CN111581873B - Tunnel illumination calculation method considering side wall bidirectional reflection distribution function - Google Patents

Tunnel illumination calculation method considering side wall bidirectional reflection distribution function Download PDF

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CN111581873B
CN111581873B CN202010560205.0A CN202010560205A CN111581873B CN 111581873 B CN111581873 B CN 111581873B CN 202010560205 A CN202010560205 A CN 202010560205A CN 111581873 B CN111581873 B CN 111581873B
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何世永
任昱豪
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Chongqing Jiaotong University
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Abstract

The invention relates to a tunnel illumination calculation method considering a side wall bidirectional reflection distribution function, which belongs to the field of tunnel illumination calculation and comprises the following steps: s1: calculating the illuminance of a road surface calculation point caused by direct irradiation of the lamp; s2: discretizing the side wall of the tunnel, discretizing the tunnel interior material into a series of units with Bidirectional Reflection Distribution Functions (BRDF) by utilizing a finite element idea, and regarding the units as unit light sources in the lighting calculation process; s3: sequentially calculating the illumination of each lamp to the light reflecting units on each side wall; s4: establishing a bidirectional reflection distribution function model of the side wall material; s5: calculating the light intensity in the direction of the calculation point; s6: calculating the illumination caused by the reflection effect at the point; s7: calculating the illumination of the road surface calculation point considering the side wall reflection increment; the invention overcomes the defect of overlarge deviation of the calculated value and the measured value.

Description

Tunnel illumination calculation method considering sidewall bidirectional reflection distribution function
Technical Field
The invention belongs to the field of tunnel illumination calculation, and relates to a tunnel illumination calculation method considering a side wall bidirectional reflection distribution function.
Background
The tunnel engineering scale in China is continuously enlarged, and huge operation electricity charge and maintenance cost are brought along with the tunnel engineering scale. The electricity charge for tunnel illumination in Chongqing areas reaches 2 hundred million RMB in one year, and huge energy consumption is contrary to the measures of green illumination and energy conservation and emission reduction actively promoted by the nation. How to effectively reduce the energy consumption of tunnel illumination on the premise of ensuring the driving safety is urgent. With this as background, tunnel inner wall auxiliary lighting is proposed as a new idea in the beam wave article "study on influence of diffuse reflectance of energy storage reflective material on tunnel lighting quality" and the monograph "study on energy-saving experimental study on energy-saving of energy storage reflective material auxiliary tunnel lighting": the coating material with better reflection performance is used on the tunnel arch wall, the luminous flux emitted by the lamp is reflected for multiple times in the tunnel, and the illumination level in the tunnel can be improved, so that the tunnel illumination design standard can be properly reduced, and the purposes of energy conservation and emission reduction are achieved. The tunnel interior material is explained by relevant specifications at home and abroad: the design rules for highway tunnel lighting (JTG/T D70/2-01-2014) propose that the wall surface on both sides of the road surface within the height range of 2m is suitable for being paved with materials with high reflectivity, and when the reflectivity of the wall surface reaches 0.7, the brightness of the road surface can be increased by 10 percent. "; the international association for illumination CIE 88-2004 report that "cavity wall illumination is a great benefit to visual guidance of occupants"; the North American Lighting engineering society ANSI/IESNARP-22-11 recognizes that wall coverings having an initial reflectance of at least 50% should be used; in the japanese standard of tunnel lighting, it is also proposed to take the reflection effect of the tunnel surface into consideration when calculating the luminance of the road surface illuminance.
The core of the auxiliary illumination of the inner wall of the tunnel lies in the reasonable utilization of the reflection increment. Before that, an accurate reflection increment calculation theory needs to be found, the difference between a theoretical value and a true value is reduced, more accurate tunnel illumination design standards can be established, and the method has important significance for realizing tunnel illumination energy conservation: the Pan provides DIAlux software simulation based on the Pan in the document illumination energy conservation of the tunnel side wall built-in material, and provides a method for calculating the reflection increment, but the side wall materials with different reflection characteristics are distinguished only by reflection coefficients, and the reflection characteristics of the materials are difficult to reflect comprehensively; yang tao provides in the literature "study of incremental coefficients of reflection for tunnel illumination" that incremental coefficients of tunnel illumination are proposed based on the reflection coefficient of the wall, the reflection coefficient of the road and the distribution ratio of the luminous flux, but in this way, it is difficult to reflect the difference of the intensifying effect under different materials with reflection characteristics.
