The Performance of High Resolution Neutron Powder Diffractomete

Optimization Residual Stress of High Temperature Treatment Using Genetic Algorithm and Neural Network

M. Susmikanti¹, A. Hafid¹, J.B. Sulistyo²

1Center for Nuclear Reactor Technology and Safety, PUSPIPTEK, 15314, Tangerang, Indonesia

2Center for Nuclear Facilities Engineering, PUSPIPTEK, 15314, Tangerang, Indonesia

A R T I C L E I N F O A B S T R A C T AIJ use only:

Received date Revised date Accepted date Keywords:

Residual Stress Material SS 316 Optimization Genetic Algorithm Multi-point binary Stochastic sampling

In a nuclear industry area, high temperature treatment of materials is a factor which requires special attention, for instance in weld areas. Assessment needs to be conducted on the material properties of high-temperature treatment results so as to determine the strength of the materials used. The high temperature processes on a material can cause residual stress. Residual stress values may reflect the strength properties of the material. Finding the information on the optimal residual stress is one way to determine the strength of the materials used.

In the residual stress model with some parameters sometimes is difficult to solve the optimal value with analytical or numerical calculation. In here the genetic algorithm (GA) is an efficient algorithm which can generate the optimal values, both minimum and maximum. The purposes of this research are to obtain the optimization of variabel in residual stress models using GA and to predict the residual stress distribution, with fuzzy neural network (FNN) while the artificial neural network (ANN) used for modeling. In this case the model taken a single material of the 316/316L stainless steel.The minimal residual stress with GA in temperature 650⁰C and 850⁰C converging on –711.3689 MPa and -975.556 MPa with 0.002934 mm from the center point. The distribution the residual stress concentration grouping at coordinates (-76;76) MPa. The residual stress model is the polynomial degree two with the coeficient respectively are 50.33; -76.54 and -55.2 with standard deviation is 7.874.

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INTRODUCTION^

In the industrial area, the high temperature treatments of the materials used need studied. The materials used in nuclear power plants, in general have a high temperature process. Thee process causes residual stresses. It is necessary assessment for the material strength. One of the required information is the optimal value of residual stress base on center of thermal treatment.

Basically, the genetic algorithm can be used to conducted the continum structural topological design of material structures [1]. The residual thermal stress of cylindrical steel bars was analysed using finite element method and artificial neural networks [2]. The genetic algorithm approach was used also to estimate the welded joint strength [3].

The flow stress of 304 stainless steel under cool and warm compression can be optimized by artificial neural network and genetic algorithm [4]. The

Corresponding author.

E-mail address: mike@batan.go.id

tensile stress concentration in perforated hybrid laminate was reducing by genetic algorithm [5]. To prediction of residual stress for dissimilar metals welding at nuclear power plants are use fuzzy neural network models [6]. After that, material with mixed variables was optimized based on genetic algorithm [7]. The artificial neural network modelling used to evaluate and predict the deformation behaviour of stainless steel type AISI-304L during hot torsion [8].

The stress intensity factor due to weld residual stress was evaluating by the weight funtion and finite element methods [9]. The flow curve prediction of A-Mg alloys under warm forming conditions at various strain rates was modelling by artificial neural network [10]. The residual stress was evaluation in butt-welded stell plates [11]. The residual stresses and material properties by an energy-based method was determine using artificial neural networks [12]. The optimization of laser welding process parameters for super austenitic stainless steel are using artificial neural network and genetic algorithm [13]. Finnaly, to recognize steel

are using artificial neural networks and to optimize parameter of residual stress prediction models based on genetic algorithm [14].

Here, this letter concern in optimization variabel of residual stresses in bars model for single material at high temperature treatment using genetic algorithms. Then the residual stress output from finite element method will be developed to be the model with artificial neural network. After that, the center of residual stress will be developed with fuzzy neural network. The simulation of genetic algorithm using the method of selection of stochastic sampling with replacement, while for crossing individualal in genetic algorithm using the method of binary recombination many points.

