Abstract
This paper proposes a temperature compensation method for RGBW LED mixing based on fast non-dominated sorting genetic algorithm (NSGA-II). The proposed method can achieve compensation for temperature-induced changes in LED correlated color temperature (CCT), color fidelity (Rf) and color gamut index (Rg) by predicting the spectral power distribution (SPD) at different temperatures.
Key Results: The experimental results show that the fit of the established temperature-spectral model is R²>0.98, and the deviation of the compensated mixing results from the initial state of the light source is less than 10K in CCT; the deviation value of Rf is less than 4% in the range of 2000K-7000K, and less than 2.15% in the range of 3000K-7000K; and the deviation value of Rg in the range of 2000K-7000K is less than 4.46%.
Key Performance Metrics
Research Highlights
NSGA-II Based Temperature Compensation
The method uses fast non-dominated sorting genetic algorithm (NSGA-II) to compensate for temperature-induced changes in LED color parameters, achieving high consistency in output across temperature variations.
Comprehensive Spectral Modeling
Establishes SPD-temperature model of RGBW LED light source by measuring spectral power distribution at different temperatures, with R² values above 0.98 for all fitted models.
Multi-Objective Optimization
Simultaneously optimizes for CCT deviation, color fidelity (Rf), and gamut index (Rg) with priority given to CCT compensation, followed by Rf and Rg.
Effective Compensation Across Temperature Range
The method maintains consistent performance across a wide temperature range (20°C to 90°C) and CCT range (2000K to 7000K), significantly reducing deviations caused by temperature changes.
Practical Implementation
Uses PWM duty cycle control for practical implementation, with compensation process divided into color power compensation and luminance compensation stages.
Red LED Most Temperature Sensitive
Research findings show red LED is most affected by temperature, with peak value at 90°C decreasing by over 60% compared to 20°C, while blue and green LEDs show reductions of 20% and 22% respectively.
Content Overview
Document Contents
1. Introduction
As lighting technology advances, people are no longer satisfied with using single-colour LEDs for lighting. More people are now inclined to use adjustable LED light sources. Different lighting options can create more comfortable working and living environments. Appropriate lighting can increase people's productivity and lead to better rest.
Compared to traditional light sources, LED light sources have advantages such as smaller size, lower energy consumption and longer life. However, temperature is a critical factor that affects the quality of light sources. Internal heating and extreme external conditions can cause changes in the operating temperature of LEDs, resulting in parameter deviations and affecting the stability and performance of the light sources.
The advent of adjustable correlated colour temperature (CCT) LED light sources offers a potential solution to the problem of reduced light output quality due to temperature effects. Currently, research on LED light sources with adjustable CCT is generally divided into three methods:
- Using two white LEDs with different CCT
- Using multiple single-color LEDs
- Using a combination of single-color LEDs and white LEDs
This paper focuses on exploring the optimal lighting performance of RGBW LEDs with the goal of reducing or even eliminating the variations in LED lighting caused by the heating of the LEDs themselves or by external temperature influences.
2. Experimental Description
2.1 Multi-Color Light Mixing Principle and Light Source Evaluation
The color of the light source and its ability to accurately reproduce the colors of illuminated objects depends on the spectral power distribution of the light source. The spectral power distribution of a combination of multi-color light sources is the linear sum of their individual spectral power distributions:
SRGBW = Kr * Sr + Kg * Sg + Kb * Sb + Kw * Sw
White LED light is commonly described in terms of color temperature. Color temperature is defined as the temperature at which a blackbody emits light that matches the color of the light source.
The ability of a light source to accurately reproduce the colors of illuminated objects is commonly evaluated using the standardized metric called the CIE (International Commission on Illumination) Color Rendering Index (CRI). However, as research on light sources has progressed, the CRI has been found to have some limitations in evaluating certain colors. Therefore, this research uses the Illuminating Engineering Society (IES) Color Fidelity Index (Rf) and Gamut Index (Rg) as the evaluation criteria for the illumination performance of light sources.
The Color Fidelity Index and Gamut Index use 99 color samples, which is more comprehensive than the standard CRI, which typically uses 15 color samples, allowing for a more thorough evaluation of a light source's color performance.
The calculation of Rf is based on the Euclidean distance in J'a'b' color space as the standard color difference formula in CAM02-UCS:
ΔElab,i = √((ft,i - fr,i)2 + (at,i - ar,i)2 + (bt,i - br,i)2)
Rg is a measure of chroma which is the ratio of the area of the polygon formed by the average coordinate in each hue angle box to the area of the polygon formed by the reference illuminant:
Rg = 100 * At / Ar
To provide a more intuitive evaluation of the mixed light results, a scoring system is used to quantify the results:
S = 100 - cct/10 - 2 * (100 - Rf) - |100 - Rg|
2.2 Establishment of LED Spectral Power Distribution Temperature Model
Due to the inherent characteristics of LEDs, their spectral power distribution (SPD) shifts with temperature. In general, for RGB LEDs, the peak wavelengths experience a redshift, and the peak values decrease as the temperature increases.
The research tested the spectral power distribution of R, G, B, and W LEDs at 10°C intervals from 20°C to 90°C. The red LED is the most affected by temperature, with its peak value at 90°C decreasing by over 60% compared to the peak value at 20°C, and showing a noticeable redshift phenomenon. The blue and green LEDs are less affected compared to the red LED, but their peak values also experience reductions of 20% and 22%, respectively.
