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A New Variant of Genetic Programming in Formulation of Laser Energy Consumption Model of 3D Printing Process

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Handbook of Sustainability in Additive Manufacturing

Abstract

Literature studies reveal that significant work has been done in improving the productivity of the 3D printing process, at the same time neglecting the associated environmental implications. Growing demand for customized and better product quality has resulted in an increase in energy consumption, which is one of the important factors for sub-standard environmental performance. Consequences include the adverse impacts on humans, plant life, and soil and among others. Thus, an optimization of energy consumption is needed for improving the environmental performance of the 3D printing process. In this context, the present work proposes a complexity-based-evolutionary approach of genetic programming (CN-GP) in formulation of functional expression between laser energy consumption, total area of sintering, and two inputs of 3D printing process [selective laser sintering (SLS)]. The performance of the proposed laser energy consumption models is evaluated against actual experimental data based on five statistical metrics and hypothesis testing. Relationships between laser energy consumption and two inputs are unveiled which can be used for effectively monitoring the environmental performance of the SLS process. It was found that the slice thickness has 98 % impact on the laser energy consumption in the process. A major contribution of the study is that the optimum values of inputs can be selected to optimize the energy consumption of the SLS process.

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Acknowledgments

This study was supported by Nanyang Technological University’s funding, reference number M060030008.

Author information

Authors and Affiliations

  1. School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Ave, Singapore 639798, Singapore

    Akhil Garg & Jasmine Siu Lee Lam

  2. Department of Industrial and Systems Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong

    M. M. Savalani

Authors
  1. Akhil Garg
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  2. Jasmine Siu Lee Lam
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  3. M. M. Savalani
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Corresponding author

Correspondence to Jasmine Siu Lee Lam .

