CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 52, 2016 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar Sabev Varbanov, Peng-Yen Liew, Jun-Yow Yong, Jiří Jaromír Klemeš, Hon Loong Lam 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-42-6; ISSN 2283-9216 
 

Forecasting Modeling for Energetic Efficiency  

in an Industrial Process 

Simone M. Acostaa, Angelo M. O. Sant’Annab, Osíris Canciglieri Juniorc* 

aDepartment of Electronics,  Federal University of Technology Paraná (UTFPR), Av. Sete de Setembro, 3165, Curitiba, 

Brazil 
bMechanical Engineering Department, Federal University of Bahia, Rua Aristides Novis, 2, Salvador, Brazil. 
cIndustrial and Systems Engineering Graduate Program, Pontifical Catholic University of Parana, Rua Imaculada 

Conceição, 1155, Curitiba, Brazil. 

osiris.canciglieri@pucpr.br 

The quality of products and processes is a permanent challenge for industries, and such challenge is no 

different in steelmaking processes. One of the main problems affecting the quality of steel products is the 

existence of contaminants in alloy steel, and phosphorus (P) is a major contamination element interfering with 

the steelmaking process. The increased P levels can severely affect the physical integrity of steel bonds, thus 

threatening the quality of the final product. This paper proposes a robust approach to model the phosphorus 

concentration levels in the steelmaking process. The proposed approach consists in applying the artificial 

neural networks techniques for improving the energetic efficiency of the industrial process. We used the 

improved neural network models inspired in the human nervous system for processing the information. The 

different techniques used for modelling the phosphorus levels investigate the variables that have a significant 

influence on refining process. Based on the better predictive model, the increase of phosphorus levels in the 

final product is related to initial levels of carbon, oxygen, magnesium, manganese oxide and calcium oxide. 

The results illustrate the efficiency of the techniques used in the modelling, with emphasis on the adequacy of 

the predictive models constraints in the refining process. This study presents a relevant strategy to model 

characteristics’ of raw material based on forecasting strategy to the efficiency of alloys and steel industry. 

1. Introduction 

Assuring the quality of processes and products remains a constant challenge for companies, and this is 

increasingly becoming a fundamental requirement for their endurance. This is no different in steelmaking 

companies. One of the main parameters affecting the excellence of products in this sector is the existence of 

contaminants in alloy steel. Phosphorus (P) is one of the main contaminants found to interfere in steelmaking 

processes. The ferromanganese alloys are the major sources of P contamination during the process of 

steelmaking, which demands a limited use of this kind of alloy along the process (Um et al., 2014). The 

increased P levels can significantly affect physical aspects of alloy steel, thus severely compromising its 

quality. P-rich steel compounds usually show: (i) increased hardness; (ii) decreased ductility; (iii) appearance 

of ghost lines in carbon-rich alloy steels; and (iv) increased frailty of steel bonds under high and low 

temperatures (Chaudhary et al., 2001). 

The refining process adopted by the company subject to this study uses high-purity oxygen to reduce carbon 

levels in High-Carbon Ferromanganese (FeMnHC) originating Medium-Carbon Ferromanganese (FeMnMC) 

which has higher market value. During this process, there is an alteration in levels of other elements, including 

phosphorous. Therefore, the present work proposes a model for the FeMnMC refining process in an important 

Brazilian metallurgic industry with the purpose of predicting P levels at the end of the refining process. The 

Artificial Neural Network (ANN) method, defined as data processing systems based on the behavior of the 

human nervous system, was the chosen modeling technique (De Castro, 2007). The main advantages of 

ANNs are: (i) the capacity of approximating the behavior of non-linear physical phenomena, not requiring 

                                

 
 

 

 
   

                                                  
DOI: 10.3303/CET1652181 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Acosta S. M., Sant’Anna A. M. O., Canciglieri O. J., 2016, Forecasting modeling for energetic efficiency in an 
industrial process, Chemical Engineering Transactions, 52, 1081-1086  DOI:10.3303/CET1652181   

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profound statistical comprehension of the modeled data and; (ii) the capacity of learning any input/output 

variables of the continuous form (Haykin, 2008). An ANN is usually called a black-box model, considering that 

this kind of technique approximates the relative input/output of a certain process. For the process studied 

here, input variables were FeMnHC composition, dross composition, alkalinity indexes and amounts of solid 

loads added during the process. The output variable was P concentration at the end of the process. 

