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TheApplication of Golden Section Method on Road Lighting Optimization Design

 Chu Xingwu

 

      Abstract

      In the fieldof road lighting, how to find the best design project is very important.Basically, the solving course will always evolve into an optimization problem. Thispaper will use the golden section method to solve it. One example will begiven. The golden section method is proved efficiently in the field of roadlighting design.

      Keywords:Roadlighting; optimization design; golden section method; evaluating function.

 

      1. Introduction

      Good roadlighting design will lead to energy saving, comfort light environment, safeambience, and so on. Traditionally, design procedure is usually gained byexperience.

      First, wemust choose a proper pattern of road luminaire, and then, decide the designfactors. There are many factors to influence the final result, such as thedistance between two poles (spacing), the height of lamp (height), the distancebetween lamp and road side (overhang), the inclination angle of lamp(tilt), etc. If all the factors are considered, the problem will become verycomplex. The paper deals with two factors. One is the distance between twopoles; the other is the height of lamp. The golden section method and the lightingcalculation software Philips Lighting B. V. CalcuLux Road Version 6.4.1 will beused to solve the problem.

 

      2. Standards for road lighting

      This paper consults the Standard for LightingDesign of Urban Road commended by CIE as follows: (see table 1)

      3. Golden section method

      When we begin to deal with the optimization problem, simplex shape method,Newton-Raphson method, climb mountain method, secantmethod, and quadratic approximation method are oftenused. In practice, we also use the golden section method to solve theoptimization problem. It is one of the best ways to seek the optimum solution,especially for the problem that has no closed-form equation for which traditional calculustechniques can be applied to find a maximum (minimum) value solution.It can reduce the seeking field rapidly.

      What is the golden section? The golden section is a line segment divided into twoparts. The ratio of the short half to the long half is equal to the ratio ofthe long half to the whole. The ratio of the golden section is:

≈0.618

      4. Optimization calculation

      How does thegolden section method apply to road lighting optimization design? There aremany parameters to influence the final result, such as the distance between twopoles, the height of lamp, the inclination angle of lamp, etc. If all the parameters areconsidered, the problem will become very complex. The thesis deals with two parameters.One is the distance between two poles; the other is the height of lamp.

 

      4.1 Themethod


      Figure1 illustrates a reference diagram of the two-factor golden section method,which includes the following steps:

      Step1:Confirm the initial changing range of every variable.

      Step2:Draw a square, and mark the unit of two factors on horizontal axis and verticalaxis. Define four calculative points.

      Step3:Calculate the values of evaluating function for the four points, and comparethe values of them.

      Step4:Save the sub-square including the maximum value of evaluating function, and cutthe rest.

      Step5:Repeat step3 to step4 until getting a satisfying result. But the point thatalready has a result needs not to calculate again.


      4.2 Aboutthe evaluating function

      There are five main variables to evaluate the result: average luminance (Lave),overall uniformity of luminance (U0), longitudinal uniformity ofluminance (Ul), threshold increment (TI), and surroundings ratio(SR). So the evaluating function is defined like this:



      4.3 An example

      an example is presented to explain themethod.

      The calculation model:

      Lighting class: M2

      The overall maintenance factor: 0.75.

      Road arrangement: central

      Central Reserve (C): 2.00 m

      Road Width (W): 8.00 m

      Number of lanes: 2

      Reflection Table: Asphalt CIE R3

      Q0 of Table: 0.070

      Installation: Twin Central

      Overhang (O): 1.50m

      Tilt (T): 5°

      The distance between two poles, orspacing(S), the initial changing range: 29-30m

      The height of lamp (H), theinitial changing range: 10-11m

      TheLuminaire chosen:

      Luminaire Type: PHILIPS SGS203 PC P5

      Lamp Type: SON-TPP150W

      Power (W): 169.0

      Flux (lm): 17500





The results






 

      5. Discussion

      1). Usingthe golden section method to solve the problem, the evaluating function musthave only one maximum value. Otherwise, the answer is unsolvable.

      2). Forbetter efficiency, lighting calculation software ought to combine anoptimization algorithm.

      3). Gettingan exactly evaluating function is very important for that of problem. Furtherwork in this aspect is necessary.

      4). Othermethods can be tried on this optimization design problem.

 

      6. Conclusions

      Using golden section method to solve roadlighting optimization design problem is proved a good method. For betterefficiency, lighting calculation software ought to combine a proper optimizationalgorithm.

 

      7. Acknowledgements

      The author wishes to thank to Tong Junguo,the General Manager of Zhejiang Zhongqi Industrial Co., Ltd. and othercolleagues of the company for their supports, and to my wife and son for their understanding.

 

      References

      [1].Mario Livio. (2002) “The Golden Ratio: The Story of Phi, theWorld's Most Astonishing Number”. New York,Broadway Books,

      [2].Walser Hans. (2001) “The goldensection”. Mathematical Association of America, Washington, D.C.

      [3].CIE Technical Report 115-1995, “Recommendations for theLighting of Roads for Motor and Pedestrian Traffic”.

      [4].CJJ45-1991. “Standard for Lighting Design of Urban Road”. (In Chinese)

      [5].Chu Xingwu. (2006) “Sensitivity Analysis ofRoad Lighting Design Parameters”. China Road Lighting Forum, Hangzhou, China.(In Chinese)

 

 

      注:本文发表于CIE26, 2007.7.4-11,Beijing,China,国际照明委员会第26届大会




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