Lighting system tolerance sensitivity analysis method based on Latin hypercube sampling

Abstract

The invention belongs to the technical field of optical design, and particularly relates to an illumination system tolerance sensitivity analysis method based on Latin hypercube sampling. Comprising the following steps: S1, determining at least two tolerance items of the lighting system, and setting a central value and a tolerance change range for each tolerance item; s2, taking each tolerance item as a sampling dimension, and performing multi-dimensional sampling by adopting a Latin hypercube sampling method to obtain a sampling point set; s3, sequentially mapping sampling points contained in the sampling point set to a tolerance change range of a corresponding tolerance item to obtain a mapped discrete point set; s4, calculating evaluation function values in one-to-one correspondence with discrete points contained in the discrete point set based on a ray tracing method, and constructing a multi-dimensional fitting model; and S5, sequentially substituting the central value of each tolerance item into the multi-dimensional fitting model, correspondingly obtaining a response curve of each tolerance item, and completing sensitivity analysis of each tolerance item. According to the method, the problem of multivariable tolerance analysis in illumination design can be clearly and efficiently solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of optical design, and particularly relates to a lighting system tolerance sensitivity analysis method based on Latin hypercube sampling. BACKGROUND

[0002] In the design and manufacturing process of a lighting system, tolerance analysis of the system is an indispensable process. Lighting products have high requirements on optical performance, and optical systems are often sensitive to the geometric size, position and material parameters of components. Small deviations can cause problems such as unbalanced light intensity distribution, insufficient illumination, color shift, etc. in the actual application of the lighting system, thereby affecting product performance and user experience. Through systematic tolerance analysis, the influence of manufacturing and assembly errors on optical performance can be evaluated at the design stage, and key tolerance sources can be identified to provide a basis for subsequent manufacturing process control and quality management. In addition, tolerance analysis of the lighting system helps to achieve design optimization and cost control.

[0003] At the same time, the tolerance analysis of the lighting system usually relies on a large number of ray tracing to evaluate the influence of each tolerance on the system performance. In a typical tolerance analysis process, a large number of variable combinations in the design are iteratively calculated through Monte Carlo simulation or parameter perturbation. Each tolerance configuration requires complete ray tracing simulation to evaluate key performance indicators such as illumination distribution, luminous flux efficiency, glare control, etc. However, as a highly precise optical simulation method, ray tracing has a very high computational cost, especially in complex optical systems, a large number of rays are often required to obtain stable statistical results. In the tolerance analysis of the lighting system, it is more critical to design an effective sampling strategy among multiple parameters. Usually, a lighting system involves multiple geometric, material and assembly tolerance parameters, such as lens displacement, light source offset, curved surface curvature, refractive index variation, etc. For such a multi-variable system, if the sampling distribution is unreasonable, not only will it cause waste of simulation resources, but also may cause deviation or non-convergence of the analysis results.

[0004] In the sampling analysis of high-dimensional space of multiple parameters, the uniformity of sampling between parameters has a decisive influence on the reliability and computational efficiency of the results. Traditional random sampling methods often have the problem of uneven distribution in high-dimensional space, and a large number of samples are often required to cover the entire tolerance space, which has a very high computational cost for lighting systems that rely on ray tracing. In summary, reasonable design of a multi-parameter sampling strategy is one of the important technologies for efficient optical analysis of high-dimensional tolerance space, and has important significance for speeding up simulation and improving reliability. SUMMARY

[0005] In view of this, the present application aims to provide a lighting system tolerance sensitivity analysis method based on Latin hypercube sampling, to solve the problem that the traditional random sampling method cannot evenly distribute samples in a multi-parameter high-dimensional space, requires a large number of samples to cover the entire tolerance space, and the light tracing simulation calculation cost relied on by the tolerance analysis is extremely high, which not only wastes simulation resources, but also may cause the analysis result to deviate or not converge. The present application is a multi-parameter tolerance analysis method based on Latin hypercube sampling (LHS), which performs multi-dimensional fitting between the evaluation function value and the sampling points after sampling, and converts the surface projection to a single variable space after fitting, thereby clearly and efficiently solving the problem of multi-variable tolerance analysis in lighting design.

