Processing apparatus, system, and method

Abstract

Provided are a processing device, a system, a method, and a program capable of improving the accuracy of decomposition by performing non-negative matrix factorization on a measurement profile of X-ray powder diffraction and correcting at least a part of a base profile.SOLUTION: A processing device 400 for performing non-negative matrix factorization on a measurement profile of X-ray powder diffraction includes a measurement profile acquisition unit 410 that acquires a plurality of measurement profiles, a decomposition unit 420 that performs non-negative matrix factorization on the measurement profile and calculates a base profile, an index calculation unit 430 that acquires the base profile and calculates an index based on unevenness of the base profile, a base profile classification unit 440 that classifies the base profile into a plurality of groups based on the index, and a base profile correction unit 450 that performs correction based on the index on at least one of the plurality of groups and calculates a corrected base profile.SELECTED DRAWING: Figure 3

Description

[Technical Field]

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

[0002] X-ray powder diffraction is used in a variety of fields. For example, by analyzing the measurement profile of X-ray powder diffraction, it is possible to identify (qualitative analysis) and quantify the constituents of a powder sample. Conventionally, crystalline phases have been identified by comparing the measurement profile or a dI list created from the measurement profile with the diffraction pattern of a known substance.

[0003] Patent Document 1 discloses a crystalline phase identification method for identifying a crystalline phase contained in a sample from the powder diffraction pattern of the sample using a database, the method comprising: {a total pattern fitting step, in which, using information about the crystalline phases contained in the sample, a first diffraction pattern, which is the powder diffraction pattern of the sample, is subjected to total pattern fitting to calculate a theoretical diffraction pattern of the already identified crystalline phase}; {a residual information generation step, in which residual information of the sample is generated based on the difference between the theoretical diffraction pattern and the first diffraction pattern}; and {a residual information search and match step, in which the residual information is compared with the database to select a new crystalline phase contained in the sample}.

[0004] Patent Document 2 discloses a spectral data analysis device that performs non-negative matrix decomposition on a set of observed spectral data obtained for a signal to be analyzed to obtain a plurality of basis spectral data and activation data representing the magnitude of each basis spectrum, and that obtains the plurality of basis spectral data and the activation data by searching for a minimum value of an objective function that includes a regularization term that evaluates the degree of deviation between the set of observed spectral data and a set of estimated spectral data calculated from the plurality of basis spectral data and the activation data, as well as the linear independence of the plurality of basis spectral data or the activation data. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2014-178203 [Patent Document 2] Japanese Patent Application Publication No. 2019-87042 Summary of the Invention [Problem to be solved by the invention]

[0006] When X-ray powder diffraction measurement profiles contain a large amount of mixtures or amorphous profiles, the peaks in each profile tend to overlap. However, in such cases, applying the conventional method described in Patent Document 1, which performs search and match using a dI list without processing the measurement profile, results in poor qualitative analysis accuracy.

[0007] Furthermore, the technology described in Patent Document 2 improves the accuracy of decomposition by assuming that profiles are highly independent of each other. However, unlike crystalline profiles, amorphous profiles often lack sharp peaks and are broad. Therefore, if the measured profile contains an amorphous profile, or if some profiles are broad, imposing regularization on linear independence and searching for combinations with high linear independence increases the risk of not being able to achieve high-accuracy decomposition, resulting in poor accuracy in subsequent qualitative and quantitative analyses.

[0008] As a result of extensive research, the present inventors have discovered that when a measured profile of X-ray powder diffraction contains a broad profile, by subjecting the measured profile to nonnegative matrix factorization and correcting at least some of the basis profiles, the accuracy of the decomposition and the accuracy of the subsequent qualitative and quantitative analyses can be improved compared to simple nonnegative matrix factorization, and have completed the present invention.

[0009] The present invention has been made in consideration of the above circumstances, and aims to provide a processing device, system, method, and program that can improve the accuracy of the decomposition by performing non-negative matrix factorization on an X-ray powder diffraction measurement profile and correcting at least a portion of the basis profiles. [Means for solving the problem]

[0010] (1) In order to achieve the above object, the processing device of the present invention is a processing device that performs non-negative matrix factorization on a measurement profile of X-ray powder diffraction, and is characterized by comprising: a measurement profile acquisition unit that acquires multiple measurement profiles; a decomposition unit that performs non-negative matrix factorization on the measurement profile and calculates a basis profile; an index calculation unit that acquires the basis profile and calculates an index based on the unevenness of the basis profile; a basis profile classification unit that classifies the basis profile into multiple groups based on the index; and a basis profile correction unit that performs correction based on the index on at least one of the multiple groups and calculates a corrected basis profile.

[0011] (2) In the processing device of the present invention, the decomposition unit performs non-negative matrix factorization on the measurement profile using the corrected base profile as an initial condition.

[0012] (3) In the processing device of the present invention, the index is RTV (relative total variation).

[0013] (4) Furthermore, in the processing apparatus of the present invention, the plurality of groups are two, and the group for which correction based on the index is performed is the group that includes the base profile derived from an amorphous material.

[0014] (5) The processing device of the present invention is characterized by further comprising a profile number setting unit that sets the number of the base profiles included in the group that is to undergo correction based on the index.

[0015] (6) In the processing apparatus of the present invention, one of the corrections performed by the base profile correction unit is a correction that reduces the value of the RTV.

