A method for calculating the brightness of road lighting

Abstract

The present invention discloses a method for calculating the road lighting brightness. Taking a street lamp as a single light source, under the condition that the power of the street lamp and the vertical height between the lamp and the road surface are both constants, a mathematical model expression of the road surface brightness is established. This mathematical model of the road surface brightness depicts the brightness values of each point within the lighting coverage of the lamp. Through measured data, the trust region algorithm is used to fit this mathematical model of the road surface brightness to obtain relevant parameters. Then, according to the road surface range to be calculated, the mathematical model of the road surface brightness is integrated, and then divided by the road surface area to obtain the average brightness, and it is judged whether the specification requirements are met. The advantages of the present invention are: only relying on a luminance meter to measure a small amount of data can be used to estimate the lighting effect of street lamps, without the need for complex indoor tests, having the advantages of high efficiency and low cost, and being applicable to the lighting design requirements of temporary roads in municipal engineering.

Description

Technical Field

[0001] The present invention belongs to the technical field of lighting, and particularly relates to a method for calculating the brightness of road lighting. Background Art

[0002] During the construction of large-scale infrastructure such as urban roads, bridges, and subways, the original roads are occupied, and temporary roads need to be built for social vehicles and pedestrians to pass through, and corresponding street lights are configured to ensure the smoothness and safety of the roads.

[0003] Due to the attenuation of the lighting effect of the original street lights after long-term use, one problem that must be faced when relocating and using them is whether the actual lighting effect of the street lights can meet the needs of the temporary road. The lighting effect of the original street lights is affected by various factors such as the cumulative usage time, the location, the sanitation environment, and the characteristics of the street lights themselves, and it is difficult to obtain the result through theoretical calculation. Summary of the Invention

[0004] The object of the present invention is to provide a method for calculating the brightness of road lighting according to the deficiencies of the above-mentioned prior art. The calculation method takes the street light as a single light source, and under the condition that the power of the street light and the vertical height of the lamp to the road surface are both constants, a mathematical model expression of the road surface brightness is established. The mathematical model of the road surface brightness depicts the brightness values of each point within the lighting coverage of the lamp. Through the measured data, the mathematical model of the road surface brightness is fitted with the trust region algorithm to obtain relevant parameters, and then the mathematical model of the road surface brightness is integrated according to the road surface range to be calculated, and then divided by the road surface area to obtain the average brightness, and it is judged whether it meets the specification requirements.

[0005] The object of the present invention is achieved by the following technical solutions:

[0006] A method for calculating the brightness of road lighting, characterized in that the calculation method includes the following steps:

[0007] (1) Taking the orthographic projection of the lamp of the street light to be measured as the coordinate origin, taking the longitudinal direction of the road as the X-axis direction, and taking the transverse direction of the road as the Y-axis direction, to establish a plane rectangular coordinate system; under the condition that the power of the street light and the vertical height of the lamp to the road surface remain unchanged, select several points within the road range covered by the lamp lighting for actual measurement of the brightness values, and record the coordinates of each point and the corresponding brightness values;

[0008] (2) Establish the following mathematical model expression of the road surface brightness:

[0009] L = A·(x - x0) 2 + B·(y - y0) 2 + C Equation 1

[0010] In the formula:

[0011] L is the brightness value of the desired point, with the unit of cd / m 2 ;

[0012] x and y are the coordinates of the desired point, with the unit of m;

[0013] x0 and y0 are the coordinates of the road surface brightness center, determined by fitting, with the unit of m;

[0014] A, B, and C are all undetermined coefficients, obtained by fitting. The units of A and B are cd / m 4 , and the unit of C is cd / m 2 ;

[0015] Among them, the values of A, B, C, x0, and y0 are determined by fitting calculation using the trust region algorithm based on the principle of least squares data fitting;

[0016] (3) After the undetermined coefficients (A, B, C, x0, y0) in Equation 1 are determined by fitting calculation, perform a double integral on Equation 1 to solve for the total road brightness L within the road range covered by the lighting Z , and the calculation formula is:

[0017] Equation 2

[0018] In the formula:

[0019] L Z represents the total road brightness within the rectangle enclosed by x2 - x1 and y2 - y1;

[0020] x2 and x1 are respectively the starting point and ending point of the coordinates of the road range covered by the lighting of the street lamp on the X-axis;

[0021] y2 and y1 are respectively the starting point and ending point of the coordinates of the road range covered by the lighting of the street lamp on the Y-axis;

[0022] (4) Divide the total road brightness L within the rectangle enclosed by x2 - x1 and y2 - y1 Z by the area of the lighting coverage area to obtain the average brightness L of the street lamp to be measured in the lighting coverage area 平均 , and the calculation formula is:

[0023] L 平均 = L Z / [(x2 - x1) · (y2 - y1)] Equation 3;

[0024] (5) Compare the average brightness L of the street lamp to be measured in the lighting coverage area 平均 with the specification threshold, and adjust the power of the street lamp and change the spacing between adjacent street lamps to make the average brightness L 平均 meet the requirements of the specification threshold.

[0025] The method for fitting and calculating A, B, C, x0, and y0 by using the trust region algorithm based on the least squares data fitting principle in step (2) includes the following steps:

[0026] (a) Assume initial values for a set of parameters A, B, C, x0, and y0 to be fitted. Substitute the coordinates x i and y i of each measured point in step 1 into Equation 1, and calculate the corresponding brightness calculation value Li i ’ for the i-th point one by one. Then, according to Equation 3, subtract the brightness calculation value Li i ’ of the i-th point from the measured brightness value Li i of the i-th point to find the error, square it, and then perform cumulative summation:

[0027] Equation 4

[0028] In the formula:

[0029] n represents the number of measured points;

[0030] (b) Use the simplified quadratic function m k to approximate the objective function f(x) shown in Equation 3. The quadratic function m k adopts the first three terms of the Taylor expansion of the objective function f(x) at the point X k . The calculation formula is as follows:

[0031] Equation 5

[0032] Select a trust radius △ k , and find the update amount d that makes the quadratic function m k decrease fastest as the iteration step size. Iterate the quadratic function m k k times to obtain the decrease amount △m k . The calculation formula is as follows:

[0033] Equation 6

[0034] In the formula:

[0035] g k is the first derivative of the objective function f(x) at the k-th point, ;

[0036] H k is the second derivative of the objective function f(x) at the k-th point, ;

[0037] When the quadratic function mk When the first derivative approximation reaches 0, it can be considered that the extreme point has been reached, and the undetermined coefficients A, B, C, x0, and y0 at this time are obtained.

[0038] The advantages of the present invention are as follows: Only a small amount of data measured by a luminance meter can be used to estimate the lighting effect of street lamps, without the need for complex indoor tests. It has the advantages of high efficiency and low cost, and is suitable for the lighting design requirements of temporary roads in municipal engineering. Brief Description of the Drawings

[0039] Figure 1 is a schematic plan view of the street lamp layout in the present invention;

[0040] Figure 2 is a schematic diagram of the fitting result of the pavement luminance mathematical model in the present invention. Detailed Embodiment

[0041] The features of the present invention and other related features are further described in detail below with reference to the accompanying drawings through embodiments for the understanding of those skilled in the same industry:

[0042] As Figure 1-2 , each label in the figure is: lamp 1.

[0043] Embodiment: As Figure 1 , 2 shown, this embodiment specifically relates to a calculation method for road lighting luminance. In order to meet the requirements for pavement luminance in the road lighting code and adapt to the needs of rapid adjustment of temporary roads, with the street lamp as a single light source, when the power of the street lamp and the vertical height between the lamp and the road surface are both constants, a pavement luminance mathematical model expression is established. This pavement luminance mathematical model depicts the luminance values of each point within the illumination range of lamp 1. Through measured data, the pavement luminance mathematical model is fitted with a trust region algorithm to obtain relevant parameters. Then, according to the pavement range to be calculated, the pavement luminance mathematical model is integrated, and then divided by the pavement area to obtain the average luminance, and it is judged whether it meets the code requirements. If it exceeds the allowable range of the code, measures such as adjusting the power of the street lamp lamp 1 and changing the street lamp spacing can be taken to improve it, achieving the purpose of meeting the lighting requirements and saving energy.

