# Problem B of 2021 Higher Education Society Cup National College Students' mathematical modeling competition problem 2 solution ideas for ethanol coupling preparation of C4 olefins

Posted by shezz on Sun, 07 Nov 2021 06:31:34 +0100

The following table "sheet2" is sorted out by A1~A14 (loading mode I) in Annex 1 "performance data sheet":

 wt%Co/SiO2 Mass ratio of Co/SiO2 and HAP Total catalyst Ethanol concentration temperature Ethanol conversion (%) C4 olefin selectivity (%) C4 olefin yield (%) 0.5 1 400 1.68 250 4.0 9.6 0.386665445 0.5 1 400 1.68 275 12.1 8.6 1.042826728 0.5 1 400 1.68 300 29.5 10.7 3.159887673 0.5 1 400 1.68 325 43.3 18.9 8.184209991 0.5 1 400 1.68 350 60.5 27.3 16.47764673 0.5 1 400 1.68 400 88.4 41.0 36.27781909 1 0.4925 100 1.68 250 2.5 1.9 0.047111815 1 0.4925 100 1.68 275 5.3 2.6 0.136038297 1 0.4925 100 1.68 300 10.2 3.6 0.366488509 1 0.4925 100 1.68 350 24.0 10.8 2.602654614 1 0.4925 100 1.68 400 53.6 22.3 11.95620228 1 0.5556 140 1.68 250 0.2 0.1 0.000227692 1 0.5556 140 1.68 275 0.5 1.0 0.00516312 1 0.5556 140 1.68 300 1.6 1.8 0.029257461 1 0.5556 140 1.68 350 8.2 4.4 0.357029779 1 0.5556 140 1.68 400 32.6 7.9 2.584664401 1 1 100 0.3 250 19.7 5.8 1.130236757 1 1 100 0.3 275 29.0 6.6 1.90534913 1 1 100 0.3 300 40.0 8.8 3.534617971 1 1 100 0.3 350 58.6 18.6 10.9239714 1 1 100 0.3 400 76.0 33.3 25.27911589 1 1 100 0.9 250 6.3 5.6 0.352760989 1 1 100 0.9 275 8.8 8.5 0.746485761 1 1 100 0.9 300 13.2 13.8 1.821344417 1 1 100 0.9 350 31.7 25.9 8.212479623 1 1 100 0.9 400 56.1 41.4 23.24340866 1 1 100 1.68 250 1.4 6.2 0.088953466 1 1 100 1.68 275 3.5 8.1 0.281711425 1 1 100 1.68 300 6.9 11.2 0.77579429 1 1 100 1.68 350 19.9 22.3 4.432477459 1 1 100 1.68 400 44.5 36.3 16.16619292 1 1 100 2.1 250 2.1 5.4 0.110870727 1 1 100 2.1 275 3.0 9.7 0.290648933 1 1 100 2.1 300 4.7 16.1 0.761401301 1 1 100 2.1 350 13.4 31.0 4.157107976 1 1 100 2.1 400 40.8 42.0 17.15112728 1 1 400 0.9 250 9.7 5.5 0.531815513 1 1 400 0.9 275 19.2 8.0 1.546649604 1 1 400 0.9 300 29.3 17.0 4.975464725 1 1 400 0.9 325 37.6 28.7 10.79274197 1 1 400 0.9 350 48.9 36.9 18.03330095 1 1 400 0.9 400 83.7 53.4 44.72805978 1 1 400 0.9 450 86.4 49.9 43.11844167 1 1 400 1.68 250 2.07 34.1 0.703871198 1 1 400 1.68 275 5.85 37.4 2.190299165 1 1 400 1.68 300 14.97 46.9 7.026397666 1 1 400 1.68 325 19.68 49.7 9.781635471 1 1 400 1.68 350 36.80 47.2 17.37376011 1 2.0303 100 1.68 250 1.3 5.2 0.069906624 1 2.0303 100 1.68 275 2.3 7.6 0.175675746 1 2.0303 100 1.68 300 4.1 12.7 0.518101314 1 2.0303 100 1.68 350 14.6 23.5 3.43425681 1 2.0303 100 1.68 400 40.0 27.9 11.17716077 2 1 400 0.3 250 14.8 2.0 0.289828794 2 1 400 0.3 275 12.4 6.7 0.826196719 2 1 400 0.3 300 20.8 10.1 2.105827939 2 1 400 0.3 325 28.3 13.9 3.929155582 2 1 400 0.3 350 36.8 18.8 6.902171053 2 1 400 0.3 400 76.0 38.2 29.06238183 2 1 400 1.68 250 4.60 18.1 0.8317616 2 1 400 1.68 275 17.20 17.3 2.971389123 2 1 400 1.68 300 38.92 19.6 7.62876008 2 1 400 1.68 325 56.38 30.6 17.26430932 2 1 400 1.68 350 67.88 39.1 26.54080464 5 1 100 2.1 250 0.3 2.2 0.007007211 5 1 100 2.1 275 1.0 1.7 0.016754982 5 1 100 2.1 300 1.7 2.2 0.036557463 5 1 100 2.1 350 9.0 3.3 0.297621751 5 1 100 2.1 400 28.6 10.3 2.942362809 5 1 400 1.68 250 13.4 3.3 0.441850092 5 1 400 1.68 275 12.8 7.1 0.907450345 5 1 400 1.68 300 25.5 7.2 1.829407723 5 1 400 1.68 350 55.8 10.7 5.937910401 5 1 400 1.68 400 83.3 37.3 31.11366512

