WO2019003644A1 - Rare event interpretation device, rare event interpretation method and rare event interpretation program recording medium - Google Patents

Abstract

Provided is a noble method which can automatically and reliably interpret an extremely rare and fatal event in an objective series. A histogram calculation unit receives N past parameters and N past evaluation values, and calculates a histogram where an evaluation value is depicted as a class and the number of parameters in each class is depicted as a frequency. A random number distribution defining unit defines, on the calculated histogram, a random number distribution for generating N parameters to be used for N number of simulations in a current test such that random numbers are obtained which give a histogram in which a frequency of parameters in each class, which is a threshold value or greater determined for the classes of the histogram, is greater than that of the parameters in each class, which is the threshold value or smaller. A parameter generation unit generates each parameter to be used for each simulation in the current test on the basis of the defined random number distribution.

Description

Rare event analyzer, rare event analysis method, and rare event analysis program recording medium

The present invention relates to a rare event analysis device, a rare event analysis method, and a rare event analysis program recording medium.

When designing an optical system such as a telescope, it is necessary to design so that stray light does not occur. Here, "stray light" is light that arises potentially in optical design and is caused by a rare incoherent ray that does not follow the design light path. That is, a light beam coming into the light receiving surface in an irregular path (optical path) is called stray light, which causes a decrease in image contrast and noise.

However, the conditions under which incoherent rays occur in complex and large systems are so complex that stray light is rare, even if the expert has extensive experience and good intuition. Experts sometimes overlook them. This fact not only causes the performance degradation of the designed system, but also reduces the credibility and the credibility.

On the other hand, it is difficult as a practical matter to apply all possible conditions by optical simulation and automatically search for all very rare conditions.

Simulation methods for analyzing stray light are known. For example, Patent Document 1 splits one light beam into a transmitted light beam and a reflected light beam, and enables tracking of stray light by tracking both light beams, thereby achieving an "optical simulation apparatus" based on a more accurate light ray tracing method. Is realized.

Japanese Patent Application Publication No. 06-213769

However, Patent Document 1 does not suggest or disclose at all a device for determining a combination of parameters (events) to be input to an optical simulation apparatus in order to efficiently detect a rare event of stray light.

An object of the present invention is to provide a rare event analysis device, a rare event analysis method, and a rare event analysis program recording medium, which solve the problems described above.

The rare event analyzer according to the present invention is a rare event analyzer for discovering the possibility of occurrence of a rare event, and N in each test k (1 ≦ k ≦ K) based on the proposed distribution Q (X). An evaluation function that determines N parameters X _k each defining an event, which is used for the simulation of one cycle, and sequentially defines the possibility of the rare event occurring one by one the N parameters X _k A parameter determination unit that supplies a simulator having C (X); and an evaluation value acquisition unit that acquires N evaluation values C (X _k ) output from the simulator corresponding to the N parameters X _k. And the parameter determination unit includes N past parameters X _k-1 used for N simulations of the past test (k-1) and the N past parameters X _k-1 N times against N parameters X _k to be used for N simulations in the current test _k are determined based on the N past evaluation values C (X _k-1 ) acquired in the simulation, and the parameter determination The part inputs the N past parameters X _k-1 and the N past evaluation values C (X _k-1 ), sets the evaluation value as a class, and counts the number of parameters of each class A histogram calculation unit for calculating a histogram to be; and a distribution of random numbers for generating N parameters X _k used for N simulations in the current test k based on the calculated histogram. Histo frequency parameters of the threshold value C _th or more of each class defined with respect to classes is such that more than the frequency of the parameters in the threshold C _th following each class As random numbers to provide a ram is obtained, the random number distribution definition section for defining; based on the distribution of random numbers the definition, a parameter generating unit that generates the parameters X _k to be used for each simulation in the present study k ;

The rare event analysis method of the present invention is a rare event analysis method for finding out the possibility of occurrence of a rare event, and N in each test k (1 ≦ k ≦ K) based on the proposed distribution Q (X). An evaluation function that determines N parameters X _k each defining an event, which is used for the simulation of one cycle, and sequentially defines the possibility of the rare event occurring one by one the N parameters X _k Determining a parameter to be supplied to a simulator having C (X); and obtaining N evaluation values C (X _k ) output from the simulator corresponding to the N parameters X _k And determining the parameters includes N past parameters X _k-1 used for N simulations of the past test (k-1), and the N past parameters X _k N for _-1 N parameters X _k to be used for N simulations in the current test _k are determined based on N past evaluation values C (X _k-1 ) obtained in The determination of the parameters may be performed by inputting the N past parameters X _k-1 and the N past evaluation values C (X _k-1 ), and taking the evaluation values as classes, each class Calculating a histogram whose frequency is the number of parameters of the parameter; distribution of random numbers for generating N parameters X _k to be used for N simulations in the current test k based on the calculated histogram a frequency parameter of the threshold value C _th or more of each class defined with respect to classes of the histogram, becomes larger than the frequency of the parameters in the threshold C _th following each class Una as the random number to provide a histogram obtained, be defined as: based on the distribution of the random number the defined, wherein the generating the parameters X _k to be used for each simulation in the present study k: including.

The rare event analysis program recording medium of the present invention is a recording medium recording a rare event analysis program for finding out the possibility of occurrence of a rare event in a computer, wherein the rare event analysis program is proposed distribution in the computer Based on Q (X), determine N parameters X _k each defining an event to be used for N simulations in each test k (1 ≦ k ≦ K), and determine the N parameters A parameter determination procedure for supplying to a simulator having an evaluation function C (X) which defines the possibility of occurrence of the rare event sequentially one by one X _k ; and the simulator corresponding to the N parameters X _k an evaluation value obtaining step of obtaining the output is the N evaluation value C (X _k) from; to execute the said parameter determination procedure, the computer, in the past Test (k-1) and N times the simulation of N past parameters X _k-1 used in the of the N pieces of past parameters X _k-1 of N past acquired in N times of simulation for The N parameters X _k to be used for N simulations in the current test _k are determined based on the evaluation value C (X _k-1 ) of G. A histogram in which the N past parameters X _k-1 and the N past evaluation values C (X _k-1 ) are input, the evaluation value is a class, and the number of parameters of each class is a frequency Of a random number for generating N parameters X _k to be used for N simulations in the current test k based on the histogram calculation procedure for calculating; Distribution, power parameters of the threshold value C _th or more of each class defined with respect to classes of the histogram, giving a histogram as larger than the frequency of the parameters in the threshold C _th following each class random number Execute a parameter generation procedure for generating each parameter X _k used for each simulation in the current test k based on the defined random number distribution definition procedure and the distribution of the defined random number so as to obtain .

According to the present invention, extremely rare and fatal events in the target system can be analyzed automatically and reliably.

It is a figure which shows schematic structure of the designed optical system of the telescope to which this invention is applied. It is explanatory drawing for demonstrating the multicanonical MCMC method used in this invention. It is explanatory drawing which shows four variables which define the event X in the light-receiving surface of the designed optical system shown in FIG. It is a figure which shows the result of the search of the stray light in four-dimensional parameter space. FIG. 7 is a diagram showing an example of a histogram showing sampled events on a fatal degree (evaluation function) C (X) in the multicanonical MCMC method. It is a figure for explaining the Multicanonical MCMC method specialized for rare event search. FIG. 7 shows a comparison of the number of rays obtained that cause stray light to the number of histogram updates between the standard Multicanonical MCMC method (sm-MCMC) and the proposed Focused Multicanonical MCMC method (fm-MCMC) . FIG. 1 is a block diagram showing an optical system design support system according to a first embodiment of the present invention. It is a block diagram which shows in detail the structure of the parameter determination part used in the optical system design support system shown in FIG. It is a block diagram showing the optical system design support system by a 2nd example of the present invention. It is a block diagram which shows in detail the structure of the parameter determination part used for the optical system design support system shown in FIG. It is a block which shows the rare event analyzer according to the 3rd Example of this invention. It is a block diagram which shows the structure of the parameter determination part used for the rare event analyzer shown in FIG. 12 in detail.

First, in order to facilitate the understanding of the present invention, the meaning of the terms used herein will be briefly described.

