Optimization of roll forming process with evolutionary algorithm for green product

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 12, pp. 2127-2135 DECEMBER 2013 / 2127

© KSPE and Springer 2013

Optimization of Roll Forming Process with Evolutionary

Algorithm for Green Product

Hong Seok Park1,# and Trung Thanh Nguyen1

1 School of Mechanical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, South-Korea, 680-749# Corresponding Author / E-mail: [email protected], TEL: +82-52-259-2294, FAX: +82-52-259-1680

KEYWORDS: Roll forming process, Knowledge-based neural network, Hill climbing, Genetic algorithm

Knowledge-Based Neural Network model is known as one of the most useful methods which can predict every single variability to

create the process parameters for the data on Roll Forming process. To get the best quality of product and process parameters in

roll forming, the Knowledge-Based Neural Network has to be trained with high reliability. To obtain the target aimed, this paper

proposes a new novel of the optimal algorithm for training in the Knowledge-Based Neural Network model with the integration

between Genetic Algorithm and Hill Climbing Algorithm. Initially, a global optimization method is carried out to find the global

optimum area by using Genetic Algorithm, and then the Hill climbing Algorithm will effectively detect the positions of that local

optimal region with high accuracy in the training of the Knowledge-Based Neural Network model. Additionally, to obtain the trained

data set of the Knowledge-Based Neural Network model, the Finite Element Analysis result of the high fidelity Finite Element Model

is used. From the results of simulation, we can find out that the efficiency of the proposed method is higher than the conventional

methods in optimization of the roll forming process.

Manuscript received: June 4, 2013 / Accepted: August 15, 2013

1. Introduction

Roll forming (RF) is one of the most widely-adopted manufacturing

processes with effective and economical method in the automotive

industry. Previously, different grades of steel and iron were used as the

primary materials of roll formed parts. However, these materials have

been transitioning from iron and steel to aluminum alloys to reduce

weight and saving energy. These changes in materials have resulted in

unexpected defects, namely: spring back, twist, edge wave and

longitudinal curve. Therefore, there are three major problems: residual

longitudinal strain, remaining of fracture, higher spring back angle at

the final step. In addition, it is not easy to measure their value directly

by the experiments nor meaningful to inspect the quality and

deformation behavior of roll formed parts with various process

parameters. For that reason, the roll forming process of aluminum parts

needs to be optimized to obtain the best products and reduce costs in

manufacturing.

Different approaches have been performed for the modeling and

optimizing roll forming process to achieve a more logical and preferable

technology. Lindgren1 had proved the dependence of longitudinal peak

strain and the deformation length with the integration between

experiments and modeling on an increment of the yield stress.

Furthermore, a numerical optimization study, including modeling of the

RF process, was mainly carried out by Zeng et al.2 The optimal design

of the U channel RF process has been determined in the decrement of

spring back and longitudinal strains by using the Response Surface

Method (RSM). Initially, the series of experiments was proceeded to

obtain from simulation results. Then, the relationship between the

process parameters and the part quality was established to have

Response Surface formulae. Finally, optimal process parameters were

NOMENCLATURE

d = inner distance between roll stands (mm)

ω = rotation velocity of rolls (rad/s)

f = friction coefficient

r = ratio between the roll gap and sheet thickness

D = damage variable

α = spring back angle

DOI: 10.1007/s12541-013-0288-3

2128 / DECEMBER 2013 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 12

carried out by performing nonlinear optimizations for Response Surface

models with constraints of process parameters. However, the deformation

behavior of the aluminum sheet is higher in nonlinear functions, so the

RSM is not a powerful method to optimize the RF process.

To optimize the complicated RF process, the RSM is not a possible

method. Paralikas et al.3 improved the product quality by using Taguchi

method to minimize the elastic longitudinal strain and shear strain at the

strip edge for each roll station. An extensive general view on optimizing

the roll forming process design of rolling parameters by using the

Taguchi method can be found in Chen and Chen.4 However, it was

incapable to get the best process parameters because the fidelity of this

approach could be further estimated the amount of parameter levels.