EXPERIMENTAL METHODS Genetic Algorithm

Genetic algorithm (GA) is an algorithm that is widely applied to some optimal problem-solving both problems the maximum or minimum. The genetic algorithms are starting to be used for settlement of the issue of models. This algorithm follows the science of genetics and natural selection process. The genetic algorithm can also be used for problem solving and relating to a variable or parameter whose value within a certain range. In addition, the genetic algorithm can be used for problems which have certain restrictions or constraints. Terms of use of this algorithm should have the purpose or function of a general model.

In genetic algorithm, the population of the settlement called individual samples. In the completion of the optimization, the algorithm is looking for into the search for a better solution. In every solution, every prospective individual chromosome has properties that can mutate and change. In the simplest solution, the initial solution is represented in binary as the values 0 and 1 or in the real numbers. The evolution usually starts from a population with a generation of individuals at random, with the process repeated. Repetition is expressed as so-called next-generation iterations. In every generation, the suitability of each individual in the population is evaluated in a match function (fitness). Match value function is usually referred to as the value of the objective function in optimization problem solving.

The individuals are more appropriate in the selected population stochastic. And each individual is modified in a way that made crossing back recombination (crossover) and displacement (mutation) at random to form a new generation. The new generation of the chosen solution is then used

in the next iteration. Repetition of the above is expressed in a set of binary numbers or binary digits in the range of (binary digit / bit) as well as in the ranks of real numbers (the real). The algorithm ends when the maximum number of generations has been produced, or the best approximation level has been reached.

There are two operators on genetic algorithm, namely the operator to perform recombination and mutation operators. Recombination operators are subdivided into binary valued recombination, the real worth and permutations. While mutations divided into the real-value mutation and binary valued. In this case the recombination and mutation of binary value are selected [15].

The following example is the early initialization procedure member's generation population ranks first in the form of binary digits and value before recombination;

First Chromosome 1000 | 0100 | 0010 Second Chromosome 1110 | 0000 | 1000 After crossing many points, obtained following children chromosomes;

First Chromosomees 1000 | 1000 | 0000 Second Chromosome Child 1110 | 0010 | 0100 Mutations in the genetic algorithm are to change the random digit binary value at a given position. Suppose randomly selected in the range of binary digits in position-9 to a particular chromosome, then the position-9 if there is a binary value 1 then it will be replaced with the binary value 0 or vice versa on the selected chromosome. Here is an example of before and after the selected chromosomal mutations.

Before mutation:

Chromosome Second Child 1110 | 0010 | 0100 After mutation:

Chromosome Second Child 1110 | 0010 | 1100 Determination of parameters in the genetic algorithm, including the parameters that control the size of the population declared (popsize), chances recombination / crossover (pc) and opportunities mutation (pm). The use of a constant value of pc and pm, to maintain the variety and adjustment and is determined by solving the problem, pc and pm depends on the size of the completion of the scope of the fitness value. Population size (popsize) must be at least greater than or equal to 30.

The method of selection method is a stochastic sampling with replacement. In this method the selected probability of selection of individuals with the fitness value of the largest to the smallest start. Largest fitness value is taken so as to have a chance to reproduce.

Here is shown a flowchart of the process of genetic algorithm in Fig. 1.

Fig. 1: Flow Diagram of Genetic Algorithms Process

Artificial Neural Networks

The mmodeling of artificial neural network (ANN) is learning and adjustment an object.

Perceptron method is learning method with observation in neural network systems, so that network yielded must have organically parameter by the way of changing through study order with observation. Neural network consisted of a number of associative neurons and a number of inputs. In designing neural network need attention in many specifications which will be identified. Preparation use perceptron for the application of pattern recognition described as element matrix between 0 and 1. First Layer of perceptron express a "sign detector" as input signals to know special sign.