Markov chain Monte Carlo methods (MCMC method) is a general term for an algorithm for sampling a probability distribution based on creating a Markov chain having the probability distribution to be determined as an equilibrium distribution. In other words, the MCMC method is a method combining "Markov chain" and "Monte Carlo method" as its name suggests. Specifically, the MCMC method is a method of sampling from a probability distribution using properties of a stochastic process called Markov chain to perform various calculations.

Multicanonical method (Multicanonical algorithm) is one of sampling methods in MCMC method, and is used when integrating an integrand having an arbitrary form by Metropolis Hasting method. In the multicanonical method, sampling is performed according to the reciprocal of the density of states. In the multicanonical method, the density of states is previously calculated by another method such as the One-Landau method.

The Metropolis Hastings method (or MH algorithm) (Metropolis-Hastings algorithm) is used to construct Markov chains used to generate sequences of statistical samples from probability distributions that are difficult to sample directly It is a method. This arrangement is used as an approximation (histogram) of the target distribution in the MCMC method, or for those requiring integral calculations such as expected values.

The Wang and Landau algorithm is one of the Monte Carlo methods used to calculate the density of states of a system. In the One-Landau method, a non-Markov chain random walk is performed to quickly calculate the energy of all possible states of the system necessary for calculating the density of states. The One-Landau method is important for calculating the density of states, which is necessary for performing multicanonical methods.

One of the gist of the present invention is that the Multicanonical MCMC method is applied to the application of discovery of stray light (rare event) at the design stage of an optical system such as a telescope.

However, combining the two is not easy for the following reason.

Because the Multicanonical MCMC method is used in some scientific and mathematical fields for generating random numbers according to distributions with long tails, it is used for rare event analysis that does not generally have long tails in engineering fields It is because it is not done.

Also, the Multicanonical MCMC method has been applied in various fields in statistical mathematics, physics, and chemistry. For example, the Multicanonical MCMC method has been used to sample random matrices, random graphs, very rare instances of chaotic dynamics. In a more application-oriented aspect, the Multicanonical MCMC method has been used to sample scarce noise to theoretically evaluate the ideal performance of error correction codes in telecommunications. However, the applicability and scalability of the Multicanonical MCMC method for practical real-world problems has not been demonstrated.

Generally, in the simulation method for stray light analysis, the simulation of the light path (light ray) was started from the light receiving surface of the telescope designed by back propagation, and there was a light path (light ray) which ended in a place other than the regular light entrance. In the case where there is an optical path other than the correct one, it is determined that the optical path (ray) is a possibility of stray light.

The light receiving surface is represented by points (x, y) in two-dimensional coordinates in the horizontal direction and the vertical direction, and light paths (light rays) are represented by angles α and β in the latitudinal direction and the longitudinal direction with respect to each point. That is, one light path (light ray) is represented by a set of parameter values consisting of four variables (x, y, α, β). In other words, each light path (ray) is defined by four variables (a set of parameter values) (defined by a vector in a four-dimensional space having four parameters as coordinates). Therefore, in order to search for stray light, it is necessary to perform simulation on a huge number of optical paths (light rays) while sequentially changing the four variables (a set of parameter values).

[Description of the Summary of the Invention]
We apply this statistical sampling approach to the search for very rare and fatal events for a credible and credible engineering design. The proposal of the present invention is summarized as follows.

We propose a novel approach to analyze very rare and fatal events in a target system automatically and reliably using Multicanonical MCMC method.

We also propose, in particular, an extension of the Multicanonical MCMC method for the purpose of achieving a more efficient search for rare and fatal events.

We confirm the superior capabilities of our method in experiments using the full scale design of the telescope, our analysis is within the order of 10 ³ simulation tests, I succeeded in finding all the stray lights. This is five orders of magnitude less than the number of tests required by simulations based on known grid searches. Here, “grid search” refers to a method of searching for a parameter that generates an event (stray light in the example of the present stray light analysis) that is desired to search for a combination of parameters in a round-robin manner.

[Analysis for search for stray light]
The purpose of stray light analysis is to determine if an unwanted ray has propagated to the light receiving surface of the imager and if its intensity is large enough to cause noise in the image. For example, the optical system 10 of the telescope shown in FIG. 1 has four mirrors.

In FIG. 1, the optical system 10 of the telescope includes a first mirror 11, a second mirror 12, a third mirror 13, a plane mirror 14, and a light receiving surface 15.

In FIG. 1, the solid line 16 represents the optical path of normal light designed to be focused on the light receiving surface 15 to form an image. On the other hand, the broken line 17 represents the optical path of the stray light that has reached the light receiving surface 15 in an irregular optical path.

The purpose of stray light analysis is to search an optical path that reaches the light receiving surface with a non-negligible light amount, following the optical path of regular light that occurs in a designed telescope.

Tools for stray light analysis were mainly developed by using one of two Monte Carlo principles. A simple approach is to use the forward propagation principle, in which light rays are emitted at random angles from a random position at a given light source, to assess the arrival at the receiving surface of the telescope. This principle requires a wide range of positions and angles of emission to be simulated. Because the light source potentially surrounds the telescope. Therefore, analysis using forward propagation (forward propagation) generally tends to be less efficient. Because of this difficulty, most tools for analyzing stray light use the back propagation principle, in which light rays are virtually emitted at random angles from random locations on the telescope's light receiving surface. And check their presence outside the telescope. With the exception of optical conversion devices with asymmetric light input / output characteristics such as spectrometers, all the optical elements of the telescope are symmetrical with respect to the light incidence and emission. Thus, back propagation (back propagation) provides the same light path as forward propagation (forward propagation). The latter principle is more efficient than the former. This is because the range of angles and positions at which light is emitted from the light receiving surface is limited in most cases.

If the probability of occurrence of stray light is very low, the efficiency of the tool using the back propagation principle is not sufficient to enable the search for blinded light. Thus, these tools are used by experts to simulate several light paths that heuristically reach the light receiving surface towards the generation of stray light. We propose a synthesis method combining expert knowledge and this tool to try to increase the reliability and efficiency of stray light analysis. However, the analysis performed by human experts depends on the skills and knowledge of the experts and in some cases can not search all the stray light. Because the conditions under which stray light is generated are very complicated and occur infrequently. In addition, human analysis can not handle the limited usefulness of skilled professionals.

[Rare and fatal event search for engineering design]
The following features are needed to discover the rare events that cause fatal consequences given in many engineering design tasks.

(1) Many types of rare and fatal events are efficiently searched in real-world systems characterized by discontinuities, nonlinearity and complexity.
(2) Events implicitly given and subject to very low occurrences are searched efficiently.
(3) The probability of event occurrence is quantitatively evaluated.

The third feature can not be ignored in the optical design task. Because a quantitative assessment of the probability of a fatal event occurring is often required in engineering design tasks. If the probability of occurrence of an event is very low, it can be ignored in the optical design task.

With respect to (1), methods such as convex optimization, which assume certain features of the objective function in the search space, are not applicable to this problem. Because the type of feature is unknown. In this regard, the evolutionary optimization framework, the probabilistic optimization framework, and the informatics optimization framework are candidates for searching for stray light conditions. Because they can search for a large number of local maxima. For example, genetic algorithms and simulated annealing are typical algorithms and are often implemented to find multiple local maxima in various problems. Because, these algorithms ideally do not require any assumptions about the underlying matching features. In recent years, Bayesian optimization has often been used in various engineering applications. This assumes that the unknown underlying fit feature is well approximated by a surrogate model generated by some principles such as Gaussian processes, and is the point of highest uncertainty in feature estimation. Find the local maxima of the feature by evaluating. This approach is effective and efficient when the objective feature function is expensive to evaluate, non-differentiable, non-convex and multi-modal.

However, in order for the search principles of these frameworks to be convenient and probabilistic, they need to be detected by unforeseen events because of their very low unknown probability, high segregated and high local It is easy to overlook the transformed maxima. In addition, optimization techniques generally do not provide information about the probability of occurrence of rare and fatal events in the system. Because they do not evaluate the probability distribution of event occurrences in their search mechanism. Thus, these approaches do not satisfy requirements (2) and (3).

