Tolerance Sensitivity Analysis Method for Lighting Systems Based on Latin Hypercube Sampling

Abstract

This invention belongs to the field of optical design technology, and particularly relates to a tolerance sensitivity analysis method for lighting systems based on Latin hypercube sampling. The method includes: S1: Determining at least two tolerance items of the lighting system and setting a center value and tolerance variation range for each tolerance item; S2: Treating each tolerance item as a sampling dimension, performing multi-dimensional sampling using the Latin hypercube sampling method to obtain a set of sampling points; S3: Mapping the sampling points contained in the set of sampling points sequentially to the tolerance variation range of the corresponding tolerance item to obtain a set of mapped discrete points; S4: Calculating the evaluation function values ​​corresponding one-to-one with the discrete points contained in the set of discrete points based on ray tracing, and constructing a multi-dimensional fitting model; S5: Substituting the center value of each tolerance item sequentially into the multi-dimensional fitting model to obtain the response curve of each tolerance item, thus completing the sensitivity analysis of each tolerance item. This invention can clearly and efficiently solve the problem of multivariate tolerance analysis in lighting design.

Description

Technical Field

[0001] This invention belongs to the field of optical design technology, and in particular relates to a tolerance sensitivity analysis method for lighting systems based on Latin hypercube sampling. Background Technology

[0002] In the design and manufacturing process of lighting systems, tolerance analysis is an essential step. Lighting products have high requirements for optical performance, and optical systems are often sensitive to the geometric dimensions, position, and material parameters of their components. Even minor deviations can lead to problems such as unbalanced light intensity distribution, insufficient illuminance, and color shifts in practical applications, thus affecting product performance and user experience. By conducting systematic tolerance analysis, the impact of manufacturing and assembly errors on optical performance can be assessed during the design phase, key tolerance sources can be identified, and a basis for subsequent manufacturing process control and quality management can be provided. Furthermore, tolerance analysis of lighting systems helps to achieve design optimization and cost control.

[0003] Meanwhile, tolerance analysis of lighting systems typically relies on extensive ray tracing to assess the impact of various tolerances on system performance. In a typical tolerance analysis process, Monte Carlo simulations or parametric perturbation methods are used to iteratively calculate multiple combinations of variables in the design. Each tolerance configuration requires a complete ray tracing simulation to evaluate key performance indicators such as illumination distribution, luminous flux efficiency, and glare control. However, ray tracing, as a highly accurate optical simulation method, is computationally very expensive, especially in complex optical systems where a vast number of rays are often needed to obtain stable statistical results. In tolerance analysis of lighting systems, the design of an effective sampling strategy among multiple parameters is even more crucial. Typically, a lighting system involves multiple geometric, material, and assembly tolerance parameters, such as lens displacement, light source offset, surface curvature, and refractive index variations. For these multivariable systems, an unreasonable sampling distribution not only wastes simulation resources but may also lead to biased analysis results or non-convergence.

[0004] In multi-parameter high-dimensional space sampling analysis, the uniformity of sampling among parameters has a decisive impact on the reliability of the results and computational efficiency. Traditional random sampling methods often suffer from uneven distribution in high-dimensional spaces, requiring a large number of samples to cover the entire tolerance space, which is computationally extremely costly for lighting systems that rely on ray tracing. In conclusion, the rational design of multi-parameter sampling strategies is one of the important techniques for achieving efficient optical analysis in high-dimensional tolerance spaces, and it is of great significance for accelerating simulations and improving reliability. Summary of the Invention

[0005] In view of this, the present invention aims to provide a tolerance sensitivity analysis method for lighting systems based on Latin hypercube sampling. This addresses the problems of uneven sampling distribution in multi-parameter high-dimensional spaces, the need for a large number of samples to cover the entire tolerance space, and the extremely high computational cost of ray tracing simulations relied upon for tolerance analysis. These issues not only waste simulation resources but may also lead to biased or non-convergent analysis results. The present invention provides a multi-parameter tolerance analysis method based on Latin hypercube sampling (LHS). After sampling, it performs multi-dimensional fitting between the evaluation function values ​​and the sampling points. After fitting, the surface projection is transformed into a univariate space, thus clearly and efficiently solving the problem of multivariate tolerance analysis in lighting design.

[0006] To achieve the above objectives, the technical solution created by this invention is implemented as follows:

[0007] A tolerance sensitivity analysis method for lighting systems based on Latin hypercube sampling includes the following steps:

[0008] S1: Determine at least two tolerance items for the lighting system, and set the center value and tolerance variation range for each tolerance item;

[0009] 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;

[0010] 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;

[0011] 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;

[0012] 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.