Application of ANN to model different chemical and industrial processes is relevant and several authors have 

profited from the approximation of processes with complex behavior allowed by this technique in their work, 

such as Bakar et al. (2013) that performed a study to identify values of key parameters for prediction of heat 

exchanger of a bio-methanol production plant. Joo et al. (2013) propose to control the temperature of a 

polymerization reaction of styrene in suspension and to compare with classical controller PID systems. 

Osuolale and Zhang (2014) evaluated different ANN models for forecasting hourly load of an electricity 

market. Yong et al. (2015) minimized the heat exchanger for waste heat under varying feed conditions using 

neural network model, allowing lower time and cost in manufacturing, while Gao and You (2015) developed an 

approach to optimize the pattern of filter networks, offering practitioners a relevant trade-off between quality 

and cost. This paper proposes a robust approach to model the phosphorus concentration levels in the 

steelmaking process. The proposed approach consists in applying the artificial neural networks techniques for 

improving the industrial process energetic efficiency.  

2. Backgroud  

Artificial Neural Networks are systems that manipulate information through the interaction of basic processing 

units called artificial neurons (Haykin, 2008). Artificial neurons, in turn, are basic units that receive and process 

external inputs generating outputs. Du and Swamy (2013) asserted that an artificial neuron comprises the 

following components: (i) a group of synaptic weights that can balance the importance of input signals; (ii) a 

threshold term or Bias that enables to increase or decrease the impact of different inputs on neuronal function; 

(iii) an adder, which can add up values of inputs balanced according to synaptic weights and (iv) an activation 

function that controls the output signal. The artificial neural are usually organized in layers which can be 

categorized into output and hidden layers. 

An ANN may have a variable number of hidden layers, but according to Kolmogorov’s theorem and to the 

second theorem of universal approximation only one hidden layer is enough to approximate any function of 

continuous nature (Scarselli and Tsoi, 1998). This allows a reduction in the complexity of the model, but 

occurrence an increased number of neurons are required. An ANN model with two layers may be 

mathematically described by the Eq(1), 

 
(1) 

where yt is the estimated network output, wkj and wkj are the synaptic weights of the output and hidden layers, 

bj represents the threshold terms, xt is the values of input variables and f() symbolizes the exchange between 

neurons in output and hidden layers. Even though there are several forms of transfer functions, the most 

commonly studied are the sigmoid logistic and the linear and hyperbolic tangent functions.  

The choice of the most suitable activation function is a crucial step and a linear function is typically used for 

the output layer in issues of function approximation, whereas logistic or tangent hyperbolic functions are 

employed in the hidden layers. Before the learning process starts, the data are standardized according to the 

activation function in the hidden layer. For logistic function, the data are standardized in the interval [0,1] 

whereas the interval [-1,1] is used for the hyperbolic tangent function. This standardization process is ruled by 

the Eq(2), 

 
(2) 

where ts is the standardized variable, tmin and tmax are the minimum and maximum values to ts, respectively, xt 

is the original variable, xmin and xmax are the minimum and maximum values of xt. 

These functions are chosen due to easy the derivation and simplification of the network learning process, at 

the synaptic weight regulation (Engelbracht, 2006). The learning process consists of two basic steps: (i) the 

prediction stage, where synaptic weights are adjusted based on a group of training data, and (ii) the test 

stage, that determines whether the prediction model is able to generalize. 

The synaptic weights are set through an optimization algorithm called learning algorithm, which for multiple 

layer ANNs is usually the error Backpropagation algorithm. It consists on the minimization of the mean 

quadratic error (Eq(4)) of output variables generated by the ANN relative to real measured values. 

There are several variations of the error Backpropagation algorithm, being the Levenberg-Marquadt algorithm 

amongst the most efficient. This algorithm, however, tends to cause overfitting, where the model specializes in 

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the training data. For that reason, a Bayesian regularization term can be employed in the ANN cost function. 

The ANN cost function was then modified as Eq(3), 

 

(3) 

where et = (yi – yt) is the estimated error, yi is the actual value measured at the system, yt is the output 

estimated by the ANN, n is the number of samples,  and   are terms estimated by the learning algorithm 

with a cost function, wkj and wji are the synaptic weights of output and hidden layers, respectively. 

To evaluate the generalization capacity of an ANN error minimization strategies are used, such as the root 

mean square error (RMSE) and the mean absolute percentage error (MAPE), theses can be determined 

according to Eq(4) and 5, 

  

(4) 

  

(5) 

An important way for evaluation of an ANN model is to estimate the number of parameters or synaptic weights 

(W) and the amount of data used for model estimation (N), where corrected Akaike Information Criteria (AICc) 

is suitable (Sant’Anna, 2015), see Eq(6), and the number of synaptic weight in an ANN with two layers can be 

defined by the Eq(6). 

