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响应曲面法与设计

于 2020-12-05 发布
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响应曲面法与设计,原理及实际的操作应用,对选用该法做实验的同学比较受用!7050等高当前运线图行条件最人值7D60504010040120x,=温度(C]160(10x2=压强si的162响应曲面的等高线图∑x,+∑Rnx+∑(16-2)几乎所有的RSM问题都用这些近似多项式中的一个或多个。当然,一个多项式模型在自变量的整个空间上是真实函数关系的合理的近似式是不可能的,但在-个相对小的区域内通常做的很好。第15章讨论的最小乘方法可用来估计近似多项式的参数然后在拟合曲面上儆嘀应曲面分析,如果拟合曲面是真实响应函数的个合适的近似式,则拟合曲面的分析就近似地等价于实际591系统的分析。如果能怜当地利用实验设计来收集数据,就能够最有效地估计模型参数。关于拟合响应曲面的设计叫做响应曲面设计。在16-4节中讨论这些设计RSM是一序贯方法。通常,当我们是在响应曲面相应的自变量区域内的某个点时,例如,像图162中当前运行条件那样的点,在此点处系统具有微小的弯曲,从而用一阶模型是恰当的。现在,我们的目的是要引导实验者快速而有效地到达最优点所在的邻近区域。一旦最优点的区域被找到,就可以用更精细的模型,例如阶模型并进行分析以便确定最优点的位置。由图162见出,响应曲面的分析法可以想像为“爬”一样,山顶代表响应的最大值点。如果真实的最优点是啊应的最小值点,则可设想为“落进山谷”。RSM的最终目的是确定系统的最优运行条件或确定因素空间中满足运行规范的区域。RSM主要不是用来了解系统的实际机制的,尽管RSM有助于得到这类知识。还有,RSM的“最优”是按特定的意义使用的。RSM的“爬山”方法只能保证收敛于局部的最优点162最速上升法系统最优运行条件的初步估计常常远离实际的最优点。在这种情况下实验者的目的是要快速地进入到最优点的附近区域。我们希望利用又简单又经济有效的实验方法。当远离最优点时,通常假定在x的一个小区域范围内一阶模型是真实曲面的合适近最速上升法是沿着最速上升的路径,郡响应有最大增量的方向逐步移动的方法。当然,如果求的是最小值,则叫做最速下降法。拟合的一阶模型是592·y=Rn+∑R;x与一阶响应曲面相应的y的等高线,是一系列平行的直线,如图l6-3所示。最速上升的方向就是y增加得最快的方面。这一方向一阶拟合响应最速上升路径曲面的区域=夕-20y-3图16-3--阶响应曲画的等高线与最速土升路径平行于合响应曲面等高线的法线方向。通常取通过所感兴趣的区城的中心并且垂直于拟合曲面等高线的直线为最速上升路径这样一来,沿着路径的步长就和回归系数{P}成正比。实际的步长大小是由实验者根据工序知识或其他的实际考虑来确定的实验是沿着最速上升的路径进行的直到观察到的响应不再593◆增加为止。然后,拟合一个新的一阶模型,确定-·条新的最速上升路径、继续按上述方法进行。最后,实验者到达最优点的附近区域。这一点,通常由一阶模型的拟合不足来指出。这时,进行如16-3节所述的添加的实验,会求得最优点的更为精确的估计例t6位化学工程帅要确定使化工产品收率最大的运行条件。影响收率的两个可控变量是:反应时和反应温度。工程师当前使用的运行条件是反应时同为35分钟,温度为155F,收率约为40%。因为此区域不大可能包含最优值←她拟合-阶模型并应用最速上升法。程师决定拟合一阶模型的探测区域应是反应时间为(30,40)分钟和(150,160)°F。为简化计算,将自变量规范在(-1,1)区间内。于是,如果记尔为自然时间变量,与:为自然温度变量,则规范变量是5155数据如表161所水。用来收集这些数据的设计是增加五个中心点的22析因设计,在中心点处的重复观察值是用来估计实验误差的,并可以用来检阶模型的适合性。还有,过程的当前运行条件也就在设计的中心点处用最小二乘法将一阶模型来拟合这些数据。用第15章的方法,求得以规范变量表示的下列模型y=49,44+0.775x1+0.325x2在沿着最速上升路径探测之前,应研究-阶模型的适合性。有中心点的22设计允许实验者去做1.求出误差的个估计量2.检测模型的交互作用(交叉乘积项3检测二次效应(弯曲性)。中心点处的重复观察值可月来计算误差的估计量如下:(40.3)2+(40.5)2+(49.7)2+(40,2)2+(40.6)2=(202.3)2/50.0430594表16-1拟會一阶模型的过程数据首然变量规范变量响应了1301539.3301604u.(小01504U.9404J.53543.335010.5351534(.了35l5544.235l554〔.6阶模型假定变量r2和x2对响应有可加的效应。变量间的交互作用可用增加于模型的交叉乘积项x2的系数12来度量。此系数的最小二乘估计恰好是按普通22析因设计算得的交作用效应的二分之一,或B=1[(1×3.93)÷(1×41-5)+(-1×40.0)+(-1×40.9-0。1)0.025单自由度的交可作用平方和是SS交互作甲〔.02比较SS炊作用和。给出下刘拟合个足统计量:交五卡0.0250.0430=0058与F…进行比较。显然.交可作用是不显著的对直线模型适合性的另一个检测是比较设计的析因部分的四个点处的平均响应,即y=40,425、和在设计的中心点处的平均响应,即兴=40.46如果设计于弯曲的曲面上·则yr-y是曲面的总弯曲性的度量。如果月1与A2“纯二次”项x与x的系数,则y-y是A1+R的一个估计量。在我们的例中,纯二次项的个估计量是B1:+B40.425—40.460.35与零假设H:1+P2=0有关的单自由度的平方和是tf(÷)(5)(-优35)24+027其中7利n分别是析因部分的点数和中心点数。因F0,0027。063〔.0430将它与F、,比较。没有显示出纯二次项的影响。此模型的方差分析概括在表15-2中。交互作用和弯曲性的检测都是不显菩的,前总回归的F检验是显著的。还有,月和P2的标准差是MS0.94300.10=1,24问归系数月和B2相对于它们的标准差都较大。在这一点上.我们没有理由怀疑阶模型的适合性要离开设计中心·点(x:=0,x2=0)—沿最速上升跸径移动,就要对沿x2方向每移动0.325个单位.我们将沿x1方向移动0.775个单位。于是,最速上升路径经过点(x1-0,xz=0)且斜率为0.325/0.775。工程师决定用5分钟反应时间作为基本步长。用与x1之间的关系式,知道5分钟反应时问等价于规范变量x1的步长为4x=1。因此,沿最速上升路径的步长是△x1-1.00和4x2=(0.325/0.775)△x;=042。L程师计算了沿此路径的点并观察了在这些点处的收率直至响应下降为止。其结果见表16-3,表中既列出了规范变量也列出了自然变量。虽然规范变量在数学上容易计算,但在过程运有中必须用自然变量。图16-4画出了沿最速上升路径的每一步处的收率图。直到第十步所观察到的响应都是增加的;但是,这以后的每·步收率都是减少的。因此,另一一个一阶模型应该在点(41=85,2=175)的附近区域进行拟合。596·衰L42一阶模型的方差分析变差来源平方和自由度均方西归(月1,A2)825:214412547.83残差0.1772(交互作用(0.自025)0.4025).058〔纯二次)U.0027)0.00270.053纯误差)0.⊥7200.0430总和3.002281%的显着性表16-3例16-1的最谅上升实验规范变量自然变量响应步长_巴原点351550.42原点+△1.0,42401574且,原点+2△2.000.8445ig42原点十343.001.2650原点+444.[0685563原点+5▲5.2.106016553.8原点+646-供2.526516759.9原点十7▲7.002.9470l6965.0原点+88.03.:6751710.4原点+9△78173原点+10419.420L75原点+11411.004.6290ITs76原点十12412.00549575.上个新的一阶模型在点〔51=85,52=175)附近拟合。探测的区域对与是[80,90],对2是[170,180],于是。规范变量是5979F0Z了456785t112步长图16-4例16-1中沿最速上升路径的收率对步长的图形35,-175再次用五个中心点的2设计。数据见表6-在。拟合表16-4的规范数据的一阶模型是y=:78,97+1.00x1+0.50x2此模型的方差分析,包括交作用和纯次项的检测,如表16-5所示。交可作用和纯次项的检测表明、阶模型不是合适的近似。真实曲的弯曲性指岄了我们已接近最优点。为更精确地确定最优点,在该点必须做进步的分忻2由例16-1见出,最速上升路径是和拟合的一阶模型598

