Prediction and multi-objective optimization of high-strength concrete parameters via soft computing approaches

https://doi.org/10.1016/j.eswa.2008.07.017Get rights and content

Abstract

The optimization of composite materials such as concrete deals with the problem of selecting the values of several variables which determine composition, compressive stress, workability and cost etc. This study presents multi-objective optimization (MOO) of high-strength concretes (HSCs). One of the main problems in the optimization of HSCs is to obtain mathematical equations that represents concrete characteristic in terms of its constitutions. In order to solve this problem, a two step approach is used in this study. In the first step, the prediction of HSCs parameters is performed by using regression analysis, neural networks and Gen Expression Programming (GEP). The output of the first step is the equations that can be used to predict HSCs properties (i.e. compressive stress, cost and workability). In order to derive these equations the data set which contains many different mix proportions of HSCs is gathered from the literature. In the second step, a MOO model is developed by making use of the equations developed in the first step. The resulting MOO model is solved by using a Genetic Algorithm (GA). GA employs weighted and hierarchical method in order to handle multiple objectives. The performances of the prediction and optimization methods are also compared in the paper.

Introduction

Real-life decision making frequently requires that a compromise be reached between conflicting objectives. The compromises required to strike a balance between wealth and quality of life, between performance and the cost of a car, or between health and pleasure of eating rich foods, are familiar ones. Similar conflicts arise in the production and design of composite materials such as high-strength concretes (HSCs) (Ashby, 2000). HSC is a composite material in which the ingredient consists of water, cement, aggregate, chemical and mineral admixtures. Compressive strength is the most important concrete parameter and main parameter for quality control, concretes over 40 MPa can be defined as HSCs. Many countries on the world such as Turkey are on the earthquake zone. Earthquakes can cause big damages for example, during recent earthquakes in Turkey (Adana-Ceyhan earthquake in 1998, Adapazarı-Gölcük earthquake in 1999 and Bingöl earthquake in 2003) more than 20,000 people died and more than 90,000 buildings collapsed completely. The investigations which are carried out after these earthquakes have pointed out the poor quality of the concrete used as one of the major reason behind these devastating losses (Özkul and Öztaş, 1998, Öztaş, 2003). Low cost is the main reason for producing and using of poor quality concrete. Presumably this was done in order to lower the cost despite the fact that the quality of concrete is much more important in countries which are in an earthquake zone. Therefore the high-strength concrete (HSC) must be produced and used but if the technical properties of concrete are improved, their costs are increased and their usage probability is decreased.

The property profiles of all engineering materials are very diverse. Optimum selection requires that the best match be found between the available profiles and the requirements of the design. Methods exist for achieving this when the design has a single objective. But it is rare that a design has a single objective; generally there are several objectives, and optimized selection requires that a balance be struck between them (Ashby, Brechet, Coben, & Salvo, 2004). Today, HSC can be produced all over the world but there must be simultaneous production and design optimization of HSCs considering technical performance and manufacturing costs.

Several studies have been performed related to implementation of MOO in the construction material and construction management areas. Muthukumar and Mohan (2004) optimized mix proportions of polymer concrete to have minimum void. The mechanical properties were studied for each polymer concrete combination in their work. Mechanical properties such as compressive strength, flexural strength, tensile strength and splitting tensile were optimized and compared with the experimental data. Chung, Woo, Woo, and Alain (2004) proposed a MOO methodology which simultaneously considers the mechanical performance and the manufacturing cost from the early stage of design of composite laminated plates. Sahab, Ashour, and Toropov (2005) optimized the cost of reinforced concrete flat slab buildings. The objective function was the total cost of the building including the cost of floors, columns and foundations. Karihaloo and Kornbak (2001) demonstrated how rigorous mathematical programming techniques can be employed in the design of fibre-reinforced concrete mixes which have both high tensile strength and high ductility.

In this study, multi-objective optimization of HSC is investigated. One of the main problems in the optimization of HSCs is to obtain mathematical equations that represents concrete characteristic in terms of its constitutions. In order to solve this problem, a two step approach is used in this study. In the first step, the prediction of HSCs parameters is performed by using regression analysis, neural networks and Gen Expression Programming (GEP). The output of the first step is the equations that can be used to predict HSCs properties (i.e. compressive stress, cost and workability). In order to derive these equations the data set which contains many different mix proportions of HSCs is gathered from the literature. In the second step, a MOO model is developed by making use of the equations developed in the first step. The resulting MOO model is solved by using a Genetic Algorithm (GA). GA employs weighted and hierarchical method in order to handle multiple objectives and determine Pareto curves. The performances of the prediction and optimization methods are also discussed and compared in the paper.

Section snippets

An overview of high-strength concretes (HSCs)

Nowadays, HSCs are extensively applied in construction projects (Bache, 1981, Shah, 1993). A HSC is defined as concrete that meets special combination of performance and uniformity requirements that cannot be achieved routinely by using conventional constituents and normal mixing, placing, and curing procedures. Several new advanced concretes have been transferred from laboratory research to practical applications and they already occupy a noticeable share of the market. Based on the latest

Prediction of high-strength concrete parameters using soft computing algorithms

As it is mentioned previously, the main problem in the successful optimization of HSC parameters is the derivation of high quality analytical equations that can be used to predict concrete parameters. The most widely used approach in the literature for prediction purposes is the classical regression analyses. The prediction ability of regression analyses may be limited for highly non-linear problems (Baykasoğlu, Dereli, & Tanış, 2004). Neural networks (NN) are also widely used in the literature

Multi-objective optimization of HSC parameters

In this section of the paper MOO models are constructed based on the equations derived from the GEP and regression analyses for the determination of optimal mix proportions of HSC. In the first model GEP equations are used in the second one regression equations are used. The resulting models are solved by using a Genetic Algorithm (GA). GA employs weighted and hierarchical methods in order to handle multiple objectives.

Conclusion

In this work a soft computing approach is used to predict and optimize parameters of HSC. For the prediction study GEP, NN and regression analyses are used. It is found that NN generates the most accurate predictions. GEP is also very good in prediction and has the ability to relate input parameters with output parameters in terms of mathematical equations which are necessary for generating optimization models. A regression analysis is the worst performing one in prediction. But regression

Acknowledgement

The first (corresponding) author is grateful to Turkish Academy of Sciences (TÜBA) for supporting his scientific studies.

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