Heat treatment technique optimization for 7175 aluminum alloy by an arti cial neural network and a genetic algorithm

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1 Journal of Materials Processing Technology ) 84±88 Heat treatment technique optimization for 7175 aluminum alloy by an arti cial neural network and a genetic algorithm R.G. Song a,*,q.z. Zhang b a College of Science, Beijing University of Aeronautics and Astronautics, Beijing , PR China b Department of Automation and Control, Beijing Institute of Mechanical Industry, Beijing , PR China Received 7 July 2000 Abstract A systematic experimental investigation of the effect of heat-treatment technique on the mechanical properties of 7175 aluminum alloy was carried out. Particularly,an arti cial neural network and a genetic algorithm were used to search for the optimum technique,adapted for 7175 aluminum alloy. The results indicated strongly that an arti cial neural network combined with a genetic algorithm indeed offer a new effective means for the optimization of materials processing technique. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Heat treatment; Technique optimization; Arti cial neural network; Genetic algorithm; 7175 aluminum alloy 1. Introduction The technique of the optimization of materials processing has been investigated by trial-and-error for a long time. This way is of very large blindness in action,thus wasting a lot of manpower and money. For this reason,it is desirable for materials scientists to conduct less experiments and yet attain a expected goal. Recently,the wish has become possible with the development of materials and computer science,especially intelligent technology,and some progresses have been made in the eld of materials design and processing [1±5]. The neural network,as one of the most attractive branches in arti cial intelligence,has the potentiality to handle problems such as modeling,estimating, prediction,diagnosis,and adaptive control in complex non-linear systems [6]. It has been established that there exist different effects of deformation,solid solution and aging time on the mechanical properties of high strength aluminum alloys [7]. Numerous experiments must be conducted in order to nd an appropriate technique that renders an aluminum alloy of the maximum strength. Therefore,how to obtain an optimal technique is one pending problem. For this purpose,a * Corresponding author. Present address: Nano-biotechnology Group, Research Institute of Biological Resources,AIST Hokkaido,National Institute of Advanced Industrial Science and Technology, , Tsukisamu-Higashi,Toyohiro-ku,Sappora ,Japan. Tel.: ; fax: address: songrg@hniri.gro.jp R.G. Song). systematic experimental investigation of the effect of heat-treatment technique on the mechanical properties of 7175 aluminum alloy was carried out in the present research work. On this basis,an arti cial neural network ANN) and a genetic algorithm GA) were introduced to optimize the technique for 7175 aluminum alloy. 2. Experimental work The material tested was a 43 mm thick 7175 forged aluminum alloy with the chemical composition as shown in Table 1. The techniques used to impose different values of plastic deformation on the 7175 aluminum alloy are shown in Table 2. The specimens for the tensile test were solid solutioned at 753 K for 10,70 and 130 min,followed by an immediate quenching in ambient water and then aging at 443 K for 6, 16 and 36 h. The longitudinal axis of the tensile specimens was parallel to the rolling direction. The tensile tests were performed on a computer controlled AG-10TA model test machine. 3. Modeling using an ANN Table 3 gives the tensile test results for 7175 aluminum alloy under different heat-treatment conditions. It can be /01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S )

2 R.G. Song, Q.Z. Zhang / Journal of Materials Processing Technology ) 84±88 85 Table 1 Chemical composition of 7175 aluminum alloy Element Zn Mg Cu Cr Mn Ti Fe Si Al wt.% Balance Table 2 Techniques of deformation Technique mm 738 K hot rolling!8:8 mm cold rolling!1:5 mm mm 738 K hot rolling!8:8 mm 738 K hot rolling!4:1 mm cold rolling!1:5 mm mm 738 K hot rolling!8:8 mm 738 K hot rolling!2:5 mm cold rolling!1:5 mm seen that all the heat-treatment parameters have an effect on the mechanical properties of the 7175 aluminum alloy. Obviously,there exist complicated non-linear relations between the heat-treatment conditions and the mechanical properties. In order to search for the optimum heat-treatment technique, rst the problem of how to establish these relations must be solved. ANN models or simply ``neural networks'' go by many names such as connectionist models,parallel distributed processing models,and neuromorphic systems. Whatever the name,all of these models attempt to achieve good performance via dense interconnection of simple computational elements. In this respect,an ANN structure is based on the present understanding of biological nervous systems. These models are composed of many non-linear computational elements operating in parallel and arranged in a pattern reminiscent of a biological neural network. There are several algorithms in a neural network and the one which used here is the back-propagation BP) training algorithm. This algorithm is an iterative gradient algorithm designed to minimize the mean-square error between the actual output of a multi-layer feed-forward network and the desired output, Table 3 Prediction points of the ANN model and experimental results Sample Aging time h) Yield strength MPa) Ultimate tensile strength MPa) Desired, D 1 Output, s 1 Desired, D 2 Output, s a a a a Testing sample.

