## 5 Conclusions  
In this paper, a novel parameter extraction procedure was presented that is based on a modified Nelder-Mead optimization algorithm. The modifications greatly improved the robustness of the optimization process, as, due to the applied heuristics, the success rate increased from 50% to 100%.  
The reproducibility of the new method was tested with different initializations. Over 10,000 extraction runs were performed on the measured IVL characteristics of 52 high-power LEDs from various types.  
Compared to the previous parameter extraction process used in the previous Delphi4 LED project, the new parameter extraction procedure provides multiple advantages, where, at least by an order of magnitude faster (reduced computational resource need), the original method lasts for 2-6 h (and needs manual operations). The new method finds the required data within a minute (typically 10-18 s), while the accuracy does not decrease or fall into the range of the supposed model and measurement accuracy for both optical and electrical domains, that is, 1% and 5% for maximum relative errors for the forward voltage and emitted flux, respectively.  
The new method demonstrates a high level of robustness, achieving a 100% success rate in a benchmark test. This allows for an autonomous, unsupervised operation, making it suitable for automated web-based model parameter extraction services, as it can be found on [[https://extractor.ai-twilight.org/](https://extractor.ai-twilight.org/)]([https://extractor.ai-twilight.org/](https://extractor.ai-twilight.org/)) (accessed on 10 August 2024), which has been publicly available and in use since March 2023 without any robustness issues.  
Additionally, the new parameter extraction process simplifies the use of measurement data from less complex and faster LED IVL tests. It eliminates the need for standard isothermal characterization processes that require precise junction temperature control. Instead, it is sufficient to wait for any equilibrium state, rather than ensuring the junction temperature aligns with a reference point. This approach allows for the use of all measured data points, even if the reference junction temperature is not achieved, thereby reducing the number of measurements needed to create the model. Moreover, parameter extraction for a specific LED type can be completed in a single session using the test data from multiple samples of that type.  
Conceptualization, M.N. and A.P.; methodology, M.N., software, M.N.; validation, J.H., G.H.; formal analysis, M.N.; investigation, M.N.; resources, J.H. and G.H.; data curation, J.H. and G.H.; writing--original draft preparation, A.P. and M.N; writing--review and editing, M.N. and A.K.A.; visualization, M.N.; supervision, A.P.; project administration, A.P.; funding acquisition, A.P. All authors have read and agreed to the published version of the manuscript.  
Funding: This research was funded by European Union's Horizon 2020 research and innovation program, grant number: 101007319; Hungarian government, grant number: 2019-2.1.3-NEMZ_ECSEL-2021-00008.  
Data Availability Statement: Data are contained within the article.  
The work presented received funding from the European Union's Horizon 2020 research and innovation program through the H2020 ECSEL project AI-TWILIGHT (grant agreement number: 101007319). Co-financing of the AI-TWILIGHT project by the Hungarian government through the 2019-2.1.3-NEMZ_ECSEL-2021-00008 grant from the National Research, Development and Innovation Fund is also acknowledged. We are also thankful for the additional support from project no. TKP2021-NVA-02, which has been implemented with the support provided by the Ministry of Culture and Innovation of Hungary from the National Research, Development and Innovation Fund, financed under the TKP2021-NVA funding scheme.  
The authors declare no conflict of interest.