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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 66, 2018 

A publication of 

 
The Italian Association 

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

Guest Editors: Songying Zhao, Yougang Sun, Ye Zhou
Copyright © 2018, AIDIC Servizi S.r.l. 
ISBN 978-88-95608-63-1; ISSN 2283-9216 

Analytical Chemometrics Research Based on Artificial 
Intelligence Algorithm 

Guohua Zou 

School of Software, East China University of Technology, Nanchang 330013, China 
ghzou@ecit.cn 

This paper conducted analytical chemometrics research based on artificial intelligence algorithms. It combined 
the Ant Colony Optimization (ACO) with the fuzzy clustering to perform clustering twice to determine the 
hidden layer nodes of the radial basis function (RBF) network. By introducing the concept of fuzzy 
mathematics, it performed flexible partitioning of ant colony clustering algorithms. The ant colony optimization-
fuzzy c-means-radial basis function network (ACO-FCM-RBF) was used to obtain satisfactory results for the 
simultaneous determination of bismuth and zirconium. In this paper, a new color system of DBS-
chlorophosphonazo-zirconium was established, which lays the foundation for the simultaneous determination 
of bismuth and zirconium. This paper also established a new method of analytical chemometrics, compared 
with the test results of RBF network method, the ACO-FCM-RBF had better calculation result accuracy. 

1. Introduction 

Nowadays, the boundaries between disciplines have long been rather vague, multi disciplines infiltrate with 
each other to establish interdisciplinary subject has become a feature of the progress of today's subjects. 
Chemometries is a new branch of chemistry that appears at the intersection of chemistry, computer science, 
mathematics, and statistics (Kowalkowski et al., 2006). It effectively uses computer science, mathematics, 
statistics, and other theories and measures of relevant subjects to optimize the chemical measurement 
process and obtains practical chemical information from chemical measurement information as much as 
possible. 
Artificial intelligence algorithms are a kind of iterative search algorithms that simulate or explain the 
development, evolution and variation of some natural phenomena (Cavus, 2010; Chen et al., 2015). The 
advantages of artificial intelligence algorithms are: they can perform global search, have fast convergence 
speed, high numerical accuracy, good generality, etc. (Hetmani et al., 2015; Kargarian et al., 2014; Kim et al., 
2017). Currently widely used intelligent algorithms include Particle Swarm Optimization (PSO), Genetic 
Algorithm (GA), Ant Colony Optimization (ACO), and neural network algorithm (Zhang et al., 2018). Radial 
Basis Function (RBF) neural network is a kind of forward-type network with excellent performance, it has been 
receiving much attention and has been widely used, and there have been many improvements and 
developments in recent years. The determination of hidden layer nodes in RBF networks is directly related to 
the accuracy of network prediction. Therefore, many scholars have proposed different determination methods. 
This paper connected the ACO with the fuzzy clustering, and used the ACO-FCM-RBF network system for the 
simultaneous detection of zirconium and bismuth to construct a new analytical chemometrics measures. 

2. Basic theory and algorithm 

2.1 Basic theory of ACO 

ACO is a "natural" algorithm that appeared and inspired by the specific actions of various creatures in the 
natural world. It comes from the analysis of various actions of ant colonies (Ding et al., 2008; Ding et al., 2003; 
Saidi-Mehrabad et al., 2015). Ant colony optimization (ACO) is a key content of this system. The theory of ant 
colony system is shown in Figure 1 for details: 

                                

 
 

 

 
   

                                                  
DOI: 10.3303/CET1866139 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Zou G., 2018, Analytical chemometrics research based on artificial intelligence algorithm, Chemical Engineering 
Transactions, 66, 829-834  DOI:10.3303/CET1866139   

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Figure 1: Principle of ACO 

As shown in the figure, if A is an ant nest, F is a food source. 16 ants crawled from A to F, and then the 16 
ants returned to A from F. At t=1, 16 ants are at B and D; at t=2, 8 ants are at B and D; 16 ants are at E. At 
this time, the distribution of the pheromones concentration on each route is: τBE=8, τED=8, τAB=16, τCD=16, 
τBC=16, τFD=16, for the amount of pheromones on the routes, BCD is two times of BED. Therefore, with the 
progress of time, most ants pick the route BCD, by the end, all ants make the same selection to achieve the 
optimization of the process. 