3 86 R.G. Song, Q.Z. Zhang / Journal of Materials Processing Technology ) 84±88 net k ˆ X7 jˆ1 W jk Y j ; k ˆ 1; 2 3) s k ˆ f net k 4) e x f x ˆ1 1 e x 5) V j4 and W 7k offer thresholds for the neurons in the hidden layer and output layer because the output value of X 4 and Y 7 are constant and equal to 1. Step 4. Compute the system error E ˆ 1 X 2 X P D nk s nk 2 6) 2P kˆ1 nˆ1 Fig. 1. Learning process and structure of an ANN. as shown in Fig. 1. In order to model the relationship between heat-treatment parameters and mechanical properties,a three-layered feed-forward neural networks with three neurons in the input layer,six in the hidden layer and two in the output layer was used in this paper as shown in Fig. 2. The input elements X 1, X 2 and X 3 represent the value of deformation,solid solution time and aging time,respectively; with Y j j ˆ 1; 2;...; 6,the output of the hidden neurons; the ultimate tensile strength s 1 ) and the yield strength s 2 ),being the output of the ANN. The network was designed to approximate the effects of heat-treatment on the mechanical properties of 7175 aluminum alloy. V ji is the connection weight between the input layer and the hidden layer; and W jk the weight between the hidden layer and the output layer. The learning algorithm can be summarized as follows: Step 1. Select the learning rate Z ˆ 0:1,momentum coefficient a ˆ 0:3 and X 4 ˆ Y 7 ˆ 1. Step 2. Take a group of random numbers within 0.5, 0.5) as the initial values of V ji and W jk. Step 3. Compute the outputs of all neurons layer by layer,starting with the input layer as follows: net j ˆ X4 iˆ1 Y j ˆ f net j V ji X i ; j ˆ 1; 2;...; 6 1) 2) where P represents the total number of patterns, D nk the desired outputs experimental values) and s nk the ANN actual outputs. Step 5. If E is small enough or the learning iteration is too big,stop learning. Step 6. Compute the learning errors for every neuron layer by layer: d k ˆ D k s k f 0 net k ; k ˆ 1; 2 7) d j ˆ X2 kˆ1 W jk d k f 0 net j ; j ˆ 1; 2;...; 6 8) Step 7. Update the weights along the negative gradient of E: W jk t 1 ˆW jk t Zd k Y j a W jk t W jk t 1 9) V ji t 1 ˆV ji t Zd j X i a V ji t V ji t 1 10) Step 8. Repeat by going to Step 3. Randomly select 24 from 27 samples to train the ANN after 7000 iterations,the system error is less than The remaining three samples are used to verify the generalization capability of the ANN. The predicted results are shown in Table 3. The outputs s 1 and s 2 of the ANN are close enough to the corresponding expected outputs D 1 and D 2,respectively,not only for training samples but also for testing samples. This fact indicates that the ANN is good enough. In the next section,the heat-treatment technique of 7175 aluminum alloy will be optimized by means of the ANN trained above. 4. Technique optimization using a GA Fig. 2. Structure of a BP network. The fundamental approach to optimization is to formulate a single standard of measurement Ð a cost function Ð that summarizes the performance or value of a decision and iteratively improve this performance by selecting from among the available alternatives. Most classical methods