[0016] (7) Furthermore, the processing device of the present invention further includes a dendrogram creation unit that calculates statistics between the plurality of measurement profiles and creates a dendrogram, and the decomposition unit performs non-negative matrix factorization on clusters containing similar profiles selected by the processing device or by a user from the dendrogram.

[0017] (8) The processing device of the present invention is further characterized by including a peak search unit that performs a peak search on the basis profile after the nonnegative matrix factorization and creates a dI list, and a qualitative unit that performs qualitative analysis using the dI list.

[0018] (9) The processing device of the present invention is characterized by further comprising a quantification unit that performs quantitative analysis using the qualitatively analyzed data.

[0019] (10) The system of the present invention is characterized by comprising an X-ray diffraction apparatus having an X-ray generating unit that generates X-rays, a detector that detects X-rays, and a goniometer that controls the rotation of the sample, and the processing apparatus described in any one of (1) to (9) above.

[0020] (11) Furthermore, the method of the present invention is a method for non-negative matrix factorization of a measurement profile of X-ray powder diffraction, characterized by including the steps of acquiring a plurality of measurement profiles, non-negative matrix factorizing the measurement profiles to calculate a base profile, acquiring the base profiles and calculating an index based on the unevenness of the base profiles, classifying the base profiles into a plurality of groups based on the index, and performing correction based on the index for at least one of the plurality of groups and calculating a corrected base profile.

[0021] (12) Furthermore, the program of the present invention is a program for performing non-negative matrix factorization on a measurement profile of X-ray powder diffraction, and is characterized in that it causes a computer to execute the following processes: acquiring a plurality of measurement profiles; performing non-negative matrix factorization on the measurement profiles and calculating a base profile; acquiring the base profile and calculating an index based on the unevenness of the base profile; classifying the base profile into a plurality of groups based on the index; and performing correction based on the index on at least one of the plurality of groups and calculating a corrected base profile. [Brief explanation of the drawings]

[0022] [Figure 1] FIG. 1 is a conceptual diagram illustrating non-negative matrix factorization. [Figure 2] FIG. 1 is a conceptual diagram showing an example of the configuration of an X-ray diffraction measurement system. [Figure 3] FIG. 2 is a block diagram showing an example of the configuration of a control device and a processing device. [Figure 4] FIG. 10 is a block diagram showing a modified example of the configuration of the control device and the processing device. [Figure 5] FIG. 10 is a block diagram showing a modified example of the configuration of the control device and the processing device. [Figure 6] FIG. 10 is a block diagram showing a modified example of the configuration of the processing device. [Figure 7] FIG. 10 is a block diagram showing a modified example of the configuration of the processing device. [Figure 8] FIG. 10 is a block diagram showing a modified example of the configuration of the processing device. [Figure 9] 1A is a schematic diagram showing an example of a UI for setting the component analysis function, etc. FIG. 1B is a schematic diagram illustrating some of the functions of the component analysis UI. [Figure 10] FIG. 10 is a schematic diagram showing an example of a UI for setting up dendrogram creation, etc. [Figure 11] FIG. 10 is a schematic diagram showing an example of a UI for setting search and match and quantification functions. [Figure 12] 10 is a flowchart illustrating an example of the operation of the processing device. [Figure 13] 10 is a flowchart showing a modified example of the operation of the processing device. [Figure 14] 10 is a flowchart showing a modified example of the operation of the processing device. [Figure 15] 10 is a flowchart showing a modified example of the operation of the processing device. [Figure 16] 2(a) and 2(b) are graphs showing the decomposed basal profiles of Example 1 and Comparative Example 1, respectively. [Figure 17] Graphs (a) to (c) show the true content ratios of Samples 91 to 101, the analytical results of Example 1, and the analytical results of Comparative Example 1, respectively. [Figure 18] 1 is a graph showing the changes over time in temperature and humidity in the environments in which the samples of Example 2 and Comparative Example 2 were placed. [Figure 19]1 is a graph showing amorphous basal profiles of Example 2 and Comparative Example 2. [Figure 20] 2(a) and 2(b) are graphs showing the analysis results of Example 2 and Comparative Example 2, respectively. DETAILED DESCRIPTION OF THE INVENTION

[0023] Next, an embodiment of the present invention will be described with reference to the drawings. To facilitate understanding of the description, the same reference numerals are used to designate the same components in the drawings, and duplicated descriptions will be omitted.

[0024] [principle] X-ray powder diffraction measurement profiles contain overlapping profiles and backgrounds from multiple substances. When there are many mixtures or amorphous profiles are included, there is a lot of overlapping peaks. In such cases, the accuracy of peak searches decreases, and traditional search-and-match methods using dI lists are often not suitable.

[0025] Non-negative matrix factorization (NMF) is the decomposition of a non-negative matrix into a product of non-negative matrices. To facilitate search and match, we consider decomposing a measured X-ray powder diffraction profile into a weighted sum of multiple profiles (which may include background profiles). Since each profile and its weight are non-negative, non-negative matrix factorization is suitable for expressing a measured X-ray powder diffraction profile as a weighted sum of multiple profiles.

