Data-driven analysis on ultimate axial strain of FRP-confined concrete cylinders based on explicit and implicit algorithms
Introduction
Accumulating proofs underlie the widely accepted view that the lateral confining pressure makes concrete columns under the state of triaxial compression, which can effectively enhance the strength and the ductility of the core concrete [1]. Serving as a new class of building materials in the field of civil engineering, fiber reinforced polymer (FRP) composites have been extensively employed in the construction, retrofitting and rehabilitation projects [2], [3]. A considerable number of experimental and theoretical studies have corroborated that FRP-confined concrete (specifically, FRP-wrapped concrete) can improve the mechanical performance, durability, safety, and service life of the structures [4], [5]. Multiple empirical models have been developed to date in order to predict the behavior of FRP-wrapped concrete under axial loading, with heavy focus on the confined compressive strength fcc and the ultimate axial strain ɛcu, which is defined as the axial strain at peak compressive stress [6], [7], [8].
A pioneering research was conducted by Fardis and Khalili [9] to compare two predictive models of fcc respectively proposed by Richart et al. [10] and Newman and Newman [11]. Later, a large number of models were promptly developed by employing a similar combination of variables, mainly the lateral confinement ratio and the strain ratio, while the influence of other potential contributing parameters was being explored using a range of modelling methods. Sadeghian and Fam [12] investigated a variety of models and acquired the best fit from a regression analysis. Keshtegar et al. [13] amended the conventional harmony search (HS) algorithms for resolving the complex nonlinear system modeling problems and Keshtegar et al. [14] proposed a dynamic chaos control method, which retained the nonlinearity of the Logistic map system and obtained unknown parameter values via the new and previous iterations. However, it has been pointed out that earlier studies were limited by the small datasets used, which hindered the universality of these models and the ability to generalize their predictions to independent data [15], [16], [17]. As a result, creating reliable and more comprehensive data has been regarded as key research need to aid the modelling.
A large experimental database has been compiled for better assessment of the peak conditions of the FRP-confined concrete (see Table 1). From this table, it can be seen that the spread of the confined to unconfined compressive stress ratio was much smaller than the respective strain at peak stress. This discrepancy is mainly ascribed to the differences in the test equipment and conditions. The load is mainly measured by the built-in force sensors with a consistent degree of accuracy [18]. However, the strain is acquired by the external force sensors, which were much more sensitive to the test setups and material properties [19]. This poses a challenge for empirical formulas to produce consistent and reliable readings for the strain behavior. Therefore, advanced modelling tools should be adopted to evaluate additional parameters that were previously neglected and may contribute to this uncertainty.
Bayesian probabilistic predictive model provides a parameter estimation method to perform in-depth data mining to calibrate these existing models using the compiled database. Large datasets were shown to be especially advantageous for revealing additional parameters using this technique [20], [21]. The unknown model parameters are preselected and then eliminated by the analysis, continuously modifying and improving the model [22]. The prior information of specimens and unknown model parameters are essential for obtaining the posterior distribution. The Bayesian probabilistic prediction model is generally less biased than traditional mathematical regression for optimization problems. In addition to the accuracy achievable through the modified model, the method also offers numerous other advantages, such as stable classification efficiency, enforceable mathematical algorithms and low sensitivity for missing data [23]. Recently, Liu et al. [24] established a probabilistic shear strength model for deep flexural members based on conjugate prior distribution and Kim et al. [25] successfully applied the method to investigate the joint shear behavior of reinforced concrete beam-column connections. The Bayesian probabilistic prediction model was also demonstrated to be useful for predicting the durability of concrete and the structural seismic performance evaluation problems due to its simplicity and efficiency [26], [27]. Thus, more research is warranted to develop state-of-the-art Bayesian method possessing the high accuracy and promising engineering applications for predicting the ultimate axial strain ɛcu of FRP-confined concrete.
