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 increaseResults (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.