[0026] Figure 1 is a conceptual diagram showing nonnegative matrix factorization. The left side of Figure 1 shows a matrix consisting of n X-ray powder diffraction measurement profiles with m measurement points. The right side of Figure 1 shows the result of nonnegative matrix factorization of this matrix. Note that the wavy equal sign in Figure 1 does not only indicate a strict match, but also includes cases where the degree of discrepancy, which indicates the degree of closeness between the left and right sides, is less than a predetermined value.

[0027] The measured profile of X-ray powder diffraction may include a broad profile. For example, a broad profile may include an amorphous structure. In such a case, performing non-negative matrix factorization, which involves regularization of linear independence to search for combinations with high linear independence, as in Patent Document 1, is not appropriate because it may result in poor accuracy in the subsequent search and match.

[0028] The method of the present invention corrects at least some of the base profiles obtained by nonnegative matrix factorization of an X-ray powder diffraction measurement profile when the measurement profile contains a broad profile. The correction is performed to smooth out the irregularities in the profile for some base profiles that are considered more accurate when they are broad. The method of the present invention can perform nonnegative matrix factorization with high accuracy when the measurement profile contains a broad profile, thereby improving the accuracy of subsequent qualitative and quantitative analyses. While various methods have been proposed for nonnegative matrix factorization when a nonnegative matrix is ​​given, the present invention can use a general method. The method of the present invention will be described in detail in the embodiments.

[0029] [Embodiment] [Overall system] Figure 2 is a conceptual diagram showing an example of the configuration of an X-ray diffraction measurement system 100. The system 100 includes an X-ray diffraction instrument 200, a control device 300, and a processing device 400. The X-ray diffraction instrument 200 forms an optical system that irradiates X-rays onto a sample and detects diffracted X-rays generated from the sample, and the optical system includes a goniometer. Note that the configuration shown in Figure 2 is just one example, and various other configurations can be adopted.

[0030] The control device 300 is connected to the X-ray diffraction instrument 200 and controls the X-ray diffraction instrument 200 and processes and stores acquired data. The processing device 400 performs nonnegative matrix factorization on the measured X-ray powder diffraction profile and corrects at least a portion of the basis profiles. The control device 300 and processing device 400 are devices equipped with a CPU and memory, and may be PC terminals or cloud servers. Furthermore, not only the entire device, but also some of the devices or some of the functions within the devices may be provided on the cloud. The input device 510 is, for example, a keyboard or mouse, and inputs data to the control device 300 and processing device 400. The display device 520 is, for example, a display, and displays the measured profile, the results of nonnegative matrix factorization, etc.

[0031] By using such a system 100, it is possible to measure an X-ray powder diffraction profile, perform non-negative matrix factorization on the measured profile, and correct at least some of the basis profiles. Furthermore, qualitative and quantitative analysis can be performed using the basis profiles obtained by performing non-negative matrix factorization and correcting at least some of the basis profiles.

[0032] In FIG. 2, the control device 300 and the processing device 400 are depicted as a single PC. However, the method of the present invention can acquire a measurement profile and correct at least a portion of the basis profiles obtained by nonnegative matrix factorization, independently of the X-ray diffraction device 200 and the control device 300. Therefore, as shown in FIG. 3, the processing device 400 may be configured as a device separate from the control device 300. FIG. 3 is a block diagram showing an example of the configuration of the control device 300 and the processing device 400. As shown in FIG. 4, the processing device 400 may be configured as a partial function included in the control device 300. As shown in FIG. 5, the processing device 400 and the control device 300 may be configured as an integrated device. FIGS. 4 and 5 are block diagrams showing modified configurations of the control device 300 and the processing device 400. The following describes the case where the control device 300 and the processing device 400 are configured as separate devices.

[0033] [X-ray diffractometer] The X-ray diffraction apparatus 200 includes an X-ray generation unit 210 that generates X-rays from an X-ray focus, i.e., an X-ray source, an incident-side optical unit 220, a goniometer 230, a sample stage 240 on which a sample is placed, an exit-side optical unit 250, and a detector 260 that detects X-rays. The X-ray generation unit 210, incident-side optical unit 220, goniometer 230, sample stage 240, exit-side optical unit 250, and detector 260 that configure the X-ray diffraction apparatus 200 may be general components, and therefore description thereof will be omitted.

[0034] [Control device] The control device 300 is configured by a computer having a CPU (Central Processing Unit), ROM (Read Only Memory), RAM (Random Access Memory), and memory connected via a bus. The control device 300 is connected to the X-ray diffraction device 200 and receives information from it.

[0035] The control device 300 comprises a control unit 310, a device information storage unit 320, a measurement data storage unit 330, and a display unit 340. Each unit can send and receive information via a control bus L. The input device 510 and the display device 520 are connected to the CPU via an appropriate interface.

[0036] The control unit 310 controls the operation of the X-ray diffraction instrument 200. The instrument information storage unit 320 stores instrument information acquired from the X-ray diffraction instrument 200. The instrument information includes information about the X-ray diffraction instrument 200, such as the instrument name, type of radiation source, wavelength, background, etc. Other information may be included, such as information necessary for non-negative matrix factorization of the X-ray powder diffraction measurement profile, such as the type and composition of the constituent elements of the sample, and information necessary for correcting the basis profile, such as a Gaussian filter, a polynomial approximation method, a TV regularization method, etc.

