ANN-based modelling and estimation of daily global solar
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名词解释中英文对比<using_information_sources> social networks 社会网络abductive reasoning 溯因推理action recognition(行为识别)active learning(主动学习)adaptive systems 自适应系统adverse drugs reactions(药物不良反应)algorithm design and analysis(算法设计与分析) algorithm(算法)artificial intelligence 人工智能association rule(关联规则)attribute value taxonomy 属性分类规范automomous agent 自动代理automomous systems 自动系统background knowledge 背景知识bayes methods(贝叶斯方法)bayesian inference(贝叶斯推断)bayesian methods(bayes 方法)belief propagation(置信传播)better understanding 内涵理解big data 大数据big data(大数据)biological network(生物网络)biological sciences(生物科学)biomedical domain 生物医学领域biomedical research(生物医学研究)biomedical text(生物医学文本)boltzmann machine(玻尔兹曼机)bootstrapping method 拔靴法case based reasoning 实例推理causual models 因果模型citation matching (引文匹配)classification (分类)classification algorithms(分类算法)clistering algorithms 聚类算法cloud computing(云计算)cluster-based retrieval (聚类检索)clustering (聚类)clustering algorithms(聚类算法)clustering 聚类cognitive science 认知科学collaborative filtering (协同过滤)collaborative filtering(协同过滤)collabrative ontology development 联合本体开发collabrative ontology engineering 联合本体工程commonsense knowledge 常识communication networks(通讯网络)community detection(社区发现)complex data(复杂数据)complex dynamical networks(复杂动态网络)complex network(复杂网络)complex network(复杂网络)computational biology 计算生物学computational biology(计算生物学)computational complexity(计算复杂性) computational intelligence 智能计算computational modeling(计算模型)computer animation(计算机动画)computer networks(计算机网络)computer science 计算机科学concept clustering 概念聚类concept formation 概念形成concept learning 概念学习concept map 概念图concept model 概念模型concept modelling 概念模型conceptual model 概念模型conditional random field(条件随机场模型) conjunctive quries 合取查询constrained least squares (约束最小二乘) convex programming(凸规划)convolutional neural networks(卷积神经网络) customer relationship management(客户关系管理) data analysis(数据分析)data analysis(数据分析)data center(数据中心)data clustering (数据聚类)data compression(数据压缩)data envelopment analysis (数据包络分析)data fusion 数据融合data generation(数据生成)data handling(数据处理)data hierarchy (数据层次)data integration(数据整合)data integrity 数据完整性data intensive computing(数据密集型计算)data management 数据管理data management(数据管理)data management(数据管理)data miningdata mining 数据挖掘data model 数据模型data models(数据模型)data partitioning 数据划分data point(数据点)data privacy(数据隐私)data security(数据安全)data stream(数据流)data streams(数据流)data structure( 数据结构)data structure(数据结构)data visualisation(数据可视化)data visualization 数据可视化data visualization(数据可视化)data warehouse(数据仓库)data warehouses(数据仓库)data warehousing(数据仓库)database management systems(数据库管理系统)database management(数据库管理)date interlinking 日期互联date linking 日期链接Decision analysis(决策分析)decision maker 决策者decision making (决策)decision models 决策模型decision models 决策模型decision rule 决策规则decision support system 决策支持系统decision support systems (决策支持系统) decision tree(决策树)decission tree 决策树deep belief network(深度信念网络)deep learning(深度学习)defult reasoning 默认推理density estimation(密度估计)design methodology 设计方法论dimension reduction(降维) dimensionality reduction(降维)directed graph(有向图)disaster management 灾害管理disastrous event(灾难性事件)discovery(知识发现)dissimilarity (相异性)distributed databases 分布式数据库distributed databases(分布式数据库) distributed query 分布式查询document clustering (文档聚类)domain experts 领域专家domain knowledge 领域知识domain specific language 领域专用语言dynamic databases(动态数据库)dynamic logic 动态逻辑dynamic network(动态网络)dynamic system(动态系统)earth mover's distance(EMD 距离) education 教育efficient algorithm(有效算法)electric commerce 电子商务electronic health records(电子健康档案) entity disambiguation 实体消歧entity recognition 实体识别entity recognition(实体识别)entity resolution 实体解析event detection 事件检测event detection(事件检测)event extraction 事件抽取event identificaton 事件识别exhaustive indexing 完整索引expert system 专家系统expert systems(专家系统)explanation based learning 解释学习factor graph(因子图)feature extraction 特征提取feature extraction(特征提取)feature extraction(特征提取)feature selection (特征选择)feature selection 特征选择feature selection(特征选择)feature space 特征空间first order logic 一阶逻辑formal logic 形式逻辑formal meaning prepresentation 形式意义表示formal semantics 形式语义formal specification 形式描述frame based system 框为本的系统frequent itemsets(频繁项目集)frequent pattern(频繁模式)fuzzy clustering (模糊聚类)fuzzy clustering (模糊聚类)fuzzy clustering (模糊聚类)fuzzy data mining(模糊数据挖掘)fuzzy logic 模糊逻辑fuzzy set theory(模糊集合论)fuzzy set(模糊集)fuzzy sets 模糊集合fuzzy systems 模糊系统gaussian processes(高斯过程)gene expression data 基因表达数据gene expression(基因表达)generative model(生成模型)generative model(生成模型)genetic algorithm 遗传算法genome wide association study(全基因组关联分析) graph classification(图分类)graph classification(图分类)graph clustering(图聚类)graph data(图数据)graph data(图形数据)graph database 图数据库graph database(图数据库)graph mining(图挖掘)graph mining(图挖掘)graph partitioning 图划分graph query 图查询graph structure(图结构)graph theory(图论)graph theory(图论)graph theory(图论)graph theroy 图论graph visualization(图形可视化)graphical user interface 图形用户界面graphical user interfaces(图形用户界面)health care 卫生保健health care(卫生保健)heterogeneous data source 异构数据源heterogeneous data(异构数据)heterogeneous database 异构数据库heterogeneous information network(异构信息网络) heterogeneous network(异构网络)heterogenous ontology 异构本体heuristic rule 启发式规则hidden markov model(隐马尔可夫模型)hidden markov model(隐马尔可夫模型)hidden markov models(隐马尔可夫模型) hierarchical clustering (层次聚类) homogeneous network(同构网络)human centered computing 人机交互技术human computer interaction 人机交互human interaction 人机交互human robot interaction 人机交互image classification(图像分类)image clustering (图像聚类)image mining( 图像挖掘)image reconstruction(图像重建)image retrieval (图像检索)image segmentation(图像分割)inconsistent ontology 本体不一致incremental learning(增量学习)inductive learning (归纳学习)inference mechanisms 推理机制inference mechanisms(推理机制)inference rule 推理规则information cascades(信息追随)information diffusion(信息扩散)information extraction 信息提取information filtering(信息过滤)information filtering(信息过滤)information integration(信息集成)information network analysis(信息网络分析) information network mining(信息网络挖掘) information network(信息网络)information processing 信息处理information processing 信息处理information resource management (信息资源管理) information retrieval models(信息检索模型) information retrieval 信息检索information retrieval(信息检索)information retrieval(信息检索)information science 情报科学information sources 信息源information system( 信息系统)information system(信息系统)information technology(信息技术)information visualization(信息可视化)instance matching 实例匹配intelligent assistant 智能辅助intelligent systems 智能系统interaction network(交互网络)interactive visualization(交互式可视化)kernel function(核函数)kernel operator (核算子)keyword search(关键字检索)knowledege reuse 知识再利用knowledgeknowledgeknowledge acquisitionknowledge base 知识库knowledge based system 知识系统knowledge building 知识建构knowledge capture 知识获取knowledge construction 知识建构knowledge discovery(知识发现)knowledge extraction 知识提取knowledge fusion 知识融合knowledge integrationknowledge management systems 知识管理系统knowledge management 知识管理knowledge management(知识管理)knowledge model 知识模型knowledge reasoningknowledge representationknowledge representation(知识表达) knowledge sharing 知识共享knowledge storageknowledge technology 知识技术knowledge verification 知识验证language model(语言模型)language modeling approach(语言模型方法) large graph(大图)large graph(大图)learning(无监督学习)life science 生命科学linear programming(线性规划)link analysis (链接分析)link prediction(链接预测)link prediction(链接预测)link prediction(链接预测)linked data(关联数据)location based service(基于位置的服务) loclation based services(基于位置的服务) logic programming 逻辑编程logical implication 逻辑蕴涵logistic regression(logistic 回归)machine learning 机器学习machine translation(机器翻译)management system(管理系统)management( 知识管理)manifold learning(流形学习)markov chains 马尔可夫链markov processes(马尔可夫过程)matching function 匹配函数matrix decomposition(矩阵分解)matrix decomposition(矩阵分解)maximum likelihood estimation(最大似然估计)medical research(医学研究)mixture of gaussians(混合高斯模型)mobile computing(移动计算)multi agnet systems 多智能体系统multiagent systems 多智能体系统multimedia 多媒体natural language processing 自然语言处理natural language processing(自然语言处理) nearest neighbor (近邻)network analysis( 网络分析)network analysis(网络分析)network analysis(网络分析)network formation(组网)network structure(网络结构)network theory(网络理论)network topology(网络拓扑)network visualization(网络可视化)neural network(神经网络)neural networks (神经网络)neural networks(神经网络)nonlinear dynamics(非线性动力学)nonmonotonic reasoning 非单调推理nonnegative matrix factorization (非负矩阵分解) nonnegative matrix factorization(非负矩阵分解) object detection(目标检测)object oriented 面向对象object recognition(目标识别)object recognition(目标识别)online community(网络社区)online social network(在线社交网络)online social networks(在线社交网络)ontology alignment 本体映射ontology development 本体开发ontology engineering 本体工程ontology evolution 本体演化ontology extraction 本体抽取ontology interoperablity 互用性本体ontology language 本体语言ontology mapping 本体映射ontology matching 本体匹配ontology versioning 本体版本ontology 本体论open government data 政府公开数据opinion analysis(舆情分析)opinion mining(意见挖掘)opinion mining(意见挖掘)outlier detection(孤立点检测)parallel processing(并行处理)patient care(病人医疗护理)pattern classification(模式分类)pattern matching(模式匹配)pattern mining(模式挖掘)pattern recognition 模式识别pattern recognition(模式识别)pattern recognition(模式识别)personal data(个人数据)prediction algorithms(预测算法)predictive model 预测模型predictive models(预测模型)privacy preservation(隐私保护)probabilistic logic(概率逻辑)probabilistic logic(概率逻辑)probabilistic model(概率模型)probabilistic model(概率模型)probability distribution(概率分布)probability distribution(概率分布)project management(项目管理)pruning technique(修剪技术)quality management 质量管理query expansion(查询扩展)query language 查询语言query language(查询语言)query processing(查询处理)query rewrite 查询重写question answering system 问答系统random forest(随机森林)random graph(随机图)random processes(随机过程)random walk(随机游走)range query(范围查询)RDF database 资源描述框架数据库RDF query 资源描述框架查询RDF repository 资源描述框架存储库RDF storge 资源描述框架存储real time(实时)recommender system(推荐系统)recommender system(推荐系统)recommender systems 推荐系统recommender systems(推荐系统)record linkage 记录链接recurrent neural network(递归神经网络) regression(回归)reinforcement learning 强化学习reinforcement learning(强化学习)relation