Expert Systems with Applications 36 (2009) 11671–11674

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Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

Artificial neural networks for optimization of gold-bearing slime smelting

David Liu a,c,*, Yudie Yuan b, Shufang Liao a

a Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, 111 Ren Ai Road, Dushu Lake Higher Education Town, Suzhou Industrial Park, Suzhou, Jiangsu, PR Chinab Novelis Global Technology Centre, 945 Princess St., P.O. Box 8400, Kingston, Ontario, Canada K7L 5L9c School of Science, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China

a r t i c l e i n f o

Keywords:Gold slimeNeural networkGoldOptimum flux composition

0957-4174/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.eswa.2009.03.016

* Corresponding author. Address: Department of MJiaotong-Liverpool University, 111 Ren Ai Road, DushuSuzhou Industrial Park, Suzhou, Jiangsu, PR China.

E-mail address: David.liu@xjtlu.edu.cn (D. Liu).

a b s t r a c t

Pyrometallurgy is often used in the industrial process for treating gold-bearing slime. Slag compositionshave remarkable influences on the recovery of gold and the gold content in slag. A method for determin-ing optimum flux compounding with neural networks is studied in this paper, and the neural networkmodel for estimating the gold contents with different slag compositions is presented. On the basis ofthe neural network model, an algorithm for searching the optimum flux compounding in the gold-slimesmelting process is proposed, and the optimum flux compositions are obtained accordingly.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

In the gold manufactory industry, pyrometallurgy (Marsden &House, 2006) is commonly used to process gold-bearing slime orgold slime for short. In this process, appropriate fluxing agents(i.e. slag compositions) are added at high temperature into thesmelting furnace, which results in separating precious metals (goldand sliver) from oxides and gangue with the latter go into the re-mains called slag. In this way, gold–silver alloys are obtained bypyrometallurgy. In the smelting process, slag compositions essen-tially determine the amounts of gold left in slag, hence, the recov-ery of gold. To maximum the recovery of gold, it is of greatimportance to optimize the slag composition so as to minimisethe gold content in slag. In fact, research outcomes on determining‘best’ slag compositions have been reported (Yuan, Yao, Qiu, & Li,1995) based on the nonlinear regression technique. However,smelting gold slime is a complicated process which involves chem-ical reactions of multi-phases. Therefore, it is usually hard to de-scribe the relationship between slag compositions and goldcontent in slag explicitly. The application of nonlinear regressionmethod requires that some presumptions be made about the formof distributions of data or the functional relations among theparameters concerned. Therefore, human errors are likely intro-duced to the problem. It is the above difficulty that has motivatedus to search for a new method.

In the last two decades, artificial neural network (ANN) has re-vealed its huge potential in many areas of science and engineering,with the rapid development in its learning algorithms. Its excep-

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athematical Sciences, Xi’anLake Higher Education Town,

tional function of self-organising, self-study, fault tolerance andhigh robustness has paved the way for its wide applications suchas pattern recognition, pattern classification, tendency analysis,prediction and nonlinear functions. The neural network has alsoproven to be a powerful tool in many areas including industrialprocesses (Schlang, Lang, Poppe, Runkler, & Weinzierl, 2001), pre-diction of materials properties such as steel (Bahrami, MousaviAnijdan, & Ekrami, 2005; Capdevila, Garcia-Mateo, Caballero, &Garcl’a de Andre’s, 2006; Guo & Sha, 2004), etc. In addition, thereare many other reports that the neural network approach has beenused in material science based research as discussed by Sha andEdwards (2007). Artificial neural networks are now well estab-lished, and prominent in the literature. However, its applicationto pyrometallurgy industries has not been examined thoroughly.

As such, the ANN approach is adopted in this paper as the sub-stitute for nonlinear regression to identify the optimum slag com-positions for the process of gold recovery in pyrometallurgy. Wehas constructed a neural network model for estimating gold con-tent in slag for the ternary system B2O3–SiO2–Na2O in our previousstudies (Liu, Yuan, & Liao, 2009), and aim at developing a algorithmby which the neural network model can be used to predict theoptimum slag compositions in this study. For the continuity of thispaper, we will describe the model briefly in Section 2, followingwhich, in Section 3, the algorithm for optimization of slag compo-sitions will be discussed.

2. The neural network model

As mentioned above, an artificial neural network model wasdeveloped for estimating or predicting gold content in slag in pyro-metallurgy. As known, artificial neural network is a network withnodes or neurons analogous to the biological neurons. The nodes

11672 D. Liu et al. / Expert Systems with Applications 36 (2009) 11671–11674

are interconnected to the weighted links and organised in layers.The performance of a neural network depends mainly on theweights of its connections. The knowledge is represented andstored by the weights (strength) of the connections between theneurons (processors). If correct weights can be trained then anANN can do an exceptional job.