[0037] The measurement data storage unit 330 stores the measurement profile acquired from the X-ray diffraction instrument 200. In addition to the measurement profile, the data may also include information necessary for non-negative matrix factorization of the X-ray powder diffraction measurement profile, such as the type of radiation source, wavelength, background, and type and composition of the constituent elements of the sample, as well as information necessary for correcting the basis profile, such as a Gaussian filter, a polynomial approximation method, and a TV regularization method. The display unit 340 displays the measurement profile and the basis profile on the display device 520, allowing the user to confirm the measurement profile and the basis profile. The user can also issue instructions and specifications to the control device 300, the processing device 400, etc., based on the measurement profile and the basis profile.

[0038] [Processing equipment] The processing device 400 is configured by a computer having a CPU, a ROM, a RAM, and a memory connected via a bus. The processing device 400 may be connected to the X-ray diffraction device 200 via the control device 300.

[0039] The processing device 400 includes a measurement profile acquisition unit 410, a decomposition unit 420, an index calculation unit 430, a basis profile classification unit 440, and a basis profile correction unit 450. Each unit can send and receive information via a control bus L. If the processing device 400 and the control device 300 have separate configurations, the input device 510 and the display device 520 are also connected to the CPU of the processing device 400 via an appropriate interface. In this case, the input device 510 and the display device 520 may be different from those connected to the control device 300.

[0040] The measurement profile acquisition unit 410 acquires multiple measurement profiles. The measurement profile acquisition unit 410 may acquire the measurement profiles directly from the X-ray diffraction instrument 200 or via the control device 300. In addition to the measurement profiles, the measurement profile acquisition unit 410 may acquire information necessary for non-negative matrix factorization of the X-ray powder diffraction measurement profile, such as the type of radiation source, wavelength, background, and type and composition of constituent elements of the sample, as well as information necessary for correcting the basis profile, such as a Gaussian filter, a polynomial approximation method, or a TV regularization method. This information may be stored in a memory unit of the processing device 400 (not shown).

[0041] The decomposition unit 420 performs non-negative matrix factorization on the measurement profile to calculate the basis profiles. For example, let X be an N-row, M-column matrix in which N X-ray powder diffraction measurement profiles having M measurement points are arranged. In this case, the non-negative matrix factorization of X is expressed as in the following formula (1). W is a coefficient matrix, and B is a basis matrix. W represents the weight of B. Each row of the basis matrix B is a basis profile (basis vector). Furthermore, R is a hyperparameter indicating the number of basis profiles. Note that M, N, and R represent the maximum values ​​of variables, and m, n, and r represent variables.

[0042]

number

[0043] Non-negative matrix factorization can be applied to optimization methods such as alternating least squares, multiplicative update, and coordinate descent with regularization. Regularization can be achieved by imposing sparsity on the weights or the profiles to be decomposed.

[0044] The decomposition unit 420 preferably performs nonnegative matrix factorization on the measured profile using the corrected basis profile as an initial condition. Performing nonnegative matrix factorization on the measured profile using the corrected basis profile as an initial condition means updating the coefficient matrix W with respect to a matrix in which some rows of the basis matrix B are replaced with the corrected basis profile, and further updating the basis matrix B with respect to the updated coefficient matrix W, thereby performing nonnegative matrix factorization on the measured profile.

[0045] The index calculation unit 430 acquires a base profile and calculates an index based on the concavity and convexity of the base profile. The index may be defined in any way, but it is an index that can represent the concavity and convexity characteristics of the base profile and that allows comparison of those characteristics. This allows the base profiles to be classified into multiple groups according to the concavity and convexity characteristics of the base profile.

[0046] The index is preferably RTV (Relative Total Variation). RTV is an index generally defined by the following formula (2) for a function f. RTV is a representative index that can effectively represent the convex and concave characteristics of a function. For the above basis matrix B(r,m), when the basis profile of row r of the basis matrix B(r,m) is expressed as Br(m) as in the following formula (3), it is defined by the following formula (4).

[0047]

number

[0048]

number

[0049]

number

[0050] The index is preferably RTV, but other indices can be used as long as they can represent the characteristics of the unevenness of the base profile. For example, evaluation can be made from the amount of displacement before and after smoothing the base profile, the number of peaks when a peak search is performed on the base profile, the half-width, and the integrated intensity, or a combination of these indices.

[0051] The basal profile classification unit 440 classifies the basal profiles into multiple groups based on the indices calculated by the index calculation unit 430. The classification of the basal profiles can be performed, for example, by setting multiple non-overlapping numerical ranges for the indices and classifying the basal profiles having index values ​​within the numerical ranges as basal profiles belonging to the group of the numerical ranges. Classification into multiple groups can also be performed using the K-means algorithm.

[0052] The number of groups is two, and the group to be subjected to index-based correction is preferably the group containing the basis profile derived from the amorphous material, thereby enabling index-based correction to be performed on the basis profile derived from the amorphous material.

[0053] The base profile correcting unit 450 performs correction based on the index on at least one of the multiple groups classified by the base profile classifying unit 440, and calculates a corrected base profile. The base profile correcting unit 450 may perform correction on two or more of the multiple classified groups. Alternatively, the base profile correcting unit 450 may perform correction on all of the groups. In these cases, each correction may be different.

[0054] When the index is RTV, it is preferable that one of the corrections performed by the base profile correction unit 450 is a correction that reduces the RTV value. This allows correction to bring a base profile, such as an amorphous profile, closer to an actual profile when the RTV value is smaller, closer to the actual profile. Even when an index other than RTV is used, if an index whose absolute value decreases when the base profile has small irregularities, is used, it is preferable that one of the corrections performed by the base profile correction unit 450 is a correction that reduces the absolute value of the index value, as described above.