All parameters affecting ethanol conversion and C4 olefin selectivity are used for fitting:

xx1: Co/SiO2

xx2: mass ratio of Co/SiO2 and HAP

xx3: total catalyst

xx4: ethanol concentration

xx5: temperature

Ethanol conversion:    y1=f(xx1,xx2,xx3,xx4,xx5) (Universal Taylor formula power series is used, and the fitting formula is shown in the code)

C4 olefin selectivity: y2=f(xx1,xx2,xx3,xx4,xx5) (Universal Taylor formula power series is used, and the fitting formula is shown in the code)

Three order Taylor formula expansion
!!!using["luopt","math"]; //using namespace std
objective function (xx1,xx2,xx3,xx4,xx5,  //There are 101 fitting parameters in total
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,
a211,a212,a213,a214,a215,
a222,a223,a224,a225,
a233,a234,a235,
a244,a245,
a255,
a311,a312,a313,a314,a315,
a322,a323,a324,a325,
a333,a334,a335,
a344,a345,
a355,
a411,a412,a413,a414,a415,
a422,a423,a424,a425,
a433,a434,a435,
a444,a445,
a455,
a511,a512,a513,a514,a515,
a522,a523,a524,a525,
a533,a534,a535,
a544,a545,
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+
a211*x2*x1*x1+a212*x2*x1*x2+a213*x2*x1*x3+a214*x2*x1*x4+a215*x2*x1*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+
a311*x3*x1*x1+a312*x3*x1*x2+a313*x3*x1*x3+a314*x3*x1*x4+a315*x3*x1*x5+
a322*x3*x2*x2+a323*x3*x2*x3+a324*x3*x2*x4+a325*x3*x2*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+
a411*x4*x1*x1+a412*x4*x1*x2+a413*x4*x1*x3+a414*x4*x1*x4+a415*x4*x1*x5+
a422*x4*x2*x2+a423*x4*x2*x3+a424*x4*x2*x4+a425*x4*x2*x5+
a433*x4*x3*x3+a434*x4*x3*x4+a435*x4*x3*x5+
a444*x4*x4*x4+a445*x4*x4*x5+
a455*x4*x5*x5+
a511*x5*x1*x1+a512*x5*x1*x2+a513*x5*x1*x3+a514*x5*x1*x4+a515*x5*x1*x5+
a522*x5*x2*x2+a523*x5*x2*x3+a524*x5*x2*x4+a525*x5*x2*x5+
a533*x5*x3*x3+a534*x5*x3*x4+a535*x5*x3*x5+
a544*x5*x4*x4+a545*x5*x4*x5+
a555*x5*x5*x5,
s=s+[y1-py]^2    //Fitting ethanol conversion
//S = S + [Y1 PC] ^ 2 / / fit C4 olefin selectivity
},
sqrt[s/max]          //Mean square deviation RMSE is the value of objective function
};
main(::tyArray,max)=
{
tyArray=matrix{ //Storage of experimental data: use loading mode I to store all data
"
0.5	1	400	1.68	250	4.0 	9.6
0.5	1	400	1.68	275	12.1 	8.6
0.5	1	400	1.68	300	29.5 	10.7
0.5	1	400	1.68	325	43.3 	18.9
0.5	1	400	1.68	350	60.5 	27.3
0.5	1	400	1.68	400	88.4 	41.0
1	0.4925	100	1.68	250	2.5 	1.9
1	0.4925	100	1.68	275	5.3 	2.6
... ...((omitted)
"
},
len[tyArray,0,&max],
Opt1[@objective function , optmax,1000, optmode,20, optdeep,20, optwaysimdeep, optwayconfra, optwaylme] //Global optimization of Opt1 function
};