Taking second Layer output from special sign in first layer and classifies data pattern given. The learning process makes relevant relationship between weight (wi) and threshold value ( ). For problem two classes, layer output had only one node. Function in layer-1 is constant calculated before all or some of input patterns into binary value xi {-1, 1} or value bipolar xi {0, 1}. Set of output is

element of linear threshold with threshold value following in Eq. (1),







 ⁿ

i i

ix w

w f

0

0)

 ( , w0 ^

(1)

wi: weight can be modified due to arrival of signal xi, and w0 = - ( ) be approach. Eq. (1) indicates that threshold described as weight the relation of between set of output and an arrival signal of shadow x0 (Fig. 2). Function of f(.) is function of activation perceptron and this thing is special applied to a transfer function of tansigmoid:

step(x) = 1 if x > 0 = -1 if other

Learning procedure takes weight correlating to set of output (in last layer). If only predecessor weight at last layer altered, perceptron in Fig. 2 considered as perceptron layer unique. Learning algorithm of perceptron single layer is repeated to follows step following until convergent;

1. Select an input vector x from training data 2. If perception gives wrong answer, modification of all weights wi as accordingwi tixi, tiis target of output and



is level of learning. Learning rule can be used with changing threshold value  (=-w0) according to equation (1). For example architecture from neural network consisted of by neuron s and input r and tan-sigmoid transfer function can expressed in Fig. 2 a) and b) [16, 17];

Fig. 2 a). Architecture of ANN

Fig. 2 b). Transfer function Tan-Sigmoid

Fuzzy Neural Network

The fuzzy neural network (FNN) are described in Eq. (2) [6],

) ...

exp( ₁E_{1 2}E_{2 3}E_{3 k}E_k

F      

(2)

Where ₁,₂,₃,....,kare the weighting coefficients and E₁,E₂,...,Ekhave a concept of energy.

The center value parameters are folows in Eq. (3),







 ^Ni

i

i i

i

i y k y k

E N

1

_))2

( ) (

1 (

(3)

Residual Stress

A simple model [Tim A. Osswald, 1998] for the calculation of residual stress of bars on a single material is given in Eq. (4) [18, 19].

2) 1 2 )(3 3 (

) 2

( ₂

2 





 L

T z T E

z  _{s f}

 (4)

Residual stress distribution is follow to the quadratic temperature distribution. We assume no additional residual stresses during the phase change. This function can be used to estimate the distribution of residual stress in thin sampel. In this case, the parameter Tf is the final temperature of the part, E is young's modulus,



is the coefficient of thermal expansion, L is half the thickness and Ts is the solidification temperature. The unit of residual stress(z) is in MPa and the unit of

z

^{is in mm.}

The parameter

z

is the distance from center point which heating temperature process has been done.

RESULTS AND DISCUSSION

In equation residual stress, there are some parameters that can be expressed in constant or restrictions in certain intervals. We use the material 316/316L SS which more ressistance corosion to alloy 304/304L SS. The parameters of the initial temperature in the solid state Ts is 20⁰C (room temperature) and high temperature Tf are 650⁰C and 1000⁰C. The parameter L shows the average thickness has a value between 0.25 mm to 6.35 mm.

The constant E indicates young's modulus of 200000 MPa. The coefficient of thermal expansion



is expressed with a value of 19.4 x10^-6 at the

temperature range 20⁰C-1000⁰C and 18.2x10^-6 at the temperature range 20⁰C-500⁰C [20]. The values of

z

which a center point of high temperature treatment are given in range (-5; 5) mm.

Based on the assumption that the temperature distribution is parabolic [19], the parabolic models can be used to illustrate how the residual stress during high temperature processes. It starts from temperature tf1 and tf2 are 100⁰C and 500⁰C which is show in Fig. 3.

Fig. 3 Residual stress during temperature process at 100⁰C and 500⁰C

The optimization of a genetic algorithm with multiple parameters using existing facilities function in MATLAB. Optimization is performed on the residual stress equation in this case is expressed as a function of the genetic algorithm.

Determination of control parameters in genetic algorithm selected population size (pop size) a minimum of 30, chances of crossover (pc) selected by 0.25 and opportunities mutation (pm) selected by 0.01.

The simulations are achieve the objective function of minimal residual stress with the distance z. The residual stresses in the simulation iterations performed to reach the 50-th generation, with each generation have population size of 30.

The optimal value of residual stress was obtained when reaches the fitness of objective function. The minimal value of the residual stress 316/316L SS in temperature 650⁰C convergent in -711.3689 MPa, which is given in Fig. 4 and Table 1. This position

z

is obtained in 0.002934 mm from the center point.

