由附件1“性能数据表”中A1~A14（用装料方式I）整理得下表“sheet2”：
使用全部影响乙醇转化率和C4 烯烃选择性的参数做拟合：
xx1：Co/SiO2
xx2：Co/SiO2 和 HAP 的质量比
xx3：催化剂总量
xx4：乙醇浓度
xx5：温度
乙醇转化率： y1=f(xx1,xx2,xx3,xx4,xx5)（使用万能的泰勒公式-幂级数，拟合公式见代码）
C4 烯烃选择性：y2=f(xx1,xx2,xx3,xx4,xx5)（使用万能的泰勒公式-幂级数，拟合公式见代码）
三级泰勒公式展开!!!using["luopt","math"]; //使用命名空间目标函数(xx1,xx2,xx3,xx4,xx5, //共61个拟合参数a,a1,a2,a3,a4,a5,a11,a12,a13,a14,a15,a22,a23,a24,a25,a33,a34,a35,a44,a45,a55,a111,a112,a113,a114,a115,a122,a123,a124,a125,a133,a134,a135,a144,a145,a155,a222,a223,a224,a225,a233,a234,a235,a244,a245,a255,a333,a334,a335,a344,a345,a355,a444,a445,a455,a555: i,s,x1,x2,x3,x4,x5,y1,y2,py,pc : tyArray,max)={i=-1, s=0, (++i<max).while{x1=tyArray(i,0)-xx1, x2=tyArray(i,1)-xx2, x3=tyArray(i,2)-xx3, x4=tyArray(i,3)-xx4, x5=tyArray(i,4)-xx5, py=tyArray(i,5), pc=tyArray(i,6),y1= a+a1*x1+a2*x2+a3*x3+a4*x4+a5*x5+a11*x1*x1+a12*x1*x2+a13*x1*x3+a14*x1*x4+a15*x1*x5+a22*x2*x2+a23*x2*x3+a24*x2*x4+a25*x2*x5+a33*x3*x3+a34*x3*x4+a35*x3*x5+a44*x4*x4+a45*x4*x5+a55*x5*x5+ a111*x1*x1*x1+a112*x1*x1*x2+a113*x1*x1*x3+a114*x1*x1*x4+a115*x1*x1*x5+a122*x1*x2*x2+a123*x1*x2*x3+a124*x1*x2*x4+a125*x1*x2*x5+a133*x1*x3*x3+a134*x1*x3*x4+a135*x1*x3*x5+a144*x1*x4*x4+a145*x1*x4*x5+a155*x1*x5*x5+a222*x2*x2*x2+a223*x2*x2*x3+a224*x2*x2*x4+a225*x2*x2*x5+a233*x2*x3*x3+a234*x2*x3*x4+a235*x2*x3*x5+a244*x2*x4*x4+a245*x2*x4*x5+a255*x2*x5*x5+a333*x3*x3*x3+a334*x3*x3*x4+a335*x3*x3*x5+a344*x3*x4*x4+a345*x3*x4*x5+a355*x3*x5*x5+a444*x4*x4*x4+a445*x4*x4*x5+a455*x4*x5*x5+a555*x5*x5*x5,s=s+[y1-py]^2 //拟合乙醇转化率//s=s+[y1-pc]^2 //拟合C4烯烃选择性},sqrt[s/max]//均方差RMSE为目标函数值};main(::tyArray,max)={tyArray=matrix{ //存放实验数据：使用装料方式I全部数据"0.514001.682504.0 9.6 0.514001.6827512.1 8.6 0.514001.6830029.5 10.7 0.514001.6832543.3 18.9 0.514001.6835060.5 27.3 0.514001.6840088.4 41.0 10.49251001.682502.5 1.9 10.49251001.682755.3 2.6 ... ...（略）"},len[tyArray,0,&max],Opt1[@目标函数, optmax,1000, optmode,20, optdeep,20, optwaysimdeep, optwayconfra, optwaylme] //Opt1函数全局优化};
结果及讨论：
对应乙醇转化率Y1的最优参数及均方差RMSE：
2.417402744750639 -0.2039147139106143 275.8011306772221 0.4156384853693174 260.1013882930106 14.8390185772 0.317318572539172 -19.50790611027291 -3.588076207774742e-002 -6.855005447168541 -4.086740657820882e-002 -1.460941918741034 -0.4367844784685392 3.425230738907303e-002 11.49855862581616 4.904074627155117e-002 12.37311562403754 9.190390656233782e-002 2.893081399660135 -8.277525297568886e-002 -5.116674454929938e-004 -3.922081102157155e-003 3.238624290254206e-005 -2.034325083811818 5.339523080291108e-003 3.387818581763618e-003 -8.649776365931871 1.907021895486433 3.717192575220874e-003 0.2081378685138888 -2.614230849096533e-002 0.8020982822085792 1.067869051018692e-002 13.65608817413937 8.19594575288e-003 -1.559228490839049e-004 5.447393901609546e-003 -6.670850845389642e-005 3.286334739062546 -3.95352575062304e-002 7.496760379706923e-005 -1.666984727364169 -2.45598856334926e-004 -2.942456600663122 4.646162907471563e-002 5.272516733906026e-005 2.86629773902457e-002 5.44992912475403e-004 26.46808705338533 -1.218629532938329e-003 1.496886943412408e-005 2.675602420290519e-007 2.753847472266319e-004 1.455617526774928e-005 -4.091460730469629e-002 9.190733722458817e-004 -1.477766443432227e-006 -8.220395243069316 -8.389116545320428e-003 3.364704951845783e-004 -1.132804688837243e-005 3.685019008260015
对应C4烯烃选择性Y2的最优参数及均方差RMSE：
1.9861580043017242.45043307197632367.498199324551580.208662313445064256.49685738389991.799578875493056-5.974066210514014 -11.56553740063614 -0.1545396393604948 5.1725231197521780.1540143576135561 -17.45297800630631 -0.1090062772880443 -1.310984675110006e-002 -14.03392383507257 -4.289169392186376e-002 22.25748000512774-2.245456583454652e-002 8.212272604609786e-002 6.271792925982265e-003 -6.669459749834531e-005 -1.903100059080562e-002 7.217058706506922e-004 -9.15304420446407-3.741345572514077e-002 2.559970423512096e-003 11.473732826652689.3419218178299523.264886165514432e-002 -6.472974026168921e-003 -2.121310819655539e-003 5.51933035952529-5.171538944184857e-003 4.9891553225599920.1533949251601508 -1.698477968040691e-004 -2.204068286556028e-002 2.761963091700759e-004 4.07988630137639.376124672502875e-002 2.641556051018874e-004 4.100002442739125-4.734441692273163e-003 -1.961348488352317 -0.1706020449016992 2.700080312269564e-004 -9.322610320728019e-004 1.622536988804513e-003 11.72316720890722-0.1463931085480807 -5.872822055720774e-004 1.205698763703183e-006 1.28679573773e-004 6.839371475233182e-006 3.721430144278198e-002 -4.335815325906642e-004 -1.157491548269355e-007 9.860323047148855-1.16777723885e-002 -1.625346889836123e-004 -1.228545092598462e-005 2.394257044586305
因参数多，耗时较长，等Opt::ShowMin输出稳定（半天多时间），取以上结果。
因耗时较长，未多次运行；若多台电脑同时运行，或许有更优结果。
因目标函数值稍大（均方差RMSE为3.69（对应Y1）和2.39（对应Y2）），说明三级泰勒公式展开精度欠佳，四级泰勒公式展开将有更好结果，但拟合参数将增加到131个，耗时将更长。
由以上拟合参数求C4烯烃收率（Y1*Y2）最大值，可求最佳参数xx1,xx2,xx3,xx4,xx5。