[0055] Any correction that reduces the RTV value may be used, such as smoothing using a filter such as a Gaussian filter, polynomial approximation using a low-order polynomial, for example, a polynomial of degree five or less, or TV regularization.

[0056] With this configuration, when a measured X-ray powder diffraction profile contains a broad profile, it is possible to correct at least a portion of the basis profiles obtained by subjecting the measured profile to non-negative matrix factorization, thereby improving the accuracy of the decomposition.

[0057] Fig. 6 is a block diagram showing a modified example of the configuration of the processing device 400. As shown in Fig. 6, the processing device 400 preferably includes a number-of-profiles setting unit 435. The number-of-profiles setting unit 435 sets the number of base profiles included in a group for which correction based on an index is performed. The number of profiles set by the number-of-profiles setting unit 435 is a value smaller than the value of the hyperparameter R.

[0058] The profile number setting unit 435 preferably sets the number of basal profiles to be included in a group for which index-based correction is to be performed, based on the index of each basal profile calculated by the index calculation unit 430, or in response to a user instruction. When the profile number setting unit 435 sets the number of basal profiles to be included in a group for which index-based correction is to be performed, the base profile classification unit 440 classifies the set number of basal profiles into groups for which index-based correction is to be performed. This makes it possible to appropriately correct the basal profiles corresponding to these even when the measurement profile includes two or more broad profiles, thereby improving the accuracy of decomposition.

[0059] Fig. 7 is a block diagram showing a modified example of the configuration of the processing device 400. As shown in Fig. 7, the processing device 400 preferably includes a dendrogram creation unit 415. The dendrogram creation unit 415 calculates statistics between a plurality of measurement profiles and creates a dendrogram.

[0060] When the dendrogram creation unit 415 creates a dendrogram, the decomposition unit 420 preferably performs non-negative matrix factorization on clusters containing groups of similar profiles selected by the processing device 400 or the user from the created dendrogram.

[0061] By calculating statistics between multiple measurement profiles, creating a dendrogram, selecting clusters containing similar profiles from the created dendrogram, and performing non-negative matrix factorization, it is expected that measurement profiles that are unlikely to contain a common characteristic profile can be removed.As a result, multiple measurement profiles can be accurately subjected to non-negative matrix factorization.

[0062] Fig. 8 is a block diagram showing a modified example of the configuration of the processing device 400. As shown in Fig. 8, the processing device 400 preferably includes a dendrogram creation unit 415, a number of profiles setting unit 435, a peak search unit 460, a qualitative unit 470, and a quantitative unit 480. The dendrogram creation unit 415 and the number of profiles setting unit 435 are functional units similar to those described above.

[0063] The peak search unit 460 performs a peak search on the basis profiles after nonnegative matrix factorization to create a dI list. The peak search is performed on one selected from the basis profiles resulting from the nonnegative matrix factorization. The selection of the basis profile may be performed by the user, or by the peak search unit 460 or another functional unit of the processing device 400. In addition, a dI list is created for each basis profile for which a peak search has been performed. It is preferable to perform a peak search on all profiles other than those determined to be background.

[0064] The qualitative unit 470 performs qualitative analysis using the dI list. The qualitative analysis can be performed by searching and matching the created dI list. The qualitative analysis can be performed using a known method. Since a basal profile corrected by nonnegative matrix factorization is expected to be more accurate than a basal profile without correction, performing qualitative analysis using a dI list created from the corrected basal profile often makes it easier to identify components and improves the accuracy of identification.

[0065] The quantification unit 480 performs quantitative analysis using the qualitatively analyzed data. The quantitative analysis can be performed using a known method. In the configuration of Figure 8, the dendrogram creation unit 415, the profile number setting unit 435, the peak search unit 460, the qualitative unit 470, and the quantification unit 480 are optional functional units, and the configuration may be such that one or more of them are omitted.

[0066] With this configuration, the measurement profile of X-ray powder diffraction measured by an X-ray diffractometer can be subjected to non-negative matrix factorization to correct part of the basis profile, which can then be used for qualitative and quantitative analysis.

[0067] [User Interface] When parameters of the processing device 400 are set by user instructions, it is preferable to use a user interface (UI) function that allows various settings to be made by, for example, mouse or keyboard operations. Furthermore, it is preferable that the functions of the processing device 400 are configured to cooperate with the functions of other devices. Below, an example of a UI for setting parameters of the processing device 400 and a UI when the functions of the processing device 400 cooperate with the functions of other devices will be described. It is assumed that the functions of the processing device 400 are implemented as software.

[0068] FIG. 9(a) is a schematic diagram showing an example of a UI for setting the component analysis function. FIG. 9(b) is a schematic diagram illustrating some of the functions of the component analysis UI (the UI of FIG. 9(a)). On the screen of FIG. 9(a), the user can issue instructions to the processing device 400, such as acquiring measurement profiles, setting parameters, setting the number of profiles, calculating dendrograms, performing nonnegative matrix factorization, displaying measurement profiles, displaying base profiles, and transferring data. The parameter setting panel allows the user to set the optimization method for nonnegative matrix factorization, hyperparameter values, the number of iterations, regularization, and the number of base profiles belonging to the group for which index-based correction is performed. The hyperparameter values ​​may be automatically estimated and set using the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC), or the estimated values ​​may be displayed using the Estimate button. The Data Transfer button transfers the data resulting from nonnegative matrix factorization to the search / match and quantification functions.

