Evaluation of ultimate conditions of FRP-confined concrete columns using genetic programming
Introduction
It is now well understood that the confinement of concrete with fiber reinforced polymer (FRP) composites can substantially enhance concrete strength and deformability. A large number of studies undertaken to date have produced over 3000 test results on FRP-confined concrete and resulted in the development of over 90 models. The conventional models that were developed using regression analysis can be classified into two broad categories namely the design-oriented models and the analysis-oriented models. In predictions of the ultimate condition of FRP-confined concrete, the design-oriented models use closed-form empirical expressions that were derived directly from database results. The analysis-oriented models, on the other hand, use a combination of empirical and theoretical expressions through an incremental procedure to consider the interaction mechanism between the external FRP jacket and the internal concrete core. The analysis-oriented models are built on the assumption of stress path independence, which assumes that the axial stress and axial strain of FRP-confined concrete at a given lateral strain are the same as those of the same concrete actively confined with a constant confining pressure equal to that supplied by the FRP shell.
As indicated by the assessment results of these models using a comprehensive experimental database, the performances of a large proportion of the conventional models were compromised when they were assessed against a large database covering parametric ranges that are much wider than the original databases used to develop these models [1], [2]. This can be attributed to the limited capability of the design-oriented models in handling uncertainties in complex experimental database, whereas the assumption adopted by the analysis-oriented models has recently been shown to be inaccurate [3], [4]. In addition, the development of these existing conventional models is often based on the expressions proposed by Richart et al. [5], with refinement subsequently applied to those earlier expressions to incorporate new research findings. Given the dependencies of the conventional models on the base expressions and the gradual refinement process, an efficient alternative approach is therefore required. Recently, new models based on artificial neural network, genetic programming, stepwise regression, and fuzzy logic algorithms have been proposed by many researchers [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. Models in this category could handle complex databases containing large number of independent variables, identify the sensitivity of input parameters, and provide mathematical solutions between dependent and independent variables. However, the complexity of modeling frameworks and the dependency of these models on computers have significantly reduced their versatility in design applications. The computer generated statistical solutions have also compromised the physical significance unfolding the structural behavior of FRP-confined concrete. In addition, several common modeling issues identified from the assessment of these models include: (i) limited size of database results, (ii) overfitted with redundant test parameters that cause unreliable prediction beyond their original observation range, and (iii) lack of consideration of important test parameters, including the ultimate rupture strain of FRP jacket.
With proper treatments given to the aforementioned modeling issues, genetic programming (GP) can be a potential candidate to address these shortcomings. GP is an evolutionary algorithm attempting to find key variables for a problem in a given search space, and generates mathematical expressions to explain the relations between the variables. By using GP based on the principles of symbolic regression (SR) analysis, the relationships between the dependent and independent variables of a complex database involving uncertainties and variability can be solved. SR is a process of finding a mathematical expression by minimizing the errors between given finite data set as well as providing a method of function identification [19]. Symbolic regression, as opposed to other regression techniques, discovers both the form of the model and its parameters from the search space. In other words, a measured dataset is fitted to an appropriate mathematical formula by a fitness function. Determination or identification of key variables and variable combinations, providing comprehension of developed models are among the benefits of symbolic regression analysis. In this research, SR analysis was conducted using GP approach which fits well to wide range of engineering problems.
In the recent years, the use of GP for optimum solution and function identification of engineering problems have been gaining acceleration as the approach is capable of dealing with complex database that contains a large number of parameters. GP progressively improves solution while it maintains the versatility of the model in closed-form expressions (e.g. [20], [21], [22], [23], [24], [25]). For example, Johari et al. [26] has successfully applied GP for the prediction of soil–water characteristic curve. Baykasoglu et al. [27] applied multi expression programming (MEP), gene expression programming (GEP) and linear genetic programming (LGP) to estimate compressive and tensile strength of limestone for the first time with good predictions. Javadi et al. [28] introduced a new technique based on GP for the determination of liquefaction induced lateral spreading. Cabalar and Cevik [29] applied GP for the prediction of peak ground acceleration using strong-ground-motion data from Turkey. The use of GP for the prediction of axial compressive strength of FRP-confined concrete has also been demonstrated by Cevik 3 [11], Cevik and Cabalar [6], and Cevik et al. 1 [8]. Results from these studies [6], [7], [8] proved that highly accurate prediction models can be developed by using genetic programming.
