Integrating Machine Learning and the Finite Element Method for Assessing Stiffness Degradation in Photovoltaic Modules

This study introduces a novel machine learning (ML) method utilizing a stacked auto-encoder network to predict stiffness degradation in photovoltaic (PV) modules with pre-existing cracks. The input data for the training process was derived from numerical simulations, ensuring a comprehensive representation of module behavior under various conditions. The findings highlight the robust predictive capability of the model, as evidenced by its impressive R 2 value of 0.961 and notably low root mean square error (RMSE) of 4.02%. These metrics significantly outperform those of other conventional methods, including the artificial neural network with R 2 of 0.905 and RMSE of 9.43%, the space vector machine with R 2 of 0.827 and RMSE of 17.93%, and the random forest (RF) with R 2 of 0.899 and RMSE of 11.02%. Moreover, the findings suggest that the predictive dynamics of degradation are affected by the varying weight functions of different input parameters, such as climate temperature (CT), grain size (GS), material effort, and pre-crack size, as the degradation level changes. Furthermore, a geometric analysis reveals model deficiencies where significant overestimations correlate with thicker glass components, while pronounced underestimations are predominantly associated with thinner layers of polycrystalline silicon wafer and Ethylene Vinyl Acetate in the module. As a case study, it demonstrated that to maintain a constant degradation level between 1.30 and 1.32 in a PV module with components featuring consistent geometric attributes, the input parameters must be kept within specific ranges: CT ranging from 33 °C to 57 °C, GS ranging from 36 to 81 μ m, material effort ranging from 0.74 to 0.81, and pre-crack size ranging from 24 to 32 μ m. Therefore, this underscores that the ML model not only predicts degradation but also delineates the parameter space required to achieve a consistent output value.