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Application of an optimized SA-ANN hybrid model for parametric modeling and optimization of LASOX cutting of mild steel

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Abstract

Laser assisted oxygen cutting (LASOX) process is an efficient method for cutting thick mild steel plates compared to conventional laser cutting process. However, scanty information is available as to modeling of the process. The paper presents an optimized SA-ANN model of artificial neural network (ANN) and simulated annealing (SA) to predict and optimize cutting quality of LASOX cutting process of mild steel plates. Optimization of SA-ANN parameters is carried out first where the ANN architecture and initial temperature for SA are optimized. The optimized ANN architecture is further trained using single hidden layer back propagation neural network (BPNN) with Bayesian regularization (BR). The trained ANN is then used to evaluate the objective function during optimization with SA. Experimental dataset employed for the purpose consists of input cutting parameters comprising laser power, cutting speed, gas pressure and stand-off distance while the resulting cutting quality is represented by heat affected zone (HAZ) width, kerf width and surface roughness. Results indicate that the SA-ANN model can predict the optimized output with reasonably good accuracy (around 3%). The proposed approach can be extended for prediction and optimization of operational parameters with reasonable accuracy for any experimental dataset.

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Abbreviations

ANN:

Artificial neural networks

SA:

Simulated annealing

LASOX:

Laser assisted oxygen cutting

GA:

Genetic algorithm

BPNN:

Back propagation neural network

LM:

Levenberg Marquardt algorithm

BR:

Bayesian regularization

V:

Cutting speed (mm/min)

PR:

Gas pressure (bar)

P:

Laser power (W)

F:

Stand off distance (mm)

HAZ:

Heat affected zone

H:

HAZ width (mm)

K:

Kerf width (mm)

R:

Surface roughness (μm)

X :

Input vector, \( {\mathbf{X}} = \left[ {\begin{array}{*{20}c} {\text{V}} & {\text{PR}} & {\text{P}} & {\text{F}} \\ \end{array} } \right] \)

D :

Output vector, \( {\mathbf{D}} = \left[ {\begin{array}{*{20}c} {\text{H}} & {\text{K}} & {\text{R}} \\ \end{array} } \right] \)

J :

Cutting quality factor of LASOX cutting

HLN:

Hidden layer neurons in ANN

T:

Initial temperature for SA

S :

A solution point of quasi-Newton search algorithm, \( {\mathbf{S}} = \left[ {\begin{array}{*{20}c} {{\mathbf{HLN}}} & {\mathbf{T}} \\ \end{array} } \right] \)

H:

Hessian matrix

BFGS:

Broyden-Fletcher-Goldfrad-Shanno updating formula

X max , X min :

Maximum and minimum real values of input

D max :

Maximum real values of output

X nor , T nor :

Normalized input and output vector

w :

Weight vector associated with hidden layer neurons

M:

Activation value of hidden layer neurons

Z:

Output signals of hidden layer neurons

O :

Output signal of the network

SSE :

Sum of the squared errors

SSW :

Sum of the squared weights

Φ :

A factor indicates a linear combination of SSE and SSW

α, β:

Regularization parameters

MSE:

Mean of squared errors

E:

Energy state in simulated annealing algorithm

k:

Boltzmann constant or cooling rate

N :

A solution point of SA optimisation

t:

Iteration count for SA

r:

Random number between 0 and 1

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Authors and Affiliations

  1. Department of Automobile Engineering, MCKV Institute of Engineering, 243, G.T. Road (N), Liluah, Howrah, West Bengal, 711204, India

    S. Chaki

  2. Department of Mechanical Engineering, Jadavpur University, Kolkata, West Bengal, 700032, India

    S. Ghosal

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  1. S. Chaki
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Correspondence to S. Chaki.

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Chaki, S., Ghosal, S. Application of an optimized SA-ANN hybrid model for parametric modeling and optimization of LASOX cutting of mild steel. Prod. Eng. Res. Devel. 5, 251–262 (2011). https://doi.org/10.1007/s11740-011-0298-x

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