In contrast, the probabilistic sampling framework described next does not require any assumptions about the underlying fitting features, but by weighting the search space according to its fatality, it is a targeted and unknown rare The search is efficiently accomplished by focusing on deadly events. Furthermore, it efficiently obtains fair probability information of rare and fatal events by preserving their probability distributions throughout the search. Thus, this framework is sufficient to meet all three requirements.

[Efficient probabilistic sampling of rare and fatal events]
The histogram method, the multicanonical MCMC method, and the replica exchange MCMC method are representative methods of probabilistic sampling for efficiently generating events including rare and fatal events. These methods are mainly developed in the field of statistical physics, which require that events characterized by various features with their weights that preserve a given probability distribution accurately be analyzed The

The histogram method simply samples events from events that have a distribution that is independent of their probability according to the reciprocal of their probability density function. However, the method requires a probability density function explicitly known as prior knowledge, and is supported on space with only a few dimensions for search efficiency.

The Multicanonical MCMC method uses a single Markov Chain Monte Carlo (MCMC) method, and a single MCMC method seeks out sequential events from an implicit given probability distribution over the highest possible dimensional space. While repeating the sampling process, the Multicanonical MCMC method iteratively updates the weighting functions of the sampled events to ensure that they are uniformly distributed with respect to their fatality degree. Thus, the Multicanonical MCMC method efficiently lists various events, including targeted rare and fatal events, with their weights, which maintain their probability distribution accurately, without any bias. become.

The replica exchange MCMC method uses MCMC methods in layers in parallel, but is also known as parallel tempering or Metropolis-coupled MCMC. Each MCMC method follows the implicit probability distribution, the MCMC method of the top layer follows the probability distribution of interest, and the MCMC method of the deep layer follows a flatter distribution. This technique exchanges, sequentially and randomly, events generated in one layer with other events in adjacent layers while meeting its detailed balance. As the upper layer introduces events following the flatter distribution from the lower layer without disturbing its distribution, it acquires various events including rare and fatal events in the top MCMC method according to the probability distribution of interest . Although this exchange mechanism can generate rare and fatal events more efficiently than the Multicanonical MCMC method, each step of the MCMC method is to check the fatality degree of the generated event. The parallel MCMC method, including simulation, takes a lot of computation time.

Throughout the years these techniques have been applied in various fields in statistical mathematics, physics and chemistry. For example, they were used to sample random matrices, random graphs, very rare instances of chaotic dynamics. In a more application-oriented aspect, these techniques have been used to sample scarce noise to theoretically evaluate the ideal performance of error correction codes in telecommunications. However, the applicability and scalability of these techniques for practical real-world problems has not been demonstrated.

The very rare and fatal event search method for industrial design that requires high reliability that we propose use the Multicanonical MCMC method, and this research is particularly very complicated and not effective. Applies to stray light analysis of telescopes with continuous features. This approach is suitable for problems where the probability distribution of the optical events generated by the Monte Carlo simulator is not explicitly known, and the generation of the events by the simulator is expensive.

[Multicanonical MCMC method]
We first describe the use of weighted sampling to find events by applying weights based on the proposed distribution. Subsequently, MCMC sampling with multi-canonical weights for efficiently sampling events including rare and fatal events will be described. Furthermore, an algorithm for obtaining an appropriate proposed distribution in the Multicanonical MCMC method is described.

Given a discrete event space S, X∈S is an event. It should be noted that the event space S may be discrete or continuous. When the event space S is continuous, the sum Σ on the subset of event space S is subsequently rewritten by ∫. Furthermore, the probability distribution that event X occurs is given by P (X). The probability distribution P (X) is explicitly given in many engineering design problems whose objective is an artificial system, while the probability distribution P (X) is a record observed in the past in many problems with natural objects Implicitly given by We define the set of fatal events R = {X∈S | C _th ≦ C (X)}. here,

And C _th ∈ [C _min , C _max ] is its fatality level of an event and its threshold level given to define a fatal event (hereinafter also referred to simply as “threshold”). Here we use a histogram consisting of the range C _i , i = 1,..., B on [C _min , C _max ]. Here, the height of the range C _i is expressed by the following equation.

For a given event X, P (C (X)) represents P (C _i ). Here, the fatal degree C (X) ∈C _i . The fatal degree is also called an evaluation function or an energy function. The range C _i is also called a class, and the height (number of events) of the range C _i is also called a frequency.

Assuming that event X is a fatal event with probability distribution P (X) that occurs with very low probability, it is possible to obtain almost rare event X by searching directly from probability distribution P (X) Can not. Therefore, the objective is to efficiently derive rare and fatal events that satisfy the threshold C _th ≦ C (X) under a given probability distribution P (X), and to reduce the overall rare and fatal events. Probability of R: To obtain a good estimate of P (R) = P (C _th ≦ C (C)).

[Important sampling]
To efficiently generate a fatal event for a given probability distribution P (X), we artificially raise the event by R by the multicanonical weight G (C (X)) Apply weighted sampling, sampled from the proposed distribution Q (X) XG (C (X)) P (X). Emphasis sampling means a method of obtaining an expected value using weighted samples. Here, the present inventors assume that the proposed distribution Q (X) ≠ 0 whenever the probability distribution P (X) ≠ 0.

[MCMC sampling with multi-canonical weights]
Selection of the appropriate proposed distribution Q (X) is key to the efficient occurrence of events including rare and fatal events in weighted sampling. The Multicanonical MCMC method selects a proposed distribution Q (X) approximately expressed by the following Equations 3 and 4.

Here, c is a constant, and G (C (X)) corresponding to each C _i , i = 1,..., B is known as a multicanonical weight.

By substituting Eq. 4 into Eq. 3, Eq. 5 is obtained on {XεS | C (X) εC _i } for all value ranges C _i , i = 1,. .

Here, a _{Z = Σ S P (X)} / P (C (X)). Thus, the Multicanonical MCMC method is rare in R = {X∈S | C _th ≦ C (X)} by sampling with uniform distribution over the region [C _min , C _max ], as shown in FIG. Get many samples of fatal events. The MCMC method is used to efficiently sample the event X from the proposed distribution Q (X), since the event X is generally a high-dimensional vector.

[Iterated estimation of proposal distribution]
As mentioned above, although the probability distribution P (X) is given, the probability distribution P (X) is not given directly in many practical problems, and thus the number 4 is the multicanonical weight G (C It can not be applied directly to obtain (X)). Therefore, we apply the One-Landau method to efficiently estimate multi-canonical weights G (C (X)) using iterative correction in all MCMC steps.

The key idea is to gradually modify G (C (X)) with each value range C _i , i = 1, ..., B, and the corresponding proposed distribution Q (C (X)) spans the interval [C It is guaranteed to be uniform on _min , C _max ]. The simplest algorithm is the entropic sampling method, in which all multi-canonical weights G (C _i ) are updated after a sufficiently large number of sampled events have been accumulated in the range. In contrast, the One Landau method updates the range directly after sample events are generated in the range by the MCMC method. This frequent update more efficiently estimates the objective multicanonical weight G (C (X)).

The One Landau Act works as follows. After each step of the MCMC process, the corresponding multi-canonical weights G (C (X)) are multiplied by a constant factor 0 <F <1 if the generated event belongs to the range C _i . This update is repeated until the histogram is almost flat. At this point, all histogram bins are reset to 0 and F is corrected to √F. Then, the above update of the multicanonical weights G (C _i ) is repeated again until the histogram is sufficiently flat. Finally, the multicanonical weights G (C _i ), i = 1,..., B are obtained, which guarantee a sufficiently uniform proposed distribution Q (C (X)).

[Probability of rare and fatal events]
Given the samples X _i , i = 1,..., M found from the proposed distribution Q (X), the probability of the set R of fatal events is given as the following equation 6.

Here, I (C _th ≦ C (X _i )) is an indicator function and is defined as the following equation 7.

This formula is inconvenient to calculate. This is because the proposed distribution Q (X) is not easily obtained from G (C (X)) P (X) as a practical matter. Therefore, we handle it by replacing it with Eqs. 3 and 4 and easily derive the following Eq. 8 consisting only of multicanonical weights G (C (X)) calculate.

Here, the following Equation 9 is used.