[0044] The calculation method for road lighting luminance in this embodiment specifically includes the following steps:

[0045] (1) As Figure 1The following is a schematic plan view of the street lamp layout in this embodiment. The lamp post projects from the outside of the road edge to the inside of the road edge. The lamp post is 25 m away from the left lamp post and 20 m away from the right lamp post. The lighting coverage area of the street lamp can be approximately regarded as an ellipse. Taking the orthographic projection of the lamp of the street lamp as the coordinate origin, with the longitudinal direction of the road as the X-axis direction and the transverse direction of the road as the Y-axis direction, a plane rectangular coordinate system is established. Under the condition that the power of the street lamp and the vertical height of the lamp from the road surface are both constants, several points are selected within the illumination range of the lamp for actual measurement of the brightness values, and the point coordinates and the corresponding brightness values are recorded.

[0046] (2) Under the condition that the power of the street lamp and the vertical height of the lamp from the road surface are both constants, the following mathematical model expression of the road surface brightness is established:

[0047] L = A·(x - x0) 2 + B·(y - y0) 2 + C Formula 1

[0048] In the formula:

[0049] L is the brightness of the point to be obtained, with the unit of cd / m 2 ;

[0050] x, y are the coordinates of the point to be obtained, with the unit of m;

[0051] x0, y0 are the coordinates of the road surface brightness center, determined by fitting, with the unit of m; It should be noted that due to factors such as the geometric shape, pitch angle, and installation error of the street lamp head, the brightness center is not necessarily at the coordinate origin (the orthographic projection position of the lamp), so two parameters x0 and y0 are introduced in Formula 1 as the coordinates of the brightness center and determined by data fitting;

[0052] A, B, and C are all undetermined coefficients, obtained by fitting. The units of A and B are cd / m 4 , and the unit of C is cd / m 2 ;

[0053] It should be noted that for A, B, C, x0, y0, the Trust Region algorithm designed based on the least squares principle is cited. This algorithm has been developed over the years and can be implemented by a computer. The principle of least squares fitting is as follows: First, assume initial values for a set of parameters to be fitted (consisting of A, B, C, x0, y0), substitute each group of measured values x i , y i into Formula 1, and calculate the corresponding L i ’ one by one. Then, compare L i ’ with L iSubtract to find the error, and then find the sum of squares, as shown in Equation 2 below. The set of parameters that minimizes the sum of squares is the desired fitting result;

[0054] Equation 2

[0055] In the formula:

[0056] L i ’ is the calculated value of the brightness at the i-th point;

[0057] L i is the measured value of the brightness at the i-th point;

[0058] n is the number of groups of measured data.

[0059] The expanded form after applying the above least squares fitting principle to Equation 1 is as follows:

[0060] Equation 3

[0061] In the formula:

[0062] f(x) represents the sum of the squares of the errors between the calculated brightness value and the measured brightness value obtained by fitting each point (including coordinates x, y, and brightness value L) through the road surface brightness mathematical model. The set of coefficients (A, B, C, x0, y0) when this value f(x) reaches the minimum is the best fitting result. This is the basic principle of least squares data fitting.

[0063] It should be noted that the trust region algorithm is specifically implemented to apply this least squares data fitting principle. The following Equations 4 and 5 are the basic steps of this trust region algorithm: A simplified quadratic function m k is used to approximate the objective function f(x) (i.e., Equation 3). The quadratic function m k uses the first three terms of the Taylor expansion of the objective function f(x) at the point X k ; then a trust radius △ k is selected, and the update amount d that makes m k decrease the fastest is found within it as the iteration step size. m k is used as the quadratic function. When its first derivative approaches 0, it can be considered that the extreme point has been reached, and the undetermined coefficients (A, B, C, x0, y0) at this time are obtained;

