Analysis device, analytical method, and program

Abstract

To provide an analysis device that can estimate a component contained in an analysis target in a relatively short time when estimating the component using a spectrum of the analysis target.SOLUTION: An analysis device includes: a data acquisition unit that acquires observation data of a spectrum of an analysis target and, for each candidate component contained in the analysis target, peak information of a spectrum of the candidate component; a basis selection unit that determines, for each of the candidates, a value of a basis selection parameter, which is a binary variable indicating estimated information as to whether the candidate is included in the analysis target; and a parameter calculation unit that calculates a parameter of a fitting function so as to bring a value of the fitting function having a parameter including the basis selection parameter and generated using the peak information of the spectrum close to the value of the observation data, thereby acquiring estimated information on a component contained in the analysis target.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to an analysis device, an analysis method, and a program. [Background technology]

[0002] X-ray diffraction is known as one of the methods for characterizing a crystal structure (for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Special Publication No. 2022-527323 Summary of the Invention [Problem to be solved by the invention]

[0004] When estimating the components contained in an analysis target using the spectrum of the analysis target obtained by X-ray diffraction or the like, it is preferable to be able to complete the estimation in as short a time as possible.

[0005] An example of an object of the present invention is to provide an analysis device, an analysis method, and a program that can estimate components contained in an analysis target in a relatively short time when using the spectrum of the analysis target. [Means for solving the problem]

[0006] According to a first aspect of the present invention, an analytical apparatus includes a data acquisition unit that acquires observation data of a spectrum of an analysis target and, for each candidate component included in the analysis target, information on the spectrum peak of the candidate component; a basis selection unit that determines, for each of the candidates, a value of a basis selection parameter that is a binary variable indicating estimated information as to whether or not the candidate is included in the analysis target; and a parameter calculation unit that has parameters including the basis selection parameter and calculates parameters of the fitting function so that the value of the fitting function generated using the information on the spectrum peak approaches the value of the observation data, thereby acquiring estimated information on the components included in the analysis target.

[0007] According to a second aspect of the present invention, an analytical apparatus includes a data acquisition unit that acquires observation data of a spectrum of an analysis target and information on the spectrum peak of each candidate component contained in the analysis target, and a parameter calculation unit that acquires estimated information on components contained in the analysis target and information indicating a degree of reliability of the information by calculating a probability distribution of parameter values ​​of the fitting function generated using the spectrum peak information so as to bring the value of the fitting function closer to the value of the observation data.

[0008] According to a third aspect of the present invention, a method for analysis includes a computer acquiring observation data of a spectrum of an analysis target and, for each candidate component included in the analysis target, information on the spectrum peak of the candidate component, determining, for each of the candidates, a value of a basis selection parameter which is a binary variable indicating estimated information as to whether the candidate is included in the analysis target, and calculating parameters of a fitting function having parameters including the basis selection parameter and based on information on the spectrum peak so as to approximate a value of the observation data, thereby acquiring estimated information on the components included in the analysis target.

[0009] According to a fourth aspect of the present invention, a program causes a computer to obtain observation data of a spectrum of an analysis target and, for each candidate component included in the analysis target, information on the spectrum peak of the candidate component; determine, for each of the candidates, a value of a basis selection parameter which is a binary variable indicating estimated information as to whether the candidate is included in the analysis target; and calculate parameters of the fitting function having parameters including the basis selection parameters and based on the information on the spectrum peak so as to approximate the value of the observation data, thereby obtaining estimated information on the components included in the analysis target. Effect of the Invention

[0010] According to the present invention, when components contained in an analysis target are estimated using the spectrum of the analysis target, it is expected that the estimation can be performed in a relatively short time. [Brief description of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram illustrating an example of a configuration of a diffraction system according to an embodiment. [Diagram 2] FIG. 1 is a diagram illustrating an example of a configuration of an analysis device according to an embodiment. [Diagram 3] 5 is a diagram illustrating an example of a procedure of a process in which the analysis device according to the embodiment performs a component analysis of an analysis target. FIG. [Figure 4] FIG. 11 is a diagram illustrating an example of a processing procedure in which a sampling unit according to an embodiment samples parameter values ​​using a replica exchange Monte Carlo algorithm. [Diagram 5] FIG. 2 is a diagram showing names of candidates for crystal phases used in an experiment according to an embodiment. [Figure 6] FIG. 13 is a diagram showing an estimation result of a crystal phase contained in an analysis target in an experiment according to an embodiment. [Figure 7] FIG. 11 is a diagram showing the calculation results of the spectrum of each crystal phase contained in an analysis target in an experiment according to an embodiment. [Figure 8]FIG. 13 is a diagram showing the calculation results of a profile function fitted to observed data in an experiment according to the embodiment. [Figure 9] FIG. 13 is a triangular diagram showing the estimation results of the component ratios of the crystal phases contained in the analysis target in the experiment according to the embodiment. [Figure 10] FIG. 13 is a diagram showing a frequency distribution of the estimation results of the component ratio of the crystal phase contained in the analysis target in the experiment according to the embodiment. [Figure 11] FIG. 13 is a diagram showing a frequency distribution of the estimated results of the signal intensity from each crystal phase contained in an analysis target in an experiment according to an embodiment. [Figure 12] FIG. 13 is a diagram showing a frequency distribution of an estimated result of a shift amount of a diffraction peak in observed data in an experiment according to the embodiment. [Figure 13] FIG. 13 is a diagram showing, in the form of a frequency distribution, the estimation results of the value of a parameter indicating the ratio of the influence of a Gaussian function and a Lorentzian function in the profile function for each crystal phase in an experiment according to the embodiment. [Figure 14] FIG. 13 is a diagram showing, in the form of a frequency distribution, the estimation results of the value of a parameter indicating the asymmetry of a peak function in the profile function for each crystal phase in an experiment according to the embodiment. [Figure 15] FIG. 13 is a diagram showing, in the form of a frequency distribution, the estimation results of the value of a parameter indicating the degree of spread of a Gaussian distribution in a profile function for each crystal phase in an experiment according to the embodiment. [Figure 16] FIG. 13 is a diagram showing, in the form of a frequency distribution, the estimation results of the value of a parameter indicating the degree of spread of the Lorentz distribution in the profile function for each crystal phase in an experiment according to the embodiment. [Figure 17] FIG. 1 illustrates an example configuration of a computer in accordance with at least one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] The following describes embodiments of the present invention, but the following embodiments do not limit the scope of the invention. Furthermore, not all of the combinations of features described in the embodiments are necessarily essential to the solution of the invention. 1 is a diagram showing an example of the configuration of a diffraction system according to an embodiment. In the configuration shown in FIG.

[0013] The diffraction system 1 performs component analysis by diffraction such as X-ray diffraction. In particular, the diffraction system 1 estimates the crystalline phase actually contained in the component analysis target from among candidates of the crystalline phase contained in the component analysis target. The target of component analysis by the diffraction system 1 is also simply referred to as the analysis target. The candidates for crystal phases contained in the analysis target are also simply referred to as the candidates for crystal phases.

[0014] In the following, an example will be described in which the diffraction system 1 performs component analysis using X-ray diffraction (XRD). However, the diffraction used by the diffraction system 1 is not limited to X-ray diffraction as long as it is capable of identifying a crystal phase. For example, the diffraction system 1 may perform component analysis using gamma ray diffraction.

[0015] The analysis device 100 may also perform a component analysis of the analysis target using a photoelectron spectroscopy spectrum of the analysis target by X-ray photoelectron spectroscopy (XPS) or the like. In this case, the analysis device 100 may analyze the composition of the analysis target, or may analyze the chemical bonding state of elements in the components of the analysis target in addition to or instead of the composition analysis. In this way, the components to be analyzed in the present invention are not limited to crystalline phases.

[0016] Diffraction instrument 200 measures the X-ray diffraction spectrum of the object to be analyzed, and outputs the obtained measurement data to analysis instrument 100. The measurement data of the X-ray diffraction spectrum is also referred to as observation data. The method of outputting the observation data from the diffraction device 200 to the analysis device 100 is not limited to a method of outputting the observation data directly from the diffraction device 200 to the analysis device 100. For example, the diffraction device 200 may record the observation data on a recording medium, and the analysis device 100 may acquire the observation data from the recording medium.