[Methodology for rare stray light search]
We propose a new methodology for the search for rare stray light based on simulation for the engineering design of telescopes. This methodology consists of the Multicanonical MCMC method and the simulator of the target telescope.

We define event X by a vector that provides the operating conditions of the target system. It is assumed that the event X follows a given probability distribution P (X). The MCMC method is used to generate an event X that follows the proposed distribution Q (X) initially identical to the probability distribution P (X) under multi-canonical weights G (C _i ). Here, i = 1,..., B, and all histograms are uniform (all bins are uniform). Then, the simulation of the target system Sim (X) is derived using the event X generated as the input operating condition, and the fatal degree in the situation of the simulation result from the input event X is given to the heuristic It is evaluated by the measure (evaluation function) C (X). This fatality level updates the count in the range of the corresponding histogram Q (C _i ) from the value of its initial zero, and the multi-canonical weight G (C _i ) of the range by the one-Landau method between them Used to update. These updates provide updates of the proposed distribution as Q (X) ∝G (C (X)) P (X), and the generation and fatality of the next event X according to the new proposed distribution Q (X) by MCMC method The simulation of the objective system providing a certain degree (evaluation function) C (X) is repeated. This process continues until the histogram Q (C _i ), i = 1,..., B is almost flat, and the degree to which the multicanonical weights G (C _i ), i = 1,. , And a sufficient number of events X are accumulated.

Algorithm 1 in Table 1 below represents the pseudo code for this method. It contains a double 'while' loop, and the inner loop has the proposed distribution Q (X) until the output histogram Q (C _i ), i = 1, ..., B is sufficiently uniform. With the intention of continuing the MCMC method, the outer loop repeats the correction of the multicanonical weights G (C _i ), i = 1,..., B until it finally reaches optimum. Intended. We apply the Metropolis method, a standard MCMC algorithm, to the transition function T _δ (X) to generate the next candidate event X ′ from the current event X. After the convergence of the multicanonical weights G (C _i ) is optimal, a data set D consisting of M events with weights is generated, and the probability of fatal events P (R) is estimated from the data set D.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The configurations described in the following embodiments are merely examples, and the technical scope of the present invention is not limited thereto.
[Summary of the invention]

The present invention relates to an optical system simulator Sim (X), which is commercially available and standard in the field of optical system design, including telescopes, as described below. This simulator shows the condition that event X is emitted from the light receiving surface 15 (see FIG. 1) of the imaging sensor by the method of back propagation (back propagation). Thus, event X is also called a condition. It consists of four variables X = [x, y, α, β] ^T as shown in FIG. In FIG. 3, x and y are horizontal and vertical positions of the emission on the light receiving surface 15 defined as x と し て [−x _range , x _range ] and y∈ [−y _range , y _range ], respectively. . In addition, α and β are, respectively, the latitudinal and longitudinal angles of the emitted light in orthogonal space. The normal vector of the light receiving surface 15 is 0 degrees. The range of angles is α∈ [−90, 90] and β∈ [−90, 90], respectively. The event (four variables) X is also called a parameter (input parameter).

The probability distribution P (X) is given by the product of four independent Gaussian distributions as the following number 10.

Here, d = 4 and _{P P} is expressed by the following equation 11.

This distribution is centered at the origin of the coordinate space. σ _x and σ _y are set as x _range and y _range , respectively, and σ _α and σ _β are each 90 degrees.

This distribution is very broad, which is slightly higher at the center, but almost uniform in the vertical direction of the light receiving surface. This choice of probability distribution P (X) reflects the symmetric geometry and mirror configuration of the telescope.

The critical degree (evaluation function) C (X) is a heuristic but needs to be specified carefully. Because it defines a fatal event. In the analysis of the embodiment of the present invention, the fatal degree is due to the fact that the light beam emitted from the light receiving surface 15 under the condition X reaches the outside of the telescope through back propagation (back propagation). Mainly prescribed. cr (X) is 1 if this happens and 0 otherwise. However, cr (X) is not critical for a given condition X due to random reflections and refractions on the light path. Therefore, the intrinsic fatality degree of condition X is evaluated by obtaining the average of cr (X) for n tests such as the following equation 12.

Here, cr _i (X) is the result in the i-th test. The fatal degree (evaluation function) C (X) monotonously increases with respect to the probabilistic approximation to the fatal situation, and the fatal degree (evaluation function) C (X) equal to or higher than the threshold level C _th Condition X has a fatal event. The threshold level C _th is set to 0.6, and most of the conditions X in n tests result in a fatal situation in this simulation. The value of n needs to be determined in consideration of the relationship between the computational cost of the critical degree (evaluation function) C (X) and the statistical stability. The fatal degree (evaluation function) C (X) follows the binomial distribution, and its relative standard error is approximately √ (1-C (X)) / nC (X), which is It monotonously increases with n and the fatal degree (evaluation function) C (X). n is set to 100 in our experiments. The reason is that the error is sufficiently suppressed with respect to the fatal condition X in which the fatal degree (evaluation function) C (X) is close to one.

We use the following transition function Tδ (X) where the output X 'is given randomly by a multivariate independently distributed Gaussian centered at condition X as follows:

Here, d = 4 and Σ _T is expressed by the following equation 14.

d _x , d _y , d _α , d _β are respectively spatial or angular resolutions of the light behavior, which are known in optics based on the wavelength of visible light and the scale of the telescope. The hyperparameter δ governs the deviation of the new condition X ′ from the condition X. If the hyperparameter δ is too large, the range in which the new condition X ′ deviates from the condition X misses the fatal event in which the new condition X ′ approaches the condition X. If the hyperparameter δ is too small, then the new condition X 'remains mostly close to the condition X and hardly any fatal events away from the condition X can be found. Therefore, it is necessary to properly adjust the value of hyperparameter δ using a trial and error approach method.

The maximum number of histogram updates K _max and the maximum number of MCMC steps M _max were set to 10 and 5000, respectively, throughout all our experiments. The former is sufficient to bring F close to unity, and finely adjust the multicanonical weight G (C _i ). The latter also allows sufficient relaxation of the MCMC process. The last parameter to be adjusted is the number B of histogram bins on the critical degree (rating function) C (X). Since the events of the maximum number M _max or less are uniformly distributed over these B value ranges, the probability of all events occurring in one value range is the same, and the number of events in one value range is the relative Poisson distribution with a typical standard deviation ε ≦ √ (B / M _max ). We set B = 20, which maintains reasonably small ε = 0.05-0.10.

Embodiment
Next, a mode for carrying out the present invention will be described using the embodiment.

[Experiment setup]
We used the lighting design analysis software named Light Tools, released by Synopsys, Inc. This software is widely used in optical design and analysis. This software is capable of Monte Carlo ray tracing. The objective optical system is a real scale mockup of the designed telescope. We know empirically that the two light paths cause stray light of similar intensity in the two symmetrical regions of the receiving surface 15 due to the geometrical symmetry of the telescope.

The assumptions and conditions of this simulation are as follows.
We assume that the model used in the simulation is a perfect duplicate of the real-world full-scale system.
The mechanism for generating stray light is well approximated by geometric optics only.
All traced rays are well approximated by a single wavelength.
"Back propagation" is used for efficient analysis in all experiments.
Ray tracing is stopped under either of the following conditions:

-The normalized energy of the configuration has become smaller than the threshold _{th th} . This threshold _{th th} is considered to be a non-negligible lower limit of relative light intensity. In practice, _{th th} is set to 10 ^-4 times the original ray energy.

Rays reach the infinite space outside the telescope without encountering any obstacles.
The reflection and refraction are calculated as follows:

The modes of reflection and refraction at the object are selected according to the parameters given to the object and its surface.

The angles of reflection and refraction at the object are selected stochastically according to the given parameters.

Some rays do not split at any reflection point or any refraction point, and the incident light is attenuated to become reflected light.

The main program including the above Algorithm 1 was implemented by Python as a programming language. The Light Tools Simulator was performed by the main program through the Excel VBA and Light Tools user interface for each step of the MCMC method. All calculations in our experiments were performed using a general purpose personal computer with a 3.4 GHz Intel Core i7 core processor and 16 MB of memory without additional hardware.