[0064] Equation 4

[0065] Equation 5

[0066] In the formula:

[0067] △m kDenotes the quadratic function descent of the objective function \(f(x)\) in Equation 3 after \(k\) iterations;

[0068] X k Denotes the descent of the objective function \(f(x)\) at the \(k\)-th point;

[0069] g k Is the first derivative of \(f(x)\) at the \(k\)-th point, ;

[0070] H k Is the second derivative of \(f(x)\) at the \(k\)-th point, ;

[0071] It should be noted that it is defined r k = Equation 5 / Equation 4; If r k Is close to 1, it indicates that the quadratic function descent is approximately the objective function. At this time, r k Can be used as a new iteration point; If r k <0, then X k Cannot be used as an iteration point, and the trust region radius needs to be reduced to re-solve the quadratic function. The trust region algorithm is essentially an iterative algorithm suitable for computer operation. It can be regarded as testing whether it has reached flat ground at each step down in the dark. It is a process of gradually approaching the extreme point. Because the objective function may be very complex, for example, the geometric shape of its function is like a bowl with undulating inner walls. During the computer iteration process, it may fall into the "local minimum", which is very common in the fields of fitting and machine learning algorithms. It is equivalent to a person going downstairs in the dark, thinking that they have reached the bottom flat ground, but actually still staying on the middle floor. Therefore, the trust region algorithm uses the first 3 terms of the Taylor expansion of the objective function to approximately replace the objective function. The advantage is that the approximate function is smooth, continuous, and differentiable, and its second derivative is the Hessian positive definite matrix, with very good convex optimization properties. It can avoid falling into the "local minimum".

[0072] For the specific algorithm, at the iteration point, let the independent variable increase by 1 step size \(d\), calculate the change in the objective function at this time, and at the same time calculate the change in the approximate objective function, and then calculate whether the ratio of the two changes is close to 1. Its purpose is to measure the substitution effect of the approximate objective function. If it is less than 0, it means that the value of the step size \(d\) is too large, resulting in the approximate function "going too far". Then reduce the step size \(d\), for example, reduce it to \(0.5d\), and repeat the above steps until the change in the function is less than a certain preset minimum value, then terminate the operation. At this time, the independent variable is the required value, which in this case is the fitting parameters \(A\), \(B\), \(C\), \(x0\), \(y0\).

[0073] In engineering problems, it is almost impossible to encounter a situation where the calculation result is exactly zero. A value less than a certain minimum value is sufficient. The accuracy of approximating with the first three terms of the Taylor expansion can meet the accuracy requirements of most engineering problems.

[0074] (3) After determining the fitting and solving of each undetermined coefficient (A, B, C, x0, y0) in Equation 1, perform a double integral on Equation 1 to solve for the total road brightness L within the rectangular range. Z , and the calculation formula is:

[0075] Equation 6

[0076] In the formula:

[0077] L Z represents the total brightness of the road within the rectangular range enclosed by x2 - x1 and y2 - y1;

[0078] x2 and x1 are respectively the starting and ending abscissas of the road range covered by the street lamp lighting;

[0079] y2 and y1 are respectively the starting and ending ordinates of the road range covered by the street lamp lighting.

[0080] (4) Divide the total brightness L of the road within the rectangular range enclosed by x2 - x1 and y2 - y1 Z by the area of the street lamp calculation area to obtain the average brightness L of the street lamp calculation area 平均 , and the calculation formula is:

[0081] L 平均 = L Z / [(x2 - x1) · (y2 - y1)] Equation 7

[0082] In the formula:

[0083] L 平均 is the average brightness of the street lamp calculation area.

[0084] (5) Determine whether the calculated average brightness L 平均 meets the specification requirements. If it exceeds the allowable range of the specification, measures such as adjusting the street lamp power and changing the street lamp spacing can be taken to improve it, achieving the purpose of meeting the lighting requirements and saving energy.

