Metaheuristic-Optimized Machine Learning Models for Predicting Shear Strength of Circular Concrete-Filled Steel Tubes with SHAP-Based and PDP Interpretability

Imagine you are building a skyscraper or a massive bridge. To make these giants stand tall against wind, earthquakes, and heavy traffic, engineers often use a clever trick: they pour concrete inside a hollow steel tube. Think of it like a chocolate-covered marshmallow, but instead of a soft treat, you have a super-strong steel shell hugging a concrete core. The steel stops the concrete from cracking, and the concrete stops the steel from buckling, creating a super-material that can hold up incredible weight. This is called a Concrete-Filled Steel Tube (CFST).

However, there is a sneaky danger in these structures. While they are great at holding up heavy loads from above, they can suddenly snap sideways if pushed too hard from the side. This is called "shear failure," and it happens so fast that buildings don't get a chance to warn you before they crumble. For decades, engineers have tried to predict exactly how much force these tubes can take before snapping using complex math formulas. But these old formulas are like trying to guess the weather by looking at a single cloud; they often miss the complicated ways the steel and concrete interact. That's why scientists are turning to "machine learning"—computer programs that learn from past experiments to find patterns humans might miss. The big question is: Can a computer learn the secret recipe for a safe, unbreakable tube better than the old math books?

This paper dives into that question by teaching four different computer "brains" to predict the shear strength of circular concrete-filled steel tubes. The researchers gathered data from 230 past experiments, like a chef collecting 230 different recipes for the perfect cake. They then fed this data into four smart models: two that use a method called "Particle Swarm Optimization" (which works like a flock of birds searching for the best food source) and two that use "Bayesian Optimization" (which acts like a detective making educated guesses to solve a mystery). These models were paired with two different learning styles: "Random Forest" (which asks many questions and takes an average answer) and "CatBoost" (a super-fast learner that is great at handling messy data).

The results were exciting. The computer models didn't just guess; they learned the patterns with incredible precision. The best performer was a combination called "BO-Cat" (Bayesian Optimization with CatBoost). In the testing phase, where the model faced new data it hadn't seen before, it got an accuracy score (R²) of 0.9817. To put that in perspective, if the perfect score is 1.0, this model was almost spot-on. The second-best model, "PSO-Cat," also did a fantastic job with a score of 0.9874. The paper explicitly shows that these smart models are far better than the traditional, old-school math formulas, which often struggle with the complex, non-linear dance between the steel and the concrete.

But the researchers didn't just want a "black box" that gave answers without explaining why. They wanted to know why the computer made those predictions. Using a tool called SHAP (which acts like a spotlight, highlighting which ingredients mattered most), they discovered that the most important factors were the size of the concrete core and the size of the steel tube. Interestingly, the ratio of the tube's length to its width also played a huge role, while the specific strength of the steel or concrete mattered less than you might think. The team even built a simple "Graphical User Interface" (a friendly app-like tool) so that any engineer could type in their numbers and instantly get a safe prediction, complete with an explanation of what drove that number.

In short, this study suggests that by combining smart search algorithms with powerful learning models, we can predict the safety of these critical building blocks much more accurately than before. The paper confirms that the new models are reliable, with the BO-Cat and PSO-Cat models proving to be the most trustworthy guides for designing safer, stronger structures. While the paper notes that more data and different types of tubes could make these models even better in the future, the current findings offer a powerful new tool for keeping our bridges and buildings standing tall.