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  • altera公司IP核使用手册.PDF
    altera公司IP核使用手册,对于学习EDA技术的学生或工程师有用A吉RAContentsChapter 1. About this MegaCore FunctionRelease informat1-1Device Family Support···Introduction.··········FeaturesOpen core plus evaluation1-3Performance···Chapter 2. Getting StartedDesign Flow衡·鲁·,看·,音番2-1Megacore Function walkthrough2-2Create a New quartus II Pi2-2Launch the mega Wizard Plug-in ManagerStep 1: Parameterize2-5Step 2: Set Up SimulationStep 3: Generate..,2-11Simulate the design2-13Compile the design2-13Pa Device2-14Set Up Licensing2-15ppend the license to yourdat file2-15Specify the License File in the Quartus II Software...2-15Example Simulation and Compilation..2-16Example quartus Ii project2-16Example simulation with Test Vectors,,,,,,2-16Chapter 3. SpecificationsyperTransport Technology Overview1HT SyStems3-2HT Flow ControlHyper Transport MegaCore Function SpecificationPhysical InterfaceSynchronization and alignment ...Protocol interfClocking Options.......HyperTransport Mega Core Function Parameters and HT Link Performance3-10Signals3-14CSR Module...3-31OpenCore plus time-Out BehaviorAppendix A. ParametersIntroduction鲁鲁鲁A-1Parameter listsDevice Family and Read Only registers···········,,,,,,,,,,A-1Base Address Registers番鲁,A-2Clocking OptionsA-3Advanced settingso March 2009 Altera corporationHyperTransport MegaCore Function User GuideAppendix B. Stratix Device Pin AssignmentsIntroductionB-1GuidelinesAppendix C. Example designGeneral descriptionAdditional informationRevision historyInto-lHow to Contact alteraInfo-1Typographic Conventions ..........Info-2Hyper Transport MegaCore Function User Guideo March 2009 Altera CorporationA吉RA1. About this MegaCore FunctionRelease InformationTable 1-1 provides information about this release of the Hyper Transport Mega CoretfunctioTable 1-1. Hyper Transport Mega Core Function Release InformationitenlDescription∨ ersion9.0Release dateMarch 2009Ordering codeIP-HTProduct ID(s)0098Vendor iD(s)6AF7Altera verifies that the current version of the quartus@ll software compiles theprevious version of each MegaCore function. Any exceptions to this verification arereported in the Mega Core lP Library release Notes and Errata. Altera does not verifycompilation with Mega Core function versions older than one releaseDevice Family SupportMegaCore functions provide either full or preliminary support for target Alteradevice families:Full support means the Mega Core function meets all functional and timingrequirements for the device family and may be used in production designsa Preliminary support means the Mega Core function meets all functionalrequirements, but may still be undergoing timing analysis for the device family;itmay be used in production designs with cautionTable 1-2 shows the level of support offered by the Hyper Transport MegaCorefunction for each of the altera device familiesTable 1-2. Device Family SupportDevice FamilySupportHard Copy Stratix@FullStratixFulStratix IIFulStratix‖GXPreliminaryStratix GXOther device familiesNo supportC March 2009 Altera CorporationHyperT ransport Mega Core Function User Guide1-2Chapter 1: About this MegaCore FunctionIntroductionIntroductionThe