Quality Control of Led Light Sources Based on Fractal Modeling of Temperature Fields

This paper presents a mathematical model for predicting the degradation of LED light sources, based on fractal analysis of temperature fi elds and generative modeling of probabilistic fl uctuations. Temperature fi elds are treated as fractal surfaces with a pronounced self-similar structure, arising from technological deviations and local thermal effects. The Hurst exponent, calculated using the box-counting method, is employed as a diagnostic feature. To generate realistic temperature maps, a modifi ed random displacement algorithm (diamond-square) and a generalized fractal Weierstrass series are used. The proposed model accounts for the infl uence of fractal inhomogeneity on the rate of thermal degradation and allows for the construction of a predictive map of the time remaining until luminous fl ux drops to a specifi ed level. The results demonstrate high accuracy when compared with experimental data (mean deviation less than 2 °C). The model can be implemented in automated quality control systems at the manufacturing stage, including thermographic diagnostics, adaptive testing, and sorting of products based on parameter stability criteria.