Similarly, Shahani et al.5 introduced a neural network algorithm for

determining the effect of parameters rolling process with Finite

Element (FE) simulation results. This study indicates that neural network

is an application tool for forecasting the effects of various parameters

on the hot rolling process. Nevertheless, the training data pools were

not sufficient for accurate prediction results in optimizing RF process.

The literature reviews present the research topics of optimal process

parameters design, many optimization methods were proposed. In this

study, new evolution optimization method is employed for optimizing

the RF process of aluminum parts by using an integration between

Genetic Algorithm (GA) and Hill Climbing Algorithm (HCB) within

the Knowledge Based Neural Network (KBNN). In Knowledge Based

Neural Network (KBNN), two developed structures are employed in

the optimization process. In the first structure proposed, the prior

knowledge was used to define a network topology and the initial

weights within this network. This network was trained by using a set

of classified examples and a standard neural learning technique. In the

second structure proposed, the knowledge having the form of empirical

functions was incorporated inside a neural network. The final results

were the combination of learning from the empirical knowledge and

learning by example. In this paper, a more powerful KBNN has been

developed with multi-outputs and general multi-layer neural networks.

Compares to the previous investigation, new developed optimization

method is acceptable and significant for application in realistic field.

The rest of the paper is organized as follows. First of all, in order to

automatically generate design of experiments for training data from FE

simulation results, a framework of the integration between CAD-CAE

tools are utilized. It will overcome the normal of the previous methods

to generate experiment data. Then, the simulated experiments will be

used to organize and verify the optimization results. Finally, the

training error of the KBNN model is the optimum value which is less

than 6% after the integration between HCB and GA detects the best

location area in global optimization.

2. Design of Experimental Model

2.1 Original design and FEM model

In this paper, the optimization problems are considered on U channel

forming product which the experiment was performed at the Roll

Engineering Company (ROLL. ENG.), Korea. The forming line is

composed five roll stands, the bending angle is 20o, 38o, 56o, 74o, and

90o in the last stand to ensure the right angle of the final product and

initial sheet thickness is 1.4 mm (Fig. 1).

The selected process parameters can be easily determined and

adjusted to range in roll forming line. There are four process parameters

in an RF process of aluminum parts which have the ranges defined by

the manufacturing conditions. Table 1 shows process parameters with

four levels for the high fidelity FE model. Table 2 shows five levels for

each factor for the low fidelity FE model.

In this study, the ABAQUS software was used to perform FEA

results with S4R shell elements of aluminum sheet and analytical rigid

element for roller model. The self moving aluminum sheet uses the

friction force in access to surface to surface between the sheet and roll.

The final results were determined after the simulation had been done.

There were three problems occurring in the RF process of aluminum

parts: existence of a fracture in the aluminum sheet, excessive values

of longitudinal strains, value of spring back angle2 in order to produce

high quality aluminum part. These are also applied in this paper to

calculate the damage, define the value of the strain limit in the RF

process of a U channel as 0.9% and the spring back angle has to be

lower than 3o from the experiment of the company.

2.2 Integration between CAD and CAE program to obtain data

training

It is very difficult to obtain directly the value of damage variability

Fig. 1 The cross section of the U channel part in experiment

Table 1 Process parameters and their levels of high fidelity FE model

Process parametersLevel

1 2 3 4

Inner distance between roll

stands d (mm)350 366.6667 383.3333 400

Rotation velocity of

rolls ω (rad/s)1 2.33 3.66 5

Friction coefficient f 0.1 0.2333 0.3667 0.5

The ratio between the roll

gap and sheet thickness r1 1.05 1.1 1.15

Table 2 Process parameters and their levels of low fidelity FE model

Process parametersLevel

1 2 3 4 5

Inner distance between roll

stands d (mm)350 362.5 375 387.5 400

Rotation velocity of

rolls ω (rad/s)1 2 3 4 5

Friction coefficient f 0.1 0.2 0.3 0.4 0.5

The ratio between the roll

gap and sheet thickness r1 1.0375 1.075 1.1125 1.15

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 14, No. 12 DECEMBER 2013 / 2129