[Experimental result]
We performed stray light analysis using the above [Methodology] and above [Setup]. FIG. 4 shows the result of the search for stray light in the four-dimensional parameter space.

FIG. 4A shows a result histogram of the light ray 17 passing through an irregular path and the reaching position (x, y) on the light receiving surface 15. Higher ray counts are represented by lighter colors. This histogram shows two significant peaks that represent non-negligible non-normal rays, ie, sets of stray light.

FIGS. 4 (b-1) and (b-2) respectively show histograms of rays belonging to the selected area around the two peaks. These are represented in the space of the incident direction (α, β), and clearly indicate that there are two light paths symmetrical with respect to β, which are each path that produced one of the two peaks. The results obtained for these positions and paths and the intensity of the stray light 17 correspond well to the stray light obtained in the experimental results of the full scale telescope.

FIG. 5 (a) is a histogram showing sampled events on the critical degree (evaluation function) C (X) in the Multicanonical MCMC method of this analysis. In FIG. 5 (a), the horizontal axis represents the evaluation function C (X), and the vertical axis represents the sampled event. The total number of simulation tests and their calculation time to achieve this convergence and obtain the results shown in FIG. 4 were 5 × 10 ⁴ and 17.3 hours, respectively.

FIG. 5A shows a histogram in which the evaluation value is a class and the number of sampled events (parameters) in each class is a frequency. The histogram in FIG. 5A is normalized so that the maximum value of the class is 1.0.

[Multicanonical MCMC method specialized for rare event search]
As mentioned above, this approach follows the standard Multicanonical MCMC method for sampling events, and includes rare events with weights that accurately maintain a given probability distribution. This requires accurate analysis of the rare event probability P (R) and its associated statistics in statistical physics and other applications. The correct weights are obtained by generating various events on the area of critical degree [C _min , C _max ] in order to avoid statistical deviations, so that the objective histogram Q (C _i ), i = 1 , ..., B are uniformly set.

An alternative goal in practical problems, including our current application in engineering design, is to discover many rare and fatal events, rather than derivatives of events with precise weights. is there. This can be achieved efficiently by focusing on the area of fatal events [ _Cth , _Cmax ] over the other areas [ _Cmin , _Cth ], as shown in FIG. The following analysis shows that, without searching the entire event space S evenly, the range in which a fatal event is observed is reduced most efficiently in an intensive manner, thereby focusing on the fatal event. deal with.

[Optimal proposal distribution]
The well-relaxed MCMC process meets the details and the event X generated is in steady state. Thus, the condition of the optimal proposed distribution Q (C (X)) makes it possible to deduce from the analysis of a single transition step of the MCMC process the fatal events to be generated efficiently.

Since the fatal events of our goal are located in many regions belonging to the event space S, as demonstrated by the analysis of the inventors in the above [experimental results], the event space S Can be modeled as S = R∪ / R. Where R is the next number 15

And R _i ∩R _j = 0 and / R = S \ R for all i 、 j, j, j = 1,. R _i is a set of fatal events, and / R is a set of non-fatal events. We refer to each event set as a meta-event for simplicity. Each fatal meta-event Ri is assumed to be well localized at a particular location and well separated from other fatal meta-events.

Assume that Q (Y ′ | Y) is the transition probability of event X from meta-event Y to another meta-event Y ′ in the MCMC process that generates events according to the proposed distribution Q (X). From the above assumption it is further assumed that discrete transitions between any fatal meta-events are ignored. Therefore, only non-zero transition probabilities between all R _i and / R are considered. The next condition holds by the detailed balance between the state of the overall meta-event probability and R _i and / R.

Considering the event space S in the most efficient way to avoid overlooking any scarce and deadly events requires the largest transition probability between R _i and / R as a whole.

By replacing Eq. 16 and differentiating by Q (R _i ), the following condition is obtained for the maximum value.

Further, this equation is replaced by Eq. 17, the sum at all i's is taken, and the following simple condition is obtained by applying Eq.

This result derives Q (R) = Q (/ R) = 0.5, that is, the following equation 21:

Since the uniform distribution of Q (C (X)) provides the minimum deviation of any statistical estimate, Q (C) is constant at R _i and / R, respectively, while satisfying the above conditions. Use the next target histogram of C (X)).

Since C _th given to define a fatal event is generally close to the upper limit of [C _min , C _max ], the value of Q (C (X)) for a fatal event is not Greater than that for fatal events.

[Focused Multicanonical MCMC Method]
Based on the results given in the previous [best proposed distribution], the present inventors named Multicanonical named "Focused Multicanonical MCMC method" to efficiently discover rare and fatal events. We propose an extension of the MCMC method. In Algorithm 1 of Table 1 above, the shape of the objective histogram necessary for Q (Ci), i = 1,..., B to converge is not a flat but a step function given by Equation 22. . With the exception of this change, no other changes are required to the above algorithm.

The probability of rare and fatal events P (R) is also easily calculated. The stepwise histogram of Q (C (X)) in Eq. 22 is provided by Eq.

Here, c (C (X)) is represented by the following equation 24.

Then, a _{Z C = Σ S c (C} (X)) P (X) / P (C (X)). This is by substituting Eq. 23 into Eq. 3 and by marginalizing it in {XεS | C (X) εC _i } for all C _i , i = 1,. , Easily confirmed.

Substituting Equations 3, 23 and 24 into Equation 6, the following Equation 26 is obtained.

Here, the following equation 27 is used.

Thus, once G (C (Xi)) is obtained by the One Landau method, the probability P (R) of rare and fatal events is calculated in the same manner as the standard method.

[Experimental Results of Focused Multicanonical MCMC Method]
FIG. 5 (b) shows a histogram of sampled events on C (X) in our Focused Multicanonical MCMC method using the threshold C _th = 0.6 as described above. This histogram has a step-like shape and is balanced by the threshold C _th . The total number of simulation experiments and their calculation time to achieve this convergence were 6.1 × 10 ⁴ and 20.7 hours, respectively.

FIG. 7 shows a comparison of the number of rays obtained that cause stray light on the histogram update between the standard Multicanonical MCMC method (sm-MCMC) and the proposed Focused Multicanonical MCMC method (fm-MCMC). As is easily confirmed from this figure, the efficiency for obtaining rare stray light by the proposed method converges to approximately twice as high efficiency as that of the standard Multicanonical MCMC method.

[Compare with other methods]
Table 2 shows the performance comparison of grid search, Bayesian optimization, standard Multicanonical MCMC method, and Focused Multicanonical MCMC method. Grid search is an exhaustive search algorithm of the entire event space, providing baseline performance. We have not evaluated genetic algorithms and simulated annealing. Because they are infeasible by requiring a huge number of simulations.

The first and second columns of Table 2 indicate the probability of finding rare and fatal events for each simulation test, that is, the efficiency of the search. The first column shows the efficiency when searching for the direction [α, β] of the incident light causing the stray light by fixing the position [x, y] at the position where the stray light was observed. The efficiency of Bayesian optimization is one order of magnitude greater than that of grid search, while the efficiency of standard Multicanonical MCMC and Focused Multicanonical MCMC is two orders of magnitude higher. The second column of Table 2 shows the efficiency when searching the entire four-dimensional space. Due to the large search space, Bayesian optimization, in dealing with 10 ⁵ number of tests, could not find any fatal events. In contrast, the two Multicanonical MCMC methods can successfully find one rare and fatal event within 1000 trials, and this efficiency is five orders of magnitude higher than grid search. In both the 2 and 4 dimensional cases, the efficiency of the Focused Multicanonical MCMC method is twice that of the standard Multicanonical MCMC method. These results follow the arguments in [Multicanonical MCMC method specialized for rare event search].

The last column of Table 2 shows an estimate of the probability P (R) of rare and fatal events, ie the risk of stray light. Grid search estimates are expected to contain high uncertainty. Because grid search can only find a very limited number of rays that cause stray light, thus leading to large statistical errors. Bayesian optimization can not provide this probability. Because it does not possess probabilistic information in the search. The numbers 8 and 26 of the standard Multicanonical MCMC method and the Focused Multicanonical MCMC method provide estimates with the same order of magnitude as the probability obtained by the grid search.

