Inversion of extinction coefficient and refractive index of variable transparency solid-solid phase change material based on a hybrid model under real climatic conditions

The application of phase change materials (PCMs) in transparent building envelopes has received extensive attention. However, most of the studies have simplified the optical parameters of the PCMs in their models. Because the temperature of PCMs cannot be controlled when using the spectrophotometer, it is difficult to measure the changing trend of optical parameters versus temperature. In this study, an inverse approach was developed for the first time, based on a hybrid model, to fit the accurate function expressions between the extinction coefficient and the refractive index of PCM and temperature. The hybrid model was a combination of experimental data-driven, mathematical models, and multi-objective optimization. Firstly, a test platform of the variable transparency solid–solid PCM (VTSS-PCM) window was constructed and tested last for a year to collect the datasets. Secondly, the photo-thermal coupling model of the window was established, in which the hysteresis and the total internal reflection phenomena were considered. Then, taking the unknown coefficients in the function expressions as decision variables, a bi-objective optimization model was built, based on two error statistics of experimental values and simulated values, and solved by genetic algorithm. Finally, the inversion dataset and validation dataset were used to prove the reliability of the inversion results. The results showed that the refractive index and extinction coefficient of the VTSS-PCM were 1.11 and 25.73 m⁻¹ in the transparent phase, and 5.33 and 152.82 m⁻¹ in the opaque phase. Within the phase change temperature range, the function expressions between the refractive index and extinction coefficient and the temperature were obtained respectively. The verification results showed that the function curves obtained by inversion were reliable. No matter whether the inversion dataset or validation dataset was used as input, the values of RMSE and CV(RMSE) met the ASHRAE Guidelines. The inversion method is meaningful to get the optical parameters of PCMs, to accurately evaluate the performance of PCM-built envelope.