Linear genetic programming for shear strength prediction of reinforced concrete beams without stirrups
Graphical abstract
Introduction
Although several research programs have been conducted to predict the shear capacity of concrete (e.g. [1]), there is still no clear expression to predict the shear failure mechanisms of concrete elements. Most of the available shear design expressions have different forms and do not provide a consistent factor of safety against shear failure. Thus, the behavior of concrete beam has been extensively investigated during the last three decades. Numerous theoretical models have been established in recent years to investigate the interaction between several forces including axial, shear, bending, and torsion [2], [3].
Recently, application of machine learning has attracted much attention for solving structural engineering problems. The machine learning systems are powerful tools for design of computer programs. They automatically learn from experience and extract various discriminators [4]. Artificial neural networks (ANNs) are the most widely used branch of machine learning. There have been some researches focusing on the application of ANNs to the evaluation of the shear strength of reinforced concrete beams without reinforcement. Recently, Choi et al. [5] used another machine learning method, namely fuzzy logic (FL) for the modeling of the shear strength of slender reinforced concrete beams. Although ANNs and FL are successful in prediction, they are not usually able to produce practical prediction equations. Furthermore, for the ANN-based modeling, the structure of the network should be identified a priori. Besides, determination of the fuzzy rules in FL is a difficult task. These methods are mostly appropriate to be used as a part of a computer program [6]. Genetic programming (GP) [7] is a developing subarea of the machine learning techniques. GP is known as an extension genetic algorithm (GA) where the solutions are computer programs rather than fixed length binary strings [6]. Classical (standard) GP and its variants have been recently employed to derive greatly simplified formulations for structural engineering problems and especially concrete structures modeling (e.g. [8], [9], [10]). Linear genetic programming (LGP) [11] is a new subset of GP. LGP operates on computer programs that are represented as linear sequences of instructions of an imperative programming language [6]. In contrast with ANNs, GA and classical GP, application of LGP in the field of civil engineering is quite new and restricted to a few areas [6], [12], [13], [14], [15], [16]. It is worth mentioning that classical GP and new variants of GP have been, respectively, used by Ashour et al. [17] and Gandomi et al. [18], [19] to predict the load capacity of RC deep beams. Gandomi et al. [20] have applied LGP to the modeling of fibrous RC beams. Recently, Kara [21] employed GP for the prediction of the shear strength of FRP-reinforced concrete beams without stirrups upon a limited number of experimental test results. Moreover, Pérez et al. [22] applied GP to the optimal adjustment of EC-2 shear formulation for RC beams without web reinforcement.
However, applications of the GP-based approaches to directly obtain a simple formula to predict the shear strength of RC beams are conspicuous by its absence. There are approaches which present simple formulation, but based on other advanced approaches [23]. The main purpose of this study is to utilize the LGP technique to build a simple predictive model for the shear strength of RC beams without stirrups. The shear strength was formulated in terms of shear span to depth ratio, concrete cylinder strength at date of testing, amount of longitudinal reinforcement, lever arm and maximum specified size of coarse aggregate. The predictions made by models were further compared with those provided by several well-known building codes.
Section snippets
Machine learning
Machine learning is a branch of artificial intelligence essentially inspired from biological learning. The machine learning approach deals with the design of computer models that are able to automatically learn with experience [4], [24]. The machine learning methods extract knowledge and complex patterns from machine readable data [4]. The major focus of the machine learning research is on data mining problems, difficult-to-program applications, and software applications customizing to the
Formulation of the shear strength of RC beams without stirrups
To develop the LGP model, the shear strength of RC beams without stirrups was considered to be a function of the following influencing parameters:where vu (MPa) is the shear strength (vu = Vu/(bwd)); Vu (kN) is the ultimate shear force; bw (mm) is the web width; d (mm) is the effective depth; Z is the mechanic arm (Z = 0.9d); f′c (MPa) is the 28-day concrete compressive strength; a/d is the shear span to depth ratio; (%) is the amount of longitudinal reinforcement (ρ = A/bwd); A is
Parametric analyses
For verification of the LGP-based prediction model, a parametric analysis was performed in this study. The parametric analysis investigates the response of the predicted shear strength from the LGP model to a set of hypothetical input data generated over the ranges of the minimum and maximum data used for the model training. The methodology is based on the change of only one input variable at a time while the other variables are kept constant at the average values of their entire data sets. A
Model validity
Smith [53] suggested the following criteria for judging performance of a model:
- •
if a model gives |R| > 0.8, a strong correlation exists between the predicted and measured values.
- •
if a model gives 0.2 < |R| < 0.8 a correlation exists between the predicted and measured values.
- •
if a model gives |R| < 0.2, a weak correlation exists between the predicted and measured values.
