## 6 Model Results
### Partial Dependence Analysis  
A Partial Dependence Plot (PDP) is a data visualization tool that illustrates the marginal effect of a feature on the predicted outcome of a machine learning model. It essentially displays the variation in prediction of the model, on average, as a specific feature changes, while keeping other features constant. The concept of \"partial\" is derived from the process in which the plot averages the predictions of the model across all instances in the dataset, thereby \"partially\" factoring in the impact of other variables. The plot is constructed by calculating the model's prediction for several fixed values of a selected feature, while maintaining constant values for other features. These predictions are then averaged over all instances and plotted as a function of the fixed values of the chosen feature. PDPs offer insights into the interaction between features and the target variable and can indicate whether these relationships are linear, monotonic, or more complex in nature. The slope of the PDP can be interpreted to understand the influence of the feature on the prediction: a steep slope indicates strong influence, while a flat slope suggests little impact. Figure 7: Assessment indicators for different models. Looking at the data of PDP plot in Figure 9, the CS seems to peak around a W/B ratio of 0.25, and then begins to decline. This might be because, at lower W/B ratios, there is insufficient water for the hydration process, which would limit the CS. At a W/B ratio of 0.25, there may be an optimal balance of water and binder for the hydration process, which maximizes the CS. As the W/B ratio increases beyond this point, the excess in water could create larger capillary pores as it evaporates, which would weaken the structure and reduce the CS. There is a slight increase in CS again around the W/B ratio of 0.38-0.4, which may be due to specific properties of the mixture used, such as the presence of certain additives or the particle-size distribution. However, the general trend is that the CS decreases with increasing W/B ratio. This is consistent with the known behavior of cement-based materials, where a higher W/B ratio typically leads to a lower CS due to the increased porosity [60]. As the age at testing increases, so does the CS. This is in line with the understood property of concrete that it gains strength over time due to the ongoing hydration process of the cement, which progressively forms more crystalline hydrate products responsible for concrete's strength. Looking at the model's predictions, at 7 days, the early stage of concrete curing, the average CS is approximately 28.07 MPa. At 28 days, a common industry benchmark, the average CS increases to about 37.20 MPa, reflecting the designed strength of standard concrete mixes. The average CS rises to about 38.99 MPa at 56 days and 44.10 MPa at 90 days, showing that the concrete continues to cure and gain strength, albeit at a slower pace. These numbers align with the known behavior of concrete, which strengthens over time due to the continued hydration process. However, the exact rates and values can differ based on factors such as the specific concrete mix used and the curing conditions. Figure 8: A Taylor chart illustrating different models used for predicting CS. When interpreting these numbers, it is evident that at 0% GGBFS, where only regular cement is used, the average predicted CS is approximately 39.29 MPa. As the percentage of GGBFS increases to 25%, replacing regular cement, there is a slight decrease in the predicted average CS to around 35.80 MPa. This trend of decreasing CS continues as the GGBFS percentage increases. At 100% GGBFS, the lowest average predicted CS of about 27.52 MPa is observed. These findings suggest that increasing the GGBFS proportion in the binder results in a decrease in the immediate average predicted CS of concrete, as per the model's predictions. This could be attributed to the slower reaction rate of GGBFS compared to regular cement, leading to slower immediate strength gains.