CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 51, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-43-3; ISSN 2283-9216 

Vector Machines Regression Applied in Penicillin 
Fermentation Process Control 

Lei Wang*a, Qian Fengb 
aMinistry of Organization, North China University of Science and Technology, Tangshan 063009, China 
bCollege of Mechanical Engineering, North China University of Science and Technology, Tangshan 063009, China  
anshiqi2008@163.com 

According to the characteristics of biochemical processes, this paper studied the small samples of the data 
process. Small amount of data can be quickly measured variable modeling. Introduces the support vector 
machine (SVM) modeling as small sample theory, the least squares support vector machine (LS-SVM) 
algorithm based on improved SVM applied to the typical fermented penicillin biochemical processes in the 
past. Online prediction model only off-line testing of important process variables based on the simulation 
results simulation platform show that the method is only by learning the few batches of sample data. Establish 
a penicillin product concentration, cell concentration and substrate concentration. This paper analyzes the 
characteristics of the penicillin fermentation process, and the use of SVM method for modeling, give potency 
relationship between the factors and its influence. Through experiments, the influence of SVM model 
parameters to adjust performance. Through a variety of models from the established field data can be found, 
SVM is better than ANN modeling. 

1. Introduction 

Nowadays, with the advent development of bio-engineering era and plant cell culture technology, fermentation 
industry catches more and more attention by the scientific community (Yimam-Seid, 2003)). Technical and 
economic indicators of China fermentation industry are behind the international advanced level (Yu, 2012). 
Line detection of the fermentation process, real time control and optimization of the process flow plus is an 
effective way to improve the overall level of fermentation, but fermentation process of biomass key variable 
(cell concentration, product concentration and substrate concentration), due to biological limit level sensor 
technology development, has not been solved, leading to advanced control algorithms and optimization 
strategy can only stay in the theoretical study (Gu, 2015). In recent years, starting from the inferential control, 
and gradually formed a soft-sensing technology to solve this problem, the variables are online estimate (Yu, 
2012). The basic idea of the soft measurement technology is important for those who are difficult to measure 
variables cannot be measured oath or transcript (called dominant variable), select a group of leading variables 
related measurable variables (called secondary auxiliary variables or variable), by construct a mathematical 
relationship to extrapolate and estimate the dominant variables in software instead of hardware (sensors) 
function (Yuan, 2014). 
Existing models established fermentation process can be divided into three categories: white box model and 
gray box model, black-box model (Jia, 2012). White-box model to determine a priori knowledge of the 
structure and mechanism of the model, this model requires the mechanism of process of dynamic 
characteristics, transmission characteristics and biochemical characteristics have a better understanding 
(Yuan and Mori, 2014). It is generally from a smart balance, monod equation, arrhenius equation and so 
starting the establishment of kinetics-based, reflecting the opening mechanism model between biomass and 
measurable variables (Schmidberger and Ni, 2015). For white-box model, although a clear physical meaning 
of each parameter, gives the relationship between biomass and testability auxiliary variables, however, the 
soft measurement model intelligent balance, monod equation type (Campbel and Dom, 2003). Based on the 
established, since bacteria in the fermentation process growth on the theoretical treatment reaction is greatly 
simplified, resulting model cannot reflect the true nature of the reaction of microbial growth, poor adaptability: 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651224

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Wang L., Feng Q., 2016, Vector machines regression applied in penicillin fermentation process control, Chemical 
Engineering Transactions, 51, 1339-1344  DOI:10.3303/CET1651224   

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microbial fermentation process and is now still lack sufficient understanding of many unknown microbial 
reactions can not direct modeling, thus establishing direct effective mechanism model fermentation process 
difficult. 
Introduces the support vector machine (SVM) modeling small sample theory, the least squares support vector 
machine (LS-SVM) This fast algorithm based on improved SVM applied to the typical fermented penicillin 
biochemical processes in the past. Online prediction model only off-line testing of important process variables 
based on the simulation results simulation platform show that the method is only by learning the few batches 
of sample data, the establishment of a penicillin product concentration, cell concentration and substrate 
concentration . This paper analyzes the characteristics of the penicillin fermentation process, and the use of 
SVM method for modeling, give potency relationship between the factors and its influence. Through 
experiments, the influence of SVM model parameters to adjust performance. And through a variety of models 
from the established field data can be found, SVM is better than ANN modeling. 

