own DL research group in the past quarter-century.For these reasons,the present draft should be viewed as merely a snapshot of an ongoing credit assignment process.To help improve it,please do not hesitate to send corrections and suggestions to juergen@idsia.ch.Contents1Introduction to Deep Learning(DL)in Neural Networks(NNs)3 2Event-Oriented Notation for Activation Spreading in FNNs/RNNs3 3Depth of Credit Assignment Paths(CAPs)and of Problems4 4Recurring Themes of Deep Learning54.1Dynamic Programming(DP)for DL (5)4.2Unsupervised Learning(UL)Facilitating Supervised Learning(SL)and RL (6)4.3Occam’s Razor:Compression and Minimum Description Length(MDL) (6)4.4Learning Hierarchical Representations Through Deep SL,UL,RL (6)4.5Fast Graphics Processing Units(GPUs)for DL in NNs (6)5Supervised NNs,Some Helped by Unsupervised NNs75.11940s and Earlier (7)5.2Around1960:More Neurobiological Inspiration for DL (7)5.31965:Deep Networks Based on the Group Method of Data Handling(GMDH) (8)5.41979:Convolution+Weight Replication+Winner-Take-All(WTA) (8)5.51960-1981and Beyond:Development of Backpropagation(BP)for NNs (8)5.5.1BP for Weight-Sharing Feedforward NNs(FNNs)and Recurrent NNs(RNNs)..95.6Late1980s-2000:Numerous Improvements of NNs (9)5.6.1Ideas for Dealing with Long Time Lags and Deep CAPs (10)5.6.2Better BP Through Advanced Gradient Descent (10)5.6.3Discovering Low-Complexity,Problem-Solving NNs (11)5.6.4Potential Beneﬁts of UL for SL (11)5.71987:UL Through Autoencoder(AE)Hierarchies (12)5.81989:BP for Convolutional NNs(CNNs) (13)5.91991:Fundamental Deep Learning Problem of Gradient Descent (13)5.101991:UL-Based History Compression Through a Deep Hierarchy of RNNs (14)5.111992:Max-Pooling(MP):Towards MPCNNs (14)5.121994:Contest-Winning Not So Deep NNs (15)5.131995:Supervised Recurrent Very Deep Learner(LSTM RNN) (15)5.142003:More Contest-Winning/Record-Setting,Often Not So Deep NNs (16)5.152006/7:Deep Belief Networks(DBNs)&AE Stacks Fine-Tuned by BP (17)5.162006/7:Improved CNNs/GPU-CNNs/BP-Trained MPCNNs (17)5.172009:First Ofﬁcial Competitions Won by RNNs,and with MPCNNs (18)5.182010:Plain Backprop(+Distortions)on GPU Yields Excellent Results (18)5.192011:MPCNNs on GPU Achieve Superhuman Vision Performance (18)5.202011:Hessian-Free Optimization for RNNs (19)5.212012:First Contests Won on ImageNet&Object Detection&Segmentation (19)5.222013-:More Contests and Benchmark Records (20)5.22.1Currently Successful Supervised Techniques:LSTM RNNs/GPU-MPCNNs (21)5.23Recent Tricks for Improving SL Deep NNs(Compare Sec.5.6.2,5.6.3) (21)5.24Consequences for Neuroscience (22)5.25DL with Spiking Neurons? (22)6DL in FNNs and RNNs for Reinforcement Learning(RL)236.1RL Through NN World Models Yields RNNs With Deep CAPs (23)6.2Deep FNNs for Traditional RL and Markov Decision Processes(MDPs) (24)6.3Deep RL RNNs for Partially Observable MDPs(POMDPs) (24)6.4RL Facilitated by Deep UL in FNNs and RNNs (25)6.5Deep Hierarchical RL(HRL)and Subgoal Learning with FNNs and RNNs (25)6.6Deep RL by Direct NN Search/Policy Gradients/Evolution (25)6.7Deep RL by Indirect Policy Search/Compressed NN Search (26)6.8Universal RL (27)7Conclusion271Introduction to Deep Learning(DL)in Neural Networks(NNs) Which modiﬁable components of a learning system are responsible for its success or failure?What changes to them improve performance?This has been called the fundamental credit assignment problem(Minsky, 1963).There are general credit assignment methods for universal problem solvers that are time-optimal in various theoretical senses(Sec.6.8).The present survey,however,will focus on the narrower,but now commercially important,subﬁeld of Deep Learning(DL)in Artiﬁcial Neural Networks(NNs).We are interested in accurate credit assignment across possibly many,often nonlinear,computational stages of NNs.Shallow NN-like models have been around for many decades if not centuries(Sec.5.1).Models with several successive nonlinear layers of neurons date back at least to the1960s(Sec.5.3)and1970s(Sec.5.5). An efﬁcient gradient descent method for teacher-based Supervised Learning(SL)in discrete,differentiable networks of arbitrary depth called backpropagation(BP)was developed in the1960s and1970s,and ap-plied to NNs in1981(Sec.5.5).BP-based training of deep NNs with many layers,however,had been found to be difﬁcult in practice by the late1980s(Sec.5.6),and had become an explicit research subject by the early1990s(Sec.5.9).DL became practically feasible to some extent through the help of Unsupervised Learning(UL)(e.g.,Sec.5.10,5.15).The1990s and2000s also saw many improvements of purely super-vised DL(Sec.5).In the new millennium,deep NNs haveﬁnally attracted wide-spread attention,mainly by outperforming alternative machine learning methods such as kernel machines(Vapnik,1995;Sch¨o lkopf et al.,1998)in numerous important applications.In fact,supervised deep NNs have won numerous of-ﬁcial international pattern recognition competitions(e.g.,Sec.5.17,5.19,5.21,5.22),achieving theﬁrst superhuman visual pattern recognition results in limited domains(Sec.5.19).Deep NNs also have become relevant for the more generalﬁeld of Reinforcement Learning(RL)where there is no supervising teacher (Sec.6).Both feedforward(acyclic)NNs(FNNs)and recurrent(cyclic)NNs(RNNs)have won contests(Sec.5.12,5.14,5.17,5.19,5.21,5.22).In a sense,RNNs are the deepest of all NNs(Sec.3)—they are general computers more powerful than FNNs,and can in principle create and process memories of ar-bitrary sequences of input patterns(e.g.,Siegelmann and Sontag,1991;Schmidhuber,1990a).Unlike traditional methods for automatic sequential program synthesis(e.g.,Waldinger and Lee,1969;Balzer, 1985;Soloway,1986;Deville and Lau,1994),RNNs can learn programs that mix sequential and parallel information processing in a natural and efﬁcient way,exploiting the massive parallelism viewed as crucial for sustaining the rapid decline of computation cost observed over the past75years.The rest of this paper is structured as follows.Sec.2introduces a compact,event-oriented notation that is simple yet general enough to accommodate both FNNs and RNNs.Sec.3introduces the concept of Credit Assignment Paths(CAPs)to measure whether learning in a given NN application is of the deep or shallow type.Sec.4lists recurring themes of DL in SL,UL,and RL.Sec.5focuses on SL and UL,and on how UL can facilitate SL,although pure SL has become dominant in recent competitions(Sec.5.17-5.22). Sec.5is arranged in a historical timeline format with subsections on important inspirations and technical contributions.Sec.6on deep RL discusses traditional Dynamic Programming(DP)-based RL combined with gradient-based search techniques for SL or UL in deep NNs,as well as general methods for direct and indirect search in the weight space of deep FNNs and RNNs,including successful policy gradient and evolutionary methods.2Event-Oriented Notation for Activation Spreading in FNNs/RNNs Throughout this paper,let i,j,k,t,p,q,r denote positive integer variables assuming ranges implicit in the given contexts.Let n,m,T denote positive integer constants.An NN’s topology may change over time(e.g.,Fahlman,1991;Ring,1991;Weng et al.,1992;Fritzke, 1994).At any given moment,it can be described as aﬁnite subset of units(or nodes or neurons)N= {u1,u2,...,}and aﬁnite set H⊆N×N of directed edges or connections between nodes.FNNs are acyclic graphs,RNNs cyclic.Theﬁrst(input)layer is the set of input units,a subset of N.In FNNs,the k-th layer(k>1)is the set of all nodes u∈N such that there is an edge path of length k−1(but no longer path)between some input unit and u.There may be shortcut connections between distant layers.The NN’s behavior or program is determined by a set of real-valued,possibly modiﬁable,parameters or weights w i(i=1,...,n).We now focus on a singleﬁnite episode or epoch of information processing and activation spreading,without learning through weight changes.The following slightly unconventional notation is designed to compactly describe what is happening during the runtime of the system.During an episode,there is a partially causal sequence x t(t=1,...,T)of real values that I call events.Each x t is either an input set by the environment,or the activation of a unit that may directly depend on other x k(k<t)through a current NN topology-dependent set in t of indices k representing incoming causal connections or links.Let the function v encode topology information and map such event index pairs(k,t)to weight indices.For example,in the non-input case we may have x t=f t(net t)with real-valued net t= k∈in t x k w v(k,t)(additive case)or net t= k∈in t x k w v(k,t)(multiplicative case), where f t is a typically nonlinear real-valued activation function such as tanh.In many recent competition-winning NNs(Sec.5.19,5.21,5.22)there also are events of the type x t=max k∈int (x k);some networktypes may also use complex polynomial activation functions(Sec.5.3).x t may directly affect certain x k(k>t)through outgoing connections or links represented through a current set out t of indices k with t∈in k.Some non-input events are called output events.Note that many of the x t may refer to different,time-varying activations of the same unit in sequence-processing RNNs(e.g.,Williams,1989,“unfolding in time”),or also in FNNs sequentially exposed to time-varying input patterns of a large training set encoded as input events.During an episode,the same weight may get reused over and over again in topology-dependent ways,e.g.,in RNNs,or in convolutional NNs(Sec.5.4,5.8).I call this weight sharing across space and/or time.Weight sharing may greatly reduce the NN’s descriptive complexity,which is the number of bits of information required to describe the NN (Sec.4.3).In Supervised Learning(SL),certain NN output events x t may be associated with teacher-given,real-valued labels or targets d t yielding errors e t,e.g.,e t=1/2(x t−d t)2.A typical goal of supervised NN training is toﬁnd weights that yield episodes with small total error E,the sum of all such e t.The hope is that the NN will generalize well in later episodes,causing only small errors on previously unseen sequences of input events.Many alternative error functions for SL and UL are possible.SL assumes that input events are independent of earlier output events(which may affect the environ-ment through actions causing subsequent perceptions).This assumption does not hold in the broaderﬁelds of Sequential Decision Making and Reinforcement Learning(RL)(Kaelbling et al.,1996;Sutton and Barto, 1998;Hutter,2005)(Sec.6).In RL,some of the input events may encode real-valued reward signals given by the environment,and a typical goal is toﬁnd weights that yield episodes with a high sum of reward signals,through sequences of appropriate output actions.Sec.5.5will use the notation above to compactly describe a central algorithm of DL,namely,back-propagation(BP)for supervised weight-sharing FNNs and RNNs.