 

(6) 

where W = [(kj) + j] + [(ji) + i], k represents the number of input variables, j is the number of neurons in the 

hidden layer and i the number of neurons in the output layer. (Vining and Kuwalski, 2011) assert that, an ANN 

model must have N > W based on the Occam theorem that represents a system employing a minimum 

number of parameters and synaptic weights.  

3. Case Study 

Several kinds of steel are affected by high levels of phosphorus or manganese, which can compromise their 

quality. The refining process of ferromanganese consists of carbothermic reaction that involves the reduction 

and control of the percentage of carbon in the liquid metal by injection of oxygen in the bath.  

The chamber for the refining process of ferromanganese on the oxygen converter has an internal layer 

covered of magnesium oxide (MgO), and two pipes (N2-cooled) and vertical stream (water-cooled) blow 

oxygen. Inside the converter, the FeMnHC alloy has an average carbon level of 6.5 %, which increases the 

efficacy of the oxidant dephosphorylation. The Lime is also used during the dephosphorylation step, causing 

significant loss of manganese with no substantial effect on P levels. When lime is dissolved in the molten bath 

it increases the alkalinity of dross, which prevents the loss of manganese into the dross. Before the oxygen 

blow begins, approximately 60 kg of CaO per ton of FeMnHC dissolved in the bath are added, in a process 

divided into 3 stages. 

On the first stage, dephosphorylation and decarburization start to occur and significant amounts of 

manganese are lost to the dross through volatilization, because of the excess of oxygen. During the second 

stage, called decarburization, bath temperature rises, reducing manganese oxidation and increasing the rate 

of decarburization as well as Mn volatilization. Rephosphorylation occurs as a consequence of such 

temperature variations because P2O5 is highly unstable at high temperatures. As the temperature continues to 

rise, rephosphorylation can only be halted if the activity of phosphor pentoxide is reduced, which can be 

achieved by dissolving P2O5 into the dross in the presence of Lime. At the third stage, there is the addition of a 

solid deoxidizing load containing 110 kg of HCFeMn or MCFeMn, 150 kg of FeSiMn and 40 kg of CaO per ton 

of liquid HCFeMn in the bath, which helps to cool the mixture and contributes to reducing manganese 

volatilization. At this point, a blow of inert CO2 gas at 200 Nm3/h begins with the only purpose of stirring the 

bath. 

3.1 Experimental design 
The 21 initial input variables defined as relevant for modeling the dephosphorization process were grouped as: 

(i) composition of metal alloys (x1, …, x6); (ii) composition of slag (x7, …, x15); (iii) composition of solid loads 

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(x16, x17, x18); and (iv) levels of alkalinity: binary; quaternary e optical basicity (x19, x20, x21), see Table 1. The 

data selected covered a sample of 248 observations. 

Table 1: Description of characteristics of sustainable products 

Group Specifications Und 

Alloys composition Si*, P*, Fe*, Ti*, C*, O2 % 

Slag composition MgO, MnO, CaO, SiO2, Al2O3, BaO, K2O, TiO2, FeO wt-% 

Loads composition Initial, Liquid, Dross Nm3 

Alkalinity levels BB, BQ, BO Nm3 

 

Considering the large number of analyzed variables, a correlation analysis was needed in order to select 

those which are actually linked to the P concentration levels at the final process. The Pearson correlation test 

is a statistical tool which indicates the correlation between two variables (to value p<0.01). After the correlation 

test was applied it became clear that from the 21 initial variables only 4 (four) variables were significantly 

correlated with P level output variables at the final refining process, as the initial phosphorus level (P*), the 

initial carbon level (C*), the manganese oxide level (MnO) and the loads composition (liquid). The other 

variables present in the dephosphorization process haven’t high influence to predict P concentration level at 

the final process. Table 2 presents the statistical analysis of outcome elements and P concentration level 

(output variable) and the Figure 1 illustrates the Phosphorus level data at the final refining process. 

 

 

Figure 1: Phosphorus concentration level at the final process 

Table 2: Summary of the variables selected 

Group Variable Mean Std. dev. Max Min Correlation 

Alloys P* 0.216 0.025 0.280 0.155 0.687 

Alloys C* 6.759 0.140 7.070 6.077 -0.291 

Slag MnO 39.056 5.848 51.993 24.202 0.289 

Loads Liquid 9.889 1.543 12.700 5.510 -0.295 

Output P 0.260 0.026 0.331 0.204 1.000 

 

The design of the proposed approach was performed using MATLAB©. The chosen output variable to the 

neural network was the P concentration level at the final Ferromanganese refining process. The relevant input 

variables selected were: initial phosphorus level (P*), initial carbon level (C*), manganese oxide level (MnO) 

and loads composition (Liquid).  

