## 5 Conclusions
Sensitivity analysis obtained from the first DOE under steady-state conditions showed that the three most important input parameters were the thermal conductivity of Layer 3 (LWMA), the thermal conductivity of Layer 2 (LWBA25), and the emissivity of the cavities in the block. A multicriteria optimization based on second DOE analysis under transient thermal conditions was used to fit the experimental and numerical results. Thermal flux amplitude and phase Equation were used as an objective function according to Equation (11). From this optimization, the thermal conductivity of Layer 3 (LWMA) and Layer 2 (LWBA25) was obtained and used in FEM numerical models for transient- and steady-state analyses. Numerical, empirical and experimental comparison  
Numerical and empirical thermal transmittance results of steady-state analyses were in good agreement, showing differences of less than 6%. In the transient-state numerical analysis, the temperature amplitude on the indoor face of the wall was lower than the experimental amplitude. Thus, the numerical decrement factor was lower than the value obtained experimentally or empirically. More research is necessary to better understand this effect in the transient state. In this sense, numerical FEM models could be solved with a different time discretization (smaller time steps and lower heat tolerance). In addition, dynamic heat transfer phenomena inside cavities, specifically convection and radiation, must be deeply studied. Numerical and experimental time lags showed good agreement, with a difference of less than 3% between values. However, results of empirical calculations presented lower values. This study presents a new hybrid numerical and experimental methodology based on a double DOE analyses including a multicriteria optimization over a FEM two-dimensional multi-layer wall. With the help of experimental tests, it is possible to build an accurate numerical model able to predict the steady-state and dynamic performance of walls made of porous materials, including air cavities. Furthermore, as shown in previous works [19; 20; 33; 34], the moisture content in porous materials has a great influence on the thermal performance of this type of lightweight concrete wall. The thermal conductivity is related to the characteristics of the pore structure and internal moisture distribution. Future studies should focus on the development of coupled numerical models, taking into account hygothermal transport [19] and dynamic heat transfer within cavities. They could also analyze other wall compositions in order to validate the empirical formulation indicated in the Standard [3]. Finally, the numerical model developed in this work is an original contribution and a useful tool to simulate the steady-state and dynamic response of multi-layer building walls under different environmental conditions. Conceptualization, J.J.d.C.-D. and F.P.A.-R.; methodology, J.J.d.C.-D.; validation, F.P.A.-R., M.A.-M. and J.E.M.-M.; formal analysis, M.A.-M.; investigation, F.P.A.-R. and J.E.M.-M.; resources, J.J.d.C.-D.; data curation, F.P.A.-R.; writing--original draft preparation, J.J.d.C.-D.; writing--review and editing, M.A.-M. and J.E.M.-M.; supervision, J.J.d.C.-D.; project administration, F.P.A.-R.; funding acquisition, J.J.d.C.-D. and F.P.A.-R. All authors have read and agreed to the published version of the manuscript. This research was partially funded by the Spanish Ministry of Science, Innovation and Universities and the FICYT, both co-financed with FEDER funds under the Research Projects PGC2018-098459-B-I00 and FC-GRUPIN-IDI/2018/000221. Not applicable. Data availability StatementData are available on request. Authors thank the manufacturer WEBER Saint-Gobain for their technical support and materials provided, and to Swanson Analysis Inc. for the use of ANSYS University Research program. The authors declare no conflict of interest.