[0006] To achieve the above purpose, the technical scheme of the present application is as follows: A lighting system tolerance sensitivity analysis method based on Latin hypercube sampling, specifically comprising the following steps: S1: determining at least two tolerance items of the lighting system, and setting a center value and a tolerance variation range for each tolerance item; S2: taking each tolerance item as a sampling dimension, using the Latin hypercube sampling method for multi-dimensional sampling to obtain a set of sampling points; S3: mapping the sampling points contained in the set of sampling points to the tolerance variation range of the corresponding tolerance item in turn to obtain a set of discrete points after mapping; S4: calculating the evaluation function value corresponding to each discrete point in the set of discrete points based on the light tracing method, and constructing a multi-dimensional fitting model; S5: substituting the center value of each tolerance item into the multi-dimensional fitting model in turn to obtain the response curve of each tolerance item, and completing the sensitivity analysis of each tolerance item.

[0007] Further, in step S1, the tolerance items of the lighting system are geometric parameters, material parameters or assembly parameters.

[0008] Further, in step S3, the sampling points are mapped to the tolerance interval of the corresponding tolerance item by the following formula to obtain the discrete points after mapping: ; Wherein, is the variable of the kth discrete point in the i th sampling dimension, , is the tolerance variation range of the i th sampling dimension, is the variable of the kth sampling point in the i th sampling dimension.

[0009] Further, in step S4, the evaluation function is the uniformity of illumination or the total illuminance of the target surface.

[0010] Further, in step S4, the multi-dimensional fitting model F is: ; wherein, , and are fitting coefficients, n is the total number of dimensions, i and j are dimension serial number indexes, is the tolerance term corresponding to the i-th sampling dimension, is the tolerance term corresponding to the j-th sampling dimension.

[0011] Compared with the prior art, the present application can achieve the following beneficial effects: The present application discloses a lighting system tolerance sensitivity analysis method based on Latin hypercube sampling. After sampling, the evaluation function value is multi-dimensionally fitted with the sampling points. After fitting, the surface projection is converted to a single variable space, thereby clearly and efficiently solving the problem of multi-variable tolerance analysis in lighting design. BRIEF DESCRIPTION OF DRAWINGS

[0012] The accompanying drawings, which form a part of the present application, are used to provide further understanding of the present application, and serve as an aid in explaining the present application. The schematic embodiments of the present application and their descriptions serve to explain the present application, and do not constitute an improper limitation on the present application. In the drawings: Figure 1 FIG. 1 is a flowchart of the lighting system tolerance sensitivity analysis method based on Latin hypercube sampling according to an embodiment of the present application; Figure 2 FIG. 2 is a diagram of sampling effects according to an embodiment of the present application; Figure 3 FIG. 3 is a diagram of index comparison between random sampling and LHS sampling according to an embodiment of the present application; Figure 4 FIG. 4 is a diagram of a tolerance analysis model according to an embodiment of the present application; Figure 5 FIG. 5 is a diagram of two-dimensional fitting effects according to an embodiment of the present application; Figure 6 FIG. 6 is a diagram of single variable tolerance response according to an embodiment of the present application.

[0013] Explanation of reference signs: 1, point light source; 2, single lens; 3, target surface. DETAILED DESCRIPTION

[0014] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below with reference to the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and do not constitute a limitation on the present application.

[0015] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0016] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0017] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0018] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] like Figure 1 As shown, this invention provides a tolerance sensitivity analysis method for lighting systems based on Latin hypercube sampling, specifically including the following steps: S1: Determine at least two tolerance items for the lighting system, and set the center value and tolerance variation range for each tolerance item; S2: Treat each tolerance item as a sampling dimension and use the Latin hypercube sampling method to perform multi-dimensional sampling to obtain a set of sampling points; S3: Map the sampling points contained in the sampling point set to the tolerance variation range of the corresponding tolerance item in sequence to obtain the mapped discrete point set; S4: Based on the ray tracing method, calculate the evaluation function value corresponding one-to-one with the discrete points contained in the discrete point set, and construct a multidimensional fitting model; S5: Substitute the center values ​​of each tolerance item into the multidimensional fitting model in sequence to obtain the response curves of each tolerance item, and complete the sensitivity analysis of each tolerance item.

