## 2 Materials and Methods
### Dataset and Related Results  
The dataset consisted of 640 samples from four different types of LWAC that were intentionally segregated by compacting them for different vibration times, following the experimental procedure explained in [6] (see Table 1). To manufacture the samples, each of the four types of concrete was mixed in a vertical shaft, and cylindrical moulds (with diameter 150 mm and height 300 mm) were filled and compacted using a needle vibrator (for 0, 10, 20, 40 and 80 s). The laying time was also taken into account in order to simulate  
Figure 7: Ranking a set of models. (**a**) Discrete ranking; (**b**) continuous ranking. the laying of LWAC under real conditions, as fresh concrete loses its workability over time. The mixture proportions of each type of LWAC were computed according to the Fanjul method [71]. A total of 160 cylinders were manufactured. The type of LWAC depended on both the type of LWA used to produce the concrete and the target density of the produced concrete (1700 or 1900 kg/m\({}^{3}\)). Two types of LWA were considered, consisting of expanded clay (from the company Saint-Gobain) with different particle densities, the first with a density of 482 kg/m\({}^{3}\) and a granulometric fraction with sizes 6/10, and the second with a density of 1019 kg/m\({}^{3}\) and fraction 4/10. The lighter LWA has a high-porosity structure (36.6% of water absorption at 24 h) and is typically used for ultra-lightweight concrete applications, whereas the denser LWA (12.20% of water absorption at 24 h) is mainly used for structural concrete applications. Two cores of diameter 50 mm were extracted from each LWAC cylinder produced in this way and were cut into four 70 mm lengths. The variables considered in this problem were the theoretical density of the concrete according to the Fanjul method [71], the particle density of the LWA, the laying time of the concrete, the vibration time, the dry density of the specimen obtained experimentally after 28 days, the \(P\)-wave velocity and the segregation index. The segregation index used in this work was based on the \(P\)-wave velocities and was proposed in [6] as an alternative to the segregation index put forward by [PERSON] [12] for the case where several cores from a concrete specimen are considered rather than one complete specimen. To obtain the segregation index based on the \(P\)-wave velocity, the longitudinal velocity (\(V_{p}\)) of each core was determined using 250 kHz transducers. The mean value of the \(P\)-wave velocity of an LWAC was then computed based on the four \(P\)-wave velocities of the cores (\(V_{pm}\)), considering the position of the core in the original specimen (\(V_{pSi}\)). The segregation index was computed for each core as the ratio between the \(P\)-wave velocity of the core (\(V_{pSi}\)) and the mean \(P\)-wave velocity of the four cores of the corresponding LWAC cylinder (\(V_{pm}\)) [6]. To determine the influence of segregation, the compressive strength of each core sample was obtained using a 200 kN machine with a loading rate of 0.25 MPa/s. A preliminary statistical study showed significant differences in compressive strength depending on the type of LWAC. As expected, the higher the LWA particle density or LWAC density, the greater the compressive strength [19]. Table 2 summarises the statistical characteristics of the variables involved in this problem: minimum (min), maximum (max), mean, median, first quartile (\(Q_{1}\)) and third quartile (\(Q_{3}\)). \begin{table}
\begin{tabular}{c c c} \hline \hline
**LWAC Type** & **LWA Particle Density (kg/m\({}^{3}\))** & **LWAC Fixed Density (kg/m\({}^{3}\))** \\ \hline
1 & 482 & 1700 \\
2 & 482 & 1900 \\
3 & 1019 & 1700 \\
4 & 1019 & 1900 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of types of LWAC. “Adapted with permission from Ref. [19]. Copyright 2019, Elsevier”.