[0017] The spectrum database 300 is a database system that provides data on X-ray diffraction spectra of various crystal phases of various substances having a crystal structure. In particular, the spectrum database 300 provides data on X-ray diffraction spectra of candidates for crystal phases to the analysis device 100. The X-ray diffraction spectrum data of the candidate crystal phase is also referred to as candidate data. The set of candidate data is also referred to as a candidate data set. The candidate crystal phase may be a crystal phase whose candidate data is included in the candidate data set.

[0018] The spectrum database 300 may be configured as a part of the diffraction system 1, or may be configured externally to the diffraction system 1. The spectrum database may be configured integrally with the analysis device 100, or may be configured as a device separate from the analysis device 100. For example, when the spectrum database 300 is configured as a device separate from the analysis device 100, the spectrum database 300 may be configured as a server device using a computer.

[0019] The analysis device 100 performs a component analysis of the analysis target. In particular, the analysis device 100 calculates a probability distribution of parameter values ​​of a function based on candidate data obtained from the spectrum database 300 so that the function fits the observation data obtained from the diffraction device 200. The analysis device 100 provides, based on the calculated probability distribution, an estimation result of the crystal phase contained in the analysis target, an estimation result of the composition ratio of each crystal phase estimated to be contained in the analysis target, and information indicating the reliability of these estimation results. The reliability here refers to the degree of reliability, and is not limited to the "reliability" defined in statistics.

[0020] The function based on the candidate data (the function that fits the observed data) is also called a profile function. The profile function is an example of a fitting function (a function used for fitting data). The analysis device 100 may be configured using a computer such as a workstation (WS) or a personal computer (PC).

[0021] Fig. 2 is a diagram showing an example of the configuration of analysis device 100. In the configuration shown in Fig. 2, analysis device 100 includes a communication unit 110, a display unit 120, an operation input unit 130, a storage unit 180, and a control unit 190. The control unit 190 includes a data acquisition unit 191, a basis selection unit 194, and a parameter calculation unit 195. The data acquisition unit 191 includes an observation data acquisition unit 192 and a candidate data acquisition unit 193. The parameter calculation unit 195 includes a sampling unit 196. The sampling unit 196 includes a Bayesian estimation unit 197.

[0022] The communication unit 110 communicates with other devices. For example, the communication unit 110 may receive observation data from a diffraction device 200. The communication unit 110 may also receive a candidate data set from a spectrum database 300. The display unit 120 has a display screen such as a liquid crystal panel or an LED (Light Emitting Diode) panel, and acquires various images. For example, the display unit 120 may display the results of component analysis by the analysis device 100.

[0023] The operation input unit 130 includes input devices such as a keyboard and a mouse, and accepts user operations. For example, the operation input unit 130 may accept a user operation for making various settings related to the operation of the analysis device 100, such as repeating a search when the analysis device 100 searches for a parameter value of a profile function.

[0024] The storage unit 180 stores various data. For example, the storage unit 180 may store the observation data obtained from the diffraction device 200, the candidate data set obtained from the spectrum database 300, and the profile function. The storage unit 180 is configured using a storage device provided in the analysis apparatus 100 .

[0025] The control unit 190 performs various processes by controlling each unit of the analysis device 100. In particular, the control unit 190 performs component analysis of the analysis target. The functions of the control unit 190 are implemented, for example, by a CPU (Central Processing Unit) included in the analysis device 100 reading out a program from the storage unit 180 and executing it.

[0026] The data acquisition unit 191 acquires data for the analysis device 100 to perform component analysis of the analysis target. The observation data acquisition unit 192 acquires the observation data. For example, the observation data acquisition unit 192 may extract the observation data from the data received from the diffraction device 200 by the communication unit 110, store the extracted observation data in the storage unit 180, and read out the observation data from the storage unit 180.

[0027] The candidate data acquiring unit 193 acquires the candidate data. For example, the candidate data acquiring unit 193 may extract a candidate data set from data received from the spectrum database 300 by the communication unit 110, store the candidate data set in the storage unit 180, and read out the candidate data from the storage unit 180 every time the candidate data is required. Alternatively, the candidate data acquiring unit 193 may acquire the candidate data from the spectrum database 300 via the communication unit 110 every time the candidate data is required.

[0028] The basis selection unit 194 determines the value of a basis selection parameter. The basis selection parameter is a binary variable that indicates, for each of the crystal phase candidates, estimated information on whether or not the candidate is included in the analysis target. The basis selection unit 194 determining the value of the basis selection parameter can be considered as estimating the crystal phase included in the analysis target among the crystal phase candidates.

[0029] The basis selection unit 194 calculates the similarity between each of the candidate data and the observed data, and calculates a prior distribution of the basis selection parameter values ​​for each crystal phase candidate based on the calculated similarity. Then, the basis selection unit 194 determines the basis selection parameter values ​​based on the prior distribution of the basis selection parameter values ​​or the probability distribution updated according to fitting of the profile function to the observed data.

[0030] By the basis selection unit 194 determining the value of the basis selection parameter, it is possible to limit the number of candidate data to be considered when fitting the profile function to the observation data. This reduces the amount of calculation required for fitting the profile function to the observation data, and it is expected that fitting can be performed in a relatively short time. In this respect, the analysis device 100 is expected to be able to estimate the crystal phase contained in the analysis target in a relatively short time when estimating the crystal phase using the diffraction spectrum.

[0031] The parameter calculation unit 195 calculates the probability distribution of the parameter values ​​of the profile function. In particular, the parameter calculation unit 195 repeatedly updates the probability distribution of the parameter values ​​of the profile function so that the profile function fits the observed data.

[0032] The sampling unit 196 samples the parameter values ​​according to the probability distribution of the parameter values ​​of the profile function. In particular, the sampling unit 196 uses an evaluation function that indicates a better evaluation as the profile function value is closer to the observed data value, searches for parameter values ​​that will improve the evaluation indicated by the evaluation function, and samples the parameter values. The process of sampling the parameter values ​​by the sampling unit 196 can be considered as a process of fitting the profile function to the observed data.

[0033] In the following, an example will be described in which the sampling unit 196 samples parameter values ​​by a replica exchange Monte Carlo (REMC) method using Bayesian estimation or Bayesian inference. However, the method by which the sampling unit 196 samples parameter values ​​is not limited to a specific method. As a method by which the sampling unit 196 samples parameter values, various sampling methods can be used that use an evaluation function to perform sampling and can sample a global solution.

[0034] The Bayesian estimation unit 197 calculates the posterior distribution of the parameter values ​​of the profile function under the observed data by Bayesian estimation. The Bayesian estimation performed by the Bayesian estimation unit 197 is used as an algorithm for determining sampling points in the replica exchange Monte Carlo method performed by the sampling unit 196. Hereinafter, the process of obtaining candidates for sampling points by the sampling unit 196 is also referred to as solution search. However, the analysis device 100 does not search for only one set of parameter values ​​of the profile function, but obtains a posterior distribution of the parameter values ​​of the profile function under the measurement data of the spectrum to be analyzed. The analysis device 100 can be considered as performing distribution estimation using the parameters of the profile function as random variables and Bayesian estimation as a framework. The process in which the Bayesian estimation unit 197 calculates the posterior distribution of the parameter values ​​of the profile function can be considered as a process of fitting the profile function to the observation data.

[0035] The component analysis performed by the analysis device 100 will be further described. The candidate data set is shown as in equation (1).

[0036]

number

[0037] K is an integer greater than or equal to 1, and indicates the number of crystal phase candidates. Hereinafter, k may be expressed as an identification number for identifying a candidate crystal phase, such as "the kth candidate crystal phase," where k is an integer of 1≦k≦K. F k indicates candidate data. Here, the candidate data is data showing the diffraction peaks of individual crystal phases. The kth candidate of the crystal phase is the candidate data F k This is a candidate for a crystalline phase, as shown by the diffraction peak by Candidate Data F k is expressed as equation (2).