2.2 Basic theory of fuzzy clustering 

Chapter 2 Clustering refers to the automatic classification of data with different degrees of similarity, so as to 
minimize the similarities between different classes, and maximize the similarity within the same class. The 
most widely used means clustering algorithm is the C-means clustering algorithm. The fuzzy C-means 
clustering (FCM) algorithm is an improvement of the common C-means clustering algorithm to make it fit 
better with the RBF networks. The algorithm is shown in Figure 2. 

   

Figure 2: Improved fuzzy clustering methods                 Figure 3: Structure of RBF neural network 

2.3 Basic theory of RBF neural network 

For Radial Basis Function (RBF) neural network, it is a forward artificial neural network and is composed of 
three layers of neurons: input layer, hidden layer, and output layer, its basic idea is: to use RBF as a basis of 
the hidden module to form the space range of the hidden layer, and to map the input vector straight into the 

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hidden space. The mapping of the hidden layer space range to the output layer space range is linear, that is, 
the output is the linear weighting of the hidden module output. 
For the RBF neural network, its topological structure is shown in Figure 3 in detail: 
The connotations of layers of this network are as follows: 
(l) For the first layer, it is the input layer, the input layer neurons only functions effectively as a linkage, and 
does not transform the signal. 
(2) For the second layer, it is the hidden layer. Assume the correlation coefficient from the i-th neuron in the 
input layer to the j-th neuron in the hidden layer is vij(1≤i≤I,1≤j≤H), the correlation coefficient vector from input 
layer neurons to the j-th neuron in the hidden layer is Vj=(v1j,v2j,…,vij)

t (1≤j≤H), the transition function of hidden 
layer neuron is a Gaussian function, and the current state of the corresponding input x of the j-th neuron in the 

hidden layer is: = − = exp −∑ − /(2 ), where σj(1≤j≤H) is the specific width of the basis 
function of the j-th neuron in the hidden layer. 
(3) For the third layer, it is the output layer. Assume the j-th neuron in the hidden layer is connected to the K-th 
neuron in the output layer, its specific actual coefficient is wjk(1≤j≤H,1≤K≤O), and the correlation coefficient 
vector from the hidden layer neuron to the output layer K-th neuron is Wk=(w1k,w2k,...,wHK)

t, (1≤K≤O). 

3. Algorithm improvement 

The research algorithm of RBF network focuses on: the nearest neighbor clustering research algorithm, self-
starting research algorithm, ACO, randomized algorithm, and fuzzy clustering algorithm, this is used to select 
the main body of RBF. The paper uses fuzzy clustering and ACO to perform clustering twice to clearly 
determine the main body of RBF, it’s called ACO-FCM-RBF network research algorithm. 
The actual steps of the research algorithm of the RBF network are as follows: 

3.1 Determine the main body of the basis function 

The actual algorithm is described below: 
l) First randomly selecting M typical points or selecting according to the experience. This paper uses the 
random selecting measures to determine the original typical points; 
2) Initializing parameters: Assume N, ε0, r, m, τs(0) = 0, β, α, M, P0, η; 

3) Calculating Euclidean distance dij: = ( − ) = ∑ ( − )  ; 
4) Calculating the amount of pheromones of each route: ( ) = 1, ≤0, >  
5) Calculating the probability combining Xi to Xj: = ( ) ( )∑ ( ) ( )∈  
6) Judging whether Pij(t)≥P0 is true; if it’s true, proceed next step, else i=i+1, go to step 3; 

7) Calculating the new clustering main body = ∑ , ∈ ; 
8) Calculating deviation errors and global errors: the deviation of the j-th clustering is:  = ∑ ∑ ( − )    
Where vji represents the i-th component in the j-th cluster. The global error of the calculation is: = ∑ . 
9) Judging whether ε≤ε0 is true. If it’s true, stop the calculation, and output the results; else go to step 3 and 
proceed effective iteration; 
10) Through effective ant colony clustering, the actual number of clusters c (2≤c≤n) is obtained, and the 
conclusion of the ant colony clustering is taken as the original reflection point of fuzzy clustering, then further 
select the specific index weight m'(1<m'<∞); 
11) Calculating the actual matrix U it belongs to; 
12) Calculating the actual value function. If it is smaller than a certain threshold, or compare to its previous 
value function, its change value is smaller than a certain threshold, then the algorithm stops naturally; 
13) Calculating the new clustering main body, and then return to step 11; 
14) Effectively output the ultimate clustering main body. 