FIG. 8 is a block diagram showing an optical system design support system 100 according to the first embodiment of the present invention, which uses the above-mentioned optical system simulator Sim (X). The optical system design support system 100 is a system for discovering the possibility of generation of stray light in a designed optical system 10 such as a telescope as shown in FIG.

The optical system design support system 100 includes a processing unit 200 and a storage unit 300. The processing unit 200 includes, for example, a processor such as a central processing unit (CPU), but is of course not limited to this. The storage unit 300 includes, for example, a random access memory (RAM) or a read only memory (ROM), but is of course not limited thereto.

The processing unit 200 includes a parameter determination unit 210, a trajectory calculation unit 220, and an evaluation value calculation unit 230. The storage unit 300 includes a parameter storage unit 310, an optical model storage unit 320, and an evaluation value storage unit 330.

The parameter determination unit 210 determines parameters as described later. As described above, the parameter determination unit 210 determines, as each parameter, a two-dimensional position (x, y) on the light receiving surface 15 of the designed optical system 10 and an angle (α in two directions at which light enters the light receiving surface 15). , Β) to determine a combination of four dimensional variables in total. The parameter storage unit 310 stores the determined parameter.

The locus calculation unit 220 uses the determined parameters to calculate the locus of the light beam in the designed optical system 10 as described later. The locus calculation unit 220 calculates a locus along which the light beam propagates backward from the light receiving surface 15 toward the light entrance. The optical model storage unit 320 stores an optical model in which a plurality of optical components are arranged on the optical path from the light entrance to the light receiving surface 15 in the designed optical system 10. This optical model corresponds to the designed optical system 10. The locus calculation unit 220 receives an input of the optical model stored in the optical model storage unit 320, and calculates a locus indicating the behavior of a light beam in the optical model.

The evaluation value calculation unit 230 calculates an evaluation value indicating the possibility of generation of stray light with respect to the parameter based on comparison between the calculated locus and the locus expected under the parameter in the ideal optical system. Do. In other words, the evaluation value calculation unit 230 has an evaluation function C (X) uniquely defined according to the designed optical system 10 (optical model). That is, the optical system simulator Sim (X) has an evaluation function C (X). The evaluation value calculation unit 230 receives the calculated trajectory and the determined parameters, and calculates an evaluation value according to the evaluation function C (X). The evaluation value storage unit 330 stores the calculated evaluation value.

Therefore, the parameter storage unit 310 stores the parameters used to calculate the past trajectory. The evaluation value storage unit 330 stores the evaluation value calculated for the parameter.

Based on the parameters stored in the parameter storage unit 310 and the evaluation value stored in the evaluation value storage unit 330, the parameter determination unit 210 uses for calculating the locus from the next time onward so that the higher the evaluation value, the closer to the parameter Determine the parameters.

The parameter determination unit 210 defines a distribution of random numbers such that random numbers closer to the parameters can be obtained as the evaluation value is higher, and generates parameters to be used for calculating the next and subsequent trajectories based on this distribution.

FIG. 9 is a block diagram showing the configuration of the parameter determination unit 210 used in FIG. 8 in detail. The parameter determination unit 210 includes a histogram calculation unit 212, a random number distribution definition unit 214, and a parameter generation unit 216.

The operation of the optical system design support system 100 will be described in more detail below with reference to FIGS. 8 and 9.

The parameter storage unit 310 stores N parameters used to calculate a past trajectory.

The parameter determination unit 210 determines N parameters to be used for calculating the trajectory N times from the next time on the basis of the distribution.

The trajectory calculation unit 220 calculates N trajectories for each of the determined N parameters.

The evaluation value calculator 230 calculates N evaluation values for each of the determined N parameters and the calculated N trajectories. The evaluation value storage unit 330 stores N evaluation values calculated for N parameters.

The histogram calculation unit 212 receives N parameters used for calculation of the past trajectory from the parameter storage unit 310, and receives N evaluation values calculated for the N parameters from the evaluation value storage unit 330. The histogram calculation unit 212 calculates a histogram in which the evaluation value is a class and the number of parameters of each class is a frequency.

Based on the calculated histogram, the random number distribution definition unit 214 generates a distribution of random numbers for generating N parameters to be used for calculating N times of trajectories from the next time on, the random numbers such that the histogram becomes substantially flat. Define as obtained (see the figure on the left of FIG. 6).

The parameter generation unit 216 generates each parameter to be used for calculation of each trajectory after the next time according to the defined distribution of random numbers. That is, as shown in FIG. 5A, the parameter generation unit 216 generates N parameters so that the histogram is substantially flat.

Therefore, the parameter determination unit 210 determines N parameters to be used for calculating N times of trajectories from next time using the standard Multicanonical MCMC method.

More specifically, when random numbers (parameters) are generated randomly, as the evaluation value, as shown in the left side of FIG. 2, many frequencies of the parameter of the evaluation value smaller than the threshold C _th = 0.6 are obtained. Will be Therefore, although the parameter determination unit 210 adopts all random numbers (parameters) for which an evaluation value of threshold C _th = 0.6 or more is obtained, random numbers (parameters) for which an evaluation value smaller than threshold C _th = 0.6 is obtained. By discarding most of the data and adopting it occasionally, N parameters are determined so that the histogram is substantially flat, as shown in the right side of FIG.

The optical system design support system 100 may determine N parameters so that the histogram is finally substantially flat as shown in FIG. 5A by repeating the above operation a plurality of times. it can. Here, "substantially flat" means that the frequency in each class falls within a predetermined error range with respect to the average frequency. This will be described by taking the case of FIG. 5 (a) as an example. It is assumed that the average frequency is 75 and the predetermined error is 15. In this case, the frequency in each class is in the range of 60 to 90.

As apparent from the above description, according to the first embodiment, it is possible to automatically and surely analyze stray light in the optical system.

FIG. 10 is a block diagram showing an optical system design support system 100A according to a second embodiment of the present invention, which uses the above optical system simulator Sim (X). The optical system design support system 100A is also a system for discovering the possibility of generation of stray light in a designed optical system 10 such as a telescope as shown in FIG.

The illustrated optical system design support system 100A has the same configuration as the optical system design support system 100 shown in FIG. 8 except that the configuration and operation of the processing unit are different as described later. Therefore, the processing unit is given the reference numeral 200A. The same reference numerals are assigned to components having the same functions as those shown in FIG. 8 and the description thereof will be omitted to simplify the description.

The processing unit 200A has the same configuration as the processing unit 200 shown in FIG. 8 except that the configuration and the operation of the parameter determination unit are different as described later. Therefore, the parameter determination unit is given the reference numeral 210A.

FIG. 11 is a block diagram showing in detail the configuration of the parameter determination unit 210A used in the optical system design support system 100A of FIG. The parameter determination unit 210A has the same configuration as the parameter determination unit 210 shown in FIG. 9 except that the configuration and operation of the random number distribution definition unit are different as described later. Therefore, the random number distribution definition unit is given the reference numeral 214A.

The random number distribution definition unit 214A determines, based on the calculated histogram, the distribution of random numbers for generating N parameters to be used for calculating N times of trajectories from the next time, according to the threshold C _th defined for the class of the histogram. It defines so that the random number which gives the histogram that the frequency of the parameter in each above class is higher than the frequency of the parameter in each class below threshold value _Cth is obtained.

In the illustrated example, the maximum value of the class of the histogram is normalized to be 1.0, and the threshold C _th is equal to 0.6.

Random distribution defining unit 214A is a random number that the total of the frequencies of the sum and the threshold value C _th following parameters of the frequency threshold C _th or more parameters determined for the class of the histogram and gives histogram as substantially equal Define the distribution so that Here, "substantially equal", within a predetermined error range, it means that the threshold value C _th or more in total with a threshold value C _th following parameters of the frequency parameter frequency total and are equal.

The parameter generation unit 216 generates, according to the defined distribution of random numbers, each parameter to be used for calculation of each locus after the next time, as shown in FIG. 5B. That is, as shown in FIG. 5B, the parameter generation unit 216 makes the histogram substantially equal to the sum of the frequencies of the parameters of the threshold C _th or more and the sum of the frequencies of the parameters of the threshold C _th or less. As such, N parameters are generated.