With the advent of the era of big data and the rapid rise of computer-aided computing, machine learning (ML) algorithms have been increasingly used in the field of artificial intelligence and pattern recognition [28], [29]. ML algorithms are characterized by a form of “model” to capture the underlying mechanisms on a certain computer platform, despite the lack of information regarding specific parameters [30], [31]. ML algorithms were especially beneficial for uncovering information from large and complex civil engineering problems. For instance, Abuodeh et al. [32] successfully adopted ML algorithms to study the shear strength and behavior of RC beams strengthened with externally bonded FRP sheets, which demonstrated that ability of ML algorithms to identify factors affecting the confined RC beams. Cevik and Guzelbey [33], Naderpour et al. [34], Jalal and Ramezanianpour [35], Naderpour et al. [36], Gandomi et al. [37], and Cascardl et al. [38] used 101, 213, 128, 95, 101, and 465 data points, respectively to predict the fcc using a variety of ML algorithms, including artificial neural networks, gene expression programming, linear genetic programming, etc. In contrast, only a small number of researches were implemented to develop ML models to predict the ɛcu, and most of these studies employed small datasets and typically a single ML algorithm, which may again limit the universality of the proposed models [39], [40]. Thus, more research is warranted to compare the performance of different ML algorithms over a large database.
By analyzing the data and mining the information from large database, the present study aims at initiating feasible Bayesian posterior model and three different ML models (i.e., back-propagation artificial neural network, multi-gene genetic programming, and support vector machine) for the prediction of ultimate axial strain ɛcu of FRP-confined concrete cylinders. For this purpose, a comprehensive database containing 471 test results on the ultimate conditions of FRP-confined concrete cylinders that was elaborately compiled from 44 published literatures (see Table 1). The proposed models herein can improve the predictability of the compressive behavior of FRP-confined concrete, which is crucial for high precision analytical and numerical analysis of structures made or repaired using this composite material.
Section snippets
Experimental database
The experimental test database used in this study was collected from 44 experimental studies of FRP-confined concrete, as presented in Table 1. The database comprises 471 data points of FRP-confined concrete cylinders at ultimate conditions. The following information is given for each specimen: the type of FRP, with carbon (CFRP), glass (GFRP), and aramid (AFRP); the cylinder diameter (D); the axial compressive strength of unconfined concrete (fco); the confined compressive strength of
Bayesian principle and derivation
In this study, Bayesian probabilistic methods were used to further refine the two existing models for predicting the ultimate axial strain of FRP-confined concrete cylinders. Bayesian theory was employed to conduct statistical inferences on the objective information. For instance, the potential influential parameters associated with the strain enhancement ratio (εcu/εco) were assessed and eliminated to evolve the model [117]. This updating procedure can be defined as:
Modeling the strain enhancement ratio (εcu/εco) using machine learning (ML) algorithms
In this section, three powerful machine learning (ML) algorithms, namely the back-propagation artificial neural network, multi-gene genetic programming, and support vector machine, are employed to predict the strain enhancement ratio (εcu/εco) of FRP-confined concrete cylinders based on the 471 test results presented in Table 1. In order to guarantee the consistency of the results, the 8 input parameters (i.e., D, tf, fco, fcc, εco, flu,a, Ef, and εh,rup) and the only one output parameter εcu/ε
Prediction results and discussions
This section presents the results of two Bayesian posterior models and three different ML models for predicting the ultimate axial strain in FRP-confined concrete. These aforementioned models were implemented and their prediction performances are discussed herein. Purposefully, the statistical metrics (i.e., Mean, RMSE, and CI) are adopted to examine the prediction error of each model. Comparisons of the Bayesian model predictions with respect to the experimental results of the strain
Conclusions and remarks
This study presented some advanced data-driven prediction methods to predict the ultimate axial strain of FRP-confined concrete cylinders. The ultimate axial strain of FRP-confined concrete cylinders can be accurately predicted using the Bayesian probabilistic and machine learning models and the proposed models exhibit superior performance over the existing prediction models. A comprehensive existing experimental dataset, including 471 test results on the ultimate conditions of FRP-confined
CRediT authorship contribution statement
Wenguang Chen: Conceptualization, Formal analysis, Investigation, Writing - original draft. Jinjun Xu: Investigation, Methodology, Visualization, Writing - review & editing, Funding acquisition. Minhao Dong: Investigation, Validation, Supervision. Yong Yu: Investigation, Supervision, Funding acquisition. Mohamed Elchalakani: Conceptualization, Investigation, Writing - review & editing. Fengliang Zhang: Conceptualization, Supervision, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The research reported in this paper was supported by National Natural Science Foundation of China [Project Numbers: 51708289, 51878419and 52008108], Key Research and Development Project of Shaanxi Province [Project Number: 2020SF-392] and Guangdong Basic and Applied Basic Research Foundation [Project Number: 2019A1515110481].
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