3.2 Determine the basis function center width σj 

The basis function center represents a certain measured quantity of the samples in the sub-sample set 
associated with each center, and many methods can be determined clearly. This paper uses the following 
formula to determine: 

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
=

=
N

j
jiij udj

1
σ

                                                                                                                                           （1） 

Where, dij is the actual Euclidean distance from sample xi to the j-th clustering main body. Uij is the specific 
degree of membership of sample xi to the j-th cluster. 
3.3 Specify the correlation weight wij from the hidden layer module to the output layer module 
If we mark the corresponding expected output of xui as y

u
i, then the average error measurement standard is a 

smaller square error, that is: 


= =

−=
P

u

u
i

M

i

u
i OyE

1

2

1
)(

2
1

                                                                                                                         （2） 

After determine the parameters of the basis function, E in the above formula belongs to the function of Wij, and 
the solution can be obtained by using the least squares method. 
This paper uses mathematical models and calculations, and uses the MATLAB language and C/C++ language 
to program the process. 

4. Test results and discussion 

4.1 Main equipment and reagents 

Table 1: Main reagents and equipment 

Reagents and equipments SPEC Concentration 
ultraviolet and visible 
spectrophotometer 

UV-265 (Shimadzu) - 

Bi AR 5μ/L 
ZrOCl2·8H2O AR 5μ/L 
Cu AR 5μ/L 
DBS- chlorophosphonazo AR 0.5g/L 
H2SO4 AR 1.0mol/L 
Ethanol AR 99.5% 

4.2 Test methods 

Accurately absorb a certain amount of zirconium and bismuth standard solution in a 25-mL volumetric flask, 
and gradually add 0.5 g/LDBS-chlorophosphonazo 2.2 mL; l.0 mol/L sulfuric acid 7.0 mL; absolute ethanol 2.5 
mL, add water and dilute to a certain scale, shake it to make it uniform, effective color reaction for 60 minutes, 
and then use the blank reagent as a control, use 1cm cuvette, in the 599nm ~ 656nm wavelength range, 
detect the absorbance every 3 nm, calculate by using ACO-FCM-RBF and RBF methods respectively.  
The original parameters of ACO-FCM-RBF are: N=100, ε0=0, r=0.l, m=2, τs(0)=0, β=1, P0=0.6, α=1, M=2 , 
η=0.9. 

4.3 Results and discussion 

4.3.1 Absorption spectrum 

In the H2SO4 medium, the larger absorption wavelength of the blank reagent is substantially at 525 nm, and 
for the larger absorption wavelength of bismuth and the color developing agent complex, it is specifically at 
638 nm; while for the larger absorption wavelength of zirconium and the color developing agent complex, it is 
specifically at 636 nm, their actual contrast reaches113 nm and 111 nm, respectively, the complex absorption 
wavelength is extremely overlapped. As shown in Figure 4. 

4.3.2 Color conditions 

In the luminosity study test, a new same color was developed, that is the same color with DBS-
chlorophosphonazo-zirconium, and no relevant reports were found in the literature. 
In a series of media such as perchloric acid, hydrochloric acid, phosphoric acid, sulfuric acid, and nitric acid, 
the sensitivity of color development in sulfuric acid medium is very high, Under the actual conditions of 
simultaneous detection, when the amount of 1.0 mol/L sulfuric acid is 0.5-12.0 mL, the absorbance value of 
the complex is large and very stable, the actual amount of sulfuric acid used in the test is 7.0mL.  

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Under the condition of simultaneous detection, in 1.0mol/L sulfuric acid medium, when the amount of 0.5g/L 
DBS-chlorophosphine solution is 1.0-3.0mL, the absorbance value reaches the maximum and is very stable. 
The test chooses to use color developing agent, and its actual amount reaches 2.2mL. 
Increase the sensitivity through the use of alcohol to change the feature of the media, add a small amount of 
absolute ethanol into 1.0 mol/L sulfuric acid media, make the complex appear and move evenly, so as to 
achieve sensitivity increasing effect, the sensitivity increases by approximately 37%, when the amount of 
absolute ethanol reaches 0.510mL, the absorbance of the complex is large and very stable, the actual amount 
of ethanol used in the test is 2.5mL. 
At room temperature, zirconium and bismuth reacted with DBS-chlorophosphonazo. After 60 minutes of color 
development, a blue-violet complex appeared. It was determined by the test that the complex was stable for at 
least 5.5 hours, and the absorbance remained unchanged. 
In the range of 0~20μg/25mL, bismuth conforms to the Lambert-Beer law, the actual linear equation is: 
A=0.01736+0.0l3l02C, r=0.9995. The apparent molar absorption coefficient is 7.9×10

