Diagnosing Lumen Depreciation in LED Lighting Systems: An Estimation Approach Jianfei Dong, Ashish Pandharipande, Willem van Driel, and Guoqi Zhang Abstract—Lumen depreciation, the condition that the light output falls below a fraction of its peak output, is known to be the main failure mode in light emitting diodes (LEDs). In lighting systems comprising multiple LEDs, lumen depre- ciation leads to reduced average illuminance and a distorted illumination rendering. Diagnosing lumen depreciation in LED lighting systems is thus an important problem. We propose an estimation approach to diagnosing individual LED failures using a photosensor system. We specifically study the impact of perturbations in the photosensor positions on diagnosability by analyzing the sensor output matrix - the matrix relating the luminous flux values of the multiple LEDs to the measurements at the photosensor system. The conditions on diagnosability are first derived in terms of bounds on the smallest singular value of the sensor output matrix. Subsequently, sufficient conditions are derived on the photosensor positions to ensure that individual LED lumen depreciations are diagnosable. Numerical results are provided to validate our analytical results. Index Terms—LED lighting systems, Lumen depreciation di- agnosis, Estimation, Photosensor position perturbation. I. I NTRODUCTION L Ighting systems based on light emitting diodes (LEDs) hold the promise of providing energy-efficient dynamic and interactive artificial illumination [1]. LED lighting systems are becoming prevalent in general lighting applications with increased incorporation of LEDs in luminaires seen in office buildings, retail spaces and outdoor public areas. The quality of illumination is important in such applications from an end- user experience perspective. Thus it is of interest to diagnose underlying LED failures that adversely affect the quality of illumination rendered from LED lighting systems. We shall treat the problem of diagnosing lumen depreciation resulting from individual LED failures in LED lighting systems. Lumen depreciation due to a LED failure refers to the condition that the light output falls below a fraction of its peak output. To illustrate the effect of lumen depreciation of LEDs in a lighting system, consider Fig. 1.(a) with a system of 64 LEDs, each with a half-power beam angle of 17 degree corresponding to a Lambertian mode number [2] of 15.5, arranged on a square grid with an LED spacing of 0.4 meters. At peak output, the rendered illumination pattern on a plane 1.5 meters away is shown in Fig. 1.(c). Now consider that 33 LEDs are degraded with 50% lumen depreciation, with the case shown in Fig. 1.(b). The resulting illumination pattern from this configuration is depicted in Fig. 1.(d), where the average Copyright c ⃝2012 IEEE. J. Dong and A. Pandharipande are with Philips Research, High Tech Cam- pus 34, 5656 AE, Eindhoven, The Netherlands. W. van Driel and G. Zhang are with Philips Lighting, Mathildelaan 1, 5611 BD, Eindhoven. G. Zhang is also with DIMES center for SSL technologies, TU Delft, 2628 CT, Delft, The Netherlands (e-mail: jianfei.dong@philips.com; ashish.p@philips.com; willem.van.driel@philips.com; g.q.zhang@philips.com). illuminance on the target plane drops from 535 lux to 392 lux. Clearly, the effects at the system level due to LED failures are in the form of decrease in illumination levels and a distorted illumination rendering. Failures in LEDs can be attributed at the chip level, package level and the system level [3], [4]. It is known that LEDs rarely fail catastrophically, and that failures are rather in the form of gradual degradation over time [5] resulting in lumen depreciation [6], [7]. The main reasons causing lumen depre- ciation at the chip level are excessive heat at the p-n junction of an LED chip [5] and excessive drive current density [8]. At the package level, excessive junction temperature and drive current also cause phosphor degradation, epoxy yellowing, and silicone glue darkening [4]. This also worsens the chromatic properties of LEDs, resulting in color drift. On the other hand, LED light sources have to be contained in a fixture, which also contains other components, e.g. electronics, connectors, heat sink, and cooling module. These components may also degrade. An overall evaluation of all the component failures inside an LED source has been reported in [4], where it is reported that besides chip level luminous degradation induced by thermal propagation, solder interconnection fatigue damage driven by thermal cycling also represents a high risk to cause potential failures of LED light sources. Given that lumen depreciation of LEDs is the main failure mode, we shall focus on the diagnosis of such failures. Automatic methods for diagnosing lumen depreciation in LEDs become relevant in public lighting applications, e.g. office buildings, retail spaces and tunnels. The reasons are two fold. First, the current applications of LED light sources are dominant in the public lighting domain because of their energy saving benefits and initial higher investment. Second, the maintenance of such facilities is usually not in the charge of their direct users, but controlled by building services or municipalities, depending on the application. These entities are usually responsible for a large number of lighting facilities, which makes it impractical to schedule visual inspections of the lamps on a regular basis. Automatic diagnosis is hence important for reporting LED failures in a timely manner, so as to limit service interruptions that may otherwise impact user comfort and safety. Existing methods for diagnosing LED lumen depreciation focus on circuit level solutions inspired by the fact that junc- tion temperature is a main cause of lumen depreciation. How- ever, due to the difficulty in directly measuring the temperature at the p-n junction of a LED chip, indirect methods have been proposed to monitor the shift in the light wavelength [9], [10]. However, these methods cannot monitor the wavelengths of multiple LEDs, which simultaneously work in one system, because the measured light at one point is a mixture of the