(D), maximum longitudinal strain (MLS) and spring back angle (α) in

the experiment. Once the prototype has failed, that means these different

factors are meaningless. Hence, this paper used the FEA tool to obtain

the training data for the network training. To decrease the computational

cost, the sixteen orthogonal simulations of this high fidelity FE model

which were performed with four levels for each process parameter. On

the contrary, a larger number of the FEA of the low fidelity FE model

can be done because of its less simulation time. The low fidelity FE

model has a coarse mesh and smaller number of elements while the

high fidelity has a fine mesh and larger number of elements. In this

paper, the twenty five simulations of the low fidelity model were

employed by using the L25 orthogonal with five levels for each process

parameter. The results of numerical experiments are listed in Table 3

and Table 4.

The schematic description procedure is shown in Fig. 2 by integrating

between CAE and CAD to automatically obtain the data for training the

network. Coupling CAD and CAE systems in engineering analysis

based on common scripting and programming languages is one of the

ways to save time and cost for experiments.

Initially, the array indicating the series of experiment is built in

MATLAB program. Then, corresponding to each experiment, the

MATLAB calls the CATIA program through a VB script to model the

CAD data of rolls. Subsequently, the MATLAB calls a Python code for

running the ABAQUS program. The CAD data is automatically imported

to ABAQUS. The analysis process was performed sequentially with the

variation of input parameters to obtain response values. The D, MLS

and α are calculated and stored in a text file for the training of the

network later. Finally, the new loop for next experiments is done until

all necessary data are obtained.

3. Modeling Roll Forming Process by Using Knowledge-

Based Neural Network

Artificial Neural Network has been recently recognized as a powerful

tool for modeling and optimizing. Several types of neural network

structures have been developed without using any approximate models

to meet different needs of modeling problems. The most popular neural

network is a multilayer network used for predicting various processes.6-9

In order to ensure sensitive model, a number of training data are

necessarily performed. However, generating large amount of teaching

data would be very expensive and takes much time. The pure neural

network cannot be solved in terms of time consuming, cost saving

because of the contradiction between requirement accurate modeling

and data generation.