extraction 关系抽取relational database 关系数据库relational learning 关系学习relevance feedback (相关反馈)resource description framework 资源描述框架restricted boltzmann machines(受限玻尔兹曼机) retrieval models(检索模型)rough set theroy 粗糙集理论rough set 粗糙集rule based system 基于规则系统rule based 基于规则rule induction (规则归纳)rule learning (规则学习)rule learning 规则学习schema mapping 模式映射schema matching 模式匹配scientific domain 科学域search problems(搜索问题)semantic (web) technology 语义技术semantic analysis 语义分析semantic annotation 语义标注semantic computing 语义计算semantic integration 语义集成semantic interpretation 语义解释semantic model 语义模型semantic network 语义网络semantic relatedness 语义相关性semantic relation learning 语义关系学习semantic search 语义检索semantic similarity 语义相似度semantic similarity(语义相似度)semantic web rule language 语义网规则语言semantic web 语义网semantic web(语义网)semantic workflow 语义工作流semi supervised learning(半监督学习)sensor data(传感器数据)sensor networks(传感器网络)sentiment analysis(情感分析)sentiment analysis(情感分析)sequential pattern(序列模式)service oriented architecture 面向服务的体系结构shortest path(最短路径)similar kernel function(相似核函数)similarity measure(相似性度量)similarity relationship (相似关系)similarity search(相似搜索)similarity(相似性)situation aware 情境感知social behavior(社交行为)social influence(社会影响)social interaction(社交互动)social interaction(社交互动)social learning(社会学习)social life networks(社交生活网络)social machine 社交机器social media(社交媒体)social media(社交媒体)social media(社交媒体)social network analysis 社会网络分析social network analysis(社交网络分析)social network(社交网络)social network(社交网络)social science(社会科学)social tagging system(社交标签系统)social tagging(社交标签)social web(社交网页)sparse coding(稀疏编码)sparse matrices(稀疏矩阵)sparse representation(稀疏表示)spatial database(空间数据库)spatial reasoning 空间推理statistical analysis(统计分析)statistical model 统计模型string matching(串匹配)structural risk minimization (结构风险最小化) structured data 结构化数据subgraph matching 子图匹配subspace clustering(子空间聚类)supervised learning( 有support vector machine 支持向量机support vector machines(支持向量机)system dynamics(系统动力学)tag recommendation(标签推荐)taxonmy induction 感应规范temporal logic 时态逻辑temporal reasoning 时序推理text analysis(文本分析)text anaylsis 文本分析text classification (文本分类)text data(文本数据)text mining technique(文本挖掘技术)text mining 文本挖掘text mining(文本挖掘)text summarization(文本摘要)thesaurus alignment 同义对齐time frequency analysis(时频分析)time series analysis( 时time series data(时间序列数据)time series data(时间序列数据)time series(时间序列)topic model(主题模型)topic modeling(主题模型)transfer learning 迁移学习triple store 三元组存储uncertainty reasoning 不精确推理undirected graph(无向图)unified modeling language 统一建模语言unsupervisedupper bound(上界)user behavior(用户行为)user generated content(用户生成内容)utility mining(效用挖掘)visual analytics(可视化分析)visual content(视觉内容)visual representation(视觉表征)visualisation(可视化)visualization technique(可视化技术) visualization tool(可视化工具)web 2.0(网络2.0)web forum(web 论坛)web mining(网络挖掘)web of data 数据网web ontology lanuage 网络本体语言web pages(web 页面)web resource 网络资源web science 万维科学web search (网络检索)web usage mining(web 使用挖掘)wireless networks 无线网络world knowledge 世界知识world wide web 万维网world wide web(万维网)xml database 可扩展标志语言数据库附录 2 Data Mining 知识图谱(共包含二级节点15 个,三级节点93 个)间序列分析)监督学习)领域 二级分类 三级分类。
Package‘dccmidas’October13,2022Type PackageTitle DCC Models with GARCH-MIDAS Specifications in the UnivariateStepVersion0.1.0Description Estimates a variety of Dynamic Conditional Correlation(DCC)models.More in de-tail,the'dccmidas'package allows the estimation of the cor-rected DCC(cDCC)of Aielli(2013)<doi:10.1080/07350015.2013.771027>,the DCC-MIDAS of Colacito et al.(2011)<doi:10.1016/j.jeconom.2011.02.013>,the Asymmet-ric DCC of Cappiello et al.<doi:10.1093/jjfinec/nbl005>,and the Dynamic Equicorrela-tion(DECO)of Engle and Kelly(2012)<doi:10.1080/07350015.2011.652048>.'dccmidas'of-fers the possibility of including standard GARCH<doi:10.1016/0304-4076(86)90063-1>,GARCH-MIDAS<doi:10.1162/REST_a_00300>and Double Asymmetric GARCH-MIDAS<doi:10.1016/j.econmod.2018.07.025>models in the univariate estimation.Fi-nally,the package calculates also the var-cov matrix under two non-parametric models:the Mov-ing Covariance and the RiskMetrics specifications.License GPL-3LinkingTo Rcpp,RcppArmadilloEncoding UTF-8LazyData trueRoxygenNote7.1.1RdMacros RdpackDepends R(>=4.0.0)Imports Rcpp(>=1.0.5),maxLik(>=1.3-8),rumidas(>=0.1.1),rugarch(>=1.4-4),roll(>=1.1.4),xts(>=0.12.0),tseries(>=0.10.47),Rdpack(>=1.0.0),lubridate(>=1.7.9),zoo(>=1.8.8),stats(>=4.0.2),utils(>=4.0.2)Suggests knitr,rmarkdownNeedsCompilation yesAuthor Vincenzo Candila[aut,cre]Maintainer Vincenzo Candila<****************************>Repository CRANDate/Publication2021-03-1510:00:07UTC12cov_eval R topics documented:cov_eval (2)dcc_fit (3)Det (7)ftse100 (7)indpro (8)Inv (9)nasdaq (9)plot_dccmidas (10)sp500 (11)Index13 cov_eval Var-cov matrix evaluationDescriptionEvaluates the estimated var-cov matrix H_t with respect to a covariance proxy,under different robust loss functions(Laurent et al.2013).The losses considered are also used in Amendola et al.(2020).Usagecov_eval(H_t,cov_proxy=NULL,r_t=NULL,loss="FROB")ArgumentsH_t Estimated covariance matrix,formatted as arraycov_proxy optional Covariance matrix,formatted as arrayr_t optional List of daily returns used to calculate H_t.If parameter’cov_proxy’is not provided,then r_t must be included.In this case,a(noise)proxy will beautomatically usedloss Robust loss function to use.Valid choices are:"FROB"for Frobenius(by de-fault),"SFROB"for Squared Frobenius,"EUCL"for Euclidean,"QLIKE"forQLIKE and"RMSE"for Root Mean Squared ErrorsValueThe value of the loss for each tReferencesAmendola A,Braione M,Candila V,Storti G(2020).“A Model Confidence Set approach to the combination of multivariate volatility forecasts.”International Journal of Forecasting,36(3),873-891.doi:10.1016/j.ijforecast.2019.10.001.Laurent S,Rombouts JV,Violante F(2013).“On loss functions and ranking forecasting perfor-mances of multivariate volatility models.”Journal of Econometrics,173(1),1–10.doi:10.1016/ j.jeconom.2012.08.004.Examplesrequire(xts)#open to close daily log-returnsr_t_s<-log(sp500[ 2010/2019 ][,3])-log(sp500[ 2010/2019 ][,1])r_t_n<-log(nasdaq[ 2010/2019 ][,3])-log(nasdaq[ 2010/2019 ][,1])r_t_f<-log(ftse100[ 2010/2019 ][,3])-log(ftse100[ 2010/2019 ][,1])db_m<-merge.xts(r_t_s,r_t_n,r_t_f)db_m<-db_m[complete.cases(db_m),]colnames(db_m)<-c("S&P500","NASDAQ","FTSE100")#list of returnsr_t<-list(db_m[,1],db_m[,2],db_m[,3])#estimationK_c<-144N_c<-36cdcc_est<-dcc_fit(r_t,univ_model="sGARCH",distribution="norm",corr_model="DCCMIDAS",N_c=N_c,K_c=K_c)cov_eval(cdcc_est$H_t,r_t=r_t)[(K_c+1):dim(cdcc_est$H_t)[3]]dcc_fit DCCfit(first and second steps)DescriptionObtains the estimation of a variety of DCC models,using as univariate models both GARCH and GARCH-MIDAS specifications.Usagedcc_fit(r_t,univ_model="sGARCH",distribution="norm",MV=NULL,K=NULL,corr_model="cDCC",lag_fun="Beta",N_c=NULL,K_c=NULL)Argumentsr_t List of daily returns on which estimate a DCC model.Each daily return must bean’xts’object.Note that the sample period of the returns should be the same.Otherwise,a merge is performeduniv_model Specification of the univariate model.Valid choices are:some of the specifica-tions used in the rugarch(ugarchspec)and rumidas(ugmfit)packages.Morein detail,the models coming from rugarch are:model Valid models(currentlyimplemented)are’sGARCH’,’eGARCH’,’gjrGARCH’,’iGARCH’,and’cs-GARCH’.The models implemented from rumidas are:’GM_skew’,’GM_noskew’,’DAGM_skew’,and’DAGM_noskew’distribution optional Distribution chosen for the univariate estimation.Valid choices are:"norm"(by default)and"std",respectively,for the Normal and Student’s t dis-tributionsMV optional MIDAS variable to include in the univariate estimation,if the modelspecificied is a GARCH-MIDAS(GM,Engle et al.(2013))or a Double Asym-metric GM(DAGM,Engle et al.(2013)).In the case of MIDAS-based models,please provide a list of the MIDAS variables obtained from the mv_into_matfunction.If the same MV variable is used,then provide always a list,with thesame(transformed)variable repeatedK optional The number of lagged realization of MV variable to use,if’univ_model’has a MIDAS termcorr_model Correlation model used.Valid choices are:"cDCC"(the corrected DCC ofAielli(2013)),"aDCC"(the asymmetric DCC model of Cappiello et al.(2006)),"DECO"(Dynamic equicorrelation of Engle and Kelly(2012)),and"DCCMI-DAS"(the DCC-MIDAS of Colacito et al.(2011)).By detault,it is"cDCC"lag_fun g function to use.Valid choices are"Beta"(by default)and"Al-mon",for the Beta and Exponential Almon lag functions,respectively,if’univ_model’has a MIDAS term and/or if’corr_model’is"DCCMIDAS"N_c optional Number of(lagged)realizations to use for the standarized residualsforming the long-run correlation,if’corr_model’is"DCCMIDAS"K_c optional Number of(lagged)realizations to use for the long-run correlation,if’corr_model’is"DCCMIDAS"DetailsFunction dcc_fit implements the two-steps estimation of the DCC models.In thefirst step,a variety of univariate models are considered.These models can be selected using for the pa-rameter’univ_model’one of the following choices:’sGARCH’(standard GARCH of Bollerslev (1986)),’eGARCH’of Nelson(1991),’gjrGARCH’of Glosten et al.(1993),’iGARCH’(Integrated GARCH of Engle and Bollerslev(1986)),’csGARCH’(the Component GARCH of Engle and Lee (1999)),’GM_noskew’and’GM_skew’(the GARCH-MIDAS model of Engle et al.(2013),respec-tively,without and with the asymmetric term in the short-run component),and’DAGM_noskew’and’DAGM_skew’(the Double Asymmetric GARCH-MIDAS model of Amendola et al.(2019), respectively,without and with the asymmetric term in the short-run component).Valuedcc_fit returns an object of class’dccmidas’.The function summary.dccmidas can be used to print a summary of the results.Moreover,an object of class’dccmidas’is a list containing the following components:•assets:Names of the assets considered.•model:Univariate model used in thefirst step.•est_univ_model:List of matrixes of estimated coefficients of the univariate model,with the QML(Bollerslev and Wooldridge1992)standard errors.