[0038]

number

[0039] M k indicates the number of diffraction peaks of the kth candidate crystal phase, M k It is an integer greater than or equal to 1. p m (k) indicates the position of the m-th diffraction peak of the k-th candidate crystal phase. The position of the diffraction peak is expressed, for example, by the diffraction angle 2θ [degrees], and takes a real value in the range of (0, 180). The order of the diffraction peaks can be, for example, the order in which the diffraction peak positions are arranged in ascending order of the diffraction angle 2θ. In the following, the diffraction angle 2θ is also used as the position in diffraction. I m (k) indicates the relative intensity of the m-th diffraction peak of the k-th candidate crystal phase. The relative intensity of a diffraction peak is, for example, a real value in the range of [0,1].

[0040] Moreover, the observation data D is expressed as in equation (3).

[0041]

number

[0042] (x i ,y i ) indicates the observed data point. N is a positive integer indicating the number of observed data points. x i indicates the position of the observation point. i is the position x i indicates the strength of the signal measured at

[0043] Next, the profile functions will be described. First, the profile functions that do not introduce basis selection parameters will be described. Profile function f F (x i ;Θ) is the signal spectrum S as shown in equation (4). F (x i ;Θ S ) and background B(x i ;Θ B ) is expressed as a linear sum.

[0044]

number

[0045] Profile function f F (x i ;Θ) is a function for fitting the observed data D and can be thought of as a model for representing the observed data D. set Θ={Θ S ,Θ B} is the profile function f F (x i ;Θ), which is also referred to as the parameters of the signal spectrum. set Θ S is the signal spectrum S F (x i ;Θ S ) is the set of parameters of the set Θ B is the background B(x i ;Θ B ) parameters.

[0046] Signal spectrum S F (x i ;Θ S ) is a model for expressing the signal from the component with a crystalline structure in the observation data D. The signal spectrum S F (x i ;Θ S ) represents a composite of the signal spectra from each candidate crystalline phase represented in the candidate data set F. Signal spectrum S F (x i ;Θ S ) is the profile function C of the diffraction peak of the kth candidate of the crystal phase as shown in equation (5). Fk (x i ;Θ s (k) )

[0047]

number

[0048] h k denotes the intensity of the signal from the kth candidate crystalline phase. Profile function C of the diffraction peak for the kth candidate crystal phase Fk (x i ;Θ s (k) ) is defined as in equation (6).

[0049]

number

[0050] Θ S (k) is the profile function C Fk (x i ;Θ s (k) ) parameters. ρ mk indicates the position of the peak in the peak function. The peak function here is a function used to represent the diffraction peak. Pseudo-Voigt Function V(x i ), Gaussian Function G(x i ), and the Lorentz Function L(x i ) are both examples of peak functions. Peak position ρ mk is expressed as equation (7).

[0051]

number

[0052] μ k is a real parameter indicating the peak shift. The peak shift here refers to the shift (deviation) of the peak position. r k is a parameter that adjusts the ratio of the influence of the Gaussian function G and the Lorentzian function L in the representation (fitting) of the diffraction peak of the kth candidate of the crystal phase, and 0≦r k Takes a real value ≦1. V(x i ) is a pseudo-Voigt function, shown in equation (8).

[0053]

number

[0054] Here, the function V(x i) we use a split Voigt function. G(x i ) denotes the Gaussian function. L(x i ) denotes the Lorentz function. Σ k is a parameter indicating the degree of spread of the Gaussian distribution, and is expressed as shown in equation (9).

[0055]

number

[0056] u k , v k , w k are parameters relating to the degree of spread of the Gaussian distribution. α k is a parameter related to the asymmetry of the peak function, and α k Takes a real value >0. A(x i ;α k ) is a function for expressing the asymmetry of the diffraction peak, and is expressed as shown in equation (10).

[0057]

number

[0058] sign(·) is the sign function and is expressed as in equation (11).

[0059]

number

[0060] Ω k is a parameter indicating the degree of spread of the Lorentz distribution, and is expressed as shown in equation (12).

[0061]

number

[0062] s k , t k are parameters related to the degree of spread of the Lorentz distribution. sec(·) is the secant function, as shown in equation (13).

[0063]

number

[0064] Signal spectrum S F A set of parameters for Θ S is expressed as equation (14).

[0065]

number

[0066] Θ S (k) is expressed as equation (15).

[0067]

number

[0068] Background B(x i ;Θ B ) is expressed as equation (16).

[0069]

number

[0070] a is the pseudo-Voigt function V(x i ) and takes a real value a>0. σ bg is a parameter that indicates the degree of spread of the distribution, and σ bg Takes a real value >0. Parameter r bg is a parameter that adjusts the ratio of the influence of the Gaussian function G and the Lorentz function L, and 0≦r bg Takes a real value ≦1. b is a parameter indicating an offset and takes a real value of b>0. Background S B A set of parameters for Θ B is expressed as equation (17).

[0071]

number

[0072] Here, the vector Y is expressed as Y=(y1,y2,...,y N ), and the vector X is X=(x1,x2,...,x N ), and the observed data D can also be expressed as equation (18).

[0073]

number

[0074] The observed data D can be considered to be probabilistically distributed due to noise during observation. Therefore, the observed data D and the profile function f F (x i Consider a joint distribution P(Y,Θ) P(Y,Θ) with the set of parameters Θ. The joint distribution P(Y, Θ) can be expressed as in equation (19).

[0075]

number

[0076] By using Bayes' Theorem to switch the order of Y and Θ, we can obtain equation (20) from equation (19).

[0077]

number

[0078] Therefore, the posterior probability P(Θ|Y) is expressed as in equation (21).

[0079]

number

[0080] The probability P(Θ|Y) represents the posterior distribution in Bayesian estimation. P(Θ) represents the prior distribution in Bayesian estimation. The probability P(Y|Θ) represents the conditional probability of a vector Y given a set of parameters Θ. Data points (x i ,y i ) are mutually independent, then under the parameter set Θ, Y = (y1, y2, , y N The posterior probability P(Y|Θ) that the vector Y is observed is expressed as follows:

[0081]

number

[0082] The X-ray diffraction spectrum is a count data measured by counting X-ray photons with a counter. i The signal strength y i The posterior probability P(y i |Θ) follows the Poisson distribution and is expressed as equation (23).

[0083]

number

[0084] P Poisson indicates a Poisson distribution. exp indicates the power of Napier's constant e. In addition, we define the Negative Log-Likelihood (NLL) loss function shown in equation (24) as the cost function E(Θ).

[0085]

number

[0086]

number

[0087] The posterior distribution P(Θ|Y) of the values ​​of the parameter set Θ is expressed as shown in equation (26) using the cost function E(Θ) and the prior distribution P(Θ).

[0088]

number

[0089] Here, in general, it is considered that when performing X-ray diffraction, it is unknown which of the candidate crystal phases is included in the analysis target. Therefore, we introduce a vector g of basis selection parameters, which is shown in equation (27).

[0090]

number

[0091] g k denotes the basis selection parameter of the kth candidate of the crystal phase. The basis selection parameter g k is a binary variable that indicates the estimated information of whether the kth candidate of the crystal phase is included in the sample, and takes the value of 0 or 1. k = 0 indicates that the kth candidate crystalline phase is not included in the sample. k = 1 indicates that the kth candidate crystalline phase is not included in the sample.

[0092] A profile function f with vector g F (x i ;g,Θ) is expressed as equation (28).

[0093]

number

[0094] The analysis device 100 calculates the profile function f F (x i ;g,Θ) is used to perform component analysis of the object to be analyzed. The combination of a vector g and a set of parameters Θ defines a profile function f F (x i ;g,Θ) parameters. Signal spectrum S with vector g introduced F (x i ;g,Θ S ) is expressed as equation (29).

[0095]

number

[0096] The joint distribution P(g, Y, Θ) introducing the vector g is expressed as shown in equation (30).

[0097]

number

[0098] Using Bayes' theorem, the posterior distribution P(g,Θ|Y) is expressed as in equation (31).

[0099]

number

[0100] The cost function E(g, Θ) introducing the vector g is expressed as shown in Equation (32).

[0101]

number

[0102] The cost function E(g,Θ) is the fitting function (profile function f F (x i ;g, Θ)) corresponds to an example of an evaluation function that indicates a better evaluation as the value of the observed data is closer. Alternatively, the parameter calculation unit 195 may use a function that indicates a better evaluation as the function value is larger. Based on the joint distribution P(g,Y,Θ) and the marginal posterior distribution, the posterior distribution p(g|Y) of a vector g is expressed as shown in Equation (33).

