Internat. J. Sci. Eng., Vol. 8(1)2015:26-37 January 2015, Rachna Aggarwal et al. 26 © IJSE – ISSN: 2086-5023, January 2015, All rights reserved International Journal of Science and Engineering(IJSE) Home page: http://ejournal.undip.ac.id/index.php/ijse Reliability Based Design Optimization of Concrete Mix Proportions Using Generalized Ridge Regression Model Rachna Aggarwal 1) , Maneek Kumar 2) , R.K.Sharma 3) , M.K.Sharma 3) 1) Department of Mathematics, M.L.N. College, Yamunanagar, Haryana, India 2) Department of Civil Engineering, Thapar University, Patiala, India 3) School of Mathematics and Computer Applications, Thapar University, Patiala, India Email: rachnaaggarwal1976@gmail.com 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— Concrete; Compressive strength; Reliability; Optimization; Ridge regression Submission: 10 October 2014 Corrected : 25 November 2014 Accepted: 10 December 2014 Doi: 10.12777/ijse.8.1.26-37 [How to cite this article: Aggarwal R., Kumar M., Sharma R.K. and Sharma M.K. (2015). Reliability Based Design Optimization of Concrete Mix Proportions Using Generalized Ridge Regression Model, International Journal of Science and Engineering, , 8(1),36-47, Doi: 10.12777/ijse.8.1.26-37 I. INTRODUCTION Sustainable development while conserving the environment with an objective of welfare and safety of the people has been a subject of increasing concern during last few decades. At the same time, optimal allocation of available natural and financial resources is considered very important. Therefore methods of risk and reliability analysis developed during the last few decades are becoming more and more important as decision support tools in civil engineering applications (Sorenson, 2004). Concrete is the most widely used man made construction material. Every year billion tons of cement is converted into concrete world-wide. Concrete is a mixture of cement, water, fine aggregate, coarse aggregate and admixtures. A good amount of work has been done by researchers to optimally allocate the ingredients proportions for concrete mixes while satisfying specific requirements related to compressive strength, slump, tensile strength etc. Yeh (1999, 2003, 2007, and 2009) determined optimal concrete mix compositions with lowest cost and required performance using nonlinear programming technique. Karihaloo and Kornbak (2001) optimized tensile strength and ductility, simultaneously, for a given compressive strength in the design of fiber reinforced concrete mixes. Lim et al. (2004) used genetic algorithm to find appropriate concrete mix proportions for high performance concrete under specified requirements. Optimal concrete mix proportions for maximum compressive strength of concrete using Taguchi method and genetic algorithm were determined by Őzbay et al. (2006). Jayaram et al. (2009) proposed elitist genetic algorithm models for the optimization of high volume fly ash concrete. Lee et al. (2009) used convex hull approach to define effective region constrained by the domain defined by limited data base and then, genetic algorithm was used to find optimal concrete mix parameters in the effective region. Baykasoğlu et al. (2009) solved a multi-objective optimization model for high strength concrete parameters using genetic algorithm with prediction models based on regression analysis and Gene Expression Programming (GEP). The formulation of a structural optimization problem that ignores the scattering of various design parameters is termed as Deterministic Design Optimization (DDO). A numerically feasible optimum design, according to the deterministic formulation, once applied in a real physical system, may lose its feasibility due to the unavoidable dispersion on the values of structural parameters (material properties, dimensions, loads, etc.). Performance of the applied design may be far worse than expected. As such, in real world applications, if uncertainties are not taken into account, the significance of the optimum solutions would be