(FNNs may be viewed as RNNs with certainﬁxed zero weights.)Sec.6will address the more general RL case.3Depth of Credit Assignment Paths(CAPs)and of ProblemsTo measure whether credit assignment in a given NN application is of the deep or shallow type,I introduce the concept of Credit Assignment Paths or CAPs,which are chains of possibly causal links between events.Let usﬁrst focus on SL.Consider two events x p and x q(1≤p<q≤T).Depending on the appli-cation,they may have a Potential Direct Causal Connection(PDCC)expressed by the Boolean predicate pdcc(p,q),which is true if and only if p∈in q.Then the2-element list(p,q)is deﬁned to be a CAP from p to q(a minimal one).A learning algorithm may be allowed to change w v(p,q)to improve performance in future episodes.More general,possibly indirect,Potential Causal Connections(PCC)are expressed by the recursively deﬁned Boolean predicate pcc(p,q),which in the SL case is true only if pdcc(p,q),or if pcc(p,k)for some k and pdcc(k,q).In the latter case,appending q to any CAP from p to k yields a CAP from p to q(this is a recursive deﬁnition,too).The set of such CAPs may be large but isﬁnite.Note that the same weight may affect many different PDCCs between successive events listed by a given CAP,e.g.,in the case of RNNs, or weight-sharing FNNs.Suppose a CAP has the form(...,k,t,...,q),where k and t(possibly t=q)are theﬁrst successive elements with modiﬁable w v(k,t).Then the length of the sufﬁx list(t,...,q)is called the CAP’s depth (which is0if there are no modiﬁable links at all).This depth limits how far backwards credit assignment can move down the causal chain toﬁnd a modiﬁable weight.1Suppose an episode and its event sequence x1,...,x T satisfy a computable criterion used to decide whether a given problem has been solved(e.g.,total error E below some threshold).Then the set of used weights is called a solution to the problem,and the depth of the deepest CAP within the sequence is called the solution’s depth.There may be other solutions(yielding different event sequences)with different depths.Given someﬁxed NN topology,the smallest depth of any solution is called the problem’s depth.Sometimes we also speak of the depth of an architecture:SL FNNs withﬁxed topology imply a problem-independent maximal problem depth bounded by the number of non-input layers.Certain SL RNNs withﬁxed weights for all connections except those to output units(Jaeger,2001;Maass et al.,2002; Jaeger,2004;Schrauwen et al.,2007)have a maximal problem depth of1,because only theﬁnal links in the corresponding CAPs are modiﬁable.In general,however,RNNs may learn to solve problems of potentially unlimited depth.Note that the deﬁnitions above are solely based on the depths of causal chains,and agnostic of the temporal distance between events.For example,shallow FNNs perceiving large“time windows”of in-put events may correctly classify long input sequences through appropriate output events,and thus solve shallow problems involving long time lags between relevant events.At which problem depth does Shallow Learning end,and Deep Learning begin?Discussions with DL experts have not yet yielded a conclusive response to this question.Instead of committing myself to a precise answer,let me just deﬁne for the purposes of this overview:problems of depth>10require Very Deep Learning.The difﬁculty of a problem may have little to do with its depth.Some NNs can quickly learn to solve certain deep problems,e.g.,through random weight guessing(Sec.5.9)or other types of direct search (Sec.6.6)or indirect search(Sec.6.7)in weight space,or through training an NNﬁrst on shallow problems whose solutions may then generalize to deep problems,or through collapsing sequences of(non)linear operations into a single(non)linear operation—but see an analysis of non-trivial aspects of deep linear networks(Baldi and Hornik,1994,Section B).In general,however,ﬁnding an NN that precisely models a given training set is an NP-complete problem(Judd,1990;Blum and Rivest,1992),also in the case of deep NNs(S´ıma,1994;de Souto et al.,1999;Windisch,2005);compare a survey of negative results(S´ıma, 2002,Section1).Above we have focused on SL.In the more general case of RL in unknown environments,pcc(p,q) is also true if x p is an output event and x q any later input event—any action may affect the environment and thus any later perception.(In the real world,the environment may even inﬂuence non-input events computed on a physical hardware entangled with the entire universe,but this is ignored here.)It is possible to model and replace such unmodiﬁable environmental PCCs through a part of the NN that has already learned to predict(through some of its units)input events(including reward signals)from former input events and actions(Sec.6.1).Its weights are frozen,but can help to assign credit to other,still modiﬁable weights used to compute actions(Sec.6.1).This approach may lead to very deep CAPs though.Some DL research is about automatically rephrasing problems such that their depth is reduced(Sec.4). In particular,sometimes UL is used to make SL problems less deep,e.g.,Sec.5.10.Often Dynamic Programming(Sec.4.1)is used to facilitate certain traditional RL problems,e.g.,Sec.6.2.Sec.5focuses on CAPs for SL,Sec.6on the more complex case of RL.4Recurring Themes of Deep Learning4.1Dynamic Programming(DP)for DLOne recurring theme of DL is Dynamic Programming(DP)(Bellman,1957),which can help to facili-tate credit assignment under certain assumptions.For example,in SL NNs,backpropagation itself can 1An alternative would be to count only modiﬁable links when measuring depth.In many typical NN applications this would not make a difference,but in some it would,e.g.,Sec.6.1.be viewed as a DP-derived method(Sec.5.5).In traditional RL based on strong Markovian assumptions, DP-derived methods can help to greatly reduce problem depth(Sec.6.2).DP algorithms are also essen-tial for systems that combine concepts of NNs and graphical models,such as Hidden Markov Models (HMMs)(Stratonovich,1960;Baum and Petrie,1966)and Expectation Maximization(EM)(Dempster et al.,1977),e.g.,(Bottou,1991;Bengio,1991;Bourlard and Morgan,1994;Baldi and Chauvin,1996; Jordan and Sejnowski,2001;Bishop,2006;Poon and Domingos,2011;Dahl et al.,2012;Hinton et al., 2012a).4.2Unsupervised Learning(UL)Facilitating Supervised Learning(SL)and RL Another recurring theme is how UL can facilitate both SL(Sec.5)and RL(Sec.6).UL(Sec.5.6.4) is normally used to encode raw incoming data such as video or speech streams in a form that is more convenient for subsequent goal-directed learning.In particular,codes that describe the original data in a less redundant or more compact way can be fed into SL(Sec.5.10,5.15)or RL machines(Sec.6.4),whose search spaces may thus become smaller(and whose CAPs shallower)than those necessary for dealing with the raw data.UL is closely connected to the topics of regularization and compression(Sec.4.3,5.6.3). 4.3Occam’s Razor:Compression and Minimum Description Length(MDL) Occam’s razor favors simple solutions over complex ones.Given some programming language,the prin-ciple of Minimum Description Length(MDL)can be used to measure the complexity of a solution candi-date by the length of the shortest program that computes it(e.g.,Solomonoff,1964;Kolmogorov,1965b; Chaitin,1966;Wallace and Boulton,1968;Levin,1973a;Rissanen,1986;Blumer et al.,1987;Li and Vit´a nyi,1997;Gr¨u nwald et al.,2005).Some methods explicitly take into account program runtime(Al-lender,1992;Watanabe,1992;Schmidhuber,2002,1995);many consider only programs with constant runtime,written in non-universal programming languages(e.g.,Rissanen,1986;Hinton and van Camp, 1993).In the NN case,the MDL principle suggests that low NN weight complexity corresponds to high NN probability in the Bayesian view(e.g.,MacKay,1992;Buntine and Weigend,1991;De Freitas,2003), and to high generalization performance(e.g.,Baum and Haussler,1989),without overﬁtting the training data.Many methods have been proposed for regularizing NNs,that is,searching for solution-computing, low-complexity SL NNs(Sec.5.6.3)and RL NNs(Sec.6.7).This is closely related to certain UL methods (Sec.4.2,5.6.4).4.4Learning Hierarchical Representations Through Deep SL,UL,RLMany methods of Good Old-Fashioned Artiﬁcial Intelligence(GOFAI)(Nilsson,1980)as well as more recent approaches to AI(Russell et al.,1995)and Machine Learning(Mitchell,1997)learn hierarchies of more and more abstract data representations.For example,certain methods of syntactic pattern recog-nition(Fu,1977)such