三级泰勒公式展开，优化求最佳C4烯烃收率!!!using["luopt","math"];; //使用命名空间init(:: //拟合参数赋值aa1,aa2,aa3,aa4,aa5,a,a1,a2,a3,a4,a5,a11,a12,a13,a14,a15,a22,a23,a24,a25,a33,a34,a35,a44,a45,a55,a111,a112,a113,a114,a115,a122,a123,a124,a125,a133,a134,a135,a144,a145,a155,a222,a223,a224,a225,a233,a234,a235,a244,a245,a255,a333,a334,a335,a344,a345,a355,a444,a445,a455,a555,bb1,bb2,bb3,bb4,bb5,b,b1,b2,b3,b4,b5,b11,b12,b13,b14,b15,b22,b23,b24,b25,b33,b34,b35,b44,b45,b55,b111,b112,b113,b114,b115,b122,b123,b124,b125,b133,b134,b135,b144,b145,b155,b222,b223,b224,b225,b233,b234,b235,b244,b245,b255,b333,b334,b335,b344,b345,b355,b444,b445,b455,b555) =new[real_s,61].SetArray["1.605961168999771 -0.4410695905557486 235.7757505227786 ... ...（这里放对应Y1的输出结果）"].in[0 :&aa1,&aa2,&aa3,&aa4,&aa5,&a,&a1,&a2,&a3,&a4,&a5,&a11,&a12,&a13,&a14,&a15,&a22,&a23,&a24,&a25,&a33,&a34,&a35,&a44,&a45,&a55,&a111,&a112,&a113,&a114,&a115,&a122,&a123,&a124,&a125,&a133,&a134,&a135,&a144,&a145,&a155,&a222,&a223,&a224,&a225,&a233,&a234,&a235,&a244,&a245,&a255,&a333,&a334,&a335,&a344,&a345,&a355,&a444,&a445,&a455,&a555],new[real_s,61].SetArray["0.6291493182031664 0.2958183812514781 -0.4652893843549317 ... ...（这里放对应Y2的输出结果）"].in[0 :&bb1,&bb2,&bb3,&bb4,&bb5,&b,&b1,&b2,&b3,&b4,&b5,&b11,&b12,&b13,&b14,&b15,&b22,&b23,&b24,&b25,&b33,&b34,&b35,&b44,&b45,&b55,&b111,&b112,&b113,&b114,&b115,&b122,&b123,&b124,&b125,&b133,&b134,&b135,&b144,&b145,&b155,&b222,&b223,&b224,&b225,&b233,&b234,&b235,&b244,&b245,&b255,&b333,&b334,&b335,&b344,&b345,&b355,&b444,&b445,&b455,&b555];;f(xx1,xx2,xx3,xx4,xx5 //目标函数: x1,x2,x3,x4,x5, y1, y2: aa1,aa2,aa3,aa4,aa5,a,a1,a2,a3,a4,a5,a11,a12,a13,a14,a15,a22,a23,a24,a25,a33,a34,a35,a44,a45,a55,a111,a112,a113,a114,a115,a122,a123,a124,a125,a133,a134,a135,a144,a145,a155,a222,a223,a224,a225,a233,a234,a235,a244,a245,a255,a333,a334,a335,a344,a345,a355,a444,a445,a455,a555,bb1,bb2,bb3,bb4,bb5,b,b1,b2,b3,b4,b5,b11,b12,b13,b14,b15,b22,b23,b24,b25,b33,b34,b35,b44,b45,b55,b111,b112,b113,b114,b115,b122,b123,b124,b125,b133,b134,b135,b144,b145,b155,b222,b223,b224,b225,b233,b234,b235,b244,b245,b255,b333,b334,b335,b344,b345,b355,b444,b445,b455,b555) ={x1=xx1-aa1, x2=xx2-aa2, x3=xx3-aa3, x4=xx4-aa4, x5=xx5-aa5,y1= a+a1*x1+a2*x2+a3*x3+a4*x4+a5*x5+a11*x1*x1+a12*x1*x2+a13*x1*x3+a14*x1*x4+a15*x1*x5+a22*x2*x2+a23*x2*x3+a24*x2*x4+a25*x2*x5+a33*x3*x3+a34*x3*x4+a35*x3*x5+a44*x4*x4+a45*x4*x5+a55*x5*x5+ a111*x1*x1*x1+a112*x1*x1*x2+a113*x1*x1*x3+a114*x1*x1*x4+a115*x1*x1*x5+a122*x1*x2*x2+a123*x1*x2*x3+a124*x1*x2*x4+a125*x1*x2*x5+a133*x1*x3*x3+a134*x1*x3*x4+a135*x1*x3*x5+a144*x1*x4*x4+a145*x1*x4*x5+a155*x1*x5*x5+a222*x2*x2*x2+a223*x2*x2*x3+a224*x2*x2*x4+a225*x2*x2*x5+a233*x2*x3*x3+a234*x2*x3*x4+a235*x2*x3*x5+a244*x2*x4*x4+a245*x2*x4*x5+a255*x2*x5*x5+a333*x3*x3*x3+a334*x3*x3*x4+a335*x3*x3*x5+a344*x3*x4*x4+a345*x3*x4*x5+a355*x3*x5*x5+a444*x4*x4*x4+a445*x4*x4*x5+a455*x4*x5*x5+a555*x5*x5*x5,x1=xx1-bb1, x2=xx2-bb2, x3=xx3-bb3, x4=xx4-bb4, x5=xx5-bb5,y2= b+b1*x1+b2*x2+b3*x3+b4*x4+b5*x5+b11*x1*x1+b12*x1*x2+b13*x1*x3+b14*x1*x4+b15*x1*x5+b22*x2*x2+b23*x2*x3+b24*x2*x4+b25*x2*x5+b33*x3*x3+b34*x3*x4+b35*x3*x5+b44*x4*x4+b45*x4*x5+b55*x5*x5+ b111*x1*x1*x1+b112*x1*x1*x2+b113*x1*x1*x3+b114*x1*x1*x4+b115*x1*x1*x5+b122*x1*x2*x2+b123*x1*x2*x3+b124*x1*x2*x4+b125*x1*x2*x5+b133*x1*x3*x3+b134*x1*x3*x4+b135*x1*x3*x5+b144*x1*x4*x4+b145*x1*x4*x5+b155*x1*x5*x5+b222*x2*x2*x2+b223*x2*x2*x3+b224*x2*x2*x4+b225*x2*x2*x5+b233*x2*x3*x3+b234*x2*x3*x4+b235*x2*x3*x5+b244*x2*x4*x4+b245*x2*x4*x5+b255*x2*x5*x5+b333*x3*x3*x3+b334*x3*x3*x4+b335*x3*x3*x5+b344*x3*x4*x4+b345*x3*x4*x5+b355*x3*x5*x5+b444*x4*x4*x4+b445*x4*x4*x5+b455*x4*x5*x5+b555*x5*x5*x5,-y1*y2/100 //C4烯烃收率的负值为目标函数值};Opt1[@f, optrange: 0.4,5.1; 0.4,2.1; 90.0,410.0; 0.2,2.2; 230.0, 470.0]; //指定范围内求解，超出范围恐误差加大
结果（xx1,xx2,xx3,xx4,xx5及目标函数值）及讨论：
5.099999000000042.099999992453416409.999999 2.199999982171348469.9999990026478-1951.17328362952
从拟合结果可以看出，目标函数值C4烯烃收率超过了100%，明显不符合实际情况，但仍对实验设计有指导意义。
xx1：Co/SiO2（实验数据提供了0.5、1、2、5共4个参数）最佳值在设定参数上限，应增加该参数进行实验。
xx2：Co/SiO2 和 HAP 的质量比（实验数据提供了0.4925、0.5556、1、2.0303共4个参数）最佳值在设定参数上限，应增加该参数进行实验。
xx3：催化剂总量（实验数据提供了100、140、400共3个参数）最佳值在设定参数上限，应增加该参数进行实验。
xx4：乙醇浓度（实验数据提供了0.3、0.9、1.68、2.1共4个参数）最佳值在设定参数上限，应增加该参数进行实验。
xx5：温度（实验数据提供较多）最佳值在设定参数上限，如果条件允许应增加该参数进行实验。
指定条件（Co/SiO2和HAP的质量比为1，催化剂总量为100）求最优值：
Opt1[@f, optwaycom, optrange: 0.4,5.1; 0.999,1.001; 99.999,100.0; 0.3,2.2; 230.0, 470.0]; //指定范围内求解，超出范围恐误差加大
结果（xx1,xx2,xx3,xx4,xx5及目标函数值）：
2.0593793934745951.00099999715131599.99900058470012.199999994350263452.9225113865244-49.9568032788798
猜想：如果xx1,xx2,xx3,xx4数据更多些，拟合结果或许会更好。
下面使用Lu脚本优化库中新增的泰勒展开式计算函数FunTaylor，不仅代码量大幅减少，运行速度也大幅提高：