•corr_coef_mat:Matrix of estimated coefficients of the correlation model,with the QML stan-dard errors.•mult_model:Correlation model used in the second step.•obs:The number of daily observations used for the estimation.•period:The period of the estimation.•H_t:Conditional covariance matrix,reported as an array.•R_t:Conditional correlation matrix,reported as an array.•R_t_bar:Conditional long-run correlation matrix,reported as an array,if the correlation ma-trix includes a MIDAS specification.•est_time:Time of estimation.•Days:Days of the sample period.•llk:The value of the log-likelihood(for the second step)at the maximum.ReferencesAielli GP(2013).“Dynamic conditional correlation:on properties and estimation.”Journal of Business&Economic Statistics,31(3),282–299.doi:10.1080/07350015.2013.771027.Amendola A,Candila V,Gallo GM(2019).“On the asymmetric impact of macro–variables on volatility.”Economic Modelling,76,135–152.doi:10.1016/j.econmod.2018.07.025.Bollerslev T(1986).“Generalized autoregressive conditional heteroskedasticity.”Journal of Econo-metrics,31(3),307–327.doi:10.1016/03044076(86)900631.Bollerslev T,Wooldridge JM(1992).“Quasi-maximum likelihood estimation and inference in dy-namic models with time-varying covariances.”Econometric Reviews,11,143–172.doi:10.1080/ 07474939208800229.Cappiello L,Engle RF,Sheppard K(2006).“Asymmetric dynamics in the correlations of global equity and bond returns.”Journal of Financial Econometrics,4(4),537–572.doi:10.1093/jjfinec/ nbl005.Colacito R,Engle RF,Ghysels E(2011).“A component model for dynamic correlations.”Journalof Econometrics,164(1),45–59.doi:10.1016/j.jeconom.2011.02.013.Engle R,Kelly B(2012).“Dynamic equicorrelation.”Journal of Business&Economic Statis-tics,30(2),212–228.doi:10.1080/07350015.2011.652048.Engle RF,Bollerslev T(1986).“Modelling the persistence of conditional variances.”Econometric Reviews,5(1),1–50.doi:10.1080/07474938608800095.Engle RF,Ghysels E,Sohn B(2013).“Stock market volatility and macroeconomic fundamen-tals.”Review of Economics and Statistics,95(3),776–797.doi:10.1162/REST_a_00300.Engle RF,Lee GJ(1999).“A Long-run and Short-run Component Model of Stock Return V olatil-ity.”In Engle RF,White H(eds.),Cointegration,Causality,and Forecasting:A Festschrift in Honor of Clive W.J.Granger,475–497.Oxford University Press,Oxford.Glosten LR,Jagannathan R,Runkle DE(1993).“On the relation between the expected value and the volatility of the nominal excess return on stocks.”The Journal of Finance,48(5),1779–1801.doi:10.1111/j.15406261.1993.tb05128.x.Nelson DB(1991).“Conditional heteroskedasticity in asset returns:A new approach.”Econo-metrica,59,347–370.doi:10.2307/2938260.Examplesrequire(xts)#open to close daily log-returnsr_t_s<-log(sp500[ 2005/2008 ][,3])-log(sp500[ 2005/2008 ][,1])r_t_n<-log(nasdaq[ 2005/2008 ][,3])-log(nasdaq[ 2005/2008 ][,1])r_t_f<-log(ftse100[ 2005/2008 ][,3])-log(ftse100[ 2005/2008 ][,1])db_m<-merge.xts(r_t_s,r_t_n,r_t_f)db_m<-db_m[complete.cases(db_m),]colnames(db_m)<-c("S&P500","NASDAQ","FTSE100")#list of returnsr_t<-list(db_m[,1],db_m[,2],db_m[,3])#MV transformation(same MV for all the stocks)require(rumidas)mv_m<-mv_into_mat(r_t[[1]],diff(indpro),K=12,"monthly")#list of MVMV<-list(mv_m,mv_m,mv_m)#estimationK_c<-144N_c<-36dccmidas_est<-dcc_fit(r_t,univ_model="GM_noskew",distribution="norm",MV=MV,K=12,corr_model="DCCMIDAS",N_c=N_c,K_c=K_c)dccmidas_estsummary.dccmidas(dccmidas_est)Det7 Det Matrix determinantDescriptionCalculates the determinant of a numeric matrix.UsageDet(x)Argumentsx a numeric matrixValueThe determinant of x.Examplesx<-matrix(sample(1:25,25,replace=TRUE),ncol=5)Det(x)ftse100FTSE100dataDescriptionDaily data on FTSE100collected from the realized library of the Oxford-Man Institute(Heber et al.2009).Usagedata(ftse100)FormatAn object of class"xts".Detailsftse100includes the open price(open_price),the realized variance(rv5),and the close price(close_price).The realized variance has been calculated using intradaily intervals offive minutes(Andersen and Bollerslev1998).8indproSourceRealized library of the Oxford-Man InstituteReferencesAndersen TG,Bollerslev T(1998).“Answering the Skeptics:Yes,Standard V olatility Models do Provide Accurate Forecasts.”International Economic Review,39,885–905.doi:10.2307/2527343.Heber G,Lunde A,Shephard N,Sheppard K(2009).“OMI’s realised library,version0.1.”Oxford–Man Institute,University of Oxford.Exampleshead(ftse100)summary(ftse100)indpro Monthly U.S.Industrial ProductionDescriptionMonthly data on the U.S.Industrial Production index(IP,index2012=100,seasonally adjusted) collected from the Federal Reserve Economic Data(FRED)archive.The IP has been used as MIDAS term in different contributions(see,for instance,Engle et al.(2013),Conrad and Loch (2015),and Amendola et al.(2017)).Usagedata(indpro)FormatAn object of class"xts".SourceArchive of the Federal Reserve Economic Data(FRED)ReferencesAmendola A,Candila V,Scognamillo A(2017).“On the influence of US monetary policy on crude oil price volatility.”Empirical Economics,52(1),155–178.doi:10.1007/s0018101610695.Conrad C,Loch K(2015).“Anticipating Long-Term Stock Market V olatility.”Journal of Applied Econometrics,30(7),1090–1114.doi:10.1002/jae.2404.Engle RF,Ghysels E,Sohn B(2013).“Stock market volatility and macroeconomic fundamentals.”Review of Economics and Statistics,95(3),776–797.doi:10.1162/REST_a_00300.Inv9Exampleshead(indpro)summary(indpro)plot(indpro)Inv Inverse of a matrixDescriptionCalculates the inverse of a numeric matrixUsageInv(x)Argumentsx a numeric matrixValueThe inverse of x.Examplesx<-matrix(sample(1:25,25,replace=TRUE),ncol=5)Inv(x)nasdaq NASDAQ dataDescriptionDaily data on NASDAQ collected from the realized library of the Oxford-Man Institute(Heber et al.2009).Usagedata(nasdaq)FormatAn object of class"xts".10plot_dccmidas Detailsnasdaq includes the open price(open_price),the realized variance(rv5),and the close price(close_price).The realized variance has been calculated using intradaily intervals offive minutes(Andersen and Bollerslev1998).SourceRealized library of the Oxford-Man InstituteReferencesAndersen TG,Bollerslev T(1998).“Answering the Skeptics:Yes,Standard V olatility Models do Provide Accurate Forecasts.”International Economic Review,39,885–905.doi:10.2307/2527343.Heber G,Lunde A,Shephard N,Sheppard K(2009).“OMI’s realised library,version0.1.”Oxford–Man Institute,University of Oxford.Exampleshead(nasdaq)summary(nasdaq)plot_dccmidas Plot method for’dccmidas’classDescriptionPlots of the conditional volatilities on the main diagonal and of the conditional correlations on the extra-diagonal elements.Usageplot_dccmidas(x,K_c=NULL,vol_col="black",long_run_col="red",cex_axis=0.75,LWD=2,asset_sub=NULL)sp50011Argumentsx An object of class’dccmidas’,that is the result of a call to dcc_fit.K_c optional Number of(lagged)realizations to use for the long-run correlation,,if ’corr_model’is"DCCMIDAS"vol_col optional Color of the volatility and correlation plots."black"by defaultlong_run_col optional Color of the long-run correlation plots,if present."red"by default cex_axis optional Size of the x-axis.Default to0.75LWD optional Width of the plotted lines.Default to2asset_sub optional Numeric vector of selected assets to consider for the plot.NULL by defaultValueNo return value,called for side effectsExamplesrequire(xts)#open to close daily log-returnsr_t_s<-log(sp500[ 2010/2019 ][,3])-log(sp500[ 2010/2019 ][,1])r_t_n<-log(nasdaq[ 2010/2019 ][,3])-log(nasdaq[ 2010/2019 ][,1])r_t_f<-log(ftse100[ 2010/2019 ][,3])-log(ftse100[ 2010/2019 ][,1])db_m<-merge.xts(r_t_s,r_t_n,r_t_f)db_m<-db_m[complete.cases(db_m),]colnames(db_m)<-c("S&P500","NASDAQ","FTSE100")#list of returnsr_t<-list(db_m[,1],db_m[,2],db_m[,3])#estimationK_c<-144N_c<-36cdcc_est<-dcc_fit(r_t,univ_model="sGARCH",distribution="norm",corr_model="DCCMIDAS",N_c=N_c,K_c=K_c)plot_dccmidas(cdcc_est,K_c=144)sp500S&P500dataDescriptionDaily data on S&P500collected from the realized library of the Oxford-Man Institute(Heber et al.2009).Usagedata(sp500)12sp500FormatAn object of class"xts".Detailssp500includes the open price(open_price),the realized variance(rv5),and the close price(close_price).The realized variance has been calculated using intradaily intervals offive minutes(Andersen and Bollerslev1998).SourceRealized library of the Oxford-Man InstituteReferencesAndersen TG,Bollerslev T(1998).“Answering the Skeptics:Yes,Standard V olatility Models do Provide Accurate Forecasts.”International Economic Review,39,885–905.doi:10.2307/2527343.Heber G,Lunde A,Shephard N,Sheppard K(2009).“OMI’s realised library,version0.1.”Oxford–Man Institute,University of Oxford.Exampleshead(sp500)summary(sp500)Index∗datasetsftse100,7indpro,8nasdaq,9sp500,11cov_eval,2dcc_fit,3,11Det,7ftse100,7indpro,8Inv,9mv_into_mat,4nasdaq,9plot_dccmidas,10sp500,11summary.dccmidas,5ugarchspec,4ugmfit,413。