Although, there are different types of ANN, feed-forward multi-layer perception (MLP) is probably the most widely used due to itspowerful modelling capability (Hornik, Stinchcombe, & White,1989; Kurkova, 1992). It had been shown that MLP was a suitabletype of neural network for estimating gold content in slag (Liuet al., 2009). Fig. 1 shows the neural network model, which is ofthe type of feed-forward multilayer perception, and used for predict-ing the gold contents in slag. It consists of three layers: the inputlayer, the output layer and the hidden layers. The neurons in the in-put layer take the information about slag compositions xi (indepen-dent variables), and the output layer generates the outcomes of goldcontent in slag oi (dependent variables). The number of nodes in thehidden layer is 5, which was of enough sophistication to deal withthe pyrometallurgical experiments. In addition, there are four nodesin the input layer corresponding to the four fluxing agents, and onenode in the output layer to represent for gold content in slag. Theback-propagation algorithm was used to train the network, whichis an iterative gradient algorithm designed to minimise the mainsquare between the predicted output and desired output.

As mentioned earlier, in order to improve the overall recoveryof gold, appropriate fluxing agents should be used. In addition,the amounts of fluxing agents and their combinations should beoptimized when smelting the gold-bearing slime. In the previousresearch, a ternary system B2O3–SiO2–Na2O is used as the basicslag type (Yuan, 1995), and small-scale pyrometallurgical experi-ments in melting pot had been carried out to simulate the indus-trial processes. The detailed experimental methodology can befounded in Yuan (1995). The experiments were organised by usingthe orthogonal design of four-factor regression of second degree.The experimental results are listed in Table 1.

As seen in Table 1, a total of 25 experiments had been done byvarying the combinations of slag compositions. The correspondinggold content in each experiment was also measured ranging fromca. 100 g/t to ca. 660 g/t.

Yuan et al. (1995) studied the problem by using nonlinearregression technique. A regression formula for estimating goldcontent was deduced for these results as the follows:

y ¼ �66:84x1 � 7:1x2 � 19:32x3 � 48:75x4 � 42:92x1x2

� 0:094x1x3 � 12:17x1x4 þ 18:47x2x3 þ 7:02x2x4

þ 61:72x3x4 þ 66:98x21 þ 43:44x2

2 þ 69:75x23 � 5:38x2

4

þ 152:36 ð1Þ

X1 X2….. Xn

Input layer

Hidden layer

Output layer

O

Fig. 1. The neural network for optimization of processing gold slime.

This formula was used for calculating or estimating the gold contentin slag for the completed experiments.

On the other hand, the neural network was trained by the train-ing data which are listed in Table 1. The training process had seenthe rapid convergence, and the network was used to predict thegold contents in slag for all the 25 experiments involving differentslag compositions (Liu et al., 2009).

It had been demonstrated that the neural network had betterpredicted the gold content in slag for different slag compositionswith higher precision compared with the traditional regressionmethod. The most important results were shown in Fig. 2, inwhich the estimated values given by the network and regressionformula were plotted against the actual experimental results,especially for gold content between 200 and 400 g/t. As seen inFig. 2, the neural network values, compared with the experimen-tal results, were generally within 10–15 g/t of the actual goldcontents in slag, while the regression method yields the errorsthat were normally larger than 30–40 g/t with some worst caseas high as 90–100 g/t. This is because that regression methodwas based upon the presumption about the nonlinear relation-ship between slag compositions and gold content in slag, whichis sometimes unrealistic.

3. Optimizing flux composition using the neural network

In the section above, we have described the established neuralnetwork, which is capable of calculating the gold contents in slagfor the pyrometallurgical experiments. Because the trained net-work has already ‘stored’ the nonlinear relationships between slagcompositions and gold content in slag, we can now adopt an opti-mization procedure, which determines the optimum slag com-pounding that minimises the gold content in slag. The problemcan be interpreted mathematically as the follows:

Given V = {V1,V2, . . . ,Vp} is the set of all possible combinations,there exists an objective function C, and C(Vi) P 0,i 2 {1,2,3, . . . ,p}. The optimum solution is then V* 2 V andC(V*) = min C(Vi), i 2 {1,2,3, . . . ,p}.

The proposed algorithm for locating the optimum solution byusing the neural network is as the follows:

(1) Input any initial state V(0) 2 V as the current solution, andset the number of iteration (or time) t = 0;

(2) Set state V(t) = V(0);(3) Generate next candidate state V0 (V0 is the nearest neighbour

of V(t)) based upon some rule, and V0 = F(V(t)), where F is arandom function.

(4) Use the trained BP neural network to do the reasoning andfind the change of the objective function, i.e.DC = C(V0) � C(V(t)). If DC < 0, then accept V0 as the next cur-rent state, and set V(t + 1) = V0, otherwise, reject V0;

(5) Set t = t + 1, and decide if the system has converged to itspre-set criteria. If not, go to step (3). If yes, stop the loop.