[0020] In some embodiments, in step S1, the tolerances of the lighting system are geometric parameters, material parameters, or assembly parameters.

[0021] In some embodiments, in step S3, the sampling points are mapped to the tolerance interval of the corresponding tolerance item using the following formula to obtain the mapped discrete points: ; in, Let be the variable of the k-th discrete point in the i-th sampling dimension, that is, one of the elements of the mapped discrete point, [ , [ ] represents the tolerance variation range of the i-th sampling dimension. Let be the variable of the k-th sampling point in the i-th sampling dimension, that is, one of the elements of the sampling point.

[0022] In some embodiments, in step S4, the evaluation function is illumination uniformity or total illuminance of the target surface.

[0023] In some embodiments, in step S4, the multidimensional fitting model F is: ; in, , and All are fitting coefficients, where n is the total number of dimensions, and i and j are both dimension indices. For the tolerance term corresponding to the i-th sampling dimension, This is the tolerance term corresponding to the j-th sampling dimension.

[0024] The specific process is as follows: First, set the variables to be analyzed as tolerances, and define their center value and range of variation. Theoretically, any variable can be set as a tolerance term, such as the spectrum of a light source, the position parameters of a lens, or the radius of curvature of a surface. Then, sample the tolerance terms to be analyzed as set above.

[0025] Traditional multidimensional random sampling involves directly generating random variables within each dimension. Assuming the dimension of the tolerance to be analyzed is n, and the number of sampling points is K, then for the k-th sampling point in the i-th dimension, the method for generating the sampling point is as follows: , This refers to computer-generated random numbers that satisfy a uniform distribution. For example... Figure 2 As shown in (a), when the sampling dimension n=2 and the number of sampling points K=20, a two-dimensional distribution result can be generated through random sampling. Observation Figure 2(a) in FIG. 1 shows that the distribution of the generated multiple sampling points is not uniform using ordinary random sampling. There are often oversampling in a small area (e.g. the small ellipse in (a) in FIG. 1) and undersampling in a large area (e.g. the large ellipse in (a) in FIG. 1). Figure 2 Figure 2 The sampling points in the small ellipse in (a) in FIG. 1 are too close to each other, and the sampling points in the large ellipse in (a) in FIG. 1 are too far from each other. When using Latin hypercube sampling, the sampling area of each dimension data is segmented, and uniform sampling is performed in each segment of each dimension. After sampling, the different dimension data are randomly combined to generate 20 sampling points. The sampling effect of LHS is shown in (b) in FIG. 1. Figure 2

[0026] For the two sampling methods, the uniformity is quantitatively analyzed. Assuming that the two-dimensional sampling points are , the kth sampling point can be expressed as . For all sampling points, the Euclidean distance d between different sampling points can be calculated, thereby obtaining the Euclidean distance set D composed of the Euclidean distances between different sampling points. The Euclidean distance between the k1th sampling point and the k2th sampling point is calculated using the following formula: , ; wherein and are the k1th sampling point and the k2th sampling point, respectively.

[0027] The sampling uniformity and stability of the two sampling methods can be evaluated by the following two indicators.

[0028] The first indicator is the minimum distance (MD). When the minimum distance is larger, the distance between the sampling points is larger, and the sampling points are more dispersed, so that the situation that the sampling points are gathered together can be avoided. For the Euclidean distance set D, the expression of the minimum distance is: .

[0029] The second indicator is the standard deviation (Std) of the distance between the sampling points. Assuming that the number of sampling points is K, the intermediate variable is defined, and then . When the standard deviation of the distance between the sampling points is smaller, the sampling points are more dispersed. The standard deviation of the distance between the sampling points is as follows: ; wherein is the arithmetic mean of the elements contained in the Euclidean distance set D.