The existing tunnel lighting method is difficult to accurately describe the reflection characteristic of the inner wall, so that the difference between the calculated value and the measured value is large, and the invention of the accurate tunnel lighting calculating method is urgent.
Disclosure of Invention
In view of this, the present invention provides a tunnel illumination calculation method considering a bidirectional reflection distribution function of a side wall, which aims to overcome the defect that a difference between a theoretical calculation value and an actual measurement value is large, and accurately describes the reflection characteristics of the side wall of a tunnel by introducing the bidirectional reflection distribution function of the inner wall of the tunnel to obtain a side wall reflection increment, thereby reducing a difference between the theoretical calculation value and the actual measurement value and achieving a good calculation precision.
In order to achieve the purpose, the invention provides the following technical scheme:
a tunnel illumination calculation method considering a sidewall bidirectional reflection distribution function comprises the following steps:
s1: calculating the illuminance of a road surface calculation point caused by direct radiation of a lamp;
s2: discretizing the side wall of the tunnel, discretizing the tunnel interior material into a series of units with Bidirectional Reflection Distribution Functions (BRDF) by utilizing a finite element idea, and regarding the units as unit light sources in the illumination calculation process, wherein the specific size depends on the calculation precision requirement, and the smaller the discrete size is, the higher the calculation precision is;
s3: sequentially calculating the illumination of each lamp to the light reflecting units on each side wall;
s4: establishing a bidirectional reflection distribution function model of the side wall material;
s5: calculating the light intensity in the direction of the calculation point;
s6: calculating the illumination caused by the reflection effect at the calculation point;
s7: calculating the illumination of the road surface calculation point considering the side wall reflection increment; and adding the calculation results of the step S1 and the step S6 at each point to obtain the illuminance value of the road surface calculation point considering the reflection increment of the side wall of the tunnel.
Further, in the step S1, the illuminance generated at the calculation point by the direct lighting of the luminaire can be calculated by using a cosine formula, as shown in formula (1):
Figure BDA0002545828790000021
the illuminance at the calculation point for multiple direct lighting fixtures is shown in equation (2):
Figure BDA0002545828790000022
wherein E ispiIs the horizontal illumination generated by a lamp at a calculation point of a tunnel opening road surface(ii) a Gamma is the lamp ray incidence angle (°) corresponding to the calculated point; i iscyThe light intensity value (cd) of the lamp at a calculation point is obtained by checking a light distribution curve of the lamp; m is the maintenance coefficient of the lamp; φ is the rated luminous flux (lm) of the luminaire; h is the height (m) from the center of the light source of the lamp to the road surface; epThe sum of the horizontal illuminance generated by a plurality of lamps at a calculation point, n is the number of the lamps, and a group is taken before and after a calculation area during calculation.
Further, in step S3, equation (3) is obtained by using the cosine equation:
Figure BDA0002545828790000023
wherein EabHorizontal illuminance (lx), I (c) generated on the b unit light source for the a-th luminaireabγab) The light intensity value (cd) of the a-th lamp on a certain unit light source is taken according to a lamp light intensity table, betaabThe light ray incidence angle (degree), theta of the a-th lamp corresponding to a certain unit light sourceabIs the angle (degree), H, between the connecting line of the a-th lamp and the center of a certain unit light source and the normal direction of the unit light sourceabThe vertical distance between the a-th lamp and the central point of a certain unit light source is defined, phi is the rated luminous flux (lm) of the lamp, and M is the maintenance coefficient of the lamp.
