The modeling of spectral characteristics of light-emitting diodes (LED) has been addressed in various studies. We extend the current state of knowledge by modeling the spectral characteristics of commercially available high-power LEDs, exhibiting a temperature-dependent degradation, by using a different modeling strategy. To this end, the state of the art approach of an additive superposition of probability density functions (PDF) is compared with an unsupervised machine learning approach called non-negative matrix factorization (NMF). The stress test data used in our modeling routine was collected for a period of 6000 hours at four different case temperatures between 55 C and 120 C. The results of the accelerated stress tests indicate a temperature-activated aging process, which can be described using the Arrhenius equation. By combining the Arrhenius equation with the modeling parameters, the spectral characteristics can be modeled for 6000 hours of stress at four different stress test temperatures. The introduced spectral modeling approach using non-negative matrix factorization achieves CIE 1976 UCS chromaticity differences primarily smaller than Δ u'v'≤ 0.001 and proves to be superior to superimposed probability density functions in terms of colorimetric reconstruction accuracy, modeling complexity and robustness against spectral outliers.

This study explores a novel approach to monitor the spectral emission of LEDs by estimating the spectral power distribution from the spectral sensor responses during an accelerated aging experiment. Two methods for reconstructing the actual LED spectra from sensor responses are presented and tested, one solely requires sensor datasheet information and the other uses a full spectral characterization of the sensor's spectral sensitivities. The reconstruction results show that a spectral sensor can provide accurate spectral estimates even after severe LED degradation. Only for an LED that suffered a phosphor crack, affecting its spatial radiation characteristics, limited ability to estimate the true spectral power distribution without prior assumptions about the spectral changes must be reported. Overall, the use of a spectral sensor, even without detailed characterization of the sensor itself, allows for an accurate monitoring of the true emission of LEDs, with a maximum radiometric error of 0.73 %, a maximum colormetric error of 0.0017Δ u'v' and a maximum spectral nRMSE error of 0.0097 compared to a spectroradiometric measurement. This advance holds great promise for improving lighting technology, particularly in applications that require constant radiometric output and stable color.