The key to solve that problem is knowledge-based neural network

(KBNN)10-12,14 which can be used to handle the actual knowledge in the

form of an empirical function model together with the power learning

neural network to obtain faster and more accurate model. There are two

parallel parts of the KBNN structures: knowledge path and neural

network path. The knowledge path contains the approximate model

Table 4 FEA results of the low fidelity FE model

No. d (mm) ω (rad/s) f r D MLS α

1 350 1 0.1 1 0.881 2.2029 1.8567

2 350 2 0.2 1.0375 0.8477 3.4299 0.3808

3 350 3 0.3 1.075 0.807 3.1972 1.0111

4 350 4 0.4 1.1125 0.832 3.0279 1.5057

5 350 5 0.5 1.15 0.894 7.3697 2.9371

6 362.5 1 0.2 1.075 0.791 2.1747 3.2827

7 362.5 2 0.3 1.1125 0.806 2.9682 1.6989

8 362.5 3 0.4 1.15 0.762 3.2266 2.3528

9 362.5 4 0.5 1 1.071 10.1128 5.3400

10 362.5 5 0.1 1.0375 0.911 2.1167 1.0457

11 375 1 0.3 1.15 0.735 2.7074 1.6689

12 375 2 0.4 1 0.922 9.1823 3.3698

13 375 3 0.5 1.0375 1.026 10.4570 4.2875

14 375 4 0.1 1.075 0.849 2.1557 0.6901

15 375 5 0.2 1.1125 0.8295 3.0536 1.1651

16 387.5 1 0.4 1.0375 0.8406 3.3365 3.7167

17 387.5 2 0.5 1.075 1.057 2.5660 1.9465

18 387.5 3 0.1 1.1125 0.796 2.4337 2.1984

19 387.5 4 0.2 1.15 0.794 9.8617 2.3057

20 387.5 5 0.3 1 1.058 11.9276 2.9181

21 400 1 0.5 1.1125 0.759 10.0052 4.0068

22 400 2 0.1 1.15 0.769 2.9804 0.7669

23 400 3 0.2 1 0.9496 8.5431 3.8900

24 400 4 0.3 1.0375 0.886 2.4655 0.5851

25 400 5 0.4 1.075 0.879 2.5437 1.8534

Table 3 FEA results of the high fidelity FE model

No. d (mm) ω (rad/s) f r D MLS α

1 350 1 0.1 1 0.7827 3.4549 2.2210

2 350 2.33 0.2333 1.05 1.1860 3.2962 3.8876

3 350 3.66 0.3667 1.1 1.6290 7.0126 1.4463

4 350 5 0.5 1.15 0.9079 7.6484 2.8887

5 366.6667 1 0.2333 1.1 1.2480 3.6410 4.8691

6 366.6667 2.33 0.1 1.15 0.6652 3.6322 0.8453

7 366.6667 3.66 0.5 1 0.6899 9.4174 4.0845

8 366.6667 5 0.3667 1.05 1.2312 10.2350 1.6724

9 383.3333 1 0.3667 1.15 0.6588 3.8034 5.2059

10 383.3333 2.33 0.5 1.1 1.0288 9.6317 3.9950

11 383.3333 3.66 0.1 1.05 0.7499 3.2183 2.4770

12 383.3333 5 0.2333 1 1.3617 11.2844 3.6614

13 400 1 0.5 1.05 1.5420 6.2718 2.4347

14 400 2.33 0.3667 1 1.8147 9.4184 1.1523

15 400 3.66 0.2333 1.15 1.1600 3.1686 0.4999

16 400 5 0.1 1.1 0.7217 3.7733 2.6188

Fig. 2 The framework of the integration between CAD-CAE programs


which could be empirical functions and the training data is represented

by a neural network. This method is expected to obtain desirable results

when the output of an approximation model together with the prediction

of the trained neural network becomes the overall output of two paths.

In this study, the knowledge path is RSM models obtained by using

the FEA results of the low fidelity FE model. The inputs are processed

by the weights and biases of the knowledge layer. After that, the RSM

models are used as the transfer functions to calculate the almost proper

outputs. Besides that, a multilayer NN plays a role as second path which

has three layers, namely the boundary layer, region layer, and normalized

layer.10 The number of hidden layers and neurons in the second path is

increased until they reach the sufficient flexibility to get a reliable

solution. The final results were the combination of learning from the

example and empirical knowledge.

3.1 The role of multi-fidelity FE model

It is very important to define the relationship between the setting

process parameters and the quality of the final product of aluminum

part in RF process. In this paper, from the designers’ experiments, the

KBNN using the FE model is developed because the improvement of

empirical model is established by using the approximation methods

RSM. On one hand, to reduce the time and cost in simulation in the

construction of KBNN, the low fidelity FEA results with coarse mesh

and a small number of elements are used to define the RSM model. On

the other hand, the high fidelity FE model with fine mesh and large

number of elements provides the accuracy, but long time and expensive

FEA results. In section 3.2, the detail structure of the KBNN is

proposed.

3.2 Structure of the KBNN

In modeling RF process, the number of major process parameters and

factors is the same as the amount of inputs and outputs of the KBNN

which indicates the quality of products. Our KBNN for the RF process

of aluminum parts has four inputs, i.e., d, ω, f, r, and three outputs i.e.,

D, MLS, α which are considered to optimize the process parameters.

