“Feasibility of Deep Neural Network Surrogate Models in Fluid Dynamics”
Authors: Niels C. Bender, Torben Ole Andersen and Henrik C. Pedersen,Affiliation: Aalborg University
Reference: 2019, Vol 40, No 2, pp. 71-87.
Keywords: Artificial Neural Networks, CFD, Digital Valves, Flow-induced Forces, Reduced Order Models, Lumped Parameter Models
Abstract: This paper studies reduced-order-models for the fluid flow problem of a digital valve, and whether it may efficiently be formulated by a deep Artificial Neural Network (ANN) to model e.g. the valve flow, flow-induced force, stiction phenomena and steep local pressure gradients that arise before plunger impact, which may otherwise require CFD to be accurately modeled. Several methodologies are investigated to evaluate both the required computation time and the accuracy. The accuracy is benchmarked against CFD solutions of flows and forces. As basis for comparison an analytical model is proposed where some fitting parameters are allowed, and the equation is tested outside its fitting range. A similar model is built as a deep ANN which is trained with data from the analytical model to investigate the amount of data required for an ANN and its fitting capabilities. The results show that in higher dimensions the required training data can be maintained low if data is structured by a Latin Hypercube, otherwise the amount becomes infeasible. This makes an ANN surrogate feasible when compared to a look-up table, and may be expanded to higher dimension where dynamical effects are included. However, the required data and computational cost for this is too extensive for the valve design considered as basis for the analysis. Instead, for this specific problem, the derived analytical model is sufficient to describe the valve dynamics and reduces the computation time significantly.
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DOI: 10.4173/mic.2019.2.1DOI forward links to this article:
| [1] Jie Ren and Shi-Jie Cao (2020), doi:10.1016/j.buildenv.2020.106671 |
| [2] Mireia Yurrita, Arnaud Grignard, Luis Alonso and Kent Larson (2022), doi:10.1007/978-3-030-94548-0_10 |
| [3] Dongwon Ko, Jeongseop Lee and Sanghyun Kim (2024), doi:10.1080/00221686.2023.2294713 |
[1] Amirante, R., Catalano, L., and Tamburrano, P. (2014). Amirante, R, , Catalano, L., and Tamburrano, P. The importance of a full 3D fluid dynamic analysis to evaluate the flow forces in a hydraulic directional proportional valve. Int. J. Comput. Eng. Softw.. 31(5):898--922. doi:10.1108/EC-09-2012-0221
[2] Amirante, R., Moscatelli, P.G., and Catalano, L.A. (2007). Amirante, R, , Moscatelli, P.G., and Catalano, L.A. Evaluation of the flow forces on a direct (single stage) proportional valve by means of a computational fluid dynamic analysis. Energy Convers. Manag.. 48(3):942--953. doi:10.1016/j.enconman.2006.08.024
[3] Bender, N.C., Andersen, T.O., and Pedersen, H.C. (2019). Bender, N, C., Andersen, T.O., and Pedersen, H.C. Parameter Correlation by Static and Dynamic Evaluations Utilizing a Mechatronic Design Procedure for a Digital Displacement Unit. IEEE/ASME Trans. Mechatronics. pages 1--11. .
[4] Bender, N.C., Pedersen, H.C., and Norgaard, C. (2017). Bender, N, C., Pedersen, H.C., and Norgaard, C. Experimental Validation of Flow Force Models for Fast Switching Valves. In ASME/BATH Symp. Fluid Power Motion Control. Sarasota. doi:10.1115/FPMC2017-4230
[5] Bender, N.C., Pedersen, H.C., Winkler, B., and Plockinger, A. (2018). Bender, N, C., Pedersen, H.C., Winkler, B., and Plockinger, A. Numerical Investigation of Switching Features of a Hydraulic Seat Valve with Annular Flow Geometry. Int. J. Fluid Power. 19(3). doi:10.1080/14399776.2018.1491755
[6] Benner, P., Gugercin, S., and Willcox, K. (2015). Benner, P, , Gugercin, S., and Willcox, K. A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems. SIAM Rev.. 57(4):483--531. doi:10.1137/130932715
[7] Borghi, M., Milani, M., and Paoluzzi, R. (2000). Borghi, M, , Milani, M., and Paoluzzi, R. Stationary axial flow force analysis on compensated spool valves. Int. J. Fluid Power. 1(1):17--25. doi:10.1080/14399776.2000.10781079
[8] Borutzky, W., Barnard, B., and Thoma, J. (2002). Borutzky, W, , Barnard, B., and Thoma, J. An orifice flow model for laminar and turbulent conditions. Simul. Model. Pract. Theory. 10(3-4):141 -- 152. doi:10.1016/S1569-190X(02)00092-8
[9] Forrester, A.I., Bressloff, N.W., and Keane, A.J. (2006). Forrester, A, I., Bressloff, N.W., and Keane, A.J. Optimization using surrogate models and partially converged computational fluid dynamics simulations. Proc. R. Soc. A Math. Phys. Eng. Sci.. 462(2071):2177--2204. doi:10.1098/rspa.2006.1679
[10] Funk, J.E., Wood, D.J., and Chao, S.P. (1972). Funk, J, E., Wood, D.J., and Chao, S.P. The Transient Response of Orifices and Very Short Lines. J. Basic Eng.. 94(2):483--489. doi:10.1115/1.3425456
[11] Jinasena, A., Ghaderi, A., and Sharma, R. (2018). Jinasena, A, , Ghaderi, A., and Sharma, R. Modeling and Analysis of Fluid Flow through A Non-Prismatic Open Channel with Application to Drilling. Model. Identif. Control A Nor. Res. Bull.. 39(4):261--272. doi:10.4173/mic.2018.4.3
[12] Knutson, A.L. and Van de Ven, J.D. (2016). Knutson, A, L. and Van de Ven, J.D. Modelling and experimental validation of the displacement of a check valve in a hydraulic piston pump. Int. J. Fluid Power. 17(2):114--124. doi:10.1080/14399776.2016.1160718
[13] Lang, J., Nathan, R., and Wu, Q. (2019). Lang, J, , Nathan, R., and Wu, Q. Experimental Study of Transient Squeezing Film Flow. J. Fluids Eng.. 141(August):1--7. doi:10.1115/1.4042758
[14] Leati, E., Gradl, C., and Scheidl, R. (2016). Leati, E, , Gradl, C., and Scheidl, R. Modeling of a Fast Plate Type Hydraulic Check Valve. J. Dyn. Syst. Meas. Control. 138(6):061002. doi:10.1115/1.4032826
[15] Lee, S.Y. and Blackburn, J.F. (1952). Lee, S, Y. and Blackburn, J.F. Contributions to Hydraulic Control, part I, Steady-State Axial forces on Control-Valve Pistons. ASME. 74(8):1005--111. .