[0013] Furthermore, in step S1, the tolerance items of the lighting system are geometric parameters, material parameters, or assembly parameters.

[0014] Furthermore, 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:

[0015] ;

[0016] 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.

[0017] Furthermore, in step S4, the evaluation function is either the uniformity of illumination or the total illuminance of the target surface.

[0018] Furthermore, in step S4, the multidimensional fitting model F is:

[0019] ;

[0020] 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.

[0021] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0022] This invention presents a tolerance sensitivity analysis method for lighting systems based on Latin hypercube sampling. After sampling, the evaluation function values ​​are multidimensionally fitted to the sampling points. The fitted surface is then projected into a univariate space, thus clearly and efficiently solving the problem of multivariate tolerance analysis in lighting design. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0024] Figure 1 A schematic flowchart of the tolerance sensitivity analysis method for lighting systems based on Latin hypercube sampling as described in the embodiments of the present invention;

[0025] Figure 2 This is a schematic diagram illustrating the sampling effect described in an embodiment of the present invention;

[0026] Figure 3 A comparison chart of the indices of random sampling and LHS sampling as described in the embodiments of the present invention;

[0027] Figure 4 The tolerance analysis model diagram described in the embodiments of the present invention;

[0028] Figure 5 The two-dimensional fitting effect diagram described in the embodiment of the present invention;

[0029] Figure 6 The univariate tolerance response diagram described in the embodiment of the present invention.

[0030] Explanation of reference numerals in the attached figures:

[0031] 1. Point light source; 2. Single lens; 3. Target surface. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0033] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0034] 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.

[0035] 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.

[0036] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] 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:

[0038] S1: Determine at least two tolerance items for the lighting system, and set the center value and tolerance variation range for each tolerance item;

[0039] 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;

[0040] 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;

[0041] 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;

[0042] 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.

[0043] In some embodiments, in step S1, the tolerances of the lighting system are geometric parameters, material parameters, or assembly parameters.

[0044] 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:

[0045] ;

[0046] 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.

[0047] In some embodiments, in step S4, the evaluation function is illumination uniformity or total illuminance of the target surface.

[0048] In some embodiments, in step S4, the multidimensional fitting model F is:

[0049] ;

[0050] 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.

[0051] 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.

[0052] 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 As shown in (a), the distribution of multiple sampling points generated using ordinary random sampling is relatively uneven. Oversampling often occurs within a small area (e.g., ...). Figure 2 (a) The sampling points within the small ellipse are too close together, and there is undersampling in a large region (e.g.) Figure 2 (As shown in the large ellipse in (a)). In Latin hypercube sampling, the sampling region for each dimension is segmented, and uniform sampling is performed within each segment of each dimension. After sampling, data from different dimensions are randomly combined to generate 20 sampling points. The LHS sampling effect is as follows: Figure 2 As shown in (b) of the diagram.

[0053] A quantitative analysis of the uniformity of the two sampling methods is performed. Assume the two-dimensional sampling points are... Then the kth sampling point can be represented as For all sampling points, the Euclidean distance d between different sampling points can be calculated, thus 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:

[0054] , ;

[0055] in, and These are the k1th and k2th sampling points, respectively.

[0056] The sampling uniformity and stability of the two sampling methods can be evaluated using the following two indicators.

[0057] The first metric is Minimum Distance (MD): a larger minimum distance indicates greater distance and dispersion between sampling points, thus preventing point clustering. For the Euclidean distance set D, the expression for minimum distance is: .

[0058] The second metric is the standard deviation (Std) of the distance between sampling points: assuming the number of sampling points is K, an intermediate parameter is defined. ,but The smaller the standard deviation of the sampling points with respect to distance, the more dispersed the sampling points are. The standard deviation of the sampling points with respect to distance in this case is as follows:

[0059] ;

[0060] in, Let be the arithmetic mean of the elements contained in the Euclidean distance set D.

[0061] For the same number of sampling points, sample 10 times and calculate the average of the two indicators above. The results are as follows: 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.

[0062] 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:

[0063] ;

[0064] At this point, the discrete point set obtained by Latin sampling can be calculated. .

[0065] 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.

[0066] 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:

[0067] ;

[0068] 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:

[0069] ;

[0070] By combining all the eigenvectors, we can obtain the design matrix. :

[0071] ;

[0072] Meanwhile, the column vector composed of the evaluation functions is Based on the above analysis, the objective function can be constructed as follows:

[0073] ;

[0074] The analytical solution to the above equation is:

[0075] ;

[0076] The value of each coefficient can be obtained by expanding the resulting coefficient vector:

[0077]

[0078] If the variable dimension is greater than 2, the calculation can be expanded accordingly. The solution approach remains unchanged.