In KBNN structure, the inputs are processed by the weights and

biases of the knowledge layer in knowledge path and the RSM models

are used to transfer functions to calculate proper outputs. Therefore,

knowledge path has only one layer with the outputs which are calculated

directly from RSM models. The outputs of the knowledge path are

given by:

(1)

Where,

p : input vector

wKN : weights matrices

bKN : biases matrices

At the same time, the inputs are processed in the second path by the

flexible multilayer NN. The hidden layers use tansig transfer function

while the output layers use purelin transfer function. At each layer, the

values of the inputs are multiplied by the weights and added to the

biases. The second path outputs can be calculated by:

(2)

Where,

f iMLP : transfer function at the layer i

w iMLP : weights at layer i of MLP network

b iMLP : biases matrices of MLP network

Finally, the final outputs of KBNN can be generated from the overall

of knowledge layer outputs and multilayer perception (MLP) outputs.

Many studies have combined the results from two KBNN layers by

taking multiplication. This idea was expected to be more efficient in

some specific problems and inspired from the HONEST network.15

However, to improve the trainable algorithm, the KBNN will become

more complex and requires a significant effort. For simply calculation,

additional operator for the combination is used for calculating the final

outputs as follows:

(3)

The error vector is defined by:

(4)

After training the network, the performance of the network was

estimated by the mean square error (MSE):

(5)

Where n is the number of training examples.

The whole KBNN structure is illustrated in Fig. 3.

3.3 Training approach of KBNN

Normally, multi-layer perceptrons is the most commonly used to

configure neural network, it can define models correctly. However, the

model needs a large amount of training data to obtain the suitable input/

output relationship.14 On the contrary, in KBNN, the gap between

empirical model and desirable determination can be connected by using

neural network. Moreover, the Marquardt Algorithm was illustrated by

Hagan, M. T., and Menhaj, M. B.15 is applied to teaching a KBNN.

The target of training work is to minimize the error of vector E

between prediction results and actual output values.

(6)

{x} : weights w and bias b vector

{x} will be updated by LM

(7)

µ : damping factor

J : Jacobian matrix

The derivatives of errors in MLP path and knowledge path are two

parts in J({x}). To calculate derivatives of errors in MLP path, the back

propagation17 was utilized.

a0

KN p=

n1

KN wKN a0

KN⋅ bKN+=

a1

KN fRSM n1

KN( )=

a0

MLP p=

n0

MLP wiMLP a

i 1–

MLP⋅ biMLP+=

Amp fiMLP n

iMLP( )=

aKBNN aKN aMLP+( )=

e t aKBNN–=

MSE Σ ti

2a2

KBNN i–( )/n=

E Σei

2x{ }( )=

x∆ JT

x{ }( )J x{ }( ) µI+[ ]1–

J x{ }( )e x{ }( )=


(8)

(9)

vh = [e1, e2, e3, …] is the error vector. The weight and biases of

Jacobian matrix can be given by:

- For weight xl:

(10)

=

- For biases xl:

(11)

=

The Marquadrt sensitivity:

at the output layer M (12)

(13)

Here, Fm is the transfer function at layer m of the network.

The knowledge path values can be obtained by using the response

surface functions which are polynomials

ah = c1·n1 + c2·n2 + … + ci·n12 + ci+1·n2

2 + … + cj·n1·n2

+ cj+1·n1·n3 +… (14)

Where,

ci : coefficient i of the response surface functions

ni : input i to the response surface functions of the knowledge path

ah : output h of the knowledge path.

The derivative of error vh

(15)

(16)

By using Levenberg-Marquadrt algorithm, the error of trained KBNN

between prediction results and actual values reached the value 3.3167e-15

at the 15th epoch (Fig. 4).

The verification process was realized to confirm the reliability of

KBNN. In this process, the results predicted by using KBNN and actual

values have mean square error within the limits of 1~8% (Fig. 5, Fig.

6, Fig. 7). The error validation is acceptable and the network can be

used for online prediction of RF process with sufficient accuracy.