Further, in said step S4, the BRDF is modeled by a five parameter model, as in formula (4):
Figure BDA0002545828790000031
Figure BDA0002545828790000032
wherein
Figure BDA0002545828790000033
Is a material BRDF that defines the angle of incident scattering,
Figure BDA0002545828790000034
the first term on the right side of the equation is a coherent component reflecting the specular reflection condition of the surface of the material, and the second term is a diffuse reflection coherent component reflecting the surface of the material; wherein k isa，kd，krA and b are both undetermined parameters,
Figure BDA0002545828790000035
is a masking function, taking the value 1;
the selection standard of each parameter of the model is that the standard deviation of simulation experiment data is minimum, and the mean square error of the standard deviation is calculated according to the formula (6):
Figure BDA0002545828790000036
wherein x ═ kb，kd，kr，a，b]TColumn vectors that are model parameters; f. ofrFitting data for the model;
Figure BDA0002545828790000037
is the measured data; g1(θi) And g2(θr) The weighting functions are used for adjusting the influence of each error on the total error when the test interval is not uniform, and are all measured at equal intervals, so that both the weighting functions take 1.
Further, in said step S5, the brightness in the direction of the calculation point is represented as L, and the light intensity in this direction is represented as IabExpressed as described in equation (7):
Figure BDA0002545828790000038
wherein S is the area of the light emitting cell and C is the cleaning coefficient of the sidewall material;
wherein
Figure BDA0002545828790000039
Is a material BRDF that defines the angle of incident scattering,
Figure BDA00025458287900000310
respectively, angle of incidence, angle of reflection, azimuth.
Further, in the step S6, the illuminance calculation is performed on the illuminance increment E generated by the reflected light at the calculation point f under the action of all the side wall light emitting unitsuAs shown in equation (8):
Figure BDA00025458287900000311
wherein IfbCalculating the horizontal illuminance (lx) generated by the point P for the road surface, m is the number of unit light sources, omegabIs the included angle (degree) between the normal direction of the light-emitting unit b and the connecting line from the geometric central point thereof to the road surface calculation point P, taubAn included angle (degree), H, between a connecting line of a central point of the light reflecting unit b and a road surface calculation point P and the normal direction of the road surfacebThe vertical distance (m) between the center point of the light emitting unit b and the road surface is calculated.
Further, in the step S7, the road surface calculation point is calculated by considering the illuminance of the side wall reflection increment, as shown in the following equation (9):
E＝Ep+Eu (9)
wherein E is the road surface calculation point illumination taking the side wall reflection synergistic effect into consideration, EpIs the illuminance produced by the direct projection of the lamp at the road surface calculation point, EuIs the reflective increment of the sidewall.
The invention has the beneficial effects that:
1. the invention introduces bidirectional reflection distribution of the tunnel sidewall material to describe the reflection characteristic of the tunnel sidewall, and overcomes the defect of overlarge deviation between a calculated value and an actually measured value caused by fuzzy description of the reflection characteristic of the tunnel sidewall material in the conventional calculation method.
2. In the illumination calculation method, the bidirectional reflection distribution function of the side wall is introduced, so that different tunnel side wall materials can be distinguished.
3. With the above illumination calculation method, the evaluation of the energy saving effect, the auxiliary illumination effect, and the like can be performed on the material used as the tunnel sidewall in terms of the reflection characteristics and the like.
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In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a schematic diagram of the relationship between geometric relationships in a bi-directional reflection model;
FIG. 2 is a schematic cross-sectional view of a tunnel;
FIG. 3 is a schematic diagram of the layout of lamps and computation points in a tunnel;
FIG. 4 is a schematic diagram of a light distribution curve of the lamp;
FIG. 5 is a sample of energy-storing reflective luminescent material;
FIG. 6 is a fitting result of a five-parameter model of an energy-storage reflective luminescent material;
FIG. 7 is a comparison result between the measured value and the calculated value of the illuminance of the calculated point on the first and second rows of road surfaces;
FIG. 8 is a comparison result between the measured values and the calculated values of the illumination of the third and fourth rows of road surface calculation points;
fig. 9 is a flowchart illustrating a tunnel illumination calculation method considering a sidewall bidirectional reflection distribution function according to this embodiment.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1-8, the illuminance of the road surface calculation point is calculated for the cross section shown in fig. 2, and the layout of the lamps and the calculation points is shown in fig. 3. The lamps in the tunnel adopt LED lamps, and the light distribution curve of the LED lamps is shown in figure 4. The energy storage reflective luminescent material is selected as the side wall material of the tunnel, and a sample wafer of the material for measuring the bidirectional reflection distribution function of the material is shown in figure 5.