2. SVM regression estimation theory 

2.1 Linear regression based on support vector machine 

There n samples: (x1, y1), (x2, y2),…(xn, yn), in it yi∈R, i=1,2,…,n, A function f = w⋅ x + b fitting n samples, And 
assume that all samples can be in accuracy ε (called insensitive loss function) without error fitting, namely: 

1, 2,...,
i i

i i

y w x b
i n

w x b y





   


     

(1) 

Taking into account the fitting error, by introducing a relaxation factor 
*

0, 0
i i
    and * 0

i i
    

relaxation of the constraints, then (1) is converted to the formula: 

*
1, 2,...,

i i i

i i i

y w x b
i n

w x b y

 

 

    


      

(2) 

Based on support vector machine linear regression method is to make it  
2 *

1

1

2

n
j

i i

i

w C  


    

minimize, where C is the penalty coefficient. Using dual theory, establish Lagrange equation. In 

conditions  * *
1

0 0, , 1, 2,...,
n

i i i i

i

a a a a C i n


      by maximizing the objective function: 

   

     

* *

1

* * *

1 , 1

,

1

2

n

i i

i

n n

i i i i i j j i j

i i j

W a a a a

y a a a a a a x x




 

   

   



 
 

(3) 

On only a portion of a formula solution is not equal to zero, corresponding to the sample called support 
vectors. Corresponding regression function is: 

 

  * *
1

 =
n

i i i j

i

f x w x b

a a x x b


  

 
 (4) 

2.2 SVM regression estimation theory 

The topology SVM support vector may decide to avoid the neural network topology requires trial and error 
experience limitations, is considered as the best theory for small sample classification and regression 
problems. Therefore, in pattern recognition, regression estimation, probability density function estimation, etc. 
are widely used and achieved good results. But its application in the industrial sector is relatively small, in the 
application of biochemical processes is even rarer. 

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First, consider the use of a linear function f(x)=<w, x>+b to fit the sample data set {xi, yi } (i=1,2,…,n; xi ∈Rd) 
and linear insensitive loss function, such as (1) the formula, where x is the independent variable, y is the 
dependent variable, ε Representative for controlling the fitting accuracy is not sensitive parameters. 

 

 

 

 

, ,

,

0 ,

,

L y f x a

L y f x a

y f x a

y f x a others





  

   

  
 

   

(5) 

SVM is to look at the formula (1) constraints best fit hyperplane that minimize 1 / 2‖w‖ so that all training data 
can be used in precision ε at fitting a linear function, where y is a scalar xi and w is d-dimensional vector. And 
the introduction of (non-negative) slack variables ξi, ξ * i and slack variables for controlling role in the objective 
function of (positive) penalty coefficient C, C representative of the larger error ε beyond the penalties stronger. 

SVM control function sets the complexity of the method is to return to function most flat, so regression 
modeling will be converted to the target as shown in functional constraint minimization problem in the formula. 

   
2* *

1

1
min , ,

2

n
j

i i i i

i

x w C   


      (6) 

Lagrange multiplier method for solving the quadratic programming problems with linear inequality constraints 
can be obtained dual optimization problem as represented by the formula: 

 

   

   

*

* *

1 1

* *

, 1

max ,

1
,

2

n n

i i i i i

i i

n

i i j j i j

i j

W

y

x x

 

    

   

 



    

  

 



 
(7) 

Regression function: 

     *
1

,
n

i i i

i

f x K x x b 


    (8) 

Common linear kernel function kernel function, polynomial kernel function, radial basis function (RBF), 
multilayer perceptron kernel of four, using a common kernel function of RBF paper form. 

3. Experiments and results 

3.1 Penicillin fermentation process modeling 
Data using batch, each batch represents a complete fermentation process. The first batch of data as training 
data 185, divided into 55 samples. The first batch of 191 data as the test data, is divided into 54 samples. To 
reflect the fermentation process is nonlinear, radial basis function, so the main parameters of SVM insensitive 
coefficient ε, penalty coefficient C and the width of the coefficient σ. Using the mean relative error of each 

sample point  
1

1
ˆ

n

i i i

i

MER y y y
n 

   Model training error and prediction error, n is the number of 

samples, yi are actual and estimated value. Model structure for the 

        1 8, , ,...,y t t f y t t x t x t   y (t) representative of the time potency, t representative of the 
fermentation time, x1-x8 representing other eight input model variables; y (t+Δt) representative of the model 
output, i.e., time t of potency. 
 

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In Matlab software, select the parameter σ = 10000, C = 80000, ε = 300, the results of the first batch of 185 

training data in Figure 1, the number of support vectors is 29, the mean relative error of the training is 
0.011299. The mean prediction relative error is 0.0092825. As can be seen from Figure 2, the effect is very 
good modeling, model SVM method established in the test data show higher performance on the training data. 
 