Results and discussion:

Optimal parameters and mean square deviation RMSE corresponding to ethanol conversion Y1:

1.605961168999771         -0.4410695905557486       235.7757505227786         -0.329837112872408        89.78598768229873         20.05502365079599         -42.76413669021677        -7.744783802865953        -0.330658787799879        -20.91358757136002        -0.3520691839528313       -9.053272922935264        34.03445937950385         -6.688818825087674e-002   1.910450081826346         7.52417263883647e-002     5.360893240121412         2.094748794553468e-002    37.73934747147025         -0.1292497811475342       -4.147831556037419e-004   -0.2749634559384725       -1.016271325893973e-003   -12.45723836096927        -0.1074117654887022       1.329260041868394e-003    -8.50723004489431         19.3040038433537          -2.775212715667194e-002   -0.9514198268894782       -5.376838367861148e-002   -4.567590785407559        1.656476334631148e-002    23.24778568424907         5.540662101179693e-002    4.720650275633447e-004    3.070455686518996e-002    -5.304744078555087e-004   6.000438180572427         2.916826412249359e-002    -4.025194873891306e-006   -4.553899811798563        -29.45554646556685        -0.143965735216047        -9.907859318733358        1.506220580849777e-002    -1.542941119693729        7.738831790881103e-002    -7.005988988762844        -7.60327324504986e-002    6.072570904512441e-004    0.2387348474041152        1.673927632412995e-004    37.14253203210593         -0.3207121128426113       2.668094958762711e-004    6.054872996553735e-002    7.794022905759623e-002    -3.139725033185572e-004   1.289530835792764e-003    -1.743785151081295e-004   6.347384976815082e-002    -4.195545814258753e-004   -2.697575089708201e-002   1.229189010048387e-003    -1.105420561442776e-006   -2.7800429608818e-003     2.426192417104856e-006    -4.16072215526872e-002    -3.432332997494584e-004   2.851780024548635e-007    5.263445716294873         32.83044672374795         1.280067392340407e-002    -17.94368059692175        -0.1385037031061965       2.731682565063538         1.184440508984389e-002    -8.015762476802667        0.1307452215133851        9.78861155011708e-004     -2.520280926166166e-002   1.489784516006709e-003    -6.360844348307658        -2.771473551933863e-002   5.634778544953946e-005    2.98656815200299e-002     2.563295397047698e-002    5.667535852364258e-004    2.230235061923244e-002    6.949791572104501e-005    0.1363657902506849        -1.304588388846196e-003   6.304769126477201e-002    1.485212688711085e-004    1.304223398190621e-005    -7.456617386292806e-005   -1.940980567767639e-006   1.187675828942093e-002    7.007649927097195e-004    -2.573778942035362e-006   3.872971760941088

Optimal parameters and mean square deviation RMSE corresponding to C4 olefin selectivity Y2:

0.6291493182031664        0.2958183812514781        -0.4652893843549317       0.7622062674553209        392.0915498191997         -12.12997297477396        -2.722118671840135        -1.434666274768651        -6.296875182924813e-002   19.16546798801177         0.1576626739540456        -9.473338892189091        -91.28865158923242        -9.580403804322646e-002   39.14814933931461         0.1088834405161888        83.85524812061144         0.6508381048478721        23.19673012324472         0.2889415751716025        -1.517196432282561e-003   0.1550064281119293        -3.905615672075377e-003   41.58590589551277         0.2804256438228481        -1.612752851575893e-003   11.47372993071932         -41.1001221097123         -0.1178354186790367       -0.1339223958708456       5.732395276741618e-002    27.98592837522371         0.5915671407208571        -9.50722923477921         0.6845348790491092        -4.674310768122246e-004   -0.1259889637267923       -9.473077509356255e-003   24.03027817441679         -0.3709244874517346       1.94356129101405e-003     -14.78623371224686        25.92593235572944         -0.2855033845735219       -12.53246596351226        -0.7067104769855241       -3.484569374140125        0.2524720887210766        6.452561996215707         9.288059203984306e-003    1.019750138893331e-003    0.1777795873679074        8.12498844204392e-004     16.50168647446635         0.2621577359139685        -5.120275859213446e-004   7.284282071445269e-002    0.3431359163170912        8.541396344568307e-004    -0.1116510982221482       1.568480263232336e-003    -0.5908786285261998       3.49638380764357e-004     -0.25563038379701         3.970640203357752e-003    -9.392195530317841e-007   4.623999241835095e-004    6.856533700992917e-006    -2.584985495795081e-002   2.851594565138132e-003    -9.94157221748607e-006    -0.2022772396681483       -55.01685449273354        -7.523894405880521e-002   15.41134103814506         0.6481539820154305        -99.85271827848968        0.1309466603197193        -31.7029427792642         1.185145217235263         7.809158942324601e-004    -0.5676232287558368       -3.078487970836266e-003   9.860307453096967         -2.979096768654461e-002   -1.165012792165202e-003   -5.944528957575301e-002   -0.3523595373494553       8.180793646082381e-003    -0.1834684331576924       -1.679406475817102e-003   -0.1798901138165366       -2.368847815176337e-004   -1.816171626152732        -7.525569785629429e-005   -5.01446491627077e-006    -2.066878499250355e-004   9.82582478116308e-006     1.858963080314847e-002    1.00248221936984e-003     -1.228544743091241e-005   2.394257044563218

Due to many parameters and long time-consuming, take the above results when the output of Opt::ShowMin is stable (more than one day).

Not running for many times due to long time consuming; If multiple computers run at the same time, there may be better results.

Because the value of the objective function is slightly larger (the mean square deviation RMSE is 3.87 (corresponding to Y1) and 2.39 (corresponding to Y2)), it shows that the expansion accuracy of the third-order Taylor formula is poor, and the expansion of the fourth-order Taylor formula will have better results, but the fitting parameters will increase to 476 and the time will be longer.

Calculate the maximum C4 olefin yield (Y1*Y2) from the above fitting parameters, and the best parameters xx1, XX2, XX3, xx4 and XX5 can be obtained.