[0103]

number

[0104] The parameter calculation unit 195 updates the prior distribution P(g) of the vector g to the posterior distribution p(g|Y) of the vector g by using the formula (32). The basis selection unit 194 updates the value of the vector g by sampling the value of the vector g according to the probability distribution of the vector g updated by the parameter calculation unit 195.

[0105] Next, a description will be given of the sampling of parameter values ​​performed by the sampling unit 196. As described above, a case will be described here as an example in which the sampling unit 196 samples parameter values ​​by the replica exchange Monte Carlo method using Bayesian estimation.

[0106] In the replica exchange Monte Carlo method, a solution search is performed using an evaluation function for each of multiple inverse temperatures, and the solution obtained in the solution search with the largest inverse temperature is adopted as the sampling value. In addition, in the replica exchange Monte Carlo method, in order to prevent the sampling value from falling into a local solution, state exchange (exchange of solution values ​​during search) is performed between solution searches with adjacent inverse temperatures.

[0107] The sampling unit 196 performs a solution search for each inverse temperature according to the probability distribution shown in equation (34) so ​​that the value of the evaluation function shown in equation (32) becomes as large as possible.

[0108]

number

[0109] This solution search is performed by Bayesian estimation performed by the Bayesian estimation unit 197. The sampling unit 196 detects the inverse temperature β τ = β1, β2, . . . , β Τ For each of the above, we search for parameter values ​​(values ​​of vector g and value of parameter set Θ) according to the probability distribution shown in equation (34). τ , 0=β1<β2<···<β Τ =1. The sampling unit 196 then detects the inverse temperature β τ The solution obtained in the solution search for =1 is adopted as the sampling value.

[0110] Furthermore, the sampling unit 196 calculates a probability distribution for each parameter value based on the sampled values. For example, when a predetermined number of sampled values ​​are obtained, the sampling unit 196 calculates a frequency distribution of the parameter values ​​for each parameter. Then, the sampling unit 196 divides the frequency of each interval (class) by the total frequency of all intervals to calculate a probability distribution of the parameter values ​​for each parameter. However, the method by which the sampling unit 196 calculates the probability distribution of the parameter values ​​is not limited to a specific method, and various methods capable of calculating the probability distribution based on the sampled values ​​can be used.

[0111] Here, as described above in relation to the processing performed by the basis selection unit 194, the basis selection parameter g k By introducing the vector g, the amount of calculation required to fit the profile function to the observed data is reduced, and it is expected that the fitting can be completed in a relatively short time. In this regard, first consider the calculation of the cost function E(·) when the vector g is not introduced. In this case, as shown in equation (25), the sampling unit 196 calculates the profile function f F (x i ) value needs to be calculated.

[0112] Profile function f F (x i In calculating the value of ), as shown in Equation (4) and Equation (5), the sampling unit 196 calculates the profile function C for each candidate crystal phase. Fk (x i ) value needs to be calculated. Profile Function C Fk (x i In calculating the value of x , the sampling unit 196 calculates the pseudo-Voigt function V(x ) for each diffraction peak of the candidate crystal phase as shown in formula (6). i ) value needs to be calculated.

[0113] Therefore, the sampling unit 196 calculates the pseudo-Voigt function V(x i ) value needs to be calculated. Furthermore, the sampling unit 196 calculates a profile function f F (x i) must be calculated by multiplying the number of data points N included in the observation data, the number of crystal phase candidates K, and the number of diffraction peaks per candidate by the number of times the sampling unit 196 performs a solution search.

[0114] In contrast, the introduction of vector g makes g k If = 0 (the kth candidate of the crystal phase is not selected), the profile function C Fk (x i ) is not necessary. The sampling unit 196 selects the candidates {F k |g k = 1}, the profile function C Fk (x i The selected candidates are those that are presumed to be included in the analysis target among the candidates for the crystal phase.

[0115] Pseudo-Voigt function V(x i ), the sampling unit 196 needs to calculate the value of N the number of times that the number of data points N included in the observation data is multiplied by the number of selected candidates by the number of diffraction peaks per candidate, and further by the number of times that the sampling unit 196 performs a solution search.

[0116] In general, it is considered that only a part of the candidates for the crystal phase is included in the analysis target, and the number of selected candidates is considered to be smaller than the number of the candidates for the crystal phase. Therefore, it is expected that the amount of calculation of the sampling unit 196 is reduced. When the ratio of the number of the crystal phases included in the analysis target to the number of the candidates for the crystal phase is small, it is expected that the effect of reducing the amount of calculation is particularly large.

[0117] Next, the calculation of the initial values ​​of the basis selection parameters performed by the basis selection unit 194 will be described. In calculating the initial values ​​of the basis selection parameters of the k-th candidate of the crystal phase, the basis selection unit 194 selects F k (Diffraction peak data of the kth candidate crystal phase) p m(k) (the m-th peak position). For example, the basis selection unit 194 resamples data points that are close to x i and the value of p m (k) Alternatively, the data point with the smallest magnitude of difference from the value of

[0118] Then, the basis selection unit 194 selects a vector y′ of data points obtained by resampling and a vector I k Calculate the similarity with

[0119]

number

[0120] The basis selection unit 194 may use, for example, cosine similarity as the similarity of vectors, but is not limited to this. The basis selection unit 194 applies the calculated similarity to the event g k = 1, and subtract the similarity from 1 to define the self-declared g k Set the probability distribution to =0. Depending on the type of vector similarity, the basis selection unit 194 may normalize the calculated similarity so that the value set as the probability distribution of the basis selection parameter values ​​conforms to the definition of probability.

[0121] FIG. 3 is a diagram showing an example of a procedure for the analysis device 100 to perform component analysis of an analysis target. In the process of FIG. 3, the data acquisition unit 191 acquires the observed data D and the candidate data set F (step S101). Next, the control unit 190 starts a loop L11 in which processing is performed for each crystal phase candidate (step S102).

[0122] In the process of loop L11, the basis selection unit 194 selects the observation data D and candidate data F of the candidate of the crystal phase to be processed in loop L11. kThe similarity between them is calculated (step S103). Next, the basis selection unit 194 sets a prior distribution of the values ​​of the basis selection parameters of the candidates for the crystal phase being processed in the loop L11 (step S104). Then, the basis selection unit 194 samples and sets the prior distribution of the values ​​of the basis selection parameters according to the probability distribution set in step S104 (step S105).

[0123] Next, the control unit 190 performs a termination process of the loop L11 (step S106). Specifically, the control unit 190 judges whether or not the process of the loop L11 has been performed on all the candidates of the crystal phase. If it is judged that there is a candidate for which the process of the loop L11 has not yet been performed, the control unit 190 continues to perform the process of the loop L11 on the unprocessed candidate. On the other hand, if it is judged that the process of the loop L11 has been performed on all the candidates of the crystal phase, the control unit 190 ends the loop L11.

[0124] When the control unit 190 ends the loop L11, the parameter calculation unit 195 initializes the probability distribution of the values ​​of the parameters (set Θ) of the signal spectrum (step S107). A prior distribution of the parameter values ​​may be determined in advance for each parameter. Then, the parameter calculation unit 195 may set the predetermined prior distribution for each parameter.

[0125] Next, the sampling unit 196 samples the values ​​of each parameter using the replica exchange Monte Carlo method (step S108). Then, the sampling unit 196 calculates and updates the probability distribution of the parameter value for each parameter based on the sampling result (step S109).

[0126] Next, the control unit 190 determines whether or not a termination condition for updating the distribution of parameter values ​​is satisfied (step S110). The termination condition here is not limited to a specific one. For example, the termination condition here may be that the sampling unit 196 has sampled the parameter values ​​a predetermined number of times or more, or that the value of the cost function E(g, Θ) has become smaller than or equal to a predetermined value. If the control unit 190 determines that the end condition is not met (step S110: NO), the process returns to step S108.

[0127] On the other hand, if the control unit 190 determines in step S110 that the termination condition is satisfied (step S110: YES), the analysis device 100 outputs a probability distribution of the parameter values ​​(step S111). For example, the probability distribution of the basis selection parameter values ​​probabilistically indicates an estimation result of whether or not a crystal phase candidate is included in the analysis target. In addition, a parameter h k The probability distribution of the value of represents the probability of the proportion (component ratio) of the kth crystal phase candidate contained in the analysis target when viewed relatively in comparison with other candidates.