三级泰勒公式展开!!!using["luopt","math"]; //使用命名空间目标函数(a :: tyArray,Array,max)={FunTaylor[2,5,3,a,tyArray], //计算泰勒展开式的函数值sqrt{sum{[(tyArray[all:5]-Array).reshape()].^2.0}/max} //均方差RMSE为目标函数值};main(:a:tyArray,Array,max)={//实验数据：使用装料方式I全部数据，最后一列为乙醇转化率（或者C4 烯烃选择性）tyArray=matrix{"0.514001.682504.0 0.514001.6827512.10.514001.6830029.5 0.514001.6832543.3 0.514001.6835060.50.514001.6840088.410.49251001.682502.5 10.49251001.682755.3 "},len[tyArray,0,&max], Array=tyArray[all:5],a=new[real_s,FunTaylor(0,5,3)], //申请数组，存放泰勒展开式系数Opt1[a, @目标函数, optmax,1000, optmode,20, optdeep,20, optwaysimdeep, optwayconfra, optwaylme] //Opt1函数全局优化};
运行结果与前述相同。
下面的代码可输出泰勒公式展开式：
输出泰勒公式展开式!!!using["luopt","math"]; //使用命名空间main(:a)={a=new[real_s,FunTaylor(0,5,3)].SetArray{ //申请数组"2.41749698355 -0.2038158183643675 275.7788602686833 ... //存放泰勒展开式系数"},FunTaylor(1,5,3,a) //输出泰勒展开式};
结果：y=f(y0,y1,y2,y3,y4) 乙醇转化率 的三级泰勒展开
x0=y0-(2.41749698355), x1=y1-(-0.2038158183643675), x2=y2-(275.7788602686833), x3=y3-(0.4157150578775843), x4=y4-(260.1130205122635),
y=(14.8339916081916)+(0.3166092689262277)*x0+(-19.5191890572145)*x1+(-3.579769353416268e-002)*x2+(-6.851231734885069)*x3+(-4.081252504690269e-002)*x4
+(-1.462185975049673)*x0*x0+(-0.4399498529512698)*x0*x1+(3.424728880639916e-002)*x0*x2+(11.50149493634983)*x0*x3+(4.899775046562916e-002)*x0*x4+(12.37566086214654)*x1*x1+(9.179605162184748e-002)*x1*x2+(2.890613812179718)*x1*x3+(-8.280205689469142e-002)*x1*x4+(-5.112768904844806e-004)*x2*x2+(-3.945340831718832e-003)*x2*x3+(3.216395934710691e-005)*x2*x4+(-2.02763843455804)*x3*x3+(5.330066275526738e-003)*x3*x4+(3.38768061375748e-003)*x4*x4
+(-8.64941211238461)*x0*x0*x0+(1.906979904073245)*x0*x0*x1+(3.715034007924377e-003)*x0*x0*x2+(0.2072410484718987)*x0*x0*x3+(-2.614438938622829e-002)*x0*x0*x4+(0.8077179983441646)*x0*x1*x1+(1.067299977263131e-002)*x0*x1*x2+(13.64855878020005)*x0*x1*x3+(8.218774646838642e-003)*x0*x1*x4+(-1.558999302693181e-004)*x0*x2*x2+(5.46432176380897e-003)*x0*x2*x3+(-6.669493109849741e-005)*x0*x2*x4+(3.28977261781)*x0*x3*x3+(-3.952670192258448e-002)*x0*x3*x4+(7.497001157885084e-005)*x0*x4*x4+(-1.664062662934021)*x1*x1*x1+(-2.11898392118816e-004)*x1*x1*x2+(-2.94415280401644)*x1*x1*x3+(4.647403064153688e-002)*x1*x1*x4+(5.293074439992591e-005)*x1*x2*x2+(2.86869330256e-002)*x1*x2*x3+(5.447745594835923e-004)*x1*x2*x4+(26.46740180486084)*x1*x3*x3+(-1.230102336289828e-003)*x1*x3*x4+(1.493155915585734e-005)*x1*x4*x4+(2.693155624482926e-007)*x2*x2*x2+(2.753552958995272e-004)*x2*x2*x3+(1.455718067712246e-005)*x2*x2*x4+(-4.09069242216141e-002)*x2*x3*x3+(9.190931133968552e-004)*x2*x3*x4+(-1.477757220874119e-006)*x2*x4*x4+(-8.219787163776919)*x3*x3*x3+(-8.378418878388916e-003)*x3*x3*x4+(3.364395602770745e-004)*x3*x4*x4+(-1.132849569198336e-005)*x4*x4*x4
