数学建模大全
充分了解数学建模的相关知识，其中包括各种算法以及MATLAB在数学建模中的具体应用以及相关的程序代码，综合各方面的知识，方便我们了解例如线性规划maxx s.t. Ax>b的Maab标准型为min -cx s.Axcx∑anx,=bi=12,…,mst≥可行解满足约束条件(4)的解x=(x1,x2,…,xn),称为线性规划问题的可行解,而使目标函数(3)达到最大值的可行解叫最优解可行域所有可行解构成的集合称为问题的可行域,记为R14线性规划的图解法101+x2=106z=12图1线性规划的图解示意图图解法简单直观,有助」了解线性规划问题求解的基木原坦。我们先应用图解法来求解例1。对于每一固定的值z,使目标函数值等于z的点构成的直线称为目标函数等位线,当z变动时,我们得到一族平行直线。对于例1,显然等位线截趋于右上方,其上的点具有越大的目标函数值。不难看出,本例的最优解为x*=(2,6),最优目标值26从上面的图解过程可以看出并不难证明以下断言:(1)可行域R可能会出现多种情况。R可能是空集也可能是非空集合,当R非空时,它必定是若干个半平面的交集(除非遇到空间维数的退化)。R既可能是有界区域,也可能是无界区域(2)在R非空,线性规划既可以存在有限最优解,也可以不存在有限最优解(其目标函数值无界)。(3)若线性规划存在有限最优解,则必可找到具有最优目标函数值的可行域R的“顶点”。上述论断可以推广到一般的线性规划问题,区别只在」空问的维数。在一般的n维空间中,满足一线性等式∑a1x=b的点集被称为一个超平面,而满足一线性不等式氵=1∑ax≤b(或∑a1x,≥b)的点集被称为一个半空间(其中(a1…,an)为一n维行向量,b为一实数)。若千个半空间的交集被称为多胞形,有界的多胞形又被称为多面体。易见,线性规划的可行域必为多胞形(为统一起见,空集Φ也被λ为多胞形)。在一般n维空问中,要直接得出多胞形“顶点”概念还有一些困难。二维空间中的顶点可以看成为边界直线的交点,但这一几何概念的推广在一般n维空间中的几何意义并不十分直观。为此,我们将采用另一途径来定义它。定义1称n维空间中的区域R为一凸集,若Vx,x2∈R及元∈(01),有x+(1-4)x2∈R定义2设R为n维空间中的一个凸集,R中的点x被称为R的一个极点,若不存在x、x2∈R及∈(0,1),使得x=4x+(1-4)x2。定义1说明凸集中任意两点的连线必在此凸集中;而定义2说明,若x是凸集R的个极点,则x不能位于R中任意两点的连线上。不难证明,多胞形必为凸集。同样也不难证明,维空间中可行域R的顶点均为R的极点(R也没有其它的极点)1.5求解线性规划的 Matlab解法单纯形法是求解线性规划问题的最常用、最有效的算法之一。这里我们就不介绍单纯形法,有兴趣的读者可以参看其它线性规划书籍。下面我们介绍线性规划的 Matlab解法Matlab中线性规划的标准型为min c rAx shs t.Aeq. x=beb
- 2020-12-01下载
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基于高光谱成像的蓝莓内部品质检测 特征波长选择方法研究
在特征波长选取方面有一些创新，可以作为参考。在特征波长选取方面有一些创新，可以作为参考。（基于高光谱成像的蓝莓内部品质检测特征波长选择方法研究古文君1 ，田有文 1* ，张芳1 ，赖兴涛 1 ，何宽1 ，姚萍1 ，刘博林 2）586-482016620010~15mm0.8~2.3g。fone3:(InSpector V10E, Spectral InFinland)1392pix×1040pixCCDL CCD2(IGV-B141OM, IMPERX Incorporated, USA), 150W1. CCD Camera; 2.Spectrometer; 3.Shot; 4. Light source; 5. Samples(3900 Illuminatior, Illumination Tech6.Translationplatform7.Lightsourcecontroller;8.computernologies inc.,USA)、(IRCP0076-19. Translation platform controllerCOM,)、(120cm×50cmx(DELL VoStro 5560D-1528Figure 1 Schematic diagram of hyperspectral imagingcmsystem400~1000nm,4722.8nmRRGY-4(10mm)(DBR45(successive projections algorithm, SPA(stepwise multiple linear regression, SMLR)(SPA)(SMLR)SPASPASMLRSPA-SPA、SMLR_SMLR、SPA- SMLRSMLR-SPA21994-2018ChinaAcadcmicJournalElcctronicPublishingHousc.Allrightsrcscrved.http://www.cnki.nct5871.6BP(error back propagation)BP17(correlation coeffiient of calibration, Re)(root mean square error of calibration set, RMSEC)correlation coeffiient of pre-diction, Rp)(root mean square error of prediction set, RMSEP)ENVI 4.8(Research System Inc, ), MATLAB 2014a(The Math Works Inc)、TheUnscrambler9.7、 Excel2010(Ⅵ icrosoftdgle banddWcvef.BP models for soluble solidsThe selected characteristic wavelengthCurve of relative reflectanceExtract the region of interescontent and firmness prediction2figure 2 Flow chart of data processing280mm,68ms,28mm·s-。99%202.2600nm600nm2b2c)21994-2018ChinaAcadcmicJournalElcctronicPublishingHousc.Allrightsrcscrved.http://www.cnki.nct5884823(2f)BPSavitzky-Golasavitzky -golayTable 1 The effect of different spectra preprocessingCalibration setPredictioSpectrum typeRMSECRMSEPOriginal spcctrum0.933/0.9230.3510.4040.9200.9100.508/0.319MSCThe spectrum after MSC processing0.940/0.9450.56lO.3120.9190.9320.516/0.282SNThe spectrum after SNV processin0.93709340.60210.24309220.9010.6320.462Savitzky-golayThe spectrum after Savitzky-Golay processing 0.955/0.9550.3240.2410.951/0.9490.400/0.2782.5SPA-SPA SMLRSMLR SPA-SMLR SMLR-SPASPA-SPASPASavitzky-GolaySPATable 2 The results of multi-stage characteristic wavelength selection methodnmCharacteristie wavelength selection