 

Figure 1: Data estimated results 

3.2 Online prediction model based Pensim simulation platform 

Penicillin fermentation process is more typical biochemical processes, due to the strong nonlinear 
fermentation process, when the variability and uncertainty, and the current lack of such product concentration, 
cell concentration and substrate concentration on-line detection equipment, a serious impact on the critical 
process variables the fermentation process of effective control and optimization, thus establishing online 
forecasting models for these key process variables has important practical significance. It should be noted 
that, although the article is a penicillin fermentation process, for example the typical biochemical research, but 
below the proposed method is fully applicable to the modeling of other biochemical processes. 
In this paper, used for modeling data from Pensim simulation platform, the software kernel uses Bajpai 
mechanism model based on improved Birol model on this platform can achieve a series of simple simulation 
penicillin fermentation process, studies have indicated that the practical simulation platform and effectiveness. 
Typical non-structural model as Bajpai models, Birol model is mainly based on experimental data and other 
Pirt Bajpai model was improved. In this model, considering not only the pH value, temperature, air flow, stirring 
on power, acceleration rate bottoms stream and other control variables bacteria and penicillin production, and 
the cell growth, carbon dioxide, penicillin production, substrate consumption, the heat of reaction and other 
factors are also included in the comprehensive model to go, so they can comprehensively reflect the penicillin 
fermentation process. 
To carry out the first batch i predict, before then i -1 sample batch by batch was sliced, and arranged in order 
according to the batch-moment view three-dimensional form of penicillin fermentation process data array, in 
Figure 2 as a number of training samples obtained prediction models and to predict the i-th batch. 
 
 
 

1342



I J
I=1

I=2

I=1

time

K

I J

Variables

Ba
tc
he
s

1
2

I
1
2

1K

2K
.
.
.
.
.
.

..

..

X=I×J×K X=1K×J  

Figure 2: Unfolding of batch process data by preserving variable direction 

3.3 Effect parameter adjustment of SVM modeling 
Different penalty coefficient C, insensitive and width coefficient ε σ coefficient calculation training error and the 

prediction error, the error is calculated using the MER, as shown in Table 1. 

Table 1: The effect of parameters on Model quality 

Penalty 
Coefficient 

Insensitive 
Coefficient 

Width 
Coefficient 

Training Error 
Prediction 
Error 

Support Vector 

1e8 300 10000 0.0093124 0.018549 29 

80000 1000 10000 0.021673 0.019959 7 

80000 300 3e5 0.22905 0.24056 52 

80000 300 50000 0.019477 0.018003 36 

80000 300 10000 0.011299 0.0092825 29 

80000 50 10000 0.010111 0.0097281 48 

80000 20 10000 0.0097822 0.0099574 52 

80000 200 8000 0.011886 0.0095004 32 

80000 300 5000 0.0091384 0.012209 31 

80000 300 2000 0.010919 0.038832 38 

80000 300 1000 0.011552 0.11254 51 

5000 300 10000 0.048549 0.049298 33 

1000 500 10000 0.27273 0.28433 45 

 

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By analyzing the data in Table 1, C the greater the more stringent punishment for the error, which is fitting for 
high precision, making training difficult, very time-consuming. Thus, as C increases, the fitting error and the 
prediction error will be reduced when C increased to a certain extent, the fitting error stabilized, when C is too 
large, there will be "over-fitting" phenomenon, this time instead, the prediction error will increase. 

4. Conclusion 

Optimal control requires reliable, it can reflect the changes of the model parameters and their relationship in 
the process. Due to the lack of non-linear fermentation process, time-varying and biosensors, as well as 
among the parameters associated with severe, classical systems theory can hardly establish an appropriate 
model for the complex fermentation process. Online prediction model only off-line testing of important process 
variables based on the simulation results simulation platform show that the method is only by learning the few 
batches of sample data, the establishment of a penicillin product concentration, cell concentration and 
substrate concentration . This paper analyzes the characteristics of the penicillin fermentation process, and 
the use of SVM method for modeling, give potency relationship between the factors and its influence. Through 
experiments, the influence of SVM model parameters to adjust performance. And through a variety of models 
from the established field data can be found, SVM is better than ANN modeling. 

Acknowledgments 

This work is supported by the Science and technology research Youth Fund Project of Hebei Province: 
Internal model control based on support vector machine in the process of biological fermentation(No. 
QN2016254). 

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