The ITU-T published J.144, a measurement of quality of service, for the transmission of television and other multimedia digital signals over cable networks. This defines the relationship between subjective assessment of video by a person and objective measurements taken from the network.The correlation between the two are defined by two methods:y Full Reference (Active) – A method applicable when the full reference video signal is available, and compared with the degraded signal as it passes through the network.y No Reference (Passive) – A method applicable when no reference video signal or informationis available.VIAVI believes that a combination of both Active and Passive measurements gives the correct blendof analysis with a good trade off of accuracy and computational power. T eraVM provides both voice and video quality assessment metrics, active and passive, based on ITU-T’s J.144, but are extended to support IP networks.For active assessment of VoIP and video, both the source and degraded signals are reconstituted from ingress and egress IP streams that are transmitted across the Network Under T est (NUT).The VoIP and video signals are aligned and each source and degraded frame is compared to rate the video quality.For passive measurements, only the degraded signal is considered, and with specified parameters about the source (CODEC, bit-rate) a metric is produced in real-time to rate the video quality.This combination of metrics gives the possibility of a ‘passive’ but lightweight Mean Opinion Score (MOS) per-subscriber for voice and video traffic, that is correlated with CPU-expensive but highly-accurate ‘active’ MOS scores.Both methods provide different degrees of measurement accuracy, expressed in terms of correlation with subjective assessment results. However, the trade off is the considerable computation resources required for active assessment of video - the algorithm must decode the IP stream and reconstitute the video sequence frame by frame, and compare the input and outputnframesto determine its score. The passive method is less accurate, but requires less computing resources. Active Video AnalysisThe active video assessment metric is called PEVQ– Perceptual Evaluation of Video Quality. PEVQ provides MOS estimates of the video quality degradation occurring through a network byBrochureVIAVITeraVMVoice, Video and MPEG Transport Stream Quality Metricsanalysing the degraded video signal output from the network. This approach is based on modelling the behaviour of the human visual tract and detecting abnormalities in the video signal quantified by a variety of KPIs. The MOS value reported, lies within a range from 1 (bad) to 5 (excellent) and is based on a multitude of perceptually motivated parameters.T o get readings from the network under test, the user runs a test with an video server (T eraVM or other) and an IGMP client, that joins the stream for a long period of time. The user selects the option to analysis the video quality, which takes a capture from both ingress and egress test ports.Next, the user launches the T eraVM Video Analysis Server, which fetches the video files from the server, filters the traffic on the desired video channel and converts them into standard video files. The PEVQ algorithm is run and is divided up into four separate blocks.The first block – pre-processing stage – is responsible for the spatial and temporal alignment of the reference and the impaired signal. This process makes sure, that only those frames are compared to each other that also correspond to each other.The second block calculates the perceptual difference of the aligned signals. Perceptual means that only those differences are taken into account which are actually perceived by a human viewer. Furthermore the activity of the motion in the reference signal provides another indicator representing the temporal information. This indicator is important as it takes into account that in frame series with low activity the perception of details is much higher than in frame series with quick motion. The third block in the figure classifies the previously calculated indicators and detects certain types of distortions.Finally, in the fourth block all the appropriate indicators according to the detected distortions are aggregated, forming the final result ‒ the mean opinion score (MOS). T eraVM evaluates the quality of CIF and QCIF video formats based on perceptual measurement, reliably, objectively and fast.In addition to MOS, the algorithm reports:y D istortion indicators: For a more detailed analysis the perceptual level of distortion in the luminance, chrominance and temporal domain are provided.y D elay: The delay of each frame of the test signal related to the reference signal.y Brightness: The brightness of the reference and degraded signal.y Contrast: The contrast of the distorted and the reference sequence.y P SNR: T o allow for a coarse analysis of the distortions in different domains the PSNR is provided for theY (luminance), Cb and Cr (chrominance) components separately.y Other KPIs: KPIs like Blockiness (S), Jerkiness, Blurriness (S), and frame rate the complete picture of the quality estimate.Passive MOS and MPEG StatisticsThe VQM passive algorithm is integrated into T eraVM, and when required produces a VQM, an estimation of the subjective quality of the video, every second. VQM MOS scores are available as an additional statistic in the T eraVM GUI and available in real time. In additionto VQM MOS scores, MPEG streams are analysed to determine the quality of each “Packet Elementary Stream” and exports key metrics such as Packets received and Packets Lost for each distinct Video stream within the MPEG Transport Stream. All major VoIP and Video CODECs are support, including MPEG 2/4 and the H.261/3/3+/4.2 TeraVM Voice, Video and MPEG Transport Stream Quality Metrics© 2020 VIAVI Solutions Inc.Product specifications and descriptions in this document are subject to change without notice.tvm-vv-mpeg-br-wir-nse-ae 30191143 900 0620Contact Us +1 844 GO VIAVI (+1 844 468 4284)To reach the VIAVI office nearest you, visit /contacts.VIAVI SolutionsVoice over IP call quality can be affected by packet loss, discards due to jitter, delay , echo and other problems. Some of these problems, notably packet loss and jitter, are time varying in nature as they are usually caused by congestion on the IP path. This can result in situations where call quality varies during the call - when viewed from the perspective of “average” impairments then the call may appear fine although it may have sounded severely impaired to the listener. T eraVM inspects every RTP packet header, estimating delay variation and emulating the behavior of a fixed or adaptive jitter buffer to determine which packets are lost or discarded. A 4- state Markov Model measures the distribution of the lost and discarded packets. Packet metrics obtained from the Jitter Buffer together with video codec information obtained from the packet stream to calculate a rich set of metrics, performance and diagnostic information. Video quality scores provide a guide to the quality of the video delivered to the user. T eraVM V3.1 produces call quality metrics, includinglistening and conversational quality scores, and detailed information on the severity and distribution of packet loss and discards (due to jitter). This metric is based on the well established ITU G.107 E Model, with extensions to support time varying network impairments.For passive VoIP analysis, T eraVM v3.1 emulates a VoIP Jitter Buffer Emulator and with a statistical Markov Model accepts RTP header information from the VoIP stream, detects lost packets and predicts which packets would be discarded ‒ feeding this information to the Markov Model and hence to the T eraVM analysis engine.PESQ SupportFinally , PESQ is available for the analysis of VoIP RTP Streams. The process to generate PESQ is an identical process to that of Video Quality Analysis.。
一种齿轮时变啮合刚度的通用计算方法李大磊; 李安民; 张二亮【期刊名称】《《重庆理工大学学报(自然科学版)》》【年(卷),期】2019(033)010【总页数】6页(P61-66)【关键词】时变啮合刚度; 势能法; 有限元法; 装配误差【作者】李大磊; 李安民; 张二亮【作者单位】郑州大学机械工程学院郑州450001【正文语种】中文【中图分类】TH132.4齿轮箱是现代机械传动系统中的重要部件之一,由于其恒定的传动比、大功率及高效率等特点,被广泛应用于各类工程机械。
振动与噪声是评价齿轮箱工作性能的主要指标,齿轮在传动过程中啮合刚度的时变特性是引起齿轮箱产生振动与噪声的主要原因[1]。
因此,齿轮时变啮合刚度的计算研究得到了国内外学者的广泛关注。
齿轮时变啮合刚度的计算方法主要分为3类:基于势能原理的解析法[2-7]、基于有限元的数值计算方法[8-11]和解析有限元法[12-15]。
势能解析法的基本思想是视轮齿为基圆上的变截面悬臂梁,并根据弹性力学理论,推导齿轮啮合过程中储存在轮齿中的应变能,进而计算齿轮啮合刚度。
Yang等[2]考虑了轮齿的弯曲势能、径向压缩势能以及轮齿接触赫兹能,计算了齿轮的啮合刚度;Wu等[3]进一步考虑了齿轮啮合时的剪切变形能,完善了解析算法;Wan和Xiang等[4-5]考虑了轮齿基体的应变能和齿轮基圆与齿根圆不重合的情况,提高了解析法的计算精度,但也增加了算法的复杂度。
随着有限元软件几何建模能力的日益增强,基于数值分析的齿轮啮合刚度计算也得到了重视和发展,其主要途径有:① 通过有限元方法分析计算轮齿接触部位沿啮合方向的位移量,提取啮合轮齿的法向载荷,根据刚度的定义计算齿轮的啮合刚度,如:唐进元等[8]应用有限元分析软件构建螺旋锥齿轮模型并计算出法向接触力和综合弹性变形量,得到单齿啮合刚度和多齿综合啮合刚度;Song等[9]利用有限元法研究了渐开线行星轮系的扭转刚度。
② 在准静态条件下(转速很低),通过计算齿轮副的传递误差,获得齿轮的啮合刚度。
遥感类英文期刊、与GIS相关的SCI(EI)期刊遥感类英文期刊[1]. REMOTE SENSING OF ENVIRONMENTISSN: 0034-4257版本: SCI-CDE出版频率: Monthly出版社: ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY, 10010-1710出版社网址:http://www.elsevier.nl/期刊网址:http://www.elsevier.nl/inca/publications/store/5/0/5/7/3/3/index.htt影响因子: 1.697(2001),1.992(2002)主题范畴: REMOTE SENSING; ENVIRONMENTAL SCIENCES; IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY[2]. International Journal of Remote Sensing国际遥感杂志,这是英国出版的一本专业遥感杂志,由Taylor & Francis出版社出版,我看得不多,不好多说,大家可以到/上查该杂志目录和摘要,全文可以到系资料室复印。
Taylor&Francis注册邮箱为cumtlp#.[3]. PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSINGISSN: 0099-1112版本: SCI-CDE出版频率: Monthly出版社: AMER SOC PHOTOGRAMMETRY, 5410 GROSVENOR LANE, SUITE 210, BETHESDA, MD, 20814-2160出版社网址:/期刊网址:/publications.html影响因子: 0.841(2001);1.176(2002)主题范畴: GEOGRAPHY, PHYSICAL; GEOSCIENCES, MULTIDISCIPLINARY; REMOTE SENSING; PATHOLOGY美国摄影测量与遥感协会的会刊,摄影测量工程与遥感(Photogrametry Engineering and remote sensing)杂志,网址,网上可看论文摘要,全文可去系图书室复印,该杂志南大很全,过去50年的都有,同时你可以发现测绘学报、遥感学报、武测学报甚至国外的文章中参考文献许多来自该刊,在2000年SCI地学类杂志排名中该刊名列第三,相当地不容易,南大校友美国 berkeley加州大学副教授宫鹏就曾三次获得该刊的年度最佳论文奖,由此奠定其在国际遥感学界的地位。