as grammar induction discover hierarchies of formal rules to model observations. The partially(un)supervised Automated Mathematician/EURISKO(Lenat,1983;Lenat and Brown,1984) continually learns concepts by combining previously learnt concepts.Such hierarchical representation learning(Ring,1994;Bengio et al.,2013;Deng and Yu,2014)is also a recurring theme of DL NNs for SL (Sec.5),UL-aided SL(Sec.5.7,5.10,5.15),and hierarchical RL(Sec.6.5).Often,abstract hierarchical representations are natural by-products of data compression(Sec.4.3),e.g.,Sec.5.10.4.5Fast Graphics Processing Units(GPUs)for DL in NNsWhile the previous millennium saw several attempts at creating fast NN-speciﬁc hardware(e.g.,Jackel et al.,1990;Faggin,1992;Ramacher et al.,1993;Widrow et al.,1994;Heemskerk,1995;Korkin et al., 1997;Urlbe,1999),and at exploiting standard hardware(e.g.,Anguita et al.,1994;Muller et al.,1995; Anguita and Gomes,1996),the new millennium brought a DL breakthrough in form of cheap,multi-processor graphics cards or GPUs.GPUs are widely used for video games,a huge and competitive market that has driven down hardware prices.GPUs excel at fast matrix and vector multiplications required not only for convincing virtual realities but also for NN training,where they can speed up learning by a factorof50and more.Some of the GPU-based FNN implementations(Sec.5.16-5.19)have greatly contributed to recent successes in contests for pattern recognition(Sec.5.19-5.22),image segmentation(Sec.5.21), and object detection(Sec.5.21-5.22).5Supervised NNs,Some Helped by Unsupervised NNsThe main focus of current practical applications is on Supervised Learning(SL),which has dominated re-cent pattern recognition contests(Sec.5.17-5.22).Several methods,however,use additional Unsupervised Learning(UL)to facilitate SL(Sec.5.7,5.10,5.15).It does make sense to treat SL and UL in the same section:often gradient-based methods,such as BP(Sec.5.5.1),are used to optimize objective functions of both UL and SL,and the boundary between SL and UL may blur,for example,when it comes to time series prediction and sequence classiﬁcation,e.g.,Sec.5.10,5.12.A historical timeline format will help to arrange subsections on important inspirations and techni-cal contributions(although such a subsection may span a time interval of many years).Sec.5.1brieﬂy mentions early,shallow NN models since the1940s,Sec.5.2additional early neurobiological inspiration relevant for modern Deep Learning(DL).Sec.5.3is about GMDH networks(since1965),perhaps theﬁrst (feedforward)DL systems.Sec.5.4is about the relatively deep Neocognitron NN(1979)which is similar to certain modern deep FNN architectures,as it combines convolutional NNs(CNNs),weight pattern repli-cation,and winner-take-all(WTA)mechanisms.Sec.5.5uses the notation of Sec.2to compactly describe a central algorithm of DL,namely,backpropagation(BP)for supervised weight-sharing FNNs and RNNs. It also summarizes the history of BP1960-1981and beyond.Sec.5.6describes problems encountered in the late1980s with BP for deep NNs,and mentions several ideas from the previous millennium to overcome them.Sec.5.7discusses aﬁrst hierarchical stack of coupled UL-based Autoencoders(AEs)—this concept resurfaced in the new millennium(Sec.5.15).Sec.5.8is about applying BP to CNNs,which is important for today’s DL applications.Sec.5.9explains BP’s Fundamental DL Problem(of vanishing/exploding gradients)discovered in1991.Sec.5.10explains how a deep RNN stack of1991(the History Compressor) pre-trained by UL helped to solve previously unlearnable DL benchmarks requiring Credit Assignment Paths(CAPs,Sec.3)of depth1000and more.Sec.5.11discusses a particular WTA method called Max-Pooling(MP)important in today’s DL FNNs.Sec.5.12mentions aﬁrst important contest won by SL NNs in1994.Sec.5.13describes a purely supervised DL RNN(Long Short-Term Memory,LSTM)for problems of depth1000and more.Sec.5.14mentions an early contest of2003won by an ensemble of shallow NNs, as well as good pattern recognition results with CNNs and LSTM RNNs(2003).Sec.5.15is mostly about Deep Belief Networks(DBNs,2006)and related stacks of Autoencoders(AEs,Sec.5.7)pre-trained by UL to facilitate BP-based SL.Sec.5.16mentions theﬁrst BP-trained MPCNNs(2007)and GPU-CNNs(2006). Sec.5.17-5.22focus on ofﬁcial competitions with secret test sets won by(mostly purely supervised)DL NNs since2009,in sequence recognition,image classiﬁcation,image segmentation,and object detection. Many RNN results depended on LSTM(Sec.5.13);many FNN results depended on GPU-based FNN code developed since2004(Sec.5.16,5.17,5.18,5.19),in particular,GPU-MPCNNs(Sec.5.19).5.11940s and EarlierNN research started in the1940s(e.g.,McCulloch and Pitts,1943;Hebb,1949);compare also later work on learning NNs(Rosenblatt,1958,1962;Widrow and Hoff,1962;Grossberg,1969;Kohonen,1972; von der Malsburg,1973;Narendra and Thathatchar,1974;Willshaw and von der Malsburg,1976;Palm, 1980;Hopﬁeld,1982).In a sense NNs have been around even longer,since early supervised NNs were essentially variants of linear regression methods going back at least to the early1800s(e.g.,Legendre, 1805;Gauss,1809,1821).Early NNs had a maximal CAP depth of1(Sec.3).5.2Around1960:More Neurobiological Inspiration for DLSimple cells and complex cells were found in the cat’s visual cortex(e.g.,Hubel and Wiesel,1962;Wiesel and Hubel,1959).These cellsﬁre in response to certain properties of visual sensory inputs,such as theorientation of plex cells exhibit more spatial invariance than simple cells.This inspired later deep NN architectures(Sec.5.4)used in certain modern award-winning Deep Learners(Sec.5.19-5.22).5.31965:Deep Networks Based on the Group Method of Data Handling(GMDH) Networks trained by the Group Method of Data Handling(GMDH)(Ivakhnenko and Lapa,1965; Ivakhnenko et al.,1967;Ivakhnenko,1968,1971)were perhaps theﬁrst DL systems of the Feedforward Multilayer Perceptron type.The units of GMDH nets may have polynomial activation functions imple-menting Kolmogorov-Gabor polynomials(more general than traditional NN activation functions).Given a training set,layers are incrementally grown and trained by regression analysis,then pruned with the help of a separate validation set(using today’s terminology),where Decision Regularisation is used to weed out superﬂuous units.The numbers of layers and units per layer can be learned in problem-dependent fashion. This is a good example of hierarchical representation learning(Sec.4.4).There have been numerous ap-plications of GMDH-style networks,e.g.(Ikeda et al.,1976;Farlow,1984;Madala and Ivakhnenko,1994; Ivakhnenko,1995;Kondo,1998;Kord´ık et al.,2003;Witczak et al.,2006;Kondo and Ueno,2008).5.41979:Convolution+Weight Replication+Winner-Take-All(WTA)Apart from deep GMDH networks(Sec.5.3),the Neocognitron(Fukushima,1979,1980,2013a)was per-haps theﬁrst artiﬁcial NN that deserved the attribute deep,and theﬁrst to incorporate the neurophysiolog-ical insights of Sec.5.2.It introduced convolutional NNs(today often called CNNs or convnets),where the(typically rectangular)receptiveﬁeld of a convolutional unit with given weight vector is shifted step by step across a2-dimensional array of input values,such as the pixels of an image.The resulting2D array of subsequent activation events of this unit can then provide inputs to higher-level units,and so on.Due to massive weight replication(Sec.2),relatively few parameters may be necessary to describe the behavior of such a convolutional layer.Competition layers have WTA subsets whose maximally active units are the only ones to adopt non-zero activation values.They essentially“down-sample”the competition layer’s input.This helps to create units whose responses are insensitive to small image shifts(compare Sec.5.2).The Neocognitron is very similar to the architecture of modern,contest-winning,purely super-vised,feedforward,gradient-based Deep Learners with alternating convolutional and competition lay-ers(e.g.,Sec.5.19-5.22).Fukushima,however,did not set the weights by supervised backpropagation (Sec.5.5,5.8),but by local un supervised learning rules(e.g.,Fukushima,2013b),or by pre-wiring.In that sense he did not care for the DL problem(Sec.5.9),although his architecture was comparatively deep indeed.He also used Spatial Averaging(Fukushima,1980,2011)instead of Max-Pooling(MP,Sec.5.11), currently a particularly convenient and popular WTA mechanism.Today’s CNN-based DL machines proﬁta lot from later CNN work(e.g.,LeCun et al.,1989;Ranzato et al.,2007)(Sec.5.8,5.16,5.19).5.51960-1981and Beyond:Development of Backpropagation(BP)for NNsThe minimisation of errors through gradient descent(Hadamard,1908)in the parameter space of com-plex,nonlinear,differentiable,multi-stage,NN-related systems has been discussed at least since the early 1960s(e.g.,Kelley,1960;Bryson,1961;Bryson and Denham,1961;Pontryagin et al.,1961;Dreyfus,1962; Wilkinson,1965;Amari,1967;Bryson and Ho,1969;Director and Rohrer,1969;Griewank,2012),ini-tially within the framework of Euler-LaGrange equations in the Calculus of Variations(e.g.,Euler,1744). Steepest descent in such systems can be performed(Bryson,1961;Kelley,1960;Bryson and Ho,1969)by iterating the ancient chain rule(Leibniz,1676;L’Hˆo pital,1696)in Dynamic Programming(DP)style(Bell-man,1957).A simpliﬁed derivation of the method uses the chain rule only(Dreyfus,1962).The methods of the1960s were already efﬁcient in the DP sense.However,they backpropagated derivative information through standard Jacobian matrix calculations from one“layer”to the previous one, explicitly addressing neither direct links across several layers nor potential additional efﬁciency gains due to network sparsity(but perhaps such enhancements seemed obvious to the authors).。