[0128] Analysis device 100 can present the analysis result and the degree of reliability of the analysis result by outputting the probability distribution of the parameter values. The display unit 120 may display the probability distribution of the parameter values ​​as a graph or numerical values, or the communication unit 110 may transmit data indicating the probability distribution of the parameter values ​​to another device. After step S111, the analysis device 100 ends the process of FIG.

[0129] 4 is a diagram showing an example of a processing procedure in which the sampling unit 196 samples parameter values ​​by the replica exchange Monte Carlo method. The sampling unit 196 performs the processing of FIG. 4 in step S108 of FIG. In the process of Figure 4, the inverse temperature setting values ​​β1, β2, . . ., β τA solution search problem is set to search for the value of vector g and the value of set Θ that maximizes the value of the cost function E(g,Θ) for each of the above. The initial position of the solution search uses the current values ​​of vector g and set Θ (the most recent values ​​at that time).

[0130] 4, the sampling unit 196 searches for parameter values ​​(values ​​of vector g and value of set Θ) that maximize the value of the cost function E(g, Θ) for each set value of the inverse temperature (step S201). Specifically, the sampling unit 196 performs a solution search by Bayesian estimation performed by the Bayesian estimation unit 197.

[0131] Next, the sampling unit 196 judges whether or not the replica exchange timing has arrived (step S202). The criterion for judging whether or not the replica exchange timing has arrived is not limited to a specific one. For example, the replica exchange timing may be determined by repeating the search for the parameter value in step S201 a predetermined number of times or more.

[0132] If the sampling unit 196 determines that the replica exchange timing has not arrived (step S202: NO), the process returns to step S201. On the other hand, when it is determined that the replica exchange timing has arrived (step S202: YES), the sampling unit 196 determines whether or not the replica exchange condition is satisfied (step S203). The replica exchange condition is determined by the replica exchange Monte Carlo method.

[0133] If it is determined that the replica exchange condition is satisfied (step S203: YES), the sampling unit 196 exchanges parameter values ​​(the value of the vector g and the value of the set Θ) between the adjacent inverse temperature setpoints for which it is determined that the replica exchange condition is satisfied (step S204). Here, the parameter values ​​are examples of replicas.

[0134] Next, the sampling unit 196 determines whether or not a burn-in period has elapsed (step S205). The burn-in period is a predetermined period that is set as a period during which the parameter values ​​are influenced by initial values ​​(prior distribution of parameter values). When it is determined that the burn-in period has elapsed (step S205: YES), the sampling unit 196 records the parameter values ​​(the value of the vector g and the value of the set Θ) in the solution search problem in which the value of the inverse temperature is larger as sample data. For example, the sampling unit 196 may store the parameter values ​​in the storage unit 180.

[0135] Next, the sampling unit 196 determines whether or not a condition for ending the sampling of the parameter value is satisfied (step S207). The condition for ending the sampling of the parameter value here may be, but is not limited to, that the recording of the sample data in step S206 has been repeated a predetermined number of times or more.

[0136] If the sampling unit 196 determines that the end condition is not met (step S207: NO), the process returns to step S201. On the other hand, if it is determined that the end condition is met (step S207: YES), the sampling section 196 ends the processing of FIG.

[0137] On the other hand, if the sampling unit 196 determines in step S203 that the replica exchange condition is not satisfied (step S203: NO), the process proceeds to step S205. On the other hand, in step S205, if the sampling section 196 determines that the burn-in period has not elapsed (step S205: NO), the process proceeds to step S207.

[0138] Next, an experiment to confirm the operation of the analysis device 100 and the results of that experiment will be described. In the experiment, we set the parameters Θ S The following distributions were used as prior distributions for the values ​​of each parameter: Parameter h of the signal intensity from the kth candidate crystal phase k As the prior distribution of the value of , the distribution shown in equation (36) was used.

[0139]

number

[0140] Probability distribution P Gannma (k G ,θ G ) denotes the gamma distribution. The parameter k of the gamma distribution G is the shape parameter, and k G The parameter θ is a real value >0. G is the scale parameter, and θ G >0 Takes a positive real value. y max are the y1, y2, . . . y contained in the observed data D. N is the maximum value of y min are the y1, y2, . . . y contained in the observed data D. N is the minimum value of Parameter μ indicating peak shift k As the prior distribution of the value of , the distribution shown in equation (37) was used.

[0141]

number

[0142] Probability distribution P Normal (μ N ,σ N ) indicates normal distribution. The parameter μ of normal distribution N indicates the average value and takes a real value. The parameter σ N denotes the standard deviation, and σ N Takes a real value >0. Parameter α for the asymmetry of the peak function k As the prior distribution of the value of , the distribution shown in equation (38) was used.

[0143]

number

[0144] Parameter r adjusts the ratio of the influence of the Gaussian function and the Lorentzian function k As the prior distribution of the value of , the distribution shown in equation (39) was used.

[0145]

number

[0146] Probability distribution P Uniform (u U ,l U ) denotes the uniform distribution. The parameter u of the uniform distribution U is the maximum value and takes a real value. The parameter l of the uniform distribution U indicates the minimum value and takes a real value. Parameter u relating to the degree of spread of the Gaussian distribution k As the prior distribution of the value of , the distribution shown in equation (40) was used.

[0147]

number

[0148] Parameter v relating to the degree of spread of the Gaussian distribution k As the prior distribution of the value of , the distribution shown in equation (41) was used.

[0149]

number

[0150] Parameter w relating to the degree of spread of the Gaussian distribution k As the prior distribution of the value of , the distribution shown in equation (42) was used.

[0151]

number

[0152] Parameter s relating to the spread of the Lorentz distribution k As the prior distribution of the value of , the distribution shown in equation (43) was used.

[0153]

number

[0154] Parameter t relating to the spread of the Lorentz distribution k As the prior distribution of the value of , the distribution shown in equation (44) was used.

[0155]

number

[0156] Background B(x i ;Θ B ) for the pseudo-Voigt function V(x i As the prior distribution of the value of the parameter a, which is the coefficient multiplied by , the distribution shown in equation (45) was used.

[0157]

number

[0158] Background B(x i ;Θ B ) distribution spread parameter σ bg As the prior distribution of the value of , the distribution shown in equation (46) was used.

[0159]

number

[0160] Background B(x i ;Θ B ) Parameter r adjusts the ratio of the influence of the Gaussian function and the Lorentzian function bgAs the prior distribution of the value of , the distribution shown in equation (47) was used.

[0161]

number

[0162] Background B(x i ;Θ B ), the distribution shown in equation (48) was used as the prior distribution of the value of parameter b, which indicates the offset in

[0163]

number

[0164] In the replica exchange Monte Carlo method, calculations were performed for 2000 steps, and the first 1000 steps of the 2000 steps were excluded from sampling as a burn-in period. Reverse temperature β τ was set as shown in equation (49).

[0165]

number

[0166] τ takes integer values ​​of 0, 1, 2, ..., T. η indicates the ratio (base of power) and takes a real value η > 0. The value of the ratio η was set to η = 1.2. T indicates the number of temperatures (= the number of inverse temperatures) and takes an integer value of T ≥ 1. The value of the number of temperatures T was set to T = 64.

[0167] The sample used for the analysis was a titanium dioxide (TiO2) sample containing rutile, anatase, and brookite in a mass fraction of 33.4:33.1:33.5. As data on candidate crystal phases, we prepared spectrum data for 50 types of crystal phases, including titanium (Ti) and oxygen (O). The spectrum data was obtained from Atom Work, a database of organic matter.

[0168] FIG. 5 is a diagram showing the names of the candidates for the crystal phases used in the experiment. The 50 types of crystal phases shown in Figure 5 were selected as candidates for the crystal phases contained in the analysis target, and their X-ray diffraction spectrum data was prepared.

[0169] Figure 6 shows the estimation results of the crystal phases contained in the analysis target. The horizontal axis of the graph in Figure 6 shows the inverse temperature index in the replica exchange Monte Carlo method. The vertical axis shows the names of each candidate crystal phase. Figure 6 shows the final calculation results of the probability that each candidate crystal phase is included in the analysis target for each inverse temperature. Specifically, the probability that the basis selection parameter value for each crystal phase is 1 is shown.