[0069] Fig. 10 is a schematic diagram showing an example of a UI for setting up dendrogram creation, etc. On the screen of Fig. 10, the user can give instructions to the processing device 400, such as setting up statistics for creating a dendrogram, setting up data processing, and selecting clusters.

[0070] Fig. 11 is a schematic diagram showing an example of a UI for setting search-match and quantification functions, etc. Pressing the data transfer button on the screen of Fig. 9(a) opens the screen of Fig. 11. On the screen of Fig. 11, the user can give instructions to the processing device 400 or other devices to perform search-match, set compound information, etc.

[0071] 9 to 11 are merely examples, and even when the user sets these, it is possible to set only some of them or all of them. Also, there may be setting items and functions that are not shown in FIGS.

[0072] [Measurement method] A sample S is placed in the X-ray diffraction instrument 200, and the goniometer is driven under predetermined conditions under the control of the control device 300. X-rays are then incident on the sample, and diffracted X-rays generated from the sample are detected. This acquires diffraction data. The X-ray diffraction instrument 200 transmits the acquired diffraction data and other information about the instrument to the control device 300 as measurement data.

[0073] [Disassembly method] (Explanation of the basic flow of non-negative matrix factorization) FIG. 12 is a flowchart showing an example of the operation of the processing device 400. FIG. 12 shows an example of the basic operation of nonnegative matrix factorization and correction of basis profiles. First, the processing device 400 acquires a measurement profile (step S1). Next, parameters are set (step S2). The parameters to be set are the number of basis profiles to be decomposed (hyperparameter values), parameters required for optimization such as the optimization method, etc. The parameters may be set by inputting them by the user, or may be set by the processing device 400 based on the measurement profile or information related to the measurement profile.

[0074] Next, matrix W is updated (step S3). Next, matrix B is updated (step S4). Updating matrix W and matrix B is performed by creating a matrix consisting of the measurement profile and optimizing the coefficient matrix W and basis matrix B. Updating matrix W and matrix B includes initial settings and calculations. If there is a corrected basis profile, updating matrix W and matrix B is performed by setting the corrected basis profile as the basis matrix and optimizing the coefficient matrix W and basis matrix B. Updating matrix W and matrix B together can be said to perform nonnegative matrix factorization.

[0075] Next, an index is calculated for the basis profile of each row of the basis matrix B (step S5). Next, the basis profiles are classified into multiple groups (step S6). The classification of the basis profiles is performed only in the first loop, and the initial classification may be used as is in the second and subsequent loops. Next, correction based on the index is performed on at least one of the multiple groups (step S7). The corrected basis profile is called the corrected basis profile. Next, it is determined whether the termination condition is met (step S8). If the termination condition is not met (step S8-NO), the process returns to step S3, the corrected basis profile is set as the basis matrix, and non-negative matrix factorization is performed.

[0076] On the other hand, if the termination condition is met (step S8-YES), the results are output as necessary (step S9) and the process ends. The results may be stored and output only when instructed by the user. In this way, multiple measurement profiles of X-ray powder diffraction can be subjected to nonnegative matrix factorization to correct at least some of the basis profiles.

[0077] Various conditions can be used as the termination condition. For example, the number of loops may be set as the termination condition. Alternatively, the amount of change in the corrected base profile before and after the loop, the amount of change in some or all of the indices, the amount of change in some or all of the coefficient matrix, the amount of change in some or all of the basis matrix, the degree of agreement between one or more measured profiles and the corresponding calculated profile, etc. may be defined, and a threshold may be set for these, and the process may terminate when the amount of change exceeds or falls below the threshold. The amount of change refers to the magnitude or rate of change. The calculated profile refers to a profile obtained by multiplying a certain row of the coefficient matrix corresponding to a measured profile by the basis matrix. In some cases, such as when a known profile is used as the initial value of the base profile, it is possible to expect to obtain a result close to the desired result without performing loop processing. In such cases, the process may terminate at step S7 in FIG. 12.

[0078] (Explanation of the flow when setting the number of base profiles) FIG. 13 is a flowchart showing a modified example of the operation of the processing device 400. FIG. 13 shows an example of the operation when setting the number of base profiles. In the following explanation of the flowchart, characteristic operations will be explained in detail, and explanation of operations that have already been explained may be omitted. Steps T1 to T5 are the same as steps S1 to S5 described above. Next, the processing device 400 sets the number of base profiles included in the group for which index-based correction is performed (step T6). If the number of base profiles is set based on the index, it is necessary to set the number of base profiles after step T5. In this case, setting the number of base profiles is skipped in the second and subsequent loops. Furthermore, if the number of base profiles is not set based on the index, the number of base profiles may be set simultaneously with, for example, parameter setting. The subsequent steps T7 to T10 are the same as steps S6 to S9 described above.

[0079] (Explanation of the flow for creating a dendrogram) Fig. 14 is a flowchart showing a modified example of the operation of the processing device 400. Fig. 14 shows an example of the operation when creating a dendrogram. First, the processing device 400 acquires a measurement profile (step U1). Step U1 is similar to step S1.