The first step is as follows: as shown in fig. 1, firstly, calculating the illuminance of a road surface calculation point caused by direct radiation of a lamp according to the formulas (1) and (2); the illuminance produced at the calculation point by the direct lighting of the luminaire can be calculated using the cosine formula, as shown in formula (1):
Figure BDA0002545828790000051
the illuminance at the calculation point for multiple direct lighting fixtures is shown in equation (2):
Figure BDA0002545828790000052
wherein E ispiThe horizontal illuminance generated by a lamp at a tunnel opening road surface calculation point; gamma is the lamp ray incidence angle (°) corresponding to the calculation point; I.C. AcyThe light intensity value (cd) of the lamp at a calculation point is obtained by looking up a light distribution curve of the lamp; m is the maintenance coefficient of the lamp; phi is the rated luminous flux (lm) of the luminaire; h is the height (m) from the center of the light source of the lamp to the road surface. EpThe sum of the horizontal illuminance generated by a plurality of lamps at a calculation point, n is the number of the lamps, and a group is taken before and after a calculation area during calculation.
The second step: discretizing the side wall of the tunnel, discretizing the tunnel interior material into a series of units with bidirectional reflection distribution functions by utilizing a finite element idea, and regarding the units as unit light sources in the illumination calculation process, wherein the specific size depends on the calculation precision requirement, and the smaller the discrete size is, the higher the calculation precision is. In the present embodiment, the tunnel sidewalls in the computation section are discretized into 30cA rectangular light emitting cell of m x 10 cm.
The third step: and sequentially calculating the illumination of each lamp to the light reflecting units on each side wall. Equation (3) can be obtained by using the cosine equation:
Figure BDA0002545828790000053
wherein EabHorizontal illuminance (lx) generated on the b unit light source for the a-th luminaire)，I(cab，γab) The light intensity value (cd) of the a-th lamp on a certain unit light source is taken according to a lamp light intensity table, betaabThe light ray incidence angle (degree), theta of the a-th lamp corresponding to a certain unit light sourceabIs an angle (degree), H, between a connecting line of the a-th lamp and the center of a certain unit light source and the normal direction of the unit light sourceabIs the vertical distance between the a-th lamp and the center point of a unit light source. Phi is the rated luminous flux (lm) of the lamp, and M is the maintenance coefficient of the lamp.
The fourth step: in the modeling of the bidirectional reflectance distribution function BRDF of the sidewall material, a five-parameter model is used, as in equation (4):
Figure BDA0002545828790000054
wherein
Figure BDA0002545828790000055
Is a material BRDF that defines the angle of incident scattering,
Figure BDA0002545828790000056
respectively, angle of incidence, angle of reflection, azimuth. The first term on the right side of the middle number in the formula is a coherent component reflecting the specular reflection condition of the surface of the material, and the second term reflects a coherent component reflecting the diffuse reflection condition of the surface of the material. Wherein k isa，kd，krA and b are both undetermined parameters,
Figure BDA0002545828790000057
the method is a covering function, energy storage reflective luminescent materials, tunnel special putty and cement mortar materials are used as tunnel side wall materials, the tunnel side wall materials are all semi-smooth surface materials, and the covering function can be set as 1 for simple calculation. Other parameters in the formula are shown in formula (5):
Figure BDA0002545828790000061
the selection standard of each parameter of the model is that the standard deviation of simulation experiment data is minimum, and the mean square error of the standard deviation is calculated according to the formula (6):
Figure BDA0002545828790000062
wherein x ═ kb，kd，kr，a，b]TColumn vectors that are model parameters; f. ofrFitting data for the model;
Figure BDA0002545828790000063
is the measured data; g1(θi) And g2(θr) The weighting functions are used for adjusting the influence of each error on the total error when the test interval is not uniform, and the two weighting functions are both measured at equal intervals in the experiment, so that 1 is taken as each weighting function.
