Generalized Additive Modeling of Photovoltaic Backsheet Tensile Strength Degradation Under Multi-Stressor Field Conditions

Photovoltaic module reliability depends on the long-term mechanical durability of polymeric backsheets that provide electrical insulation, moisture protection, and structural support. Accurate prediction of backsheet degradation is therefore essential for reliability-centered operation, maintenance scheduling, and lifecycle management of photovoltaic systems. This study develops a Generalized Additive Model (GAM) with penalized thin-plate regression splines and ridge regularization to predict tensile strength degradation under multi-stressor field conditions, benchmarked against ordinary least squares (OLS), weighted least squares (WLS), and Random Forest (RF) regression using 511 consecutive daily field observations of a PET/PET/EVA multilayer photovoltaic backsheet. The GAM achieves in-sample R² = 0.998 and RMSE = 0.8 MPa, compared with R² = 0.925 and RMSE = 4.69 MPa for OLS, and R² = 0.92 and RMSE = 4.84 MPa for WLS. RF achieves R² = 1.0 and RMSE = 0.2 MPa in-sample but captures no physically interpretable structure beyond UV dominance. Residual variance scales with cumulative UV dose at an exponent of α = 0.592 (SE = 0.105, p < 0.001). A biphasic degradation regime is identified, with tensile strength declining at 0.18 MPa/(MJ/m²) below a UV threshold of 196.5 MJ/m², and accelerating to 0.574 MPa/(MJ/m²) above it, a factor of 3.19. The GAM framework provides a physically interpretable and statistically defensible tool for forecasting photovoltaic backsheet degradation trajectories, with direct implications for predictive maintenance scheduling, module replacement planning, and reliability certification of photovoltaic systems.

photovoltaic backsheet; tensile strength degradation; generalized additive model; penalized splines; ridge regularization

1. Khan, Z.U.; Khan, A.D.; Khan, K.; AlKhatib, S.A.K.; Khan, S.; Khan, M.Q.; Ullah, A. A Review of Degradation and Reliability Analysis of a Solar PV Module. IEEE Access 2024, 1–1, doi:https://doi.org/10.1109/access.2024.3432394. [Google Scholar] [Crossref]

2. Al Mahdi, H.; Leahy, P.G.; Alghoul, M.; Morrison, A.P. A Review of Photovoltaic Module Failure and Degradation Mechanisms: Causes and Detection Techniques. Solar 2024, 4, 43–82, doi:https://doi.org/10.3390/solar4010003. [Google Scholar] [Crossref]

3. Mansour, D.E.; Barretta, C.; Pitta Bauermann, L.; Oreski, G.; Schueler, A.; Philipp, D.; Gebhardt, P. Effect of Backsheet Properties on PV Encapsulant Degradation during Combined Accelerated Aging Tests. Sustainability 2020, 12, 5208, doi:https://doi.org/10.3390/su12125208. [Google Scholar] [Crossref]

4. Gaddam, S.K.; Pothu, R.; Boddula, R. Advanced Polymer Encapsulates for Photovoltaic Devices − a Review. Journal of Materiomics 2021, 7, 920–928, doi:https://doi.org/10.1016/j.jmat.2021.04.004. [Google Scholar] [Crossref]

5. Julien, S.E.; Kempe, M.D.; Eafanti, J.J.; Morse, J.; Wang, Y.; Fairbrother, A.; Napoli, S.; Hauser, A.W.; Ji, L.; O’Brien, G.S.; et al. Characterizing Photovoltaic Backsheet Adhesion Degradation Using the Wedge and Single Cantilever Beam Tests, Part I: Field Modules. Solar Energy Materials and Solar Cells 2020, 215, 110669, doi:https://doi.org/10.1016/j.solmat.2020.110669. [Google Scholar] [Crossref]

6. Gebhardt, P.; Rivera, M.; Fokuhl, E.; Reise, C.; Schnabel, E.; Pander, M.; Hädrich, I. UV-Induced Degradation: Comparative Analysis of PV Module Testing and Stabilization Procedures against Outdoor Behavior. EPJ Photovoltaics 2026, 17, 15, doi:https://doi.org/10.1051/epjpv/2026007. [Google Scholar] [Crossref]

7. Acar, I.; Pozan, G.S.; Özgümüş, S. Thermal Oxidative Degradation Kinetics and Thermal Properties of Poly(Ethylene Terephthalate) Modified with Poly(Lactic Acid). Journal of Applied Polymer Science 2008, 109, 2747–2755, doi:https://doi.org/10.1002/app.28142. [Google Scholar] [Crossref]

8. Lomakin, S.; Mikheev, Y.; Usachev, S.; Rogovina, S.; Zhorina, L.; Perepelitsina, E.; Levina, I.; Kuznetsova, O.; Shilkina, N.; Iordanskii, A.; et al. Evaluation and Modeling of Polylactide Photodegradation under Ultraviolet Irradiation: Bio-Based Polyester Photolysis Mechanism. Polymers 2024, 16, 985, doi:https://doi.org/10.3390/polym16070985. [Google Scholar] [Crossref]

