Adisorn Owatsiriwong

**Introduction**

In structural engineering, accurately determining the compressive strength of concrete is crucial for ensuring the safety and durability of a building. Engineers often rely on site investigations, such as rebound hammer tests, to estimate the in-situ strength of concrete. However, interpreting the results of these tests can be challenging, especially when dealing with varying factors like different floor levels and types of structural members.

In this article, we’ll explore how Naive Bayes, a simple yet effective machine learning algorithm, can be applied to classify the compressive strength of concrete based on site investigation data. We’ll walk through a practical example using MATLAB to demonstrate how this approach can be implemented and how it can provide valuable insights into the structural integrity of a building.

**Problem Statement**

Imagine we have collected concrete strength data from a multi-story building. The data includes the following:

• **Floor Level (X1):** Floors 1 through 8

• **Type of Structural Member (X2):** Beam, Column, Slab, or Stair

• **Compressive Strength (fc’) (Y):** Values obtained from rebound hammer tests, ranging between 20 MPa and 30 MPa

Our goal is to classify each measurement into one of the following categories based on the compressive strength:

• **Class A:** fc’ > 28 MPa

• **Class B:** 24 < fc’ ≤ 28 MPa

• **Class C:** fc’ ≤ 24 MPa

**Generating and Preparing Data**

For this example, we’ll generate random data to simulate the site investigation results. Each floor will have 10 samples, with compressive strength values randomly distributed between 20 MPa and 30 MPa. Once the data is generated, we apply the Naive Bayes classifier to predict the class of each data point. The classifier uses the floor level and the type of structural member as features to predict the compressive strength class.

**Visualizing the Classification Results**

Finally, we visualize the decision boundaries and the classification results using a contour plot. The plot helps us understand how the Naive Bayes classifier has segmented the data into different classes based on the input features.

**Conclusion**

In this example, we demonstrated how to apply Naive Bayes classification to estimate the compressive strength of concrete based on site investigation data. By using features such as floor level and member type, we were able to classify the compressive strength into different categories and visualize the decision boundaries.

Naive Bayes is particularly effective in this scenario due to its simplicity and ability to handle small datasets with stable results. As you collect more data over time, you may explore more advanced machine learning techniques, but Naive Bayes provides a solid foundation for initial analysis and classification tasks.