Three level Taylor formula expansion, optimization and optimization C4 Olefin yield
!!!using["luopt","math"];; //using namespace std
init(::       //Fitting parameter assignment
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,
a211,a212,a213,a214,a215,
a222,a223,a224,a225,
a233,a234,a235,
a244,a245,
a255,
a311,a312,a313,a314,a315,
a322,a323,a324,a325,
a333,a334,a335,
a344,a345,
a355,
a411,a412,a413,a414,a415,
a422,a423,a424,a425,
a433,a434,a435,
a444,a445,
a455,
a511,a512,a513,a514,a515,
a522,a523,a524,a525,
a533,a534,a535,
a544,a545,
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,
b211,b212,b213,b214,b215,
b222,b223,b224,b225,
b233,b234,b235,
b244,b245,
b255,
b311,b312,b313,b314,b315,
b322,b323,b324,b325,
b333,b334,b335,
b344,b345,
b355,
b411,b412,b413,b414,b415,
b422,b423,b424,b425,
b433,b434,b435,
b444,b445,
b455,
b511,b512,b513,b514,b515,
b522,b523,b524,b525,
b533,b534,b535,
b544,b545,
b555) =
new[real_s,101].SetArray[
"
1.605961168999771         -0.4410695905557486       235.7757505227786  ... ...(Put the corresponding here Y1 Output results of)
"].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,
&a211,&a212,&a213,&a214,&a215,
&a222,&a223,&a224,&a225,
&a233,&a234,&a235,
&a244,&a245,
&a255,
&a311,&a312,&a313,&a314,&a315,
&a322,&a323,&a324,&a325,
&a333,&a334,&a335,
&a344,&a345,
&a355,
&a411,&a412,&a413,&a414,&a415,
&a422,&a423,&a424,&a425,
&a433,&a434,&a435,
&a444,&a445,
&a455,
&a511,&a512,&a513,&a514,&a515,
&a522,&a523,&a524,&a525,
&a533,&a534,&a535,
&a544,&a545,
&a555],
new[real_s,101].SetArray[
"
0.6291493182031664        0.2958183812514781        -0.4652893843549317  ... ...(Put the corresponding here Y1 Output results of)

"].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,
&b211,&b212,&b213,&b214,&b215,
&b222,&b223,&b224,&b225,
&b233,&b234,&b235,
&b244,&b245,
&b255,
&b311,&b312,&b313,&b314,&b315,
&b322,&b323,&b324,&b325,
&b333,&b334,&b335,
&b344,&b345,
&b355,
&b411,&b412,&b413,&b414,&b415,
&b422,&b423,&b424,&b425,
&b433,&b434,&b435,
&b444,&b445,
&b455,
&b511,&b512,&b513,&b514,&b515,
&b522,&b523,&b524,&b525,
&b533,&b534,&b535,
&b544,&b545,
&b555];;
f(xx1,xx2,xx3,xx4,xx5  //objective function
: 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,
a211,a212,a213,a214,a215,
a222,a223,a224,a225,
a233,a234,a235,
a244,a245,
a255,
a311,a312,a313,a314,a315,
a322,a323,a324,a325,
a333,a334,a335,
a344,a345,
a355,
a411,a412,a413,a414,a415,
a422,a423,a424,a425,
a433,a434,a435,
a444,a445,
a455,
a511,a512,a513,a514,a515,
a522,a523,a524,a525,
a533,a534,a535,
a544,a545,
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,
b211,b212,b213,b214,b215,
b222,b223,b224,b225,
b233,b234,b235,
b244,b245,
b255,
b311,b312,b313,b314,b315,
b322,b323,b324,b325,
b333,b334,b335,
b344,b345,
b355,
b411,b412,b413,b414,b415,
b422,b423,b424,b425,
b433,b434,b435,
b444,b445,
b455,
b511,b512,b513,b514,b515,
b522,b523,b524,b525,
b533,b534,b535,
b544,b545,
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+
a211*x2*x1*x1+a212*x2*x1*x2+a213*x2*x1*x3+a214*x2*x1*x4+a215*x2*x1*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+
a311*x3*x1*x1+a312*x3*x1*x2+a313*x3*x1*x3+a314*x3*x1*x4+a315*x3*x1*x5+
a322*x3*x2*x2+a323*x3*x2*x3+a324*x3*x2*x4+a325*x3*x2*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+
a411*x4*x1*x1+a412*x4*x1*x2+a413*x4*x1*x3+a414*x4*x1*x4+a415*x4*x1*x5+
a422*x4*x2*x2+a423*x4*x2*x3+a424*x4*x2*x4+a425*x4*x2*x5+
a433*x4*x3*x3+a434*x4*x3*x4+a435*x4*x3*x5+
a444*x4*x4*x4+a445*x4*x4*x5+
a455*x4*x5*x5+
a511*x5*x1*x1+a512*x5*x1*x2+a513*x5*x1*x3+a514*x5*x1*x4+a515*x5*x1*x5+
a522*x5*x2*x2+a523*x5*x2*x3+a524*x5*x2*x4+a525*x5*x2*x5+
a533*x5*x3*x3+a534*x5*x3*x4+a535*x5*x3*x5+
a544*x5*x4*x4+a545*x5*x4*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+
b211*x2*x1*x1+b212*x2*x1*x2+b213*x2*x1*x3+b214*x2*x1*x4+b215*x2*x1*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+
b311*x3*x1*x1+b312*x3*x1*x2+b313*x3*x1*x3+b314*x3*x1*x4+b315*x3*x1*x5+
b322*x3*x2*x2+b323*x3*x2*x3+b324*x3*x2*x4+b325*x3*x2*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+
b411*x4*x1*x1+b412*x4*x1*x2+b413*x4*x1*x3+b414*x4*x1*x4+b415*x4*x1*x5+
b422*x4*x2*x2+b423*x4*x2*x3+b424*x4*x2*x4+b425*x4*x2*x5+
b433*x4*x3*x3+b434*x4*x3*x4+b435*x4*x3*x5+
b444*x4*x4*x4+b445*x4*x4*x5+
b455*x4*x5*x5+
b511*x5*x1*x1+b512*x5*x1*x2+b513*x5*x1*x3+b514*x5*x1*x4+b515*x5*x1*x5+
b522*x5*x2*x2+b523*x5*x2*x3+b524*x5*x2*x4+b525*x5*x2*x5+
b533*x5*x3*x3+b534*x5*x3*x4+b535*x5*x3*x5+
b544*x5*x4*x4+b545*x5*x4*x5+
b555*x5*x5*x5,
-y1*y2/100  //The negative value of C4 olefin yield is the objective function value
};
Opt1[@f, optrange: 0.4,5.1; 0.4,2.1; 90.0,410.0; 0.2,2.2; 230.0, 470.0]; //Solve within the specified range, otherwise the error will increase