[0170] It is considered that the larger the inverse temperature index, the larger the inverse temperature value, and therefore the smaller the value of the cost function E(g,Θ). The column on the far right of the figure, with an inverse temperature index of 62, shows the estimated probability that each crystal phase is included in the analysis target. In Figure 6, the probability that rutile, brookite, and anatase are all included in the analyzed sample is nearly 100%, and the probability of other crystal phases is nearly 0%. Therefore, it can be evaluated that the crystal phases included in the analyzed sample have been correctly estimated.

[0171] Figure 7 shows the calculation results of the spectrum of each crystal phase contained in the analysis target. The horizontal axis of the graph in Figure 7 shows the diffraction angle 2θ. The vertical axis shows the count value (number of counts) of X-ray photons as the signal intensity. The line L111 shows the calculation result of the spectrum of anatase. The line L112 shows the calculation result of the spectrum of brookite. The line L113 shows the calculation result of the spectrum of rutile. Specifically, the profile function C Fk (x i ;Θ s (k) ) for each diffraction angle 2θ.

[0172] Figure 8 shows the calculation results of the profile function fitted to the observation data. The horizontal axis of the graph in Figure 8 represents the diffraction angle 2θ. The vertical axis represents the X-ray photon count value as the signal intensity. Figure 8 shows the profile function f F (x i ;g,Θ) for each diffraction angle 2θ.

[0173] FIG. 9 is a ternary diagram showing the estimated results of the component ratios of the crystal phases contained in the analysis target. Figure 9 shows the component ratios of anatase, brookite, and rutile in a triangular diagram. Specifically, the posterior distribution of the peak area ratios of anatase, brookite, and rutile is shown as a percentage. Here, the profile function C of the diffraction peak of the kth candidate of the crystal phase is Fk The numerical integration of in the angular direction corresponds to the peak area of ​​the candidate. The peak area ratio of anatase, brookite, and rutile is the ratio of the peak areas of these three crystal phases.

[0174] The anatase content is indicated by the numbers and horizontal lines on the right, and is shown to be between approximately 35% and just under 40%. The brookite content is shown using numbers on the left and a line from the top left to the bottom right, and is shown to be between just over 30% and approximately 35%. The rutile content is indicated by the numbers at the bottom and a line from the bottom left to the top right, and is shown to be between approximately 30% and just under 35%.

[0175] In this way, the analysis device 100 can display the component ratio with a range. The narrower this range, the greater (higher) the reliability of the component ratio estimation result. In this way, the analysis device 100 can display the component ratio estimation result together with its reliability.

[0176] Figure 10 shows the frequency distribution of the estimated results of the component ratio of the crystal phase contained in the analysis target. The horizontal axis of the graph in Figure 10 shows the peak area ratio in %, and the vertical axis shows the frequency. The frequency here is the number of times that the parameter value was sampled in each interval (class) of values ​​shown on the horizontal axis by the replica exchange Monte Carlo method.

[0177] Region A111 shows the frequency distribution in the case of anatase, region A112 shows the frequency distribution in the case of brookite, and region A113 shows the frequency distribution in the case of rutile. The ratio of the heights of these regions can be regarded as indicating the estimated values ​​of the component ratios of the respective crystal phases. The widths of these regions can be regarded as indicating the reliability of the estimated results of the component ratios. In this way, the analysis device 100 can display the estimated results of the component ratios together with the reliability thereof.

[0178] FIG. 11 is a graph showing the frequency distribution of the estimated signal intensity from each crystal phase contained in the analysis target. The horizontal axis of the graph in FIG. 11 shows the signal intensity as the count value of X-ray photons. Specifically, the horizontal axis shows the parameter h k The vertical axis shows the frequency. The frequency here is the number of times that the parameter value was sampled in the interval (class) of values ​​shown on the horizontal axis by the replica exchange Monte Carlo method.

[0179] Area A121 shows the frequency distribution in the case of anatase, area A122 shows the frequency distribution in the case of brookite, and area A123 shows the frequency distribution in the case of rutile. The height of these regions can be regarded as indicating the estimated value of the signal strength, and the width of these regions can be regarded as indicating the reliability of the estimated result of the signal strength. In this way, the analysis device 100 can display the estimated result of the signal strength together with its reliability.

[0180] Fig. 12 is a graph showing the frequency distribution of the estimated shift amount of the diffraction peak in the observed data. The horizontal axis of the graph in Fig. 12 shows the shift amount in terms of the diffraction angle 2θ. The vertical axis shows the frequency. The frequency here is the number of times that the parameter value is sampled in each interval (class) of values ​​shown on the horizontal axis by the replica exchange Monte Carlo method.

[0181] Area A131 shows the frequency distribution in the case of anatase, area A132 shows the frequency distribution in the case of brookite, and area A133 shows the frequency distribution in the case of rutile. The height of these regions can be regarded as indicating the estimated result of the shift amount. The width of these regions can be regarded as indicating the reliability of the estimated result of the shift amount. In this way, the analysis device 100 can display the estimated result of the shift amount of the diffraction peak together with the reliability.

[0182] Figure 13 shows the parameter r, which indicates the ratio of the influence of the Gaussian function and the Lorentzian function in the profile function for each crystal phase. k The horizontal axis of the graph in FIG. 13 shows the frequency distribution of the estimation results of the parameter r k The values ​​of the parameters r are shown. Since the width of the middle part of the distribution is narrower in the Lorentzian distribution than in the Gaussian distribution, k The larger the value of r, the more the crystal phase (parameter r k This can be seen as a narrow middle range of the spectrum of the distribution of the crystal phase being examined. The vertical axis of the graph in Fig. 13 indicates frequency, which is the number of times that the parameter value is sampled in each interval (class) of values ​​shown on the horizontal axis by the replica exchange Monte Carlo method.

[0183] Area A141 shows the frequency distribution in the case of anatase, area A142 shows the frequency distribution in the case of brookite, and area A143 shows the frequency distribution in the case of rutile. The height of these regions is the parameter r k The width of these regions can be considered as the estimated value of the parameter r k In this way, the analysis device 100 uses the parameter r k The estimated value of can be shown along with its confidence level.

[0184] Figure 14 shows the parameter α, which indicates the asymmetry of the peak function in the profile function for each crystal phase. k The horizontal axis of the graph in FIG. 14 is the frequency distribution of the estimation result of the parameter α k The parameter α k The larger the value of α, the more the crystal phase (parameter α k This can be interpreted as a large asymmetry in the spectrum of the crystal phase being studied. The vertical axis of the graph in Fig. 14 indicates frequency. The frequency here is the number of times that the parameter value is sampled in each interval (class) of values ​​shown on the horizontal axis by the replica exchange Monte Carlo method.

[0185] Area A151 shows the frequency distribution in the case of anatase, area A152 shows the frequency distribution in the case of brookite, and area A153 shows the frequency distribution in the case of rutile. The height of these regions is determined by the parameter α k The width of these regions can be considered to represent the estimated value of the parameter αk In this way, the analysis device 100 uses the parameter α k The estimated value of can be shown along with its confidence level.

[0186] Figure 15 shows the parameter Σ, which indicates the degree of spread of the Gaussian distribution in the profile function for each crystal phase. k The horizontal axis of the graph in FIG. 15 shows the frequency distribution of the estimated value of parameter Σ k The parameter Σ k The larger the value of α, the more the crystal phase (parameter α k This can be interpreted as the broadening of the Gaussian distribution components of the spectrum of the crystal phase being examined. The vertical axis of the graph in Fig. 15 indicates frequency. The frequency here is the number of times that the parameter value is sampled in each interval (class) of values ​​shown on the horizontal axis by the replica exchange Monte Carlo method.

[0187] Area A161 shows the frequency distribution in the case of anatase, area A162 shows the frequency distribution in the case of brookite, and area A163 shows the frequency distribution in the case of rutile. The height of these regions is the parameter Σ k The width of these regions can be considered to represent the estimated value of the parameter Σ k In this way, the analysis device 100 uses the parameter Σ k The estimated value of can be shown along with its confidence level.