[0080] Next, a dendrogram is created (step U2). The dendrogram is created by calculating statistics between the multiple measurement profiles obtained. Next, clusters are selected (step U3). Clusters may be selected by the user or by the processing device 400. Selecting clusters, which are groups of similar profiles, from the dendrogram improves the resolution accuracy.

[0081] Next, parameters are set (step U4). Next, nonnegative matrix factorization is performed (step U5). Step U5 is a step that combines steps S3 to S8. Then, the results are output as necessary (step U6), and the process ends. In this way, after creating a dendrogram and selecting clusters, nonnegative matrix factorization can be performed to correct at least some of the base profiles.

[0082] (Explanation of the flow of a modified example when qualitative analysis or further quantitative analysis is performed) Fig. 15 is a flowchart showing a modified example of the operation of the processing device 400. Fig. 15 shows a modified example of the operation when performing qualitative analysis or further quantitative analysis after performing nonnegative matrix factorization to correct at least some of the base profiles. The steps from the step of acquiring a measurement profile (step V1) to the step of performing nonnegative matrix factorization (step V5) are the same as steps U1 to U5.

[0083] Next, a peak search is performed (step V6). The peak search is performed on one selected basal profile from the results of non-negative matrix factorization. The selection of the basal profile may be performed by the user or by the processing device 400. A dI list is created for each basal profile for which a peak search has been performed. It is preferable to perform a peak search on all basal profiles other than the basal profile determined to be background.

[0084] Next, qualitative analysis is performed (Step V7). The qualitative analysis can be performed by performing search and match based on the created dI list. If the search and match does not find a profile with a degree of match equal to or greater than a predetermined value, the process may return to Step V4 and perform non-negative matrix factorization again from the parameter settings.

[0085] Next, quantitative analysis is performed (Step V8). Quantitative analysis determines the content of the substances identified by the qualitative analysis using various methods. For example, direct derivation (DD), RIR, or Rietveld analysis can be used. The results are output as needed (Step V9), and the process ends. In this way, multiple measurement profiles of X-ray powder diffraction are subjected to nonnegative matrix factorization, and at least some of the basis profiles are corrected. Then, qualitative analysis can be performed, and this can be used to perform quantitative analysis.

[0086] 15, after the qualitative analysis in step V7, the results may be output as needed (step V9) without performing quantitative analysis, and the process may be terminated. In this way, multiple X-ray powder diffraction measurement profiles can be subjected to nonnegative matrix factorization, and at least some of the basis profiles can be corrected before performing qualitative analysis.

[0087] The order of steps in each of the above-described flowcharts is not fixed, and the order may be changed or steps may be processed in parallel as long as they can be processed correctly. Also, each flowchart may be applied in combination with other flowcharts.

[0088] [Examples and Comparative Examples] Example 1 Using the system 100 configured as described above, X-ray diffraction data was measured for the indomethacin mixture of Samples 1 to 101. For the measured profiles of Samples 1 to 90, the method of the present invention was used to calculate the basis profiles of indomethacin α-form, indomethacin γ-form, and amorphous indomethacin. Specifically, the hyperparameter was set to 3, the termination condition was set to 200 iterations, nonnegative matrix factorization was performed, and the basis profile considered to be the amorphous profile was corrected to calculate each basis profile.

[0089] (Comparative Example 1) For the same measured profiles, non-negative matrix factorization was performed using the conventional alternating least squares method with the hyperparameter set to 3 to calculate the basal profiles of indomethacin α, indomethacin γ, and amorphous indomethacin.

[0090] 16(a) and 16(b) are graphs showing the respective basal profiles of Example 1 and Comparative Example 1. Fig. 16(a) shows that the basal profile considered to be the amorphous profile of Example 1 is broad and smooth. In contrast, Fig. 16(b) shows that the basal profile considered to be the amorphous profile of Comparative Example 1 has fine peaks and has characteristics different from the amorphous profile actually measured.

[0091] Next, the content ratios of indomethacin α-form, indomethacin γ-form, and amorphous in Samples 91 to 101 were quantitatively analyzed using each base profile calculated in Example 1 or Comparative Example 1. Samples 91 to 101 were mixtures in which the content ratios of each component were known, and each content ratio was taken as the ground truth. Figures 17(a) to 17(c) are graphs showing the true content ratios of Samples 91 to 101, the analytical results of Example 1, and the analytical results of Comparative Example 1, respectively.

[0092] The residual square error (MSE) between the analysis results of Example 1 or Comparative Example 1 and the true content ratio was calculated. As a result, the MSE for Example 1 was 57.30, and the MSE for Comparative Example 1 was 60.57. This indicates that the analysis results of the method of the present invention are closer to the true content ratio than the analysis results of the conventional method. In other words, it was confirmed that the method of the present invention has high accuracy even in quantitative analysis.

[0093] Example 2 Next, using a similar system 100, trehalose was placed on a sample stage with variable temperature and humidity, and multiple X-ray diffraction data were measured while the temperature and humidity were changed over time. Figure 18 is a graph showing the changes in temperature and humidity over time in the environments in which the samples of Example 2 and Comparative Example 2 were placed. Based on the measured profiles, the method of the present invention was used to calculate the basal profiles of amorphous (non-crystalline), dihydrate, anhydrous α, and anhydrous β trehalose. Specifically, the hyperparameter was set to 4, the termination condition was set to 200 iterations, and non-negative matrix factorization was performed. Each basal profile was calculated by correcting the basal profile considered to be an amorphous profile.