methodSPA-SPA452,455,470,482,490,785,893,912,921,942,950455,470,482,785,893.912SMLR-SMLR457,508,516,534,543,51,556,568,712,720.774,778508,534,543,712,720,774SPA-SMLR452,455,470,482,490,785,893,912,921,942,950452,470,482,490,893,912SMLR-SPA457,508,516,534,543,551,556,568,712,720,774,78534,7202.6Savilzky-gola(FS)392SPA-SPASMLR-SMLRSMLR-SMLRSMLR-SPABPBP0.001500021994-2018ChinaAcadcmicJournalElcctronicPublishingHousc.Allrightsrcscrved.http://www.cnki.nct589BPBPSPA-SPARp RMseP0.9520.391°Brix,RpRMSEP0.9530.234BrixTable 3 Detection results of soluble solid content and firmness of blueberry based on different multi-stagecharacteristic wavelength selection methodsCalibration setPrediction setCharacteristic selection method Wavelength numberRMSECRMSEP3929550.9550.324/0.2410.9510.9490.400/0.278SPA-SPA0.9590.9560.3180.1530.9520.9530.391/0.234SMLR-SMLR0.9560.9340.414/0.243912109020.559/0.349SPA SMLR0.828/0.8581.3670.58582208091.440/0.719SMLR- SPA20.958/0.9360.402/0.3359320.9280.435/0,4041387nm1229nm91.5%BPRRMSEP0.904215.163lBP3Rv0.84V0.94Rv0.83,SEV0.63。400-1000nmSavitzky-GolayBPSPA-SPASPA-SPA21994-2018ChinaAcadcmicJournalElcctronicPublishingHousc.Allrightsrcscrved.http://www.cnki.nct59048[1 KADER F,ROVEL. B Fractionation and identification of the phenolic compounds of highbush blueberries(Vaccinium corymbosumLUJ].Food Chemistry, 1996,55(1): 35-40「J,2012,33(1):340-342,2017,38(2):301-305.[4 MENDOZA F, LU R, ARIANA D,et al. Integrated spectral and image analysis of hyperspectral scattering data for prediction ofple [ruil firmness and soluble solids conlenl[J] Poslharvesl Biology and Technology, 2011, 62(2: 149-160[5 SUN M J, ZHANG D, LIU L,et al. How to predict the sugariness and hardness of melons a near-infrared [J]. Food Chemistry,2017,218(3:413-42116 SIEDLISKA A, BARANOWSKI P, MAZUREK W, ct al. Classification models of bruise and cultivar detection on the basis of hy-perspectral imaging data[J]. Computers and Electronics in Agriculture, 2014, 106: 66-74[7 LIU D, SUN D W, ZENG X N, el al. Recenl aDvances in wavelength seleclion lechniques for hyperspectral image processing inthe food industry[J]. Food Bioprocess Technol, 2014, 7: 307-323[8 ZHANG C, GUO C T, LIU F,et al. Hyperspectral imaging analysis for ripeness evaluation of strawberry with support vector ma-chine[j] Journal of Food Engincering, 2016, 179: 11-18[9J,2016,47(5:634-6402009,29(:1611-1615201536(12)171-17612]J,2012,32(11:3093309[13] LI B C, HOU B L, ZHANG D W,et al. Pears characteristics (soluble solids content and firmness prediction, varieties) testingInethods based on visible-near infrared hyperspecTral imaging[J]. OpLik, 2016, 127: 2624-2630[14] FAN S X, ZHANG B H,LI J B, et al. Prediction of soluble solids content of apple using the combination of spectra and textural features of hyperspectral reflectance imaging data[J. Postharvest Biology and Technology, 2016, 121: 51-61[15 RAJKUMAR P, WANG N,EIMASRY G, et al.Studies on banana fruit quality and maturity stages using hyperspectral imaging[ JIJournal of Food Engineering 2012, 108: 194-200,2015,36(16):10172015,35(8:2297-2302[18]WANG N,2007,23(2:151-155.「192008,39(5):91-9320」201536(10:70-74.[21] WU D, SUN D WAdvanced applications of hyperspectral imaging technology for food quality and safety analysis and assess-ment a review part T[J]. Innovative Food Science and Emerging Technologies, 2013, 19(4): 1-14J2014,35(8:57-61BP,2012.124」13,44(2):142-146.25],201523(6:1530-1537M011:41-48.[27,2013,24(10:1972-19762010,30(10):2729-2733?1994-2018ChinaAcadcmicJournaleLcctronicPublishingHousc.Allrightsreservedhttp://www.cnki.nct
- 2020-12-07下载
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