4 R.G. Song, Q.Z. Zhang / Journal of Materials Processing Technology ) 84±88 87 Table 4 Optimization results for the heat-treatment technique Sample Aging time h) Yield strength MPa) Ultimate tensile strength MPa) Table 5 Verifying experimental result Verifying sample Aging time h) Yield strength MPa) Ultimate tensile strength MPa) Prediction Experiment Prediction Experiment of optimization generate a deterministic sequence of trial solutions based on the gradient or higher-order statistics of the cost function. Under regularity conditions on this function,these techniques can be shown to generate sequences that converge asymptotically to locally optimal solutions, and in certain cases they converge quickly exponentially [8]. However,the methods often fail to perform adequately when random perturbations are imposed on the cost function. Further,locally optimal solutions often prove insuf cient for real-world engineering problems. However,a GA can solve the problems mentioned above very well. The GA which was proposed by Fraser [9,10] is a kind of optimization method based on the law of evolution of living things,i.e.,survival of the ttest,natural selection,inheritance and variation. Its basic thoughts are typically implemented as follows. Considering a non-linear optimization problem in n dimensions: C ˆ F x 1 ; x 2 ;...; x n 11) Randomly selecting m points within n dimensions to construct the population, C is used to evaluate every individual, superior and inferior. 1. Compute C i I-1,2,..., m) for every point. Half of the population will survive; the surviving probability is proportional to the corresponding value of C i for the individual. 2. Cross breed. Copy the m/2 surviving individuals firstly and pair them randomly,then exchange part elements of every pair randomly to generate new individuals. 3. Mutation. Select several individuals randomly in the population,and mutate some elements in the selected individuals [add a small random number within 0.05, 0.05)]. 4. A new generation has been generated. Return to step 1, and start to breed the next generation. In this way,the whole population will move to the area which corresponds to high C values. Finally,some individuals are close enough to the maximum of F Optimization for the heat-treatment technique of 7175 aluminum alloy In the present investigation, m ˆ 27, n ˆ 3, C ˆ s 1 s 2. For the GA,working over 1000 iterations,the optimization results are given in Table 4. It can be seen that the rst three individuals are close to the optimal values,i.e.,the optimum heat-treatment technique adapted to 7175 aluminum alloy with the optimal mechanical properties is 85.1% for the value of deformation,133.0 min solid solution time and 6 h aging time at 443 K Verifying experiment Table 5 gives the verifying experiment result. It can be concluded that an arti cial neural combined with a GA predicts the optimum technique very well. 5. Conclusions 1. An ANN can be applied very well to model the effects of the heat-treatment technique on the mechanical properties of 7175 aluminum alloy,and the complexity of constructing a mathematical model as well as the limitations of optimization when using them can be avoided. 2. A GA is a kind of technique of multi-points random optimization based on the law of evolution of living things. The optimal technique adapted for 7175 aluminum alloy has been obtained by means of this method, and the verifying experiment has shown that the theoretical prediction agrees with the experimental result.

5 88 R.G. Song, Q.Z. Zhang / Journal of Materials Processing Technology ) 84±88 3. An ANN combined with a GA offers a simple and effective new tool for searching for the optimum technique in materials processing. References [1] R.G. Song,Q.Z. Zhang,M.K. Tseng,B.J. Zhang,The application of artificial neural networks to the investigation of aging dynamics in 7175 aluminum alloys,mater. Sci. Eng. C ) 39±41. [2] I. Wadi,R. Balendra,Using neural networks to model the blanking process,j. Mater. Process. Technol ) 52±65. [3] L.A. Dobrzanski,W. Sitek,The modelling of hardenability using neural networks,j. Mater. Process. Technol. 92± ) 8±14. [4] P.D. Hodgson,L.X. Kong,C.H.J. Davies,The prediction of the hot strength in steels with an integrated phenomenological and artificial neural network model,j. Mater. Process. Technol ) 131± 138. [5] M.S. Chun,J. Biglou,J.G. Lenard,J.G. Kim,Using neural networks to predict parameters in the hot working of aluminum alloys,j. Mater. Process. Technol ) 245±251. [6] R.P. Lippman,An introduction to computing with neural nets,ieee ASSP Mag ) 4±22. [7] R.G. Song,B.J. Zhang,M.K. Tseng,Effects of deformation,solid solution and aging on the strength of 7175 aluminum alloy,youse Kuangye ) 29±32 in Chinese). [8] N.Y. Liu,The Optimization Methods,Liaoning Education Press, Shenyang,1986,pp. 11±15 in Chinese). [9] A.S. Fraser,Simulation of genetic systems by automatic digital computers. I. Introduction,Aust. J. Biol. Sci ) 484± 491. [10] A.S. Fraser,Simulation of genetic systems,j. Theor. Biol ) 329±346.