Hyper Transport Mega Core function implements high-speed packet transfersbetween physical(PhY) and link-layer devices, and is fully compliant with theHyperTransport l/O Link Specification, Revision 1.03. This Mega Core function allowsdesigners to interface to a wide range of Hyper TransportTm technology(hT)enableddevices quickly and easily, including network processors, coprocessors, videochipsets, and ASICsFeaturesThe Hyper Transport Mega Core function has the following features8-bit fully integrated hT end-chain interfacePacket-based protocolDual unidirectional point-to-point linksUp to 16 Gigabits per second(Gbps)throughput(8 Gbps in each direction)200, 300, and 400 MHz DDR links in Stratix and Stratix GX devices200, 300, 400, and 500 MHz ddr links in Stratix II and Stratix II GX devicesLow-swing differential signaling with 100-Q2 differential impedanceHardware verified with Hyper fransport interfaces on multiple industry standardprocessor and bridge devicesFully parameterized mega core function allows flexible, easy configurationFully optimized for the altera stratix Il, Stratix, Stratix GX, and Stratix II GXevice famillesApplication-side interface uses the Altera AtlanticTM interface standardManages Hr flow control, optimizing performance and ease of useIndependent buffering for each HT virtual channelAutomatic handling of ht ordering rulesStalling of one virtual channel does not delay other virtual channels(subject toorderingFlexible parameterized buffer sizes, allowing customization depending onsystem requirementsUser interface has independent interfaces for the HT virtual channels, allowingindependent user logic designCyclic redundancy code(crc) generation and checking to preserve data integrityIntegrated detection and response to common HT error conditions■ CRC errorsEnd-chain errorsFully integrated HT configuration space includes all required configuration spaceregisters and HT capabilities list registersHyper Transport MegaCore Function User Guideo March 2009 Altera CorporationChapter 1: About this MegaCore FunctionPerformance32-bit and 64-bit support across all base address registers bars)automatically handles all csr space accessesVerilog HDL and VHdL simulation supportOpen Core Plus EvaluationWith the Altera free Open Core Plus evaluation feature, you can perform the followingSimulate the behavior of a mcgafunction(Altera MegaCore function or AMPPmegafunction) within your systema Verify the functionality of your design, as well as quickly and easily evaluate itssize and speedGenerate time-limited device programming files for designs that includeMegaCore functionsProgram a device and verify your design in hardwareYou only need to purchase a license for the Mega Core function when you arecompletely satisfied with its functionality and performance and want to take yourdesign to productiono For more information about Open Core Plus hardware evaluation using theHyperTransport MegaCore function, refer to"Open Core Plus Time-Out Behavior"onpage 3-40 and AN 320: Open Core Plus Evaluation of megafunctionsPerformanceThe Hyper Transport Mega Core function uses 20 differential I/O pin pairs and 2single-ended I/O pins, requiring 42 pins total. Table 1-3 through Table 1-5 showtypical performance and adaptive look-up table (alut) or logic element (LE)usagefor the HyperTransport MegaCore function in Stratix II GX, Stratix IL, Stratix, andStratix GX devices respectively, using the Quartus@ II software version 