Symbolic Regression for Strength Prediction of Eccentrically Loaded Concrete-Filled Steel Tubular Columns
Concrete-filled steel tubecolumns are widely recognized for their impressive strength and resilience under extreme loading conditions. These composite structures, consisting of steel tubes filled with concrete, offer increased load-bearing capacity, structural efficiency, and enhanced ductility compared to traditional reinforced concrete columns. CFST columns are frequently used in high-rise buildings, long-span bridges, and seismic-resistant structures, making their accurate strength prediction crucial for safe and effective design.
The strength of CFST columns, particularly under eccentric loading, has been studied extensively, with numerous models proposed to predict their performance. However, existing methods often struggle to balance predictive accuracy with interpretability—a critical factor for practical engineering applications. This study bridges that gap by introducing a symbolic regression model, which enhances code-based strength predictions for both circular and rectangular CFST columns under eccentric loading.
From Code Standards to Symbolic Regression
Traditionally, the design of CFST columns relies on structural design codes such as EC4 and AISC360. While these codes offer reliable guidelines, they may not always provide the most accurate predictions for complex loading scenarios, such as eccentric loads. In contrast, data-driven machine learning methods, though highly accurate, often lack the interpretability required by engineers to understand the underlying physical principles.
To address these challenges, this study develops a code-based symbolic regression model that merges the best of both worlds, code-based principles and machine learning techniques. The model leverages 464 tests for CCFST columns and 313 tests for RCFST columns under eccentric loading, ensuring a robust and comprehensive approach. The symbolic regression technique refines existing code equations, generating mathematically interpretable expressions that are aligned with the mechanical behavior of CFST columns.
Why Symbolic Regression?
Symbolic regression is a form of interpretable machine learning that evolves mathematical expressions to best fit a given dataset. Unlike traditional machine learning models, which often function as "black boxes," symbolic regression provides equations that are not only accurate but also transparent and grounded in physical principles.
The main advantage of SR is its ability to improve the accuracy of existing design equations from codes while retaining interpretability. The resulting formulas are both computationally efficient and physically meaningful, making them directly applicable in practical engineering scenarios. This hybrid approach addresses several limitations of traditional methods:
1. Improved accuracy in strength prediction for eccentric CFST columns.
2. Interpretability, allowing engineers to easily apply the models in design calculations.
3. Physical consistency, ensuring that the equations are grounded in real-world structural behavior.
4. Reduced computational demand compared to more complex methods like finite element analysis.
Comprehensive Experimental Database and Calibration
The symbolic regression model was calibrated using a detailed experimental database of 464 CCFST columns and 313 RCFST columns, covering a wide range of geometric configurations, material properties (concrete and steel), and eccentric loading conditions. This extensive dataset allowed the researchers to create a highly generalizable model that can be applied to various types of CFST columns.
To ensure the robustness of the model, its predictions were evaluated using several metrics and compared against other machine learning methods, including Gaussian Process Regression (GPR), Support Vector Regression (SVR), XGBoost (XGB), CatBoost (CATB), Random Forest (RF), and LightGBM (LGBM). In addition, the performance of the C-SR model was benchmarked against the established EC4 and AISC360 standards, demonstrating its accuracy and reliability.
Enhanced Predictions with SR: Results and Evaluation
The performance of the C-SR model was evaluated by comparing the predicted strength values with experimental data. The model showed excellent results, with mean prediction-to-actual ratios of 1.006 for CCFSTs and 0.997 for RCFSTs. The coefficient of variation (CoV) values for CCFSTs and RCFSTs were 0.117 and 0.098, respectively, indicating high prediction accuracy and low variability.
Furthermore, the C-SR model was found to outperform traditional machine learning methods in terms of both prediction accuracy and interpretability. The use of symbolic regression also enabled the generation of explainable mathematical expressions, offering valuable insights into the mechanics of CFST column behavior under eccentric loading.
Practical Implications and Future Applications
The proposed C-SR model offers significant advantages over traditional methods for strength prediction of CFST columns under eccentric loading. Its ability to generate interpretable, physically consistent equations makes it a practical tool for engineers involved in the design and analysis of CFST columns. Additionally, the model’s high accuracy and computational efficiency make it a viable alternative to more complex approaches, such as finite element analysis (FEA), which can be computationally intensive and time-consuming.
This hybrid approach, combining the strengths of code-based standards with the predictive power of symbolic regression, marks a significant advancement in the field of structural engineering. It offers reliable, user-friendly solutions for designing and analyzing CFST columns, particularly in challenging loading scenarios like eccentric loads.
As the use of CFST columns continues to grow in modern infrastructure, the C-SR model has the potential to be widely adopted in practical engineering applications, offering both enhanced prediction capabilities and ease of use for structural engineers.