Additionally, two confirmation tests with random design parameter

sets were executed to verify the accuracy of the FEA model and the new

developed method. The Table 5 lists the random data sets for verification

J x( )

∂e1

x( )

∂x1

--------------- …∂e

1x( )

∂xn

---------------

… … …

∂eN x( )

∂x1

---------------- …∂eN x( )

∂xn

----------------

=

J[ ]h l, ∂vh /∂xl ∂vh /∂nm

i q,( ) ∂nm

i q, /∂wm

i j,( )⋅= =

sm

i h, am 1–

j q,⋅

J[ ]h l, ∂vh /∂xl ∂vh /∂nm

i q,( ) ∂nm

i q, /∂bm

i( )⋅= =

sm

i h,

sM

q F nM

q( )–=

sm

q F nm

q( )– wm 1+

( )T

sm 1+

q⋅ ⋅=

∂vh ∂wi j,⁄ ∂vh ∂nj⁄( ) ∂nj ∂wi j,⁄( )⋅=

∂vh ∂bi⁄ ∂vh ∂ni⁄( ) ∂ni ∂bi⁄( )⋅ ∂vh ∂ni⁄( )= =

Fig. 3 The composition of the GA-HCB with KBNN


and the comparison of the results by the KBNN and numerical

experiment (FEA). It can be observed that the percentage errors

calculated are very small. The percentage deviations for the three

response variables between predicted results and FEA results lie within

range -1.6% to 1.6%, 1.5% to 1.6% and -2.8% to -1.3%, respectively.

The small errors indicate that the results of numerical experiments were

highly accurate. Besides, the comparative results also imply that the

developed method is adequate and can be used to predict the objective

functions with high accuracy. By comparing with computational cost of

simulation based on FEA, the developed method is a much simpler and

more efficient way to predict the outputs with the limits of variables.

4. Optimization of the Roll Forming Process of Aluminum

Parts Followed by Developed Hybrid Method

In this study, the combination between GA and HCB with KBNN

is proposed to find the best optimum process parameters and it plays an

important role in increasing the modeling ability of KBNN. Initially,

GA with the expression operation is used to generate an initial

approach for the HCB method and then to use only HCB method. In

this way, the powerful HCB algorithm in a local optimization method

is introduced to define the local search method with the optimized

global value which was obtained from the GA. The process of HCB

algorithm is based on an initial solution and then explores interactively

within the search space for better solutions. Finally, the best global

solution is then updated if a better one is found and the whole process

is repeated until reaching satisfactory results.

The optimization strategy of the roll forming process of aluminum

part is shown in Fig. 8. Firstly, process parameters were characterized

by possessing chromosomes which can be encrypted in GA. Secondly,

an initial population was generated. The fitness of the population will

be calculated by KBNN. Thirdly, the procedure makes use of three

main operators: reproduction, crossover and mutation to obtain new

population from previous generations. The fittest generation will be

chosen after each population. Finally, the GA was stopped when the

error goal has been satisfied.

Fig. 4 Training process of KBNN

Fig. 5 Prediction values of damage variable and actual values

Fig. 6 Prediction values of maximum longitudinal strain and actual

values

Fig. 7 Prediction values of spring back angle and actual values

Table 5 Comparison of the results obtained by the KBNN and

numerical experiments with random design variables

No d ω f r Method D MLS α

1 380 4.5 0.25 1.06

KBNN 0.946 7.201 2.453

FEA 0.961 7.316 2.386

Error(%) 1.6 1.6 -2.8

2 363 3 0.4 1.15

KBNN 0.831 6.827 2.385

FEA 0.818 6.93 2.354

Error(%) -1.6 1.5 -1.3


Normally, the result of the GA is not the best values which can be

obtained from optimum global region because the initial population is

chosen randomly. There are some bad individual affects to the result of

the GA and the better values should be defined by another method.

That’s why we can apply the HCB to obtain better result from GA. By

using this algorithm, we can overcome the global optimization to

define the local optimum. The HCB process is presented in Fig. 8 and

it can be summed up by following the steps:

• Step 1: Select random point in the optimum GA area

• Step 2: Compare with all neighbors

• Step 3: Select the neighbor with the best quality and change to that

better point.

• Step 4: Repeat step 2 and 4, then the lowest quality neighbor will

be chosen.

• Step 5: The process will stop when the best values are satisfied.