In all cases, the error values (e.g., MAE) should be at the minimum [54]. The model can therefore be judged as very good. Based on the
Comparative study
A comparative study was conducted to benchmark the proposed LGP model against several codes of practice including ACI 446 [58], ACI 318 [59], ASCE-ACI 445 [60], CEB-FIB [61], CSA [62], EC-2 [63], NZS [64] and ICC [65]. In order to evaluate the capabilities of the models, the RMSE, MAE and R performance measures were used. The prediction performance of different models on for entire database is summarized in Table 6. Besides, Fig. 8 visualizes the histogram plots of the ratio of the experimental
Conclusions
The LGP technique was utilized to formulate the strength capacity of RC beams. A reliable database from the literature was used for developing the model. The proposed design equation gives reliable estimations of the strength capacity of RC beams without stirrups. The validity of the model was tested for a part of test results beyond the training data domain. Furthermore, the derived prediction model efficiently satisfies the conditions of different criteria considered for its external
References (66)
- et al.
Shear strength of slender reinforced concrete beams without web reinforcement: a model using fuzzy set theory
Eng. Struct.
(2009) - et al.
Linear genetic programming for prediction of circular pile scour
Ocean Eng.
(2009) - et al.
Energy-based models for assessment of soil liquefaction
Geosci. Front.
(2012) - et al.
Flow discharge prediction in compound channels using linear genetic programming
J. Hydrol.
(2012) - et al.
Numerical modeling of concrete strength under multiaxial confinement pressures using linear genetic programming
Autom. Constr.
(2013) - et al.
Empirical modelling of shear strength of RC deep beams by genetic programming
Comput. Struct.
(2003) - et al.
An empirical model for shear capacity of RC deep beams using genetic-simulated annealing
Arch. Civil Mech. Eng.
(2013) Prediction of shear strength of FRP-reinforced concrete beams without stirrups based on genetic programming
Adv. Eng. Softw.
(2011)- et al.
Optimal adjustment of EC-2 shear formulation for concrete elements without web reinforcement using genetic programming
Eng. Struct.
(2010) - et al.
Optimization of existing equations using a new Genetic Programming algorithm: application to the shear strength of reinforced concrete beams
Adv. Eng. Softw.
(2012)
Studies of the relationship between petrography and grindability for Kentucky coals using artificial neural network
Int. J. Coal Geol.
Shear design procedure for reinforced concrete beams using artificial neural networks. Part I: beams without stirrups
Eng. Struct.
Formulation of flow number of asphalt mixes using a hybrid computational method
Constr. Build. Mater.
Beware of q2
J. Mol. Graph. Model.
Designing against size effect on shear strength of reinforced concrete beams without stirrups
J. Struct. Eng. ASCE
Limit Analysis and Concrete Plasticity
Reinforced Concrete: Mechanics and Design
New design equations for assessment of load carrying capacity of CSB: a machine learning approach
Neural Comput. Appl.
A robust data mining approach for formulation of geotechnical engineering systems
Eng. Comput.
Genetic Programming: On the Programming of Computers by Means of Natural Selection
New formulation for compressive strength of CFRP confined concrete cylinders using linear genetic programming
Mater. Struct.
A novel approach to strength modeling of concrete under triaxial compression
J. Mater. Civil Eng. ASCE
A new multi-gene genetic programming approach to nonlinear system modeling. Part I: materials and structural engineering problems
Neural Comput. Appl.
Linear Genetic Programming
Comparison between linear genetic programming and M5 tree models to predict flow discharge in compound channels
Neural Comput. Appl.
An evolutionary approach for modeling of shear strength of RC deep beams
Mater. Struct.
Nonlinear modeling of shear strength of SFRC beams using linear genetic programming
Struct. Eng. Mech.
Does machine learning really work?
AI Mag.
Improving Intrusion Detection Systems through Machine Learning. Technical Report Series no. 07-02
On the origin of species by means of natural selection or the preservation of favoured races in the struggle for life
A comparison of linear genetic programming and neural networks in medical data mining
IEEE Trans. Evol. Comput.
Where is shear reinforcement required? Review of research results and design procedures
ACI Struct. J.
Shear strength analysis and prediction for reinforced concrete beams without stirrups
J. Struct. Eng. ASCE
Cited by (70)
Prediction model of asphalt emulsion evaporation rate based on CFD simulation and genetic programming-based symbolic regression
2024, Construction and Building MaterialsA predictive mimicker for mechanical properties of eco-efficient and sustainable bricks incorporating waste glass using machine learning
2023, Case Studies in Construction MaterialsPredictive models for concrete properties using machine learning and deep learning approaches: A review
2023, Journal of Building EngineeringCitation Excerpt :Kara [220] also reported satisfactory results using the GEP model in its study on predicting the shear strength of FRP-reinforced concrete beams. Gandomi et al. [221,222] reported the GEP model's high accuracy in predicting the shear strength of reinforced concrete beams. Also, a comparative study of the GEP model with the models derived from the ACI, EC2, CSA, and NZS regulations shows the superiority of the GEP model.