Reliability based design optimization of concrete mix proportions using generalized ridge regression model
DOI: https://doi.org/10.12777/ijse.8.1.26-37
Abstract
This paper presents Reliability Based Design Optimization (RBDO) model to deal with uncertainties involved in concrete mix design process. The optimization problem is formulated in such a way that probabilistic concrete mix input parameters showing random characteristics are determined by minimizing the cost of concrete subjected to concrete compressive strength constraint for a given target reliability. Linear and quadratic models based on Ordinary Least Square Regression (OLSR), Traditional Ridge Regression (TRR) and Generalized Ridge Regression (GRR) techniques have been explored to select the best model to explicitly represent compressive strength of concrete. The RBDO model is solved by Sequential Optimization and Reliability Assessment (SORA) method using fully quadratic GRR model. Optimization results for a wide range of target compressive strength and reliability levels of 0.90, 0.95 and 0.99 have been reported. Also, safety factor based Deterministic Design Optimization (DDO) designs for each case are obtained. It has been observed that deterministic optimal designs are cost effective but proposed RBDO model gives improved design performance.
Keywords
Full Text:
FULL TEXT PDFReferences
Aggarwal, H. (2004). Reliability based design optimization: formulations and methodologies. PhD thesis, University of Notre Dame, Indiana.
Baykasoğlu, A., Öztas, A., and Özbay, E. (2009). Prediction and multi-objective optimization of high strength concrete parameters via soft computing approaches. Expert System with Applications, 36: 6144 – 6155; DOI 10.1016/j.eswa.2008.07.017
Chateauneuf, A. (2008). Principles of reliability-based design optimization. Structural design optimization considering uncertainties (eds Y. Tsompanakis, N. D. Lagaros & M. Papadrakakis), pp. 3-30. Taylor & Francis Group, London, UK.
Chen, X., Hasselman, T. K., and D. Neill, (1997). Reliability based structural design optimization for practical applications. Proceedings of 38th AIAA Conference on Structures, Structural Dynamics and Materials, April 7-10, Kissimmee, Florida, pp: 2724-2732.
Du, X., and Chen, W. (2004). Sequential optimization and reliability assessment method for efficient probabilistic design. ASME Journal of Mechanical Design, 126(2): 225-233; DOI 10.1115/1.1649968
Enevoldsen, I., and Sorensen, J. D. (1993). Reliability-based optimization of series systems of parallel systems. ASCE Journal of Structural Engineering, 119(4): 1069-1084; DOI 10.1061/(ASCE)0733-9445(1993)119:4(1069)
Gambhir, M. L., (1995). Concrete Technology. 4th Ed. Tata McGraw Hill Publishing Company Limited, India. ISBN: 0070151369, pp: 716.
Hoerl, A. E., and Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12: 55-67.
IS 10262 (2009), (First Revision), Indian standard concrete mix proportioning- Guidelines. BIS, New Delhi, India.
IS 516 (1959), Indian standard methods for tests for strength of concrete. BIS, New Delhi, India.
Jayaram, M. A., Natraja, M. C., and Ravikumar, C. N. (2009). Elitist genetic algorithm models: optimization of high performance concrete mixes. Materials and Manufacturing Processes, 24: 225-229; DOI 10.1080/10426910802612387
Karihaloo, B. L., and Kornbak, D. L. (2001). Optimization techniques for the design of high performance fibre-reinforced concrete. Structural and Multidisciplinary Optimization, 21 (1): 32-39; DOI 10.1007/s001580050165
Kumar, M. (2002). Reliability based design of structural elements. PhD thesis, Thapar University, Patiala, India.
Lagaros, N. D., Tsompanakis, Y., Fragiadakis, M., Plevris, V., and Papadrakakis, M. (2008). Metamodel-based computational techniques for solving structural optimization problems considering uncertainties. Structural design optimization considering uncertainties (eds Y. Tsompanakis, N. D. Lagaros & M. Papadrakakis), pp. 567-597. Taylor & Francis Group, London, UK.