[0085] The beneficial effect of this embodiment is that only a small amount of data measured by the luminance meter can be used to estimate the street lamp lighting effect, without the need for complex indoor tests, having the advantages of high efficiency and low cost, and being suitable for the lighting design needs of temporary roads in municipal engineering.

Claims

1. A method for calculating the brightness of road lighting, characterized in that The calculation method includes the following steps: (1) Taking the orthographic projection of the luminaire of the street lamp to be measured as the coordinate origin, with the longitudinal direction of the road as the X-axis direction and the transverse direction of the road as the Y-axis direction, a plane rectangular coordinate system is established; under the condition that the power of the street lamp and the perpendicular height of the luminaire from the road surface remain unchanged, several points within the road range covered by the luminaire illumination are selected for actual measurement of the brightness values, and the coordinates of each point and the corresponding brightness values are recorded; (2) Establish the following mathematical model expression for the road surface brightness: L = A·(x - x0) 2 + B·(y - y0) 2 + C Equation 1 In the formula: L is the luminance value of the desired point, with the unit of cd / m 2 ; x and y are the coordinates of the point to be obtained, with the unit of m; x0 and y0 are the coordinates of the center of the road surface brightness, determined by fitting, with the unit of m; A, B, and C are all undetermined coefficients obtained by fitting. The units of A and B are cd / m 4 , and the unit of C is cd / m 2 ; Among them, the values of A, B, C, x0, and y0 are determined by fitting calculation using the trust region algorithm based on the principle of least squares data fitting; After the fitting calculations of the undetermined coefficients (A, B, C, x0, y0) in Equation 1 are determined, a double integral is performed on Equation 1 to solve for the total road luminance L within the illuminated road range. Z The calculation formula is as follows: Formula 2 In the formula: L Z represents the total road luminance within the rectangle enclosed by x2 - x1 and y2 - y1; x2 and x1 are respectively the starting point and the ending point of the coordinates of the road range covered by the illumination of the street lamp on the X-axis; y2 and y1 are respectively the starting point and the ending point of the coordinates of the road range covered by the illumination of the street lamp on the Y-axis; (4) Divide the total road luminance L within the rectangle enclosed by x2 - x1 and y2 - y1 Z by the area of the lighting coverage area to obtain the average luminance L of the street lamp to be measured in the lighting coverage area 平均 , and the calculation formula is: L 平均 = L Z / [(x2 - x1)·(y2 - y1)] Equation 3; (5) Compare the average brightness L of the street lamp to be measured in the lighting coverage area 平均 with the specification threshold, and adjust the power of the street lamp and change the distance between adjacent street lamps to make the average brightness L 平均 meet the requirements of the specification threshold.

2. The calculation method of road lighting brightness according to claim 1, wherein The method for determining A, B, C, x0, and y0 by fitting calculation using the trust region algorithm based on the principle of least squares data fitting in step (2) includes the following steps: (a) Assume initial values for a set of parameters A, B, C, x0, and y0 to be fitted, and substitute the coordinates x i and y i of each measured point in step 1 into Equation 1, and calculate the corresponding calculated brightness value Li i ’ for each point one by one. Then, according to Equation 3, subtract the calculated brightness value Li i ’ of the ith point from the measured brightness value Li i of the ith point to find the error, square it, and then perform cumulative summation: Formula 4 In the formula: n represents the number of actually measured points; (b) Using the simplified quadratic function m k The objective function f(x) shown in the approximation formula 3, the quadratic function m k Using the first three terms of the Taylor expansion of the objective function f(x) at the point X k The calculation formula is as follows: Formula 5 Select a trust radius △ k , and find the update amount d that makes the quadratic function m k decrease the fastest as the iteration step size. Iterate the quadratic function m k k times to obtain the decrease amount △m k . The calculation formula is as follows: Formula 6 In the formula: g k is the first derivative of the objective function f(x) at point k, ; H k is the second derivative of the objective function f(x) at point k, ; When the first derivative of the quadratic function m k approaches 0, it can be considered that the extreme point has been reached, and the undetermined coefficients A, B, C, x0, and y0 at this time are obtained.

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