Therefore, the parameter determination unit 210A determines N parameters to be used for calculating the trajectory N times from the next time using the Focused Multicanonical MCMC method.

To be more specific, when randomly generates a random number (parameter), the evaluation value, as shown in the left diagram of FIG. 2, having a high degree of parameters in the threshold C _{th =} 0.6 smaller evaluation value Will be obtained a lot. Therefore, the parameter determination unit 210A, the threshold _C th = is 0.6 or more evaluation values to adopt all the random numbers (parameters) obtained, the threshold value _C th = 0.6 random number smaller evaluation value is obtained (parameter) For the most part, discard and occasionally adopt. Thus, as shown in FIG. 5 (b), the parameter determination unit 210A, the histogram, the sum of the frequencies of the sum and the threshold value C _th following parameters of the frequency threshold C _th or more parameters are substantially Determine N parameters to be equal.

The optical system design support system 100A repeats the above operation a plurality of times to obtain the sum of the frequencies of parameters whose threshold is greater than or equal to the threshold C _th and the frequencies of parameters whose threshold is less than the threshold C _th as illustrated in FIG. N parameters can be generated such that the sum is substantially equal.

In the present example, the random number distribution definition unit 214A sets the threshold value C _th to 0.6, but the random number distribution definition unit 214A may set the threshold value C _th to a value larger than 0.5. However, it is preferable that the random number distribution definition unit 214A set the threshold C _th within the range of 0.6 or more and 0.8 or less. However, more preferably, the random number distribution definition unit 214A sets the threshold C _th to a value of 0.6. The reason is as follows.

In general, the number of stray lights is not limited to only one, and in most cases, there are a plurality of stray lights due to the above-described symmetry or the like. In such a situation, if the threshold C _th is set higher than 0.8, most of the random numbers (parameters) of evaluation values smaller than the threshold C _th are discarded, and it is possible to search for other stray light It is because sex (probability) becomes very low. In addition, if the threshold value C _th is set lower than 0.6, a plurality of stray lights can not be searched efficiently. Therefore, it is preferable to set the threshold value C _th to a value of 0.6.

As apparent from the above description, according to the second embodiment, a plurality of stray lights in the optical system can be analyzed automatically and efficiently.

FIG. 12 is a block diagram showing a rare event analyzer 100B according to a third embodiment of the present invention. The rare event analysis device 100B is a device that discovers the possibility of occurrence of a rare event. Specifically, the rare event analysis device 100B discovers, for example, stray light generated in a designed optical system 10 such as a telescope as shown in FIG. 1 as a rare event. However, the rare event analysis device 100B can be applied not only to the simulation of such a designed optical system 10 but also to the simulation of other target systems.

The rare event analysis device 100B includes a processing unit 200B and a storage unit 300B. The processing unit 200 </ b> B includes, for example, a processor such as a CPU (Central Processing Unit), but of course is not limited to this. The storage unit 300B includes, for example, a random access memory (RAM) and a read only memory (ROM), but is of course not limited to these.

The processing unit 200B includes a parameter determination unit 210B, a simulator 220B, and an evaluation value acquisition unit 230B. The storage unit 300 includes a parameter storage unit 310B and an evaluation value storage unit 330B.

The simulator 220B may be, for example, the optical system simulator Sim (X). In this case, the simulator 220B can be realized by a combination of the optical model storage unit 320, the trajectory calculation unit 220, and the evaluation value calculation unit 230 shown in FIG. However, the simulator 220B is not limited to the optical system simulator Sim (X), and may be another simulator. The simulator 220B has an evaluation function C (X) that defines the possibility of occurrence of a rare event.

The parameter determination unit 210B determines N parameters X _k used for N simulations in each test k (1 ≦ k ≦ K) based on the proposed distribution Q (X). Each of the N parameters X _k defines an event. The parameter determination unit 210B supplies the N parameters X _k one by one to the simulator 220B. The parameter storage unit 310B stores the determined parameter.

The evaluation value acquisition unit 230B acquires N evaluation values C (X _k ) output from the simulator 220B in correspondence with the N parameters X _k . The evaluation value storage unit 330B stores the N evaluation values.

The parameter storage unit 310B stores N past parameters X _k-1 used for N simulations of the past test (k-1). The evaluation value storage unit 330B stores N past evaluation values C (X _k-1 ) obtained by N simulations for the N past parameters X _k-1 .

The parameter determination unit 210B compares the N past parameters X _k-1 stored in the parameter storage unit 310B and the N past evaluation values C (X _k-1 stored in the evaluation value storage unit 330B. And N parameters X _k to be used for N simulations in the current test k, as described later.

FIG. 13 is a block diagram showing in detail the configuration of parameter determination unit 210B used in FIG. The parameter determination unit 210B includes a histogram calculation unit 212B, a random number distribution definition unit 214B, and a parameter generation unit 216B.

The histogram calculation unit 212B calculates N past parameters X _k-1 stored in the parameter storage unit 310B and N past evaluation values C (X _k-1 ) stored in the evaluation value storage unit 330B. Receive The histogram calculation unit 212B calculates a histogram in which the evaluation value is a class and the number of parameters of each class is a frequency.

Based on the calculated histogram, the random number distribution definition unit 214B determines the distribution of random numbers for generating N parameters X _k used for N simulations of the current test k with respect to the class of the histogram. It is defined that a random number giving a histogram in which the frequency of the parameter in each class equal to or higher than the threshold C _{th is} greater than the frequency of the parameter in each class lower than the threshold C _th is obtained.

In the illustrated example, the maximum value of the class of the histogram is normalized to be 1.0, and the threshold C _th is equal to 0.6.

Random distribution definition unit 214B generates a random number that the sum of the frequencies of the sum and the threshold value C _th following parameters of the frequency threshold C _th or more parameters determined for the class of the histogram and gives histogram as substantially equal Define the distribution so that Here, "substantially equal", within a predetermined error range, it means that the threshold value C _th or more in total with a threshold value C _th following parameters of the frequency parameter frequency total and are equal.

The parameter generation unit 216B generates each parameter X _k used for each simulation in the current test k, as shown in FIG. 5 (b), based on the defined distribution of random numbers. That is, as shown in FIG. 5B, the parameter generation unit 216B makes the histogram substantially equal to the sum of the frequencies of the parameters of the threshold C _th or more and the sum of the frequencies of the parameters of the threshold C _th or less. Thus, N parameters X _k to be used for N simulations in the current test _k are generated.

Therefore, the parameter determination unit 210B determines N parameters X _k to be used for N simulations in the current test k using the Focused Multicanonical MCMC method.

To be more specific, when randomly generates a random number (parameter), the evaluation value, as shown in the left diagram of FIG. 2, having a high degree of parameters in the threshold C _{th =} 0.6 smaller evaluation value Will be obtained a lot. Therefore, although the parameter determination unit 210B adopts all random numbers (parameters) for which an evaluation value of the threshold C _th = 0.6 or more is obtained, random numbers (parameters) for which an evaluation value smaller than the threshold C _th = 0.6 is obtained. For the most part, discard and occasionally adopt. As a result, as shown in FIG. 5B, the parameter determination unit 210B substantially determines that the sum of the frequencies of the parameters of the threshold C _th or more and the sum of the frequencies of the parameters of the threshold C _th or less To be equal, generate N parameters X _k used for N simulations in the current test k.

Rare event analysis apparatus 100B, by repeating K times the test operation, as shown in FIG. 5 (b), histogram of the frequency threshold C _th or more parameters sum threshold value C _th following the frequency parameters N final parameters X _K can be generated in the final round of testing K so that the sum is substantially equal.

In this example, the random number distribution definition unit 214B sets the threshold value C _th to 0.6, but the random number distribution definition unit 214 B may set the threshold value C _th to a value larger than 0.5. However, it is preferable that the random number distribution definition unit 214B set the threshold C _th within the range of 0.6 or more and 0.8 or less. However, more preferably, the random number distribution definition unit 214B sets the threshold value C _th to a value of 0.6. The reason is as follows.