[0079] After completing the formula fitting, projecting the fitted polynomial result onto one dimension yields the single-tolerance sensitivity result. For example, in a two-dimensional fit as mentioned earlier, the tolerance term... The center value is Then we can obtain information about the tolerance term. The tolerance response is:

[0080] ;

[0081] Similarly, we can obtain information about the tolerance term. The tolerance response curve.

[0082] Example 1

[0083] This embodiment uses a transmissive illumination system based on a single lens 2 for relevant analysis, such as... Figure 4 As shown, the light source is a point light source 1, and its luminous characteristics conform to Lambert's law. The total optical power of the light source is 1W. The light emitted by the light source enters the target surface 3 after passing through a single lens 2.

[0084] The optical system parameters of the transmission illumination system based on single lens 2 are shown in Table 1.

[0085]

[0086] The first surface of the single lens 2 is set as a plane, and the second surface is set as a quadric surface. The emission half-angle of the light source is 20°. The expression of the optical quadric surface is as follows. When the surface shape of the second surface changes, the illuminance of the target surface 3 will also change.

[0087] ;

[0088] 1) Set the range of tolerance terms

[0089] For a transmissive illumination system based on a single lens 2, assuming the radius of curvature c and quadratic coefficient k of the second surface are tolerance terms, their design values ​​and variation ranges are shown in Table 2. When the radius of curvature c and quadratic coefficient k change, the total energy received on the target surface 3 will change. In particular, when the radius of curvature c decreases to a certain value, the radius of the light spot received on the target surface 3 expands, energy overflows from the target surface 3, and consequently, the energy received on the target surface 3 decreases. The following section defines the total energy of the target surface 3 as an evaluation function based on a sensitivity analysis of the system.

[0090]

[0091] Using the LHS method Two-dimensional sampling is performed within the interval, sampling a set of 100 scattered points. Since this process has already been explained in detail in Section 3, it will not be elaborated upon here. The sampled data is then transformed to the variation range of the design value (i.e., the tolerance range). For the radius of curvature c, its variation range is... For the coefficient k of the quadratic surface, its variation range is as follows: .

[0092] After transforming the sampling points of the radius of curvature c and the quadratic surface coefficient k, ray tracing is performed, and the evaluation function value is calculated. , This represents the total energy received on target surface 3. The number of ray tracing operations per ray is on the order of 1e6, which is quite large.

[0093] Since this embodiment uses two-dimensional parameters, the two-dimensional fitting model is as follows:

[0094] ;

[0095] The discrete point set calculated in the previous step is fitted using a two-dimensional fitting model. This yields the sampling points and the fitted surface, as shown below. Figure 5 As shown, substituting the initial value of the radius of curvature c, c0 = -0.1, into the two-dimensional fitting model yields the tolerance response curve for the quadratic coefficient k. Similarly, importing k0 = 0 into the two-dimensional fitting model yields the response curve for the radius of curvature c. Figure 6 As shown, where, Figure 6 In the figure, (a) is the tolerance response curve with respect to the quadratic coefficient k. Figure 6 (b) is the tolerance response curve with respect to the radius of curvature c. This completes the tolerance analysis process.

[0096] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0097] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for tolerance sensitivity analysis of a lighting system based on Latin hypercube sampling, characterized by: 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, performing multi-dimensional sampling by using a Latin hypercube sampling method to obtain a sampling point set; S3: mapping the sampling points contained in the sampling point set to the tolerance variation range of the corresponding tolerance item in sequence to obtain a discrete point set after mapping; 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; S4: calculating the evaluation function values corresponding to the discrete points contained in the discrete point set based on a ray tracing method to construct a multi-dimensional fitting model; S5: substituting the center values of the tolerance items into the multi-dimensional fitting model in sequence to correspondingly obtain the response curves of the tolerance items, and completing the sensitivity analysis of each tolerance item.

2. The method of claim 1, wherein: In step S1, the tolerance items of the lighting system are geometric parameters, material parameters or assembly parameters.

3. The method of claim 1, wherein: In step S4, the evaluation function is lighting uniformity or total illuminance of the target surface.

4. The method of claim 1, wherein: 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 index, is the tolerance term corresponding to the i-th sampling dimension, is the tolerance term corresponding to the j-th sampling dimension.

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