As shown in fig. 5, values of five parameters in the bidirectional reflection distribution function model of the energy storage reflective luminescent material of the sidewall material selected for the tunnel are found through actual measurement experiments and optimization algorithms. The fitting effect of the model is shown in fig. 6, and the parameters take the following values:
Figure BDA0002545828790000064
the fifth step: the light intensity in the direction of the calculation point is calculated. The intensity pointing in the direction of the calculation point can be expressed as L, and the intensity of the light in this direction is IabExpressed as described in equation (7):
Figure BDA0002545828790000065
where S is the area of the light emitting cell and C is the cleaning factor of the sidewall material.
Wherein
Figure BDA0002545828790000066
Is a material BRDF that defines the angle of incident scattering,
Figure BDA0002545828790000067
respectively, angle of incidence, angle of reflection, azimuth.
In this embodiment, for each reflector unit, there are 8 groups of incident light corresponding to 8 lamps in the calculation section, and 28 groups of emergent light corresponding to 28 road surface calculation points, so that at each reflector unit, 8 × 28-224 calculations need to be performed according to the formula in the disclosure, and this process can be implemented by a computer design program. All the calculation points can be obtained finally.
And a sixth step: and calculating the illumination caused by the reflection effect at the calculation point. Illuminance calculation the resulting illuminance increment E of the reflected light at calculation point f under the influence of all sidewall lighting unitsuAs shown in equation (8):
Figure BDA0002545828790000068
wherein IfbCalculating the horizontal illuminance (lx) generated by the point P for the road surface, m being the number of unit light sources, ωbIs the included angle (DEG), tau between the normal direction of the light-emitting unit b and the connecting line from the geometric central point thereof to the road surface calculation point PbAn included angle (degree), H, between a connecting line of a central point of the light reflecting unit b and a road surface calculation point P and the normal direction of the road surfacebThe vertical distance (m) between the center point of the light emitting unit b and the road surface is calculated.
The seventh step: and adding the calculation results of the first step and the sixth step at each point to obtain the illumination value of the road surface calculation point considering the reflection increment of the side wall of the tunnel. As shown in the following formula (9):
E＝Ep+Eu (9)
wherein E is the road surface calculation point illumination taking the reflection and synergy of the side wall into consideration, EpIs the illuminance produced by the direct projection of the lamp at the road surface calculation point, EuIs the reflective increment of the sidewall. The results are shown in fig. 7 and 8.
Fig. 9 is a schematic overall flow chart of the present embodiment. The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which is stored in a storage medium (such as ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal (such as a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present invention.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (6)

1. A tunnel illumination calculation method considering a sidewall bidirectional reflection distribution function is characterized in that: the method comprises the following steps:
s1: calculating the illuminance of a road surface calculation point caused by direct radiation of a lamp;
s2: discretizing the side wall of the tunnel, discretizing the tunnel interior material into a series of units with Bidirectional Reflection Distribution Functions (BRDF) by utilizing a finite element idea, and regarding the units as unit light sources in the lighting calculation process;
s3: sequentially calculating the illumination of each lamp to the light reflecting units on each side wall; in step S3, formula (3) is obtained by using the cosine equation:
Figure FDA0003621554390000011
wherein EabThe horizontal illuminance generated on the b unit light source by the a lamp is lx; i (c)ab，γab) The unit is cd which is the light intensity value of the a-th lamp on a certain unit light source and is taken according to a lamp light intensity table; beta is aabThe light incident angle of the a-th lamp corresponding to a certain unit light source is in degrees; thetaabA connecting line for connecting the a-th lamp with a certain unit light source center andthe angle between the normal directions of the unit light sources is in degrees; habIs the vertical distance between the a-th lamp and the central point of a unit light source, phi is the rated luminous flux of the lamp and the unit is lm; m is the maintenance coefficient of the lamp;
s4: establishing a bidirectional reflection distribution function model of the side wall material;
s5: calculating the light intensity in the direction of the calculation point;
s6: calculating the illumination caused by the reflection effect at the calculation point;
s7: calculating the illumination of the road surface calculation point considering the side wall reflection increment; and adding the calculation results of the step S1 and the step S6 at each point to obtain the illuminance value of the road surface calculation point considering the reflection increment of the side wall of the tunnel.