Lee, B. Y., Kim, J. H., and Kim, J. K. (2009). Optimum concrete mixture proportion based on a database considering regional characteristics. Journal of Computing in Civil Engineering, 23: 258-265; DOI 10.1061/(ASCE)0887-3801(2009)23:5(258)
Lim, C. H., Yoon, Y. S., and Kim J .H. (2004). Genetic algorithm in mix proportioning of high–performance concrete. Cement and Concrete Research, 34: 409-420; DOI 10.1016/j.cemconres.2003.08.018
Luo, X. and R. V. Grandhi, (1995). ASTROS for reliability based multidisciplinary structural analysis and optimization. Proceedings of 36th AIAA/ASME/ASCE/AHS/ASC Conference on Structures, Structural Dynamics and Materials, April 10-13, New Orleans, LA, pp: 93-102.
Ngo, S. H., Kemény, S. and Deák, A. (2004). Application of ridge regression when the model is inherently imperfect: a case study of phase equilibrium. Chemometrics and Intelligent Laboratory systems, 72: 185-194; DOI 10.1016/j.chemolab.2004.01.015
Özbay, E., A. Baykasoğlu, A. Öztas, and H. Özbebek, (2006). An experimental comparison of optimum mix proportions of high strength concrete proposed by Taguchi method and genetic algorithm. Proceedings of 5th International Symposium on Intelligent Manufacturing Systems, May 29-31, 2006, Sakarya, Türkiye, pp: 1062-1070.
Price, K. V., Storn, R. M., and Lampinen, J. A., (2005). Differential evolution: A practical approach to global optimization. Springer,Germany.
Rawling, J. O., Pantula, S. G., and Dickey, D. A., (1998). Applied Regression Analysis: A Research Tool. Springer, New York.
Royset, J. O., Kiureghian, A. D., and Polak, E. (2001). Reliability-based optimal structural design by decoupling approach. Reliability Engineering & System Safety, 73: 213-221; DOI 10.1016/S0951-8320(01)00048-5
Ryan, T. P., (1996). Modern Regression Methods. 2nd Ed. John Wiley & Sons, New York.
Sorenson, J. D., (2004). Notes in structural reliability theory and risk analysis, Aalborg, Denmark.
Thanedar, P. B., and Kodiyalam, S. (1992). Structural optimization using probabilistic constraints. Structural Optimization, 4: 236-240; DOI 10.1007/BF01742750
Valdebenito, M. A., and Schuëller, G. I. (2010). A survey on approaches for reliability-based optimization. Structural and Multidisciplinary Optimization, 42: 645-663; DOI 10.1007/s00158-010-0518-6
Wang, L., and Grandhi, R. (1995). Structural reliability optimization using an efficient safety index calculation procedure. International Journal of Numerical Methods in Engineering, 38: 1721-1738; DOI 10.1002/nme.1620381008
Yan, X. (2008). Modified nonlinear generalized ridge regression and its application to develop naphtha cut point soft sensor. Computers and Chemical Engineering, 32: 608-621; DOI: 10.1016/j.compchemeng.2007.04.011
Yeh, I. C. (1999). Design of high performance concrete mixture using neural networks and non linear programming. Journal of Computing in Civil Engineering, 13 (1): 36-42; DOI 10.1061/(ASCE)0887-3801(1999)13:1(36)
Yeh, I. C. (2003). A mix proportioning methodology for fly ash and slag concrete using artificial neural networks. Chung Hua Journal of Science and Engineering, 1 (1): 77-84.
Yeh, I. C. (2007). Computer aided design of optimum concrete mixtures, Cement and Concrete Composites, 29(3): 193-202; DOI 10.1016/j.cemconcomp.2006.11.001
Yeh, I. C. (2009). Optimization of concrete mix proportioning using a flattened simplex-centroid mixture design and neural networks. Engineering with Computers, 25 (2): 179-190; DOI 10.1007/s00366-008-0113-2
Zou, T., and Mahadevan, S.A. (2006). Direct decoupling approach for efficient reliability-based design optimization, Structural and Multidisciplinary Optimization, 31: 190-200; DOI 10.1007/s00158-005-0572-7