Modelo multivariado predictivo sobre la resistencia del concreto

Abstract

This monograph presents a study on the implementation of a multivariate regression model to predict the 28-day compressive strength of concrete, using MINITAB software and a pre-adjustment model through Principal Component Analysis (PCA). The primary objective is to identify the contribution of various predictor variables to the compressive strength of concrete, improving model accuracy and reducing multicollinearity issues. Initially, the relationships and behaviors of the variables are identified in a statistically traditional manner, conducting one-to-one relationships to be compared with the existing correlations among all these variables. Additionally, this approach includes response surface and contour plots that reveal the optimal values and behaviors of the variables in relation to compressive strength, yielding comparable results. A multivariate regression model is then developed using all the original variables from the dataset, which captures the general relationships between these variables and the compressive strength of concrete. However, this approach faces significant challenges due to the high correlation among the predictor variables, complicating interpretation and reducing model accuracy. To address these limitations, PCA is applied as an adjustment method, achieving effective dimensionality reduction and model simplification. PCA allows for the identification of linear combinations of variables that explain most of the variability in the data, highlighting the 3 importance of factors such as the water/cement ratio (W/C), Maximum Aggregate Size (MAS), and plasticizing admixtures. The results show that the model adjusted using PCA not only improves the interpretability and robustness of the model but also provides an effective tool for predicting concrete compressive strength, in contrast to multivariate regression models that encompass greater variability but suffer from multicollinearity issues and difficulty in accommodating new data. This approach can serve as a foundation for future research and practical applications in the field of civil engineering, offering a solid method for optimizing concrete mix design.