2. The method of claim 1 for computing tunnel illumination taking into account a bidirectional reflectance distribution function of a sidewall, wherein: in the step S1, the illuminance generated at the calculation point by the direct lighting of the luminaire can be calculated by using a cosine formula, as shown in formula (1):
Figure FDA0003621554390000012
the illuminance at the calculation point for multiple direct lighting fixtures is shown in equation (2):
Figure FDA0003621554390000013
wherein E ispiThe horizontal illumination generated by a lamp at a calculation point of a tunnel opening road surface is obtained; gamma is the incident light of the lamp corresponding to the calculation point; i iscyThe light intensity value of the lamp at a calculation point is obtained by checking a light distribution curve of the lamp; m is the maintenance coefficient of the lamp; phi is the rated luminous flux of the lamp; h is the height from the center of the light source of the lamp to the road surface; epThe sum of the horizontal illuminance generated by a plurality of lamps at a calculation point, n is the number of the lamps, and a group is taken before and after a calculation area during calculation.
3. The method of claim 1, wherein the method comprises: in said step S4, the BRDF is modeled by a five parameter model, as in equation (4):
Figure FDA0003621554390000021
Figure FDA0003621554390000022
wherein
Figure FDA0003621554390000023
Is a material BRDF that defines the angle of incident scattering,
Figure FDA0003621554390000024
the first term on the right side of the equation is a coherent component reflecting the specular reflection condition of the surface of the material, and the second term is a diffuse reflection coherent component reflecting the surface of the material; wherein k isb，kd，krAnd a and b are both parameters to be determined,
Figure FDA0003621554390000025
is a masking function;
the selection standard of each parameter of the model is that the standard deviation of simulation experiment data is minimum, and the mean square error of the standard deviation is calculated according to the formula (6):
Figure FDA0003621554390000026
wherein x ═ kb，kd，kr，a，b]TColumn vectors that are model parameters; f. ofrFitting data for the model;
Figure FDA0003621554390000027
is the measured data; g is a radical of formula1(θi) And g2(θr) Is a weighting function used to adjust the effect of individual errors on the total error when the trial spacing is not uniform.
4. The method of claim 1, wherein the method comprises: in said step S5, the brightness in the direction of the calculation point is represented as L, and the light intensity in this direction is represented as IabExpressed as described in equation (7):
Figure FDA0003621554390000028
wherein S is the area of the light emitting cell and C is the cleaning coefficient of the sidewall material;
wherein
Figure FDA0003621554390000029
Is a material BRDF that defines the angle of incident scattering,
Figure FDA00036215543900000210
respectively, angle of incidence, angle of reflection, azimuth.
5. The method of claim 1, wherein the method comprises: in the step S6, the illuminance calculation is performed on the generated illuminance increment E of the reflected light at the calculation point f by all the side-wall light-emitting unitsuAs shown in equation (8):
Figure FDA00036215543900000211
wherein IfbCalculating the horizontal illuminance generated by the point P for the road surface, m being the number of unit light sources, omegabCalculating point P from the normal direction of the light-emitting unit b and the geometric center point thereof to the road surfaceAngle between lines, τbCalculating an angle H between a connecting line of a central point of the light reflecting unit b and a road surface calculation point P and the normal direction of the road surfaceabThe vertical distance between the center point of the light emitting unit and the road surface P is calculated.
6. The method of claim 1, wherein the method comprises: in step S7, the road surface calculation point is calculated by taking the illuminance of the side wall reflection increment into consideration, as shown in the following equation (9):
E＝Ep+Eu (9)
wherein E is the road surface calculation point illumination taking the side wall reflection synergistic effect into consideration, EpIs the illuminance produced by the direct projection of the lamp at the road surface calculation point, EuIs the reflective increment of the sidewall.
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