## 3 Results and Discussion
### Partial Least Square Regression Prediction Analysis of SSCFC's Fluidity and Compressive Strength
#### 3.5.3. PLSR Prediction Equation and Analysis  
Leveraging orthogonal experimental results, a PLSR model with two latent variables was developed to quantify interactions among W/C ratio, SS substitution ratio, ceramsite substitution ratio, and concrete performance metrics (fluidity, 7d/14d/28d cube compressive strengths). The mathematical formulations of the PLSR model are as follows:  
\[Y_{1}=0.440X_{1}-0.777X_{2}+0.301X_{3} \tag{17}\]  
\[Y_{2}=-0.804X_{1}-0.065X_{2}+0.045X_{3} \tag{18}\]  
\[Y_{3}=-0.801X_{1}-0.072X_{2}+0.048X_{3} \tag{19}\]  
\[Y_{4}=-0.804X_{1}-0.044X_{2}+0.037X_{3} \tag{20}\]  
where \(Y_{1}\), \(Y_{2}\), \(Y_{3}\), and \(Y_{4}\) correspond to fluidity, 7d compressive strength, 14d compressive strength, and 28d compressive strength, respectively; \(X_{1}\), \(X_{2}\), and \(X_{3}\) represent the W/C ratio, SS substitution ratio, and ceramsite substitution ratio.  
Table 13 displays both unstandardized coefficients and standardized coefficients, providing a framework to dissect parameter-specific influence mechanisms on material properties. Quantitative prediction equations for concrete fluidity and compressive strength indicate that increasing the W/C ratio significantly improves flowability, whereas elevated steel slag substitution rates noticeably suppress fluidity, with ceramsite replacement rates exhibiting a moderate enhancement effect. This phenomenon is consistent with material properties: an increased W/C ratio liberates additional free water, while SS powder's rough particle surfaces and porous structure elevate paste viscosity, consequently reducing fluidity [78]. Conversely, ceramsite's spherical particles enhance aggregate gradation and exert lubrication effects [79].  
Within the compressive strength model, the W/C ratio exhibits persistent negative effects across all curing ages, demonstrating substantially stronger influence compared to other variables. For the 28d compressive strength, the fitted prediction equation validates the W/C ratio's dominant control over compactness and hydration product formation. It is noteworthy that the SS substitution rate coefficient exhibits a marginally negative value,  
Figure 13. Histogram of projected importance indicators (VIP).  
potentially linked to its low early-stage hydration activity, leading to negligible strength contribution during initial curing periods. The ceramsite substitution ratio (X\({}_{3}\)) consistently shows slightly positive coefficients (+0.037 to +0.048) in all strength equations. The sustained curing effect from its internal pores facilitates prolonged hydration of cementitious materials, partially mitigating the adverse effects of lightweight aggregates on density.  
A longitudinal analysis of variable contributions demonstrates the W/C ratio's predominantly dominant regulatory effect, evidenced by its standardized coefficients in compressive strength models being substantially higher than those of steel slag and ceramsite. This observation is consistent with previous VIP analysis results. For practical applications, reducing the W/C ratio combined with admixtures can mitigate fluidity loss, whereas optimizing the steel slag substitution rates balances early-stage adverse effects with latent long-term reactivity. Strategic utilization of ceramsite replacement rates enables simultaneous achievement of lightweight properties and long-term micro-curing benefits. The model establishes a quantitative foundation for SSCFC proportioning design. This dual principal component model captures nonlinear relationships among variables, circumventing multicollinearity issues while maintaining the physical meaning of critical parameters, ultimately providing a quantifiable and interpretable mathematical framework for concrete formulation design.