电力系统英文书籍推荐unication&control in power system 电力系统通讯与控制2.electric power systems: analysis and control 电力系统: 分析与控制3.Electrical Energy System 电能系统4.embedded generation 嵌入式发电5.fundamentals of power system economics 电力系统经济学基础6.Handbook of Electric Power Calculations 电力系统计算手册7.market operations in electric power systems 电力系统市场运行8.POWER QUALITY 电能质量9.Risk assessment of power systems 电力系统风险评估10.Switching Power Supply Design 开关供电设计11.understanding electric power systems 电力系统学习12.understanding Power Quality problems 电能质量问题学习13.electric energy economic methods 电能经济方法14.FACTS Modelling and Simulation in Power Networks 灵活交流输电: 在电网中的仿真与模拟15.HVDC.and.FACTS.Controllers.Applications.of.Static.Converters.in.Power.System s 高压直流和灵活交流控制器在电力系统中应用16.LOAD-FLOW ANALYSIS IN POWER SYSTEMS 电力系统潮流分析17.Operation of Market-oriented Power Systems 市场化电力系统运营18.Power Generation Operation and Control 发电运行和控制19.Power system economics 电力系统经济学20.power system harmonics 电力系统谐波21.Power System Operations and Electricity Markets 电力系统运行和电力市场22.Power System Restructuring and Deregulation 电力系统改制和放松管制(即电力市场)23.voltage stability of electric power systems 电力系统电压稳定24.Transients in Power Systems 电力系统(电磁)暂态25.transient stability of power systems电力系统暂态稳定26.Wind Energy Handbook 风电手册27.distrbuted generation-the power paradigmfor the new millennium分布式发电28.electric power distribution handbook 配电手册29.electric power engineering handbook 电力工程手册30.spatial load forecasting(空间)电力负荷预测31.power transer-principles and applications 电力变压器-原理和应用32.electric power transer engineering 电力系统变压器工程33.wind and solar power system 风电和太阳能发电34.Electric Power Distribution Reliability 配电网可靠性35.Aging power delivery infrastrutures 送电结构36.Renewable and Efficient Electric Power Systems 可再生与高效电力系统37.probabilityconcepts in electric power systems 电力系统概率应用38.Short Circuits in Power Systems 电力系统短路39.VOLTAGE STABILITY ASSESSMENT,PROCEDURES AND GUIDES 电压稳定性评估,措施和导则40.electric systems, dynamics and stability with AI application 电力系统动态和稳定性: 人工智能应用41.electric power system application of optimiztion 电力系统优化应用42.protective relaying theory and application 继电保护理论与应用43.vehicular electric power systems 车辆电力系统44.electric power quality control techniques 电能质量控制技术45.reliability assessment of electric power systems using monte carlo methods 利用蒙特卡罗方法进行电力系统可靠性评估petitive Electricity Markets 竞争性电力市场47.power quality enhancement using customer power devices 用户电力设备与电能质量提高48.power system harmonics: computer modelling and analysis 电力系统谐波:计算机仿真与分析49.Analysis of Faulted Power Systems 故障电力系统分析50.Dynamic and control of large power system 大电力系统动态与控制51.Distributed power generation: planning and evaluation分布式发电(规划与评估)52.AC-DC power system analysis 交直流电力系统分析53.FACTS (flexible AC transmission system) 灵活交流输电系统54.Power system in emergencies 紧急状态下的电力系统55.Power system restoration 电力系统恢复56.Electric power system quality 电能质量57.Energy Management Systems (EMS) 能量管理系统58.Automatic learning techniques in power systems 自学习技术在电力系统中的应用59.Power system protection 1-4 电力系统保护1-4册 (electricity association 培训教程)60 electrical power system protection 电力系统保护61.elements of power system analysis 电力系统分析基础62.AC power system handbook 交流电力系统手册63. Wind turbine operation in electric power systems: advanced modelling 风力发电(机)在电力系统运行64. Power system control and stability 电力系统控制与稳定性( 不是那本stability and control)65. Analysis of subsynchronous resonance in power system 电力系统次同步谐振分析putationalmethods for large sparse power systems: a object orientedapproach 大稀疏电力系统计算方法: 面向对象的途径67. Power system oscillation 电力系统振荡68. Power system restructuring: engineering and economics 电力系统市场化: 工程和经济69. Distribution system modelling and analysis 配电系统建模与分析70. Electric power engineering 电力工程71. Subsynchronous resonance in power systems 电力系统中的次同步谐振72. Computer modelling of electrical power system 电力系统计算机建模73. High Voltage Direct Current Transmission 高压直流输电74. Electricitydistribution network design (2nd)配电网规划设计75. Industrial power distribution 工业配电76. Protection ofelectricity distribution networks 配电网保护77. Energy function analysis for power system stability 电力系统稳定性的能量函数分析78. Power system commission and maintenance practice电力系统试验(调试)与检修(维护)实践79. Statistical techniques for high-voltage engineering 高电压工程中的统计技术80. Digital protection for power system电力系统数字保护81. Power system protection 电力系统(继电)保护82. Voltage quality in electrical power systems 电力系统电压质量83.Electric power applications of fuzzy systems 模糊系统的电力应用84. Artificial intelligence techniques in power system 电力系统中的人工智能技术85. Insulators in high voltages 高压绝缘体86. Electrical safety供电安全87. High voltageengineering and testing 高电压工程与试验88. Reactive power control in electric systems 电力系统无功(功率)控制93. Electric power system电力系统教程94. Computer-Aided Power systems analysis 计算机辅助电力系统分析99. Reliability evaluation of power system 电力系统可靠性评估106. Power system stability handbook 电力系统稳定性手册109. Reliability assessment of large electric power systems 大电力系统可靠性评估112. HVDC power transmission systems 高压直流输电系统128. Electric Machinery and power system fundamentals 电机与电力系统基础(MATLAB 辅助)129. Intelligent system applications in power engineering (EP and ANN) 智能系统在电力工程中应用(进化计算和神经网)130. Thyristor-based FACTS controllers for electrical transmission systems 基于晶闸管的灵活交流输电系统控制器131. The economics of power system reliability and planning 电力系统可靠性与规划的经济学132. Computational Intelligence Applications to Power systems 计算智能在电力系统中的应用133. Environmental Impact of Power Generation 发电的环境影响134. Operation and Maintenance of Large Turbo-Generators 大型涡轮发电机组运行与检修135. Power system simulation 电力系统仿真136. Advanced load dispatch for power systems 电力系统高级调度137. The development of electric power transmission 电力传输进展138. Renewable Energy Sources 可再生发电源139. Power system dynamics andstablity 电力系统动态与稳定性140. Practical electrical network automation and communication systems 电力系统自动化与通信系统实践141. Electrical power and controls 电力与控制142. Deregulation of Electric Utilities 电力企业放松管制(市场改革)143. Computational Auction Mechanisms for restructured power industry operation 电力市场运行的(计算)投标机理144. Finanicial and economic evaluation of projects in the electricity supply industry 电力工程项目的金融与经济评价145. Electricity economics and planning 电力经济与规划146. Computational Methods for electric power systems 电力系统计算方法147. Power system relaying 电力系统继电保护148. Computer relaying for power systems 电力系统计算机保护149. Modern power system planning 现代电力系统规划150. High Voltage Engineering (2nd) 高电压工程151. Operation of restructured power systems 市场化电力系统运行152. Transer and Inductor Design Handbook变压器和电感设计手册(04增强版)153. Modern power system analysis (matlab supported) 现代电力系统分析(03年含MATLAB版)154. Power distribution planning reference book 配电规划参考手册155. Understanding FACTS 理解灵活交流输电系统156. Power system analysis :short-circuit load flow and harmonics 电力系统分析: 短路潮流和谐波157. Power systems electromagnetic transients simulation 电力系统电磁暂态仿真158. Power electronic control in electrical systems 电力系统中的电力电子控制159. Protection devices and systems for high-voltage applications保护装置和系统的高压应用160. Small signal analysis of power systems 电力系统小信号分析161. Electrical power cable engineering 电力线缆工程162. Power System State Estimation: Theory and Implementation 电力系统状态估计: 理论和实现163. Dielectrics in Electric Fields电场中的电介质(绝缘体)164. spacecraft power system 航天器电力系统165. Grid integration of wind energy conversion systems 风能转换系统的电网整合(接入)166. Power loss: the origins of deregulation and restructuring in the American electricutility system网损:美国电力系统放松管制和市场化的根源167. High Voltage Circuit Breakers: Design and Applications 高压断路器:设计与应用168. Power system capacitors 电力系统电容器169. Energy Management Systems & Direct Digitial Control 能量管理系统(EMS)及直接数字控制170. Pricing in Competitive Electricity Market 电力市场电价171. Designing Competitive Electricity Markets 电力市场设计172. Power system dynamics and stability 电力系统动态与稳定性(美国)173. Theory and problems of electric power systems 电力系统的理论和问题174. Insulation coordinationfor power systems 电力系统绝缘配合175. Modal analysis of large interconnected power systems 大互联电力系统的模式分析176. Making competition work in electricity 电力市场竞争177. Power system operation 电力系统运行178. Transmission line reliability and security 输电线路安全可靠性179. Computer analysis of power systems 电力系统计算机分析89. Electical distribution engineering配电网工程90. Power systemplanning电力系统规划91. Uniquepower system problems 电力系统问题92. Tranmission and Distribution ofElectrical Energy 电力系统输配电95. Electric powertransmission system 输电系统96. Reliability Modelling in Electric power systems电力系统可靠性建模97. High voltage engineering in power system 电力系统高电压工程98. Extra High voltage AC transmission engineering 超高压交流输电工程100. Computation of power system transients 电力系统暂态计算101.Piecewise methods and application to power systems 分段法及其在电力系统中应用103. Analysis and protection of electrical power systems 电力系统分析与保护104. Power systems engineering and mathematicas电力系统工程与数学105. Stability of large power systems 大电力系统稳定性107. Power system reliability evaluation电力系统可靠性评估108.Electric power system dynamics 电力系统动态110. Power system analysis and planning 电力系统分析与规划111. Electric transmission line fundamental 输电线(工程)基础113. Transient Processes in electrical power systems 电力系统暂态过程114.Discrete Fourier transation and its applications to power system 离散傅立叶变换及其在电力系统中的应用115. Electrical Transients inpower system 电力系统暂态116. Optimal economic operation of electric power system 电力系统优化经济调度运行117.High power switching 大功率开关118. power plant engineering 电厂工程119. power plant system design 电厂系统设计120. power plant evaluation and design reference guide 电厂评估和设计参考导则121. planning engineering, and construction of electric power generationfacilities 发电设备的规划和建设工程122. Elements electrical power station design 电站设计基础123.Optimal control applications in electric power systems 电力系统最优控制应用124. applied protected relaying应用继电保护125. power station and substation maintenance 电厂与变电站维修126. Power system operation 电力系统运行127. power system reliability,safety and management 电力系统可靠性,安全与管理。