In the present study, the GP approach was used to establish models to predict the ultimate conditions of FRP-confined concrete columns under concentric compression. Based on a comprehensive experimental database that was carefully assembled using a set of selection criteria to ensure the reliability and consistency of the database, three closed-form expressions are proposed for the predictions of the compressive strength, ultimate axial strain and hoop rupture strain of FRP-confined concrete. This is the first study in the literature to establish expressions for the ultimate axial strain and hoop rupture strain of FRP-confined concrete on the basis of evolutionary algorithms. Details of the adopted approach are discussed in Section 2. A summary of the experimental database is provided in Section 3. The selection process of independent variables, functions and fitness rule, together with the proposed expressions are presented in Section 4. The predictions statistics of the proposed and the existing models with experimental results are presented in Section 5.
Section snippets
Overview of genetic programming
In this section, the GP paradigm is discussed and the essentials of GP are highlighted. Further concepts and terminology behind GP can be found from the inventor of this paradigm [19]. However, it is advised that the genetic algorithm concept developed in 1975 by Holland [30] and work from his student, Goldberg [31], can also be visited for further insight.
Database of FRP-confined concrete
The database of FRP-confined concrete was assembled through an extensive review of the literature that covered 3042 test results from 253 experimental studies published between 1991 and 2013. The suitability of the results was then assessed using a set of carefully established selection criteria to ensure the reliability and consistency of the database. Only monotonically loaded circular specimens with unidirectional fibers orientated in the hoop direction and an aspect ratio (H/D) of less than
Proposed model for ultimate condition of FRP-confined concrete
The ultimate condition of FRP-confined concrete is often characterized as the compressive strength and the corresponding axial strain of concrete and hoop strain recorded at the rupture of the FRP jacket. This makes the relationship between the ultimate axial stress (f′cc), ultimate axial strain (εcu) and hoop rupture strain (εh,rup) an important one. Using the comprehensive experimental database [34], a model consisting of three expressions for the predictions of the compressive strength (f′cc
Model validation and comparisons with existing models
To establish the relative performance of the proposed model, its prediction statistics were compared with those of the 10 best performing conventional models identified in a recent comprehensive review study reported in Ozbakkaloglu et al. [34]. In addition, the model was also compared with seven artificial intelligence (AI) models currently available in the literature that were developed using evolutionary programming techniques, including neural network (NN) [7], [9], [11], [13], [14],
Conclusions
A comprehensive experimental test database that consisted of 832 test results of FRP-confined concrete has been assembled from the published literature. Using the test database, the performances of a number of existing empirical, theoretical, and artificial intelligence models developed for FRP-confined concrete were then assessed. A close examination of the results from model assessments has led to a number of important findings on factors influencing the strengths and weaknesses of models in
References (61)
- et al.
Analysis-oriented stress–strain models for FRP-confined concrete
Eng Struct
(2007) - et al.
FRP-confined concrete in circular sections: review and assessment of stress–strain models
Eng Struct
(2013) - et al.
Neural network modeling of strength enhancement for CFRP confined concrete cylinders
Build Environ
(2008) - et al.
Soft computing based formulation for strength enhancement of CFRP confined concrete cylinders
Adv Eng Softw
(2010) - et al.
Prediction of FRP-confined compressive strength of concrete using artificial neural networks
Compos Struct
(2010) Modeling strength enhancement of FRP confined concrete cylinders using soft computing
Exp Syst Appl
(2011)- et al.
Prediction of strength parameters of FRP-confined concrete
Composites Part B
(2012) - et al.
Strength enhancement modeling of concrete cylinders confined with CFRP composites using artificial neural networks
Composites Part B
(2012) - et al.
Application of artificial neural networks to predict the bond strength of FRP-to-concrete joints
Constr Build Mater
(2013) - et al.
Automated optimum design of structures using genetic programming
Comput Struct
(2002)