4L·mol-1cm-l. 
In the range of 0~10μg/25mL, Zirconium conforms to the Lambert-Beer law, the actual linear equation is: 
A=0.023816+0.00699C, r=0.9997. The apparent molar absorption coefficient is 2.6×104L·mol-1cm-l. 
According to test measures, 10μg bismuth(zirconium)/25mL is determined, and the relative error of 
absorbance ≤5%, below are the co-existed ions (calculated with mg): Cu2+(1.1), Ni2+(0.9), Co2+(0.5), 
Mg2+(0.45), Mn2+(0.4), KNO3(1.5), Ca

2+(1.1), Si4+(0.12), Zn2+(5), ascorbic acid (6), which did not interfere the 
test. 

560 580 600 620 640 660 680 700
0.0

0.1

0.2

0.3

A
B

S

 λ / nm

4

3

1

2

 

Figure 4: Absorption spectrum (1-blank, 2-Bi 10μg/25mL, 3-Zr 10μg/25mL, 4- Bi 10μg/25mL+ Zr 10μg/25mL) 

4.4 Study of the synthetic sample 

Table 2: Analytical results of mixed standard solution 

No. addition measuredvaluebyRBF measuredvaluebyACO-FCM-RBF 
 Bi Zr Bi Zr Bi Zr 
1 4.0 2.0 4.09 2.06 4.06 2.05 
2 4.0 6.0 4.15 5.92 3.89 5.98 
3 8.0 2.0 7.64 1.96 8.29 1.97 
4 8.0 6.0 8.12 6.10 7.94 5.93 
5 12.0 2.0 11.57 2.03 11.77 2.00 
6 12.0 4.0 11.68 3.89 11.80 3.91 
Relativemeanerror 
(%) 

3.07 3.12 2.04 1.33 

 
According to the test method, 9 sets of mixed standard solutions were matched with the orthogonal table L9 
(34) as the training set, it was evenly distributed and neatly comparable; besides, 6 sets of samples were 
made as the test set. The absorbance value of the sample is taken as the input information, the amount of 
zirconium and bismuth in the sample is the network output, the detailed conclusion of the study is shown in 
Table 2. 

4.5 The discussion of the algorithm 

In this paper, the ACO-FCM-RBF algorithm and RBF algorithm were applied to the simultaneous detection of 
zirconium and bismuth, two new types of chemometrics measures were constructed and these two types of 

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algorithms were measured and compared with synthetic samples. Table 2 shows that the ACO-FCM-RBF 
algorithm error is significantly reduced compared to the RBF algorithm. 
This paper used ACO to carry out each specific clustering, relied on the specific effects brought by the ant 
colony, and then used the fuzzy clustering to specifically expand secondary clustering. Although the ant 
colony clustering algorithm can present the optimal number of actual nodes, it is a kind of means clustering, in 
other words, the cluster brought by the ACO practically belongs to a kind of hard partitioning, so we 
specifically introduced the fuzzy clustering to make flexible fuzzy partitioning of the actual conclusion of the 
clustering in substantive sense. 
With respect to the determination methods of the hidden layer nodes in the RBF network, it usually uses the 
typical C-mean clustering algorithm. Although it’s a kind of clustering algorithm with good performance, 
however, for this algorithm’s selection sensitivity of the original clustering main body, how to pick the original 
clustering main body directly determines the ultimate clustering conclusion. If the selection of original 
clustering main body is not good, or it may be caught into the actual situation of local extremum. Generally, 
ACO will not trap in a local minimum situation, although for the fuzzy clustering algorithm, it is quite sensitive 
in the original clustering point, however, clustering under the premise of ant colony clustering can prevent this 
situation. For C-means clustering, the number is artificially determined. For the ACO clustering, it is 
determined specifically by the algorithm in the operation, not determined artificially, by the end of this papery, 
it determines that the number of nodes in the hidden layer module is 7. Because the algorithm can 
independently determine the actual node number in the hidden layer, which avoids the interference of human 
factors 

5. Conclusion 

(1) This paper constructed a new ant colony optimization-fuzzy c-means clustering-radial basis function neural 
network (ACO-FCM-RBF) model and established a new analytical chemometrics method. 
(2) This paper made a comparison between the results of (ACO-FCM-RBF) model and RBF network method, 
the calculation results of ACO-FCM-RBF neural network were better in the accuracy.  
(3) A new DBS-chlorophosphonazo-zirconium color system was established for the simultaneous detection of 
zirconium and bismuth using the spectrophotometric determination. 

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