Fig. 4 Optimal residual stress 316/316L SS in 650⁰C

Table 1. Optimal Residual Stress in 650⁰

In temperature 850^oC, the optimal residual stress values convergent on -969.868 MPa, which is given in Fig. 5 and Tabel 2. The position

z

is 0.002757 mm from the center point.

Fig. 5 Optimal residual stress SS 316 in850 ⁰C Table 2. Optimal Residual Stress in 850⁰C

The residual stress during high temperature processes, at temperature 650⁰C and 850 ⁰C which is show in Fig. 6 and Table 3.

Fig. 6 Residual stress at 650⁰C and 850⁰C

Table 3. Optimal Residual Stress in high temperature process with genetic algorithm

Number of Generation

Size of Pop.

Best Fitness

1 30 -688.1

2 60 -688.1

3 90 -688.1

4 120 -688.1

5 150 -688.1

6 180 -708.8

7 210 -708.8

8 240 -708.8

9 270 -708.8

10 300 -708.8

: :

45 1350 -711.4

46 1380 -711.4

47 1410 -711.4

48 1440 -711.4

49 1470 -711.4

50 1500 -711.4

Number of

Generation Size of

Pop. Best

Fitness

1 30 2482

2 60 2482

3 90 2482

4 120 2482

5 150 2482

6 180 2482

7 210 2482

8 240 -967.9

9 270 -967.9

10 300 -967.9

: :

45 1350 -969.9

46 1380 -969.9

47 1410 -969.9

48 1440 -969.9

49 1470 -969.9

50 1500 -969.9

TEMPERATURE ( ⁰C )

RESIDUAL STRESS(z)

(MPa)

DISTANCE

z

(mm)

650⁰C -711.3689 0.002934

850⁰C -969.868 0.002757

The analytical calculation with the same as from centre point is given in Table 4.

Table 4. Residual Stress with analytic calculation TEMPERATURE

( ⁰C )

RESIDUAL STRESS

) (z

 (MPa)

DISTANCE

z

^(mm)

650⁰C -975.556 0.002934

850⁰C -1061.134 0.002757

The following data is the results residual stress based on analytic calculation are to be used for modeling, are presented in Table 5.

Tabel 5. The residual stress based on analytic calculation

) (z

 ^{-975 -711 -244 -145 -6.59 -6.59}

6 146 171 250 389 710 965

The result of the grouping or cluster for the distribution of the residual stress using FNN concentration in two-dimensional is expressed in Fig. 7. The measures central tendency for residual stress distribution is expressed in (-76,76) MPa.

Fig. 7 The center of residual stress distribution

By using ANN simulation modeling, for data training will be obtained the trend of residual stress. Here's the plot data for trend residual stress prediction using ANN shown in Fig. 8,

Fig. 8 Trend residual stress using ANN

Fig. 9 shows the coefficient adjusted residual (R) of the estimation process simulation modeling in ANN.

The coefficient adjusted residual of modeling results expressed in the parameter R = 0.94397. This means that if R close to one indicates that the results of the estimation in accordance with the expected modeling.

Fig. 9 The results of the estimation process by ANN

The residual stress model is polynomial degree two with coeficcient p1, p2 and p3 each are 50.33 (33.77; 67.28); -76.54 (-121; -32,03) and -55.2 (-133; 22.66) with error deviation is 7.874

CONCLUSION

The optimal parameter values of the residual stress model at high temperature materials processing with GA were obtained. The minimal residual stress with GA at a final temperature 650⁰C shows converging on the value -711.3689 MPa with 0.002934 mm from the center point while with analytically calculations is -975.556 MPa. In temperature 850⁰C wit GA converging on -969.868 MPa and with analytically calculations is -1061.13 MPa with 0.002757 mm from the center point. The measures of central tendency for clustering data using the FNN have coordinates (-76;76) MPa.

While the model with ANN has the polynomial degree two with adjusted coeficient is 0.94397. This value close to one, that means the results of model are quite good. The coefficients of trend residual stress p1, p2 and p3 respectively are 50.33 (33.77;

67.28); -76.54 (-121; -32,03) and -55.2 (-133; 22.66) with error deviation is 7.874.

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