结果：y=f(y0,y1,y2,y3,y4) C4 烯烃选择性 的三级泰勒展开
x0=y0-(1.986158004301724), x1=y1-(2.450433071976323), x2=y2-(67.49819932455158), x3=y3-(0.208662313445064), x4=y4-(256.4968573838999),
y=(1.799578875493056)+(-5.974066210514014)*x0+(-11.56553740063614)*x1+(-0.1545396393604948)*x2+(5.172523119752178)*x3+(0.1540143576135561)*x4
+(-17.45297800630631)*x0*x0+(-0.1090062772880443)*x0*x1+(-1.310984675110006e-002)*x0*x2+(-14.03392383507257)*x0*x3+(-4.289169392186376e-002)*x0*x4+(22.25748000512774)*x1*x1+(-2.245456583454652e-002)*x1*x2+(8.212272604609786e-002)*x1*x3+(6.271792925982265e-003)*x1*x4+(-6.669459749834531e-005)*x2*x2+(-1.903100059080562e-002)*x2*x3+(7.217058706506922e-004)*x2*x4+(-9.15304420446407)*x3*x3+(-3.741345572514077e-002)*x3*x4+(2.559970423512096e-003)*x4*x4
+(11.47373282665268)*x0*x0*x0+(9.341921817829952)*x0*x0*x1+(3.264886165514432e-002)*x0*x0*x2+(-6.472974026168921e-003)*x0*x0*x3+(-2.121310819655539e-003)*x0*x0*x4+(5.51933035952529)*x0*x1*x1+(-5.171538944184857e-003)*x0*x1*x2+(4.989155322559992)*x0*x1*x3+(0.1533949251601508)*x0*x1*x4+(-1.698477968040691e-004)*x0*x2*x2+(-2.204068286556028e-002)*x0*x2*x3+(2.761963091700759e-004)*x0*x2*x4+(4.0798863013763)*x0*x3*x3+(9.376124672502875e-002)*x0*x3*x4+(2.641556051018874e-004)*x0*x4*x4+(4.100002442739125)*x1*x1*x1+(-4.734441692273163e-003)*x1*x1*x2+(-1.961348488352317)*x1*x1*x3+(-0.1706020449016992)*x1*x1*x4+(2.700080312269564e-004)*x1*x2*x2+(-9.322610320728019e-004)*x1*x2*x3+(1.622536988804513e-003)*x1*x2*x4+(11.72316720890722)*x1*x3*x3+(-0.1463931085480807)*x1*x3*x4+(-5.872822055720774e-004)*x1*x4*x4+(1.205698763703183e-006)*x2*x2*x2+(1.28679573773e-004)*x2*x2*x3+(6.839371475233182e-006)*x2*x2*x4+(3.721430144278198e-002)*x2*x3*x3+(-4.335815325906642e-004)*x2*x3*x4+(-1.157491548269355e-007)*x2*x4*x4+(9.860323047148855)*x3*x3*x3+(-1.16777723885e-002)*x3*x3*x4+(-1.625346889836123e-004)*x3*x4*x4+(-1.228545092598462e-005)*x4*x4*x4
有了公式，拟合y=f(y0,y1,y2,y3,y4)的最优值将比较方便，有兴趣的可自行研究。
将本例五元函数泰勒四级展开，不知精度将提高多少，有兴趣的可自行研究。
以上讨论，仅供参考。
补充说明：因xx1：Co/SiO2（实验数据提供了0.5、1、2、5共4个参数）、xx2：Co/SiO2 和 HAP 的质量比（实验数据提供了0.4925、0.5556、1、2.0303共4个参数）、xx3：催化剂总量（实验数据提供了100、140、400共3个参数）、xx4：乙醇浓度（实验数据提供了0.3、0.9、1.68、2.1共4个参数）数据量少，而拟合参数多，会存在两个问题导致模型失真：
1、过拟合。
2、龙格震荡现象。