[0030] For the same number of sampling points, the above two indicators are calculated by taking the average of 10 samplings. The results are shown in​​Figure 3 As shown, where, Figure 3 (a) in the figure represents a comparison of the performance of random sampling and LHG sampling on the MD index. Figure 3 The comparison chart (b) of random sampling and LHG sampling on the Std index shows that for different sampling points, the minimum distance between LHS sampling points is greater than that of random sampling, avoiding point clustering. Furthermore, most standard deviations of LHS sampling are smaller than those of random sampling, and LHS sampling exhibits less volatility, indicating that LHS sampling is more uniform and stable than random sampling. Therefore, LHS sampling is more suitable for a small number of sampling points, where each sampling point corresponds to a large computational load.

[0031] After completing the initial LHS sampling, the sampling points Transforming to the tolerance interval, assume the maximum tolerance value of the variable in the i-th dimension is... The minimum value is The conversion formula is as follows: ; At this point, the discrete point set obtained by Latin sampling can be calculated. .

[0032] After transformation, ray tracing is performed on these discrete points, and an evaluation function is constructed. The value of the evaluation function at each discrete point is calculated. In illumination, the evaluation function can be illumination uniformity or total illuminance of the target surface, etc.

[0033] After obtaining the relationship between the distribution of the evaluation function and discrete points of different dimensions, the two are fitted together. The fitted result yields a continuous result of the evaluation function and different tolerance terms. Assume the dimension of the tolerance in LHS sampling is n, and the number of sampling points is K. To more easily illustrate the sampling principle, we will use two-dimensional sampling (n=2) as an example. For two-dimensional sampling, the k-th discrete point is... Assuming and The center value is the initial design value for the tolerance. The evaluation function vector obtained through ray tracing is... The two-dimensional fitting function can then be expressed as follows: ; in, The coefficients are undetermined, and the subscripts 1 and 2 represent the corresponding two dimensions. Assume the vector formed by the coefficients is... For each discrete sample point In this regard, the constructed feature vector is: ; By combining all the eigenvectors, we can obtain the design matrix. : ; At the same time, the column vector composed of the evaluation function is For the above analysis, the objective function can be constructed as follows: ; For the above equation, the analytical solution is: ; The obtained coefficient vector is expanded to obtain the value of each coefficient:

[0034] If the variable dimension is greater than 2, the corresponding dimension expansion can be performed on the calculation.

[0035] After the formula is combined, the fitting polynomial result is projected into a dimension to obtain the single tolerance sensitivity result. For the two-dimensional fitting mentioned above, if the central value of the tolerance term is , the tolerance response about the tolerance term is: ; Similarly, the tolerance response curve about the tolerance term can be obtained.

[0036] Example 1 This example uses a single-lens 2-based transmissive lighting system for correlation analysis, as shown in Figure 4 , the light source is a point light source 1, and the light emitting characteristics of the light source meet Lambert's law. The total optical power of the light source is 1 W. The light emitted by the light source enters the target surface 3 after passing through the single lens 2.

[0037] The optical system parameters of the single-lens 2-based transmissive lighting system are shown in Table 1.

[0038]

[0039] The first surface of the single lens 2 is set as a plane, and the second surface is set as a quadratic surface. The light emitting half angle of the light source is 20°. The expression of the optical quadratic surface is as follows, and when the surface type of the second surface changes, the illuminance of the target surface 3 will also change.

[0040] ; 1) Set the change range of the tolerance term For the single-lens 2 based transmissive illumination system, the radius of curvature c and the quadratic coefficient k of the second surface are assumed to be tolerance items, and the design values and variation ranges thereof are shown in Table 2. When the radius of curvature c and the quadratic coefficient k vary, the total energy received on the target surface 3 varies, and in particular, when the radius of curvature c drops to a certain value, the spot radius received on the target surface 3 expands, the energy overflows the target surface 3, and thus the energy received on the target surface 3 becomes smaller. In the following, the total energy of the target surface 3 is defined as an evaluation function according to the sensitivity analysis of the system.

[0041]

[0042] The LHS method is used to perform two-dimensional sampling in the interval , and 100 scattered point sets are sampled. Since the process has been described in detail in Section 3, it is not expanded here. The sampled data is converted to the variation interval of the design value (i.e. the tolerance interval), and for the radius of curvature c, the variation interval is , and for the quadratic coefficient k, the variation interval is .