7.1Table 1-3 shows the maximum supported data rates in megabits per second(Mbps)by device family and speed gradeTable 1-3. Maximum Supported Hyper Transport Data Rates (Note 1)Speed GradeDevice Family-36Stratix ll GX devices 1000 Mbps 1000 Mbps 800 MbpsNA(2)N/A(2NA(2)Stratix devices1000 Mbps 1000 Mbps 800 Mbps N/A(2)NA(2)NA(2)Stratix devicesN/A(2N/A(2)00 Mbps 800 Mbps 600 Mbps400 MbpsFlip-Chip packagesStratix devicesNA(2)NA(2)NA(2)600 Mbps400 Mbps400 Mbps(Wire Bond packagesStratix GX devicesN/A(2) N/A(2)800 Mbps 800 Mbps 600 Mbps N/A(2)Notes to table 1-3(1)Rates are per interface bit. Multiply by eight to calculate the uni-directional data rate of an 8-bit inter face(2) Devices ot this speed grade are not ottered in this device familyC March 2009 Altera CorporationHyperTransport Mega Core Function User GuideChapter 1: About this MegaCore FunctionPerformanceTable 1-4 shows performance and device utilization for the Hyper TransportMegaCore function in Stratix II and Stratix II GX devicesTable 1-4. Hyper Transport Mega Core Function Performance in Stratix ll and Stratix ll GX DevicesParametersMemoryUserRXCombinationalHT Link InterfacePosted Non-Posted Response ClockingALUTSLogicfMAX(MHz) MAx(MHz)Buffers BuffersBuffers Option(12)Registers M4K M512 ( 3)3)Shared3.5005200120500125(4RX/TX/Ref35005200500Ref/x8Shared36005400160500>150RX/TXShared4.0006,00016150RX/TX16Shared4,1006,200500125(4)RX/TX/RefShared4.1006200500125(4Ref/TxShared4.2006400160150RX/TXNotes to table 1-4.Refer to " Clocking Options "on page 3-7 for more information about these options(2 )Other parameters(BAR configurations, etc. )vary the alut and Logic Register utilization numbers by approximately +/-200(3)Figures for -3 speed grade devices only(4) When using the Shared Rx/Tx/Ref and Shared Ref/Tx options, the user interface frequency is limited to exactly the ht frequency divided byTable 1-5 shows performance and device utilization for the Hyper TransportMegaCore function in Stratix and Stratix GX devicesTable 1-5. Hyper Transport Mega Core Function Performance in Stratix and Stratix GX DevicesUser Interface fmaxParametersUtilizationHT Link fMAX MHz)MHZ)RXRXSpeed GradePosted Non-Posted Response Clocking Option LEsM4KBuffers BuffersBuffers)(2 Blocks.5-66Shared rx/tx/ref1240010073)100734448888Shared Ref/Tx 7, 60014400400100{3)100(3)Shared rxtx7,90016400400>125>100Shared rxtx8.900125>100168Shared Rx/T×Ref9,400124004001003)100316Shared ref/ ix9.500144001003)10073)16Shared rx/x9.700400125Notes to table 1-5:(1)Refer to Clocking Options"on page 3-7 for more information about these options(2 )Other parameters( BAR configurations etc. )vary the LE utilization by approximately +/-200 LES(3 )When using the Shared Rx/Tx/ Ref and Shared Ref/Tx options, the user interface frequency is limited to exactly the hT frequency divided by fourHyper Transport MegaCore Function User GuideC March 2009 Altera CorporationA吉RA2. Getting StartedDesign FlowTo evaluate the HyperTransport Mega Core function using the Open Core Plus feature,include these steps in your design flowObtain and install the HyperTransport Mega Core functionThe HyperTransport Mega Core function is part of the MegaCore IP Library, which isdistributed with the Quartus ii software and downloadable from the altera websitewww.altera.como For system requirements and installation instructions, refer to Quartus II InstallationLicensing for Windows and Linux Workstations on the Altera website atwww.altera.com/literature/lit-qts.ispFigure 