After the pre-processing phase, it was randomly chosen 198 (80 %) observations of the 248 total observations 

performed for composing the Training group and 50 (20 %) were chosen for the Test group. It was used one 

hidden layer to projects in the ANN architecture, the Kolmogorov theorem, and the Levenberg-Marquadt 

algorithm. The Kolmogorov theorem found search-space for our study is 3.0 neurons which are in agreement 

with the established restriction: N>W and T=198 observations. The modeling process consisted of estimating 

ANN models with logistic and hyperbolic activation function in the hidden layer to assess which was the most 

efficient model, using 4 (four) input variables, one output variables, crossover rate 0.8, mutation rate 1.6, 

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learning rate 0.05, momentum rate 0.1 and population 198 obs. The appendices show the realized 

performance study for logistic and hyperbolic activation function (see Table 3).  

The ANN model which better represented the process studied is with 11 neurons in the hidden layer with the 

logistic activation function, considering the error minimizing statistics and the complexity analysis of the model 

(see Tables 3). For 11 neurons in the hidden layer, the number of adjustable parameters is W = 67, keeping 

compliance to N > W. The Table 3 illustrates that as the number of neurons increases towards the top limit 

(jmax = 14) and the estimates of root mean square error (RMSE) and mean absolute percentage error (MAPE), 

highlights that the power of estimation from model decreases and its complexity increases. 

The residuals errors generated by prediction model show a random distribution varying between - 0.04 and 

0.05, without seasonal variation (see Figure 2). In general, the fitted ANN model showed a mean percentage 

error of 0.09 %, and it is possible to consider this ANN model as trustworthy for P concentration level at the 

final refining process. 

Table 3: Performance of ANN with logistic activation function 

Nodes 10 11 12 13 14 

RMSE 0.0159 0.0159 0.0159 0.0159 0.0159 

MAPE 0.000958 0.000949 0.000956 0.000955 0.000949 

AICc 53.25 59.17 65.24 71.28 77.21 

 

 

Figure 2: Residuals errors from the better ANN model 

4. Conclusions  

The process of extraction of metals, such as zinc, aluminum, iron and manganese for the production of alloys 
is very important to the industry, detaching the interest for reducing costs, environmental impacts and 
improvement performance. We propose to determine a prediction model for Ferromanganese refining process 
in a steelmaker industry that allows estimating the phosphorus concentration levels. The Ferromanganese 
refining process performed in a steelmaker industry to allow the prediction of P concentration levels. The 
development of the ANN model with the variables from Ferromanganese refining process was used as input 
and selected from correlation test. All the variables were tested with a correlation test to verify how each of 
them is related to the percentage of phosphorus in the final product. These results show that four variables 
were correlated and those were used to compose the input set of the ANN model. 
The architecture of neural network was composed by the Kolmogorov theorem, the Levenberg-Marquardt 
algorithm, and diagnostic criteria to improve the parameters estimates, increase the quality of prediction and 
decrease the statistical errors. The samples were divided into groups: one was used to the training of the ANN 
model and a second was used to test the ANN model, those groups were composed of 198 and 50 samples, 
respectively. The great number of neurons in the hidden layers made the network structure very heavy in a 
computational way which demands a little more time to achieve the results, and the diagnostic analysis 
suggests 11 neurons, hyperbolic function to better performance of ANN model. The estimation model showed 
excellent results with an average percentage error of 0.09 %, supporting the generalization capacity and 
reliability of the ANN model. Based on this created estimation model it is possible to estimate the impact of 
certain P concentration levels in FeMnMC beforehand, with a considerable amount of reliability.  

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The present study has established that dephosphorization process of ferromanganese with alloys composition 
correlated variables: initial phosphorus (< 0.28 %), initial carbon (< 7.070 %) can be carried out to significant 
influence to estimate P concentration level. As soon, the manganese oxide level (24.20 – 51.993 wt.%) and 
loads liquid (5.51 – 12.7 Nm3) for slag and loads composition for dephosphorisation of high-carbon 
ferromanganese. To future research is possible to investigate non-linear or chaotic behavior between input 
and output variables, as an interesting point to be studied to make forecasting models. 

Acknowledgments 

The authors are grateful to the National Council of Scientific and Technological Development (CNPq) under 

grants 486707/2013-0 (Universal) and scholarship for the financial support of this work. 

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