遗传算法在模拟电路故障诊断中的应用---优秀毕业论文参考文献可复制黏贴

为提高故障诊断的速度，本文提出了将灵敏度分析与遗传算法结合应用于模拟电路软故障诊断。讨论了基于模拟电路的灵敏度分析估算元件参数偏移量求解故障元件的诊断方法。将测试节点电压增量与元件参数变化量所构成诊断方程转化为以其为硬约束条件下求自变量最小值的线性规划问题。然后引入罚函数将其转化为无约束条件下的极值求解问题，最后利用遗传算法寻求最优解。本文讨论了控制参数对遗传算法性能的影响，提出了改进的自适应遗传算法，实验结果表明该方法对容差模拟电路的软故障诊断具有较好的诊断效率。关键词：模拟电路，SLPS，模拟电路故障诊断，遗传算法，灵敏度分析
In order to improve the speed of fault diagnosis, the application in soft fault diagnosis of analog circuits based on sensitivity analysis combined with the genetic algorithm is presented in this paper. We have discussed the sensitivity analysis of analog circuits. Estimate the offset of the component parameters to diagnose the fault of the analog circuits. We convert the diagnosis equation, which is constituted by the incremental test node voltage and the component parameters variation, into the linear programming problem about finding the smallest independent variable based on the hard constraints of the fault diagnosis equation. And the linear programming problem with constraints is converted to the extreme solution without constraints by the penalty function. The genetic algorithm is used to solve the optimal solution. Then, the influence of the control parameters of genetic algorithm is discussed with examples. A new Self-adaptive Genetic Algorithms was proposed and the experiments show that the method has a good efficiency on the soft fault diagnosis of tolerance analog circuits and has a higher speed.

文献综述-小波变换(Wavelet-Transform)的概念是1984年法国地球-...电子教案

文献综述小波变换（Wavelet Transform）的概念是1984年法国地球物理学家J.Morlet在分析处理地球物理勘探资料时提出来的。

小波变换的数学基础是19世纪的傅里叶变换，其后理论物理学家A.Grossman采用平移和伸缩不变性建立了小波变换的理论体系。

1985年，法国数学家Y.Meyer第一个构造出具有一定衰减性的光滑小波。

1988年，比利时数学家I.Daubechies证明了紧支撑正交标准小波基的存在性，使得离散小波分析成为可能。

1989年S.Mallat提出了多分辨率分析概念，统一了在此之前的各种构造小波的方法，特别是提出了二进小波变换的快速算法，使得小波变换完全走向了实用性。

小波分析是建立在泛函分析、Fourier分析、样条分析及调和分析基础上的新的分析处理工具。

它又被称为多分辨率分析，在时域和频域同时具有良好的局部化特性，常被誉为信号分析的“数据显微镜”。

近十多年来，小波分析的理论和方法在信号处理、语音分析、模式识别、数据压缩、图像处理、数字水印、量子物理等专业和领域得到广泛的应用。

小波变换分析在数据处理方面的应用主要集中在安全变形监测数据和GPS观测数据的处理，应为他们都对精度用较高的要求，而小波变换分析方法的优势能满足这个要求。

在安全变形数据处理主要集中在去噪处理、识别变形的突变点，也包括提取变形特征、分离不同变形频率、估计观测精度、小波变换最佳级数的确定等。

在GPS数据处理方面包括：利用小波分析法来检测GPS相位观测值整周跳变的理论与方法，GPS粗差检测、GPS信号多路径误差分析、相位周跳检测、基于小波的GPS双差残差分析等。

国内有关学者和研究人员研究工作如下：李宗春等研究了变形测量异常数据中小波变换最佳级数的确定，综合分析数据去噪效果的4 个分项评价指标，即数据的均方根差变化量、互相关系数、信噪比及平滑度，将各分项评价指标归化到[0, 1]后相加得到总体评价指标，将总体评价指标最大值所对应的级数定义为小波分解与重构的最佳级数。

中美韩合作研发出柔性人造触觉神经系统

行业动态News 6机器人技术与应用20184行业动态(新技术)5月21日，美国罗格斯大学航空航天工程系教授李镐元和韩国高丽大学机械工学部教授崔元准研究团队共同宣布，他们利用3D 打印技术，制造出智能水凝胶机器人，通过将该机器人置于水中，并对其施加电流，成功使其实现物体抓取和行走等动作。

据悉，智能凝胶相比于坚硬的固体材料成本较低，也据悉，美国麻省理工学院计算机科学与人工智能实验室（CSAIL）迪纳·卡塔比（Dina Katabi）教授的研究小组公布了一项最新研究成果，该成果来源于一个名为“RF-Pose”的项目，能通过AI 技术来训练无线设备，从而感知人们的姿势与动作，甚至在墙壁的另一侧都可以识别。

研究人员通过利用神经网络来分析从目标人物身体上反射回来的无线电信号，然后创建出动态抽象人形图。

当目标在做行走、停止、坐立或摆动四肢等动作时，这些人形图就会跟着做出相应的动作。

首先，研究人员利用无线设备与照相机收集了成千上万张人们在进行不同活动时的照片，比如：走路、说话、坐立、开门等。

其次，研究人员利用这些图像提取人形图像，并将其显示给神经网络和对应的无线电信号，以帮助该系统更好地了解无线电信号与所识别目标之间的联系。

然后，无线电信号通过人形图像来学习人体的姿态，通过反复训近日，天津南开大学电子信息与光学工程学院徐文涛团队与美国斯坦福大学、韩国首尔大学的研究人员合作研发出柔性人造触觉神经系统，该系统有望应用于机器人手术、假肢感触等领域。

据介绍，研究人员利用柔性有机材料模拟了人体SA-I 触觉神经，这种触觉神经由3个核心部件组成：电阻式压力传感器、有机环形振荡器、突触晶体管。

该系统首先利用一系列感受器感知极为细微的压力，并产生相应的电压变化，随后通过环形振荡器（人工神经纤维）将电压变化转变为电脉冲信号，而多个环形振荡器得到的电信号被突触晶体管集成并转变为突触电流，进而传递到下一级神经。