In the above network reasoning algorithm, the objective func-tion is determined for the gold content in slag, four elements inthe set V are soda, borax, silica glass, and salt. Assign the follow-ing domains to each element, i.e. soda 5–50%, borax 20–70%,silica glass 5–60%, and salt 0–30%. The optimization process forfinding the optimum slag compositions is shown in Table 2, inwhich results during searching are for gold content in slag<150 g/t.

As seen in Table 2, the slag compositions are close to their opti-mum values when the gold content in slag is decreased below

Table 1Testing results for different compositions of soda–borax–silica glass–salt slag system.

Sample number Soda (%) Borax (%) Silica glass (%) Salt (%) Gold content in slag (g/t)

1 12.9 42.9 14.4 2.9 506.42 12.9 42.9 14.4 17.1 272.73 12.9 42.9 35.6 2.9 267.04 12.9 42.9 35.6 17.1 397.15 12.9 57.1 14.4 2.9 657.06 12.9 57.1 14.4 17.1 285.07 12.9 57.1 35.6 2.9 323.88 12.9 57.1 35.6 17.1 468.69 27.1 42.9 14.4 2.9 510.010 27.1 42.9 14.4 17.1 252.011 27.1 42.9 35.6 2.9 293.312 27.1 42.9 35.6 17.1 170.613 27.1 57.1 14.4 2.9 228.714 27.1 57.1 14.4 17.1 170.515 27.1 57.1 35.6 2.9 258.916 27.1 57.1 35.6 17.1 172.317 10.0 50.0 25.0 10.0 362.918 30.0 50.0 25.0 10.0 210.519 20.0 40.0 25.0 10.0 253.320 20.0 60.0 25.0 10.0 225.921 20.0 50.0 10.0 10.0 241.222 20.0 50.0 40.0 10.0 343.323 20.0 50.0 25.0 0.0 183.924 20.0 50.0 25.0 20.0 100.025 20.0 50.0 25.0 10.0 151.2

200

240

280

320

360

400

200 240 280 320 360 400

Observed value, g/t

Est

imat

ed v

alu

e, g

/t

Neural network

Regression

Fig. 2. Neural network values and regression values against observed (experimen-tal) values.

Table 2Process of searching for the optimum slag compositions by the neural network.

Number Soda (%) Borax (%) Sili

1 20 49 202 22 49 223 22 50 214 22 52 215 22 53 206 22 52 207 22 52 228 22 52 229 22 52 2010 22 52 2011 21 51 2012 21 51 2013 20 51 2014 20 51 2015 21 50 20

D. Liu et al. / Expert Systems with Applications 36 (2009) 11671–11674 11673

100 g/t, i.e. soda 20–22%, borax 50–52%, silica glass 20–22%. There-after, the decisive factor seems to be the amounts of salt added: Byincreasing the amount of slat composition from 18% to 25%, theamounts of gold content in slag sees a rapid drop from 98.9% to56.5 g/t. However, this is only correct mathematically! Experimen-tal investigations have demonstrated that an overdose of salt(>20%) will result in the large amount of vaporization of salt, whichhas substantial negative impact on the recovery of gold. Therefore,it makes sense that the optimum salt composition should be leftwithin 18–20%.

The above optimum slag compositions can be comparedwith the similar results obtained by using nonlinear regressionby Yuan et al. (1995), where soda 20–30%, borax 45–55%,silica glass 20–30%, and salt 15–20%. Understandably, theneural network has given the results which are not only con-sistent with the previous research, but more accurate thanthose obtained by the nonlinear regression. It is, therefore,very interesting and of great importance for the future exper-imental research.

ca glass (%) Salt (%) Gold content in slag (g/t)

11 151.212 141.113 131.114 122.415 116.516 110.417 104.718 98.919 93.220 87.421 80.822 74.823 69.124 62.925 56.5

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4. Conclusions

We use artificial neural networks to optimize the slag composi-tions in pyrometallurgical processes of gold slime. (i) The paper hasdemonstrated that artificial neural network can be used to deter-mine the relationships between slag compositions and gold con-tent in slag. Compared with the traditional regression method, itmakes no functional assumptions on the relationships, hence,eliminates the errors brought in by Man. (ii) Further, the algorithmfor optimizing the slag compositions in the process of gold slime isproposed and executed by using the neural network. The optimiza-tion process yields comparable outcomes and the optimum slagcompositions are determined as soda 20–22%, borax 50–52%, silicaglass 20–22%, and salt 18–20%. These results produced by the neu-ral network seem more accurate than obtained by the traditionalregression method statistically, and has given a very good indica-tion to the direction of future experimental research.

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