[0094] (Comparative Example 2) Non-negative matrix factorization was performed on the same measurement profile using alternating least squares with the hyperparameter set to 4 to calculate the basal profiles of amorphous, dihydrate, anhydrous α, and anhydrous β trehalose.

[0095] Fig. 19 is a graph showing the amorphous basal profiles of Example 2 and Comparative Example 2. Fig. 19 shows that the amorphous basal profile of Example 2 is also broad and smooth. In contrast, the amorphous basal profile of Comparative Example 2 shows fine peaks, and has characteristics different from the amorphous profile actually measured.

[0096] The basal profiles calculated in Example 2 and Comparative Example 2 were used to determine the change in trehalose content over time. Figures 20(a) and 20(b) are graphs showing the analytical results of Example 2 and Comparative Example 2, respectively. The following is known about trehalose: (1) When the dihydrate is heated at 140°C, it transitions to anhydrous β. (2) When the dihydrate is heated under normal humidity, it transitions to amorphous. (3) When the amorphous form is heated, it transitions to anhydrous β at 150°C. (4) When the anhydrous β is heated, it melts at 210°C and transitions to amorphous. These findings confirm that the quantitative analysis of Example 2, in which anhydrous β barely appears at temperatures above 140°C, is more accurate than that of Comparative Example 2, in which anhydrous β appears at temperatures below 100°C.

[0097] The above results confirm that the processing device, system, method, and program of the present invention can improve the accuracy of the decomposition by performing non-negative matrix factorization on the measured X-ray powder diffraction profile and correcting at least some of the basis profiles. [Explanation of symbols]

[0098] 100 systems 200 X-ray Diffractometer 210 X-ray generator 220 Incident optical unit 230 Goniometer 240 Sample stage 250 Output optical unit 260 detector 300 control device 310 Control Unit 320 Device information storage unit 330 Measurement data storage unit 340 Display section 400 Processing Equipment 410 Measurement profile acquisition unit 415 Dendrogram Creation Department 420 Disassembly section 430 Indicator calculation section 435 Profile number setting section 440 Base Profile Classification Unit 450 Base profile correction unit 460 Peak Search Section 470 Qualitative Department 480 Quantification section 510 Input Device 520 Display device

Claims

1. A processing device for performing non-negative matrix factorization on a measured profile of X-ray powder diffraction, comprising: a measurement profile acquisition unit that acquires a plurality of measurement profiles; a decomposition unit that performs non-negative matrix factorization on the measurement profile to calculate a basis profile; an index calculation unit that acquires the base profile and calculates an index based on the concavity and convexity of the base profile; a base profile classification unit that classifies the base profiles into a plurality of groups based on the index; a base profile correction unit that performs correction based on the index on at least one of the plurality of groups and calculates a corrected base profile.

2. The processing device according to claim 1 , wherein the decomposition unit performs non-negative matrix factorization on the measurement profile using the corrected base profile as an initial condition.

3. 3. The processing device according to claim 1, wherein the index is RTV (relative total variation).

4. 3. The processing apparatus according to claim 1, wherein the plurality of groups are two, and the group for which the correction based on the index is performed is the group containing the base profile derived from an amorphous material.

5. 3. The processing apparatus according to claim 1, further comprising a profile number setting unit that sets the number of the base profiles included in the group that is to undergo correction based on the index.

6. 4. The processing apparatus according to claim 3, wherein one of the corrections performed by said base profile correction unit is a correction that reduces the value of said RTV.

7. a dendrogram creation unit that calculates statistics between the plurality of measurement profiles and creates a dendrogram; 3. The processing device according to claim 1, wherein the decomposition unit performs non-negative matrix factorization on clusters including similar profiles selected by the processing device or a user from the dendrogram.

8. a peak search unit that performs a peak search on the basis profile after the nonnegative matrix factorization and creates a d-I list; 3. The processing apparatus according to claim 1, further comprising: a qualitative section that performs qualitative analysis using the dI list.

9. 9. The processing apparatus according to claim 8, further comprising a quantification unit that performs quantitative analysis using the qualitatively analyzed data.

10. an X-ray diffraction apparatus including an X-ray generating unit that generates X-rays, a detector that detects X-rays, and a goniometer that controls the rotation of a sample; A system comprising: the processing device according to claim 1 or 2.

11. 1. A method for performing non-negative matrix factorization on a measured X-ray powder diffraction profile, comprising: obtaining a plurality of measurement profiles; performing non-negative matrix factorization on the measured profile to calculate a basis profile; obtaining the base profile and calculating an index based on the concavity and convexity of the base profile; classifying the basal profiles into a plurality of groups based on the index; and performing a correction based on the index on at least one of the plurality of groups and calculating a corrected basal profile.

12. A program for performing non-negative matrix factorization on a measured profile of X-ray powder diffraction, acquiring a plurality of measurement profiles; performing non-negative matrix factorization on the measured profile to calculate a basis profile; A process of acquiring the base profile and calculating an index based on the concavity and convexity of the base profile; A process of classifying the basal profiles into a plurality of groups based on the index; and performing a correction based on the index on at least one of the plurality of groups and calculating a corrected base profile.

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