[16] Lieu, T., Farhat, C., and Lesoinne, M. (2006). Lieu, T, , Farhat, C., and Lesoinne, M. Reduced-order fluid/structure modeling of a complete aircraft configuration. Comput. Methods Appl. Mech. Eng.. 195(41-43):5730--5742. doi:10.1016/j.cma.2005.08.026
[17] Lugowski, J. (2013). Lugowski, J, Steady-State Flow-Force Compensation in a Hydraulic Valve. http://cds.cern.ch/record/1633589, .
[18] Lugowski, J. (2015). Lugowski, J, One of the Mysteries in Fluid Mechanics. 2015. pages 2--6. .
[19] Mahrenholz, J. and Lumkes, J. (2009). Mahrenholz, J, and Lumkes, J. Analytical Coupled Modeling and Model Validation of Hydraulic On / Off Valves. J. Dyn. Syst. Meas. Control. 132(1):1--10. doi:10.1115/1.4000072
[20] Merritt, H.E. (1967). Merritt, H, E. Hydraulic control systems. John Wiley & Sons, Inc., New York. .
[21] Noergaard, C., Bech, M.M., Andersen, T.O., and Christensen, J. (2018). Noergaard, C, , Bech, M.M., Andersen, T.O., and Christensen, J. Flow Characteristics and Sizing of Annular Seat Valves for Digital Displacement Machines. Model. Identif. Control A Nor. Res. Bull.. 39(1):23--35. doi:10.4173/mic.2018.1.3
[22] Roemer, D.B., Johansen, P., Pedersen, H.C., and Andersen, T.O. (2013). Roemer, D, B., Johansen, P., Pedersen, H.C., and Andersen, T.O. Design and modelling of fast switching efficient seat valves for digital displacement pumps. Trans. Can. Soc. Mech. Eng.. 37(1):71--88. doi:10.1115/FPNI2014-7852
[23] Roemer, D.B., Johansen, P., Pedersen, H.C., and Andersen, T.O. (2015). Roemer, D, B., Johansen, P., Pedersen, H.C., and Andersen, T.O. Fluid Stiction Modeling for Quickly Seperating Plates Considering the Liquid Tensile Strength. ASME Fluids Eng.. 137(6):61205--61208. .
[24] Simic, M. and Herakovic, N. (2015). Simic, M, and Herakovic, N. Reduction of the flow forces in a small hydraulic seat valve as alternative approach to improve the valve characteristics. Energy Convers. Manag.. 89(1):708--718. doi:10.1016/j.enconman.2014.10.037
[25] Valdes, J.R., Rodriguez, J.M., Saumell, J., and Putz, T. (2014). Valdes, J, R., Rodriguez, J.M., Saumell, J., and Putz, T. A methodology for the parametric modelling of the flow coefficients and flow rate in hydraulic valves. Energy Convers. Manag.. 88:598--611. doi:10.1016/j.enconman.2014.08.057
[26] Zardin, B., Cillo, G., Rinaldini, C.A., Mattarelli, E., and Borghi, M. (2017). Zardin, B, , Cillo, G., Rinaldini, C.A., Mattarelli, E., and Borghi, M. Pressure losses in hydraulic manifolds. Energies. 10(3). doi:10.3390/en10030310
[27] Zhang, J.H., Wang, D., Xu, B., Gan, M.Y., Pan, M., and Yang, H.Y. (2018). Zhang, J, H., Wang, D., Xu, B., Gan, M.Y., Pan, M., and Yang, H.Y. Experimental and numerical investigation of flow forces in a seat valve using a damping sleeve with orifices. J. Zhejiang Univ. A Appl. Phys. Eng.. 19(6):417--430. doi:10.1631/jzus.A1700164
BibTeX:
@article{MIC-2019-2-1,
title={{Feasibility of Deep Neural Network Surrogate Models in Fluid Dynamics}},
author={Bender, Niels C. and Andersen, Torben Ole and Pedersen, Henrik C.},
journal={Modeling, Identification and Control},
volume={40},
number={2},
pages={71--87},
year={2019},
doi={10.4173/mic.2019.2.1},
publisher={Norwegian Society of Automatic Control}
};