[0043] After the sampling points of the radius of curvature c and the quadratic coefficient k are converted, ray tracing is performed to calculate the evaluation function value , , which represents the total energy received on the target surface 3. The number of rays traced each time is on the order of 1e6, which is relatively large.

[0044] Since the embodiment uses two-dimensional parameters, the two-dimensional fitting model is ; The discrete point set calculated in the previous step is fitted using the two-dimensional fitting model. The sampling points and the fitted surface are shown in Figure 5 . The initial value c0=-0.1 of the radius of curvature c is substituted into the two-dimensional fitting model to obtain the tolerance response curve about the quadratic coefficient k, and similarly, k0=0 is introduced into the two-dimensional fitting model to obtain the response curve about the radius of curvature c. As shown in Figure 6 , wherein Figure 6 , (a) in the figure is the tolerance response curve about the quadratic coefficient k, Figure 6 , and (b) is the tolerance response curve about the radius of curvature c. Thus, the tolerance analysis process is completed.

[0045] It should be understood that the various forms of the flow shown above can be reordered, added to, or deleted from. For example, the steps described in the present disclosure can be executed in parallel, in sequence, or in a different order, and the present disclosure is not limited herein as long as the desired results of the technical solutions of the present disclosure can be achieved.

[0046] The foregoing detailed description has set forth various embodiments of the devices and / or processes via the use of specific terminology. However, embodiments thereof can be practiced with the exact description not being presented in detail. The term "device" should be understood to encompass devices and / or processes. The embodiments are not limited to the specific devices, methods, or implementations described. The terminology used can include the use of common or specific terminology that is understood by those skilled in the art and / or as is used in the patent field. Embodiments of the devices and / or processes can be practiced with the exact description not being presented in detail. The embodiments are not limited to the specific devices, methods, or implementations described. The terminology used can include the use of common or specific terminology that is understood by those skilled in the art and / or as is used in the patent field.

Claims

1. A tolerance sensitivity analysis method for lighting systems based on Latin hypercube sampling, characterized in that: Specifically, the steps include the following: S1: Determine at least two tolerance items for the lighting system, and set the center value and tolerance variation range for each tolerance item; S2: Treat each tolerance item as a sampling dimension and use the Latin hypercube sampling method to perform multi-dimensional sampling to obtain a set of sampling points; S3: Map the sampling points contained in the sampling point set to the tolerance variation range of the corresponding tolerance item in sequence to obtain the mapped discrete point set; S4: Based on the ray tracing method, calculate the evaluation function value corresponding one-to-one with the discrete points contained in the discrete point set, and construct a multidimensional fitting model; S5: Substitute the center values ​​of each tolerance item into the multidimensional fitting model in sequence to obtain the response curves of each tolerance item, and complete the sensitivity analysis of each tolerance item.

2. The method for tolerance and sensitivity analysis of lighting systems based on Latin hypercube sampling according to claim 1, characterized in that: In step S1, the tolerances of the lighting system are geometric parameters, material parameters, or assembly parameters.

3. The method for tolerance and sensitivity analysis of lighting systems based on Latin hypercube sampling according to claim 1, characterized in that: In step S3, the sampling points are mapped to the tolerance intervals of the corresponding tolerance items using the following formula to obtain the mapped discrete points: ； in, Let [the variable be the k-th discrete point in the i-th sampling dimension], , [ ] represents the tolerance variation range of the i-th sampling dimension. Let be the variable of the k-th sampling point in the i-th sampling dimension.

4. The method for tolerance and sensitivity analysis of lighting systems based on Latin hypercube sampling according to claim 1, characterized in that: In step S4, the evaluation function is either the uniformity of illumination or the total illuminance of the target surface.

5. The method for tolerance and sensitivity analysis of lighting systems based on Latin hypercube sampling according to claim 1, characterized in that: In step S4, the multidimensional fitting model F is: ； in, , and All are fitting coefficients, where n is the total number of dimensions, and i and j are both dimension indices. For the tolerance term corresponding to the i-th sampling dimension, This is the tolerance term corresponding to the j-th sampling dimension.

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