In general, the rare event is not limited to only one, and in many cases there are a plurality of rare events. In such a situation, if the threshold C _th is set higher than 0.8, most of the random numbers (parameters) of evaluation values (classes) smaller than the threshold C _th are discarded, and other rare events The probability (probability) of being able to search for is extremely low. In addition, setting the threshold C _th lower than 0.6 makes it impossible to efficiently search for a plurality of rare events. Therefore, it is preferable to set the threshold value C _th to a value of 0.6.

As is clear from the above description, according to the third embodiment, a plurality of rare events in the target system can be analyzed automatically and efficiently.

The present invention is not limited to the above embodiment as it is, and at the implementation stage, the constituent elements can be modified and embodied without departing from the scope of the invention. In addition, various inventions can be formed by an appropriate combination of a plurality of components.

Each part of the optical system design support system (rare event analyzer) may be realized using a combination of hardware and software. In the form of combining hardware and software, an optical system design support (rare event analysis) program is developed in a RAM (random access memory), and based on the optical system design support (rare event analysis) program Each part is realized as various means by operating processor hardware such as processing unit). Further, the optical system design support (rare event analysis) program may be recorded on a recording medium and distributed. The optical system design support (rare event analysis) program recorded in the recording medium is read into a memory via a wired, wireless, or recording medium itself to operate a processor (CPU) or the like. Incidentally, examples of the recording medium include an optical disk, a magnetic disk, a semiconductor memory device, a hard disk and the like.

Describing the first and second embodiments in another expression, the computer that operates as the optical system design support system is based on the optical system design support program developed in the RAM, the parameter determination unit 210, 210A, the locus This can be realized by operating as a combination of the calculation unit 220 and the evaluation value calculation unit 230.

Describing the third embodiment in another expression, the computer that operates as the rare event analysis device is based on the rare event analysis program developed in the RAM, the parameter determination unit 210B, the simulator 220B, and the evaluation value acquisition unit It is possible to realize by operating as a combination of 230B.

Further, the specific configuration of the present invention is not limited to the above-described embodiment, and any changes without departing from the scope of the present invention are included in the present invention.

Although the present invention has been described above with reference to the embodiment, the present invention is not limited to the above-described embodiment. The configurations and details of the present invention can be modified in various ways that those skilled in the art can understand within the scope of the present invention.

The present invention can be used in combination with an optical system simulator such as optical communication and a camera. The invention can also be used in conjunction with other simulators, such as ultimate condition search in engineering design.

This application claims priority based on Japanese Patent Application No. 2017-129002 filed on Jun. 30, 2017, the entire disclosure of which is incorporated herein.

10 Designed optical system (telescope)
11 first mirror 12 second mirror 13 third mirror 14 plane mirror 15 light receiving surface 16 optical path of regular light 17 optical path of stray light 100, 100A optical system design support system 100B rare event analyzer 200, 200A, 200B processor 210 210A parameter determination unit 212, 212B histogram calculation unit 214, 214A, 214B random number distribution definition unit 216, 216B parameter generation unit 220 trajectory calculation unit 220B simulator 230 evaluation value calculation unit 230B evaluation value acquisition unit 300, 300B storage unit 310, 310B Parameter storage unit 320 Optical model storage unit 330, 330B Evaluation value storage unit

Claims (7)

1. A rare event analyzer that discovers the possibility of occurrence of rare events,
   Based on the proposed distribution Q (X), determine N parameters X _k each defining an event to be used for N simulations in each test k (1 ≦ k ≦ K), A parameter determination unit which supplies a parameter X _k of one by one sequentially to a simulator having an evaluation function C (X) that defines the possibility of occurrence of the rare event;
   An evaluation value acquiring unit for acquiring N evaluation values C (X _k ) output from the corresponding simulator, corresponding to the N parameters X _k ,
   The parameter determination unit performs N simulations on N past parameters X _k-1 used for N simulations of the past test (k-1) and the N past parameters X _k-1 Determine N parameters X _k to be used for N simulations in the current test k, based on the N past evaluation values C (X _k-1 ) obtained in
   The parameter determination unit
   A histogram in which the N past parameters X _k-1 and the N past evaluation values C (X _k-1 ) are input, the evaluation value is a class, and the number of parameters of each class is a frequency A histogram calculation unit that calculates
   The distribution of random numbers for generating N parameters X _k used for N simulations in the current test k based on the calculated histogram is a threshold C _th determined for the class of the histogram. A random number distribution definition unit that defines a random number giving a histogram in which the frequency of parameters in each class above is greater than the frequency of parameters in each class below the threshold C _th ;
   A parameter generation unit for generating each parameter X _k used for each simulation in the current test k based on the defined distribution of random numbers;
   , Rare event analyzer.
2. The random number distribution definition unit obtains a random number giving a histogram such that the sum of the frequencies of parameters above the threshold determined for the class of the histogram and the sum of the frequencies of the parameters below the threshold are substantially equal. The system for rare event analysis according to claim 1, wherein the distribution is defined as follows.
3. The rare event analysis device according to claim 2, wherein the random number distribution definition unit sets the threshold value to a value larger than 0.5 when the maximum value of the class is normalized to be 1.0. .
4. The rare event analysis device according to claim 3, wherein the random number distribution definition unit sets the threshold value in a range of 0.6 or more and 0.8 or less.
5. The rare event analysis device according to claim 4, wherein the random number distribution definition unit sets the threshold value to a value of 0.6.
6. A rare event analysis method for detecting the possibility of occurrence of a rare event, comprising:
   Based on the proposed distribution Q (X), determine N parameters X _k each defining an event to be used for N simulations in each test k (1 ≦ k ≦ K), sequentially parameters X _k one by one, and supplies the simulator with an evaluation function C (X) to the rare event defines the likelihood of occurrence, determining the parameters,
   Obtaining N evaluation values C (X _k ) output from the simulator corresponding to the N parameters X _k ,
   Determining the parameters includes N past parameters X _k-1 used for N simulations of the past test (k-1) and N times for the N past parameters X _k-1 It is to determine N parameters X _k to be used for N simulations in the current test k, based on the N past evaluation values C (X _k-1 ) acquired in the simulations of
   Determining the parameters is
   A histogram in which the N past parameters X _k-1 and the N past evaluation values C (X _k-1 ) are input, the evaluation value is a class, and the number of parameters of each class is a frequency To calculate
   The distribution of random numbers for generating N parameters X _k used for N simulations in the current test k based on the calculated histogram is a threshold C _th determined for the class of the histogram. Defining so as to obtain a random number giving a histogram in which the frequency of the parameter in each class above is greater than the frequency of the parameter in each class below the threshold C _th ;
   Generating each parameter X _k used for each simulation in the current test k based on the defined distribution of random numbers;
   Rare event analysis methods, including:
7. A recording medium recording a rare event analysis program for finding out the possibility of occurrence of a rare event on a computer, the rare event analysis program comprising:
   Based on the proposed distribution Q (X), determine N parameters X _k each defining an event to be used for N simulations in each test k (1 ≦ k ≦ K), sequentially parameters X _k one by one, and a parameter determination procedure supplies the simulator with an evaluation function C (X) to the rare event defines the possibility of occurrence,
   Performing an evaluation value acquisition procedure of acquiring N evaluation values C (X _k ) output from the simulator, corresponding to the N parameters X _k ;
   The parameter determination procedure includes, in the computer, N past parameters X _k-1 used for N simulations of the past test (k-1) and the N past parameters X _k-1 N parameters X _k to be used for N simulations in the current test _k are determined based on N past evaluation values C (X _k-1 ) acquired in N simulations. Yes,
   The parameter determination procedure comprises:
   A histogram in which the N past parameters X _k-1 and the N past evaluation values C (X _k-1 ) are input, the evaluation value is a class, and the number of parameters of each class is a frequency A histogram calculation procedure for calculating
   The distribution of random numbers for generating N parameters X _k used for N simulations in the current test k based on the calculated histogram is a threshold C _th determined for the class of the histogram. A random number distribution definition procedure to be defined such that a random number giving a histogram in which the frequency of the parameter in each class above is greater than the frequency of the parameter in each class below the threshold C _th is obtained;
   A parameter generation procedure for generating each parameter X _k used for each simulation in the current test k based on the defined distribution of random numbers;
   Rare event analysis program recording medium to run.
   

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