To mathematically model the SPD of each LED, a Gaussian model is used for single-color LEDs, with parameters to be determined: peak value, peak wavelength, and full width at half maximum (FWHM). White LEDs typically have two peaks, so a double Gaussian model is used to describe them.
After establishing the model, the SPD of LED light sources can be represented by three parameters: peak value, peak wavelength, and full width at half maximum (FWHM). By linearly fitting these parameters at different temperatures, the relationship between SPD and temperature is obtained.
The validation of the model shows that the calculated results using the model closely match the actual spectral power distributions, with R² greater than 0.98.
3. Results and Discussion
3.1 Effect of Temperature on Light Mixing Results
The goal of LED temperature compensation is to keep the light output as constant as possible within the target temperature range. First, the light mixing results of the RGBW LED light source at 20°C are obtained as the initial state.
As the temperature increases, using the LED on time directly for light mixing without temperature compensation can result in large variations. The main problem caused by temperature increase is the increase of the color temperature of the light source, and the Rg and Rf performance is slightly lower at most color temperatures.
RGBW LED Mixing Results at 20°C
| CCT (K) | Rf | Rg | Red | Green | Blue | White |
|---|---|---|---|---|---|---|
| 2000 | 34.36 | 170.06 | 0.3809 | 0.0129 | 0 | 0.6061 |
| 3000 | 74.55 | 107.11 | 0.1458 | 0.0745 | 0 | 0.7796 |
| 4000 | 87.05 | 105.67 | 0.0907 | 0.1412 | 0.0358 | 0.7320 |
| 5000 | 91.96 | 105.14 | 0.0476 | 0.1466 | 0.0839 | 0.7218 |
| 6000 | 92.59 | 102.26 | 0.0512 | 0.2541 | 0.0834 | 0.6112 |
| 7000 | 90.49 | 100.00 | 0.0787 | 0.3309 | 0.0975 | 0.4927 |
At 55°C compared with 20°C, the maximum deviation of the CCT = 2000K, the deviation value is 333K, the maximum deviation of Rf = 15.95, the maximum deviation of Rg = 34.5. At 85°C compared with 20°C, the maximum deviation of CCT = 6500K, the maximum deviation of Rf = 31.94, and the maximum deviation of Rg = 53.7.
3.2 Temperature Compensation of the LED Light Source
The compensation process is mainly divided into two steps: color power compensation and luminance compensation. First, to maintain the consistency of the color of the light output as much as possible, the result of temperature compensation should be as close as possible to the initial state of the light mixing results.
Non-dominated Sorted Genetic Algorithm (NSGA-II) is used for multi-objective optimization. The objective is to optimize the deviation, Rf and Rg between the mixed color temperature and the target color temperature by controlling each color LED by varying the PWM duty cycle.
The algorithm parameters are set as: initial population size M=30, end of evolutionary generations G=300, crossover probability Pc=0.8, mutation probability Pm=0.1.
The priority of the optimization target is set as: CCT deviation compensation first, followed by Rf compensation and finally Rg compensation. Under this objective, the deviation of the color temperature of the light source from the target color temperature is usually within 10K.
Rf can also be very close to the performance, with deviation values all less than 3. At 55°C, the deviation of the Rf in the interval of 2000K-7000K is less than 4%, and the deviation of the Rf in the interval of 3000K-7000K is less than 2.15%. At 85°C, the Rf deviation is less than 6% in the 2000K-7000K interval and less than 2.21% in the 3000K-7000K interval.
Rg has a lower compensation priority and has a slightly higher deviation than CCT and Rf, but the deviation values are also usually less than 5. The Rg deviation is less than 4% at 55°C and less than 4.46% at 85°C.
After color compensation is completed, luminance compensation is performed to make the luminous intensity of the light source consistent with that before color compensation.
4. Conclusion
Multi-color LED mixed lighting represents a future trend in the lighting industry. Based on lighting effect, control difficulty and cost considerations, the most common multi-color LED mixed lighting solutions on the market are two-color temperature as well as RGBW.
Due to the characteristics of the LED itself, the LED spectral power distribution of different colors will produce different degrees of change when the temperature rises. This research models the LED spectral power distribution-temperature relationship, and uses the NSGA-II algorithm to compensate the spectral temperature of RGBW LEDs based on the spectral superposition theorem, with the goal of making the light output effect of LEDs at different temperatures consistent.
The compensation priority for each light output parameter of the light source is color temperature first, Rf second, and Rg last. The results show that in the selected group of light sources, the CCT deviation is less than 10K; Rf deviation value in the range of 2000K-7000K is less than 4%, 3000K-7000K range is less than 2.15%; Rg deviation value in the range of 2000K-7000K is less than 4.46%.
For different application scenarios, different compensation priorities can be controlled to achieve the desired lighting effect.
References
The complete reference list is available in the PDF document. Key references include works on LED temperature effects, color rendering metrics, multi-color LED mixing, and genetic algorithm applications in optimization problems.
Note: The above is a summary of the research paper content. The complete document contains extensive experimental data, mathematical models, visualizations, and detailed analysis. We recommend downloading the full PDF for in-depth reading.