In optimal problem, we need to minimize the fitness function of

damage variable D, maximum longitudinal strain MLS and spring back

angle α. The damage variable was given in scalar damage equation to

find the stress tensor in the material:

(17)

The failure has occurred when D = 1

Farzin presented buckling limit strain (BLS) in the RF process and

conducted that the waviness or wrinkle will occur when BLS is lower

than longitudinal strain in the aluminum sheet.16 Therefore, MLS has to

be kept less than BLS and Tehrani defined the value of BLS is 0.9%.17

The spring back angle of the aluminum sheet has to be kept less

than an allowable limit which was identified in the factory as 3o.

In addition, the manufacturing conditions were also the constraints

set on the process parameters. The inner distance between roll stands

d, rotation velocity of rolls ω, friction coefficient f, and the ratio

between the roll gap and the sheet thickness are where the variables

optimized. In sum, the optimization problem can be formulated with

the following expression:

Optimization variables: d, ω, f, r

Optimization objective: D, MLS and α have to be kept in the

constraint below:

+0 ≤ MLS ≤ 9%

+0 ≤ α ≤ 3o

+0 ≤ D < 1

To obtain the best configuration of these parameters, different

combinations of setting were tried and their optimization performances

were compared to each other. In our optimization, after the comparison,

the GA was configured as:

Population size: 200.

Initial range of population: [-2, 2].

Fitness scaling option: Rank scaling.

Reproduction option: Elite count of 1 and cross over fraction of 95%.

Mutation option: Shrink option with a shrink value of 1.

After using the KBNN, GA, HCB to optimize, the optimized results

were obtained and listed in Table 6. The quality of aluminum roll-

formed parts in the optimal RF process was also shown in this table.

The modeling error results of the roll forming process of U channel

product are shown in Fig. 9 with the range lie in 1~6%.

In the Fig. 10, the roll forming process of U channel product is

validated in ABAQUS with the result after optimization process. The

value of maximum longitudinal strain is 3.521e-3 in the high fidelity

σ 1 D–( ) σ′⋅=

Fig. 8 Flow diagram for implementing hill climbing

Table 6 The optimum values of design variables and desirability

Optimized parameters Desirability

d (mm) ω (rad/s) f r D MLS A

371 1.4 0.2 1.15 0.478 3.293 0.47

Fig. 9 The plot of modeling errors in modeling the RF process of the

aluminum U channel


FEM model, spring back angle is 0.475o and there is no damage to the

simulation model at the end of simulation process.

In Fig. 11, the confirmative simulation and experiment is shown with

no fracture in prototype.

Therefore, it can be concluded that the RF process of an aluminum

automotive component with the optimal configuration of parameters

obtained by the optimization in this paper satisfies all the initial

requirements. It proves the reliable efficiency of the presented

optimization strategy.

5. Conclusions

In this paper, a new effective optimization method has been proposed

to optimize RF process of aluminum U channel by using a combination

of the Knowledge-Based Neural Network (KBNN), Genetic Algorithm

(GA) and Hill Climbing. This paper presents the basic concept of the

combination GA-HCB hybrid method with KBNN for optimizing the

RF process of aluminum parts. This approach explores both the

excellent modeling ability of the KBNN and the powerful optimizing

ability of the GA and improvement of HCB from the result of the GA.

From this paper, we can find out the best optimal values of process

parameters in a short running time with high reliability. As the result of

the optimization, the optimization objective was to minimize the damage

variable D while keeping the maximum longitudinal strain MLS and

spring back angle α less than the allowable limits. The optimization

results were verified by the confirmative experiment and simulation. It

can be concluded that the integration of GA and HCB with KBNN

method is an excellent tool for optimizing the RF process of aluminum

parts. In summary, its optimal results are better than those of others. It

can be concluded that the developed method is not only a useful tool

for the RF process of aluminum parts, but also a powerful tool for

optimizing other forming processes.

ACKNOWLEDGEMENT

This work was supported by the MKE (Ministry of Knowledge

Economy), Korea, under the Industrial Source Technology Development

Programs supervised by the KEIT (Korea Evaluation Institute of

Industrial Technology).

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Documents

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