这种人造触觉神经能够很好地模拟人类皮肤的触觉功更容易进行设计和控制，主要用于制造软体机器人。

基于深度卷积-长短期记忆神经网络的整车道路载荷预测

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拟路谱技术和基于机器学习的路谱识别技术。前者首先通过激光扫描技术获取试验场路面不平度信号，然后对包括轮胎、衬套悬置等弹性元件的整车模型进行动力学仿真分析；后 [1-4] 者首先利用合适的机器学习模型直接根据方便测量的整车参数预测道路载荷，然后利用整车动力学仿真分析获取底盘结构件的动态响应载荷。 [5-8] 通过对比这 2 种方法，发现与虚拟路谱技术相比，基于机器学习的路谱识别技术省去了操作复杂且代价高昂的路面不平度测量工作，且不需要在整车动力学模型中建立轮胎模型。
经网络（DCNN-LSTM）模型，提出了基于数据驱动的整车轮心载荷预测方法。对比试验结果表明，该方法预测的整车轮心
载荷与试验场采集数据非常接近，有利于逐步取消路谱采集试验并极大地提高整车耐久性分析的效率。
主题词：道路载荷深度学习数据库疲劳耐久分析深度卷积神经网络长短期记忆
每小块求取统计值（如均值或最大值）即可得到池化层的输出信息。在整车道路载荷预测中，需要处理的汽车
算和求和运算，然后通过非线性转换获得卷积层的输出信息。在池化层，输入的数据被分为很多小块，通过对
运行参数属于一维时序数据，因此 DCNN 层选用如图 2 所示的一维卷积神经网络层。
x(1) x(2)
x(S - 1) x(S)
1 前言
在现有的汽车底盘结构疲劳耐久分析流程中，为了获得整车的道路载荷谱，通常需要在项目开发早期开展整车道路耐久试验，该试验需要特制的试制样车、测量设备、试验场所以及数周的试验时间。随着控制成本和缩减开发周期的要求日益严格，道路试验成本高、周期长的问题更加突出，亟待解决。