[0188] Figure 16 shows the parameter Ω, which indicates the degree of spread of the Lorentzian distribution in the profile function for each crystal phase. k The horizontal axis of the graph in FIG. 16 shows the frequency distribution of the estimated value of the parameter Ω. k The parameter Ωk The larger the value of α, the more the crystal phase (parameter α k This can be interpreted as the broadening of the Lorentzian distribution component of the spectrum of the crystal phase being studied. The vertical axis of the graph in Fig. 16 indicates frequency, which is the number of times that the parameter value is sampled in each interval (class) of values ​​shown on the horizontal axis by the replica exchange Monte Carlo method.

[0189] Area A171 shows the frequency distribution in the case of anatase, area A172 shows the frequency distribution in the case of brookite, and area A173 shows the frequency distribution in the case of rutile. The height of these regions is the parameter Ω k The width of these regions can be considered to represent the estimated value of the parameter Ω k In this way, the analysis device 100 uses the parameter Ω, which indicates information about the spectrum waveform, to estimate the reliability of the result of the estimation. k The estimated value of can be shown along with its confidence level.

[0190] The display unit 120 may display the screens exemplified in FIG. 6 to FIG. 16 or a part of these screens. For example, the display unit 120 can display the probability that each of the crystal phase candidates is included in the analysis target, as in the example of Figure 6, thereby showing estimated information on whether each of the crystal phase candidates is included in the analysis target and the reliability of the estimated information.

[0191] For example, if the probability is 50% or more, it can be said that the estimated information indicates that the crystalline phase is included in the analysis target, and in this case, the higher the probability, the higher the reliability of the estimated information. On the other hand, if the probability is less than 50%, it can be said that the estimated information indicates that the crystalline phase is not included in the analysis target, and in this case, the lower the probability, the higher the reliability of the estimated information.

[0192] Alternatively, the display unit 120 may display information only about some of the candidates for the crystal phase. For example, the display unit 120 may display information only about the candidates designated by the user. Alternatively, the display unit 120 may display information only about the crystal phases determined to be included in the analysis target, as in the examples of FIG. 7 and FIG. 9 to FIG. 16.

[0193] Furthermore, the display unit 120 may display a frequency distribution of the estimated values ​​as shown in Figures 10 to 16. In this case, for example, the value with the highest frequency is the estimated value, and the extent of the distribution can be considered to represent the reliability of the estimated value. Alternatively, the parameter calculation unit 195 may normalize the frequency of the frequency distribution of the estimated values ​​to convert it into a probability distribution, and the display unit 120 may display the probability distribution of the estimated values. In this case, for example, it can be considered that the value with the highest probability is the estimated value, and the extent of the distribution represents the reliability of the estimated value. Furthermore, the method by which analytical device 100 outputs information is not limited to the method by which display unit 120 displays information. For example, communication unit 110 may transmit information to another device.

[0194] As described above, the data acquiring unit 191 acquires observation data of the spectrum of the analysis target, and a candidate data set indicating information on the spectrum peak of each candidate crystal phase included in the analysis target. The basis selection unit 194 determines, for each of the candidates for a crystal phase, the value of a basis selection parameter, which is a binary variable indicating estimated information as to whether or not the candidate is included in the analysis target. The parameter calculation unit 195 has parameters including basis selection parameters, and calculates a fitting function (profile function f F By calculating the parameters of the fitting function so that the value of (x, g, Θ) approaches the value of the observed data, estimated information regarding the crystalline phase contained in the analysis target is obtained.

[0195] In the analysis device 100, the basis selection unit 194 determines the value of the basis selection parameter, thereby limiting the number of candidate data to be considered when fitting the profile function to the observation data. This reduces the amount of calculation required for fitting the profile function to the observation data, and is expected to allow fitting to be performed in a relatively short time. In this respect, the analysis device 100 is expected to allow estimation of the crystal phase contained in the analysis target in a relatively short time when estimating the crystal phase using the diffraction spectrum.

[0196] Furthermore, the parameter calculation unit 195 acquires estimated information on whether or not at least one of the crystal phase candidates is included in the analysis target, based on the basis selection parameters. In this manner, the analytical device 100 can estimate whether or not a candidate for a crystal phase is included in the analysis target based on the value of the basis selection parameter.

[0197] In addition, the basis selection unit 194 calculates a prior distribution of the values ​​of the basis selection parameters for each candidate based on the similarity between the data point of the spectrum peak of the candidate and the data point of the observation data that is located closest to the position of the spectrum peak of the candidate. In the analysis device 100, it is possible to limit the data points of the observation data that are used when the basis selection unit 194 calculates the prior distribution of the values ​​of the basis selection parameters. In this respect, the analysis device 100 is expected to be able to calculate the prior distribution of the values ​​of the basis selection parameters in a relatively short time.

[0198] Furthermore, the parameter calculation unit 195 calculates the probability distribution of the parameter values ​​of the fitting function to obtain estimated information regarding the crystalline phase contained in the analysis target and information indicating the degree of reliability of the information. According to the analytical device 100, in addition to the estimated information regarding the crystalline phase contained in the analysis target, the degree of reliability of the estimated information can be presented.

[0199] In addition, the parameter calculation unit 195 samples the parameter values ​​of the fitting function using an evaluation function that indicates a better evaluation the closer the value of the fitting function is to the value of the observed data, and calculates a probability distribution of the parameter values ​​of the fitting function using the sampled values. Analysis device 100 can perform fitting by sampling the parameter values ​​of the fitting function.

[0200] Furthermore, the parameter calculation unit 195 samples the parameter values ​​of the fitting function using the replica exchange Monte Carlo method. It is expected that the analysis device 100 can sample the parameter values ​​of the fitting function without falling into a local solution. In other words, it is expected that the analysis device 100 can perform sampling with higher accuracy over the entire domain of the parameters of the fitting function. As a result, it is expected that the analysis device 100 can calculate a probability distribution with higher accuracy over the entire domain of the parameters of the fitting function.

[0201] The data acquiring unit 191 also acquires observation data of the spectrum of the analysis target, and a candidate data set indicating information on the spectrum peak of each candidate crystal phase included in the analysis target. The parameter calculation unit 195 calculates a probability distribution of the parameter values ​​of the fitting function so that the value of the fitting function generated using the spectrum peak information approaches the value of the observed data, thereby obtaining estimated information on the crystalline phase contained in the analysis target and information indicating the degree of reliability of the information. According to the analytical device 100, in addition to the estimated information regarding the crystalline phase contained in the analysis target, it is possible to present information indicating the degree of reliability of the information.

[0202] Moreover, the display unit 120 displays a probability distribution graph of the parameter values ​​of the fitting function. According to the analytical device 100, by displaying a probability distribution graph of the parameter values ​​of the fitting function, in addition to the estimated information regarding the crystal phase contained in the analysis target, information indicating the degree of reliability of the information can be presented.

[0203] FIG. 17 illustrates an example configuration of a computer according to at least one embodiment. In the configuration shown in FIG. 17, a computer 700 includes a CPU 710, a main memory device 720, an auxiliary memory device 730, an interface 740, and a non-volatile recording medium 750.

[0204] The above-mentioned analysis device 100 may be implemented in a computer 700. In this case, the operation of each of the above-mentioned processing units is stored in the auxiliary storage device 730 in the form of a program. The CPU 710 reads the program from the auxiliary storage device 730, develops it in the main storage device 720, and executes the above-mentioned processing according to the program. The CPU 710 also secures a storage area corresponding to each of the above-mentioned storage units in the main storage device 720 according to the program. Communication between each device and other devices is executed by the interface 740 having a communication function and performing communication according to the control of the CPU 710. The interface 740 also has a port for the nonvolatile recording medium 750, and reads information from the nonvolatile recording medium 750 and writes information to the nonvolatile recording medium 750.

[0205] When the analysis device 100 is implemented in a computer 700, the operations of the control unit 190 and each of its units are stored in the form of a program in an auxiliary storage device 730. The CPU 710 reads the program from the auxiliary storage device 730, loads it into the main storage device 720, and executes the above-mentioned processing according to the program.

[0206] Furthermore, CPU 710 allocates a storage area for storage unit 180 in main memory device 720 in accordance with the program. Communication with other devices by communication unit 110 is performed by interface 740 having a communication function and operating under the control of CPU 710. Display of images by display unit 120 is performed by interface 740 having a display device and displaying images under the control of CPU 710. Reception of user input by operation input unit 130 is performed by interface 740 having an input device and accepting user operation.

