Assessment of artificial neural network and genetic programming as predictive tools
Introduction
Empirical modeling and formulation by soft computing techniques remain highly-researched topics, especially for engineering modeling [25]. Soft computing-based models differ from conventional models that are based on engineering principles (e.g., elasticity and plasticity theories), as they are based on experimental data rather than theoretical derivations. Soft computing-based models are usually complex and often cannot build an explicit formula. Therefore, they are most appropriate for use as a part of a computer program, limiting their applicability.
The most well-known soft computing predictive tool is the artificial neural network (ANN), which has been used successfully in structural engineering modeling (e.g. [36]. ANNs are inspired by biological neural networks [30]. Although ANNs typically build “black box” models, explicit formulas can be derived for a trained ANN model. A derivative-free optimization algorithm should be added to the training process of the ANN algorithm to avoid local minima, which lead to false convergence of the ANN model [38]. Some researchers have already combined ANN and global optimization algorithms to improve ANN efficiency (e.g., [41], [46].
Another robust soft computing technique for modeling is genetic programming (GP), which is inspired by the principle of Darwinian natural selection. The machine code generated by GP can be translated as a mathematical formula, which makes it very suitable for mathematical modeling. GPs, especially new variants such as gene expression programming (GEP), have been successfully applied to several engineering problems, particularly in structural engineering (e.g., [21].
In this study, the performance of ANN and GP techniques are evaluated based on several criteria, including over-fitting potential, parametric study results, and simplicity of the generated formulas. To demonstrate this performance comparison, the punching shear strength of reinforced concrete slabs is modeled using a comprehensive database containing 241 experimental test results. We present the explicit slab strength prediction formulas from a well-trained ANN and from a proposed GP model. A subsequent parametric study was carried out to evaluate the trends of the ANN and GP models with respect to each parameter. The results show that although the ANN model outperforms the GP model in terms of error and correlation, it tends to be overfitted (with respect to design code values) due to its complexity. The GP models tend to have acceptable error and correlation characteristics while performing well in the parametric studies (with respect to the physics of the problem as verified by the design codes).
Section snippets
Methodologies: Soft computing techniques
Soft computing includes, but is not limited to, evolutionary algorithms, ANNs, support vector machine and fuzzy logic. Soft computing predictive tools have wide-ranging applications and are often used to model the nonlinear relationship between input parameters and output value(s). Advances in computer hardware have made soft computing techniques more efficient. In addition, soft computing techniques may be used to model problems where conventional approaches, such as regression analysis, fail
Case study: Punching shear strength of concrete slabs
Evaluation of the punching shear strength of concrete slabs has traditionally been a difficult task. Several estimates of punching shear strength have been developed, indicating that punching shear strength is mainly influenced by several important parameters: column side dimension (c), effective depth to the center of the tensile reinforcement (d), concrete compressive strength (f́c), and flexural reinforcement ratio (ρ). These properties of an RC slab are indicated schematically in Fig. 5.
Model validity
Model validity and accuracy can be determined based on high values of correlation (R) and low values of error (e.g., RRMSE) [45]. According to these criteria, the proposed ANN and GP models, which have high R values and low RRMSE values (as indicated in Table 5, Table 7) predict the punching shear capacity with a high degree of accuracy. The performance of the models on the training, validation, and testing subsets reveals that they have good predictive ability. Moreover, Golbraikh and Tropsha
Conclusions
In this study, two established soft computing techniques, a hybrid artificial neural network (ANN) and a robust variant of genetic programming (GP), were utilized to assess an engineering modeling case, predicting punching shear strength of RC slabs. Two different formulations were developed for the punching shear prediction. The models were verified based on several existing external model validation criteria. The GP- and ANN-based correlations were benchmarked against five code models for
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