ANN-based modelling and estimation of daily global solar radiation data:A case studyM.Benghanem a,1,A.Mellit b,*,1,S.N.Alamri aa Department of Physics,Faculty of Sciences,Taibah University,P.O.Box 344,Medina,Saudi ArabiabDepartment of LMD/Electronics,Faculty of Sciences Engineering,LAMEL,Jijel University,Ouled-aissa,P.O.Box 98,Jijel 18000,Algeriaa r t i c l e i n f o Article history:Received 18August 2008Accepted 21March 2009Available online 24April 2009Keywords:Global solar radiation Correlation Modelling EstimationNeural networksa b s t r a c tIn this paper,an artificial neural network (ANN)models for estimating and modelling of daily global solar radiation have been developed.The data used in this work are the global irradiation H G ,diffuse irradiation H D ,air temperature T and relative humidity H u .These data are available from 1998to 2002at the National Renewable Energy Laboratory (NREL)website.We have developed six ANN-models by using dif-ferent combination as inputs:the air temperature,relative humidity,sunshine duration and the day of year.For each model,the output is the daily global solar radiation.Firstly,a set of 4Â365points (4years)has been used for training each networks,while a set of 365points (1year)has been used for testing and validating the ANN-models.It was found that the model using sunshine duration and air temperature as inputs,gives good accurate results since the correlation coefficient is 97.65%.A comparative study between developed ANN-models and conventional regression models is presented in this study.Ó2009Elsevier Ltd.All rights reserved.1.IntroductionLong-term average values of the instantaneous (or hourly,daily,monthly)global and diffuse irradiation on a horizontal surface are needed in many applications of solar energy designs.The measured values of these parameters are available at a few places.When the measurement data are not available,the usual practice is to esti-mate them from theoretical or empirical models that have been developed based on measured values.Knowledge of the amount of solar radiation falling on a surface of the earth is of prime impor-tance to engineers and scientists involved in the design of solar-en-ergy systems.In particular,many design methods for thermal and photovoltaic systems require monthly average daily radiation on a horizontal surface as an input,in order to predict the energy pro-duction of the system on a monthly basis [1].In practice,it is very important to appreciate the order of measurements prior to any modelling study for both solar radiation and sunshine duration or daylight.There is a relative abundance of sunshine duration data and therefore it is a common practice to correlate the solar radia-tion to sunshine duration measurements.In many countries,diur-nal bright sunshine duration is measured at a wide number of places [1].Solar radiation data and its compound play very impor-tant role in designing,sizing and performance of energy and renewable energy systems [2].An artificial neural network (ANN)provides a computationally efficient way of determining an empirical,possibly nonlinear rela-tionship between a number of inputs and one or more outputs.ANN has been applied for modelling,identification,optimization,prediction,forecasting and control of complex systems.In solar radiation modelling and prediction,many studies have been per-formed using an ANN.Most of them use the geographical coordi-nate and meteorological data such as relative humidity,air temperature,pressure,sunshine duration,etc ...as inputs of the network for estimation of global solar radiation,and only few works were interested by using only the meteorological data for estimation of solar radiation.Mohandes et al.[3]used data from 41collection stations in Saudi Arabia.From these,the data for 31stations were used to train a neu-ral network and the data for the others 10stations for testing the network.The input values to the network are latitude,longitude,altitude and sunshine duration.The results for the testing stations obtained are within 16.4%and indicate the viability of this approach for spatial modelling of solar radiation.Alawi and Hinai [4]used ANNs to predict solar radiation in areas not covered by direct mea-surement instrumentation.The input data to the network are the location,and the monthly values of data as pressure,temperature,relative humidity,wind speed and sunshine duration.The monthly-predicted values of the ANN-model compared to the ac-tual global radiation values for this independent dataset produced an accuracy of 93%and a mean absolute percentage error of 5.43.Mohandes et al.[5]used radial basis function (RBF)networks for modelling monthly mean daily values of global solar radiation on horizontal surface and compared its performance with that of0196-8904/$-see front matter Ó2009Elsevier Ltd.All rights reserved.doi:10.1016/j.enconman.2009.03.035*Corresponding author.Tel.:+213551998982.E-mail addresses:a.mellit@ ,amellit@ictp.it (A.Mellit).1Present address:The International Centre for Theoretical Physics (ICTP),Strada-Costiera,1134014Trieste,Italy.Energy Conversion and Management 50(2009)1644–1655Contents lists available at ScienceDirectEnergy Conversion and Managementj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /e n c o n m ana multilayer perception(MLP)model and a classical regression model.The proposed network employs as inputs the latitude,lon-gitude,altitude and sunshine duration.According to the authors, the results on locations that are not included in the modelling indi-cate viability of the neural network methods to solve such prob-lems when compared with a classical regression model.Although the data sample is relatively small,representing only1year from each of32locations,it demonstrates the concept.The average mean absolute error(MAPE)for the MLP network is12.6and the average MAPE for radial basis function(RBF)networks is10.1.An ANN based model for estimation of monthly daily and hourly val-ues of solar global radiation were proposed by Reddy and Manish [6].Solar radiation data from13stations spread over India have been used for training and testing the ANN.The maximum mean absolute error between predicted and measured hourly global radi-ation is 4.07%.The results indicate that the ANN-model show promise for predicting solar global radiation at places where mon-itoring stations are not established.Sozen et al.[7]used a neural network for the estimation of solar potential based on geographical coordinates(latitude,longitude and altitude),meteorological data(sunshine duration and mean temperature)and the corresponding month as inputs of the net-work.The measured data from seventeen stations in Turkey col-lected between the years2000and2002were used.One set with data for11stations was used for training a neural network and the other dataset from six stations was used for testing.According to the authors,the maximum mean absolute percentage error was found to be less than 6.7%and a correlation coefficient about 99.89%for the testing stations.The predictions from the ANN-mod-els could enable scientists to locate and design solar-energy sys-tems in Turkey and determine the appropriate solar technology. Mellit et al.[8]proposed a simplified hybrid model for generating sequences of total daily solar radiation,which combine a neural network and Markov chain.This model is called ANN–MTM(Mar-kov transition matrix).The inputs of the proposed model are the geographical coordinates while the outputs are the daily global so-lar radiation.It can be used for generating sequences of solar radi-ation at long term and it was applied for Algeria.The unknown validation data set produced very accurate prediction with a root mean square error(RMSE)not exceeding8%between the mea-sured and predicted data.A correlation coefficient ranging from 90%to92%has been obtained.Hontoria et al.[9]used a MLP for developing a solar radiation map for Spain.The inputs are the previous irradiation,clearness in-dex(K t)and the hour order number of the K t.The classical methods are unable to generate solar radiation series in places where no solar information is available.Nevertheless,the methodology proposed is able to do the generation;it is more versatile than the classical methods and so is able to draw maps of the zone.This methodology is easily extendable to other places.The only require-ment is the knowledge of the hourly solar radiation from only one site of the zone where the map is going to be drawn.Tymvios et al.[10]presented a comparative study of Angstroms and artificial neural network methodologies in estimating global solar radiation, where several models have been proposed.The parameters used as inputs were the daily values of measured sunshine duration,theo-retical sunshine duration,maximum temperature and the month number.According to the authors,the best ANN-model was the one with all inputs except the month number and the results showed a MBE and RMSE of0.12%and0.67%,respectively.The ANN methodology is a promising alternative to the traditional ap-proach for estimating global solar radiation,especially in cases where radiation measurements are not readily available.Mellit et al.[11]proposed a new model for the prediction of dai-ly solar radiation.This model combines neural network and fuzzy logic(ANFIS).The inputs of this model are the mean daily air tem-perature and sunshine duration.The correlation coefficient ob-tained for the validation data set is98%and the mean relative error(MRE)was found less than1%.A methodology for estimating of daily global irradiation on station located in complex terrain is proposed by Bosch et al.[12],the proposed technique is based on the using of neural network.The ANN-model developed provides a satisfactory performance with an RMSE of6.0%when comparing the estimated values with the measured ones over the whole val-idation data set.On the other hand,model performance for each station has presented no dependence with the distance to the ref-erence station or with the altitude,with RMSE below7.5%and mean relative error(MBE)lower than1%for most of the stations. In addition,this methodology can be applied to other areas with a complex topography.Mellit et al.