State prediction and optimal scheduling for fed-batch fermentation

State prediction and optimal scheduling
for fed-batch fermentation
J. Q. Yuan 1 , J. Liu 1 and P. Vanrolleghem 2
School of Electronics and Informatics, Shanghai Jiaotong University, PR China
BIOMATH, Ghent University, Coupure Links 653, B-9000 Gent, Belgium
• Development of software prediction technology
• Testing results
• Prediction of the profit function
• Online classification and optimal scheduling
• Demonstration of the software
S, X, P, g/L
Typical time course of penicillin fed-batch
fermentation
60
50
40
30
20
10
X
V
0
0
0 200
Fermentation time, h
FS
P
S
320
280
240
200
160
120
80
40
FS, L/h ; V, m 3
Integrated substrate consumption & product formation
TO2, TCO2, TPAA, TS, TP
1.0
TO2
TCO2
0.8 TP
TPAA
TS
0.6
TD TP2
TP1
0.4
0.2
0.0
0 16 32 48 64 80 96 112 128 144 160 176 192
t, h
Input: discretized process variables within T D
Output: variables to be predicted up to 5-steps-ahead
step length: 8h for antibiotic fermentation
Generation of input-output data-pairs: MDW-technique
Training database: θ = {θ 1~n
θ n+1
}
Most important factors (Yuan and Vanrolleghem, JB, 1999):
• selection of historical batches
• time span covered by historical batches
• off-line and online updating of the database
• detection and remediation of bad local minima
The kth data-pair [X(T k
), Y(T k
)] is presented by
Rolling learning-prediction procedure
Tk
xT ( k )
xT ( k - 1τ
)
XT ( k ) = xT ( k - 2τ
)
xT
( k - mτ
)
x(T k
)=[TO 2
(T k
) TCO 2
(T k
) TP(T k
) TPAA(T k
) TS(T k
) .. ..] T
Y(T k
)=[P(T k
+T P1
) P(T k
+T P2
), .... P(T k
+T P5
)] T
Input
variables of
bioreactor
θ 1~n
(n+1)th batch
Measurements
and assay data
Data pretreatment
θ n+1 X(T k ) n+1
{w, b}
ANN training ANN prediction
P ANN (T k +T P1 ) n+1
P ANN (T k +T P2 ) n+1
•
•
•
P ANN (T k +T P2 ) n+1

I
i
j
l
l
t
t
t
Product concentration, g/L
Industrial fed-batch fermentations for testing
of ANN-predictor
35
30
25
20
15
10
5
bg B
52
58 59 60 6
az ba
51
BABBBC bb bc BD bd be bf 56
57
50
49
47
48 AYAZBABBBCBDBEBFBGBH bh b
53 54
55
bf
bg
avaw 52
46
AW AXAYAZ ax ay 51
be
45
AX AYAZBABBBCBD
ay az ba bb bc bd
as at au AV 50
44
ax ay az ba bb
ar as
41 42 43 AR ASATAUAVAW 49 ax
ar
48
AQ
avaw
aq
AS ATAUAVAW au
40
39 AO at au avaw
AR
an ao ap as
41 42 43 44 45 46 47
ao
AO APAQARASATAU ap aq
Batch 17
al am
35 36 37 38 AK ALAMAN 40
ao ap aq ar
AL AMAN am an
39
AM ANAOAPAQ 34
AL
ah ai aj ak 33AH AI AJ AK 38
al aman
ag ah ai aj ak al
31AF
32 AG 35 36
ag
AG AH AI AJAK AD 30 AE ag ah ai aj ak 37
AG AH AI AJ aeAF
af 33 34
32
ae
AE AF af AC
adAE
af
Batch 27 (aberrant)
29 acAD
AB
28 AD
ab ad 31 ae
Z AA ab 30 ad
27AB AC aa
AB AC ac
26
AA
28 29
X Y y 27
Zz
aa Batch 39 (aberrant)
AA ab
25 Y Z
W 24 Y
y
26 z
25
23
U V 24 X
v w x x
22
22
v 23
u W
V
w
T
21 U
V
S
U u
v s
20
Rr
19
Q
s
18 R S T q
P
p
17 Qq r
Oo
16 p
M N 15 O P m n o
14 Nn
L
13 mM
Kk
12 L
Jj
11 Kk
l j
8 9 10 J
h
H I
i
0
0 240
Fermentaton time, h
Prediction accuracy (prediction of product
concentration as an example)
Averaged prediction error
0.14
0.12
0.10
0.08
0.06
0.04
0.02
+8h
+24h
+40h
Batch 17
Batch 27
Batch 36
Batch 39
Batch 48
0.00
0 10 20 30 40 50 60
Batch number
40h-ahead prediction of product
concentration
Applications of the predicted state variables
Product concentration, g/L
32
28
24
20
16
12
Batch 53
Batch 38
Batch 59
• Improvement of daily process supervision
• Early diagnosis of abnormal batches (indicated by
unusual high prediction errors)
• Sub-optimal predictive control of feeding rates based
on the predicted precursor/substrate uptake rates
• Estimation of economic potential for individual
batches which may lead to optimal scheduling
8
0
Fermnetation time, h
240
Profit function and optimal scheduling
Profit function: J(T ) = Revenue− Total costs
f T + T f p
J(T f
), unit/h
J(T 2
)
0 T 1
T 2
T 3
T f
, h
Profit function, unit/h
40h-ahead predicted profit function in
comparison with its measurement
300
250
200
150
Batch 22
Batch 56
Batch 38
100
50
0
-50
-100
-150
-200
-250
-300
-350
-400
0 288
Fermentation time, h