基于小波神经网络的与文本无关说话人识别方法研究

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基于小波神经网络的数字信号调制方式识别

基于小波神经网络的数字信号调制方式识别梁晔;郝洁;石蕊【摘要】In view of the problem that the recognition method of digital signal modulation mode was easy to be affected by noise and the recognition error was large,we designed a recognition method of digital signal modulation mode based on wavelet neural network.Firstly,we collected digital signal and extracted the modulation recognition feature from the signal as the classification basis of the digital signal modulation mode.Secondly,we established classifier of digital signals modulation recognition based on neural network,and selected particle swarm optimization algorithm to determine the parameters of the neural network,so as to realize the digital signal modulation recognition. Finally,the simulation test of digital signals modulation recognition was realized on MATLAB 2016 platform.The test results show that,even if the signal-to-noise ratio of digital signal is low,the wavelet neural network can still obtain the ideal digital signal modulation recognition results,and the digital signal modulation recognition rate is higher than that of the contrast method,thus improving the performance of digital signal modulation recognition.%针对当前数字信号调制方式识别方法易受噪声影响、识别误差较大等问题,设计一种基于小波神经网络的数字信号调制方式识别方法.首先采集数字信号,并从信号中提取调制识别特征,作为数字信号调制方式分类依据;然后采用小波神经网络建立数字信号调制方式识别的分类器,并选择粒子群优化算法确定神经网络的参数,实现数字信号调制方式识别;最后在MATLAB 2016平台上实现数字信号调制方式识别的仿真测试.测试结果表明,即使数字信号的信噪比较低时,小波神经网络仍可获得较理想的数字信号调制方式识别结果,且数字信号调制方式识别率高于对比方法,从而提高了数字信号调制方式识别性能.【期刊名称】《吉林大学学报（理学版）》【年(卷),期】2018(056)002【总页数】7页(P382-388)【关键词】数字信号;调制方式;识别方法;神经网络;粒子群优化算法;分类器设计【作者】梁晔;郝洁;石蕊【作者单位】兰州城市学院电子与信息工程学院,兰州730070;西北民族大学电气工程学院,兰州730030;兰州城市学院电子与信息工程学院,兰州730070【正文语种】中文【中图分类】TP391.9在数字信号应用过程中, 信号的调制解调技术十分关键, 在数字信号进行解调时, 首先要知道数字信号的调制方式, 因此数字信号调制方式自动、快速准确识别的研究受到广泛关注[1-6].数字信号调制方式的识别最初采用人工方式实现, 首先通过具有相关知识的专业人员设置不同类型的解调器, 然后对接收到的数字信号进行变频处理, 将变频后的信号输入到解调器中, 最后结合自己的知识、波形以及声音得到数字信号调制方式. 该方法由于需要人工参与, 自动化程度低, 同时数字信号调制方式识别结果与专业人员自身知识密切相关, 导致数字信号调制方式识别正确率较低, 而且数字信号调制方式识别时间长, 无法满足数字信号发展的要求[7-8]. 随着数字信号和信息处理技术的不断完善, 目前已有许多新的数字信号调制方式自动识别方法, 如: 基于混沌理论的数字信号调制方式识别方法, 对数字信号进行混沌分析, 通过模式识别技术实现数字信号调制方式识别；基于星座图的数字信号调制方式识别方法；基于小波分析的数字信号调制方式识别方法; 基于高阶累积量的数字信号调制方式识别方法等. 这些方法在数字信号的信噪比较高时, 可获得较理想的数字信号调制方式识别结果[9-11], 但当信噪比减小时, 数字信号调制方式识别正确率急剧下降[12-13]. 文献[14-16]提出了基于BP神经网络的数字信号调制方式识别方法, 由于BP神经网络属于智能学习算法, 可对数字信号调制方式进行自动分类, 提高了数字信号调制方式的识别正确率, 但BP神经网络自身存在易陷入局部极小值等缺陷, 会对数字信号调制方式识别产生不利影响. 小波神经网络是小波理论和神经网络相结合的产物, 比其他神经网络具有更优的自组织、自学习和容错能力, 为数字信号调制方式识别的建模提供了一种新工具.针对目前数字信号调制方式识别方法存在正确率低等缺陷, 本文提出一种基于小波神经网络的数字信号调制方式识别方法. 首先从数字信号中提取调制方式识别的特征, 然后采用小波神经网络建立数字信号调制方式识别的分类器, 最后在MATLAB2016平台上实现数字信号调制方式识别的仿真测试. 实验结果验证了小波神经网络数字信号调制方式识别的有效性和优越性.1 小波神经网络的数字信号调制方式识别流程图1 数字信号调制方式的识别流程Fig.1 Identification process of digital signal modulation mode基于小波神经网络的数字信号调制方式识别方法工作流程可分为如下3个阶段：1) 采集数字信号, 并对信号进行预处理, 主要为信号的消噪处理;2) 提取数字信号调制方式识别的特征参数;3) 设计数字信号调制方式识别的分类器.基于小波神经网络的数字信号调制方式识别流程如图1所示.2 基于小波神经网络的数字信号调制方式识别方法设计2.1 数字信号的预处理设包含有噪声的数字信号为x(t)=s(t)+n(t), 其中s(t)和n(t)分别表示原始信号和噪声, 对x(t)进行变换可得wx(j,k)=ws(j,k)+wn(j,k), j=0,1,…,J; k=0,1,…,N,(1)其中: wm(j,k)(m=x,s,n)表示第j层上的不同信号变换系数； J表示分解层数； N 表示信号大小.由于n(t)的变换系数为wn(j,k), 因此数字信号去噪基本原理为：如果wn(j,k)小于某个固定值, 则表示其为噪声, 可以将其舍去；当wn(j,k)大于某个固定值时, 表示其为有用信号, 应该保留. 设去噪后的信号为本文选择软阈值进行去噪, 软阈值去噪函数定义为(2)其中sgn( )表示符号函数.2.2 提取数字信号的特征参数目前数字信号调制方式识别特征参数较多, 由于信号瞬时信息可更好描述数字信号调制方式的类型, 因此提取信号瞬时信息的6个特征参数:1) 数字信号幅度的标准差和均值分别为σa和u a, Rσa为两者的比值, 计算公式为(3)2) 数字信号的相位标准差和均值分别为σp和up, 其比值为Rσp, 计算公式为(4)3) A表示数字信号的零中心归一化瞬时幅度, 平均值M2的计算公式为(5)4) Af表示数字信号的零中心归一化瞬时频率,其中, af表示信号的瞬时频率; 均值MF1计算公式为(6)5) Af的归一化值为的均值MF2计算公式为(7)6) Af的相位为Ap, 均值MP1计算公式为(8)2.3 粒子群优化小波神经网络2.3.1 粒子群优化算法设粒子的位置和速度分别为Xi和Vi, 在解空间中, 粒子的位置更新通过不断跟踪自身最优解Pbest=(pi1,pi2,…,piD)和群体最优解Gbest=(pg1,pg2,…,pgD)实现, 计算公式为Vid=ω×Vid+c1×rand( )×(Pbest-xid)+c2×rand( )×(Gbest-xid),(9)Xid=Xid+Vid,(10)图2 小波神经网络结构Fig.2 Structure of wavelet neural network其中: rand( )表示随机数; d表示维数; c1和c2表示加速系数；ω表示权值.2.3.2 小波神经网络本文采用小波基函数代替隐含层激活函数产生小波神经网络, 通过小波神经网络对数字信号调制方式进行学习, 建立数字信号调制方式的分类器, 数字信号调制方式识别的小波神经网络结构如图2所示.小波函数可定义为(11)小波神经网络的隐含层第j个神经元的输入和输出分别为(12)其中：ωij表示输入层与隐含层间的连接权值；θj(k)表示隐含层的阈值. 小波神经网络的输出层第j个神经元的输入和输出分别为(14)(15)其中：ωjl表示隐含层与输出层间的连接权值；表示输出层的阈值. 通常情况下, 小波神经网络的激励函数定义为(16)小波神经网络的数字信号调制方式识别步骤如下:1) 采集数字信号, 并通过阈值法去除数字信号中的噪声;2) 从去除噪声的数字信号中提取信号瞬时信息的6个特征参数, 并做归一化处理(17)3) 根据信号瞬时信息的6个特征参数确定小波神经网络的拓扑结构, 并初始化小波神经网络相关参数;4) 确定粒子群的适应度函数, 将数字信号调制方式识别平均误差作为粒子群优化小波神经网络参数的适应函数值, 公式为(18)其中: di和tk分别表示数字信号调制方式识别类型和实际的数字信号调制方式; m 表示小波神经网络的输出节点数量； n表示数字信号调制方式的训练样本数量;5) 将数字信号调制方式识别的训练样本输入到小波神经网络进行学习, 并通过粒子群优化算法优化小波神经网络的权值和阈值;6) 根据新的粒子群适应度值对当前数字信号调制方式识别分类器参数最优解进行不断更新;7) 当找到数字信号调制方式识别分类器参数的最优解时, 粒子群算法寻优结束;8) 小波神经网络根据最优权值和阈值对数字信号调制方式识别的训练样本进行重新学习, 建立最优的数字信号调制方式识别分类器;9) 将待测试的数字信号调制方式识别样本输入到分类器中进行学习, 并输出该数字信号调制方式的类型.3 仿真测试3.1 测试环境为了分析小波神经网络的数字信号调制方式识别效果, 选择常用的7种数字调制信号作为测试对象, 仿真测试平台为MATLAB2016. 实验仿真参数设置如下: 载频为150 kHz, 采样频率为1 200 kHz, 码元速率为12 500 b/s, 采样点数为10 000; 神经网络输入层节点数为6, 神经网络的隐含层节点数为13, 神经网络输出层节点数为7; 粒子群优化算法迭代次数为100, 粒子群优化算法的粒子数为20, 粒子群优化算法的权值为0.95.3.2 结果与分析在数字信号的信噪比分别为0和20 dB条件下, 对7种不同类型的数字信号调制方式识别, 每种信号采集的样本数量均为20, 其中15个样本数量作为训练样本集, 用于建立数字信号调制方式识别的分类器, 剩余5个样本作为测试样本集, 采用基本小波神经网络和粒子群优化算法优化小波神经网络对样本进行学习和测试, 统计数字信号调制方式识别的最优目标函数值, 得到了基本小波神经网络和粒子群优化算法优化神经网络最优解对应的目标函数值变化曲线如图3所示. 由图3可见, 无论数字信号的信噪比为0或20 dB, 粒子群优化算法优化小波神经网络的最优适应度值均优于小波神经网络, 且加快了找到最优适应度值的速度, 表明采用粒子群优化算法搜索小波神经网络的连接权值和阈值可改善小波神经网络的性能.图3 不同信噪比条件下的适应度值变化曲线Fig.3 Change curves of fitness value under different signal-to-noise ratios当数字信号的信噪比为0～ 20 dB时, 采用本文数字信号调制方式识别方法对7种信号进行分类识别, 每种数字信号调制方式识别率列于表1. 由表1可见, 数字信号的信噪比越高, 数字信号调制方式识别率越高, 表明本文对原始数字信号进行去噪可获得高质量的数字信号, 能改善数字信号调制方式识别结果, 同时对于所有数字信号调制方式, 本文方法的平均识别均达90%以上, 识别率可满足数字信号处理应用85%的要求, 说明本文的数字信号调制方式识别方法是一种有效的、结果可靠的识别方法.表1 不同信噪比下的数字信号调制方式识别率(%)Table 1 Recognition rate (%)of digital signal modulation mode under different signal-to-noise ratios数字信号调制方式信噪比/dB051015202ASK91．1892．5896．4398．371004ASK89．4992．5995．3 396．3998．392FSK93．7291．4996．4597．211004FSK95．0593．8597．0197．9498．752PSK90．8093．4395．6098．101004PSK88．6893．6996．5396．5510016QAM91．8694．6896．6298．8998．95平均值91．5493．1996．2897．6499．44为表明本文提出的数字信号调制方式识别方法的优越性, 选择文献[17-18]中经典数字信号调制方式识别方法进行对比测试, 在相同的实验环境下, 数字信号的信噪比为0～ 20 dB时, 所有方法均进行10次独立的仿真实验, 统计其数字信号调制方式平均识别率和平均识别时间, 对比实验结果如图4所示.图4 与经典数字信号调制方式识别方法的性能对比Fig.4 Performance comparisons with classical methods of digital signal modulation recognition methods由图4可见:1) 在相同数字信号信噪比的条件下, 本文方法的数字信号调制方式平均识别率均高于文献[17]和文献[18]的数字信号调制方式识别方法, 这是由于本文算法通过小波神经网络建立了性能较优的数字信号调制方式识别分类器, 克服了当前数字信号调制方式识别方法错误率大、对噪声鲁棒性差等缺陷, 同时通过粒子群优化算法对小波神经网络的连接权值和阈值进行在线优化, 明显减少了数字信号调制方式识别误差, 提高了数字信号调制方式识别率;2) 在相同实验环境下, 本文方法的数字信号调制方式平均识别时间明显减少, 这是因为本文方法对原始数字信号进行了去噪处理, 抑制了噪声对数字信号调制方式建模的干扰, 提取了更优的数字信号调制方式识别特征, 简化了数字信号调制方式识别的分类器结果, 加快了数字信号调制方式识别速度, 具有更好的实用性.综上所述, 为了提高数字信号调制方式的识别和分类性能, 本文提出了一种基于神经网络的数字信号调制方式识别方法, 首先提取数字信号的瞬时特征, 并进行归一化处理作为神经网络的输入向量; 然后通过粒子群优化神经网络构建数字信号调制方式识别的分类器; 最后通过仿真测试结果表明, 无论是数字信号的信噪比高或低, 本文方法均可获得较理想的数字信号调制方式识别结果, 具有较强的抗噪性能.参考文献【相关文献】[1] Dobre O, Abid A, Bar-Ness Y, et al. Survey of Automatic Modulation Classification Techniques: Classical Approaches and New Trends [J]. IET Communieations, 2007, 21(2): 137-156.[2] WANG Jianghong, LI Bingbing, LIU Mingqian, et al. SNR Estimation of Time-Frequency Overlapped Signals for Underlay Cognitive Radio [J]. IEEE Communications Letters, 2015, 19(11): 1925-1928.[3] 徐闻, 王斌. 采用高阶累计量的时频混叠信号调制识别研究 [J]. 信息工程大学学报, 2013, 14(3): 299-305. (XU Wen, WANG Bin. Method of Modulation Recognition of Time-Frequency Overlapped Signals Based on High-Order Cumulants [J]. Journal of Information Engineering University, 2013, 14(3): 299-305.)[4] 孙运全, 孙玉坤, 杨泽斌, 等. 数字信号处理技术在馈线自动化终端中的应用 [J]. 江苏大学学报(自然科学版), 2004, 25(2)： 160-163. (SUN Yunquan, SUN Yukun, YANG Zebin, et al. Application of Digital Signal Processor in Feeder-Terminal-Unit [J]. Journal of Jiangsu University (Natural Science Edition), 2004, 25(2)： 160-163.)[5] 高建勤, 熊淑华, 赵婧. 一种基于小波的数字调制信号识别算法 [J]. 四川大学学报(自然科学版), 2007, 44(6): 1281-1284. (GAO Jianqin, XIONG Shuhua, ZHAO Jing. A Wavelet-Based Identification Algorithm of Digital Modulation Signals [J]. Journal of Sichuan University (Natural Science Edition), 2007, 44(6): 1281-1284.)[6] 李强, 明艳, 吴坤君. 基于MATLAB的《数字信号处理》辅助教学方法 [J]. 重庆邮电大学学报(自然科学版), 2007(增刊): 89-91. (Ll Qiang, MING Yan, WU Kunjun. DS Passistant Teaching Methods Based on MATLAB [J]. Journal of Chongqing University of Posts andTelecommunications (Natural Science Edition), 2007(Suppl): 89-91.)[7] 王兰勋, 孟祥雅, 佟婧丽. 基于循环谱和稀疏表示的多信号调制识别 [J]. 电视技术, 2015, 39(1): 92-95. (WANG Lanxun, MENG Xiangya, TONG Jingli. Multi-signals Modulation Recognition Based on Cyclic Spectrum and Sparse Representation [J]. Video Engineering, 2015, 39(1): 92-95.)[8] 赵雄文, 郭春霞, 李景春. 基于高阶累积量和循环谱的信号调制方式混合识别算法 [J]. 电子与信息学报, 2016, 38(3): 674-680. (ZHAO Xiongwen, GUO Chunxia, LI Jingchun. Mixed Recognition Algorithm for Signal Modulation Schemes by High-Order Cumulates and Cyclic Spectrum [J]. 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Recognition Algorithm of Wireless Communication Signal Modulation Based on Harmonic Mean Fractal Box Dimension [J]. Journal of Jiangsu University (Natural Science Edition), 2017, 38(3): 308-312.)[13] 杨伟超, 杨新权. Alpha稳定分布噪声下卫星双信号调制识别 [J]. 应用科学学报, 2017, 35(3): 309-316. (YANG Weichao, YANG Xinquan. Modulation Recognition of Double Satellite Signals in Alpha-Stable Distribution Noise [J]. Journal of Applied Sciences-Electronics and Information Engineering, 2017, 35(3): 309-316.)[14] 张洋, 彭华. 单通道混合信号调制识别 [J]. 信息工程大学学报, 2016, 17(6): 662-668. (ZHANG Yang, PENG Hua. Modulation Recognition for Mixed Signals in Single Channel [J]. Journal of Information Engineering University, 2016, 17(6): 662-668.)[15] 赵自璐, 王世练, 张炜, 等. 水下冲激噪声环境下基于多特征融合的信号调制方式识别 [J]. 厦门大学学报(自然科学版), 2017, 56(3): 416-422. (ZHAO Zilu, WANG Shilian, ZHANG Wei, et al. Classification of Signal Modulation Types Based on Multi-features Fusion in Impulse NoiseUnderwater [J]. 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211216626_小波变换和CNN_涡旋压缩机故障诊断