Editor information

Editors and Affiliations

  1. Environmental Services Manager-Asia, SGS Hong Kong Limited, Hong Kong, Hong Kong

    Subramanian Senthilkannan Muthu

  2. Dept. of Industrial and Systems Eng., The Hong Kong Polytechnic University, Hong Kong, China

    Monica Mahesh Savalani

Appendix

Appendix

$$ \begin{aligned} {\mathbf{TAS}}_{{{\mathbf{GP}}}} & = - 88628431.5699 + ( - 14421262.2035) \\ & \quad \times (\tanh (\sin (\tan (\cos ((x1) \times (( - 8.993442))))))) + (107.691) \\ & \quad \times (\sin (x2)) + (70467967.5522) \times (\sin ((x1) \times (\cos ((\tanh (x1)) \\ & \quad *(( - 8.993442)))))) + ( - 3390.7491) \times (\cos ((\cos ((x1) \\ & \quad \times (( - 8.993442)))) \times (( - 8.993442)))) + ( - 65390146.1759) \\ & \quad \times (\sin (\tanh (\tanh (x1)))) + ( - 24.1412) \times (\tan (x2)) \\ & \quad + (99531980.4057) \times (\cos (\tanh (\tan (x1)))) \\ \end{aligned} $$
(7)
$$ \begin{aligned} {\mathbf{TAS}}_{{{\mathbf{CN{\text{-}}GP}}}} & = \, 5137644.8262 + \left( { - 1706557.4605} \right) \times \left( {\tan \left( {\left( {\sin \left( {\left( {\cos \left( {x1} \right)} \right) + \left( {\left( {\left( {9.289170} \right)} \right) \times \left( {x1} \right)} \right)} \right)} \right) - \left( {\tan \left( {\tan \left( {x1} \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( { - 3439756477.4271} \right) \times \left( {\tan \left( {\left( {x1} \right) \times \left( {x1} \right)} \right)} \right) + \left( { - 107.6723} \right) \times \left( {\left( {x1} \right) - \left( {\sin \left( {x2} \right)} \right)} \right) \\ & \quad + \left( { - 26870.1687} \right) \times \left( {\left( {\tan \left( {x1} \right)} \right) \times \left( {\tan \left( {\tan \left( {\left( {\left( {9.289170} \right)} \right) \times \left( {x1} \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( {24.1369} \right) \times \left( {\left( {\left( {\sin \left( {\left( {\cos \left( {x1} \right)} \right) + \left( {\left( {\left( {9.289170} \right)} \right) \times \left( {x1} \right)} \right)} \right)} \right) - \left( {\tan \left( {x2} \right)} \right)} \right) - \left( {\tan \left( {x1} \right)} \right)} \right) \\ & \quad + \left( {4643987.9876} \right) \times \left( {\left( {\sin \left( {\left( {\cos \left( {x1} \right)} \right) + \left( {\left( {\left( {9.289170} \right)} \right) \times \left( {x1} \right)} \right)} \right)} \right) - \left( {\tan \left( {\cos \left( {\tan \left( {x1} \right)} \right)} \right)} \right)} \right) + \left( { - 574696436.1438} \right)\\ & \quad \times \left( {\left( {x1} \right) \times \left( {\left( {x1} \right) \times \left( {\left( {\left( { - 5.810103} \right)} \right) - \left( {x1} \right)} \right)} \right)} \right) \\ \end{aligned} $$
(8)
$$ \begin{aligned} {\mathbf{Laser}}{\mkern 1mu} {\mathbf{energy}}{\mkern 1mu} {\mathbf{consumption}}_{{{\mathbf{GP}}}} & = 1115180.5442 + (744275.6671) \times (\tan (\sin ((x1) \\ & \quad + (x1)))) + ( - 357003.1223) \\ & \quad \times (\tan (\tanh (\tan ((( - 8.767966)) \times (x1))))) \\ & \quad + (347109.7909) \times ((\tan (\tanh (\tan ((( - 8.767966)) \\ & \quad \times (x1))))) - ((( - 4.185710)) + (\sin ((x1) \\ & \quad + (x1))))) + ( - 4442389.3594) \\ & \quad \times (\cos (((x1) - ((0.17))) \times (((4.09)) \times (x1)))) \\ & \quad + ( - 4151) \times (\cos (\sin (((9.961556)) + (x2)))) \\ & \quad + (2149599.4264) \times (\cos (\sin (((9.961556)) \\ & \quad + (x1)))) + (0.045548) \times ((((\tan (\tan (x1))) \\ & \quad \times (\cos (\sin (x1)))) + (\sin (x1))) + (\sin (((x1) \\ & \quad - (\sin (x2))) + (\sin ((x1) + (x1)))))) \\ \end{aligned} $$
(9)
$$ \begin{aligned} {\mathbf{Laser \, energy \, consumption}}_{{{\mathbf{CN{\text{-}}GP}}}} & = \, - 594678.7278 + \left( {2241.127} \right) \times ((\cos (\tan ((\left( {x1} \right) - (( - 2.441394))) \\ & \quad - \left( {\left( {x1} \right) \times \left( {\left( {5.972072} \right)} \right)} \right)))) \times \left( {\left( {\tanh \left( {\tan \left( {\sin \left( {x1} \right)} \right)} \right)} \right) - \left( {\tanh \left( {\tanh \left( {\cos \left( {x1} \right)} \right)} \right)} \right)} \right)) \\ & \quad + ( - 3719342.8431) \times \left( {\left( {x1} \right) \times \left( {x1} \right)} \right) + \left( { - 177698.568} \right) \times (\tan (\tan (\sin ((\left( {\left( {5.372252} \right)} \right) \\ & \quad + (( - 0.213505))) + \left( {\tanh \left( {x1} \right)} \right))))) + \left( {2474839.7138} \right) \times \left( {\tan \left( {\sin \left( {\left( {\cos \left( {x1} \right)} \right) \times \left( {x1} \right)} \right)} \right)} \right) \\ & \quad + \left( { - 0.064203} \right) \times \left( {\left( {\sin \left( {x2} \right)} \right) + \left( {\tanh \left( {\left( {\left( {\cos \left( {x2} \right)} \right) + \left( {\cos \left( {x1} \right)} \right)} \right) - \left( {\left( {\tan \left( {x2} \right)} \right) - \left( {\left( {x1} \right) - \left( {x1} \right)} \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( {0.085606} \right) \times \left( {\tan \left( {\left( {\tanh \left( {\left( {\left( {6.960941} \right)} \right) \times \left( {\sin \left( {x2} \right)} \right)} \right)} \right) \times \left( {\sin \left( {\left( {\sin \left( {x2} \right)} \right) + \left( {\left( {x2} \right) + \left( {x1} \right)} \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( {41104.3208} \right) \times \left( {\cos \left( {\left( {\left( {\left( {\left( {5.372252} \right)} \right) + \left( {x1} \right)} \right) + \left( {\tanh \left( {x1} \right)} \right)} \right) \times \left( {\left( {5.972072} \right)} \right)} \right)} \right) \\ \end{aligned} $$
(10)

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Garg, A., Lam, J.S.L., Savalani, M.M. (2016). A New Variant of Genetic Programming in Formulation of Laser Energy Consumption Model of 3D Printing Process. In: Muthu, S., Savalani, M. (eds) Handbook of Sustainability in Additive Manufacturing. Environmental Footprints and Eco-design of Products and Processes. Springer, Singapore. https://doi.org/10.1007/978-981-10-0549-7_3

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