9. Zhang, J.-W.; Feng, K.; Diaham, S.; Liao, Q.-Q.; Zhou, X.; Putson, C. Lifetime Evaluation of Photovoltaic Polymeric Backsheets under Ultraviolet Radiation: From Chemical Properties to Mechanical Modeling. ACS omega 2022, 7, 45609–45616, doi:https://doi.org/10.1021/acsomega.2c06424. [Google Scholar] [Crossref]

10. Uličná, S.; Sinha, A.; Miller, D.C.; Habersberger, B.M.; Schelhas, L.T.; Owen-Bellini, M. PV Encapsulant Formulations and Stress Test Conditions Influence Dominant Degradation Mechanisms. Solar Energy Materials and Solar Cells 2023, 255, 112319, doi:https://doi.org/10.1016/j.solmat.2023.112319. [Google Scholar] [Crossref]

11. Wood, S.N. Generalized Additive Models: An Introduction with R, 2nd ed.; Chapman and Hall/CRC: Boca Raton, FL, USA, 2017; ISBN 9781315370279. [Google Scholar] [Crossref]

12. Hastie, T.; Tibshirani, R. Generalized additive models. Statistical Science 1986, 1, 297–310. doi:https://doi.org/10.1214/ss/1177013604. [Google Scholar] [Crossref]

13. International Electrotechnical Commission. IEC 62788-1-6: Measurement Procedures for Materials Used in Photovoltaic Modules—Part 1-6: Encapsulants—Test Methods for Optical Properties; IEC: Geneva, Switzerland, 2017. [Google Scholar] [Crossref]

14. Abdallah, A.A.; Abdelrahim, M.; Elgaili, M.; Pasha, M.; Mroue, K.; Abutaha, A. Degradation of Photovoltaic Module Backsheet Materials in Desert Climate. Solar Energy Materials and Solar Cells 2024, 277, 113118. doi:https://doi.org/10.1016/j.solmat.2024.113118. [Google Scholar] [Crossref]

15. Afridi, M.; Kumar, A.; ibne Mahmood, F.; Tamizhmani, G. Hotspot Testing of Glass/Backsheet and Glass/Glass PV Modules Pre-Stressed in Extended Thermal Cycling. Solar Energy 2023, 249, 467–475, doi:https://doi.org/10.1016/j.solener.2022.12.006. [Google Scholar] [Crossref]

16. Okonkwo, P.C.; Nwokolo, S.C.; Udo, S.O.; Obiwulu, A.U.; Onnoghen, U.N.; Alarifi, S.S.; Eldosouky, A.M.; Ekwok, S.E.; Andráš, P.; Akpan, A.E. Solar PV Systems under Weather Extremes: Case Studies, Classification, Vulnerability Assessment, and Adaptation Pathways. Energy Reports 2024, 13, 929–959, doi:https://doi.org/10.1016/j.egyr.2024.12.067. [Google Scholar] [Crossref]

17. Kraska, P.; Hanzel, K. Comparison of Electricity Production Prediction Models Based on Meteorological Data for PV Farms in Poland—Challenges and Problems. Solar 2026, 6, 16, doi:https://doi.org/10.3390/solar6020016. [Google Scholar] [Crossref]

18. Wu, D.; Wessel, P.; Zhu, J.; Montiel-Chicharro, D.; Betts, T.R.; Mordvinkin, A.; Gottschalg, R. Influence of Lamination Conditions of EVA Encapsulation on Photovoltaic Module Durability. Materials 2023, 16, 6945–6945, doi:https://doi.org/10.3390/ma16216945. [Google Scholar] [Crossref]

19. Haillant, O. Accelerated Weathering Testing Principles to Estimate the Service Life of Organic PV Modules. Solar Energy Materials and Solar Cells 2011, 95, 1284–1292, doi:https://doi.org/10.1016/j.solmat.2010.08.033. [Google Scholar] [Crossref]

20. Koester, L.; Lindig, S.; Louwen, A.; Astigarraga, A.; Manzolini, G.; Moser, D. Review of Photovoltaic Module Degradation, Field Inspection Techniques and Techno-Economic Assessment. Renewable and Sustainable Energy Reviews 2022, 165, 112616, doi:https://doi.org/10.1016/j.rser.2022.112616. [Google Scholar] [Crossref]

21. IEA PVPS Review of Failures of Photovoltaic Modules; 2014; [Google Scholar] [Crossref]

22. Nelson, W. Accelerated Testing: Statistical Models, Test Plans and Data Analyses. Wiley, New York.; Wiley, 1990; [Google Scholar] [Crossref]

23. Greene, W. Econometric Analysis, 8th ed.; Pearson Education: New York, NY, USA, 2020. [Google Scholar] [Crossref]

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