[13]also proposed a new hybrid model based on neuro-fuzzy and Markov chain for predicting the sequences of dai-ly clearness index,the generating solar radiation data have been used for the sizing of a PV-system.The RMSE between measured and estimated values varies between0.0215and0.0235and the mean absolute percentage error(MAE)is less than2.2%.In addi-tion,a comparison between the results obtained by the ANFIS model and artificial neural network(ANN)models was presented in order to show the advantage of the proposed hybrid model.Senkal and Kuleli[14]used an ANN for the estimation of solar radiation in Turkey.Meteorological and geographical data(lati-tude,longitude,altitude,month,mean diffuse radiation and mean beam radiation)are used in the inputs layer of the network,and so-lar radiation is the output.Additionally,the authors used a physical method for estimating the solar radiation from Meteosat-6satellite C3D data.According to the author,the monthly mean daily sum values were found as54W/m2and64W/m2(training cities), 91W/m2and125W/m2(testing cities),respectively.Recently,Rehman and Mohandes[15]used an ANN for estima-tion of daily solar radiation from air temperature and relativeNomenclatureANFIS adaptive new fussy inference system ANN artificial neural networkFFNN feed-forward neural networkMAE mean absolute error.MBE men bias errorMLP multilayer perceptionMPE mean percentage errorMRE mean relative errorRBF radial basis functionRMSE root mean square errora,b,c coefficient of regression models H G global solar irradiation(Wh/m2/day)H0extraterrestrial global solar radiation(Wh/m2/day) H u relative humidity(%)K t clearness indexLat latitude(°)Lon longitude(°)r correlation coefficientS sunshine duration(h)S0extraterrestrial sunshine duration(h)SS fraction sunshineT air temperature(°C)M.Benghanem et al./Energy Conversion and Management50(2009)1644–16551645humidity at Abha City(Saudi Arabia).A set of4years has been used for training the network,while a set of1year is used for testing and validating the model.Results show that using the relative humidity along with daily mean temperature outperforms the other cases with absolute mean percentage error of4.49%.The absolute mean percentage error for the case when only day of the year and mean temperature were used as inputs was11.8%. This error is about10.3%when maximum temperature is used in-stead of mean temperature.Our aim is to develop a best model with a few parameters as in-puts to estimate the solar radiation data,by using an artificial neu-ral network.We have tried different combination of meteorological data as inputs of the ANN-models.These data are chosen due to their correlation with the global solar radiation.Thefirst model,called ANN-S model,which has the sunshine duration(S)as input.The second model(ANN-ST)has the sunshine duration and air temperature(T)as inputs,while in the third mod-el(ANN-STH u),we use the sunshine duration,air temperature and relative humidity(H u)as inputs.For all models,the output is the daily solar radiation data,in particularly the global irradiation (H G).Since the sunshine duration S could not be available in some stations,we have developed three others model,by using as inputs the air temperature T(ANN-T model),the relative humidity H u (ANN-H u model)and the air temperature T and relative humidity (ANN-TH u model).This paper is organized as follows the next section provides a database description.A correlation between different solar radia-tion components is presented in Section3.Section4gives a brief introduction on the neural networks.Section5deals with the implementation of the ANN-models for estimating daily global solar radiation.Results and discussion are given in thefinal section.1646M.Benghanem et al./Energy Conversion and Management50(2009)1644–16552.DatabaseThe data used in this work are the global irradiation H G,diffuse irradiation H D,air temperature T and relative humidity H u.These data are available from1998to2002at the National Renewable Energy Laboratory(NREL)website.The global irradiation H G on horizontal surface has been collected each5min since1998until 2002.Therefore,we have deduced the sunshine duration(S)which is the duration time when the energy received on horizontal sur-face is above120W/m2.These data are normalized by dividing each of them by corresponding extraterrestrial value.Fig.1a shows a typical example of a daily radiation sequence H G and daily sun-shine duration received on a horizontal surface at Al-Madinah site [16].Fig.1b shows the air temperature and relative humidity mea-sured on horizontal surface during5years.Fig.2a illustrates the evolution of daily irradiation for the year 2002at AL-Madinah site.It also shows the values of H0,which rep-resents the extraterrestrial radiation.Fig.2b shows the evolution of daily sunshine duration for the year2002.Thisfigure shows clearly that there is seasonal trend with super imposedfluctuation day to day of the daily values of solar radiation data,corresponding curves of clearness indexes(K t=H G/H0)values and sunshine duration frac-tion(SS=S/S0)are presented in Fig.2c.The distribution of clearness index K t is around the yearly average clearness index0.7281.This shows that the global irradiation at Medina site is higher and many applications of solar energy will be done with good results.3.Correlation between different solar radiation componentsIn linear regression model,the dependent variable comprises the ratio of the global solar irradiation to the available radiation at the top of the atmosphere(H0);and the independent variable comprises the ratio of the measured sunshine duration to the the-oretical available sunshine duration(S0).We have investigated empirical relationships and calculated the values of diffuse solar irradiation under the weather conditions of Al-Madinah location[16].The measured data of global irradiation, the corresponding sunshine duration,the air temperature and rel-ative humidity are used in linear,multi-linear and polynomial regression analysis.3.1.Correlation between global irradiation and sunshine durationThe relations between the fraction(H G/H0)and sunshine dura-tion(S/S0)are given by the following relations:H G0¼aþbSð1ÞH G0¼aþbSþcS2ð2Þwhere a,b and c are the coefficients of regression.Fig.3a shows the correlation between daily global irradiation and sunshine duration for Al-Madinah site.The correlation coefficient is94%.3.2.Correlation between global irradiation and air temperatureFig.3b shows the correlation between the global irradiation and the air temperature at Al-Madinah.In order to evaluate the model of correlation between the air temperature and the global irradiation received on horizontal surface,we have considered the data mea-sured from sunrise until midday and the data from midday until sunset[16].The linear regression for experimental data is given by:H G H0¼a1þb1TT Maxð3Þa1and b1are the coefficients of linear regression.The correlation coefficient is68%which is less than the above(in the case of global radiation and sunshine duration).3.3.Correlation between global irradiation and relative humidityFig.3c shows the correlation between the global irradiation H Gand the relative humidity H u at Al-Madinah site.The correlationmodel is given by:H GH0¼a1þb1ÁH uH uMaxð4Þa2and b2are the coefficients of linear regression.The correlationcoefficient is72%.4.Artificial neural networksArtificial neural networks have been used widely in many appli-cation areas.Most applications use a feed-forward neural network(FFNN)with the back-propagation(BP)training algorithm.Thereare numerous variants of the classical BP algorithm and othertraining algorithms[17].All these training algorithms assume afixed ANN architecture and during training,they change theweights to obtain a satisfactory mapping of the data.The main advantage of the feed-forward neural networks is thatthey do not require a user-specified problem solving algorithm(asis the case with classic programming)but instead they‘‘learn’’from examples,much like human beings.Another advantage is that they possess inherent generalizationability.This means that they can identify and respond to patternswhich are similar but not identical to the ones with which theyhave been trained.On the other hand,the development of afeed-forward ANN-model also poses certain problems,the mostimportant being that there is no prior guarantee that the modelwill perform well for the problem at hand.A typical feed-forward neural network is shown in Fig.4.Thetraining data set consists of N training patterns{(x p,t p)},where pis the pattern number.The input vector x p and desired output vec-tor t p have dimensions N and M,respectively;y p is the networkoutput vector for the p th pattern.The thresholds are handled byaugmenting the input vector with an element x p(N+1)and settingit equal to one.The simplified diagram of the back-propagation canbe seen in Fig.5.5.ANN-based implementation of solar radiation modelsThe main objective of this study is to model and estimate theglobal solar radiation from other parameters such as sunshineduration,air temperature and relative humidity,using artificialneural network.So far,we try to develop three global solar radia-tion models.In thefirst model,we try to estimate the global solarradiation H G,from only the sunshine duration S and the day t ofyear as inputs,so:H G¼e fðt;SÞð5ÞHowever,in the second model we try to estimate the global so-lar radiation from the day t of year,the sunshine duration S and theair temperature T as inputs,so:H G¼e fðt;S;TÞð6ÞWhile in the third model,we add to the last parameters otherparameter,which is the relative humidity H u,so:H G¼e fðt;S;T;H uÞð7ÞM.Benghanem et al./Energy Conversion and Management50(2009)1644–16551647where e f is depend on the weight and the bias of the neural network (for the optimal architecture).Otherwise,some parameters could not be available like sun-shine duration.For this,we have reduced the number of inputs1648M.Benghanem et al./Energy Conversion and Management 50(2009)1644–1655M.Benghanem et al./Energy Conversion and Management50(2009)1644–16551649parameters by using only the air temperature,relative humidity and the day t of year as inputs of the ANN-model,so:H G¼e fðt;TÞð8ÞH G¼e fðt;H uÞð9ÞH G¼e fðt;T;H uÞð10ÞThe feed-forward neural network shown in Fig.4is used in this work.Where x i,(i=2,3,4)correspond,the time t,the sunshine duration S,the air temperature T and the relative humidity H u, respectively,while y i represents the output which correspond in our study to the global horizontal solar radiation.The described data set will be divided into two sets,thefirst set of4years(365Â4)will be used for training the feed-forward neu-ral network,while the second set which consists of365data,will be used for testing and validating each models.The inputs and the output for each model arefixed previously,while the number of hidden layers and neurons within each layer will be adjusted during the training