引用格式：苏莹莹, 毛海旭. 小波变换和CNN 涡旋压缩机故障诊断[J]. 中国测试，2023, 49(4): 92-97. SU Yingying, MAO Haixu.Fault diagnosis of scroll compressor based on wavelet transform and CNN[J]. China Measurement & Test, 2023, 49(4): 92-97. DOI :10.11857/j.issn.1674-5124.2021070062小波变换和CNN 涡旋压缩机故障诊断苏莹莹，毛海旭(沈阳大学机械工程学院，辽宁沈阳 110000)摘　要: 针对传统单尺度信号分析难以有效解决涡旋压缩机故障诊断中的故障特征信息多尺度耦合问题，提出一种基于小波变换和卷积神经网络的涡旋压缩机故障诊断方法。

首先将采集到的振动信号进行连续小波变换生成时频图，并对时频图进行网格化规范处理，将预处理后的时频图作为特征图输入Alexnet 卷积神经网络，通过不断调节网络参数，得出最为理想的神经网络模型，以此实现对涡旋压缩机故障类型的辨识诊断。

结果表明，该方法针对涡旋压缩机故障类型的识别准确率达到94.6%，与传统多尺度排列熵、信息熵熵距的故障诊断方法相比，该故障识别方法具有更高的准确率。

关键词: 故障诊断; 振动信号; 小波变换; 卷积神经网络中图分类号: U226.8+1;TB9文献标志码: A文章编号: 1674–5124(2023)04–0092–06Fault diagnosis of scroll compressor based on wavelet transform and CNNSU Yingying, MAO Haixu(School of Mechanical Engineering, Shenyang University, Shenyang 110000, China)Abstract : In order to solve the problem that traditional single-scale signal analysis is difficult to effectively solve the problem of multi-scale coupling of fault feature information in the fault diagnosis of scroll compressors, a fault diagnosis method based on wavelet transform and convolutional neural network(CNN) is proposed. Firstly, the collected vibration signal is analyzed by continuous wavelet transform to generate time-frequency diagram. And the generated time-frequency diagram is gridded and normalized. Then, it has to be inputtd to Alexnet convolutional neural network, and the network parameters are adjusted to obtain the most ideal network model, so as to realize the identification and diagnosis fault types of scroll compressors. The results show that the recognition accuracy reaches 94.6%, with higher accuracy than the traditional methods of multi-scale permutation entropy and distance of the information entropy.Keywords : fault diagnosis; vibration signal; wavelet transform; convolutional neural networks0 引　言涡旋压缩机因为其体积小、集成度高、运行稳定、噪声低等优点，在工业、农业、交通运输等众多领域广泛应用。

基于脉冲神经网络的类脑计算

基于脉冲神经网络的类脑计算脉冲神经网络（Spiking Neural Networks，SNNs）是一种类似于人脑的计算模型，它模拟了大脑中神经元之间的信息传递方式。

与传统的神经网络不同，SNNs使用脉冲信号来表示神经元的活动状态，这种离散的时间编码和传输方式更加符合生物神经系统的特性。

在SNNs中，每个神经元都有一个内部状态，被称为膜电位。

当膜电位超过一定阈值时，神经元会发出一个脉冲，该脉冲会通过突触传递给其他神经元。

这种脉冲的传递方式使得SNNs能够更加高效地处理和传递信息。

类脑计算是一种模拟和仿真人脑神经网络的计算模型，旨在实现大规模的并行计算和高能效的信息处理。

在类脑计算中，SNNs被广泛应用于模式识别、机器学习和智能控制等领域。

与传统的计算模型相比，SNNs 在模拟大脑认知过程方面具有独特的优势。

首先，SNNs能够更好地处理时序信息。

由于脉冲的传递方式是离散的，SNNs能够对时间精确进行编码和处理，从而更好地适应动态环境和任务需求。

这使得SNNs在处理语音识别、视频分析等需要考虑时序关系的任务中具有较大优势。

其次，SNNs具有较高的能效。

由于脉冲的传递方式更接近生物神经网络的工作原理，SNNs相对于传统的人工神经网络具有较低的能耗。

这使得SNNs在计算资源有限或功耗敏感的环境中具有更好的应用潜力。

另外，SNNs具有较好的可塑性和学习能力。

生物神经网络中的突触连接可以根据输入信号的重要性进行动态调整和改变。

类脑计算中的SNNs通过调整突触连接权重来模拟这种可塑性和学习能力，从而实现适应性和自适应性的信息处理。

尽管SNNs在类脑计算中具有很多优势，但仍然存在一些挑战和问题。

首先，SNNs的训练和优化方法相对较为复杂。

由于脉冲神经网络具有非线性和离散的特性，传统的梯度下降等优化算法不再适用。

因此，如何高效地训练和优化SNNs仍然是一个研究的热点问题。

其次，SNNs的实现和硬件支持较为困难。

尽管现有的计算硬件可以实现SNNs，但与传统的神经网络相比，SNNs的实现和硬件要求相对较高。

一种新的部分神经进化网络的股票预测(英文)