2-1 shows the directory structure after you install the HyperTransportMegaCore function, where is the installation directory. The default installationWindows is C: altera ; on Linux it islopt/alteraFigure 2-1. Directory StructureInstallation directorypContains the Altera MegaCore IP Library and third-party IP coresalteraContains the Altera MegaCore IP LibrarycommonContains shared componentshtContains the Hyper Transport Hyper Transport Megacore function files and documentationdocContains the documentation for the Hyper Transport MegaCore functionlibContains encrypted lower-level design filesexampleContains the design example for the Hyper Transport Mega Core function2. Create a custom variation of the Hyper Transport Mega Core function3. Implement the rest of your design using the design entry method of your choice4. Use the IP functional simulation model to verify the operation of your designo For more information about Ip functional simulation models, refer to the SimulatingAltera IP in Third-Party Simulation Tools chapter in volume 3 of the Quartus II Handbook5. Use the Quartus II software to compile your designC March 2009 Altera CorporationHyperT ransport Mega Core Function User Guide2-2Chapter 2: Getting StartedMega Core Function WalkthroughIg You can also generate an Open Core Plus time-limited programming file,which you can use to verify the operation of your design in hardware6. Purchase a license for the hypertransport Mega Core functionAfter you have purchased a license for the Hyper transport mega Core functionfollow these additional steps1. Set up licensing2. Generate a programming file for the Altera device(s)on your board3. Program the Altera device(s)with the completed designMegaCore Function WalkthroughThis walkthrough explains how to create a custom variation using the AlteraHyper Transport IP Toolbench and the Quartus II software, and simulate the functionusing an ip functional simulation model and the modelsim software when you arefinished generating your custom variation of the function, you can incorporate it intoⅴ our overall projectIe IP Toolbench allows you to select only legal combinations of parameters, and warnsou of any invalid configurationsIn this walkthrough you follow these stepsCreate a New Quartus II Projecta Launch the MegaWizard Plug-in Manager■Step1: Parameterizea Step 2: Set Up Simulation■Step3: Generate■ Simulate the designTo generate a wrapper file and Ip functional simulation model using default values,omit the procedure described in"Step 1: Parameterizeon page 2-5Create a New Quartus ll ProjectCreate a new Quartus II project with the New Project Wizard, which specifies theworking directory for the project, assigns the project name, and designates the nameof the top-level design entityTo create a new project, perform the following steps1. On the Windows Start menu, select Programs> Altera> Quartus II tostart the Quartus lI software. Alternatively, you can use the Quartus II Web editionsoftware2. In the Quartus II window, on the File menu, click New Project Wizard. If you didnot turn it off previously, the New Project Wizard Introduction page appears3. On the New Project Wizard Introduction page, click NextHyper Transport MegaCore Function User Guideo March 2009 Altera Corporation
    2020-12-05下载
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  • 利用多个点拟合圆
    给定多个点,根据最小二乘原理,可以拟合出一个圆形,拟合的精度很高,
    2020-12-06下载
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