process.Also,the error for stopping the process isfixed at10À4.The pseudo-code of feed-forward network trained by Levenberg–Marquardt(LM)algorithm,which is an effective BP training algorithm,is shown in Appendix A.6.Results and discussionThe computer codes for each ANN-model were developed in the MATLAB software(version7.5).Therefore,three feed-forward neu-ral networks are trained until the best performance is obtained (the cost error should less or equal to thefixated error).Once,this criterion is achieved the optimal weights and bias are saved,thatTable1Statistical test for different simulation between measured and estimated ANN-models(H G¼e fðt;SÞ;H G¼e fðt;S;TÞand H G¼e fðt;S;T;H uÞ).ANN architecture(MLP)MPE(%)RMSE MBE r(%)First model H G¼e fðt;SÞh2Â5Â1i 2.43660.046767 1.368597.34h2Â3Â1i 2.43390.045524 1.354197.33h2Â2Â1i 2.20770.049515 1.251497.44h2Â7Â1i 2.34740.046759 1.524797.20h2Â7Â1i 2.25010.046891 1.458297.16h2Â5Â3Â1i 2.46780.047431 1.541497.11Second model H G¼e fðt;S;TÞh3Â2Â1i 2.25880.046997 1.301497.40h3Â3Â1i 2.29030.044262 1.021597.65h3Â5Â1i 2.43320.046039 1.195497.48h3Â7Â1i 2.50300.046555 1.364597.35h3Â9Â1i 2.37010.045740 1.198597.54h3Â11Â1i 2.84390.047357 1.651897.03h3Â5Â3Â1i 2.52270.045738 1.185497.55Third model H G¼e fðt;S;T;H uÞh4Â2Â1i 2.52270.045738 1.184797.55h4Â3Â1i 2.80720.047032 1.354197.35h4Â5Â1i 2.52000.044121 1.178997.54h4Â7Â1i 2.91350.047847 1.545197.16h4Â9Â1i 2.75070.048074 1.658497.00h4Â5Â3Â1i 2.65210.045862 1.596597.14 1650M.Benghanem et al./Energy Conversion and Management50(2009)1644–1655M.Benghanem et al./Energy Conversion and Management50(2009)1644–16551651will be used for testing and validating the models.Fig.6a–c shows a comparison between measured and estimated daily global solar radiation for thefirst ANN-model,the second and the third ANN-model,respectively.As it can be seen,good agreement is obtained for all models. However,in the point of view of the correlation coefficient r,the second model Eq.(6)presents better accurate results than others ANN-models in this study.In order to test and validate each model,we have done a statis-tical test(root mean square error‘RMSE’,the correlation coefficient ‘r’,mean bias error,‘MBE’and mean percentage error,‘MPE’)be-tween measured and estimated global solar radiation by the1652M.Benghanem et al./Energy Conversion and Management50(2009)1644–1655ANN.The used statistical test is presented in Appendix B .Obtained results are summarized in Table 1.For several simulations,it was found that the best performance is obtained for the second ANN-model according to the correlation coefficient between both series.The obtained r is 97.65%,which is higher than other models.The MPE is 2.2903and the RMSE is 0.044251.According to this table,we can note that in all ANN-models,one hidden layer is sufficient for modelling and estimation the daily global solar radiation.Therefore,we do not need to add more than one layer.In addition,the number of neurons in hidden layer can be arranged in the interval from two to five neurons for the bestperformance,in this case all developed ANN-model can be con-verge very fast.If we increase or decrease the number of neurons from this interval,the correlation coefficient decreases and the process needs more computing time for converging.From Table 1,we can observe that the correlation coefficient for each simulation is arranged between 97.00%and 97.65%,however,we opted for the second ANN-model,and this model need in his in-put two parameters (T ,S )and day of year that are always available,and they can be measure easily.Therefore,the developed model can be given by the following approximate formula:e y ¼X M k ¼121þexp ÀP M j ¼1P Ni ¼1w 1ði ;j Þx ði ÞðÞþb 1ðj ÞÀ124350@1A w 2ðk Þb 2ð11Þwhere w 1,w 2,b 1and b 2are,respectively,the weights and the bias ofthe networks,x ,represents the inputs data which can take the sun-shine duration,air temperature,relative humidity and the day of year (according to the model).M and N are the number of neurons in the hidden layer and in the input layer,respectively.The exper-imental values of w 1,w 2,b 1and b 2are shown in Appendix C .In addition,we have developed others three ANN-models,the first ANN-model has as input the day of year and air temperature,the second has as input the day of year and relative humidity whileTable 2Statistical test between measured and estimated global solar radiation by thedeveloped ANN-models (H G ¼e f ðt ;T Þ;H G ¼e f ðt ;H u Þand H G ¼e f ðt ;T ;H u Þ).ANN architecture (MLP)MPE (%)RMSE MBE (%)r (%)First model H G ¼ef ðt ;T Þh 2Â5Â1i2.09580.063534 2.541989.20Second model H G ¼e f ðt ;H u Þh 2Â5Â1i4.00120.067655 2.842187.00Third model H G ¼e f ðt ;T ;H u Þh 3Â2Â1i3.9580.0653742.701288.99M.Benghanem et al./Energy Conversion and Management 50(2009)1644–16551653the third model combine both relative humidity,temperature and the day of year.Therefore,we develop these ANN-models in order to show the influence of each parameter for estimating daily global solar radiation.Fig.7a–c shows a comparison between measured and estimated daily global solar radiation by using neural networks for each mod-el.From these curves an acceptable agreement between measured and estimated daily global radiation is obtained by ANN.The correlation coefficient for each model is arranged between 87%and89%.Table2resumes the statistical test between mea-sured and estimated H G.It is clearly shown that,the best perfor-mance is obtained by thefirst model r=89.20%,this is proves the correlation between the global solar radiation and air temper-ature.Therefore,in the case,when we use as input only the relative humidity,the correlation coefficient is decreases to87%,Also, when we mixed both air temperature and relative humidity the correlation coefficient is weakly decreases to88.99%.In any case the best model of these three ANN-models cannot provides accurately such as the above second ANN-model devel-oped(ANN-ST model),which need in his inputs air temperature and the sunshine duration.Therefore,the last three ANN-models can be used in the case when we have not the sunshine duration, because this parameter play very important role for obtaining good accurate results.In order to show the potential of the proposed ANN-models,we have made a comparative study between designed ANN-models and conventional correlation models Eqs.(1)–(4).Therefore,the calculated parameters a,b and c for Al-Madinah are given as follows:H G H0¼À0:3824þ:2786SS0ð12ÞH G0¼0:1166À0:2202Sþ1:0723S2ð13ÞH G H0¼0:6369þ0:037TT Maxð14ÞH G0¼0:7556À0:1353H uuMaxð15ÞA comparison between measured and calculated H G by theabove formulas is illustrated in Fig.8a–d as can be seen,the second correlation formulate Eq.(13)gave better results than the others models,since the good value obtained for correlation coefficient (r=97.48%).Table3illustrates a comparison between different ANN-models and conventional regression models.According to this table,we can notice that the second model,with S and T as inputs presents better accurate results than others ANN-models done in this study. All models exhibited low MBE values(Table3).For most of the models,the MBE values are comparable to the experimental error for the ANN-models proposed by this research and it cannot be considered as decisive for the prevalence of any one of the models.7.ConclusionIn this paper,ANN-models for estimating of solar radiation in Al-Madinah(Saudi Arabia)have been developed.Measured daily global solar radiation was compared with those obtained by the different designed ANN-models.Obtained results indicate that the second ANN-model(ANN-ST model)has better accurate results than the others ANN-models.However,for each developed ANN-models the correlation coef-ficient r is grater than97%.In addition,in this study case,only one hidden layer is sufficient for estimating the daily global solar radi-ation from other parameters,and the number of neurons in the hidden layer is arranged between three andfive neurons.It should be noted that the sunshine duration play very impor-tant role for obtaining high accurate results,therefore,this has been proven in the case where we have eliminated the sunshine duration from the inputs of the three ANN-models.Also it has been demonstrated that,the ANN-models which use only the air tem-perature and day of year as inputs can give a good results to the others models in the point view correlation coefficient.Comparing the RMSE values for all model presented in this work,it can be seen that the model ANN-ST exhibits the best re-sults.The results obtained render the ANN methodology as a prom-ising alternative to the traditional approach for estimating the global solar radiation.However,in the case where we have not the sunshine duration we can use the three developed model with-out sunshine duration.AcknowledgementThe authors would like to thank the International Centre for Theoretical Physics,Trieste(Italy)for providing material for achieving the present work.Appendix APseudo-code of the Levenberg–Marquardt algorithmWhile not stop-criterion do{Calculates E p(w)for each pattern pE1<ÀP Np¼1E pðwÞT E pðwÞ;Calculates J p(w)for each pattern pRepeatCalculates D w;E2<ÀP Np¼1E pðwþD wÞT E pðwþD wÞ;If E1E2thenl<ÀlÃb;EndIfUntil E2<E1l<Àl/b;w<Àw+D w;EndWhile}Appendix BThe mean bias error:MBE¼1P Ni¼1H GðiÞÀe H GðiÞThe root mean square error:RMSE¼1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP Ni¼1H GðiÞÀe H GðiÞ2rTable3Comparative study between developed ANN-models and conventional regression models.Models r(%)RMSEANN-modelsH G¼e fðt;SÞ97.440.049515 H G¼e fðt;S;TÞ97.650.044262 H G¼e fðt;S;T;H uÞ97.540.044121 H G¼e fðt;TÞ89.200.143534 H G¼e fðt;H uÞ87.000.167655 H G¼e fðt;T;H uÞ88.990.165374 Conventional regression modelsH G H0¼À0:3824þ1:2786SS097.280.05120H G H0¼0:1166À0:2202SS0þ1:0723SS0297.480.04410H G H0¼0:6369þ0:037TT Max89.500.12154H G H0¼0:7556À0:1353H uH uMax86.590.251811654M.Benghanem et al./Energy Conversion and Management50(2009)1644–1655。