# Prediction of Compressive Strength Loss of Normal Concrete after Exposure to High Temperature
## 4 Results and Discussion  
### Modeling  
Regressions of the BP, PSO-BP and RF models are shown in Figures 6-8, respectively. In the figures, the X (Target) and Y (Output) axis represent the data (P) reported in the literature and those obtained via modeling, respectively. The dotted line refers to the output value equal to the target value, and the correlation coefficient R equals 1. The real line is the regression of the real relation between output value and target value. The closer the real line is to the dotted line, the higher the R-value. From Figure 6, it can be seen that there is a good correlation between the data samples no matter whether training, testing, validation or the whole stage of the BP modeling  
A shorter maintenance duration at the high temperatures (comparison between mixes two and five) could protect the specimens from worse thermal damage [94]; therefore, lower strength loss was observed. It is usually considered that water cooling will cause thermal stress distributed in concrete to lower its strength [45]. It was found that the shrinkage of the cement matrix with temperature could compensate for such stress [95]; therefore, in this paper, it was observed that water cooling had a less significant influence on the strength loss (comparison between mixes two and six). After cooling, resting for a certain duration before crushing allowed parts of the products of concrete, which were decomposed thermally, to rehydrate to make the concrete dense [96]. Consequently, it was found that the specimens with a one-day-resting duration showed less strength loss.  
Simultaneously, the material and heating-related parameters used in the experimental work were put in the models to run a prediction, and the results predicted are reported in Table 6 as well. The error between the results measured and predicted (100% \(\times\) | predicted value-measured value / measured value) is illustrated in Figure 11, and the statistic of the errors is summarized in Table 7. From the results, it can be seen that although in all cases the maximum error values were relatively high, i.e., more than 30%, the mean values of less than 10% were still at a low level, which could meet the requirement of engineering practice. Furthermore, concrete mix one always yielded the largest error value in all three predictions. A possible reason for that could be due to a relatively low W/B of 0.3 being used in mix one, and the temperature was not high enough, i.e., 200 \({}^{\circ}\)C; therefore, the data under such circumstances is not adequate in the literature to run sufficient training during modeling. Nevertheless, compared to the BP model, the PSO-BP and the RF models indeed improved the feasibility of the prediction as both the error range and the average error were reduced dramatically.  
Due to the sufficient feasibility of the prediction, it is suggested that in practice, engineers could input relevant parameters into the models to yield a residual strength instantly, which could also avoid secondary damage to the post-fire building caused by destructive testing, and the results would be objective and more reliable.  
Figure 7: Correlation of PSO-BP modeling.