Scheduling is done during last quarter of T f
Using average predicted value J(t,t+40) AP
to
indicate the future tendency:
+8 +16 +24 +32 +40
Present
time
Using average measured value J(t,t+40) AM
of the
profit function as basis
Profit function, unit/h
300
200
100
0
-100
Saturation value
gs
fwfxfyfzgagb gc gdgegf ggghgigj gkgl gmgngogpgqgr
24
137
129 130 131 132 133 134
135
136
138
140
139
141 142 143 144 145
128 146
127 147
126
148 149
117 118 119 120 121 122 123 124
125
150
151
152
155 156 157
159
115 116
160
161
113
99 100
101
102 103 104
105 106 107 108 109 110 111 112 114
FWFXFYFZ
GC
GEGF GG GHGI GJ GKGL GMGN GOGP GQ GR GS GT GU GV GWGX GY GZ
HAHB HCHDHE HF HG HHI HJ HKHL HM
fmfnfofpfqfrfsft fu fv fwfxfyfzgagbgcgdgegf
145 146 147 148 149 150 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
171 172
173 174 175 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 2223
224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
fefffgfh fifjfkfl fmfnfofpfqfrfsftfufv
176
eset euev ewexeyez fafbfc fd
ek gkgl gmgngogpgqgr
es
dz eaebec
edeef egeheiej ekel emeneo epeqer et
ey ez fafbfcfdfeffgfhfifjfkfl
ggghgigj gs
gt gugv gwgxgygzhahbhchdhe
129 130 131 132 133 134 135 136 137 138 139 140 141
142 143
144
egeheiej 151
euev ew
127
ex FWFXFYFZ
GA GB GC
GD GEGF GG GHGI GJ GKGL GMGN GOGP GQ GR GS GT GU GV GWGX GYGZ
HA HB HCHDHE HF HG HHI HJ HKHL HMHNHOHP HQHRHSHT HUHV HW HX HYHZ IAIBICIDIEIFIG
Average
el emeneoepeqer
du EV EWEX EYEZ FAFBFC FD FEFF
dwdxdy
9495969798
90 919293
DJ
DK DL DMDNDODP
DQDRDSDT
DUDV DWDXDYDZ
EAEBEC ED EE
EF EGEHEI EJ EKEL EMEN EOEP
EQERES
dpdqdr dsdt dudv
99 100
101 102 103 105
106 107 108
109 110 111 112
113 114 115 116
117 118 119 120 121 122 123 124 125
126 128
ETEU EV EWEX EYEZ FAFBFCFD FE FF FGFHFI FJFKFL FMFNFOFPFQFRFSFTFUFV
di dj dkdl
dmdndo
dsdt dv dwdxdydzeaeb ec edee ef
dpdqdr
dg dh
EAEBEC EDEE EF
104
dgdhdidj dkdl dmdndo DUDV
DWDXDYDZ EG EHEI EJ EKEL EMEN EOEP
EQERES
9495969798 cucv cwcxcyczdadbdcdddedf
89
DC DDDE DF DHDI
DG
cu cv cwcxcycz db dcdddedf DQDRDSDT
95% confidence limits
da
DC DDDE DF DG DI
DJ
DK DL DMDNDODP
ck cl cmcncocpcqcrcsct DH
7374 757677 7879 808182838485868788 81 828384858687888990919293 CUCV CWCXCYCZDADB
ckcl cmcncocpcqcrcsct CWCXCYCZDADB
cg chci cj
79
CQ CRCSCT CUCV
72 cd cecf cgchcicj
78 80 CQ CRCSCT
71
cb CMCNCOCP
cc 757677
CL
70
ca CJ
CI
73
-200
74 CK CL CMCNCOCP
Fermentation period
bwbxbybzcacbcccdcecf bz
65 66676869 72
CE CF CG CH 71
70bu bv bwbxby CG
CHCI CJ
when average profit
bsbtbubv
61 6263 64 bt
bs
60 66 676869 br
BYBZCA BYBZCA
CB CCCDCECF
function ertering
bn bobpbqbr
BWBX
59 64 bl
stationary phase
bm
58
BMBNBP BQ
-300
65 BTBUBV
63 bk
bm bnbobpbq BRBS
62 BR BS BTBUBV
bj
0 240
Fermentation time, h
Classification of batches according to
economic potential
If ||J(t,t+40) AP - J(t,t+40) AM || > J(t,t+40) AM × (1+β)
Then the Good category
If ||J(t,t+40) AP - J(t,t+40) AM || < J(t,t+40) AM × (1–β)
Then the Bad category
Otherwise, the Normal category
β - significance factor, confidence limit- related
β= 0.35~0.40 for the testing data set
Scheduling rules for fed-batch cultivation
_________________________________________
Category Scheduling strategy
_________________________________________
Good Maintain operation as long as possible
Normal Terminating as planned
Bad Break off at an earlier time point
_________________________________________
Feasibility of online optimal scheduling
under “golden recipe”
15
Number of batches
10
5
Software demonstration given by Mr. Liu Jun
0
120 140 160 180 200 220 240 260
Cultivation period, h