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This issue is sponsored by the Philips Romania, Lighting Division

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Tests carried out <strong>by</strong> <strong>the</strong> BRE (Building<br />

Research Establ<strong>is</strong>hment) showed a 68%<br />

increase [5] of <strong>the</strong> lighting performance on<br />

<strong>the</strong> 300 mm diameter for <strong>the</strong> new Super<br />

Silver SunPipe as compared to <strong>the</strong> original<br />

anod<strong>is</strong>ed aluminium SunPipe (see Figure 2).<br />

3. The branched SunPipe prototype<br />

The lighting performances of <strong>the</strong> SunPipe<br />

are indeed remarkable and make th<strong>is</strong> system<br />

a revolutionary solution for <strong>the</strong> lighting of<br />

many interior spaces that o<strong>the</strong>rw<strong>is</strong>e would<br />

need electric lighting.<br />

The idea of creating a prototype of a<br />

branched SunPipe emerged from <strong>the</strong> need<br />

of d<strong>is</strong>tributing daylight in several points<br />

along <strong>the</strong> light-pipe. Therefore, a Tramification<br />

was created in order to bring<br />

daylight from <strong>the</strong> vertical main duct <strong>by</strong><br />

means of a horizontal secondary duct to an<br />

imaginary interior space located between<br />

<strong>the</strong> diamond dome and <strong>the</strong> ceiling diffuser<br />

installed on <strong>the</strong> main duct.<br />

Figure 3 Branched SunPipe prototype.<br />

A Super Silver 300 mm diameter<br />

SunPipe was used as vertical main duct and<br />

a Super Silver 230 mm diameter SunPipe<br />

Approach on numerical modelling<br />

was used as horizontal secondary duct (see<br />

Figure 3).<br />

Firstly th<strong>is</strong> prototype branched system<br />

was supplied with electric light from an<br />

incandescent lamp imitating <strong>the</strong> diamond<br />

dome collecting unit. Horizontal<br />

illuminance and vertical illuminance were<br />

measured along <strong>the</strong> ax<strong>is</strong> of <strong>the</strong> main pipe<br />

and along <strong>the</strong> interior wall of <strong>the</strong> main pipe<br />

respectively, both with and without <strong>the</strong> 230<br />

mm diameter branch.<br />

Basing on <strong>the</strong> measured values, a<br />

modelling equation was created using <strong>the</strong><br />

Levenberg-Marquardt method to solve<br />

nonlinear regressions. The light losses<br />

within <strong>the</strong> vertical main duct caused <strong>by</strong> <strong>the</strong><br />

branch, as well as <strong>the</strong> light amplification<br />

within <strong>the</strong> branch were carefully assessed.<br />

4. The Levenberg-Marquardt method<br />

<strong>Th<strong>is</strong></strong> method combines <strong>the</strong> steepest-descent<br />

method and a Taylor series based method to<br />

obtain a fast, reliable technique for<br />

nonlinear optimization [2]. Nei<strong>the</strong>r of <strong>the</strong><br />

above optimization methods are ideal all of<br />

<strong>the</strong> time; <strong>the</strong> steepest descent method works<br />

best far away from <strong>the</strong> minimum, and <strong>the</strong><br />

Taylor series method works best close to<br />

<strong>the</strong> minimum. The Levenberg-Marquardt<br />

(LM) algorithm allows for a smooth<br />

transition between <strong>the</strong>se two methods as <strong>the</strong><br />

iteration proceeds.<br />

In general, <strong>the</strong> data modelling equation<br />

(with one independent variable) can be<br />

written as follows:<br />

r<br />

y = y(<br />

x;<br />

a)<br />

The above expression simply states that<br />

<strong>the</strong> dependent variable y can be expressed<br />

as a function of <strong>the</strong> independent variable x<br />

INGINERIA ILUMINATULUI 18-2006 39

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