Results (xx1,xx2,xx3,xx4,xx5 and objective function values) and discussion:

4.037060310750474         2.099999996638691         409.9999994374398         0.7728448126139009        469.9999989999984         -5093.709888185105

From the fitting results, it can be seen that the objective function value of C4 olefin yield exceeds 100%, which is obviously not in line with the actual situation, but it still has guiding significance for experimental design.

The optimum value of xx1: Co/SiO2 (four parameters of 0.5, 1, 2 and 5 are provided by the experimental data) is around 4.0.

The optimal value of the mass ratio of xx2: Co/SiO2 and HAP (the experimental data provides four parameters: 0.4925, 0.5556, 1 and 2.0303) is at the upper limit of the set parameter, and this parameter should be added for the experiment.

xx3: the optimum value of the total amount of catalyst (three parameters of 100, 140 and 400 are provided in the experimental data) is at the upper limit of the set parameter, and this parameter should be added for the experiment.

xx4: ethanol concentration (the experimental data provide four parameters: 0.3, 0.9, 1.68 and 2.1). The best value is around 0.77.

xx5: the optimal value of temperature (more experimental data are provided) is at the upper limit of the set parameter. If conditions permit, the parameter shall be increased for experiment.

The optimum value is obtained under the specified conditions (the mass ratio of Co/SiO2 and HAP is 1 and the total amount of catalyst is 100):

Opt1[@f, optwaycom, optrange: 0.4,5.1; 0.999,1.001; 99.999,100.0; 0.3,2.2; 230.0, 470.0]; // Solve within the specified range, otherwise the error will increase

Results (xx1,xx2,xx3,xx4,xx5 and objective function value):

0.8439086100949256        1.000999999653274         99.99900080078913         0.672269893443885         459.2752186129222         -34.03535778605701

Guess: if   xx1,xx2,xx3,xx4   With more data, the fitting result may be better.

The above discussion is for reference only.

Topics: script