Genetic programming for moment capacity modeling of ferrocement members
Introduction
Ferrocement is a type of thin-shell concrete. A ferrocement member includes cement mortar and wire mesh, and usually does not include steel/fiber bars or coarse aggregates. The wire mesh may have many forms; however, the most common forms are square mesh, expanded mesh, and hexagonal mesh. Ferrocement members may be used in many structures such as domes, walls, boats, pools, tanks, and deep beams [1]. Ferrocement members have some advantages over conventional reinforced concrete members. The main advantage of these members is that it can be fabricated into virtually any shape. Furthermore, raw materials are readily available and economical; ferrocement members are easy to construct and do not require highly-skilled labor; and ferrocement offers long life and better resistance against earthquakes [2].
Modeling of ferrocement members is very difficult. The analytical flexural capacity models for ferrocement members are actually derived based on several assumptions, approximations, and simplifications [3]. One of the analytical methods to calculate the moment capacity is plastic analysis which calculates it based on the condition of equilibrium of forces [4]. This method [4] assumes the ferrocement is a homogeneous ideally elastoplastic material. In addition, this method considers a bilinear stress–strain relationship for the mortar. Another method for moment capacity evaluation is mechanism approach which simplifies the method based on plastic analysis [5]. This approach assumes that the neutral axis is very close to the top surface; hence, all the reinforcement is in tension [5]. These simplifications and assumptions may not be correct and can cause errors in predicted moment capacity [3]. In this case, an empirical model built using experimental datasets can reduce modeling uncertainty. Metaheuristic tools offer an alternative empirical predictive tool for this purpose.
Several metaheuristic data mining tools have been developed recently. Due to their random nature, metaheuristic algorithms cannot be judged by the result of a single run; therefore, after tuning the parameters, the algorithms should be run several times. Generally, empirical predictive tools rely on the database; therefore, a more complete database will lead to more reliable models. An artificial neural network (ANN) is a widely used predictive method for engineering modeling [6] and specially concrete structures modeling (e.g. [7], [8]). Mashrei et al. [9] have recently utilized two ANN techniques (back-propagation neural networks (BPNN) and an adaptive neuro-fuzzy inference system (ANFIS)) to predict the moment capacity of ferrocement members. However, ANNs do not output a function that can be used to calculate the outcome using the input values (i.e., ANNs are “black box” processes), which notably limits their usefulness. Therefore, ANNs and similar techniques are mostly appropriate for use as part of a computer program [10].
Owing the general complexity of concrete modeling, genetic programming (GP) [11] can be an alternative approach for conventional models (e.g., the equivalent rectangular stress distribution method). GP can generally be defined as a recent specialization of genetic algorithms (GAs), in which the solutions are computer programs instead of binary strings. The main advantage of the GP-based approaches over other predictive tools is that GP can generate predictive equations without any prior assumption regarding relationships between input parameters. The GP-based equations are generally simple and can be easily implemented in practice. Gene expression programming (GEP) [12] is a new extension of GP. GEP solutions are computer programs of different sizes and shapes that are encoded in fixed-length linear chromosomes. Recent research has been directed at applying GEP to civil engineering modeling [13], [14], [15], particularly concrete structures (e.g., [16], [17], [18], [19]).
The purpose of this paper is to utilize the GEP technique to predict the moment capacity of ferrocement members. The proposed models are developed based on a comprehensive database obtained from previously published experimental results. After parametric study and external validation, a comparative study was conducted between the results of the proposed model and those obtained using existing models found in the literature.
Section snippets
Gene expression programming
Following the principle of Darwinian natural selection, GP creates computer programs to find relationships between input parameters and the output [11]. The GP approach was introduced by Koza [11] as a useful predictive tool. Most of the genetic mechanisms commonly implemented in GAs can also be used in GPs. However, an important difference between GPs and GAs is the representation of the solution: a GP result is a computer program that can be represented as a tree structure and declared in a
Proposed GEP models
In order to provide accurate assessment of the moment strength of ferrocement members, the effects of both geometric and mechanical properties were considered in the model development. The most important factors for the moment capacity of ferrocement members were determined on the basis of a literature review [9], [25] and through a trial and error study. Consequently, ultimate moment capacity was considered to be a function of the following parameters:where Mu is the ultimate
GEP models
After running GEP with three different learning, validation, and testing subsets, three final models were obtained: models GEP-I, GEP-II, and GEP-III. Comparisons of the GEP-predicted strength values with experimental data for three models are shown in Fig. 5. Each model accurately predicts of the moment capacity.
Model validity
Smith [36] concluded that a correlation (R) value greater than 0.8 indicates a strong correlation between the predicted and measured values. This is one criterion for judging model
Conclusion
Gene expression programming (GEP), a robust variant of genetic programming, was utilized to formulate the moment capacity of ferrocement members. Three accurate empirical models were derived for the prediction of the ultimate moment capacity with different randomized data subsets for learning, testing, and validation. The developed GEP-based models reliably estimate the ultimate capacity of ferrocement members. Moreover, the GEP prediction models satisfy several acceptance criteria considered
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