[0207] Any one or more of the above-mentioned programs may be recorded in non-volatile recording medium 750. In this case, interface 740 may read the program from non-volatile recording medium 750. Then, CPU 710 may directly execute the program read by interface 740, or may temporarily store the program in main storage device 720 or auxiliary storage device 730 and execute it.

[0208] Note that a program for executing all or part of the processing performed by the analysis device 100 may be recorded on a computer-readable recording medium, and the program recorded on the recording medium may be read into a computer system and executed to perform processing of each part. Note that the term "computer system" as used herein includes hardware such as an OS (Operating System) and peripheral devices. Furthermore, the term "computer-readable recording medium" refers to portable media such as flexible disks, optical magnetic disks, ROMs (Read Only Memory), and CD-ROMs (Compact Disc Read Only Memory), as well as storage devices such as hard disks built into computer systems. The above-mentioned program may be for realizing part of the above-mentioned functions, or may be capable of realizing the above-mentioned functions in combination with a program already recorded in the computer system.

[0209] Although an embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and designs that do not deviate from the gist of the present invention are also included.

[0210] A part or all of the above-described embodiments can be described as, but is not limited to, the following supplementary notes.

[0211] (Appendix 1) a data acquisition unit that acquires observation data of a spectrum of an analysis target and, for each candidate crystal phase included in the analysis target, information on the peak of the spectrum of the candidate; a basis selection unit that determines, for each of the candidates, a value of a basis selection parameter that is a binary variable indicating estimated information as to whether or not the candidate is included in the analysis target; a parameter calculation unit that has parameters including the basis selection parameters, and calculates parameters of the fitting function generated using information on the peaks of the spectrum so that the value of the fitting function approaches the value of the observation data, thereby acquiring estimated information on the crystalline phase contained in the analysis target; An analytical device comprising: (Appendix 2) the parameter calculation unit obtains, based on the basis selection parameters, estimated information on whether or not at least one of the candidates is included in the analysis target. 2. The analytical apparatus of claim 1. (Appendix 3) the basis selection unit calculates a prior distribution of values ​​of the basis selection parameters for each of the candidates based on a similarity between a data point of a spectrum peak of the candidate and a data point of the observation data that is located closest to the position of the spectrum peak of the candidate; 3. The analytical device of claim 1 or 2. (Appendix 4) the parameter calculation unit calculates a probability distribution of parameter values ​​of the fitting function to obtain estimated information on a crystalline phase contained in the analysis target and information indicating a degree of reliability of the information. 4. The analytical device of claim 1 . (Appendix 5) the parameter calculation unit samples values ​​of the parameters of the fitting function using an evaluation function that indicates a better evaluation as the value of the fitting function is closer to the value of the observation data, and calculates a probability distribution of the values ​​of the parameters of the fitting function using the sampled values. 5. The analytical device of claim 1 . (Appendix 6) The parameter calculation unit samples values ​​of the parameters of the fitting function using a replica exchange Monte Carlo method. 6. The analytical device of claim 5. (Appendix 7) a data acquisition unit that acquires observation data of a spectrum of an analysis target and, for each candidate crystal phase included in the analysis target, information on the peak of the spectrum of the candidate; a parameter calculation unit that calculates a probability distribution of parameter values ​​of the fitting function generated using information on the spectrum peaks so as to bring the value of the fitting function closer to the value of the observation data, thereby acquiring estimated information on a crystalline phase included in the analysis target and information indicating a degree of reliability of the information; An analytical device comprising: (Appendix 8) Further comprising a display unit for displaying the probability distribution in a graph. 8. The analytical apparatus of claim 7. (Appendix 9) The computer Obtaining spectrum observation data of an analysis target and, for each candidate crystal phase contained in the analysis target, information on the peak of the spectrum of the candidate crystal phase; determining, for each of the candidates, a value of a basis selection parameter, which is a binary variable indicating whether the candidate is included in the analysis; and calculating parameters of a fitting function, the fitting function having parameters including the basis selection parameters, based on information on peaks of the spectrum so as to bring the value of the fitting function closer to the value of the observation data, thereby obtaining estimated information on the crystalline phase contained in the analysis target. The analytical method includes: (Appendix 10) On the computer, Obtaining spectrum observation data of an analysis target and, for each candidate crystal phase included in the analysis target, information on the peak of the spectrum of the candidate crystal phase; determining, for each of the candidates, a value of a basis selection parameter, which is a binary variable indicating whether the candidate is included in the analysis; calculating parameters of a fitting function having parameters including the basis selection parameters and based on information on peaks of the spectrum so that the value of the fitting function approaches the value of the observation data, thereby obtaining estimated information on a crystalline phase contained in the analysis target; A program that performs the following. [Explanation of symbols]

[0212] 1 Diffraction System 100 Analyzer 110 Communications Department 120 Display section 130 Operation input section 180 Storage section 190 Control section 191 Data Acquisition Section 192 Observation Data Acquisition Section 193 Candidate Data Acquisition Department 194 Basis Selection Section 195 Parameter Calculation Section 196 Sampling section 197 Bayesian Estimation Section 200 Diffraction Equipment 300 Spectrum Database

Claims

1. a data acquisition unit that acquires observation data of a spectrum of an analysis target and, for each candidate component contained in the analysis target, information on the peak of the spectrum of the candidate component; a basis selection unit that determines, for each of the candidates, a value of a basis selection parameter that is a binary variable indicating estimated information as to whether or not the candidate is included in the analysis target; a parameter calculation unit that has parameters including the basis selection parameters, and calculates parameters of the fitting function generated using information on the peaks of the spectrum so as to bring the value of the fitting function closer to the value of the observation data, thereby acquiring estimated information on components contained in the analysis target; An analytical device comprising:

2. the parameter calculation unit obtains, based on the basis selection parameters, estimated information on whether or not at least one of the candidates is included in the analysis target. The analytical device of claim 1 .

3. the basis selection unit calculates a prior distribution of values ​​of the basis selection parameters for each of the candidates based on a similarity between a data point of a spectrum peak of the candidate and a data point of the observation data that is located closest to the position of the spectrum peak of the candidate; The analytical device of claim 1 .

4. the parameter calculation unit calculates a probability distribution of parameter values ​​of the fitting function to obtain estimated information on components contained in the analysis target and information indicating a degree of reliability of the information. The analytical device of claim 1 .

5. the parameter calculation unit samples values ​​of the parameters of the fitting function using an evaluation function that indicates a better evaluation as the value of the fitting function is closer to the value of the observation data, and calculates a probability distribution of the values ​​of the parameters of the fitting function using the sampled values. The analytical device of claim 1 .

6. The parameter calculation unit samples values ​​of the parameters of the fitting function using a replica exchange Monte Carlo method. The analytical device according to claim 5 .

7. a data acquisition unit that acquires observation data of a spectrum of an analysis target and, for each candidate component contained in the analysis target, information on the peak of the spectrum of the candidate component; a parameter calculation unit that calculates a probability distribution of parameter values ​​of the fitting function generated using information on the spectrum peak so as to bring the value of the fitting function closer to the value of the observation data, thereby obtaining estimated information on components contained in the analysis target and information indicating the degree of reliability of the information; An analytical device comprising:

8. Further comprising a display unit for displaying the probability distribution in a graph. The analytical device according to claim 7.

9. The computer Obtaining spectrum observation data of an analysis target and, for each candidate component contained in the analysis target, information on the peak of the spectrum of the candidate component; determining, for each of the candidates, a value of a basis selection parameter, which is a binary variable indicating whether the candidate is included in the analysis; and calculating parameters of a fitting function, the fitting function having parameters including the basis selection parameters, so that a value of the fitting function based on information on a peak of the spectrum approaches a value of the observed data, thereby obtaining estimated information on components contained in the analysis target. The analytical method includes:

10. On the computer, Obtaining spectrum observation data of an analysis target and, for each candidate component contained in the analysis target, information on the spectrum peak of the candidate component; determining, for each of the candidates, a value of a basis selection parameter, which is a binary variable indicating whether the candidate is included in the analysis; calculating parameters of a fitting function having parameters including the basis selection parameters and based on information on peaks of the spectrum so that the value of the fitting function approaches the value of the observed data, thereby obtaining estimated information on components contained in the analysis target; A program that performs the following.

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