一种新的部分神经进化网络的股票预测(英文)一种新的部分神经进化网络的股票预测自从股票市场的出现以来，人们一直在寻求能够提前预测股票走势的方法。

许多投资者和研究人员尝试使用各种技术分析工具和模型来预测股票未来的走势，但是股票市场的复杂性和难以预测性使得这变得困难重重。

因此，寻找一种能够准确预测股票走势的方法一直是金融界的热点问题。

近年来，人工智能技术在金融领域的应用日益增多。

其中，神经网络是一种被广泛使用的工具，它可以自动学习和识别模式，并根据所学的模式进行预测。

然而，传统神经网络在预测股票市场方面存在诸多问题，例如过拟合和难以处理大量数据等。

为了克服这些问题，本文提出了一种新的部分神经进化网络（Partial Neural Evolving Network, PNEN）模型来预测股票走势。

PNEN模型将神经网络和进化算法相结合，通过优化和训练来实现更准确的预测结果。

PNEN模型的核心思想是将神经网络的隐藏层拆分为多个小模块，每个小模块只负责处理一部分输入数据。

通过这种方式，模型可以更好地适应不同的市场情况和模式。

同时，采用进化算法来优化模型的参数，可以进一步提高模型的预测性能。

具体而言，PNEN模型包括以下几个步骤：1. 数据准备：从股票市场获取历史交易数据，并对数据进行预处理和归一化处理，以便更好地输入到模型中。

2. 构建模型结构：将神经网络的隐藏层拆分为多个小模块，通过进化算法来确定每个小模块的结构和参数。

进化算法通过优化模型的准确性和稳定性，以获得更好的预测结果。

3. 训练模型：使用历史数据集对模型进行训练，并通过反向传播算法来更新模型的权重和偏置。

同时，通过与进化算法的交互，不断调整模型结构和参数。

4. 预测结果：使用训练好的模型对未来的股票走势进行预测。

通过模型对市场的分析和判断，可以为投资者提供决策参考。

为了验证PNEN模型的效果，我们在实际的股票市场数据上进行了实验。

结果表明，与传统神经网络模型相比，PNEN 模型在预测股票走势方面具有更好的准确性和稳定性。

长短时记忆脉冲神经网络手语识别模型

长短时记忆脉冲神经网络手语识别模型手语是一种特殊的沟通方式，用手势和表情传递信息。

在社交和日常生活中，手语在聋哑人群体中发挥着关键作用。

然而，手语的理解和交流仍然是一个挑战，特别是对于计算机来说。

为了解决手语识别的问题，研究人员提出了许多不同的方法和技术。

其中一种被广泛应用的模型是长短时记忆脉冲神经网络（LSTM-PCNN）。

这种模型结合了长短时记忆网络（LSTM）和脉冲神经网络（PCNN）的优势，提高了手语识别的准确性和效率。

LSTM-PCNN模型的工作原理如下：首先，输入的手语图像被转换为一系列的帧。

每一帧都包含一个手势的静态图像。

然后，这些静态图像通过LSTM网络进行处理。

LSTM网络具有记忆单元，可以捕获时间序列信息。

通过这种方式，模型能够理解手语动作的连续性和上下文信息。

接下来，经过LSTM网络处理后的特征被传递给PCNN网络进行进一步处理。

PCNN网络是一种专门为脉冲信号设计的神经网络。

它通过脉冲信号传递和处理信息，模拟了人类神经系统的工作原理。

PCNN网络能够识别和提取手语动作中的关键特征，从而更好地区分不同的手势。

最后，PCNN网络的输出被送入分类器进行手语的识别。

分类器可以是传统的机器学习算法，如支持向量机（SVM），也可以是深度学习算法，如卷积神经网络（CNN）。

分类器根据PCNN网络提取的特征，判断输入的手语属于哪一类。

通过LSTM-PCNN模型，手语识别的准确性得到了显著提高。

模型能够准确捕捉手语的时间序列信息和上下文信息，同时提取关键特征进行分类。

相比传统的方法，LSTM-PCNN模型具有更好的性能和稳定性。

然而，LSTM-PCNN模型也存在一些挑战和改进空间。

首先，模型对于手语图像的质量和光照条件较为敏感，需要进一步优化和改进。

其次，对于复杂和细微的手势动作，模型的识别精度有待提高。

此外，模型的计算复杂度较高，需要更高效的算法和硬件支持。

综上所述，长短时记忆脉冲神经网络手语识别模型是一种有效的手语识别方法。

基于小波神经网络的人脸识别算法

Value Engineering 0引言利用计算机技术对人脸图像进行分析，提取出图像中的有效特征，从能够达到判别人的身份的目的，这种技术被称之为人脸识别技术。

常见的人脸识别技术有三大类，分别是基于代数特征的识别技术、基于几何特征的识别技术以及基于神经网络的识别技术。

其中基于神经网络的人脸识别技术是经过神经网络的训练，从而获得识别函数，最终能够对人脸进行识别。

针对人脸识别的特征，可以利用小波神经网络实现对人脸的识别。

将小波分析理论和人工神经网络相结合可以构造成小波神经网络，目前已经有了非常广泛的应用，比如，系统辨识、参数估计以及信号处理等。

小波神经网络的收敛性和小波函数的平移系数和伸缩系数关系密切，为了能够防止这个缺陷，可以利用梯度下降法以及递推最小二乘法对小波神经网络进行改进，进而能够得到全局最优解，提高人脸识别的准确性。

1人脸图像的预处理技术人脸图像的识别效果和以下一些影响因素有关，比如：采集设备的噪声、采集环境的光照、图像的高维度以及图像的背景等。

因此，在人脸图像识别以前，必须进行预处理。

人脸图像的归一化处理，一方面可以把不同尺寸的图像处理为相同尺寸的图像，并且将图像背景等因素的影响消除，从而能够确保人脸图像清晰度，主要包括对人脸图像的旋转操作、剪切操作等。

另外一方面，可以对人脸图像进行统一的灰度处理，从而能够使人脸图像灰度处于比较大的范围内，并且能够消除光照的影响。

可以利用直方图均衡化来进行有效的灰度处理。

2小波神经网络的理论概述小波神经网络属于一种前馈型神经网络，具有连接型的结构，小波神经网络的基本思想是以小波函数作为基函数，小波函数的伸缩系数以及平移系数分别对应着小波神经网络中从输入层到隐含层的权值系数和隐含层的阀值。

小波神经网络的基本结构如图1所示。

小波神经网络的理论数学公式如下所示：Y i =f i （X ）=l j=1Σωij Φj m k=1Σb jk x k -r j ΣΣ（1）式中，X 代表了小波神经网络的输入向量，对应的形式如下所示：X=[X 1，X 2，X 3，…，X m ]；Y 代表了小波神经网络的输出向量，对应的形式如下所示：Y=[Y 1，Y 2，Y 3，…，Y n ]；ωij 代表了小波神经网络中从节点i 到节点j 的权重；Φj 代表了小波神经网络隐含层节点j 对应的小波函数；b jk 代表了小波神经网络中小波基函数的伸缩系数；r j 表示小波神经网络中小波基函数的平移系数；l 、m 、n 分别代表了小波神经网络的隐层节点的个数、输入节点的个数以及输出节点的个数。

基于脉冲神经网络的运动想象脑机接口分类研究

基于脉冲神经网络的运动想象脑机接口分类研究近年来，脑机接口技术（Brain-Computer Interface，BCI）在医学和神经科学领域取得了显著的进展。

其中，运动想象脑机接口是一种利用脑电图（Electroencephalogram，EEG）信号实现人类运动想象控制外部设备的技术。

然而，由于脑电信号的特点和复杂性，如何准确地识别运动想象脑电信号成为了研究的热点。

近年来，脉冲神经网络（Spiking Neural Network，SNN）作为一种新型的神经网络模型，逐渐引起了研究者的关注。

不同于传统的神经网络模型，SNN模拟了神经元真实的脉冲放电行为，能够更加准确地模拟脑电信号的时序特性。

基于此，研究者们开始探索基于脉冲神经网络的运动想象脑机接口分类方法。

这项研究的目的是通过构建一个基于SNN的分类器，实现对运动想象脑电信号的准确分类。

首先，研究者采集了一组参与者的运动想象脑电信号数据，并对其进行了预处理。

然后，利用SNN模型对预处理后的脑电信号进行训练和分类。

在训练过程中，研究者通过调整SNN模型的参数，优化分类器的性能。

实验结果表明，基于脉冲神经网络的运动想象脑机接口分类方法在准确性和稳定性上均取得了显著的改进。

与传统的分类方法相比，基于SNN的分类器能够更好地捕捉脑电信号的时序特性，提高了分类的准确率。

此外，该方法对于不同参与者之间的差异具有较好的适应性，具有较强的稳定性。

基于脉冲神经网络的运动想象脑机接口分类研究为脑机接口技术的发展提供了新的思路和方法。

通过更加准确地识别和分类运动想象脑电信号，将为运动康复和残疾人辅助等领域的实际应用提供更多可能性。

然而，该研究仍存在一些局限性，例如对SNN模型的参数调整和脑电信号预处理等方面的进一步优化仍需深入研究。

未来，我们有理由相信基于脉冲神经网络的运动想象脑机接口分类研究将在脑机接口技术领域发挥重要作用，并为人类生活带来更多便利和改善。

基于深度卷积网络的运动想象脑电信号分类方法

基于深度卷积网络的运动想象脑电信号分类方法ClassificaPi os MePhod of MoPor Imagery EEG Sig sals Based os Deep Cos v oluPi onal NePwork 赵龙辉李力陈奕辉林诗柔（广东工业大学自动化学院，广东广州510006）摘要：为了提高多分类运动想象脑电信号的解码精度,以此促进脑机接口系统在生产生活中的应用。

采用基于深度卷积网络的LaNat和AlaxNat模型分析四分类运动想象脑电特性。

将脑电信号通过预处理、数据归一化和数据增强，然后分别输入两个模型中进行分类遥通过与现有不同的特征提取和分类方法对比,实验结果表明,在多分类运动想象脑电解码研究领域中，深度卷积网络模型取得的分类效果较好。

关键词:脑机接口；运动想象；深度卷积网络;脑电分类Abstract:In order to occurately extract pnd classify the EEG features of motor imagination,so os to promote th^application of the brain-computer interface system in production and life.The LeNet pnd AlexNet models based on deep convolutional networks sre used to onalyze the four-category motor imagery EEG characteristics in this paper.The EEG signals sre preprocessed,data normalized and data enhanced,and then input into two models for classification.By comparing with the existing different feature extraction and classification methods,the experimental results show that the deep convolutional network model lchieves better classification results in the field of multi-class motor imaging EEG decoding research.Keywords:brain-computer interface,motor imagination,deep convolutional network,EEG classification脑-(计算机)机接口(Brain-computar Intarfaca,BCI)可以简单定义为提供大脑控制外部设备以实现通信或控制的一个系统[1]O BCI有显著的潜力可以帮人们替代或恢复由疾病或伤害而受损的功能。